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Issue 29 G
ISSN 2634-8578
Curated By:
Damian Cortés
algorithm, Algorithmic Abstractness, Algorithmic Design
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Prospectives Writing Style Guide
author guidelines, punctuation, referencing, spelling, style guide, writing style
Provides Ng
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The purpose of this guide is to help authors ensure consistency with Prospectives Issues.
It includes the most contentious areas of spelling, punctuation and formatting. For more
general guidance on tone and style, please consult the UCL Author Guidelines and Content
Style Guide. Where this guide differs from UCL Author Guidelines or Content Style Guide, please
use this document.
If helpful, you can also consult Issue 1 of Prospectives:

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Solarpunk Building for Terraforma, Alessandro Bava, 2021
Solarpunk Building for Terraforma, Alessandro Bava, 2021
Editorial Note
B-pro, Editorial Note, Prospectives, Prospectives Issue 02, The Algorithmic form, The Bartlett
Provides Ng
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Welcome to Prospectives Issue 02

It’s been a great pleasure to be part of Prospectives – a journal that is dedicated to all researchers and designers, students and scholars, established or in their early careers. It aims to act as a hotbed, a sandbox, a platform that is “from architects, by architects, to architects” in its broadest sense – be it architects of buildings, softwares, or future(s) (or the Matrix!). It is for all who are invested in interdisciplinary and intercultural exchanges, information and idea seeding. 

According to Oxford Languages, the term “Prospective” emerged in the late 16th century, with a meaning of “looking forward, foresighting”, or “characterised by looking to the future”. The journal’s title puts the anticipatory nature of Prospective(s) into plural form; we believe “design” is the maximising of options or, as Claude Shannon put it “surprises” in a system; and the realisation of design is the collapse / negotiation / collaboration of all such possibilities into our physical reality. When the word “prospect” is translated into other languages, like my mother tongue Chinese, it adds yet another layer of meaning. The first result that Google turned up was “奔頭兒” (rushing-heads), an expression much used by local dialects in the North-East of China to describe the hard work needed to secure a promising future. Different languages and cultures map the vibrancy of Prospectives, and also of architecture and world-building. One is simultaneously enabled and constrained by the language which structures our thinking, be it architectural, mathematical or natural languages; this is why collaboration, or a collaborative intelligence, is our biggest prospect. The greatest innovations are the ones characterised by inclusivity, not exclusivity.  

Within such a context, what is the role of a journal? To ensure standards in research? To network scholars in the field? To communicate progress with the larger public? We have seen an increasing number of open source journals that are revolutionising the peer review system; not to replace it, but diversifying what can be meant by peer-to-peer (p2p). At Prospectives, we are invested in democratisation, especially in helping independent authors and designers reach a larger audience, and making literature available and accessible to all through participation and digitalisation. The future of journals (and architecture), is certainly one that can synthesise the copyrights and “copylefts”. As Prof. Mario Carpo suggests, while the marginal costs of printing (be it 2D or 3D) decrease, our capacities in mass customisation increase, and the same applies to information production. With the rise of the Omniverse, Metaverse, and MetaNets, it becomes increasingly apparent that the answer is not in the technologies themselves, but the way the social and the economic are re-structured, driven by participatory innovation. It will take the invisible (or visible) hands of the many to steer us towards the prospectives we desire.  

Issue 02: The Algorithmic form  

“Algorithm” as the adjective, “form” as the subject – connecting fundamental questions in computation to architecture. The second issue of Prospectives is driven by the provocations of the essay “Computational Tendencies”, written in 2020 by Alessandro Bava – who is also the guest curator of this issue. He problematised evolutionary thinking in architecture – the linear and unidirectional development from simplicity to complexity, from causation to correlation, from small to big data – and questioned the prospects of algorithms and forms within social and cultural urgencies. In the search for answers that are likely to fall between established fields, Alessandro invited six architects to engage in conversation with great figures from the fields of art, architecture and computation. Some of these conversations are carried out through interviews and roundtables, others through research, literature and case studies, forming dialogues between the past and present. Together with this, an open call was established to crowd-source intelligence and outsource imagination. These critical and retrospective pieces map a speculative timeline of events around “algorithmic forms” from Italian Renaissance, through the beginning of modernism, up to today.  

Prospectives Issue 02 encompasses 14 contributions. Prof. Mario Carpo starts our journey with an analogy of the German language, where grammar is “an artificial shortcut” to fluency, not its entirety. The same logic may apply to “Shape Grammar” in architecture, or the Common Data Environments of BIM, or the big-databases of Artificial Intelligence (AI). Just as he exquisitely formed a connection between the invention of book-printing and 3D-printing to predict a future of mass customisation, in this piece Mario shows us a comparative history between citationists of the Renaissance and post-modern (PoMo) architecture. The former is invested in reviving classical antiquity “piece-by-piece”, while the latter took its cues from “reference, allusion, collage and cut-and-paste”. We are also indulged with the distinguished curator Hans Ulrich Obrist’s interview with Getulio Alviani – an important figure in the international Optical-kinetic art movement throughout the 20th century. Alviani spoke of being motivated by the work of Leonardo Da Vinci; his geometric exploration arising from the “curiosity of seeing”; the tectonics between material and structure, craft and design, and finally, the immersivity of movement with the “discovery of light”. This precious and poetic piece teleported us to the Italian art scene through Alviani’s encounters, provoking us to reflect on our journey from simplicity to complexity. 

The five pieces that follow are the outcome of the B-pro Open Seminar at the Bartlett School of Architecture on 8th December, 2021. Five invited guests, including Roberto Bottazzi (The Bartlett), Francesca Gagliardi and Federico Rossi (Fondamenta), Philippe Morel (ENSA Paris-Malaquais & The Bartlett), Marco Vanucci (Open Systems), and myself (Provides Ng, The Bartlett) were invited to contemplate on and discuss the work of Luigi Moretti, Isa Genzken, Manfred Mohr, and Leonardo and Laura Mosso – important figures who had shown us new forms of aesthetics through the exploration of novel technological, geometrical, and mathematical tools. The roundtable that followed included discussions on, but not limited to, topics in Building Information Modelling (BIM), AI, blockchain, robotics, extended reality (XR) and other distributive technologies that, undeniably, should be brought to the table for their symbiosis and socioeconomic implications, positive or negative.  

Lastly, the richness of this issue is further complemented by five selected open call pieces, with topics ranging from architectural authorship, algorithmic representations, digital anthropology, computational empiricism, and the liberation of creativity through codification.  


Prospectives hopes to uncover the urgency around issues of computation and automation within the built environment, but also the communities and initiatives that are involved in such developments; from the Bartlett School of Architecture, UCL, reaching out to wider society across disciplinary and territorial borders.  

First and foremost, I owe thanks to Prof. Frederic Migayrou, who is chair of the school, director and founder of the B-pro – five exciting programs led by an international and interdisciplinary team of faculty members, which have shown the field diverse paths to architecture and education, a shelter for all who strive for “prospects”. And to Prof. Mario Carpo, a historian, a critic, a theorist, who has liberated my thinking and shown us a form of architecture that is so much more than design; a form of architect that is so much more than a builder; a form of speculation that is so much more than fiction; a form of prospect that is so much more than futuring. Mario and Frederic were my supervisors, patiently guiding me through a marvellous history of Architecture & Digital Theory; a history that has become a rock in my heart – even though the prospects of the future are not always clear, history has prevented me from confusing and losing myself, and urged me to write and research with honesty, and I hope this journal can do the same for its readers. And of course, Mollie Claypool, a dedicated advocate, a female theorist, my role model. A strong figure with a soft heart, she will always fight and speak up for, in her words, “a labour of love and perseverance”, spearheading participatory and collaborative practises in automation, design and research, and the launch of this very journal. Also Roberto Bottazzi and Gilles Retsin, programme directors of Urban Design (UD) and Architecture Design (AD) in B-pro, together with Mollie, have given me so much opportunity, trust, advice and support, facilitating a free platform of architectural expression and a warm hub of design innovation. Prof. Bob Sheil and Andrew Porter, who have relentlessly endorsed and formalised the development of Prospectives and all other initiatives within the School of Architecture, facilitating a welcoming hotbed for creativity, self-initiation and self-organisation.  

I am thankful to all those who are my colleagues, but also my mentors, including Alessandro Bava, who have curated this issue with much sincerity and commitment, bringing an amazing line up of guests and design provocations to the table; Déborah López Lobat, Hadin Charbel, Manuel Jimenez, Emmanouil Zaroukas, Clara Jaschke, Mark Garcia, Jordi Vivaldi Piera and Albert Brenchat-Aguilar, with whom I’ve had some of the most engaging and interesting disciplinary discussions and who have never hesitated to reach out a helping hand; Daniel Koehler, Valentina Soana, and all Prospectives advisory board members. Above all, Alberto Fernandez Gonzalez and David Doria; my strongest backers, my faithful ear, my collaborative hands, my motivation and my exemplars, it is my honour and blessing to be amongst such fellowship and companionship. Needless to say, we would be nothing without our communication and administration teams, the invisible heroes who have supported the running of the school, especially Drew Pessoa, Tom Mole, Ruth Evison, Gen Williams, Srijana Gurung, Abi Luter, Dragana Krsic, Sarah Barry, Jessica Buckmire, Julia Samuels, and Crystal Tung. Last but not least, Rebecca Sainsot and Dan Wheeler, who assisted the publication and copy editing of this issue with such dedication, and to those who have submitted and contributed to our open call. I am grateful to all schools of architecture, like the Bartlett, that have enabled and facilitated projects such as Prospectives, opportunities for early-career and independent scholars, and a place for aspiring talents to meet and grow.  

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Retrofit Project by Frederik Vandyck, Design Sciences Hub
Retrofit Project by Frederik Vandyck, Design Sciences Hub
Towards the computation of architectural liberty  
architectural liberty, automation, computation, design theory, fragmentation
Sven Verbruggen, Elien Vissers-Similon
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A design process consists of a conventionalised practice – a process of (personal) habits that have proven to be successful – combined with a quest for creative and innovative actions. As tasks within the field of architecture and urban design become more complex, professionals tend to specialise in one of many subsets, such as designing, modelling, engineering, managing, construction, etc. They use digital tools which are developed for these specialised tasks only. Therefore, paradoxically, automation and new algorithms in architecture and urbanism are primarily oriented to simplify tasks within subsets, rather than engaging with the complex challenges the field is facing. This fragmented landscape of digital technologies, together with the lack of proper data, hinders professionals’ and developers’ ability to investigate the full digital potential for architecture and urban design. [1] Today, while designers explore the aid that digital technologies can provide, it is mostly the conventionalised part of practice that is being automated to achieve a more efficient workflow. This position statement argues for a different approach: to overcome fragmentation and discuss the preconditions for truly coping with complexity in design – which is not a visual complexity, nor a complexity of form, but rather a complexity of intentions, performance and engagement, constituted in a large set of parameters. We will substantiate our statement with experience in practice, reflecting on the Retrofit Project: our goal to develop a smart tool that supports the design of energy neutral districts. [2]  

So, can designers break free from the established fragmentation and compute more than technical rationale, regulations and socio-economic constraints? Can they also incorporate intentions of aesthetics, representation, culture and critical intelligence into an architectural algorithm? To do so, the focus of digital tools should shift from efficiency to good architecture. And to compute good architecture, there is a need to codify a designer’s evaluation system: a prescriptive method to navigate a design process by giving value to every design decision. This evaluation system ought to incorporate architectural liberty – and therein lies the biggest challenge: differentiating between where to apply conventionalised design decisions and where (and how) to be creative or inventive. Within a 5000-year-old profession, the permitted liberty for these creative acts has been defined elastically: while some treatises allow only a minimum of liberty for a designing architect, others will lean towards a maximum form of liberty to guarantee good architecture. [3]  

A minor group of early adopters, such as Greg Lynn, Zaha Hadid Architects, and UN Studio, tried to tackle the field’s complexity using upcoming digital technologies, in the late ’90s early 2000s. They conveniently inferred their new style or signature architecture from these computational techniques. This inference, however, causes an instant divide between existing design currents and these avant-garde styles. The latter claim the notion of complexity – the justification for their computational techniques – lies mostly within the subset of form-giving, not covering the complexity of the field. This stylistic path is visible in, for example, Zaha Hadid Architects’ 2006 masterplan for Kartal-Pendik in Istanbul. The design thrives on binary decisions in 3D-modelling tool Maya, where it plays out a maximum of two parameters at once: the building block with inner court and the tower. The resulting plastic urban mesh looks novel and stylistically intriguing, yet produces no real urbanity and contains no intelligence on the level of the building type. This methodology does not generate knowledge on how well the proposed urban quarter (or constituent buildings) will perform on the level of, for example, costs, energy production and consumption, infrastructure, city utilities, diversity and health. The fluid mass still needs all conventional design operations to effectively turn it into a mixture of types, urban functions, and local identity. Arguably, the early adopters’ stylistic path avoided dealing with real complexity and remained close to simple automation. In doing so, while they promoted a digital turn, they might also have dug the foundations for today’s fragmentation in the field.  

Ironically, to some extent Schumacher’s treatise – definitely the parts that promote parametricism as a style – reads as a cover-up of the shortcomings of parametric software; for example, the inability to produce local diversity and typological characteristics beyond formal plasticity. [4] Schumacher further rejects Vitruvius to prevent structural rationale from taking primacy, and he disavows composition, harmony and proportion as outdated variable communication structures to propose the “fluid space” as the new norm. [5] This only makes sense knowing that the alternative – a higher intelligence across the whole field of architecture and urban planning, such as codified data and machine learning algorithms – did not yet exist for the early adopters. Contemporary applications such as Delve or Hypar do make use of those intelligent algorithms, yet prioritise technical and economical parameters (e.g. daylight, density, costs) to market efficiency. [6]  

Any endeavour to overcome the established fragmentation and simplified automation will ultimately find itself struggling with the question of what good architecture is. After all, even with large computational power at hand, the question remains: how to evaluate design decisions beyond the merely personal or functional, in a time where no unified design theory exists? In fact, the fragmented specialisation of today’s professionals has popularised the proclamation of efficiency. As a result, an efficiency driver (whether geared by controlling costs, management or resources) is often disguised as moral behaviour, as if its interest is good architecture first, and the profit and needs of beneficiaries only come second. If the added value of good architecture cannot be defined, the efficiency driver will continue to get the upper hand, eroding the architectural profession to an engineering and construction service providing calculations, permits and execution drawings.  

It was inspiring to encounter Alessandro Bava’s Computational Tendencies on this matter:  

The definition of what constitutes “good” architecture is, in fact, always at the center of architecture discourse, despite never finding a definite answer. Discourses around digital architecture have too often resolved the question of the “good” in architecture by escaping into the realm of taste or artistic judgment. [7] 

Bava renders Serlio’s architectural treatise as an original evaluating system that attributes universal value, and revisits Rossi’s exalted rationalism to propose a merger of architecture’s scientific qualities with its artistic qualities. He aims to re-establish architecture’s habitat-forming abilities and prevent architecture from becoming an amalgam of reduced and fragmented services. However, Serlio’s treatise did not provide a fully codified and closed formal system, as it still includes the liberty of the architect. [8] Going through Serlio’s On Domestic Architecture, an emphasis is placed on ideal building types, mostly without context. Therefore, no consideration is given to how these types ought to be modified when they need to be fitted in less ideal configurations such as non-orthogonal grids. The books also remain ignorant of the exceptions: the corner-piece-type, or fitting-parts that mediate between buildings and squares on a higher level. This is not a cheap critique of Serlio’s work. It is an awareness one needs to have when revisiting Serlio’s work as a “proto-BIM system, one whose core values are not market availability or construction efficiency, but harmonic proportions”. [9] Arguably, it is the liberty, the modifications, and the exceptions that need to be codified, to reach beyond simplified automation, across fragmentation, and towards an architectural algorithm to assist designers. 

This is easier said than done, otherwise the market would be flooded with design technologies by now. As with most design problems, the only way to solve them is by tackling them in practice. In 2021, the Design Sciences Hub, affiliated with the University of Antwerp, set up the Retrofit Project. The aim is to develop an application to test the feasibility of district developments. The solution will show an urban plan with an automatically generated function mix and optimized energetic and ecological footprint, for any given site and context. The project team collaborates with machine-learning experts and environmental engineers for the necessary interdisciplinary execution. Retrofit is currently in the proof-of-concept phase, which focuses on energy neutrality and will tackle urban health and carbon neutrality in the long run. 

The problem of modifications and exceptions seems the easiest to examine, as it primarily translates into a challenge of computational power and coping with a multitude of parameters. However, these algorithms should be smart enough to select a specific range within the necessary modifications and exceptions to comply with the design task at hand. In this case, the algorithm should select the correct modifications and exceptions needed to integrate certain types into any given site within the Retrofit application. In other words, there is a need for an intelligent algorithm that can be fed a large number of types as input data to generate entirely new or appropriate building types. The catch resides within the word “intelligent”, as algorithms aren’t created intelligent, they are trained to reach a certain level of intelligence based on (1) codifiable theory and (2) relevant training sets of data. Inquiring into a variety of evaluation systems for architectural design that emerged over the last 40 years, Verbruggen revealed the impossibility of creating a closed theoretical framework, and uniquely relating this framework to a conventionalised evaluation system in practice. [10] As such, both the codifiable theory – a unified evaluation system that integrates scientific and artistic qualities into one set of rules – and the training set  hardly exist in architecture and urban design. To complicate matters even more, today’s non-unification is itself often embraced as the precondition for good architecture [11-15] 

And so, the liberty question emerges here once again: how can different types, their modifications and exceptions, including respective relationships with different contexts, be codified? It is easy to talk about codification, but much harder to implement it within a project. When different types are inserted into a database, how are the attributes defined? This is a task that proved to be very laborious and raised many new questions in the Retrofit project. Attributes will include shape and size, yet might also include levels of privacy, preferred material usage, degree of openness, average energetic performance, historic and social acceptance in specific areas, compatibility with different functions, etc. Which values define when and where a specific type is appropriate, and how are they weighed? Do architects alone fill up the database, and if so, which architect is qualified, and why? And when an AI application would examine existing typologies within our built environment, which of these examples should be considered good, and why? Can big data or IoT sensors help in data gathering? To truly take everything into account, how much data do we really need (e.g., a structure’s age and condition, social importance, usage, materials, history, etc.). Furthermore, when the Retrofit application runs on an artificially intelligent algorithm that is trained to think beyond the capabilities of a single architect, will the results diverge (too) much from what society is used to? 

The many practical questions from the Retrofit Project show that defining the architect’s liberty is both the problem and holds the potential for digital technologies to tackle the true complexity of the field. Liberty is undeniably linked to the design process and, therefore, encoding a design process needs to (1) capture the architect’s evaluation system and (2) allow for targeted and smart data gathering. The evaluation system can then be coded into an algorithm, with the help of machine learning experts, and trained using the gathered data. Both the evaluation system and the necessary data rely heavily on the architect’s liberty. Because dealing with these liberties is a difficult task – perhaps the most difficult task in the age of digital architecture – many contemporary businesses and start-ups that claim to revolutionise the design process with innovative technologies might not revolutionise anything, because they opt for the easy route and avoid dealing with the liberty aspect. An architectural algorithm that does take the liberty aspect into account may provide designers with an artificial assistant to help tackle all complexities in the field while tapping into the full potential of today’s available computational power. 

This could be the ultimate task we set ourselves at the DSH. Studying a large dataset of design processes, steps, and creative acts might reveal codifiable patterns that could be integrated into a unified and conventionalized evaluation system. This study would target large and diverse groups of designers and users in general, including their knowledge exchange with other involved professionals. Could such an integral evaluation system, combined with data gathering, finally offer the prospect of developing a truly architectural algorithm? Eventually, this too will encounter issues that require further study, such as deciding who to involve and how to wisely navigate between the highs and lows of the wisdom of crowds: [16] can we still trust the emerging patterns detected by machine learning algorithms to constitute proper architectural liberty and, thus, good architecture? We will proceed vigilantly, but we must explore this path to avoid further fragmentation, non-crucial automation, and the propagation of false complexity. 


[1] N. Leach, Architecture in the Age of Artificial Intelligence: An Introduction for Architects (London; New York: Bloomsbury Visual Arts, 2021).

[2] The Design Sciences Hub [DSH] is a valorisation team of the Antwerp Valorisation Office. The DSH works closely with IDLab Antwerp for Machine Learning components and with the UAntwerp research group Energy and Materials in Infrastructure and Buildings [EMIB] to study energy neutrality within the Retrofit Project. Although the project will be led and executed by the University of Antwerp, the private industry is involved as well. Four real estate partners – Bopro, Immogra, Quares and Vooruitzicht – are financing and steering this project. So is the Beacon, maximizing the insights from digital technology companies. Also see:

[3] H.W. Kruft, A History of Architectural Theory: from Vitruvius to the present (London; New York: Zwemmer Princeton Architectural Press, 1994).

[4] P. Schumacher, The Autopoiesis of Architecture: A New Framework for Architecture. Vol. 1 (Chichester: John Wiley & Sons Ltd, 2011). P. Schumacher, The Autopoiesis of Architecture: A New Agenda for Architecture. Vol. 2 (Chichester: John Wiley & Sons Ltd, 2012).

[5] Ibid.

[6] Delve is a product of Sidewalk Labs, founded as Google’s urban innovation lab, becoming an Alphabet company in 2016. Hypar is a building generator application started by former Autodesk and Happold engineer Ian Keough. Also see,

[7] A. Bava, “Computational Tendencies”, In N. Axel, T. Geisler, N. Hirsch, & A. L. Rezende (Eds.), Exhibition catalogue of the 26th Biennial of Design Ljubljana. Slovenia (2020): e-flux Architecture and BIO26| Common Knowledge.

[8] H.W. Kruft, A History of Architectural Theory: from Vitruvius to the present (London; New York: Zwemmer Princeton Architectural Press, 1994).

[9] A. Bava, “Computational Tendencies”, In N. Axel, T. Geisler, N. Hirsch, & A. L. Rezende (Eds.), Exhibition catalogue of the 26th Biennial of Design Ljubljana. Slovenia (2020): e-flux Architecture and BIO26| Common Knowledge.

[10] S. Verbruggen, The Critical Residue: Creativity and Order in Architectural Design Theories 1972-2012 (2017).

[11] M. Gausa & S. Cros, Operative optimism (Barcelona: Actar, 2005)

[12] W. S. Saunders, The new architectural pragmatism: a Harvard design magazine reader. (Minneapolis: University of Minnesota Press, 2007).

[13] R. Somol & S. Whiting, Notes around the Doppler Effect and Other Moods of Modernism. (2002) In K. Sykes (Ed.), Constructing a New Agenda: Architectural Theory 1993-2009 (1st ed., pp. 188-203). (New York: Princeton Architectural Press).

[14] K. Sykes, Constructing a new agenda : architectural theory 1993-2009.  (1st ed., New York: Princeton Architectural Press, 2010).

[15] S. Whiting, (recorded in Delft, march 2006). The Projective, Judgment and Legibility: Lecture at the Projective Landscape Conference, organized by the TU Delft and the Stylos foundation.

[16] P. Mavrodiev & F. Schweitzer “Enhanced or distorted wisdom of crowds? An agent-based model of opinion formation under social influence”, Swarm Intelligence, 15(1-2), 31-46. doi:10.1007/s11721-021-00189-3 J. Surowiecki, The wisdom of crowds : why the many are smarter than the few. (London: Abacus, 2005).

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Fig. 2 Norman Foster’s sketch illustrates the generative process: each floor is rotated by 5° relative to the one below around the central core with the pillars, bearing the vertical loads, the services, the stairs, and the lifts. From the core, six ‘spokes’ host the floorspace at each level. Each floorspace is detached from the next by a void triangular area about 20° wide. The vertically open areas create light wells for the height of the tower, up to the thirty-second floor. These open areas wound in coils to flow ventilation and natural lighting inside the building.
Fig. 2 Norman Foster’s sketch illustrates the generative process: each floor is rotated by 5° relative to the one below around the central core with the pillars, bearing the vertical loads, the services, the stairs, and the lifts. From the core, six ‘spokes’ host the floorspace at each level. Each floorspace is detached from the next by a void triangular area about 20° wide. The vertically open areas create light wells for the height of the tower, up to the thirty-second floor. These open areas wound in coils to flow ventilation and natural lighting inside the building.
The Architect and the Digital: Are We Entering an Era of Computational Empiricism? 
architectural design theory and practice, case study/studies, design education, design methods, digital design, parametric design
giovanni corbellini, Luca Caneparo
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The close integration of design with computational methods is not just transforming the relationships between architecture and engineering; it also contributes to reshaping modes of knowledge development. This paper critically probes some issues related to this paradigm shift and its consequences on architectural practice and self-awareness, looking at the potential of typical teaching approaches facing the digital revolution. The authors, who teach an architectural design studio together, coming from different backgrounds and research fields, probe the topic according to their respective vantage points. 

Over the last few decades, a design agency has developed of using digital tools for the interactive generation of solutions by dynamically linking analytic and/or synthetic techniques. 

The analytic techniques make use of simulation, of the capability to forecast certain aspects of building performance. While in conventional practice simulation usually plays a consulting role in the later stages of the design process, in the new forms of agency it works as a generative device from the earlier phases. 

The synthetic techniques address, on the other hand, more organic, para-biologic concepts – for instance “emergence, self-organization and form-finding” – looking for “benefits derived from redundancy and differentiation and the capability to sustain multiple simultaneous functions”. [1] 

Structures and their conception stand out as a part of architectural design where the digital impact shows its clearest consequences. Candela, Eiffel, Nervi and Torroja considered for instance that calculations have to go in parallel with intuitive understanding of the form: “The calculation of stresses”, writes Torroja, “can only serve to check and to correct the sizes of the structural members as conceived and proposed by the intuition of the designer”. [2] “In this fundamental phase of design”, Nervi adds, “the complex formulas and calculation methods of higher mathematics do not serve. What are essential, however, are rough evaluations based on simplified formulas, or the ability to break down a complex system into several elementary ones”. [3] At the time, the computational aspects were overridingly cumbersome; Frontón Recoletos required from Torroja one hundred and fifty-eight pages of calculations with approximate methods. Classical analytical procedures provided limited tools for simulation: “It was mandatory for the engineer to supplement his analyses with a great deal of judgment and intuition accumulated over years of experience. Empiricism played a great role in engineering design; while some general theories of mechanical behaviour were available, methods for applying them were still under development, and it was necessary to fall back upon approximation schemes and data taken from numerous tests and experiments”. [4] 

After the epoch of Nervi and Torroja, research and practice have been deeply influenced by the combined actions of computation toward a unifying approach to the different theories in mechanics, thanks to exponential performance improvements in the hardware, as well as achievements in symbolic and matrix languages, and discretization methods (e.g., boundary and finite elements methods) implemented in software. At present, the wide availability of computational methods and tools can produce numerical simulations out of complex forms, with the expectation of providing a certain degree of knowledge and understanding of mechanics, energetics, fluids, and acoustics. The compelling possibilities of boundary or finite element methods, plus finite difference or volume methods, has produced a shift from science of construction pioneers’ awareness that not everything can be built, [5] to the “unprecedented morphology freedom” of the present. [6] Therefore, “We are limited in what we can build by what we are able to communicate. Many of the problems we now face”, as Hugh Whitehead of Foster and Partners points out, “are problems of language rather than technology. The experience of Swiss Re established successful procedures for communicating design through a geometry method statement”. [7] 

 “Parametric modelling”, Foster and Partners stated, “had a fundamental role in the design of the tower. The parametric 3D computer modelling process works like a conventional numerical spreadsheet. By storing the relationships between the various features of the design and treating these relationships like mathematical equations, it allows any element of the model to be changed and automatically regenerates the model in much the same way that a spreadsheet automatically recalculates any numerical changes. As such, the parametric model becomes a ‘living’ model – one that is constantly responsive to change – offering a degree of design flexibility not previously available. The same technology also allows curved surfaces to be ‘rationalized’ into flat panels, demystifying the structure and building components of highly complex geometric forms so they can be built economically and efficiently”. [8] 

Of course, communication is here understood within a very specific part of the design process, mainly connected with fabrication issues and their optimisation, but it is a concept that involves many layered levels of meaning. [9] Curiously, this shift from the physical to the immaterial reminds us of the same step made by Leon Battista Alberti, who conceived design as a purely intellectual construct and was obsessed by its transmission from idea to built form without information decay. [10] Digital innovation promises to better connect the engineering process (focus on the object) with the wider reality (the architectural perspective), enabling design teams to deal with increasingly complex sets of variables. Freedom comes, however, with the disruption of the design toolbox, usually more defined by constraints than capabilities, so that the resulting wild fluctuations of effects seem increasingly disconnected from any cause. Design choices are therefore looking for multifaceted narrative support – and the “Gherkin”, with its combination of neo-functional-sustainable storytelling and metaphorical shape, turns out to be emblematic from this point of view too. [11] 

Furthermore, extensive numerical simulations raise a question as to what extent they prove reliable, both because of their intrinsic functionality and the “black box” effect connected to the algorithmic devices. Those latter, especially in the latest applications of artificial intelligence such as neural networks, produce results through processes that remain obscure even to their designers, let alone less-aware users. Besides, the coupling of simulation with generative modelling through interactivity may not assist the designer in developing the understanding that, in several cases, (small) changes in the (coded) hypotheses can produce radically different solutions. Thus, the time spent in simulating alternatives can be more profitably spent working on different design hypotheses, and on architectural, technological and structural premises, perhaps with simpler computational models. 

Are we entering an era of computational empiricism, as some authors maintain? [12] 

Languages of innovation 

Generative modelling, morphogenesis, parametric tooling, computational and performative design… all these apparatuses have brought methodological innovation into closer integration among different disciplines, bridging the gaps between fields. Modelling the project, the main common aim of this effort, has from the beginning leaned on logics and mathematics as a shared lingua franca. [13] Since the 1960s, applied mathematics has extended its applications through the formalisation process of information technology, which has developed the tools and the models beneficial for the purposes of science and technology. Information and communication technology puts into effect “the standardisation and automation of mathematical methods (and, as such, a reversal of the relationship of domination between pure mathematics and applied mathematics and, more generally, between theory and engineering)”. [14] 

The redefinition of roles, between theories and techniques when applied to design, began in mathematics and physics with a metamorphosis of language, [15] with a shift towards symbolic languages that have gone beyond the mechanics of structures and the thermodynamics of buildings, subjecting it to automatic calculus, and finalising it in computation. [16] “Today, it is a widely held view that the advent of electronic computation has put an end to this semiempirical era of engineering technology: sophisticated mathematical models can now be constructed of some of the most complex physical phenomena and, given a sufficiently large computer budget, numerical results can be produced which are believed to give some indication of the response of the system under investigation”. [17] 

The straightforward capability to model and simulate projects, supported by the evidence of results, has given confidence in the emerging computational tools, highlighting the dualism between the desire to make these devices usable for a wide range of practitioners, in a variety of cases and contexts, and the exigency of grounding bases for deeper understanding within a reflective practice. Moreover, the very nature of using digital tools urges designers to face an increasing risk of becoming “alienated workers” who, in Marxian terms, neither own their means of production in actuality – software companies lease their products and protect them against unauthorised modifications – nor, above all, conceptually, since their complex machinery requires a specifically dedicated expertise. Therefore, within the many questions this paradigm shift is raising about the redefinition of theories and practices and their mutual relationship, a main concern regards educational content and approaches, in terms of their ability to provide useful knowledge to future practitioners and aid their impact on society. In the architectural design field – which traditionally crossbreeds arts, applied sciences, and humanities in order to fulfil a broad role of mediation between needs and desires – this means dealing with an already contradictory pedagogic landscape in which ideologically opposite approaches (namely method-oriented and case-oriented pedagogies) overlap. 

The specific of architectural design teaching does not escape this tension between methodological ambitions, nurtured by modern thinking and its quest for rationalisation, and the interplay between generations, languages and attitudes involved by learning through examples – even with its paradoxical side effects. One would expect in fact that a “positive” (according to Christopher Alexander), rule-based training should yield more open-ended outcomes than the “negative”, academic, disciplinary learning by copying. [18] But, on the one hand, the methodological approach implies an idea of linear control – towards optimisation and performance as well as in social and political terms – which reveals its origin in Enlightenment positivism. The Durandian apparatuses so widespread after World War II, with their proto-algorithmic design grammars, ended up accordingly with the reproduction of strict language genealogies. A similar trend seems to be emerging nowadays, in the convergence toward the same effective solutions in arts, sports, and whatever else, as a by-product of digital efficiency – which even the very technical camp is questioning. On the other hand, tinkering with the interpretation and application of examples makes possible the transmission of the many unspoken and unspeakable aspects connected to any learning endeavour. Getting closer to “good” examples – testing their potential according to specific situations – allows their inner quality to be grasped, reignited in different conditions, and finally transcended. Since forgetting requires something to be forgotten, Alexander is somehow right in framing this teaching attitude as “negative”: ironically, imitation provides the learning experience through which personal voices can emerge and thrive. 

Challenges ahead 

Turpin Bannister considered that in “an age of science”, architects “abandoned the scientific approach as detrimental to the pure art of design. On even the simplest question they acquiesced to their engineer and so-called experts”. [19] The pervasive penetration of computation in design would probably have met Bannister’s approval. The consequences and methodological implications are so far-reaching that they raise questions: how must education deal with the increased role of interactive computation in architectural design? And, more generally, with techno-science, its languages and methodologies? 

Architectural design still relies on a “political” attitude, and mediation between the “two cultures” [20] is a fundamental asset of its disciplinary approach. Even though the unity of knowledge has disappeared with the advent of modern science, as Alberto Pérez-Gómez stated, [21] we ideally aspire to become like renaissance polymaths, mastering state-of-the-art skills in the most disparate fields. But in the long time that separates us from Brunelleschi and Alberti, the amount of knowledge required by the different aspects of the practice, even those which are specifically architectural, has grown exponentially, and trying to get a minimum of mastery over it would demand a lifelong commitment and extraordinary personal qualities. Digital prostheses promise to close the gap between the desire for control over the many facets of the design process and the real possibility of achieving it. Some consequences of the augmented agency provided by new information and communication technologies are already evident in the overlapping occurring in the expanded field of the arts, with protagonists from different backgrounds – visual arts or cinema for instance – working as architects or curators and vice versa. [22] The power of the digital to virtually replace those “experts”, to whom, according to Turpin Bannister, architects outsource their own choices, seems to act therefore as an evolutionary agent against overspecialisation, confirming the advantage Bucky Fuller attributed to the architect as the last generalist. [23] 

However, without understanding and manipulating what happens within the black box of the algorithm, we still face the risk of being “designed” by the tools we put our trust in, going on to accept a subordinate position. Speaking machine, as John Maeda has pointed out, [24] is becoming necessary in order to contribute innovatively to any design endeavour. The well-known Asian American researcher, designer, artist and executive comes from a coding background, later supplemented with the study and practice of design and arts (along with business administration). His educational path and personal achievements indicate that such an integration of expertise is possible and desirable, even though his logical-mathematical grounding is likely the reason he mostly works with the immaterial, exploring media design and the so-called experience economy. Architectural schools are therefore facing the issue of if, when, and how to introduce coding skills into their already super-crammed syllabuses – from which, very often, visual arts, philosophy, law, storytelling and other much needed approaches and competencies are absent. One can argue that coding would provide young professionals with expertise they could immediately use in the job market, enabling them to better interact with contemporary work environments. On the other hand, a deeper perspective shows how the “resistance” of architectural specificity produced exceptional results in revolutionary times: academic education acted for the Modern masters as both a set of past, inconsistent practices to overcome and a background that enhanced the quality of their new language. 

Digitalisation looks like a further step along the process of the specialisation of knowledge, which unfolded hand-in-hand with the development of sciences, techniques, and their languages. Since the dawn of the modern age, architects have often tried to bring together a unified body of knowledge and methodology; first around descriptive geometry, and then around geometry as a specific discipline which “gives form” to mathematics, statics and mechanics. “Geometry is the means, created by ourselves, whereby we perceive the external world and express the world within us. Geometry is the foundation”, Le Corbusier writes in the very first page of his Urbanisme, trying to keep pace with modernisation and establishing a new urban planning approach according to its supposed “exactitude”. [25] But while hard sciences and their technical application rely on regularity of results in stable experimental conditions, architects are still supposed to give different answers to the same question – or, more precisely, to always reframe architectural problems, questioning them in different ways. 

Considering the volatility of the present situation, opening up and diversifying the educational offer seems a viable bet, more so than the attempt to formulate a difficult synthesis. Only by being exposed to the conflict between the selective, deterministic optimisation promise of code-wise design, and the dissipative, proliferating, unpredictable interpretation of cases can architects find their own, personal way to resolve it. 

Fig. 1 Norman Foster’s sketch for the headquarters of the Swiss Reinsurance Company, 30 St Mary Axe, in the historic core and the financial district of the City of London. Foster + Partners designed a fifty-storey tower 590ft (180 m) with a magnificent organic form that adds a distinctive identity to the skyline of the city.
Fig. 2 Norman Foster’s sketch illustrates the generative process: each floor is rotated by 5° relative to the one below around the central core with the pillars, bearing the vertical loads, the services, the stairs, and the lifts. From the core, six ‘spokes’ host the floorspace at each level. Each floorspace is detached from the next by a void triangular area about 20° wide. The vertically open areas create light wells for the height of the tower, up to the thirty-second floor. These open areas wound in coils to flow ventilation and natural lighting inside the building.
Fig. 3 The sketch of Norman Foster for the fully-glazed domed restaurant atop of the tower.
Fig. 4 The tapering profile of the tower allows reduced area at street level 160 ft (49 m), and reaches the largest diameter of 184 ft (56 m) at the 21st level, with the spatial climax at the glazed domed roof. The diagrid structure parametrises the A-shaped frames, and relieves the lateral loading from the central core. The A-shaped frames develop over two floors, and decrease the proportions from the 21st level respectively towards the pitched dome and the lobby level.

Fig. 5 Norman Foster’s sketch makes clear how the A-shaped frames take on the diagrid geometry with two diagonal columns of tubular steel 20 in (508 mm) diameter, reflecting in the diamond-shaped backgrounds of the window panes.


[1] S. Roudavski, “Towards Morphogenesis in Architecture”, International Journal of Architectural Computing, 3, 7 (2009) (accessed 24 March 2021).  

[2] E. T. Miret, J. J. Polivka and M. Polivka, Philosophy of Structures, (Berkeley: University of California Press, 1958), 331.  

[3] P. L. Nervi, Aesthetics and Technology in Building (Cambridge, Mass.; London; Harvard University Press: Oxford University Press, 1966), 199. 

[4] T. Oden, K.-J. Bathe, “A commentary on Computational Mechanics”, Applied Mechanics Reviews, 31, 8 (1978), 1055-1056. 

[5] “We can now wonder whether any type of imaginary surface, is constructible. The answer is in the negative. So: how to choose and how to judge an imagined form?” E. T. Miret, J. J. Polivka and M. Polivka, Philosophy of Structures, (Berkeley: University of California Press, 1958) 78. 

[6] M. Majowiecki, “The Free Form Design (FFD) in Steel Structural Architecture–Aesthetic Values and Reliability”, Steel Construction: Design and Research, 1, 1 (2008), 1. 

[7] A. Menges, “Instrumental geometry”, Architectural Design, 76, 2 (2006), 46. 

[8] Foster and Partners, “Modeling the Swiss Re Tower”, ArchitectureWeek, 238 (2005), (accessed 10 April 2022) 

[9] “[Marjan] Colletti aptly quotes Deleuze stating: ‘The machine is always social before it is technical.’ The direct interaction between the designer and the equipment provides a feedback system of communication. He argues that the computer should ‘be regarded neither as abstract nor as machine’, but rather as an intraface.” C. Ahrens, “Digital Poetics, An Open Theory of Design-Research in Architecture”, The Journal of Architecture, 21, 2, (2016), 315; Deleuze’s passage is in G. Deleuze, C. Parnet, Dialogues (New York: Continuum International Publishing, 1987), 126-12; Colletti’s in M. Colletti, Digital Poetics, An Open Theory of Design-Research in Architecture (Farnham: Ashgate, 2013), 96. 

[10] “We shall therefore first lay down, that the whole Art of Building consists in the Design, and in the Structure. The whole Force and Rule of the Design, consists in a right and exact adapting and joining together the Lines and Angles which compose and form the Face of the Building. It is the Property and Business of the Design to appoint to the Edifice and all its Parts their proper Places, determinate Number, just Proportion and beautiful Order; so that the whole Form of the Structure be proportionable. Nor has this Design any thing that makes it in its Nature inseparable from Matter; for we see that the same Design is in a Multitude of Buildings, which have all the same Form, and are exactly alike as to the Situation of their Parts and the Disposition of their Lines and Angles; and we can in our Thought and Imagination contrive perfect Forms of Buildings entirely separate from Matter, by settling and regulating in a certain Order, the Disposition and Conjunction of the Lines and Angles.” L. B. Alberti, The Ten Books of Architecture (London: Edward Owen, 1755 [1450]), 25. 

[11] A. Zaera-Polo, “30 St. Mary Axe: Form Isn’t Facile”, Log, 4 (2005). 

[12] See – along with Oden, Bathe, and Majowiecki – Paul Humphreys, “Computational Empiricism”, Topics in the Foundation of Statistics, ed. by B. C. van Fraassen (Dordrecht: Springer, 1997) and P. Humphreys, Extending Ourselves: Computational Science, Empiricism, and Scientific Method. (New York: Oxford University Press, 2004). 

[13] C Alexander, Notes on the Synthesis of Form (Cambridge, Mass.; London: Harvard University Press, 1964). 

[14] J. Petitot, “Only Objectivity”, Casabella, 518, (1985), 36. 

[15] E Benvenuto, An Introduction to the History of Structural Mechanics (New York, N.Y.: Springer-Verlag, 1991). 

[16] M. Majowiecki, “The Free Form Design (FFD) in Steel Structural Architecture–Aesthetic Values and Reliability”, Steel Construction: Design and Research, 1, 1 (2008), 1. 

[17] T. Oden, K.-J. Bathe, “A commentary on Computational Mechanics”, Applied Mechanics Reviews, 31, 8 (1978), 1056. 

[18] “There are essentially two ways in which such education can operate, and they may be distinguished without difficulty. At one extreme we have a kind of teaching that relies on the novice’s very gradual exposure to the craft in question, on his ability to imitate by practice, on his response to sanctions, penalties, and reinforcing smiles and frowns. … The second kind of teaching tries, in some degree, to make the rules explicit. Here the novice learns much more rapidly, on the basis of general ‘principles’. The education becomes a formal one; it relies on instruction and on teachers who train their pupils, not just by pointing out mistakes, but by inculcating positive explicit rules.” C. Alexander, Notes on the Synthesis of Form (Cambridge, Mass.; London: Harvard University Press, 1964), 35. 

[19] T. C. Bannister, “The Research Heritage of the Architectural Profession”, Journal of Architectural Education, 1, 10 (1947). 

[20] C. P. Snow, The Two Cultures and the Scientific Revolution  (Cambridge University Press, 1962). 

[21] A. Pérez-Gómez, Architecture and the Crisis of Modern Science (Cambridge, Mass.: The MIT Press, 1983). 

[22] “Artists after the Internet take on a role more closely aligned to that of the interpreter, transcriber, narrator, curator, architect.” A. Vierkant, The Image Object Post-Internet, (accessed 21 September 2015). The artist Olafur Eliasson, for instance, started up his own architectural office (, accessed 30 March 2021), and the film director Wes Anderson authored the interior design of the Bar Luce, inside the Fondazione Prada in Milan. 

[23] “Fuller … noted that species become extinct through overspecialization and that architects constitute the ‘last species of comprehensivists.’ The multidimensional synthesis at the heart of the field is the most invaluable asset, not just for thinking about the future of buildings but for thinking about the universe. Paradoxically, it is precisely when going beyond buildings that the figure of the architect becomes essential.” Mark Wigley, Buckminster Fuller Inc.: Architecture in the Age of Radio (Zürich: Lars Müller, 2015), 71. 

[24] J. Maeda, How to Speak Machine: Laws of Design for a Digital Age (London: Penguin Business, 2019). 

[25] Le Corbusier, The City of Tomorrow and its Planning (London: John Rocker, 1929 [1925]), 1. 

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Geocities’ neighbourhoods collage, 2022. Image credit: Alessandro Celli and Ibrahim Kombarji.
Geocities’ neighbourhoods collage, 2022. Image credit: Alessandro Celli and Ibrahim Kombarji.
Fostering Kinship: GeoCities’ Algorithmic Neighbourhoods
Algorithmic Neighbourhoods, civic participation, global village, Kinship, proximity, virtual city
Alessandro Celli, Ibrahim Kombarji
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The remains of a virtual city – possibly the first of its kind – can be found on servers all over the world.1 Geocities was launched as a series of districts, alleyways, and neighbourhoods where its inhabitants could build their own webpages. For the first time, the internet was given a structure in a way that its audience could relate to it on a human scale. Today, around 650 gigabytes of Geocities’s data remain accessible thanks to archiving efforts that ensured the recovery of some of the 38 million individual websites that existed at the time of GeoCities’ final closure in 2009. [2] [3] [4] [5] 

GeoCities was first launched in 1994 by David Bohnett and Dick Altman as a web hosting service, allowing its users to store and manage their website files. [6] Its initial name, Beverly Hills Internet, already hinted at the creators’ intention to develop a neighbourhood of websites, which would later mature into a geography of cities. The service offered a free plan with a generous two megabytes of storage to all users, known as the homesteaders, who were asked to choose a neighbourhood to reside in. [7] All of the city’s inhabitants occupied a defined space, in a defined surrounding, where their homepages were arranged within neighbourhoods. Each cluster of pages was spatially close to those which shared similar content, while each neighbourhood was defined by the broader topic into which they fit. As such, the company created and thematically organised its web directories into six neighbourhoods, which included Colosseum, Hollywood, RodeoDrive, SunsetStrip, WallStreet and West Hollywood. New neighbourhoods, as well as their suburbs, were later added as the site grew, and became part of the members’ unique web address with a sequentially assigned URL “civic address” (e.g., “”). Chat rooms and bulletin boards were added soon after, fostering rapid growth of the city. [8] Each neighbourhood had its own forum, live chat, and even a list of all the homesteaders who celebrated their birthday each day.  

By December 1995, when it changed its name to GeoCities, Beverly Hills Internet had over 20,000 homesteaders and over 6 million page-views per month. [9] Within this expansive organisation of web page clusters, a seamless sense of proximity between those who shared similar ideas naturally led to human behaviours such as kinship and affection between them.  

Neighbourhoods are intrinsic parts of our urban fabric and a self-evident manifestation of how the cities we live in are structured. [10] Yet, we still struggle to grasp a proper definition of their totality, given the complex layers within them. In 1926, progressive educator David Snedden defined the term neighbourhood as “those people who live within easy ‘hallooing’ distance”, illustrating it as a space where one can easily catch the attention of another. [11] 

This essay will explore the notion of an algorithmic neighbourhood, one that reflects – and derives from – parts of a physically built, “hallooing” urban neighbourhood. The internet lexicon of today descends seamlessly from a long lineage of architectural and spatial terminologies, such as firewall, coding architecture, homepage, platform, address, path, room, and location, among many others. In the translation from a physical reality that is shaped within our Latourian “critical zone”, some of these terminologies have shifted in their meaning when applied to new forms of digital space. [12] A parallel “digital critical zone” is generated, within which these algorithmic neighbourhoods sit.  

Figure 1 – Archived webpage “Tia”, West Hollywood neighbourhood. Image capture April 16 2022. Source:
Figure 2 – Archived webpage “The Gardening Girl”, Picket Fence neighbourhood. Image capture April 16 2022. Source:

Neighbourhood as a site of kinship and proximity  

The artisanal web built through GeoCities allowed “user-generated content”, which had not yet adorned itself with pompous names or revolutionary pretensions. [13] It proved that even before the invention of Web 2.0 – which was later aimed at implementing social-media profiles – the web was, above all, a story of human beings who interact with one another and discuss the subjects close to them through the means at hand.  

Urban studies professor Looker defines the United States as a nation of neighbourhoods. [14] This essay expands on this exposure of the continental urban fabric by exploring the communities of algorithmic kinship that exist within GeoCities’ virtual borders. Similar to physically built neighbourhoods, GeoCities’ urban structure fostered kinship and affection among its inhabitants. PicketFence, for example, was built to allow residents to share tips and advice on ‘Home Improvement Techniques’. The more experienced ‘Home Improvement’ users became the neighbourhood’s go-to people for navigating daily issues, reinforcing a shared communal knowledge. [15] 

West Hollywood, which was subdivided into “Gay, Lesbian, Bisexual, and Transgender topics”, is another example of such algorithmic kinship. This neighbourhood was a predecessor of today’s social-media spaces where users can gather and exchange (sometimes hidden or undisclosed) realities across communities. West Hollywood’s users could leave messages, sign a guestbook, and share contact information with one another. The neighbourhood gave people an opportunity to share similar experiences and daily struggles, form alliances with other communities, and tackle queer rights collectively. Moreover, West Hollywood fostered arenas of “block-level solidarity”, where “bonds and loyalties – whether as enacted on real-life pavements or as represented in stories, images, and speeches”, allowed connections between the intimate lives of users, their GeoCities pages, and the “city block”. [16] 

Proximity and reciprocal kinship were thus a foundational feature of GeoCities’ design: individuals, together with their personal pages, were at the centre of the Internet. In contrast, today’s platforms and digital services are structured in such a nested way that proximity is sometimes inconceivable, and individuals are reduced to anonymous consumers of information. Today, the information communications technology industry (ICT) is at the centre of the Internet. [17] Social media platforms still provide virtual spaces that allow communities to gather and share content with one another, fostering a certain degree of human interaction. However, the very structure within which they operate is fundamentally different from the ones used in early platforms such as GeoCities. While before, the digital matter – text, images, links – was spatially placed onto the transparent structure of the webpage, and you could clearly see the location of a jpeg file within the HTML lines of code, now it all runs through opaque interfaces. [18] These perfect facades are quasi-impenetrable for users, and hide the “black boxes” where algorithms operate as instruments of measurements and perception. [19] As a counterpart to algorithmic neighbourhoods, Caroline Busta defines social-media platforms as a grand bazaar, “with lanes of kiosks, grouped roughly by trade, displaying representative works to passers-by. At the back of the mini-shop is a trap door with stairs leading to a sub-basement where deals can be done”. [20] This multi-layered opaque architecture of the bazaar illustrates the complex structure that currently governs social-media platforms. In contrast, the algorithmic neighbourhoods of GeoCities attempted to encourage a transparent vision of the modes of portraiture in the digital realm, and defined tools for users to relate directly to it. 

Figure 3 – Archived webpage “Gay Ukraine International, Kiev, UA”, West Hollywood neighbourhood. Image capture April 16 2022. Source:
Figure 4 – Archived webpage “Welcome to the deep Heart of TEXAS and Our Home”, Picket Fence neighbourhood. Image capture April 16 2022. Source:

Neighbourhood as a site constantly ‘under construction’   

A digital archaeologist scavenging through GeoCities’ remains would come across a vast number of “under construction” signs strewn across the neighbourhood’s alleys, outlining its “work-in-progress” state. Surrounded by virtual scaffolding, the pages under construction were built, line after line of code, by the homesteaders, slowly undergoing organic changes and upgrades. Each individual page was constructed by its creator, from its foundations to its decorative elements, in the HTML format – the HyperText Markup Language. The coding language not only allowed users to build their pages from scratch, but also to introduce multimedia resources such as JPGs and GIFs. A page under construction implies that there was a process of creation, which aimed at an eventual final form. Similar to a construction site, the individual web page could be openly observed throughout its making, as it could be visited by GeoCities inhabitants at any moment in time. It was a facade yet to come; a page that was shaped by the algorithmic manipulation of its users as they added another ‘about me’ section, a ‘guestbook’ to be signed, or a photo gallery of low-res pictures – to fit within the 2 megabytes limit – portraying their personal lives. 

Differently, the architecture of new forms of webpages and content aggregators is now conceived with an opaque algorithmic structure. Their virtual space is not one of proximity and distance based on intelligible parameters, but one of hierarchical appearance and disappearance based on unintelligible instruments of perception. [21] For instance, Google’s page-ranking algorithm mutates and evolves over time, leaving no traces behind, except the ones it uses to train itself. When presented with Google search results, users are faced with a series of temporary choices that are the result of a very intricate mechanism of automatic selection and classification. Vladan Joler defines algorithms as “instruments of measurements and perception”; thus, algorithmic architecture can be outlined by an operation of the more-than-human. Data collection and consumer profiling are the parameters upon which the current Internet is being built, instead of it being a conscious construction process carried out by its users. 

While the architectural backdrop of a platform is constantly being redefined based on who is interacting with it, its facade – the interface – is pure and familiar. This interface which we constantly visit, however, obscures what’s beneath it. Even if it is a clear manifestation of rules, as it tells you what you can or cannot do, it does not reveal through which mechanisms it gathers and conveys information, nor how the user’s actions are exploited for profitable means. The algorithmic design of GeoCities, based on neighbourhood alliances, had not yet allowed for this opacity, avoiding instances of power structures, black boxes, and opaque interfaces. It also avoided entering the black hole of rhizomatic surveillance that now permeates the virtual realm. [22] [23]  

Algorithmic neighbourhoods can also help to expose the physical infrastructure hosting them. Similarly, to the opaqueness of interfaces, our built neighbourhoods are shaped by an underground infrastructure of fleshly cables and routers. Data centres, globally connected by a web of cables, host our digital selves, which wander through the unmeasurable geographies of the Internet. They are out of reach, transcending any geographical boundary, as they mirror the ubiquitous nature of algorithmic spaces. Cables and data centres are, in fact, the physical side of the Internet, its thickness on our planet. They are the physical neighbourhood mirroring the algorithmic one, hosting the latter through servers, cables, connections, and energy. The physical neighbourhood which creates the digital infrastructure is not, however, a direct reflection of the algorithmic one. It is instead expansive, ubiquitous, fragmented, and absent, as it is designed to operate under strict safety protocols and privacy regulations.  

Figure 5 – Archived webpage “Q Pals”, West Hollywood neighbourhood. Image capture April 16 2022. Source:
Figure 6 – Archived webpage “Monica Munro”, West Hollywood neighbourhood. Image capture April 16 2022. Source:

Neighbourhood as a site of civic participation and resistance  

In June 1998, in order to boost brand awareness and advertising impressions, GeoCities introduced a watermark on its users’ web pages. [24] The watermark, much like an on-screen graphic on some TV channels, was a transparent floating GIF image that used JavaScript to stay displayed at the bottom right of the browser window. Many users felt that the watermark interfered with their website design, and threatened to move their pages elsewhere. A year later, in 1999, Yahoo bought the platform and consequently implemented its “Terms of Service agreement” leading to a unanimous reaction by the homesteaders. [25] The “Haunting of GeoCities” was the users’ response to the threat over content rights and access control. Each neighbourhood became a ghost town, where homepages were stripped of their content and colours, replaced with excerpts of the offending Terms of Service. As authors Reynolds and Hallinan point out, “users sensed that Yahoo’s unfettered access to this content threatened their creative control and diluted their power to make decisions about how and where to display their content. … some enterprising homesteaders sought to foil Yahoo’s legal and digital access to their intellectual property by removing it from the service altogether”. [26] The collective operation, moreover, represented a strategic mobilization of GeoCities design, defined by co-founder David Bohnett as “a bottoms-up, user-generated content mode”. [27] [28] The homesteaders’ remarkable political response allowed them to preserve a certain degree of control over their content, interfering with the dominating “Terms of Service agreement” which regulates, even more so today, every action we take within a platform. 

The “Haunting” protest represented a point of resistance towards the tendency of tech-giants to channel social traffic through a corporate digital platform ecosystem – a ubiquitous model in today’s internet. [29] The organized response by the homesteaders was only possible by the virtue of the very architecture of GeoCities. Neighbourhoods allowed a bottom-up response that could contrast the overarching corporate control put in place by Yahoo. It was a gathering that was empowered by proximity and affection, while it could exploit the temporary nature of the homepages’ construction as a medium for political change. In 2009, in response to the termination of GeoCities by Yahoo, new mechanisms of neighbourly rebuttal emerged. The German hosting provider JimdoWeb, for instance, attempted to host the nomad homesteaders by launching the Lifeboat for GeoCities webpage. Simultaneously, efforts of internet archivists started to meticulously archive each homepage of GeoCities in a countering act to preserve memory and gather residues of the city. 

The archived remains of the virtual city stand as an alternative approach to the complexity and opaqueness of the algorithmic layering of contemporary web-hosting services, as much as they reveal the ‘trans-scalar’ infrastructure of the Internet. [30] These neighbourly entanglements help us make sense of the current digital “global village”, offering an entry point to analyse how it is being shaped by the effects of globalisation, market economies, and imprudent media. [31] [32] Moreover, they display how the global village is being governed by algorithmic interdependencies, which in turn affect the architectural formations in both virtual and physical realities. [33]  

Figure 7 – Archived webpage “Gay Denton”, West Hollywood neighbourhood. Image capture April 16 2022. Source:
Figure 8 – Geocities’ neighbourhoods collage, 2022. Image credit: Alessandro Celli and Ibrahim Kombarji.


[1] Archive Team. (accessed April 16, 2022).

[2] R. Vijgen. “The Deleted City”,, (2017)

[3] Restorativland, “The Geocities Gallery”,, (accessed March 1, 2022).

[4] “OoCities”,, (accessed March 1, 2022).

[5] O. Lialina & D. Espenschied, “One Terabyte of Kilobyte Age”,, (accessed March 1, 2022).

[6] A.J. Kim, Community Building on the Web: Secret Strategies for Successful Online Communities (United Kingdom: Pearson Education, 2006).

[7] B. Sawyer, D Greely, Creating GeoCities Websites, (Cincinnati, Ohio: Muska & Lipman Pub, 1999) .

[8] Ibid.

[9] C. Bassett, The arc and the machine: Narrative and new media, (Manchester: Manchester University Press, 2013).

[10] J. Jacobs, “The City: Some Myths about Diversity”, The death and life of great American cities, (New York: Random House, 1961).

[11] R. Sampson, “The Place of Context: A Theory and Strategy for Criminology’s Hard Problems”, Criminology 51 (The American Society of Criminology, 2013).

[12] B. Latour, Critical Zones: The Science and Politics of Landing on Earth, (Cambridge, MA: MIT Press, 2020).

[13]  B. Sawyer, D Greely, Creating GeoCities Websites, (Cincinnati, Ohio: Muska & Lipman Pub, 1999).

[14] B. Looker, A Nation of Neighborhoods: Imagining Cities, Communities, and Democracy in Postwar America, (Chicago: The University of Chicago Press, 2015).

[15] Ibid.

[16] Ibid.

[17] C. Busta, “Losing Yourself in the Dark”. Open Secret, KW Institute for Contemporary Art,, (accessed April 16, 2022).

[18] S.U. Noble, Algorithms of Oppression: How Search Engines Reinforce Racism,. (United States: NYU Press, 2018).

[19] V. Joler, “New Extractivism”, Open Secret, KW Institute for Contemporary Art,, (accessed April 16, 2022).

[20]  C. Busta, “Losing Yourself in the Dark”. Open Secret, KW Institute for Contemporary Art,, (accessed April 16, 2022).

[21]  V. Joler, “New Extractivism”, Open Secret, KW Institute for Contemporary Art,, (accessed April 16, 2022).

[22] D. Savat, “(Dis)Connected: Deleuze’s Superject and the Internet”, International Handbook of Internet Research, 423–36 (Dordrecht: Springer, 2009).

[23] K.D. Haggerty, R. Ericson, “The Surveillant Assemblage”. British Journal of Sociology, 51, 4, 605-622, (United Kingdom: Wiley-Blackwell for the London School of Economics, 2000).

[24] J. Hu, “GeoCitizens fume over watermark”,, (accessed March 1, 2022).

[25] R. Ku, Cyberspace Law: Cases and Materials, (New York: Wolters Kluwer, 2016).

[26] C. Reynolds, B. Hallinan, “The haunting of GeoCities and the politics of access control on the early Web”, New Media & Society, (United States: SAGE Publishing, 2021).

[27] Ibid.

[28] B McCullough, “Interview with David Bohnett, founder of GeoCities”. Internet History Podcast,, (accessed April 16, 2022).

[29] J. Van Dijck, T. Poell, M. De Waal, The Platform Society: Public Values in a Connective World, (Oxford: Oxford University Press, 2018).

[30] A. Jaque, Superpowers of Scale, (New York: Columbia University Press, 2020).

[31] M. McLuhan, The Gutenberg galaxy: the making of typographic man (Toronto: University of Toronto Press, 1962).

[32] T. Friedman, The World Is Flat: A Brief History of the Twenty-First Century, (New York: Farrar, Straus and Giroux, 2005). [1] M. McLuhan, The Gutenberg galaxy: the making of typographic man, (Toronto: University of Toronto Press, 1962).

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Figure 8 - Extraction process – on the left the digital model, and on the right the sequence of instructions resulting from the extraction process. 
Figure 8 – Extraction process – on the left the digital model, and on the right the sequence of instructions resulting from the extraction process. 
Algorithmic Representation Space
Algorithmic Abstractness, Algorithmic Design, Algorithmic Representation Space, Design Paradigms, Model Concreteness, Representation Method, Representation Space
Renata Alves Castelo Branco, Inês Caetano, António Leitão
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Architecture has always explored the latest technological advances, causing changes in the way architects represent and conceive design solutions. Over the past decades, these changes were mostly due to, first, the integration of new digital design tools, such as Computer-Aided Design (CAD) and Building Information Modelling (BIM), which allowed the automation of paper-based design processes [1], and then, the adoption of computational design approaches, such as Algorithmic Design (AD), causing a more accentuated paradigm shift within the architectural practice. 

AD is a design approach based on algorithms that has been gaining prominence in both architectural practice and theory [2,3] due to its greater design freedom and ability to automate repetitive design tasks, while facilitating design changes and the search for improved solutions. Its multiple advantages have therefore motivated a new generation of architects to increasingly adopt the programming environments behind their typical modelling tools, going “beyond the mouse, transcending the factory-set limitations of current 3D software” [3; p. 203]. Unfortunately, its algorithmic nature makes this approach highly abstract, deviating from the visual nature of human thinking, which is more attracted to graphical and concrete representations than to alphanumerical ones.  

To approximate AD to the means of representation architects typically use and thereby make the most of its added value for the practice, we need to lower the existing comprehension barriers, which hinder its widespread adoption in the field. To that end, this research proposes a new approach to the representation of AD descriptions – the Algorithmic Representation Space (ARS) – that encompasses, in addition to the algorithm, its concrete outputs and the mechanisms that contribute to its understanding. 

Algorithmic Representation Method and Design Paradigms

Despite the cutting-edge aura surrounding it, AD is a natural consequence of architects’ desire to automate modelling tasks. In this approach, the architect develops algorithms whose execution creates the digital design model [4] instead of manually modelling it using a digital design tool. Compared to traditional digital modelling processes, AD is advantageous in terms of precision, flexibility, automation, and ease of change, allowing architects to explore wider design spaces easily and quickly. Two AD paradigms currently predominate, the main difference between them lying in the way algorithms are represented: architects develop their algorithms either textually, according to the rules of a programming language, or visually, by selecting and connecting graphical entities in the form of graphs [5]. In either case, the abstract nature of the medium hinders its comprehension. 

Algorithms are everywhere and are a fundamental part of current technology. In fact, digital design tools have long supported AD, integrating programming environments of their own to allow users to automate design tasks and deal with more complex, unconventional design problems. Unfortunately, despite its advantages and potential to overcome traditional design possibilities, AD was slow to gain ground in the field, remaining, after almost sixty years, a niche approach. One of the main reasons is the fact that it requires architects to learn programming, which is an abstract task that is far from trivial. This is aggravated by the fact that, for decades, most tools have had their own programming language, which in most cases was limited and hard to use, as well as a programming environment providing little support for the development and comprehension of algorithmic descriptions. Examples include ArchiCAD’s GDL (1983); AutoCAD’s AutoLisp (1986) and Visual Lisp (2000); 3D Studio Max’s MAXscript (1997); and Rhinoceros 3D’s Rhino.Python (2011) and RhinoScript (2007). 

To make AD more appealing to architects and approximate it to the visual nature of architectural design processes, visual-based AD environments have been released in the meantime. In these environments, text-based algorithmic descriptions are replaced by iconic elements that can be connected to each other in dataflow graphs [6]. Generative Components (2003) is a pioneering example that inspired more recent ones such as Grasshopper (2007) and Dynamo (2011). These tools offer a database of pre-defined operations (components) that users can access by simply dragging an icon onto the canvas and providing it with input parameters. For standard tasks covered by existing components, this speeds up the modelling task considerably. Furthermore, since programs are represented by graph structures – with nodes describing the functions, and the wires connecting them describing the data that gets transferred between them – it is easy to see which parts of the algorithm are dependent upon others, and thus, where the changes are propagated to. However, this is only true for small algorithms, which are a rare find in visual-AD descriptions [7]. Therefore, despite solving part of the existing problems – which explains the growing popularity of this paradigm in the community – others have emerged, such as its inability to deal with more complex and larger-scale AD solutions [5,8,9]. 

In sum, AD remains challenging for most architects and a far cry from the representation methods they typically use. Human comprehension relies on concrete instances to create mental models of complex concepts [10]. Contrastingly, AD, either visual or textual, operates at a highly abstract level. This grants it its flexibility but also hinders its comprehension. 

Algorithmic Abstractness Vs Model Concreteness 

Abstraction can be regarded as the process of removing detail from a representation and keeping only the relevant features [11]. Some authors believe abstraction improves productivity: it not only focuses on the “big idea” or problem to solve [12] but also triggers creative thinking due to its vagueness, ambiguity, and lack of clarity [13].  

Abstraction in architecture can be traced back at least as far as classical antiquity. Architectural treatises, such as Vitruvius’ “Ten Books on Architecture” [14], are prime examples of abstract representations because they intend to convey not specific design instances, but rather design norms that are applicable to many design scenarios. However, the human brain is naturally more attracted to graphical explanations than textual ones [15–17], a tendency that is further accentuated in a field with a highly visual culture such as architecture. For that reason, even the referred treatises were eventually illustrated after the birth of the printing press [18]. 

The algorithmic nature of AD motivates designers to represent their ideas in an abstract manner, focusing on the concept and its formal definition. This sort of representation provides great flexibility to the design process, as a single expression of an idea can encompass a wide range of instances that match that idea, i.e., a design space. Contrariwise, most representation methods, including CAD and BIM, compel designers to rapidly narrow down their intentions towards one concrete instance, on account of the labour required to maintain separate representations for each viable alternative. 

In sum, abstraction gives AD flexibility and the ability to solve complex problems, but it also makes it harder to understand. Abstraction is especially relevant when dealing with mathematical concepts, such as recursion or parametric shapes; nature-inspired processes, such as randomness; and performance-based design principles, such as design optimisation. It is also critical when developing and fabricating unconventional design solutions, whose geometric complexity requires a design method with a higher level of flexibility and accuracy. Sadly, these are also the hardest concepts to grasp without concrete instances and visual aid. 

Nevertheless, the described comprehension barrier, apparently imposed by the abstract-concrete dichotomy, is more obvious when the AD descriptions are independent entities with little to no connection to the outcomes they produce. Figure 1 represents the current conception of AD: there is a parametric algorithm, representing a design space, which can generate a series of design models when specific parameters are provided. We propose to overthrow this notion by including the outcomes of the algorithm in the design process itself, changing the traditional flow of design creation to accommodate more design workflows and comprehension approaches.   

Figure 1 – AD workflow – an algorithm, representing a design space, generates a digital model for each design instance. 

Algorithmic Representation Space 

AD descriptions have an abstract nature, which is part of the reason they prove so beneficial to the architectural design process. However, when it comes to comprehending an AD – i.e., creating a mental model of the design space it represents – this feature becomes a burden. Human cognition seems to rely heavily on the accumulation of concrete examples to form a more abstract picture [10]. For this reason, we advocate that, for a better comprehension of an AD, the algorithms themselves do not suffice.  

This research proposes a new way to represent algorithmic descriptions that aids the development and understanding of AD projects. Under the name of Algorithmic Representation Space (ARS), this concept encompasses not only the algorithm but also its outcomes and the mechanisms that allow for the understanding of the design space it represents. AD descriptions stand to benefit significantly from the concreteness of the outputs they generate, i.e., the digital models. If we consider the models as part of the AD representation, we reduce its level of abstraction and increase its understandability, approximating it to the visual nature of human understanding. Nevertheless, we must also smooth its integration in more traditional design workflows, helping architects who still develop their models manually in digital design tools or are forced to use pre-existing models. Accordingly, the proposed ARS also enables the use of already existing digital models as starting points to arrive at an algorithmic description. 

There are two core elements in the ARS (Figure 2), the algorithm and the model. The algorithm represents a design space in a parametric abstract way, which makes the multiple design alternatives it represents difficult to perceive. Contrastingly, each model represents an instance of a design space in a static but concrete way. Combining the former’s flexibility with the latter’s perceptibility is therefore critical for the success of algorithmic representation. For conceptual reasons, the presented illustration of the ARS levels the two elements. Nevertheless, one must keep in mind that the algorithm can generate potentially infinite digital models, and the concept holds for all of them.  

We consider two entry points into the ARS: programming and modelling. Each will allow architects to traverse the ARS; in the former case, from algorithm to model, by running the instructions in the algorithm to generate a model; and in the latter, from model to algorithm, by extracting an algorithmic description capable of generating the design instance and then refactoring that description to make it parametric as well. In either case, it is important the ARS contemplates the visualisation of these algorithm-model relationships. Therefore, we propose including techniques such as traceability in any ARS. In the following section, we will use a case study, the Reggio Emilia Train Station by Santiago Calatrava, to illustrate the ARS and each of the proposed principles. 

Figure 2 – Building blocks of the ARS. 


The typical AD process entails the creation of a parametric description that abstractly defines a design space according to the boundaries set by the architect (Figure 3). The parametricity of this description, or the size of the design space it represents, varies greatly with the design intent and the way it is implemented (e.g., degrees of freedom, rules, and constraints). By instantiating the parameters in the algorithm, the architect specifies instances of the design space, whose visualisation can be achieved by generating them in a digital design tool, such as a CAD, BIM, or game engine (Figure 3 – running the algorithm). Figure 4 presents several variations of the Reggio Emilia station achieved by running the corresponding AD description with varying input parameters, namely with a different number of beams, different beam sizes, and different amplitudes and phases of the sinusoidal movement. 

Given the flexibility of this approach, the process of developing AD descriptions tends to be a very dynamic one, with the architect repeatedly generating instances of the design to assess the impact of the changes made at each stage. Consciously or not, architects already work in a bidirectional iterative way when using AD. However, this workflow can also greatly benefit from a more obvious showcasing of the existing relations between algorithm and model. Traceability mechanisms allow precisely for the visual disclosure of these relations (i.e., which instruction/component generated which geometry), and several AD tools support them already. 

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Figure 3 – Entering the ARS by programming. 
Figure 4 – Parametric variations of the Reggio Emilia station, with different numbers and sizes of beams, and different amplitudes and signs of the sinusoidal movement. 

Creating Models 

AD is not meant to replace other design approaches but, instead, to interoperate with them. This interoperability is important, to take advantage of the investment made into those well-established representation methods such as CAD and BIM, especially for projects where digital models already exist or are still being produced. Therefore, the second entry point to the ARS is the conversion of an existing digital model of a design into an AD program. This might be necessary, for instance, when we wish to optimise it for new uses and/or to comply with new standards [19]. This process entails crossing the ARS in the opposite direction to that described in the previous section (Figure 5). 

To convert a digital model into an AD description, there are two main steps: extraction and refactoring. Extraction entails the automatic generation of instructions that can reproduce an exact copy of the model being extracted. The resulting AD description, however, is non-parametric and of difficult comprehension. This is where refactoring comes in [20,21], a technique that helps to improve the AD description, increasing its readability and parametricity. While the first task can be almost entirely automated, and is currently partially supported by some AD tools, the second part depends heavily on the architect’s design intent and, thus, will always be a joint effort between man and machine. In either case, it is important that the ARS adapts to the multiplicity of digital design tools and representation systems that architects often use during their design process. They can use, for instance, 3D modelling tools, such as CADs or game engines, to geometrically explore their designs more freely, or BIM tools to enrich the designs with construction information and to produce technical documentation.  

Figure 5 – Entering the ARS through modelling. 

Navigating the ARS 

As mentioned in the previous section, there are two main elements in the ARS: algorithms abstractly describing design spaces and digital models representing concrete instances of those design spaces. Either one can be accessed from either end of the spectrum, i.e., by programming and running the algorithm to generate digital models, or by manually modelling designs and then converting them into an algorithm. To allow for this bidirectionality between the two sides, the ARS relies on three main mechanisms: (a) traceability, (b) extraction, and (c) refactoring. The first allows the system to expose the existing relationships between algorithm and model in a visual and interactive way for a better comprehension of the design intent. The latter two allow us to traverse the ARS from model to algorithm, a less common crossing but an essential one, nevertheless. The following sections describe these three mechanisms in detail. 


For a proper comprehension of ADs, architects must construct a mental model of the design space, comprehending the impact each part of the algorithm has in each instance of the design space. To that end, a correlation must be ever present between the two core elements of the ARS – algorithm and model – matching the abstract representation with its concrete realisation. Traceability establishes relationships amongst the instructions that compose the algorithm and the corresponding geometries in the digital model. This is particularly relevant when dealing with complex designs, as it allows architects to understand which parts of the algorithm are responsible for generating which parts of the model.  

With traceability, users can select parts of the algorithm or parts of the model and see the corresponding parts highlighted in the other end. Grasshopper for Rhinoceros 3D and Dynamo for Revit, two visual AD tools, present unidirectional traceability mechanisms from the algorithm to the model. Figure 6 shows this feature at play in Grasshopper: users select any component on the canvas and the corresponding geometry is highlighted in the visualised model. 


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Figure 6 – Traceability in visual AD tools – the case of Grasshopper. 

Regarding bidirectional traceability, there are already visual AD tools that support it, such as Dassault Systèmes’ xGenerative Design tool (xGen) for Catia and Bentley’s Generative Components, as well as textual AD tools, such as Rosetta [22], Luna Moth [23], and Khepri [24]. Figure 7 shows the example of Khepri, where the user selects either instructions in the algorithm or objects in the model and the corresponding part is highlighted in the model or algorithm, respectively. Programming In the Model (PIM) [25], a hybrid programming tool, offers traceability between the three existing interactive windows: one showing the model, another the visual AD description, and a third showing the equivalent textual AD description. 

Unfortunately, traceability is a computationally intensive feature that hinders the tools’ performance with complex AD programs – especially model-to-algorithm traceability, which explains why some commercial visual-based AD tools avoid it. Those that provide it inevitably experience a decrease in performance as the model grows. All referred text-based and hybrid options are academic works, built and maintained as proof of concept and not as commercial tools, which explains their acceptance of the imposed trade-offs. A possible solution for this problem is to allow architects to decide when to use this feature and only switch it on when the support provided compensates for the computational overhead [26]. In fact, traceability-on-demand is Khepri’s current approach to the problem. 


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Figure 7 – Traceability in textual AD tools – the case of Khepri. 


Extraction is the automatic conversion of a digital model into an algorithm that can faithfully replicate it. Previous studies [27,28] focused on the generation of 3D models from architectural plans or on the conversion of CAD to BIM models, using heuristics and manipulation of geometric relations. Sadly, the result is not an AD description, but rather another model, albeit more complex and/or informed. One promising line of research is the use of the probabilistic and neural-based machine learning techniques (e.g., convolutional or recurrent neural networks) that address translation from images to textual descriptions, [29] but further research is needed to generate algorithmic descriptions. 

The main problems with extracting a parametric algorithm lie, first, in the assumptions the system would need to make while reading a finished model: for instance, distinguishing whether two adjacent volumes are connected by chance or intentionally and, if the latter, deciding if such connection should constitute a parametric restriction of that model or not. Secondly, it is nearly impossible to devise a system that can consider the myriad of possible geometrical entities and semantics available in architectural modelling tools. 

Some modelling tools that favour the VP paradigm avoid this problem by placing the responsibility on the designer from the very start, restricting the modelling workflow and forcing the designer to provide the missing information. In xGen and Generative Components, the 3D model and the visual algorithm are in sync, meaning changes made in either one are reflected in the other. PIM presents a similar approach, extending the conversion to the textual paradigm as well, although it was only tested with simple 2D examples.  

In practice, these tools offer real-time conversion from the model to the algorithm. However, either solution requires the model to be parametric from the start. Every modelling operation available in these tools has a pre-set correspondence to a visual component, and designers must build their models following the structured parametric approach imposed by each tool, almost as if they were in fact constructing an algorithm but using a modelling interface. As such, the system is gathering the information it needs to build parametric relations from the very beginning. This explains why neither xGen, nor Generative Components, nor PIM, can take an existing model created in another modelling software or following other modelling rules and extract an algorithmic description from it. 

This problem has also been addressed in the TP field and promising results have been achieved in the conversion of bi-dimensional shapes into algorithms [24,30]. However, further work is required to recognise 3D shapes, namely 3D shapes of varying semantics, since architects can use a myriad of digital design tools to produce their models, such as CADs, BIMs, or game engines. Figure 8 presents an ideal scenario, where the ARS is able to extract an algorithm that can generate an identical model to that being extracted. 

In either case, even if we arrive at the extraction of the most common 3D elements any time soon, the resulting algorithm will only accurately represent the extracted model, and it will comprise a low-level program, which is very hard for humans to understand. To make the algorithm both understandable and parametric, it needs to be further transformed according to the design intent envisioned by the architect. Increasing the algorithm’s comprehension level and the design space it represents is the goal of refactoring. 


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Figure 8 – Extraction process – on the left the digital model, and on the right the sequence of instructions resulting from the extraction process. 


Refactoring (or restructuring) is commonly defined as the process of improving the structure of an existing program without changing its semantics or external behaviour [20]. There are already several semi-automatic refactoring tools [21] that help to improve the readability and maintenance of algorithmic descriptions and increase their efficiency and abstraction level. Refactoring is an essential follow-up to an extraction process, since the latter returns a non-parametric algorithm that is difficult to decipher. 

Figure 9 shows an example of a refactoring process that could take place with the algorithm extracted in Figure 8. The extracted algorithm contains numerous instructions, each responsible for generating a beam between two spatial locations defined by XYZ coordinates. It is not difficult to infer the linear variations presented in the first and fourth highlighted columns, which correspond to the points’ X values. To infer the sinusoidal variation in the remaining values, however, more complex curve-fitting methods would have to be implemented [31]. 

In either case, refactoring tools seldom work alone, meaning that a lot of user input is required. This is because there is rarely a single correct way of structuring algorithms, and the user must choose which methods to implement in each case. Refactoring tools, beyond providing suggestions, guarantee that the replacements are made seamlessly and do not change the algorithm’s behaviour. When trying to increase parametric potential, even more input is required, since it is the architect who must decide the degrees of freedom shaping the design space. 

In our example (Figure 9), the refactored algorithm shown below has a better structure and readability but is still in an infant state of parametricity. As a next stage, we could start by replacing the numerical values proposed by the refactoring tool with variable parameters to allow for more variations of the sinusoidal movement. 

Discussion and Conclusion 

Architecture is an ancient profession, and the means used to produce architectural entities have constantly changed, not only integrating the latest technological developments, but also responding to new design trends and representation needs. Architects have long adopted new techniques to improve the way they represent designs. However, while, for centuries, this caused gradual changes in the architectural design practice, with the more accentuated technological development witnessed since the 60s, these modifications have become more evident. The emergence of personal computers, followed by the massification of Computer-Aided Design (CAD) and Building Information Modelling (BIM) tools, allowed architects to automate their previously paper-based design processes [1], shaping the way they approached design issues [32]. However, these tools did little to change the way designs were represented, only making their production more efficient. It did not take long for this scenario to rapidly evolve with the emergence of more powerful computational design paradigms, such as Algorithmic Design (AD). Despite being more abstract and thus less intuitive, this design representation method is more flexible and empowers architects’ creative processes. 

Given its advantages for architectural design practice, AD should be a complement to the current means of representation. However, to make AD more appealing for a wider audience and allow architects to make the most of it, we must lower the existing barriers by approximating AD to the visual and concrete nature of architectural thinking. To that end, we proposed the Algorithmic Representation Space (ARS), a representation approach that aims to replace the current one-directional conception of AD (going from algorithms to digital models) with a bidirectional one that additionally allows architects to arrive at algorithms starting from digital models. Furthermore, the ARS encompasses as means of representation not only the algorithmic description but also the digital model that results from it, as well as the mechanisms that aid the comprehension of the design space it represents.  

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Figure 9 – Refactoring process – the sequence of extracted instructions (on top) is converted onto a more comprehensible and parametric algorithm (on the bottom). 

The proposed system is based on two fundamental elements – the algorithm and the digital model – and architects have two ways of arriving at them – programming and modelling. Considering the first case, programming, the ARS supports the development of algorithms and the subsequent visualisation of the design instances they represent by running the algorithm with different parameters. In the second case, modelling, the ARS supports the conversion of digital models into algorithms that reproduce them. The first scenario allows AD representations to benefit from the visual nature of digital design tools, reducing the innate abstraction of algorithms and obtaining concrete instances of the design space that are more perceptible to the human mind. The second case enables the conversion of a concrete representation of a design instance into an abstract representation of a design space, i.e., a parametric description that can generate possible variations of the original design, benefiting from algorithmic flexibility and expressiveness in future design tasks.  

To allow for this bidirectionality, the ARS relies on three main mechanisms: (a) traceability, (b) extraction, and (c) refactoring. Traceability addresses the non-visual nature of the first process – programming – by displaying the relationships between the algorithm and the digital model. Extraction and refactoring address the complexity of the second process – going from model to algorithm – the former entailing the extraction of the algorithmic instructions that, when executed, generate the original design solution, and the latter solving the lack of parametricity and perceptibility of the extracted algorithms by helping architects restructure them. The result is a new representation paradigm with enough (1) expressiveness to successfully represent architectural design problems of varying complexities; (2) flexibility to parametrically manipulate the resulting representations; and (3) concreteness to easily and quickly comprehend the design space embraced.  

The proposed ARS intends to motivate a more widespread adoption of AD representation methods. However, it is currently only a theoretical outline. To reach its goal, the proposed system must gain a practical character. As future work, we will focus on applying and evaluating the ARS in large-scale design scenarios, while retrieving user feedback from the experience. 


This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) (references UIDB/50021/2020, PTDC/ART-DAQ/31061/2017) and PhD grants under contract of FCT (grant numbers SFRH/BD/128628/2017, DFA/BD/4682/2020). 


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[30] A. Leitão and S. Garcia., “Reverse Algorithmic Design”. In Proceedings of Design Computing and Cognition (DCC’20) Conference, Georgia, Atlanta, USA (2021). p. 317–328. DOI: 

[31] P. Mogensen and A. Riseth, “Optim: A mathematical optimization package for Julia”. Journal of Open Source Software. 3, 24 (2018), 615. DOI: 

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Figure 5 Fun Palace in London before Demolition [61] 
Figure 5 Fun Palace in London before Demolition [61] 
Architectural Authorship in “the Last Mile”
Architectural Authorship, automation, digitalisation, Fun Palace, Leon Battista Alberti, mass-customisation, the Last Mile
Yixuan Chen
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A loyal companion to the breakthroughs of artificial intelligence is the fear of losing jobs due to a robotic takeover of the labour market. Mary L. Gray and Siddharth Suri’s research on ghost work unveiled another possible future, where a “last mile” requiring human intervention would always exist in the journey towards automation. [1] The so-called “paradox of the last mile” has been exerting impacts on the human labour market across the industrial age, recurringly re-organising itself when absorbing marginalised groups into its territory. These groups range from child labourers in factories, to the “human computer” women of NASA, to on-demand workers from Amazon Mechanical Turk (MTurk). [2] Yet their strenuous efforts are often rendered invisible behind the ostensibly neutral algorithmic form of the automation process, creating “ghost work”. [3] 

Based on this concept of “the last mile”, this study intends to excavate how its paradox has influenced architectural authorship, especially during architecture’s encounters with digital revolutions. I will firstly contextualise “architectural authorship” and “the last mile” in previous studies. Then I will discuss the (dis)entanglements between “automation” and “digitalisation”. Following Antoine Picon and Nicholas Negroponte, I distinguish between the pre-information age, information age and post-information age before locating my arguments according to these three periods. Accordingly, I will study how Leon Battista Alberti, the Fun Palace, and mass-customised houses fail in the last mile of architectural digitalisation and how these failures affect architectural authorship. From these case studies, I challenge the dominant narrative of architectural authorship, either as divinity or total dissolution. In the end, I contend that it is imperative to conceive architectural authorship as relational and call for the involvement of multi-faceted agents in this post-information age. 

Academic Context 

Architectural Authorship in the Digital Age 

The emergence of architects’ authorial status can be dated back to Alberti’s De re aedificatoria, which states that “the author’s original intentions” should be sustained throughout construction. [4] Yet at the same time, those architects should keep a distance from the construction process. [5] It not only marks the shift from the artisanal authorship of craftsmen to the intellectual authorship of architects but also begets the divide between the authorship of architectural designs and architectural end products. [6] However, this tradition can be problematic in the digital age, when multi-layered authorship becomes feasible with the advent of mass-collaboration software and digital customisation technologies. [7] 

Based on this, Antoine Picon has argued that, despite attempts to include various actors by collaborative platforms such as BIM, architects have entered the Darwinian world of competition with engineers, constructors and existing monopolies, to maintain their prerogative authorship over the profession. [8] These challenges have brought about a shifting attention in the profession, from authorship as architects to ownership as entrepreneurs. [9] Yuan and Wang, on the other hand, call for a reconciliation of architectural authorship between regional traditions and technologies from a pragmatic perspective. [10] However, these accounts did not throw off the fetters of positioning architects as the centre of analysis. In the following article, I will introduce “the last mile”, a theory from the field of automation, to provide another perspective on the issues of architectural authorship. 

“The Last Mile” as Method 

The meaning of “the last mile” has changed several times throughout history. Metaphorically, it was used to indicate the distance between the status quo and the goal, in various fields, such as movies, legal negotiations, and presidential campaigns. [11] It was first introduced in the technology industry as “the last mile” of telecommunication, on which one of the earliest traceable records was written in the late 1980s. [12] Afterwards, “the last mile” of logistics began to be widely used in the early 2000s, following the dot-com boom of the late 90s that fuelled discussions of B2C eCommerce. [13] However, in this article, I will use “the last mile” of automation, a concept from the recent “AI revolution” since 2010, to reconsider architectural authorship. [14] In this context, “the last mile” of automation refers to “the gap between what a person can do and what a computer can do”, as Gray and Suri defined in their book. [15] 

I employ this theory to discuss architectural authorship for two purposes.  

1. Understanding the paradox of automation can be of assistance in understanding how architectural authorship changes along with technological advancements. Pasquinelli and Joler suggest that “automation is a myth”, because machines have never entirely operated by themselves without human assistance, and might never do so. [16] Subsequently, here rises the paradox that “the desire to eliminate human labour always generates new tasks for humans” and this shortcoming “stretched across the industrial era”. [17] Despite being confined within the architectural profession, architectural authorship is subject to change in parallel with the alterations of labour tasks. 

2. I contend that changes in denotations of “the last mile” signal turning points in both digital and architectural history. As Figure 1 suggests, in digital history, the implication of the last mile has changed from the transmission of data to the analysis of data, and then to automation based on data. The former change was in step with the arrival of the small-data environment in the 1990s and the latter corresponds with the leap towards the big-data environment around 2010. [18] In a similar fashion, after the increasing availability of personal computers after the 90s, the digital spline in architecture found formal expression and from around 2010 onwards, spirits of interactivity and mass-collaboration began to take their root in the design profession. [19] Therefore, revisiting the digital history of architecture from the angle of “the last mile” can not only provide alternative readings of architectural authorship in the past but can also be indicative of how the future might be influenced. 

Figure 1 Changes of Meanings for “the Last Mile” in Digital History, and Digital Turns in Architectural History. 

Between Automation and Digitalisation 

Before elucidating how architectural authorship was changed by the arrival of the automated/digital age, it is imperative to distinguish two concepts mentioned in the previous section – automation and digitalisation. To begin with, although automation first came to use in the automotive industry in 1936 to describe “the automatic handling of parts”, what this phrase alludes to has long been rooted in history. [20] As Ekbia and Nardi define, automation essentially relates to labour-saving mechanisms that reduce the human burden by transferring it to machines in labour-requiring tasks, including both manual and cognitive tasks. [21] Despite its use in human history, it was not until the emergence of digital computers after WWII that its meaning became widely applicable. [22] The notion of computerised automation was put forward by computer scientist Michael Dertouzos in 1979, highlighting its potential for tailoring products on demand. [23] With respect to cognitive tasks, artificial intelligence that mimics human thinking is employed to tackle functions concerning “data processing, decision making, and organizational management”. [24] 

Digitalisation, on the other hand, is a more recent concept engendered by the society of information in the late 19th century, according to Antoine Picon. [25] This period was later referred to as the Second Industrial Revolution, when mass-production was made possible by a series of innovations, including electrical power, automobiles, and the internal combustion engine. It triggered what Beniger called the “control revolution” – the volume of data exploded to the degree that it begot revolutions in information technology. [26] Crucial to this revolution was the invention of digital computing, which brought about a paradigm shift in the information society. [27] It has changed “the DNA of information” in the sense that, as Nicholas Negroponte suggests, “all media has become digital”, by converting information from atoms to bits. [28] In this sense, Negroponte distinguishes between the information age, which is based on economics of scale, and the post-information age, founded on personalisation. [29] 

It can be observed that automation and digitalisation are intertwined in multiple ways. Firstly, had there been no advancement in automation during the Second Industrial Revolution, there would be no need to develop information technology, as data would have remained at a manageable level. Secondly, the advent of digital computers has further intermingled these two concepts to the extent that, in numerous cases, for something to be automated, it needs first to be digitalised, and vice versa. In the architectural field alone, examples of this can be found in cybernetics in architecture and planning, digital fabrication, smart materials, and so on. Hence, although these two terms are fundamentally different – most obviously, automation is affiliated with the process of input and output, and digitalisation relates to information media – the following analysis serves with no intention to differentiate between the two. Instead, I discuss “the last mile” in the context of reciprocity between these two concepts. After all, architecture itself is at the convergence point between material objects and media technologies. [30] 

Leon Battista Alberti: Before the Information Age 

Digitalisation efforts made by architects, however, appeared to come earlier than such attempts made in industrial settings of the late 19th century. This spirit can be traced back to Alberti’s insistence on identicality during information transmission, by compressing two-dimensional and three-dimensional information into digits – which is exemplified by Descriptio Urbis Romae and De statua. [31] In terms of architecture, as mentioned previously, he positions built architecture as an exact copy of architects’ intention. [32] This stance might be influenced by his views on painting. First, he maintains that all arts, including architecture, are subordinate to paintings, where “the architraves, the capitals, the bases, the columns, the pediments, and all other similar ornaments” came from. [33] Second, in his accounts, “the point is a sign” that can be seen by eyes, the line is joined by points, and the surface by lines. [34] As a result, the link between signs and architecture is established through paintings since architecture is derived from paintings and paintings from points/signs.  

Furthermore, architecture can also be built according to the given signs. In Alberti’s words, “the whole art of buildings consists in the design (lineamenti), and in the structure”, and by lineamenti, he means the ability of architects to find “proper places, determinate numbers, just proportion and beautiful order” for their constructions. [35] It can be assumed that, if buildings are to be identical to their design, then, to begin with, there must be “determinate numbers” to convey architects’ visions by digital means – such as De statua (Fig. 2). Also, in translating the design into buildings, these numbers and proportions should be unbothered by any distortions as they are placed in actual places – places studied and measured by digital means, just like Descriptio Urbis Romae (Fig. 2). 

Although the Albertian design process reflects the spirit of the mechanical age, insisting on the identicality of production, it can be argued that his pursuit of precise copying was also influenced by his pre-modern digital inventions being used to manage data. [36] Therefore, what signs/points mean to architecture for Alberti can be compared to what bits mean to information for Negroponte, as the latter is composed of the former and can be retrieved from the former. Ideally, this translation process can be achieved by means of digitalisation. 

Figure 2 Descriptio Urbis Romae (Left) and De statua (Right)37 

Yet it is obvious that the last mile for Alberti is vastly longer than that for Negroponte. As Giorgio Vasari noted in the case of Servite Church of the Annunziata, while Alberti’s drawings and models were employed for the construction of the rotunda, the result turned out to be unsatisfactory, and the arches of nine chapels are falling backwards from the tribune due to construction difficulties. [38] Also, in the loggia of the Via della Vigna Nuova, his initial plan to build semi-circular vaults was aborted because of the inability to fulfil this shape on-site. [39] These two cases suggest that the allographic design process – employing precise measurements and construction – which heralded the modern digital modelling software and 3D-printing technologies, was deeply problematic in Alberti’s time. 

This problem was recognised by Alberti himself in his De re aedificatoria, when he wrote that to be “a wise man”, one cannot stop in the middle or at the end of one’s work and say, “I wish that were otherwise”. [40] In Alberti’s opinion, this problem can be offset by making “real models of wood and other substances”, as well as by following his instruction to “examine and compute the particulars and sum of your future expense, the size, height, thickness, number”, and so on. [41] While models can be completed without being exactly precise, architectural drawings should achieve the exactness measured “by the real compartments founded upon reason”. [42] According to these descriptions, the design process conceived by Alberti can be summarised as Figure 3. 

Figure 3 Albertian Design Process 

If, as previously discussed, architecture and its context can be viewed as an assembly of points and signs, the Albertian design process can be compared to how these data are collected, analysed and judged until the process reaches the “good to print” point – the point when architects exit and construction begins. Nonetheless, what Vasari has unveiled is that the collection, analysis and execution of data can fail due to technological constraints, and this failure impedes architects from making a sensible judgement. Here, the so-called “technological constraints” are what I consider to be “the last mile” that can be found across the Albertian design process. As Vasari added, many of these technological limitations at that time were surmounted with the assistance of Salvestro Fancelli, who realised Alberti’s models and drawings, and a Florentine named Luca, who was responsible for the construction process. [43] Regardless of these efforts, Alberti remarked that only people involved in intellectual activities – especially mathematics and paintings – are architects; the opposite of craftsmen. [44] Subsequently, the challenges of confronting “the last mile” are removed from architects’ responsibilities through this ostensibly neutral design process, narrowing the scope of who is eligible to be called an architect. The marginalisation of artisanal activities, either those of model makers, draughtsmen or craftsmen, is consistent with attributing the laborious last mile of data collection, analysis and execution – measuring, model making, constructing – exclusively to their domain. 

While the division of labour is necessary for architecture, as John Ruskin argued, it would be “degraded and dishonourable” if manual work were less valued than intellectual work. [45] For this reason, Ruskin praised Gothic architecture with respect to the freedom granted to craftsmen to execute their own talents. [46] Such freedom, however, can be expected if the last mile is narrowed to the extent that, through digitalisation/automation, people can be at the same time both architects and craftsmen. Or can it? 

Fun Palace: At the Turn of the Information and Post-Information Age 

Whilst the Albertian allographic mode of designing architecture has exerted a profound impact on architectural discipline due to subsequent changes to the ways architects have been trained, from the site to the academy, this ambition of separating design from buildings was not fulfilled, or even agreed upon among architects, in the second half of the 20th century. [47] Besides, the information age on the basis of scale had limited influences on architectural history, except for bringing about a new functional area – the control room. [48] Architecture’s initial encounters with the digital revolution after Alberti’s pre-modern technologies can be traced back to the 1960s, when architects envisaged futuristic cybernetic-oriented environments. [49] Different from Alberti’s emphasis on the identicality of information – the information per se – this time, the digitalisation and information in architecture convey a rather different message. 

Gorden Pask defined cybernetics as “the field concerned with information flows in all media, including biological, mechanical, and even cosmological systems”. [50] By emphasising the flow of data – rather than the information per se – cybernetics distinguishes itself in two aspects. Firstly, it is characterised by attempts of reterritorialization – it breaks down the boundaries between biological organisms and machines, between observers and systems, and between observers, systems and their environments, during its different development phases – which are categorised respectively as first-order cybernetics (1943-1960), second-order cybernetics (1960-1985) and third-order cybernetics (1985-1996). [51]  

Secondly, while data and information became secondary to their flow, catalysed by technologies and mixed realities, cybernetics is also typified by the construction of frameworks. [52] The so-called framework was initially perceived as a classifying system for all machines, and later, after computers were made more widely available and powerful, it began to be recognised as the computational process. [53] This thinking also leads to Stephen Wolfram’s assertion that the physical reality of the whole universe is generated by the computational process and is itself a computational process. [54] This is where the fundamental difference is between the Albertian paradigm and cybernetics, as the former is based on mathematical equations and the latter attempts to understand the world as a framework/computation. [55] Briefly, in cybernetics theory, information per se is subordinate to the flow of information and this flow can again be subsumed into the framework, which is later known as computational processes (Fig. 4). 

Figure 4 Information in Cybernetics Theory 

In Cedric Price’s Fun Palace, this hierarchical order resulted in what Isozaki described as “erasing architecture into system” after its partial completion (Fig. 5). [56] Such an erasure of architecture was rooted in the conceptual process, since the cybernetics expert in charge of the Fun Palace was Gordon Pask, who founded his theory and practice on second-order cybernetics. [57] Especially so, as considering that one major feature of second-order cybernetics is what Maturana and Varela termed “allopoiesis” – a process of producing something other than the system’s original component – it is understandable that if the system is architecture, then it would generate something different than architecture. [58] In the case of the Fun Palace, it was presupposed that architecture is capable of generating social activities, and that architects can become social controllers. [59] More importantly, Cedric Price rejected all that is “designed” and instead only made sketches of indistinct elements, diagrams of forces, and functional programs, rather than architectural details. [60] All these ideas, highlighting the potential in regarding architecture as the framework of computing – in contrast to seeing architecture as information – rendered the system more pronounced and set architecture aside. 

Figure 5 Fun Palace in London before Demolition61 

By rejecting architecture as pre-designed, Price and Littlewood strived to problematize the conventional paradigm of architectural authorship. They highlighted that the first and foremost quality of the space should be its informality, and that “with informality goes flexibility”. [62] This envisages user participation by rebuking fixed interventions by architects such as permanent structures or anchored teak benches. [63] In this regard, flexibility is no longer positioned as a trait of buildings but that of use, by encouraging users to appropriate the space. [64] As a result, it delineates a scenario of “the death of the author” in which buildings are no longer viewed as objects by architects, but as bodily experiences by users – architectural authorship is shared between architects and users. [65] 

However, it would be questionable to claim the anonymity of architectural authorship – anonymous in the sense of “the death of the author” – based on an insignificant traditional architectural presence in this project, as Isozaki did. [66] To begin with, Isozaki himself has remarked that in its initial design, the Fun Palace would have been “bulky”, “heavy”, and “lacking in freedom”, indicating the deficiency of transportation and construction technologies at that time. [67] Apart from the last mile to construction, as Reyner Banham explained, if the Fun Palace’s vision of mass-participation is to be accomplished, three premises must be set – skilful technicians, computer technologies that ensure interactive experiences and programmable operations, and a secure source of electricity connecting to the state grid. [68] While the last two concerns are related to technological and infrastructural constraints, the need for technicians suggests that, despite its claim, this project is not a fully automated one. The necessary involvement of human factors to assist this supposedly automated machine can be further confirmed in Price and Littlewood’s accounts that “the movement of staff, piped services and escape routes” would be contained within “stanchions of the superstructure”. [69] Consequently, if architects can extend their authorship by translating elements of indeterminacy into architectural flexibility, and users can be involved by experiencing and appropriating the space, it would be problematic to leave the authorship of these technicians unacknowledged and confine them within service pipes. [70] 

The authorship of the Fun Palace is further complicated when the content of its program is scrutinized. Price and Littlewood envisaged that people’s activities would feed into the system, and that decisions would be made according to this information. [71] During this feed-in and feedback process, human activities would be quantified and registered in a flow chart (Fig. 6). [72] However, the hand-written proposed list of activities in Figure 6 shows that human engagement is inseparable from the ostensibly automated flow chart. The arrows and lines mask human labours that are essential for observing, recognising, and classifying human activities. These tasks are the last mile of machine learning, which still requires heavy human participation even in the early 21st century. 

For instance, when, in 2007, the artificial intelligence project ImageNet was developed to recognise and identify the main object in pictures, developers found it impossible to increase the system’s accuracy by developing AI alone (and only assisting it when it failed). [73] Finally, they improved the accuracy of ImageNet’s algorithms by finding a “gold standard” of labelling the object – not from the developments of AI itself, but by using 49,000 on-demand workers from the online outsourcing platform MTurk to perform the labelling process. [74] This example suggests that if the automation promised by the Fun Palace is to be achieved, it is likely to require more than just the involvement of architects, users, and technicians. In the time of the Fun Palace’s original conception, the attempt was not fulfilled due to the impotence of computing technologies. Yet if such an attempt was to be made in the 2020s, it is likely that architectural authorship would be shared among architects, users, technicians, and ghost workers from platforms such as MTurk. 

Figure 6 Cybernetic Diagram (Left) and Proposed Activities (Right)75 

Returning to the topic of cybernetics, whilst cybernetic theories tend to redefine territories of the architectural system by including what was previously the other parts of the system – machines, observers, adaptive environments – the example of the Fun Palace has shown that this process of blurring boundaries would not be possible without human assistance, at least initially. The flow of information between these spheres would require human interventions to make this process feasible and comprehensible because, in essence, “the information source of machine learning (whatever its name: input data, training data or just data) is always a representation of human skills, activities and behaviours, social production at large”. [76] 

Houses of Mass-Customisation: In the Post-information Age 

Although cybernetics theories have metaphorically or practically influenced architectural discourse in multiple ways, from Metabolism and Archigram to Negroponte and Cedric Price, such impact was diminished after the 1970s, in parallel with the near-total banishment of cybernetics as an independent discipline in the in the academia. [77] After a long hibernation during “the winter of artificial intelligence”, architecture’s next encounter with digital revolutions happened in the 1990s. [78] It was triggered by the increasing popularity and affordability of personal computers – contrary to the expectations of cybernetics engineers, who back in the 1960s dreamt that computers would increase both in power and size. [79] These distinctive material conditions led to the underlying difference between the second-order cybernetics in the 1960s and architecture’s first digital turn in the 1990s. I contend that this distinction can be explained by comparing Turing’s universal machine with Deleuze’s notion of the “objectile”. 

As Stanley Mathews argued, the Fun Palace works in the same way as the universal machine. [80] The latter is a precursor of modern electronic computers, which can function as different devices – either as typewriters, drawing boards, or other machines – according to different codes they receive (Fig. 7). [81] Comparatively, “objectile” connotes a situation in which a series of variant objects is produced based on their shared algorithms (Fig. 8). [82] These products are so-called “non-standard series” whose key definition relates to their variance rather than form.83  

Figure 7 Simplified Diagram of the Universal Machine 
Figure 8 Non-standard Production 

While the universal machine seems to require more power to support its every change, an infinite one-dimensional tape on which its programmers can mark symbols of any instructions to claim its universality, non-standard production can operate on a smaller scale and under less demanding environments. [84] The emphasis on variance in non-standard production processes also indicates a shift of attention from the “process” underscored by second-order cybernetics towards the product of certain parametric models. When the latter is applied to architecture, the physical building regains its significance as the variable product. 

However, it does not mean a total cut-off between cybernetics and non-standard production. Since human-machine interactions are crucial for customising according to users’ input, I maintain that mass-customisation reconnects architecture with first-order cybernetics whilst resisting the notion of chaos and complexity intrinsic in second-order cybernetics.  

Figure 9 Flatwriter85 

Such correlation can be justified by comparing two examples. First, the visionary project Flatwriter (1967) by the Hungarian architect Yona Friedman proposed a scenario in which users can choose their preferred apartment plan from several patterns of spatial configurations, locations, and orientations. [86] Based on their preferences, they would receive optimised feedback from the system (Fig. 9). [87] This optimisation process would consider issues concerning access to the building, comfortable environments, lighting, communication, and so on. [88] Given that it rejects chaos and uncertainty by adjusting users’ selections for certain patterns of order and layout, this user-computer interaction system is essentially an application of first-order cybernetics, as Yiannoudes argued. [89] Contemporary open-source architectural platforms are based on the same logic. As the founder of WikiHouse argued, since the target group of mass-customisation is the 99 per cent who are constantly overlooked by the normative production of buildings after the retreat of state intervention, designing “normal” environments for them is the primary concern – transgression and disorder should be set aside. [90] As Figure 10 illustrates, similarly to Flatwriter, in theory, WikiHouse would pre-set design rules and offer design proposals according to calculations of the parametric model. [91] These rules would follow a “LEGO-like system”, which produces designs by arranging and composing standard types or systems. [92] Both Flatwriter’s optimisation and WikiHouse’s “LEGO-like system” are pursuing design in accordance with patterns, and discouraging chaotic results. 

Figure 10 Designing Process for a WikiHouse [93

Nevertheless, neither Flatwriter nor WikiHouse has achieved what is supposed to be an automatic process of using parametric models to generate a variety of designs. For Flatwriter, the last mile of automation could be ascribed to the unavailability of computers capable of performing calculations or processing images. For WikiHouse, the project has not yet fulfilled its promise of developing algorithms for design rules that resemble how the “LEGO blocks” are organised. Specifically, in the current stage, plans, components and structures of WikiHouse are designed in SketchUp by hand. [94] The flexibility granted to users is achieved by grouping plywood lumber into components and allowing users to duplicate them (Fig. 11). Admittedly, if users are proficient in Sketchup, they could possibly customise their WikiHouse on demand – but that would then go against the promise of democratising buildings through open-source platforms. [95]  

Figure 11 SketchUp Models of WikiHouse96 

Consequently, the last mile of automation again causes a conundrum of architectural authorship. Firstly, in both cases, never mind “the death of the author”, it appears that there is no author to be identified. One can argue that it signals a democratic spirit, anonymising the once Howard Roark-style architects and substituting them with a “creative common”. Nonetheless, it must be cautioned that such substitution takes time, and during this time, architects are obliged to be involved when automation fails. To democratise buildings is not to end architects’ authorship over architecture, but conceivably, for a long time, to be what Ratti and Claudel called “choral architects”, who are at the intersection of top-down and bottom-up, orchestrating the transition from the information age of scale to the post-information age of collaboration and interactivity. [97] Although projects with similar intentions of generating design and customising housing through parametric models – such as Intelligent City and Nabr – may prove to be more mature in their algorithmic process, architects are still required to coordinate across extensive sectors – clients’ inputs, design automation, prefabrication, logistics, and construction. [98] Architectural authorship in this sense is not definitive but relational, carrying multitudes of meanings and involving multiplicities of agents. [99]  

In addition, it would be inaccurate to claim architectural authorship by the user, even though these projects all prioritise users’ opinions in the design process. By hailing first-order cybernetics while rejecting the second-order, advocating order while disapproving disorder, they risk the erasure of architectural authorship – just as those who play with LEGO do not have authorship over the brand, to extend the metaphor of the “LEGO-like system” in WikiHouse. Especially as the digital turn in terms of technology does not guarantee a cognitive turn in terms of thinking. [100] Assuming that the capitalist characteristics of production will not change, technological advancements are likely to be appropriated by corporate and state power, either by means of monopoly or censorship.  

Figure 12 Non-standard Production After Repositioning Users 

This erasure of human agency should be further elucidated in relation to the suppression of chaos in these systems. As Robin Evans explained, there are two types of methods to address chaos: (1) preventing humans from making chaos by organising humans; and (2) limiting the effects of chaotic environments by organising the system. [101] While Flatwriter and WikiHouse choose to conform according to the former at the expense of diminishing human agency, it is necessary to reinvite observers and chaos as an integral part of the system towards mass-customisation and mass-collaboration (Fig. 12). 


For Walter Benjamin, “the angel of history” moves into the future with its face turned towards the past, where wreckages were piled upon wreckages. [102] For me, addressing the paradox of “the last mile” in the history of architectural digitalisation is this backward gaze that can possibly provide a different angle to look into the future.  

This article mainly discussed three moments in architectural history when technology failed to live up to the expectation of full automation/digitalisation. Such failure is where “the last mile” lies. I employ “the last mile” as a perspective to scrutinize architectural authorship in these moments of digital revolutions. Before the information age, the Albertian notational system can be regarded as one of the earliest attempts to digitalise architecture. Alberti’s insistence on the identical copying between designers’ drawings and buildings resulted in the divide between architects as intellectuals and artisans as labourers. However, this allographic mode of architectural authorship was not widely accepted even into the late 20th century.  

At the turn of the information age and post-information age, Cedric Price’s Fun Palace was another attempt made by architects to respond to the digital revolution in the post-war era. It was influenced by second-order cybernetics theories that focused on the flow of information and the computational process. Buildings were deemed only as a catalyst, and architectural authorship was shared between architects and users. Yet by examining how the Fun Palace failed in the last mile, I put forward the idea that this authorship should also be attributed to technicians and ghost workers assisting the computation processes behind the stage. 

Finally, I analysed two case studies of open-source architectural platforms established for mass-customisation. By comparing Flatwriter of the cybernetics era and WikiHouse of the post-information age, I cautioned that both systems degrade architectural authorship into emptiness, by excluding users and discouraging acts of chaos. Also, by studying how these systems fail in the last mile, I position architects as “choral architects” who mediate between the information and post-information age. Subsequently, architectural authorship in the age of mass-customisation and mass-collaboration should be regarded as relational, involving actors from multiple positions. 


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Open Seminar – Round Table
Open Seminar – Round Table
Open Seminar – Round Table Discussion
Algorithmic Form, Discussions & Conversations, Open Seminar, Round Table
alessandro bava, Provides Ng, Marco Vannucci, Philippe Morel, Roberto Bottazzi
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(This transcription has been edited) 

Presenters: Alessandro Bava (AB), Philippe Morel (PM), Marco Vannucci (MV), Roberto Bottazzi (RB), Provides Ng (PN).  

Venue: Zoom

Date: 08th December, 2021


What I’m interested in, in this discussion – and we saw it in all the presentations – is not exclusively work that has been done with a computer per se or using proficiency in coding, but also how this can influence the practice of designing and making spaces. Going back to architecture; making spaces, constructing the human habitat. 

I think there are a number of strands we could pick up on, so I’m going to leave space for the speakers too, [but] I have a few questions and connections that I want to make. 

I think the video was amazing to end with, Philippe [Philippe Morel], because it also gave us a big platform to understand culturally how all these different things are laid out, because we really dwell in different timeframes – or timelines, one should say, it’s more fashionable today! 

I think there are these amazing overlaps and connections that allow us to expand on this, and I really want to stress our support for our guests. For the people listening, there is not so much work being done in the direction of understanding this cultural impact – I mean, Philippe mentioned quite a few moments and exhibitions that are in fact legendary, precisely because there are so few of them. 

So, there have been a few moments where of course the role of technology and computation has been understood in terms of its cultural implications. The other day, I was at another panel, another symposium, where we discussed algorithms and their impact on culture at large, and there was so much – in my view, being someone who does not consider themselves to be the most literate on the subject – I find that there is a lot of illiteracy that leads to a lot of paranoia, which actually doesn’t work. And this is something that I was surprised to find in Manfred Mohr, in the 60s, the idea that we need to push for literacy, because actually it is a tool that extends our ability, I think, especially for the purposes of architecture.  

Federico, speaking about the work of his studio today, really clarified that in a very direct and visible way; how we can use applications of computation within groups today, on the design side and the management side, and how these two things can be harmonised through technology. It’s an amazing development, and one that you know Manfred Mohr would be happy about, let’s say, as far as literacy on the subject goes. So, I’m very happy that today we are collectively contributing to this, adding to this history. 

I keep saying lately that we need new hermeneutic tools; tools for understanding computational design and computational tools and how they can be integratedinto established methodologies. How do we integrate new tools into existing methodologies? For example, in the work I did, I was really interested in seeing Moretti’s exhibition at the Triennale where he actually proposed a few buildings. Analysing that exhibition alone, we can see how certain parametric tools were used for specific typologies of buildings. Moretti could have applied this to anything, but he chose to apply it to a certain large-scale urban infrastructure, such as a sports arena, or a cinema – things that we understand as “large objects”. Large single objects that can respond to one main parameter. And actually, towards the end of your presentation, Marco, you said we “could not compute” – we need to understand the scale of algorithms and how far they can go, where they can be applied to architecture in a meaningful way and where perhaps not at all!.  


I think, yes, in retrospect, Moretti focused on typologies that, if we fast-forward 50 years, are typically parametric now, they are more or less mono-functional. Nowadays, a stadium is no longer mono-functional, but it is actually designed [so that spectators are all] looking at the pitch, and therefore we developed it into the most parametric typology. I’m not sure how aware he was of that actually, also because I think at the time the stadium itself was a rather new typology, in a way. Sport, and the “massification” of sport, and so on.  

The other thing I want to say, regarding the discussion – and I’ll just throw it in there perhaps – is that we take it for granted, that for many, many years, computational design, especially from the early 90s, has never really confronted the past. As if it was developed in a vacuum, let’s say, as if it just came out of nowhere. Of course, this is understandable, because architects were all very excited; they wanted to kind of experiment and bring this new technology to fruition to start building. The economy at the time was better than today, so there were things that were converging, let’s say, but what I find particularly important is that at some point, eventually, it is actually, really necessary to go back and see that there is a legacy there. There is a tradition; which is a very normal, traditional architecture, as we know it, and it’s not just a bunch of punks that play with computers. In terms of the cultural relevance of the discussion. 

And then, of course, we can say that we have always been parametric, or that architecture itself is a discipline that is about the idea of establishing algorithmic procedure to get something built. 


I think the knowledge that we should perhaps understand, and I think Manfred Mohr’s work really helps us with that, is that it’s perhaps just the idea of encoding certain processes that have always been part of architecture. Coding them, and then potentially automating them or doing something else with them, is what machines allow us to do, but that doesn’t necessarily change how we think about it; it’s not the end.  

I want to stress the fact of what you say about the importance of history, or how we are trying to reconnect – or rebuild bridges, if you like. For some parts of the discourse on digital computation, perhaps it’s as if history started in the Bell laboratories, or something like that? It started in the US with the beginning of mass computers and stuff like that. But I think, Roberto, of course, has done a lot of work on building bridges,  and making us understand that the bridges go a lot further back in time, in fact.  


I keep thinking about what Philippe said a second ago, and why computational logic keeps going metaphysical, and I think it’s a side note, but I can’t stop myself, I have to say it! 

There are two ways to look at it, one is that you’re totally right Philippe, [Ramon] Llull is the point of reference in this conversation, and again, if we’re talking about bridges that were burned in history there’s definitely only a vague understanding of the importance of Llullism. How could it be that a person who invents concentric wheels, who wants to basically convince Muslims that their religion is inferior, has a lasting effect throughout Europe for over 300 years? I mean, it’s not even explainable as a joke! I would say this is perhaps interesting – because it is a computation project, there is no doubt about that – it’s very interesting because computation sits at a moment in history where other notations emerge for non-visual, or non-mimetic ways of articulation, articulating reality and knowledge. That was interesting for Philippe – but his is just the last presentation we saw and I tend to have a short term memory! 

It was also interesting, for instance, for Manfred Mohr, this constant tension between the visual and the conceptual – and I think that is one of the interesting premises of computation, historically, over a very long period of time. A system to articulate something that lies between the intelligible and the sensible. Something that cannot quite be sense, and yet needs to be very clear to the mind. This tension, the fact that computational logic always tends to be in that realm, is probably something that has to do with that. 

Obviously, you could also look at it a different way, you could say, well, computational logic is a simple mathematical process that could be grasped a lot earlier in history than other, more advanced, mathematical models; or you could also relate it to the fact that, for some reason, the Christian tradition forgot the first commandment, because we should not really be able to draw God. But we decided to ignore it, for reasons that are not entirely clear to me, and the kabbalistic tradition did not ignore it, the kabbalistic tradition is a notational system for symbolic articulation of the world without generated images. So, I think all I want to say is that the short comment that Philippe made in passing could be quite powerful. 


I love that this took a theological dimension! I think it’s really crucial; this constant question on this idea of the visual and the conceptual, even in the work of Manfred Mohr – when you talked about this period when his work was purely code and, in fact, in the exhibition, there was a printing machine just printing whatever was coming out of the program. Then later on, in the 80s, with the development of the visual interfaces, his work became different – and in fact you connected it to the work of Peter Eisenman.  

So, it’s really a key question for me that today, of course, software is popularised, there is even visual computation, visual algorithms… this is possible through software such as Grasshopper. There are aids to an understanding of a visual means through code, let’s say, and I’m interested in this, because for a long time we have been discussing computation and architecture purely in terms of data – how do we get data, how do we structure data? But today, we’re in a different environment, where software is more developed and more accessible, and people don’t necessarily think about “what’s in the black box”; but nevertheless, what comes out for me, when I look at it again, I can only understand as computational. Even more so when it’s informed by the language and culture of the digital – by the culture of digital tools.  

I’m really curious to hear your position on this, whether you see where we are going in a sense? Is visual computation comparable to a purely algebraic or coded computation? Can we compare the two, can the two coexist? Philippe, I would love to hear your answer, but this question is extended to everyone. I think it touches everyone, pretty much.  


I mean, first, just a very quick note on this metaphysical issue associated with combinatory rates. My feeling is that at that moment in time – you know, in the 13th Century, or 12th Century – it was a bit extraordinary to be able to demonstrate that only a few numbers or parameters could lead to so many possibilities. So, I think there are some magic tricks for the people who know nothing about mathematics, there’s some magic associated with combinatorics – at least at that time in history. Of course, today we look at that as something which is pretty simple; we are not surprised anymore by anything to do with combinatorics and we are probably more impressed by some other domains of mathematics that are more conceptual but, I would say even in the 20th century it was impressive, there was some magic to it. My feeling is that if it’s a bit associated with metaphysics, it’s also because there is some intrinsic magic in this combinatorial explosion at some point. It’s a very sketchy hypothesis! 

Regarding the question by Alessandro; no, I believe that visual programming is not like more standard programming where we use code and symbols. It creates the same effect, but I would say probably the intellectual operations are not exactly the same – also the feeling we have is not exactly the same because, in one case we do things – it’s a much more visual operation. When you do visual programming it’s a bit like putting some order in a PowerPoint presentation, you shift some slides until it’s made, but when you do programming by writing code I think it’s a slightly more analytical approach, or it’s more textural, more text based. 


I agree. Then my question is to the end of making architecture – as of course I understand what you are saying, the two things are very different – but to the end of making architecture, toward the end of what is useful for architecture? Because if I look, for example, at someone like Federico, they use computational tools, but the input is very much like a curve that is drawn, and they use this data to then do different kinds of processes. That one curve can start influencing other curves that are drawn and things like that, but there is an input that is drawn. Whereas in a lot of computation, for the description of the visual design, there is always this question – even in the academic work at the Bartlett – of where does the data come from, and it’s almost like a theological question; it has to come from some God-given numerical formula. So I’m interested in this question, which, I think, is quite a central question, methodologically. 


I would say, probably, we are entering an era in which the data is becoming more important than the algorithms. I don’t know if it’s true scientifically speaking, by the way, but at least the mindset is maybe in favour of a deeper influence of the data, over the influence of the algorithms, maybe – but again it’s definitely not a scientific statement. Probably because it’s much easier to associate the data to everything which is happening in society at large. 

For example, we know the data of Facebook, because we see them every day. Although we don’t see all of the data, we see how it works; but we don’t know the algorithms they are using. So, even if I believe that algorithmic science is more developed and more advanced than ever – it’s absolutely crazy the complexity of algorithmic science today – most people don’t have a grasp on that. So this is why, maybe, we can say that on an everyday basis the data seems more important in today’s society. 


I agree with that. Perhaps it’s also because certain algorithmic blocks are more available. I can bring the example of my students last year: they would take existing machine-learning procedures, then completely change the data set to an architectural data set, for example on architectural typologies, and then they would tweak the machine learning “black box” to adjust the output to what they needed it to do. So, in a way, this is a different approach. I mean, scientifically it is not a purist approach to computation, but ultimately, at least what I’m interested in is, how can we use it, even if it’s about using blocks and bits, how can we then tweak them to be useful for us as designers? That is my point to you. 

Are there any more comments, or questions from the audience? We had a pretty amazing rate of people not dropping out.  


Actually, when you were asking the question about visual computation versus algebraic code computation, I wasn’t exactly sure why it was asked us a question. Maybe it’s because it’s 1 am, but when you were asking, it actually reminded me of John Nash, the guy who got the Nobel Prize for game theory. When he was 25, before he developed mental illness, he was actually famous for the “embedding theorem”, looking at high dimensional objects and whether you can actually embed them in any Euclidean space. We usually visualize this sort of embedding like a donut, with a lot of waves flowing through the donut, but actually when they interviewed John Nash everything in his brain was numbers; he was never really a visual person.– He completely hated the movie A Beautiful Mind [a biopic of John Nash] because he didn’t see things [in the way it portrayed], like his schizophrenia was a miracle – I mean that’s crazy to a very banal brain like mine. 

I don’t really see the visual and the algebraic as either/or – and also, if you look at Chinese mathematics, as Philip also showed, the entire book of change, the I Ching with the hexagrams, was not visual. They literally document everything with Chinese characters – and it’s crazy when you have to read through that, because China is an agricultural nation, so we measure everything pragmatically. The mathematics is metaphysical, but we’re measuring the depth of the soil, how much rain we need, in the book of I Ching, and they would write down “12345” in those complex characters and people would still manage to do the geometrical calculation in their mind, which is crazy. 

When talking about Facebook data, there is always this privacy/ethical question that I agree is becoming theological and inescapable – but maybe it’s just because of the mindset that we feel like we’re always dependent on a centralised platform. We’re actually making a sort of trade, where we surrender the data because they’re doing a social service for us. A computational service that would be hard to do as an individual. So maybe the mindset is, as opposed to passively surrendering data, is there a way to actively contribute data so that we get over the data privacy problem? 


I was thinking about how, for example, architecture data is scarce. When we did this research on technologies, it was really hard to find this data. Where do you go? You need to go into the old registries of each city to find the undigitised maps, and try to redraw them and things like that, so we also live in that reality.  

Also when you mentioned the abstraction versus visual idea, I was reminded of my dad, who in his career was a computer programmer, and how he always says that he sees the numbers and not the visual things, so for me this is slightly triggering on some levels!  

Anyway, any more comments or questions? 


It’s actually like CAPTCHA, right, what they really do is that they don’t hire an intern to label a data set, but instead they create an economy by distributing the labeling tasks to users, match-making two problems – problems in training machine vision and in validating humans – [to create a solution].  


Yeah, we’re waiting for a start-up to deal with the architectural algorithm!  

Provides Ng 

(Laughs) [Get people to label] doors and windows for BIM? 


Exactly. That perhaps is a good implementation.  

All right, I’m thinking that I will close this amazing session here today, just because, again, we were meant to finish at five! 

I’m really grateful to all of you for your contributions, and again, today was a kind of amazing and stellar way to present the journal that will come out next year. So thank you so much for this discussion. It’s really precious, for me a lot of ideas were really fruitful in amplifying the conversation on computational design. As we have seen, augmenting the literacy and the discourse and the different threads on it, and even the historical grounding of this discourse, is fundamental.  

So, thank you so much. 

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Figure 1 - Sea of Digital Models @FONDAMENTA
Figure 1 – Sea of Digital Models @FONDAMENTA
architectural language, BIM, Building Information Modelling, construction, Fondamenta, Generalist Architect
Office Fondamenta
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The following piece is transcribed from Fondamenta’s talk at the B-pro Open Seminar that took place at the Bartlett School of Architecture on the 8th December, 2021.

Figure 1 – Sea of Digital Models, FONDAMENTA

We are interested in the construction of spaces with a strong belief in research and experimentation, where building is the end to which architecture must strive to become itself, and technology is the tool used to reach this result. We question conventions and support contradictions; fascination for structure, and freedom from dogma are the premises of this research. Structure is the trace of space, it organises the program and generates the building. Governance through technology is the key to the creation of an architectural organism, we see our projects as opportunities to conduct research on structural systems and the use of materials. We push materials to and against their limits – we are into designing through a systematic approach, relative to structures, without forgetting that the ultimate user of this organism is the human being; we are glad to have seen four very interesting presentations. We connect with the work of Luigi Moretti a lot, who we deeply admire as an architect, being one of the first pioneers in understanding spaces as organisms, creating them with a scientific logic and having developed four precise categories to design them.

What is technology for us? It is an instrument that we face daily, we use technology to follow our purpose, and to reaffirm the central role of the Architect in the building process. Technology drives efficiency, precision and control through the entire process, allowing governance of the economy of the project. The central issue of the use of technology is always about WHO is responsible for the governance of it. We believe the answer is that the Architect should be able to take this role.

Figure 2 – Scheme showing the impact of the technological Governance of the Project, Fondamenta

Today, we don’t want to talk about specific softwares and the use we make of them but rather point out the great opportunity that a specific use of technology could give Architects today. We were trained in a university founded on Vitruvian philosophy in which Architects must have a holistic approach to Architecture, being as much generalist as possible within the field of the discipline. Over time, we have witnessed a dismantling of the so-called “Generalist Architect”, in favour of over-specialisation in specific aspects of our discipline. The Architect has been relegated to a consultant, who concurs in order to create an architectural project. Instead, we believe the Architect must be the central figure, capable of managing the complexities of today’s world, through governance of many actors and aspects. This can only be possible, in our opinion, with the aid of technology. Our last resource is to believe a generalist Architect may still exist. . .

To achieve the latter, we use existing BIM (Building Information Modelling) technology to be superimposed with our customised system. For three years we have been testing a Vocabulary of codes and protocols that are applied to BIM and that become the common “language” inside the digital model that expresses the Architectural Project, which all involved actors have to learn and share. We, as Architects, are responsible for the governance of this centralised model and system, being the one creating the laws of the digitally-organised government. We didn’t start our practice directly with this idea, it was raised as a consequence of the first project we built and the impossibility we faced to have a central role in the process. Losing power and responsibility over the process with a negative impact on the projects was the consequence. We are still working on it daily to improve it, it is an ongoing process. If we have to depict with a diagram the shift between the approach we had at the beginning, and the approach we have now, this slide expresses it [indicates screen].

The centralised system we are looking for allows different actors to interact inside a given structure, with a given language crafted by us.

Figure 3 – FONDAMENTA BIM Alphabet, Fondamenta

To get more into details, the above charts depict specific aspects of our customised Mother model. The strength of BIM is that it enables all consultants who are involved in the process to implement and add their knowledge and information inside a common, single-instance digital Model. Codes and rules were developed so as to share and communicate between the different disciplines, which belong to different worlds. The most important layer to be translated is that of economy. Each aspect of the project relates to an economical parameter that controls the cost of the projects. Starting from an existing software, we added our customised logic and vocabulary.

What we are seeing throughout our practice is that we can have control of the project from the very start. For the most part, BIM generally arises after an execution plan is in place. Instead, we deal with these premises from day zero – from concept phase – this is what makes enormous difference. Following this scheme, all actors begin to communicate at the very start, at the right time, without finding themselves in the position of compromise, but rather putting on the table all the topics that, if worked out at the right time, can surely bring the project to more radical expressions. Hence, there are incredible possibilities to push the projects to their limit, being able to build without it being jeopardised during an uncontrolled process.

We will show three different projects of ours. The first one, our first built project, is a winery in Piemonte (2018-2020).

Figure 5 – Winery Cantina dei 5 Sogni, Extract from Casabella 921 @Marco Cappelletti 
Figure 7 – Winery Cantina dei 5 Sogni, Executive drawings for Steel formwork and concrete shells geometry, FONDAMENTA and Matteo Clerici 

In this project, our awareness of technology and its potential was limited and not yet evident. That is why we run this project without using BIM to solve design and governance issues. The winery project develops research on the pursuit of a seemingly impossible balance between different structural systems, which must coexist as one organism out of concrete and steel. We designed and optimised the shell system together with our engineer, making it work as structural truss to hold the concrete pitched roof while containing part of the program. The double steel formwork of the shells, poured in one single day without pause, was directly designed, drawn and sent to the manufacturer.

After this experience, we realised that we needed more technological support to be able to control the construction process in order to push forward more projects. Particularly dealing with aspects such as economics, time and money, but also sustainability of the process. This change of guard started with the series of projects we are building in Sicily, first among all 18018EH projects of houses near Noto. From this moment, we started governing the process with the aid of BIM – our instrument – from the beginning of conception.

Figure 8 – 18018EHSR Private House, External Rendering, DIMA 

This house  is mostly underground, with only 30% of its surface exposed above ground meterage. We are trying to develop a three-dimensional project where the space develops in three axes, and all the load-bearing walls are made of local stone. The structural floor plan is created through a system of radius and circumference. Through the use of softwares, we were able to optimise the construction lines, turning them from splines to radius, working in accordance with the technical consultants to develop the BIM model. This is a snapshot showing the massive amount of information inside this model.

This is interesting because implementing information in a model is not enough to control it, there needs to be instrumental rules in order to make an architecture real. This project will be soon delivered to a construction company. Costs, money and time are essential points in our profession, in order to have the possibilities to realise our research, design cannot transcend from them. We are connected and interested in the economy of the project, which sustains architecture processes through awareness in governance and allows us to control our design according to cost.

Figure 10 – 18018EHSR Private House, Axonometry showing construction aspect and codes, FONDAMENTA 

It was incredible how we managed to control the project and design through our tools. For example, we like to show all these axonometric drawings – each code, of course, remains connected, with a clear Excel chart that reminds us of cost, quantities, and all the details that a specific part of the model has. Figuring out a way of communicating the mass of information that we were implementing in the digital model was another interesting aspect. This is something that we’re still developing to make it even more readable for the involved actors. Of course, there are just a couple of Excel spreadsheets connected to these axonometries!

Figure 11 – 18018EHSR Private House, Axonometry showing stone walls geometry and codes, FONDAMENTA 

In terms of design, we see the potential in technology as something that allows us to further push our research related to space and structure. For example, here, all the other walls will be made out of stone, blocks of stone that are one metre long, 50 centimetres high, and 30 centimetres in depth. For Grasshopper, we customised each one to come out with a sort of “abacus” of all the walls with specifications and a numbering system, then, delivered to a construction company.

This technology enables us to build within a certain amount of time. If we reflect on past projects, time is something that we really cannot negotiate – it is the hardest variable to negotiate today. Technology gives us the ability to control time more than any other aspect. We love to go back to the models, because we think that this “ping-pong” between the digital tool and the making process gives us an awareness of reality. We don’t have to lose control of what we are thinking and designing.

Figure 12 – 20027F Private House Rennovation, Axonometry showing the project strategy, FONDAMENTA 

The last aspect that we are trying to show through this house – one of the projects already into construction since four months ago – is that we reached a certain level of governance of actors during the process from the beginning. This is a renovation, where we stripped out the existing building – the partition walls – but kept working with the existing concrete cage structure. We kept the load-bearing structure, made out of concrete, and we inserted a new steel structure, changing its form but keeping the volume untouched.

Wanting it to be a precise case study, we sat with our consultants and engineers from the very beginning. All the possible actors were involved from the embryonic phase and we designed together, trying to understand immediately all the potential realistic approaches that could be achieved.

Figure 13 – 20027F Private House Rennovation, Axonometry of the BIM Model, FONDAMENTA 
Figure 14 – 20027F Private House Rennovation, Rendering, DIMA 

I’ll just show a couple of snapshots of the model that we delivered to the construction company, pointing out that it is the same model we had from the beginning. From structures, H back, to installations, every element was designed with involved actors, long before the building process started on site.

It’s really important for us to underline that Architects have to be able to see and understand consultants and potential constraints as a possibility to further the design. For us, this was not something particularly easy to understand initially, because we were trained to see consultants and all other actors as part of architecture, and came in parallel to the project. Just like the scheme we showed, they are parallel lines that, at a certain point, intertwine. In that moment, you have a connection, and this connection has to be constant. Through this system we are developing, where each actor involved in the process has to be aware of the language we share in order to achieve the project.

This is just a snapshot of the house at the moment; we’ve stripped out the partition walls and it’s just the concrete.

To conclude, BIM has a deep social impact, giving back to architecture and architects the power they should have in the process. It is then up to us to create a social resistance and approaches to contemporary society.

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Structures, Voids, and Nodes: Leonardo and Laura Mosso’s “Architecttura Programmata” 
Architecttura Programmata, Laura Mosso, Leonardo Mosso, Nodes, structures, Voids
Roberto Bottazzi
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The work of Leonardo and Laura Mosso provides a very early and original application of computation to architectural, urban, and territorial design. Although computers were actually utilised to develop their ideas (a rare event in the 1960s in Italy), the work possessed conceptual and political ambitions that exceeded both the simple (or even fetishistic) fascination for a new technology and the functional approach that conceives computers as tools to efficiently complete tasks. Rather, the computer was part of a proto-ecological approach in which artificial and natural elements worked together towards the emancipation of the individual and their environment. At the centre of their research was “Architettura Programmata”, defined as a “theory of structural design” dedicated to the design of elements, their connections, as well as a higher, meta-system which we could call “structure” in the sense that Structuralism defined this word. Computers were involved in this project under both a design and an ethical agenda to understand and define “ecocybernetic dynamic as a structure for a self-evolved language of the environment and of the form at various levels of complexity, inserted in an unforeseen chain of self-evolved cybernetics: from political cybernetic to cybernetic of information, as integrated instruments of evolution in a condition of direct articulated democracy”.[1] 

This paper will discuss how computational thinking and computers were employed in the work and research of Leonardo and Laura Mosso, by analysing three paradigmatic projects which tackled the notion of structural design at different scales and contexts. The first project will be Cittá Programmata (1967-70), a theoretical proposal for a new type of city. The project represents the first actual use of computers in the work of Leonardo and Laura Mosso. The second example will concentrate on a piece of research on Piedmont territory – the place in which they operated throughout their academic and professional careers. Although computers were not directly employed to carry this research out, the approach to territorial analysis and planning employs a form of algorithmic thinking which impacts on both how the territory is read and how it could be re-imagined. Finally, the proposal for the restoration of block S.Ottavio in the historical centre of Turin shows a very innovative use of computers to intervene on historical artefacts of relevant cultural value, as well as the possibility to use computers to manage the future life of a building. 

Structuralism played an important part in the work of Laura and Leonardo Mosso, and it is an essential element in understanding their conceptualisation of structures and the role that design and computation had in it. A slightly left-field but very fruitful interpretation of Structuralism was produced by Gilles Deleuze in 1967, at the time Leonardo and Laura were intensifying their interest in computers.[2] Deleuze emphasised the role of emptiness, more precisely, of the “zero” sign as a mechanism for the transformation and articulation of structures. The notion of empty structure and zero offer a dynamic interpretation of Structuralism that is not only relevant to computational thinking, but can also clarify how the structures designed by Mosso can be understood as dynamic and adaptive.  

Early Experiments with Computers in 1960s Italy 

Before delving into the actual discussion, it will be useful to quickly sketch out some of the cultural trends operating in Italy in the 1960s to better contextualise how Leonardo and Laura Mosso arrived at their “Architettura Programmata”. 

“Architettura Programmata” directly refers to the exhibition “Arte programmata. Arte cinetica. Opere moltiplicate. Opera aperta” organised by Olivetti in 1962. The show was curated by Bruno Munari and Giorgio Soavi, with an accompanying catalogue edited by Umberto Eco. It displayed works by a series of artists, including Enzo Mari, who generated art procedurally, opening up a different mode of production and reception of works of art, also inspired by Eco’s Open Work.[3] In the same period, Nanni Balestrini was also experimenting with computers to generate poems.[4] These two examples are perhaps useful in helping to focus on some lesser-known aspects of Italian post-war culture, which is often mentioned for the work in cinema, architecture, art, but rarely for computation or scientific work in general. Along these lines, it is also worth mentioning the cybernetic group operating in Naples under the guidance of Prof. Eduardo Renato Caianiello, who maintained regular contact with MIT and Norbert Wiener. It is in this more international and open environment that we should position the research of Leonardo and Laura Mosso. 

Leonardo studied architecture in Turin, a very active city that led the Italian post-war economic boom, thanks to the presence of Fiat, the car manufacturer and one of the largest Italian factories. After graduating, Leonardo won a scholarship to study in Finland where, eventually, he started working in Alvar Aalto’s studio around 1958. From then on, he became the point of reference for most of the works that Aalto designed for Italy—such as the design of a residence for the Agnelli family (the owners of Fiat) and the Ferrero factory. A more international profile also characterised the figure of Guiseppe Ciribini, with whom both Laura and Leonardo also collaborated. Ciribini concentrated on the modernisation of the construction industry, focusing on prefabrication and modular design. His work was not limited to Italy and expanded to a European scale through his involvement with the European Coal and Steel Community (ECSC, or CECA in Italian, the precursor of the European Union) to devise international standards for prefabrication. Leonardo and Laura Mosso also established connections with Konrad Wachsmann, incidentally Giuseppe Ciribini’s predecessor at the Ulm School of Design, invited by Tomas Maldonado in 1958. Finally, Leonardo and Laura Mosso were also involved in the early experiments with computer art (which had developed in Croatia since the early 1960s) through the magazine New Tendencies.[5]  

In all these experiences, computation played an increasingly central role. In the case of Ballestrini or for the scientific research developed in Naples, computers were actually utilised, but in other cases, the work only consisted in speculation over what tasks and possibilities could be performed and unleashed. Leonardo and Laura Mosso are among the small group of architects and artists who did make use of computers in their work. With the help of Piero Sergio Rossatto and Arcangelo Compostella, two projects utilised computers to simulate and manage their transformations. Throughout almost two decades of using computers in their work, Leonardo and Laura Mosso developed an approach that was never guided by technocratic notions of efficiency. Rather, the philosophical implications of computing architecture and the political role that information and computation could have brought to a project and society in general constituted their main interest in this new technology. The computer as used in the Mossos’ work was in fact at the service of larger cultural project that aimed at distributing, rather than concentrating, power. Computers were an instrument for change, whereas the values of efficiency and sheer industrialisation appeared to be ways to fundamentally preserve the status quo, by simply making it run more smoothly. Rather than improving how architecture could better fulfil its role under the tenets of a capitalist, industrialised economy, Leonardo and Laura wanted to change the rules of the game itself; the computer, therefore, had to play an almost moral role in radically overturning the mechanisms regulating architecture and its use.  

Central to their research was the close relationship between philosophical ideas (Structuralism), design language (which particularly concentrated on discrete elements connected through reconfigurable, dynamic nodes), and computation. Leonardo and Laura Mosso’s approach to Structuralism was already open to dynamic, cybernetic influences and, for this reason, it may be interesting to read it against the famous writing that Gilles Deleuze dedicated to the same philosophical movement. 

The Dynamics of Structural Form 

Culturally, the post-war years were characterised by the diffusion, particularly in Italy and France, of Structuralism; generally understood as a philosophy of structures rather than functions. Structures could be organised in more general systems – of which natural language represented the most complex, paradigmatic example. Linguistics was indeed the domain of Structuralism, and the source from which most of its fundamental ideas were derived. From Saussure’s Course – indicated as the first structuralist text – to Barthes, Eco, Levi-Strauss, the Bourbaki group, Althusser, and also Foucault and Lacan, structuralist thinking extended beyond the linguistic domain to provide a framework to re-conceptualise other disciplines such as anthropology, psychoanalysis, mathematics, history, or politics. 

Broadly speaking, the definition of a structure consisted of two steps: the determination of its constituent parts (taxonomy) and the definition of the mechanisms that would govern the relations between parts and their transformation (grammar). Critics of Structuralism often rebuked this particular approach to structures for its excessive formalisation and the strictness of its deductive logic. Such criticism tended to depict structuralism as a mechanical, overly linear theory of systems, resulting from the perhaps excessive importance attributed to linguistics. Perhaps such characterisation of structuralism paid too little attention to the more transformative aspects of the theory: the dynamics of change and transformation. These are present in all the major structuralist thinkers; however, Gilles Deleuze provided an original overview that concentrated on the open, topological, and playful aspects of structures which is useful to briefly summarise here. In Deleuze’s “How Do We Recognize Structuralism?”,[6] originally written in 1967, Structuralism was detectable through six different criteria: symbol, local/positional, differential/singular, differentiation/differentiator, serial, and the empty square. Throughout the analysis, the emphasis is on transformation rather than permanence, on the mechanisms that guarantee a structure can operate by straddling between the real and the imaginary in order to transform reality and be transformed by it. 

We will return to Deleuze, particularly his understanding of the notion of “zero” which offers an interesting frame in which to conceptualise the role that structures played in the work of Leonardo and Laura Mosso – and, particularly, how physical construction nodes were instrumentalised to attain a structural language able to change and be appropriated (or “spoken”) by its users. Before dwelling further on this aspect of their work, it is important to point out that the work of Jean Piaget – an author often quoted in Leonardo’s and Laura’s writings – also offered a dynamic reading of structures and Structuralism in general. Laura and Leonardo often made use of Piaget’s characterisation of structures being composed of three main characteristics: wholeness, transformation, and self-regulation.[7] In Piaget’s work, we also we find an open, interactive, “proto-cybernetic”[8] reading of Structuralism marked by a relational understanding of the connections between environment, cognition, and symbols. Particularly, the notion of assimilation outlined by Piaget in The Construction of Reality in the Child[9] outlined a cognitive model based on continuous feedback between reality and the child’s development – an image that brought Structuralism much closer to cybernetics. An eco-cybernetic approach to planning was often also advocated by Laura and Leonardo. These initial definitions are helpful, not only in framing the work of the Mossos in relation to the cultural milieu in which they operated, but also in understanding how computation was conceptualised in their projects to translate notions of structure, node, transformation. 

As mentioned, Deleuze’s survey offers a particular vantage point to understand how Structuralism dealt with change and transformation, and how this can help to frame the role that structures and nodes have in the research of Laura and Leonardo Mosso. Deleuze dedicates particular attention to the notion of the “zero” sign in Structuralism; the “zero” sign is understood as an empty place in structure, determined positionally rather than semantically, that allows transformations to occur. The empty place in a structure guarantees the possibility of its transformation in a way which is analogous to the role of empty squares on a chess board. The structure is understood as a symbolic object. Symbols are here understood according to the definition provided by C.S. Pierce’s semiotics; that is, structures have an arbitrary character that does not attempt to find the essence of the object of investigation, but rather to construct it. In Deleuze’s words: “[the structure does not have] anything to do with an essence: it is more a combinatory formula [une combinatoire] supporting formal elements which by themselves have neither form, nor signification, nor representation, nor content, nor given empirical reality, nor hypothetical functional model, nor intelligibility behind appearances”.[10] The structure is always a third, encompassing element, beyond the real and the imaginary, that allows the structure “to circulate”. In other words, the elements of a structure can only be determined relationally, as “[they] have neither extrinsic designation, nor intrinsic signification”.[11] As the order of the structure is more important that its meaning, not only is the space (or spatium, as Deleuze refers to it) a central medium for the articulation of relations and transformations, but is best described topologically, in the sense that the function of such a spatium is to logically order elements so that specific, empirical objects can occupy the different squares of the structure. The final element to note in Deleuze’s analysis is the “wholly paradoxical object or element”,[12] that is, the connective element that allows different structures or series to communicate with and orient each other in order to perform on different levels, beyond the purely symbolic one. Such an element is defined by Deleuze as the “object = x”; the “zero” sign par excellence; the “eminently symbolic” object that injects dynamic qualities into structures and therefore allows them to work.  

Leonardo and Laura Mosso dedicated large parts of their architectural research to the roles that connecting elements, or nodes, had in articulating structures. Such research produced four different types of nodes which informed their work and can be seen at work in the three projects discussed in the second part of this paper. Deleuze’s consideration on structures help us frame the Mossos’ research as well. The node in a structure is the element that allows transformations to occur. Pieces can be detached, substituted, or removed according to the possibilities and constraints set by the node connecting them. There is therefore an analogy between the physical nodes of a structure and the mechanisms of transformations at work in the philosophical concept of structure. Borrowing from Deleuze’s description, the physical node becomes the “object = x”, the “zero” sign; that is, not simply the element that makes change possible, but also the element that is syntactically operative and open in order for meaning to emerge. The analogy between the two manifestations – physical and philosophical – structure is poignant to grasp the Mosso’s work: nodes are often literally “zero” signs, voids as in the case of the particular type of node developed for Cittá Programmata is literally organised around a void, an empty space. By straddling between its physical appearance and its philosophical interpretation, the node acts structurally, that is, beyond its purely empirical presence, the node is a device that orders physical elements logically. . In both accounts of structures, the minimal unit is the phoneme – “the smallest linguistic unit capable of differentiating two words of diverse meaning”[13] – which Leonardo and Laura put at the centre of their approach to structures by speaking of “phonetic” and “programmed structures”. This approach was already visible in the first example of “programmed architecture”, the Chapel for the Mass of the Artist in Turin (1961-63) in which a static node connected together 5cm x 5cm wooden studs to produce a highly varied pattern for the interior of the Chapel. In successive projects, nodes quickly grew in complexity in order to achieve more articulate and varied configurations, as well as allowing the end user and community to be able to adapt them for future uses. Such an architectural agenda demanded a new type of node that began to be articulated as a void, an “empty square” so to speak, around which the various elements aggregate (fig.). The morphology of this new type of node consisted of a virtual cube – a void – whose eight vertexes could be reconfigured around smaller voids, each able to link together four members. None of the members physically intersected (making the implementation of changes easier) and were organised around a series of voids of different sizes. These physical and conceptual voids held some analogies with the “object = x” Deleuze spoke of in regards to Structuralism; the final configuration was dynamic, a sort of system to let the structure circulate, to make transformation possible. In other words, such an approach to structure transformed the spatial model of representations from a strictly geometrical system to a topological one in which relations between objects took precedent over the presupposed semantic qualities.  

It is also along these lines that we can read the introduction of computation into the work of Leonardo and Laura Mosso. The computer became the perfect instrument to both manage the structural logic of the design and give it the political agency the two architects had been seeking through their notion of programmed architecture. The next section will analyse three paradigmatic projects in which the conceptual issues highlighted can be seen at work.  

Cittá Programmata, 1967-70. 

Cittá Programmata is one of the most iconic projects developed by Leonardo and Laura Mosso, a manifesto that encapsulates some of the key aspects of their work; that is, the potential for a structural approach to design to provide an environment for social and political self-determination. To implement their agenda of political and spatial self-determination, Leonardo and Laura introduced the computer, which represents the other radical aspect of this project. The computer played both an operational and a moral role in enabling the appropriation and transformation of the users’ habitat. Strictly speaking, the project consisted of a series of physical models and computer-generated drawings for an entire city and its possible transformations. The city was structured through a series of cubical modules (or “voxels”) of 6m x 6m x 0.5m that could co-evolve with the life of the city and its inhabitants, resulting (as the models and drawings showed) in an interrupted field of variously extruded elements, each composed by structural elements variously transformed.  

The research for Cittá Programmata took place in a rich cultural environment in which the work of Laura and Leonardo stood out for its original take on some of the topics that animated the architectural debate of the time. As mentioned, the post-war Italian scene was characterised by a growing importance of Structuralism in all aspects of culture. On the one hand, Structuralism guided the introduction of linguistics and semiotics as a general field of study, as well as their application to architectural and urban analysis. This line of inquiry sought to detect the underlying principles of architectural form in itself and in its relation with its context. At the other hand of the spectrum, a more pragmatic understanding of structural thinking was animating the debate on pre-fabrication and modular design, to renew the construction industry and fulfil the demand to modernise the Italian landscape. It is between these two main interpretations of the notion of structure in architecture that Cittá Programmata can be understood, as it proposes a different conception of language and structures. 

Leonardo and Laura Mosso saw in the semiotic approach to architecture an excessive interest in meaning, both in its relation to the internal history of architecture and in context. Against the backdrop of semantic studies on architecture, Cittá Programmata proposed a more structural approach to language and its formalisation; a “phonological” system that would enable its users to ‘speak’ their collective mind through the groups of structures the architects provided. Pre-fabrication, on the other hand, was indeed a rich field of investigation – as mentioned, Leonardo and Laura Mosso had been in close contact with Giuseppe Ciribini. However, prefabrication was committed to a model of society that privileged economic values (through the minimisation of costs, for instance) over political, cultural and social ones. Indirectly, their critique of pre-fabrication was also a critique of the notion of programme (“programma edilizio”), understood as an excessively functional approach to design. The brief – the document through which to implement a building programme – fixed the use of structures or, at best, described a limited number of activities that a piece of architecture could house over a limited period of time. The formalisation of such an approach to programme usually resulted in a neutral outcome which favoured the design of a generic spatial container which, in principle, could adapt to future needs. Leonardo and Laura critiqued this view of design both on the basis of the vagueness of the mechanisms for programmatic determination (future activities may be impossible to predict in advance) as well as for the generic architectural response. In opposition to it they proposed a structural approach that did offer implementable choices (as opposed to programmatic vagueness) and therefore was not limited to regulating quantitative growth, but could also take into account the qualitative aspects of spatial structures. Finally, programme was also critiqued from a political point of view, as it was identified as the political instrument that guaranteed an asymmetrical distribution of power between users and designers.  

Cittá Programmata imagined an environment in which the relation between users and architects was not hierarchically organised, but rather more radically and horizontally distributed. Here, both the programmatic and semantic critique that animated the Mossos’ approach converged. The aim to generate an environment based on a horizontal distribution of power called into question the role that semiotics could play in designing structures. The analogy proposed is once again with language. As for immaterial notions, language and architecture (understood as body of knowledge) are inherently public, they exceed anyone’s ability to claim ownership of them or control them. Both the linguist and the architect can only play with the systems of signs constituting their disciplines in order to make them public and accessible. Contrary to the semiotic studies of architecture which concentrate on the internal mechanisms and references of architectural language, Leonardo and Laura Mosso proposed a rather more “extroverted” approach interested in opening architecture up and inviting users to participate in the creation of their own environment. The architect was “at the service” of architecture, rather than a custodian of the arcane mechanisms of architectural language. In a way, we can say that the position taken was reminiscent of Saussure’s distinction between langue and parole: whereas semiotic studies in architecture appear to privilege the importance of the langue, in Cittá Programmata, Leonardo and Laura Mosso worked to maintain a dynamic relation between the two terms of Saussurean categorisation: 

Architecture, understood in a traditional sense, cannot be a language; that is, it cannot speak by itself. Similarly, we cannot say that the work of a linguist on language is a language … Architecture is at [the] service of language … in the same sense that a language services the community of speakers when it is spoken; that is, when architecture becomes “a system of transformations” or possibilities, from which it is possible to generate infinite messages. 

Mosso and Mosso[14] 

It is in this context that the computer was introduced, both to support the management of the city and to simulate its future configurations. The actual machine utilised was a Univac 1108 owned by the Politecnico of Milan and programmed by Piero Sergio Rossatto – an engineer and programmer at Olivetti – with Arcangelo Compostella. The stunning drawings generated by the Univac (now part of the Centre Pompidou’s permanent collection) showed the possible growth patterns generated from an arbitrary string of signs placed at the centre of the drawing. Two parallel lines of pre-allocated units (*) and voids (-) constituted the starting input for the simulation, which could either proceed in a sequential growth, on the basis of a probabilistic algorithm, (fig.XX) or randomly (fig.XX). The process of algorithmic growth did not take place in a vacuum, rather constraints could be programmed in making growth sensitive to contextual information. 

Landscape, Structure and History (1980-1986)  

A second type of node Leonardo and Laura Mosso had been working on were a kinetic, self-managed, and elastic universal structures(Strutture autogestibili e complessizzabili a giunto universale elastico). Since the beginning of the 1970s, as part of their research on the use of different types of nodes to articulate transformations in physical structures, they had been testing this particular type of node at different scales and in contexts. The research started with the academic work that Leonardo carried out with his students at the Politecnico in Turin, then through commissons such the “Red Cloud” (Nuvola Rossa), an installation completed in Carignano Palace in 1975 in which these nodes found one of their most convincing and poetically powerful applications. This large piece consisted of a complex structure made up of individual elements connected through elastic joints, which allowed the architects to build an undulating mesh suspended between the visitors and the frescos of the palace. These elastic structures were tested at different scales: for instance, between the end of the 1970s and the beginning of the 1980s, Laura and Leonardo would put their kinetic quality to the test by using them as props accompanying the movement of the bodies of contemporary dancers, both in their work with the Conservatorio G. Verdi in Turin (1978) and the performance staged in Martina Franca (1980). It is, however, the territorial scale which is of particular interest in this discussion, since it highlights an original understanding of how structures can perform algorithmically and because of the unusually large scale of this research.  

Here, particular reference is made to the research carried out between 1980 and 1981 under the broad agenda of “methodological work aiming at devising a system of signs to program both at the level of the territory and the city”.[15] The results of this methodological analysis of territorial structures would also inform a subsequent research project and exhibition titled “Landscape, Structure, and History”,[16] which tested their structural approach to territory on the local landscape of Piedmont, its rural cultures, and their relation with their surroundings, with a view to devising a strategy for preservation. Perhaps it might appear unusual for avant-garde architects to dedicate their research to the rural, historically-layered territory of Piedmont. On the contrary, local forward-thinking architects and engineers had already focused on vernacular architectural expressions in the local countryside: Carlo Mollino extensively studied and recorded examples of Alpine vernacular architecture in Valle D’Aosta, and Giuseppe Ciribini – whose work on the industrialisation of construction has already been mentioned – also paid attention to the spontaneous architecture of Alpine and pre-Alpine territories. Some of these interests in rural and vernacular architecture were gathered together by another Torinese architect, Giuseppe Pagano, in his famous exhibition “Continuity – Modernity”, in 1936, for the 6th Triennale in Milan.  

The Mossos’ research on territorial structures consisted of both drawings and physical models of specific areas of Piedmont (Canavese and Carignanese). The work mapped and recorded the landscape of Piedmont by positioning a series of kinetic structures over a map of the existing territory. The structures consisted of a series of elements connected through elastic, kinetic nodes that allowed each element complete freedom of rotation around each vertex. The final configuration of each structure emerged from the mediation between their internal properties (length of the elements, arrangement, type of nodes) and the cartographic representation of the landscape. The drawings took this relationship to more radical conclusions: the landscape was further abstracted and re-coded through a structural approach which adapted to different contexts. Rather than an image of a superstructure, the re-codification of the landscape through models and drawings struck a complex balance between the algorithmic approach and the context.  

In this particular project, structures are understood as organisation principles rather than physical constructions. Earlier, we spoke of a algorithmic use of structural thinking, a quick definition that requires unpacking. An algorithm is a set of instructions that, once applied to a set of input data, will perform a finite number of operations to return an output. Regardless of the complexity of the operations performed, an algorithm recodes the input data into a new set of data. Chomsky’s generative grammar, for instance, could be seen as a recursive (continuous) series of algorithms that rewrites any given statement of a natural language to produce new linguistic statements. The superimposition of Laura’s and Leornardo’s structures on a map of Piedmont countryside operated in a similar fashion and, therefore, could be interpreted as an algorithmic recoding of the territory. The input data was constituted by the information recorded in the cartographic representations of the landscape, whereas the kinetic structures acted as analogue algorithms that recoded the input data according to the vast (yet finite) number of configurations allowed by their physical characteristics (length and number of members, type of joints). In short, the physical structures deployed rewrote the landscape according to a precise set of rules; more poetically, we can say that the elastic node structure allowed the landscape to speak in the language of the structures superimposed onto it; an image that Laura Mosso also evoked when she wrote about developing methods to “make the structures whistle”.   

Contrary to stricter interpretations of Structuralism, the type of algorithmic approach proposed here was not merely deduced from internal, formal rules (that is, the physical constraints set by the elastic nodes); rather it emerged from a more iterative, open relationship with the context (abstracted through cartographic representations). The results of the process set up were particularly legible in the physical models: the kinetic structures made up of interconnected springs were laid out on the map to return a ‘structural re-reading’ of the landscape. A new, structural image of the territory emerged from the interaction between nodes and territory.  

The research on territories that Laura and Leonardo Mosso completed allows us to make a series of considerations on these algorithmic operations, their formal qualities, and the implications they give rise to. First, through a structural, algorithmic approach to territory, the research rejects distinctions between natural and artificial in favour of a more holistic approach to landscape – and yet, one describable through a set of finite operations. The constraints embodied in the physical structures do not decisively distinguish between artificial and natural, symbolic and productive, and thus support Leonardo and Laura Mosso’s call for the kind of expanded notion of ecology they had been advocating for, both in projects and publications (through, for instance, the publication titled La Nuova Ecologia). The structure is the symbolic device that catalogues and organises the whole of the territory (here understood as superseding dichotomies such as urban/rural, artificial/natural), establishing principles for its preservation and transformation Similarly, algorithmic re-writing provides a diachronic reading of the territory that is re-organised along structural rather than chronological vectors. The different nodes of the elastic structures are positioned on the map to establish connections between artifacts built in different times in order to give rise to new relations between them.  Finally, there is the function performed by the elastic structures as analogue algorithms. We have already seen how an algorithm can be understood as a form of rewriting and transformation of an existing condition (input data). The types of operations performed by an algorithm are always precise (determined by the rules programmed in the algorithm), executed in their entirety (the algorithm goes through all the steps scripted to return an output), and yet partial, as the algorithm can only survey a dataset according to the set of rules that form the algorithm itself. The constraints inbuilt in the elastic kinetic nodes allow them to only perform a vast, but finite set of movements; that is, only a subset of all the signs contained in the maps of Piedmont can be computed by the physical structures-algorithms. In short, an algorithm generates a specific representation of the object it is applied to.  

To better grasp this last point, we can draw an analogy between real objects (such as buildings) and their orthographic representation. For instance, a section through a building can only return a partial image of the object it investigated, and yet how a section is drawn follows precise and rigorous rules that determine what and how the building will be captured in the section. But the section is a sign-object, not a building; it elicits further manipulations by either applying different sets of criteria (e.g., by concentrating on the structural, programmatic, material qualities of the building) or by changing the very parameters that generated it (changing the position of the section plane or the conventions applied). The approach developed to the Piedmont territory by Leonardo and Laura Mosso makes aspects of this landscape intelligible through the production of new signs which, in turn, make it amenable to further manipulations. It is important to notice that all operations performed by Laura and Leonardo are performed on a cartographic representation of the territory; photographs and other cultural aspects of the areas such as the name of places are complementary, rather than primary, information. Cartography is itself a coded, notational (rather than mimetic) representation of the territory. As a medium it therefore lends itself to the operations of re-coding and re-writing, since it is already a semiotic system; on the other hand, it acts as a recipient of the new codification of the landscape generated through a structural reading. 

Finally, the structure-algorithm becomes a marker of change, as the instrument through which modifications, and, in general, any metamorphic transformation of the territory can be foregrounded, read, and made tractable in order to preserve it or alter it. The research developed by Laura and Leornardo Mosso shows that a structural approach through algorithmic thinking should not only be confined to new, pristine domains, but can also offer innovative ways to interpret and intervene in historical contexts. The last project discussed – the proposal for S. Ottavio block in the historical centre of Turin – will further reinforce this point.  

S. Ottavio Block, Turin, 1980 

The commission for a study of the block located in the historic centre of Turin was received in 1978 and became an important, yet entirely forgotten chapter in the story of both Leonardo and Laura Mosso’s production and the integration of digital technologies in architecture. On the one hand, the brief for the project was a rather common one for Italian architects, whose practice often confronted (and still confronts) historical artefacts. Leonardo and Laura, however, saw in this commission an opportunity to advance their research on structures as well as on the use of computational tools. For purposes of simplicity, we can artificially divide the project between the physical proposed interventions and the immaterial, data-driven ones. 

The physical restoration of the block consisted in a series of more traditional interventions to reinforce the old brick walls, as well as the insertion of new levels to convert the existing spaces into inhabitable housing units. The new structures in steel and wood were elegantly laid out at a 45-degree angle, to mark a clear distinction between pre-existing and new elements. The type of node deployed in this instance was also a dynamic one, however, the only permissible movement was to slide along one of the orthogonal directions of the structure. Though the dynamics of nodes were limited (in comparison to the conceptual experiments at territorial scale), they allowed users to alter and self-organise their habitat. By deploying the same type of node at different scales and through different materials (aluminium, wood, and plexiglass), users could appropriate the environment both at the architectural and interior scale.  

Perhaps the most radical proposal of this research was the organisation of the conceptual side of the project. A computerised system was going to be set up to monitor and maintain the block. A proto-digital twin, the system would map all the elements of the project and generate a database in order for both individual users and the municipality to control, repair and maintain the whole block. For the programming of the whole system, Piero Sergio Rossatto – who had worked with Laura and Leonardo for the Citta Programmata – was consulted. The spatial representation of the block in the digital model followed the logic of voxels: a three-dimensional grid of individual cubes that provided a system of coordinates to locate every element of the project, existing or proposed, architectural or infrastructural. In Rossatto’s scheme, the project would be surveyed starting from the ground level (z=0 in the digital model) and gradually moving towards the roof by increasing the z-value in the voxel grid. Every intersection between the voxel grid and an element of the project would be recorded.  

Although the project was not well received by the local administration that could not fully grasp the innovative approach, eventually shying away from a unique opportunity to radically rethink the relation between digital technologies and historical artefacts, the project illustrated a different, complementary fact of Leonardo and Laura Mosso’s approach to algorithmic form. 

As mentioned, the project applied digital technologies to pre-existing architectural artefacts protected by preservation laws. Whereas digital technologies are invariably understood as the instrument to deliver the “new” or the “radically different”, or even to make a tabula rasa of pre-existing notions, this project showed a more nuanced, and yet still radical side of digital technologies, which could coexist with and complement the delicate pattern of a historical city.  

The structural approach, which continuously developed throughout several decades of research, here resulted in an abstract grid – a field of voxels, to be precise – that acted as a monitoring system allowing users to appropriate and control their own habitat. In the course of their research, Leonardo and Laura developed a physical model of the virtual voxel field that did not include any of the physical structures designed. The model possessed a very strong sculptural quality, but, most importantly, also showed the power of the algorithmic approach they had developed. On the one hand (and similarly to the experiments carried out in coding the Piedmont territory), the logic of the structure not only enabled its own transformation, but also determined its aesthetic qualities. The algorithmic logic guiding its own re-writing (in this case represented by the rhythm of the voxel field) returned a new type of form; an algorithmic form. As the model clearly showed, the logic of the voxel field implied a space without discontinuities or interruptions; saturated with data, the model was “all full” (as Andrea Branzi would have it), a solid block of data. As such, the research and proposal for the S.Ottavio block represents one of the earliest attempts to think of design straddling between physical and digital environments – a concept that could only be implemented through a structural approach to design whose robustness would allow it to extend to immaterial representations of space.  


The work of Leonardo and Laura Mosso not only constitutes an excellent example of very early work with computers in architecture, but also provides a rich framework through which to problematise the issue of algorithmic form. The close relationship between design, philosophy, technology and politics not only forms a complex and rich agenda, but also expands the use of computers in design well beyond a functional focus on increasing efficiency and profits. Perhaps, this is one of the aspects of their work that still resonates with contemporary research on algorithmic design: the complex relationship between ideas and techniques, and the use of computation as an instrument for change. Computation was more than a vehicle to implement their radical design agenda, it was also tasked with implementing specific ethical values by orchestrating the interaction between architects, users, and built environment. In many ways, computation, and the algorithmic forms it engendered, was utilised by the Mossos to perform one of its original and most enduring tasks: to logically order things and, therefore, to conjure up an image of a future society.  

In memory of Leonardo Mosso 1926-2020.  


[1] L. Mosso & L. Mosso, (1972). “Self-generation of form and the new ecology”. In Ekistics – Urban Design: The people’s use of urban space, vol.34, no.204, pp.316-322. 

[2] Deleuze’s text on Structuralism, however, was only published in 1971, so the connection between the two architects and the French philosopher is coincidental.  

[3] U. Eco, The Open Work, Translated by A. Cancogni. 1st Italian edition published in 1962. (Cambridge, Mass: Harvard University Press, 1989). 

[4] R. Bottazzi, Digital Architecture Beyond Computers: Fragments of a Cultural History of Computational Design (London: Bloomsbury Visuals, 2018). 

[5] L. Mosso & L. Mosso, “Computers and Human Research: Programming and self-Management of Form”, A Little-Known Story about a Movement, a Magazine, and the Computer’s Arrival in Art: New Tendencies and Bit International 1961-1973, edited by M. Rosen. (Karlsruhe, Germany: ZKM/Center for Art and Media; Cambridge, MA: MIT Press, 2011) 427-431. 

[6] G. Deleuze, “How Do We Recognize Structuralism?”, Desert Islands and Other Texts 1953-1974, Ed. D. Lapoujade, transl. by M. Taormina. (Los Angeles, CA: Semiotexte, 2004). Originally published in F. Chatelet (ed.)  Histoire de la philosophie vol. VIII: Le XXe Siècle. (Prasi: Hachette, 1972), 299-335. 

[7] J. Piaget, Structuralism. Translated and edited by C. Maschler. (London: Routledge and Kegan, 1971, 1st edition 1968). 

[8] E. Von Glaserfeld, “The Cybernetic Insights of Jean Piaget”, Cybernetics & Systems, 30, 2 (1999) 105-112. 

[9] J. Piaget, The Construction of Reality in the Child (New York: Basic Books, 1954; 1st Edition Neuchâtel, Switzerland: Delachaux et Nestlé, 1937) 

[10] G. Deleuze, “How Do We Recognize Structuralism?”, Desert Islands and Other Texts 1953-1974, Ed. D. Lapoujade, transl. by M. Taormina. (Los Angeles, CA: Semiotexte, 2004). Originally published in F. Chatelet (ed.)  Histoire de la philosophie vol. VIII: Le XXe Siècle. (Prasi: Hachette, 1972), 173 

[11] Ibid., 173 

[12] Ibid., 184 

[13] Ibid., 176 

[14] L. Mosso & L. Mosso, “Architettura Programmata e Linguaggio”, La Sfida Elettronica: realtá e prospettive dell’uso del computer in architettura (Bologna: Fiere di Bologna, 1969) 130-137. 

[15] L. Baccaglioni, E. Del Canto & L. Mosso, Leonardo Mosso, architettura e pensiero logico. Catalogue to the exhibition held at Casa del Mantegna, Mantua (1981). 

[16] L. Castagno & L. Mosso, ed. Paesaggio, struttura e storia: itinerari dell’architettura e del paesaggio nei centri storici della Provincia di Torino Canavese e Carignanese. (Turin: Provincia di Torino Assesorato all Cultura, Turismo e Sport, 1986). 

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disk turned steel. 1965
disk turned steel. 1965
discovery of light, GETULIO ALVIANI, HANS ULRICH OBRIST, immersive, raisonnée, structures
Hans Ulrich Obrist
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10 April 2015, Milan, Miartalks

First edited transcription, Paola Nicolin 

Hans Ulrich Obrist: I would like to start right from the beginning. You told me about your uncle, but above all about the importance that Leonardo Da Vinci has always had in your work … 

Getulio Alviani: As a child, in my first years of school in Udine, the fair of Santa Caterina was held, where there were stalls with books and other things; here I came across two volumes, which I bought with the few cents I had then: one on Beato Angelico and one on Leonardo Da Vinci. I lived in the countryside back then and therefore I loved nature very much. I loved seeing birds, crickets, moles, foxes, and in this book by Leonardo there was the “bestiary.” For me, it was great, because I thought it was wonderful that a man knew all those things that I experienced daily, but that I knew absolutely nothing about. So, I fell in love with Leonardo Da Vinci, and studied his drawings in small format, because at the time there were no books with colour photographs or with enlargements. I remember a surprising thing that I always have in front of my eyes, which is how he had drawn the wind. For me, thinking that the wind could be drawn was incredible. 

From the early years of my life, I lived with two uncles, one of whom was of Austrian origin and the other born on the border with Yugoslavia. They were both over 50 years older than me, so I was always alone and surrounded only by everyday things, plants, and animals. There were those who worked as farmers, doctors, streetcleaners, carpenters … I saw them all and I wondered, for example, “who knows why someone is a carpenter?”. … I got to the point where I asked myself, “Why do I live? What am I capable of doing?” I realized then that I loved doing things with my hands, and I wanted to see. Then I began to get interested in this, and to discover, above all, that all I had in my mind were not images, but “impressions” (for example, I now look at all of you, I see you, but tomorrow I will probably not remember your faces; what I will remember is the feeling I felt, whether there was empathy or not).  

With my brain I see things; for this reason, I became interested in the world of seeing and doing, and I started by going to see, for example, how an old sculptor near my house made the plaster casts for the statues destined for the graves in the cemetery. For me, seeing was the fundamental thing: seeing and knowing – for example, that plaster becomes hot with water, that if clay dries up, it breaks – and so I began to understand what the world of doing is. I started living always like this – until I did not want to do anything anymore [he laughs], like today, where everything is distorted, distorted, and exploited, because torturers and cops have taken power. 

HUO: This idea of ​​making is very clear and we will return to it later, talking about your inventions with aluminium. But I wanted to start by imagining building your catalogue raisonnée: looking, for example, at the publications of your work, you can see that they often start with the geometric line drawings of the 1950s, and you have mentioned before the constant presence of geometry in your work. Can you tell me about these early works, these drawings that arise from the curiosity of seeing? 

GA: Mine was a series of observations, in general, but always a bit shifted. As a boy, I spent a lot of time in the studio of artisans, and then of architects – much older than me – and I went to take measurements with them and did all those things that intrigued a boy. It sometimes happened that some of them went to paint in the countryside, and painted horses, for example – even if they were actually slightly futuristic horses, like those of Marcello d’Olivo; or of Mimmo Biasi, who instead had a strong interest in vegetables, plants, which then underwent a process of abstraction. 

I have to admit that I did not know what to do, because I did not want to paint what was already there and looked perfect as it was. I wanted to catch something like the threads of light in the sky; I thought that the energy was passing in there – and I wondered how it was able to pass, because I could not see it. Then, at the time, there were the first telephone lines, so I wondered “maybe that’s how rumour travels, will the message stay the same, or be changed, and in what way?” For me, there was mystery in all this: I liked that even more, the mystery, trying to understand these things. Then I became interested in these free geometries, compositions of threads of light that crossed, intersected, overlapped – there were dozens of images in the skies of the countryside.  

However, after doing some curious work on the matter, I quit, because I thought I had exhausted the subject. I have never done things out of duty; I have done them as a game, because I have always had the pleasure of doing, of discovering, of seeing. They were, therefore, limited drawings, since I was about twenty years old at the time and everything I did was for pure pleasure. For example, in that surface [he indicates a painting from the catalogue] there is a black, but when it is hit by the light it becomes white, whiter than any other white, and this was for the light. For me, these were discoveries, thinking that the white which comes out of black is whiter than “true white.” They were conversations with matter, simple non-transcendental questions… and slowly I began to live like this.  

reflection relief with orthogonal incidence, steel. 1967, 5x480x960 cm, modules 5x80x80 cm
Figure 1 – reflection relief with orthogonal incidence, steel. 1967, 5x480x960 cm, modules 5x80x80 cm

HUO: And after this phase come the “structures.” In this, we see a lot of the world of productive work, more than the world of art. Can you tell me about this epiphany that led you to build the structures, and how you discovered aluminium? 

GA: I had participated in a competition promoted by an electrical material company in Brescia (AVE – ed.) And I had designed a valve which, compared to the previous ones, was very innovative. The prize, announced by Domus, was awarded to the architecture studio, but they told me that whoever designed the valve could go to work for the company that organized the competition, to follow the production phase. So I went to Vestone (a town in the province of Brescia – ed.), where the factory was based, and there I discovered the world of more “committed” work. Because until then, for me, the world had been one of “craftsmanship”; there instead I learned a world of “doing”, with large machines, industrial materials, and many people involved. And there among the little things, I discovered new worlds, from melamine to silver contacts, from castings to presses – because I took care of both the execution of this first project of mine, and took on the role of graphic designer for the company’s product catalogues. In this context, I found myself for the first time handling aluminium pieces coloured green, red, and yellow – which were basically mirrors. Having seen these perfect mirrors in metal was a surprising innovation. I said to myself, “but how does this mirror work?” Of course, I knew why the mirror reflected, but never had I thought about the fact that a mirror might not be able to break, or even bend.  

Then, in one of these small workshops that I attended in the province of Udine, I went to dig with some cutters under this mirror, to see what was there. Initially it was all black, with a strong smell of sulphur, but I persisted again, and then a blinding light came out, stronger than sunlight! And from there, I understood how important light was, and that this material could accelerate light, just as a lens causes the sun’s rays to burn the ground.  

HUO: You always have a lens and a measuring tape with you, right? 

GA: I have two friends, who are the greatest friends I’ve ever had in life, I always have them with me, and they are the lens and the ruler. They have never betrayed me, they are always calm, safe and make no mistake.  

HUO: This is now where we can talk about the “discovery of light”. The interesting thing is that this research does not initially enter the world of art in Italy, but instead makes a first unexpected appearance passing through Ljubljana and Zagreb. I’m interested in this passage, because when I was a student I met Julije Knifer in Sète, France, where the artist had retired in the 90s, and he talked to me a lot about the Gorgona. You, Getulio Alviani, were there, at the moment of the birth of that movement, so I would like to understand how this meeting of extraordinary characters took place. 

GA: I was very attracted to Eastern [European] countries, because I have a mania for difficult things, those things that others don’t do. Everyone can do the easy things. Going to Paris, for example, was very simple, but going to Yugoslavia was quite another story. Everything was different there, even the smell of the air.  

My motivation was due a little to the fact that these countries were representatives of Central Europe, the land that my uncle, who was born in Austria, came from, and on the other hand I was fascinated by this completely different world, then beyond the “curtain” – for example, to get a visa took months, you had to have valid reasons (which in my case were linked to family reasons, since my mother and my aunt were born in places that became Yugoslavia). The roads were different, the people as well … in short, Yugoslavia at the time was another world. Furthermore, I must admit that unlike all other parts of the world, where there was a certain atmosphere of joy and lightness, Yugoslavia was a more introverted, more reflective, more intimate, and poorer land. I like poverty a lot, because in poverty many things can be solved; while in wealth nothing is ever solved – contrary to what today’s rulers think, who aim at riches, their riches, to pretend to solve problems. Problems are solved when there is simplicity and brains, and things are done for the sake of others; while today there is a lot of imbecility combined with wickedness that only causes abuse.  

So, I landed in Slovenia. I had made two small surfaces of milled aluminium, and placed them on a radiator in a small workshop, where they were noticed by Zoran Krzisnik, who came to this workshop to have furniture made. At the time, he was the director of the GAM in Ljubljana – which was very advanced in the world; it was the first city beyond the Iron Curtain to want to do innovative things, while elsewhere the situation was very stale. So Zoran Krzisnik saw these two little things, two small plates in fact, and asked me what they were. I wasn’t sure what to tell him, so I told him how I had made them. He asked me if it was possible to make some larger ones, about one metre by one metre, and that if I could he would hold a small exhibition for a small gallery he had in Ljubljana. It was called Mala Galerija, which means precisely that: small gallery. He invited me to visit it, and then organized an exhibition. And some time later, in 1961, I made this presentation, and then learned that in the meantime Krzisnik had curated exhibitions by Zoran Mušič, Giuseppe Santomaso, artists from the Ecole de Paris, and many others. Since then, these works of mine have allowed me to live in Eastern Europe For some time. 

I have continued to have a great love for crossing the border, going beyond: Slovakia, Poland, Lithuania, up to Russia. I learned from Krzisnik that at that time, in Zagreb, there were other young people exhibiting things similar to mine during the same period. So I went to Zagreb and set out to find out what was happening, and if the work was like mine. But at Gradska Galerja I found very different pieces; they had a spirit similar to mine, yet were completely different things, and so I saw the work of Almin Mavignier, Julio Le Parc, François Morellet, Marc Adrian, Ivan Picelj, and Julije Knifer. It was the “New Trends” exhibition, organized for the first time by an artist, Almin Mavignier. There, the whole world opened up for me. Krzisnik was organizing the Biennale of graphics at the time, which was at the forefront of the world of graphics, and therefore many scholars – such as Umbro Apollonio, Giulio Carlo Argan and many others – arrived in Ljubljana. In Udine that would never have occurred; the director of the Tate, or of the Moscow museum, or Umberto Eco arriving. Instead, I met everyone there, in Ljubljana, in a moment, and that world became my second home.  

It was in this context that a young person was listened to for what he was capable of doing, which I thought could never have happened in Italy. For example, the Studentski Centar in Zagreb [The Student Center] was a large experimental centre run by artists and critics, directed by Brano Horwett. There, they invited me to create silk screen works, and so I started to print them – not even knowing what they were exactly, but obtaining surprising results of crossed, overturned, superimposed, negativized, positivized lines. Then, when I came to Milan (where the headquarters of the factory I worked for were) I was able to show this kind of research to Lucio Fontana, and then to Paolo Scheggi, and they too began to work with this technique. Then Brano Horwett came to the Galleria del Deposito to develop all these graphic techniques, which in Italy had never even been thought to exist. We were involved in the fact that serigraphy could be done in series, and everyone – Max Bill, Richard Paul Lohse, Konrad Wachsmann, Victor Vasarely – explored this field, which was born from [the East]. And this is interesting.  

cube with graphic texture opalescent pvc sheets, silkscreen and light. 1964-69, 330x330x300 cm
Figure 2 – cube with graphic texture opalescent pvc sheets, silkscreen and light. 1964-69, 330x330x300 cm

HUO: One of the important aspects in interviews is that of “protesting the forgetfulness that exists in the world”, and there is a character who is rarely talked about today but who is very important: the person who set up the exhibition. The exhibition itself is often forgotten, there is an amnesia in the art world about it. I would like it if you told us a little about Edo Kovačević and what you learned from him. 

GA: I learned everything from him. He was a figurative painter who took care of the installations in the Gradska Galerija in Zagreb; before then I had never thought that my works could be exhibited like this, suspended, supported, and so on. I thought they were simply “squares”. In fact, when I then held an exhibition of mine at Gradska, my works were about twenty “little things”, but he turned them into an eight-room exhibition, making them extraordinary – not through “effects”, as might happen today by focusing lights on them, but simply by placing one work on a background, one on a base, one as a small backdrop: and so with three surfaces, a room was set up.  

Kovačević was very simple and creative, I learned a lot from him – and, in fact, I have never had a work hung on my walls at home. I keep them in the garage, because the works have to be exhibited for a short time, otherwise the eye gets used to them and you can’t see them anymore.  

I look at the works for a short time and then put them aside, to then retrieve them months later and try to understand if they are still valid or not. My impression is that the works must be done for exhibitions, so that they communicate with each other: one must see number one, number two, and understand what they mean as one line. This is what I still do now. On the other hand, I have set up more exhibitions of my colleagues work than of mine, because in this way I really discover the works, what they are and what they represent. 

I believe that the works must be kept in the head. I have a collection of works myself, but I never see them. I got them all by making exchanges: Fontana to Bill, Lhose, Albers, Mansurof, to Nelson, Kelly or Anuszkiewicz….  

The first exchange was in the early sixties, with Fontana: he asked me for something, I brought it to him and he said to me: “What do you want [for it]?” and I replied that I did not want anything, but timidly I proposed that he give me one of his works – and so it happened immediately. From then, I received everything through exchange. This then also enabled me to hold exhibitions of those artists, because I had so many works in hand: everything was possible because I had the works, avoiding transport and all the tasks required to make an exhibition that back then seemed insurmountable.  

HUO: All of this leads to your work as a curator. Andrea Bellini, who has been talking to me about your work for many years and is the origin of my research, was insistent that we talk about you as a curator. You are “the” curator of programmed art, and you have also written a lot about your colleagues, so it would be interesting if, after Ljubljana and Zagreb, we now arrive in Italy, with the N Group, and Programmed Art.  

GA: Immediately after the exhibition with Zoran Krzisnik in that small gallery, he asked me to curate a selection of works by our group of artists for the Ljubljana Biennale. So I began to collect works by those I esteemed – because otherwise I would not have had any interest: I wondered if the artist should not exist, but only the work; if it had, as it must have, a meaning and a dignity of its own to exist. And so I curated the Ljubljana Biennale. Later, I spent many years in Venezuela, directing the Jesus Soto Museum.  

HUO: Soto told me about this abandoned museum in Ciudad Bolivar and I would be interested in understanding how an artist experiences a museum in a curatorial sense. What is your vision of that today? 

GA: Exhibitions were held, and in this way I was able to see the cities and meet those who, perhaps because of their age, would not be able to do it in the future. There was always someone who hosted me. Jesús Rafael Soto was a close friend of mine, I often went to stay with him in Paris, or with his fellow Venezuelan, Otero. One day, he told me that he intended to build a large museum, and asked me to collaborate with him by gathering all the artist friends I could. So I did: from Sérgio de Camargo to Toni Costa, to Lucio Fontana, Gianni Colombo and many other good artists. 

I could not go to the inauguration, but then, after a few years, Soto called me and told me that his museum was in ruins: “se lo comiendo el diablo” [the devil is eating it], and asked me to go and see the situation, and give him a handrestoring it. So, during a Holy Week in the 1980s, I went there and saw this museum – designed by Raul Villanueva, a good architect and friend of Le Corbusier. The museum consisted of a series of huge pavilions, located in the middle of the savannah. Unfortunately, the situation was terrible; there were bats, snakes inside, the works had been ruined and were mouldy on the walls. There were about forty people who worked there: photographers, guides … and so it was that I lived in Venezuela for four or five years and worked to completely renovate it. 

HUO: Regarding Soto, and other Venezuelan artists who work a lot on the kinetic, there is one thing we haven’t talked about yet, and that is your surfaces. At a certain point, the series of “vibrating texture” surfaces begins. In a conversation with Giacinto di Pietrantonio, you said that it would be nicer to think that “neon has chosen Flavin, mirrors Pistoletto, and aluminium has chosen me”. Why did you switch from aluminium to vibrated surfaces? 

GA: Actually, after having been the art director of an aluminium factory, I had perfect, wonderful machinery at my disposal. I’ve never had a studio; I worked where they were: if, in a particular place, there was a nice factory that produced a nice material, I went there and did something. And so, being in the aluminium industry, I had these perfect tools at my disposal. That’s how it all started. I must admit that I have always done everything by myself, because at the time everything was possible: I was alone in a factory of thousands of square metres, I was alone and I was happy; I liked doing. Today, all of this would be impossible, but back then it was natural to do whatever your brain told you to do.  

HUO: In the book New trends: Notes and memories of kinetic art by a witness and protagonist, you write that the artist “is not the cult of personality, protagonism, commercialization, private galleries, elite art, fetishism, the unique work, the social purpose, the interpretation, the metaphor, the mystification, the strategy […]”. In another text I found you say that “to be called an artist is an offense, one could always speak of artifice, of something new, but I think it is more correct to speak of a plastic creator, a designer, a student of perceptual problems, an artist is synonymous of mystifier”. I would like you to tell me about your “expanded notion of the arts”… 

GA: Since I’m a physicist, I don’t like telling stories. [I don’t like] the word “creator” … lies are “created”; they are very easy to create. To be able to say things, they ought to be verifiable, tangible. If someone tells me “on your surface the light behaves like this”, you can go and see it, and you have the opportunity to see that it is true that it behaves like this. That’s not like someone who throws a stain on the ground, and then that becomes, say, “the intolerability of social life”. They say imagined things! 

Therefore, I love things, and I care that they have the dignity to exist; as for me, I have nothing to do with it; they must have the dignity of existing. Nobody knows who invented reinforced concrete, paper, the first bricks; nobody knows anything, but these objects exist and have been made. Everything has been done, things remain and, fortunately, people leave.  

One of my favourite things is to exhibit colleagues who are better than me; partly out of gratitude, because in this way I make them continue to live, and partly because in this way they have no other influences. For example, when I started collaborating with the museum in Bratislava, an exhibition relationship that lasted about ten years, I exhibited only artists who are gone: Sonia Delaunay, Joseph Albers, Lucio Fontana, Bruno Munari, Olle Baertling, Max Bill, all of whom represented something fundamental in the art world through art, and not through words or stories. The stories may be right, but they weaken the function of the eye: we receive 90% of our information through the eye; if I had to speak what I have in front of me in the blink of an eye, I would spend years saying nothing, telling unlikely stories. On the contrary, in a split second, I see everything, and everything is verifiable. One of my passions is synthesis, so it is obvious that I love the eyes. For me the eyes are everything. 

disk turned steel. 1965
Figure 3 – disk turned steel. 1965

HUO: This is beautiful and could already be a conclusion, but I still have some urgent questions. In fact, when you talk about the synthesis of art, you make me think of Max Bill… 

GA: Max Bill has been a lot, everything, to me. We often saw each other in Zurich or Zumikon or in other parts of the world. We didn’t talk [much], we communicated with synthetic words. But when we talked, the topics were quite another thing [compared to art]. We telephoned on Sundays. I always knew, ten minutes before our call, that I was dumber than I would be afterwards – with regards to everything we talked about, his turtles, the roads, the travels, everything. Because whatever Bill told me, he opened my brain, like Vix VapoRub. He was my base, his was a total critical force, first of all towards himself: [he believed that] something that was not true had no right to exist.  

HUO: And like Max Bill, who was an artist, architect, and educator with the Ulm school, you too have continued to be a designer, architect… 

GA: Yes, but never as a profession. I have done sets, some residences, a boat, I have dealt with urban planning; but I am not a craftsman, much less able to reap any benefits that were not mental. 

HUO: You have also done graphic design, for example creating [work for] Flash Art. 

GA: [Giancarlo] Politi came to me and showed me a copy of Flash Art, which at the time was innovative because at the time there was only Selearte, a magazine that devoted very little space to modern art, just a few quotes. Giancarlo, on the other hand, had made this magazine, which in the first issue had the title in “football pools” [font]; so, from the second issue, I gave him the logo again, all in lowercase Helvetica. Throughout my life, I have made many posters, layouts, catalogues, everything that had to do with graphics.  

HUO: You started making more “immersive” installations, such as those with mirrors, and many environments, so … in a certain sense architecture and setting are synthesised in your work.  

GA: Yes. For example, in this environment [he points to a photo from the book], you literally enter the middle of the colours, but in reality they are not there, the only colours are the fixed ones of the walls. By touching the metal plates that reflect the colours, yellow becomes black, red becomes yellow and everything is mixed and the resulting images are unrepeatable. There are no engines, because I’ve never loved engines. Instead, I love that the brain sets itself in motion. 

HUO: There is also the “tunnel” which is very nice, can you tell me about this job? 

GA: Do you know, I saw this work for the first time a couple of years ago, even though it was made about twenty years ago. I went to the place with Mario Pieroni and Giacinto Di Pietrantonio and they told me that they had a series of abandoned spaces. They asked me what I would do with them, and I replied that I would make lines. I made a drawing. They then had a guy make it, who was pretty good at it.  

HUO: You told me before the conference that it’s also important to have fun, and today many artists work on games. You invented a game, in 1964, using aluminium plates, didn’t you? 

GA: It’s a very simple thing. There are two aluminium plates that rest on a surface and then there are two discs which, by reflecting, multiply. Unpredictable images can be generated, but only with the hands. And we are always surprised by what we ourselves do.  

HUO: In my interviews, I often ask what the unrealized project is. There are many categories of unrealized projects, those that are too big, utopian, censored, too expensive… which one is yours? 

GA: I must admit that my restlessness is always animated by what surrounds me. I have never had a studio, much less an assistant, as Karl Gerstner or Enzo Mari or Victor Vasarely or Julio Le Parc or François Morrellet may have … although very good, they all have had and have real businesses, but I did everything by myself – and above all, I did it … for years, and [I don’t do it] anymore because I no longer find pleasure in doing it. 

In 1970, I composed the Manifesto on the “Pneumatic” Space. You will understand that it is absurd that a bus always measures from 100 to 200 cubic metres, both when it is full of people and when it is empty, or that a car occupies 5 square metres both when it is stopped and when it is in movement. Absurd! It is a hallucinatory thing. Although I love the cars on the highways, seeing the city submerged by what I call obscene, ugly, frightening “bagnarole [bathtubs] di tin and stucco” is terrible. Cars must be in motion, because otherwise they wouldn’t be called cars, they’d be called something else. My concern, therefore, lies in trying to minimize the obstruction and presence of the cars when they are not working: this is the Tire Space. I dream that the spaces could be pneumatic, transformable, transportable from one place to another. It was the first impression I had from Konrad Wachsmann, who I attended in Genoa when he had to design the port (a project that was then given to another person in his stead). Wachsmann had an idea to make the port of Genoa expandable and shrinkable: are the boats coming? It expands. It’s empty? It shrinks. Is there no longer any need for the port? I undo it and take it elsewhere. The pneumatic world, for Wachsmann, is still to come, and I took this position a little from him. I haven’t invented anything; I use things that were already there, and I always give credit to people before me. Bill, Albers, Wachsmann, Gropius; everyone who came before me. … In this way, it is a continuation, because no [new] thing is born without another [that goes before].  

So my future is Pneumatic Space, but to achieve it you need a common will; that is, that everyone is interested. I can make drawings, I have reduced very small spaces to a minimum; you can live in 9 square metres – I have designed a living room for two people which contains everything you need and which is transformable. I like this. In the 60s, I made tables that transform, today we have to remove gravity, so we won’t even need the table anymore. Back then, the table was the solution, today we know we can remove gravity, so the table is no longer needed.  

HUO: Last question. Rainer Maria Rilke wrote that beautiful text in which he gave advice to a young poet. Today there are many young artists here with us. I am very curious to know what your advice is to a young artist in 2015.  

GA: Knowing everything that has been done. Develop intelligence, and try to do something that has the dignity of existing, or that is itself useful.  

She [the work] is the centre, you have to think about what she does: and she has her dignity only if she is not a copy, only if you have made sure that she is absolutely new. Not just for a small circle of people who may not know what is around and are amazed. Today there is a great, terrible crisis: ignorance. And here we are in the homeland of this ignorance … we buy obscene, false, ugly, stupid things. Però in fondo, anche se questa cosa qualche anno fa mi disturbava, adesso mi lascia sereno, perché vuol dire che l’ignoranza di quella gente riceve quello che si merita e qui penso proprio “all’arte”, quella che non avrei mai voluto sapere esistere 

(But in the end, even if this thing bothered me a few years ago, now it leaves me calm, because it means that the ignorance of those people receives what they deserve, and here I think about “art”, the one I never wanted to know exists.)1 

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algorithmic form, 2021
algorithmic form, 2021
Introduction to Issue 02: Algorithmic Form
Algorithmic Form, Architecture, Architecture Theory, curatorial note, Philosophy
alessandro bava
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I was asked by Mollie Claypool to curate the second issue of Prospectives Journal as an ideal follow up to leading Research Cluster 0 at B-Pro in the academic year 2020/21. As such, this issue is a collection of positions that respond to my research interest during that year. 

In fact, my initial objective with RC0 was to research ways of applying computational tools to housing design for high-rise typologies: the aim was to update modernist housing standardisation derived from well-established rationalist design methodologies based on statistical reduction (such as in the work of Alexander Klein and Ernst Neufert), with the computational tools available to us now.

While the outcomes of this research were indeed interesting I was left with a sense of dissatisfaction, because it was very difficult to achieve architectural quality using purely computational tools – in a sense I felt that this attempt at upgrading modernist standardisation via computation didn’t guarantee better quality results per se, beyond merely complexifying housing typology and offering a wider variety of spatial configurations. 

In an essay I published in 2019 (which in many ways inspired the curation of this Journal), I declared my interest to be in the use of computational tools not for the sake of complexity – formal or programmatic – but for increasing architectural quality, while decrying that the positions expressed by the so-called first and second digital revolutions, at the level of aesthetics at least, seemed too invested in their own self-proclaimed novelty. My interest was in rooting them in a historical continuum, with established architectural methodologies; seeing computational design as an evolution of rationalism. 

This is why I wanted this journal to be about architectural form, and not about technical aspects of computational design: there is an urgent need to discuss design traditions connected to computational design, as an inquiry on “best practices” – that is, historical cases of what an algorithmic form has been and can be. 

Any discussion on architecture implies a twin focus, on the one hand, on the technical aspects of construction and the tools of design, and on the other, on how these are interpreted and sublimated by the artistic sensibility of an author. Ultimately, what’s interesting about architecture as the discipline of constructing the human habitat is how it is capable of producing a beautiful outcome; and in architecture, perhaps more than any other practice, the definition of beauty is collective. To be able to establish what’s beautiful, we need to develop common hermeneutic tools, which – much like in art – must be rooted in history. 

In light of this, I’m delighted with the contributions to this Journal, which offer a concise array of historical and contemporary positions that can help construct such tools. Many of the essays presented here offer a much needed insight into overlooked pioneers of algorithmic form, while others help us root contemporary positions in an historical framework – thus doing that work necessary for any serious discipline, technical or artistic, of weaving the present with the past.

My hope is that those individuals or academic institutions who are interested in how we can use emerging computational tools for architecture can re-centre their work not just on tooling and technical research but on architectural form, as the result of good old composition and proportion. The time is ripe, in my view, for bridging the gap between computational fundamentalists who believe in the primacy of code, and those with more conservative positions who foreground good form as the result of the intuition and inclination of a human author, remembering that an architectural form is only interesting if it advances the quality of life of its inhabitants and continues to evolve our collective definitions of beauty.  

algorithmic form, 2021
algorithmic form, 2021
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Collage of Isa Genzken's work
Collage of Isa Genzken’s work
The Algorithmic Form in Isa Genzken
Algorithmic Form, assemblage, attention economy, Collage, data architecture, hooks, Isa Genzken, montage, Social Architecture, social object, social science, surrealism
Provides Ng
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What’s the Hook? Social Architecture? 

Isa Genzken’s work can be seen as a synthesis of the “social” and the “object” – a visual-sculptural art that reflects on the relationship between social happenings and the scale of architectural space. She was also one of the early explorers in the use of computation for art, collaborating with scientists in the generation of algorithmic forms in the 70s. But what is the social object? What can it mean for architecture? Just as Alessandro Bava, in his “Computational Tendencies”,[1] challenged the field to look at the rhythm of architecture and the sensibility of computation, Roberto Bottazzi’s “Digital Architecture Beyond Computers”[2] gave us a signpost: the urgency is no longer about how architectural space can be digitised, but ways in which the digital space can be architecturised. Perhaps this is a good moment for us to learn from art; in how it engages itself with the many manifestations of science, while maintaining its disciplinary structural integrity. 

Within the discipline of architecture, there is an increasing amount of research that emphasises social parameters, from the use of big data in algorithmic social sciences to agent-based parametric semiology in form-finding.[3] [4] The ever-mounting proposals that promise to apply neural networks and other algorithms to [insert promising architectural / urban problem here] is evidence of a pressure for social change, but also of the urge to make full use of the readily available technologies at hand. An algorithm is “a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer”.[5] It is a finite sequence, well-defined, with performance based on the length of code – how fast and best can we describe the most. In 1975, Gregory Chaitin’s formulation of Algorithmic Information Theory (AIT) reveals that the algorithmic form is not anymore what can be visualised on the front-end, but “the relationship between computation and information of computably generated objects, such as strings or any other data structure”.[6] In this respect, what stands at the convergence of computable form and the science of space is the algorithmic social object. 

Figure 1 – Algorithmic Social Science Research Unit (ASSRU) and Parametric Semiology – The Design of Information Rich Environments. Image source: ASSRU, Patrik Schumacher.  

Social science is the broad umbrella that encompasses disciplines from history and economics, to politics and geography; within which, sociology is a subset that studies the science of society.[7] The word ‘sociology’ is a hybrid, coined by French philosopher Isidore Auguste Comte in 1830 “from Latin socius ‘associate’ + Greek-derived suffix –logie”; more specifically, “social” as the adjective dates from the 1400s, meaning “devoted to or relating to home life”; and 1560s as “living with others”.[8] The term’s domestic connotation soon accelerated from the realm of the private to the public: “Social Contract” from translations of Rousseau in 1762; “Social Darwinism” and “Social Engineering” introduced by Fisher and Marken in 1877 and 1894; “Social Network” and “Social Media” by the late 20th century from Ted Nelson. Blooming during a high time of the Enlightenment and the rise of the positivist worldview, sociology naturally claims itself to be a science, of scientific methods and empirical investigations. The connotation of –logie has been brilliantly attested by Jonathan Culler:[9] 

Traditionally, Western philosophy has distinguished ‘reality’ from ‘appearance’, things themselves from representations of them, and thought from signs that express it. Signs or representations, in this view, are but a way to get at reality, truth, or ideas, and they should be as transparent as possible; they should not get in the way, should not affect or infect the thought or truth they represent.” 

To claim a social study as a science puts forward the question of the relationship between the language that is used to empirically describe and analyse the subject with the subject matter itself. If it should be objectively and rationally portrayed, then the language of mathematics would seem perfect for the job. If we are able to describe the interaction between two or more people using mathematics as a language, then we may begin to write down a partial differential equation and map the variables of it.[10] Algorithms that are inductively trained on evidence-based data do not only seem to capture the present state of such interaction, but seem also able to give critical information in describing the future evolution of the system. This raises the question of computability: what is the limit to social computation? If there is none, then we might as well be a simulation ourselves; so the logic goes that there must be one. To leave an algorithm running without questioning the limits to social computation is like having Borel’s monkey hitting keys at random on a typewriter, or to apply [insert promising algorithm here] arbitrarily for [insert ear-catching grand challenges here].   

Figure 2– Borel’s infinite monkey theorem in 1913. Image source: Wikipedia. 

What’s the hook? 

A hook “is a musical idea, often a short riff, passage, or phrase, that is used in popular music to make a song appealing and to catch the ear of the listener”.[11] It is a monumental part of Web 2.0 that takes user attention as a scarce resource and a valuable commodity – an attention economy. Music is an artform that takes time to comprehend; as it plays through time, it accrues value in your attention.  

Figure 3 – Drum beat to Empire State of Mind, Nick’s Drum Lessons, “‘Empire State of Mind’ Jay Z – Drum Lesson”, October 5, 2014 

This is one of the most famous hooks of the late 2000s – Empire State of Mind came around the same time as the Web 2.0 boom, just after New York had recovered from the dotcom bubble. The song was like an acoustic montage of the “Eight million stories, out there in the naked’, revealing an underlying urge for social change that was concealed by the boom; just as we see Jay-Z in Times Square on stage under the “big lights that inspired” him rapping: “City is a pity, half of y’all won’t make it”.[12] It was an epoch of R&B, rhythms of cities, of the urban sphere, of the hightech low life. Just the first 15 seconds of Jay-Z’s beat is already enough to teleport a listener to Manhattan, with every bit of romanticism that comes with it. The Rhythms and the Blues constructed a virtual space of narrative and story-telling; such spatial quality taps into the affective experiences of the listener through the ear, revealing the urban condition through its lyrical expression. It is no accident that the 2000s was also a time when the artist / sculptor Isa Genzken began exploring the potential of audio in its visual-sculptural embodiment.  

The ear is uncanny. Uncanny is what it is; double is what it can become; large [or] small is what it can make or let happen (as in laisser-faire, since the ear is the most [tender] and most open organ, the one that, as Freud reminds us, the infant cannot close); large or small as well the manner in which one may offer or lend an ear.” — Jacques Derrida.[13] 

Figure 4 – “Ohr”, Isa Genzken, since 2002, Innsbruck, City Hall facade, large format print on flag fabric, 580 x 390 cm. Photograph, galeriebuchholz 

An image of a woman’s ear was placed on a facade by Genzken, personifying the building as a listener, hearing what the city has to say. At the same time, “The body is objectified and made into a machine that processes external information”.[14] The ear also symbolises the power of voice that could fill a place with a space: an acoustic space. As much as a place is a location, geographically tagged, and affects our identity and self-association of belonging; a space can be virtual as much as it can be physical. Such a space of social interaction is now being visualised on a facade, and at the same time, it is being fragmented: “To look at a room or a landscape, I must move my eyes around from one part to another. When I hear, however, I gather sound simultaneously from all directions at once: I am at the centre of my auditory world, which envelopes me. … You can immerse yourself in hearing, in sound. There is no way to immerse yourself similarly in sight”.[15] This is perhaps a prelude to augmented virtual reality.  

Figure 5 – The Surrealist doctrine of dislocation, the romantic encounter of urban objects is “as beautiful as the chance meeting of a sewing machine and an umbrella on an operating table.” – Lautréamont, Canto VI, Chapter 3. (a) The cover of the first edition of the Rem Koolhaas’ book Delirious New York, designed by Madelon Vriesendorp. (b) A photograph of New York by Isa Genzken, New York, N.Y., 1998/2000, Courtesy Galerie Buchholz, Berlin/Cologne. (c) A photography by Man Ray 1935 © The Man Ray Trust / ADAGP, Paris and DACS, London 

As much as Genzken is interested in the ‘‘exploration of contradictions of urban life and its inherent potential for social change”, Rem Koolhaas shared a similar interest in his belief that it is not possible to live in this age if you don’t have a sense of many contradictory voices.[16] [17] What the two have in common is their continental European roots and a love for the Big Apple – Genzken titled her 1996 collage book “I Love New York, Crazy City”, and with it paid homage to her beloved city. Delirious New York was written at a time when New York was on the verge of bankruptcy, yet Koolhaas saw it as the Rosetta Stone, and analysed the city as if there had been a plan, with everything starting from a grid. It was Koolhaas’ conviction that the rigor of the grid enabled imagination, despite its authoritative nature: unlike Europe, which has many manifestos with no manifestation, New York was a city with a lot of manifestation without manifesto. 

Koolhaas’ book was written with a sense of “critical paranoia” – a surrealist approach that blends together pre-existing conditions and illusions to map the many blocks of Manhattan into a literary montage. The cover of the first edition of the book, designed by Madelon Vriesendorp, perfectly captures the surrealism of the city’s socio-economy at the time: the Art Deco skyscraper Chrysler Building is in bed with the Empire State. Both structures were vying for distinction in the “Race into the Sky” of the 1920s, fueled by American optimism, a building boom, and speculative financing. [18] Just as the French writer Lautréamont wrote: “Beautiful as the accidental encounter, on a dissecting table, of a sewing machine and an umbrella”, surrealism is a paradigmatic shift of “a new type of surprising imagery replete with disguised sexual symbolism”[19] The architectural surrealism manifested in this delirious city is the chance encounter of capital, disguised as national symbolism – an architectural hook.  

Data Architecture 

Figure 6 – China Central Television Headquarters (CCTV) and Genzken’s Gate for Amsterdam Tor für Amsterdam, Außenprojekte, Galerie Buchholz, 1988.

Genzken’s sense of scale echoes Koolhaas’ piece on “bigness” in 1995. Her proposal for the Amsterdam City Gate frames and celebrates the empty space, and found manifestation in Koolhaas’ enormous China Central Television’s (CCTV) Beijing headquarters – a building as a city, an edifice of endless air-conditioning and information circularity wrapped in a structured window skin, hugging itself in the air by its downsampled geometry of a mobius loop. Just as Koolhaas pronounced, within a world that tends to the mega, “its subtext is f*** context”. One is strongly reminded of the big data approach to form-finding, perhaps also of the discrete spatial quality coming from Cellular Automata (CA), where the resolution of interconnections and information consensus fades into oblivion, turning data processing into an intelligent, ever mounting aggregation. In the big data–infused era, the scale boundary between architecture and urban design becomes obscured. This highlights our contemporary understanding of complex systems science, where the building is not an individual object, but part of a complex fabric of socioeconomic exchanges. 

Figure 7 – The Bartlett Prospective (B-pro) Show, 2017. 

As Carpo captured in his Second Digital Turn, we are no longer living in Shannon’s age, where compression and bandwidth is of highest value: “As data storage, computational processing power, and retrieval costs diminish, many traditional technologies of data-compression are becoming obsolete … blunt information retrieval is increasingly, albeit often subliminally, replacing causality-driven, teleological historiography, and demoting all modern and traditional tools of story-building and story-telling. This major anthropological upheaval challenges our ancestral dependance on shared master-narratives of our cultures and histories”.[20] Although compression as a skillset is much used in the learning process of the machines for data models, from autoencoders to convolutional neural networks, trends in edge AI and federated learning are displacing value in bandwidth with promises of data privacy – we no longer surrender data to a central cloud, instead, all is kept on our local devices with only learnt models synchronising. 

Such displacement of belief in centralised provisions to distributed ownership is reminiscent of the big data-driven objectivist approach to spatial design, which gradually displaces our faith in anything non-discursive, such as norms, cultures, and even religion. John Lagerwey defines religion in its broadest sense as the structuring of values.[21] What values are we circulating in a socio-economy of search engines and pay-per-clicks? Within trends of data distribution, are all modes of centrally-provisioned regulation and incentivisation an invasion of privacy? Genzken’s work in urbanity is like a mirror held up high for us to reflect on our urban beliefs.  

Figure 8 – Untitled, Isa Genzken  2018, MDF, brass fixings, paper, textiles, leather, mirror foil, tape, acrylic paint, mannequin, 319.5 x 92.5 x 114 cm. David Zwirner, Hong Kong, 2021.

Genzken began architecturing a series of “columns” around the same time as her publication of I Love New York, Crazy City. Evocative of skyscrapers and skylines that are out of scale, she named each column after one of her friends, and decorated them with individual designs, sometimes of newspapers, artefacts, and ready-made items that reflect the happenings of the time. Walking amongst them reminds the audience of New York’s avenues and its urban strata, but at 1:500. Decorated with DIY store supplies, these uniform yet individuated structures seem to be documenting a history of the future of mass customization. Mass customisation is the use of “flexible computer-aided manufacturing systems to produce custom output. Such systems combine the low unit costs of mass production processes with the flexibility of individual customization”.[22] As Carpo argued, mass customisation technologies would potentially make economies-of-scale and their marginal costs irrelevant and, subsequently, the division-of-labour unnecessary, as the chain of production would be greatly distributed.[23] The potential is to democratise the privilege of customised design, but how can we ensure that such technologies would benefit social goals, and not fall into the same traps of the attention economy and its consumerism?  

Refracted and reflected in Genzken’s “Social Facades” – taped with ready-made nationalistic pallettes allusive of the semi-transparent curtain walls of corporate skyscrapers – one sees nothing but only a distorted image of the mirrored self. As the observer begins to raise their phone to take a picture of Genzken’s work, the self suddenly becomes the anomaly in this warped virtual space of heterotopia.  

Utopia is a place where everything is good; dystopia is a place where everything is bad; heterotopia is where things are different – that is, a collection whose members have few or no intelligible connections with one another.” — Walter Russell Mead [24] 

Genzken’s heterotopia delineates how the “other” is differentiated via the images that have been consumed – a post-Fordist subjectivity that fulfils itself through accelerated information consumption.  

Figure 9 – Attention economy and social strata as refracted and reflected in (a) “Soziale Fassade”, Isa Genzken, 2002, Courtesy Galerie Buchholz, Berlin/Cologne, and (b) “I shop therefore I am”, Barbara Kruger, 1987 

The Algorithmic Form 

Genzken’s engagement with and interest in architecture can be traced back to the 1970s, when she was in the middle of her dissertation at the academy.[25] She was interested in ellipses and hyperbolics, which she prefers to call “Hyperbolo”.[26] The 70s were a time when a computer was a machine that filled the whole room, and to which a normal person would not have access. Genzken got in touch with a physicist, computer scientist Ralph Krotz, who, in 1976, helped in the calculation of the ellipse with a computer, and plotted the draft of a drawing with a drum plotter that prints on continuous paper.[27] Artists saw the meaning in such algorithmic form differently than scientists. For Krotz, ellipses are conic sections. Colloquially speaking, an egg comes pretty close to an ellipsoid: it is composed of a hemisphere and half an ellipse. If we are to generalise the concept of conic section, hyperbolas also belong to it: if one rotates a hyperbola around an axis, a hyperboloid is formed. Here, the algorithmic form is being rationalised to its computational production, irrelevant of its semantics – that is, until it was physically produced and touched the ground of the cultural institution of a museum. 

The 10-meter long ellipse drawing was delivered full size, in one piece, as a template to a carpenter, who then converted it to his own template for craftsmanship. Thus, 50 years ago, Genzken’s work explored the two levels of outsourcing structure symbolic of today’s digital architectural production. The output of such exploration is a visual-sculptural object of an algorithmic form at such an elongated scale and extreme proportion that it undermines not only human agency in its conception, but also the sensorial perception of 2D-3D space.[28] When contemplating Genzken’s Hyperbolo, one is often reminded of the radical play with vanishing points in Hans Holbein’s “The Ambassadors”, where the anamorphic skull can only be viewed at an oblique angle, a metaphor for the way one can begin to appreciate the transience of life only with an acute change of perspective.  

Figure 10. (a) ‘The Ambassadors’, Hans Holbein, 1533. (b) “Hyperbolos”, Genzken, 1970s. Image source: Andrea Albarelli, Mousse Magazine

When situated in a different context, next to Genzken’s aircraft windows (“Windows”), the Hyperbolo finds association with other streamlined objects, like missiles. Perhaps the question of life and death, paralleling scientific advancement, is a latent meaning and surrealist touch within Genzken’s work, revealing how the invention of the apparatus is, at the same time, the invention of its causal accidents. As the French cultural theorist and urbanist Paul Virilio puts it: the invention of the car is simultaneously the invention of the car crash.[29] We may be able to compute the car as a streamlined object, but we are not even close to being able to compute the car as a socio-cultural technology.  

Figure 11 – Genzken holding her “Hyperbolos” in 1982, and “Windows”. Eichler , Dominic. “This Is Hardcore.” Frieze, 2014.

Social Architecture? 

Perhaps the problem is not so much whether the “social” is computable, but rather that we are trying to objectively rationalise something that is intrinsically social. This is not to say that scientific methods to social architecture are in vain; rather the opposite, that science and its language should act as socioeconomic drivers to changes in architectural production. What is architecture? It can be described as what stands at the intersection of art and science – the art of the chief ‘arkhi-’ and the science of craft ‘tekton’ – but the chance encounter of the two gives birth to more than their bare sum. If architecture is neither art nor science but an emergence of its own faculty, it should be able to argue for itself academically as a discipline, with a language crafted as its own, and to debate itself on its own ground – beyond the commercial realm that touches base with ground constraints and reality of physical manifestation, and also in its unique way of researching and speculating, not all “heads in the clouds”, but in fact revealing pre-existing socioeconomic conditions.  

It is only through understanding ourselves as a discipline that we can begin to really grasp ways of contributing to a social change, beyond endlessly feeding machines with data and hoping it will either validate or invalidate our ready-made and ear-catching hypothesis. As Carpo beautifully put it:  

Reasoning works just fine in plenty of cases. Computational simulation and optimization (today often enacted via even more sophisticated devices, like cellular automata or agent-based systems) are powerful, effective, and perfectly functional tools. Predicated as they are on the inner workings and logic of today’s computation, which they exploit in full, they allow us to expand the ambit of the physical stuff we make in many new and exciting ways. But while computers do not need theories, we do. We should not try to imitate the iterative methods of the computational toolds we use because we can never hope to replicate their speed. Hence the strategy I advocated in this book: each to its trade; let’s keep for us what we do best.” [30] 


1 A. Bava, “Computational Tendencies – Architecture – e-Flux.” Computational Tendencies, January. 2020.

2 R. Bottazzi, Digital Architecture beyond Computers Fragments of a Cultural History of
Computational Design (London: Bloomsbury Visual Arts, 2020).

3 ASSRU, Algorithmic Social Sciences, (Accessed December 18, 2021)

4 P. Schumacher, Design of Information Rich Environments, 2012.

5 Oxford, “The Home of Language Data” Oxford Languages, (Accessed December 18, 2021).

6 Google, “Algorithmic Information Theory – Google Arts & Culture”, Google, (Accessed December 18, 2021).

7 Britannica, “Sociology”, Encyclopædia Britannica, inc. (Accessed December 18, 2021).

8 Etymonline, “Etymonline – Online Etymology Dictionary”, Etymology dictionary: Definition, meaning and word origins,, (Accessed December 18, 2021).

9 J. Culler, Literary Theory: A Very Short Introduction, (Oxford: Oxford University Press, 1997).

10 K. Friston, ”The free-energy principle: a unified brain theory?“ Nature reviews neuroscience, 11 (2),127-138. (2010)

11 J. Covach, “Form in Rock Music: A Primer” (2005), in D. Stein (ed.), Engaging Music: Essays in Music Analysis. (New York: Oxford University Press), 71.

12 Jay-Z. Empire State Of Mind, (2009) Roc Nation, Atlantic

13 J. Derrida, The Ear of the Other: Otobiography, Transference, Translation ; Texts and Discussions with Jacques Derrida. Otobiographies / Jacques Derrida, (Lincoln, Neb.: Univ. of Nebraska Pr., 1985).

15 Kunsthalle Wien, “Kunsthalle Wien #FemaleFool Booklet I’m Isa Genzken the …,” (2014).

16 W. Ong, Orality and Literacy: The Technologizing of the Word, (London: Methuen, 1982)

17 R. Koolhaas, New York délire: Un Manifeste rétroactif Pour Manhattan, (Paris: Chêne, 1978).

18 Kunsthalle Wien, “Kunsthalle Wien #FemaleFool Booklet I’m Isa Genzken the …,” (2014).

19 J. Rasenberger, High Steel: The Daring Men Who Built the World’s Greatest Skyline, 1881 to the Present, (HarperCollins, 2009)

20 Tate, “’L’Enigme D’Isidore Ducasse’, Man Ray, 1920, Remade 1972”, Tate., (Accessed December 18, 2021)

21 M. Carpo, ”Big Data and the End of History”. International Journal for Digital Art History, 3: Digital Space and Architecture, 3, 21 (2018)

22 J. Lagerwey, Paradigm Shifts in Early and Modern Chinese Religion a History, (Boston, Leiden: Brill, 2018).

23 Google, “Mass Customization – Google Arts & Culture.” Google, (Accessed December 18, 2021).

24 M. Carpo, The Second Digital Turn: Design beyond Intelligence, (Cambridge: MIT, 2017).

25 W.R. Mead, (Winter 1995–1996). “Trains, Planes, and Automobiles: The End of the Postmodern Moment”. World Policy Journal. 12 (4), 13–31

26 U. Loock, “Ellipsoide und Hyperboloide”, in Isa Genzken. Sesam, öffne dich!, exhibition cat. (Whitechapel Gallery, London, and Museum Ludwig, Cologne: Kasper, 2009)

27 S. Baier, “Out of sight”, in Isa Genzken – Works from 1973-1983, Kunstmuseum

28 R. Krotz, H. G. Bock, “Isa Genzken”, in exhibition cat. Documenta 7, Kassel 1982, vol. 1, p. 330-331, vol. 2, p. 128-129

29 A. Farquharson, “What Architecture Isn’t” in Alex Farquharson, Diedrich Diederichsen and Sabine Breitwieser, Isa Genzken (London 2006), 33

30 P. Virilio, Speed and Politics: An Essay on Dromology (New York: Columbia University, 1986).

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Sebastiano Serlio, Livre Extraordinaire de Architecture [...] (Lyon: Jean de Tournes, 1551), plate 18, detail
Sebastiano Serlio, Livre Extraordinaire de Architecture […] (Lyon: Jean de Tournes, 1551), plate 18, detail
Citations, Method, and the Archaeology of Collage *
algorithm, alphabet, architectural language, Citations, Collage, Method, pomo, post modern, Renaissance, shape Grammar
Mario Carpo
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But let us not have recourse to books for principles which may be found within ourselves. What have we to do with the idle disputes of philosophers concerning virtue and happiness? Let us rather employ that time in being virtuous and happy which others waste in fruitless enquiries after the means: let us rather imitate great examples, than busy ourselves with systems and opinions.  … For this reason, my lovely scholar, changing my precepts into examples, I shall give you no other definitions of virtue than the pictures of virtuous men; nor other rules for writing well, than books which are well written.  

Jean-Jacques Rousseau, Julie ou la Nouvelle Héloïse, Letter XII (William Kenrick transl., 1784)  

Children learn to speak their mother tongues through practice and observation. They don’t need grammar rules. Grammar comes later, when it is taught at school. This shows that we may know a language without knowing its grammar. Grammar is an artificial shortcut to fluency, replacing the lengthy process of learning from life. For a fifteen-year-old high school student struggling to learn German, grammar is indispensable. Yet plenty of native German speakers don’t know declensions by heart and still manage to get their word endings right – in speech as much as in writing.

At a higher level of linguistic practice, literary composition too used to have its own rules – rules that were taught at school. Until the end of the nineteenth century rhetoric was a compulsory subject in most European secondary schools. Rhetoric is the science of discourse. It teaches how to find the arguments of speech, how to arrange them in an orderly manner, and how to dress them with words. Rhetoric teaches how to be clear and persuasive. Seen in this light, rhetoric would seem to be a necessary discipline – indispensable, even. Instead, it no longer features in school and university curricula. France stopped teaching rhetoric in 1885, when French lycées replaced it with the history of classic and modern literature. Nineteenth-century educators seemed to have concluded that, when learning to write, we are better off in the company of literary masterpieces, rather than engaged in the normative study of classical (or modern) rhetoric. A century after Rousseau, Julie-Héloïse’s pedagogical programme quoted above became law.

In times gone by students would have learnt the art of discourse by systematically studying grammar and rhetoric – page after page of rules to be learnt by heart. Today high school students in all European countries are instead obliged to read the masterpieces of their respective national literatures, often ad nauseam. This evidently follows from the assumption that, by reading and re-reading these exemplary works, students will (at some point) learn to write as beautifully as these canonical authors once did. Never mind that nobody knows precisely how and when that almost magic transference, assimilation, and transmutation of talent might occur: grammar has almost completely disappeared from primary school teaching, and rhetoric barely features in higher education – now an intellectual fossil of sorts. Meanwhile, the old art of discourse tacitly lingers on, in business schools, in creative writing and marketing classes. Especially in the latter, the ancient forensic discipline is returned to one of its ancestral functions: that of persuading, even when in the wrong.

For the Humanists of the Quattrocento, the first language to learn was Latin. Not Medieval Latin of course – a corrupt and barbaric but still living language. Renaissance Humanists wanted to speak in the tongue of classical antiquity; they wanted to learn Cicero’s Latin. But Cicero’s Latin is, by definition, a dead language: quite literally so, since it died with Cicero. Cicero also wrote manuals on the art of rhetoric, but the Humanists believed that the best way to learn to write like Cicero was by imitating his way of writing. Well before the Romantics and the Moderns, they found learning from rules unappealing. They preferred to copy the style of Cicero from examples of his work.

The Humanists’ veneration of examples was not limited to languages. Their exemplarism was an épistémè – an intellectual, cultural and social paradigm, deeply inscribed within the spirit of their time. That was their rebellion against the world they grew up in. For centuries the Scholastic tradition had privileged formalism, deductive reasoning, and syllogistic demonstration. The Humanists rejected this “barbarous”, “Gothic” tradition of logic, in favour of their new way of “learning from examples”. The dry and abstract rules of medieval Scholasticism were difficult to handle. Examples, on the other hand, were concrete and tangible. Imitating an example was easier, more pleasurable, and allowed more room for creativity than merely applying rules. This is how, at the dawn of modernity, antiquity was turned from a rule book into an art gallery.

*** *** ***

Like the arts of discourse, the arts of building require schooling. At the height of the Middle Ages, when both Gothic architecture and Scholasticism were at their peak, architectural lore was the preserve of guilds, and its mostly oral transmission was regulated by secretive initiation practices. By contrast, the Humanists pursued a more open strategy – reviving the ancient custom of writing books on building. The first modern treatise, Alberti’s De Re Aedificatoria, deals with the architecture of antiquity, but the structure of Alberti’s discourse was still medieval and Scholastic. Alberti advocates classical architecture as a paragon for all modern building, but Alberti’s antiquity was an abstract model, devoid of any material, visible incarnation. Rather than an atlas of classical buildings, Alberti’s book offers a set of classical design rules – rules for building in the classical way. To put it in more contemporary terms, Alberti formalized classical architecture. Alberti’s rules replace the need to see – let alone imitate – the monuments of classical antiquity. To avoid all misunderstanding, Alberti’s book did not describe any actual ancient monument, either in writing or visually: Alberti’s De Re Aedificatoria originally did not include any illustrations, and Alberti explained that he wanted it that way.

As a commercial venture, Alberti’s De Re Aedificatoria was not a success. Renaissance architects found it easier to skip Alberti’s writings altogether, and go see, touch and learn from the extant magnificence of Roman ruins in person. Moreover, and crucially, as of the early sixteenth century drawings of ancient monuments started to be sold and circulated throughout Europe. Survey drawings in particular, for the first time made available through print, made the laborious ekphrastic and normative mediation of Alberti’s writings all but unnecessary. But models, if beautiful to behold, are not always easy to imitate. Copies will inevitably be more or less successful, depending on the individual talent of each practitioner. By the second or third decade of the sixteenth century imitation itself had become a pedagogic and didactic conundrum.

Not just architectural imitation: writers had the same problem. After all, imitating Cicero is easier said than done. Many rhetoricians in the sixteenth century will strive to transform the practice, skills, and tacit knowledge of literary imitation into a rational, transmissible technique. The modern notion of “method” was born out of sixteenth century rhetoric, but sixteenth century authors were not trying to develop a (scientific) method for making new discoveries; they were trying to develop a (pedagogic) method to better organise and teach what they already knew. Their post-Scholastic, pre-scientific method was essentially a diairetic method – a method of division: all knowledge, they argued, can be partitioned into smaller and smaller units, easier to learn, remember and work with. For sixteenth century scholars, “method” still meant “short cut” – a short cut to knowledge.

Discourse itself can be divided into modular parts: prefaces, arguments, conclusions, formulas and figures, idioms or turns of phrase, sentences, syntagms, words and letters. Sixteenth-century rhetoricians used this divisive technique to invent a new method for literary imitation. On the face of it, Cicero’s style may appear as an ineffable quintessence, but at the end of the day all writing is text, and every text can be broken down into a linear sequence of alphabetical units. Of course, breaking up a text is not a straightforward operation: the parts of speech are held together by syntactic, semantic, and functional relationships. Some of these links can be uncoupled. Others can’t. A text is a heteroclitic, variable cohesion aggregate of parts. Its segments differ in both extension and complexity. Yet even the most sophisticated literary monument can be subdivided into fragments; and once a fragment has been set apart from its compositional context, it can also be reused, reassembled, or recomposed into another text.

In reducing the art of discourse to a citationist technique – by turning ancient texts into a repository of infinitely repeatable citations – sixteenth century rhetoricians invented a new rhetoric. Ancient and modern texts came to be seen as mechanical assemblages of parts. Ancient works could be decomposed into segments, and these segments could then be reassembled to form new works. The smaller the segments, the more fluid or freer the outcome. Ciceronian Latin was an extraordinarily sophisticated and effective instrument of communication, but some modern ideas fundamentally differed from those of Cicero. The citationist method of imitation allowed Renaissance authors to use an old language to express new ideas.

Renaissance architects also needed a rational method for producing modern buildings while imitating classical examples. The greatest structures of antiquity – temples, amphitheatres, thermal baths – were of no use to modernity. Temples, in particular, while representing the pinnacle of classical architecture, had been built to house rituals and represent heathen gods whose worship had long ceased. The entire language of classical architecture had to be adapted for typologies and functions that had no precedents in antiquity. The image of antiquity itself as a building that can be endlessly dismantled and reassembled was a commonplace in the Renaissance. It was also a common practice on many building sites. Architect Sebastiano Serlio would turn this practice into a design theory.

That was no accident. Giulio Camillo, one of the main theorists of the sixteenth century citationist method, had an interest in architecture. He was also a friend of Serlio. The two were supported by the same patrons, and moved in the same circles of Evangelical (and perhaps Nicodemite) inclination. The method of Giulio Camillo’s Neoplatonist rhetoric is well known:

1. Appropriate ancient examples (literary or otherwise) must be selected. The criteria for this selection were a much-disputed matter at the time, and one on which Camillo himself did not dwell.

2. The resulting corpus of integral textual sources must be segmented or divided into parts according to functional or syntactical criteria.

3. This catalogue of dissolved fragments must be sorted, so new users know where to look for the fragments they need.

4. A modern writer (a composer, but also in a sense a compositor: an ideal type-setter) will pick, reassemble and merge, somehow, any number of chosen textual fragments.

Thus new ideas could be expressed through ancient words and phrases – fragments severed from their original context, yet validated by prior use by a recognised “authority”. In Camillo’s view, this compositional technique constituted the inner workings and the secret formula of all processes of imitation. Furthermore, this was a compositional method that could be taught and learnt.

One essential tool in implementing this pedagogical programme was Camillo’s notorious Memory Theatre, a walk-in filing cabinet where all the textual sources (and possibly some of the fragments deriving from them) would have been sorted following Camillo’s own classification system. The whole machine, which included an ingenious information retrieval device, would have been in the shape of an ancient theatre – and it appears that Camillo built at least a wooden model or mock-up of it, in the hope (soon dashed) of selling his precociously cybernetic technology to King Francis I of France.

In a long-lost manuscript (found and published only in 1983) Camillo also explains how the same principles can inform a new method for architectural design. In Camillo’s Neoplatonic hierarchy of ideas, the heavenly logos descends down into reality following seven steps or degrees of ideality. Individuals inhabit the seventh (lowest, sublunar) step; their ascent and crossing of the lunar sky occurs by dint of their separation from the accidents of space and time. In the case of architecture, actual buildings as they exist on earth must be separated from their site to become ideas of the lowest (sixth) grade. This separation of the real from its worldly context results in something similar to what we would today call “building types” – which are buildings in full, except they do not inhabit any given place. These abstract types are then further subdivided into columns and orders (of the five kinds then known: Tuscan, Doric, Ionic, Corinthian, and Composite). The five orders are then broken down into regular geometric volumes, then surfaces, all the way to Euclidian points and lines. On each grade or step, a catalogue of ready-made parts would offer any designer all the components needed to assemble a new building. Thus Camillo’s design method doubles as a shortcut to architectural imitation, and as a universal assembly kit.

A more scholarly trained Neoplatonist philosopher (and a few existed in Camillo’s time) would have objected to some of Camillo’s brutal simplifications, and could have pointed out that his theory had severe epistemic flaws. All the same, Camillo’s architectural method (which its first editor, Lina Bolzoni, dated to around 1530) is almost identical to the plan laid out by Serlio in the introduction to the first instalment of his architectural treatise, published in Venice in 1537. Some of Serlio’s seven grades did not correspond to Camillo’s order: most notably, his atlas of archaeological evidence, the base and foundation of Camillo’s Neoplatonic scaffolding, should have been on the lowest step, but was instead printed as Serlio’s Third Book (likely for commercial reasons). Additionally, one of the seven books in Serlio’s original plan, his revolutionary Sixth Book, on Dwellings for all Grades of Men, was written but never published – at least, not until 1966. Serlio also wrote an additional, Extraordinary Book (literally, a book out of the original order) – a cruel, sombre joke disguised as a book, which Serlio bequeathed to posterity shortly before dying, poor and dejected in his self-imposed French exile.

Regardless of some factual discrepancies, Serlio’s compositional method is ostensibly the same as Camillo’s. Architecture’s exemplary models are selected, and then fragmented. These fragments are sorted and classified at different levels or grades of dissolution. Instructions for their reassembly are then provided, together with examples of successful new compositions. The pivot of the whole system was the book on the five architectural orders, which Serlio published first (albeit titled Fourth Book to comply with the general plan): a catalogue of stand-alone constructive parts (columns, capitals, bases, entablatures and mouldings), destined for identical reproduction in print, in scaled drawings, and in buildings of any type. In Serlio’s method, this was the main offspring of architectural “dissolution” (or disassembling), and the basic ingredient of architectural design, i.e. re-composition. Pagan idols had to be broken down; only their fragments could be used, purified ingredients in the building of a new Christian architecture.

All the way, Serlio was aware of, and attuned to, the purpose and limits of his architectural method. Serlio turned architectural design into an assemblage of ready-made modular components. These were not actual spolia, but compositional design units, part to a universal combinatory grammar and destined for identical replication. Giulio Camillo’s rhetoric reduced the imitation of Cicero’s style, hence all literary composition, to a cut-and-paste method of collage and citation. Serlio’s treatise did the same for architecture. His theory of the orders was the keystone of the entire process. Serlio couldn’t standardise the building site (that would have made no sense in the sixteenth century), but he could standardise architectural drawings and design.

Serlio knew full well that his simplified, almost mechanical approach to design would entail a decline in the general quality of architecture. Many critics across the centuries have indeed frowned at the models and projects shown in his Seven Books. Serlio’s designs have often been seen as repetitive, banal, ungainly or chunky; lacking in inspiration and genius. But Serlio did not write for geniuses. His treatise was a pedagogical work, not an architectural one. As Serlio tirelessly reminds the reader, his method is tailored to “every mediocre”: to the “mediocre architect” – the average, middling designer. Today we might say that Serlio’s treatise aimed at creating an intermediate class of building professionals. Michelangelo and Raphael had no need for “a brief and easy method” that turned architectural invention into cut-and-paste, collage and citation.

Knowledge can be taught, not genius. Serlio’s pedagogical structure and design method were parts of an overarching ideological project. Serlio’s method promises uniform and predictable architectural standards. These are perhaps banal, or monotonous, but that’s the price one pays to make “architecture easy for everyone”. And it is a price Serlio was willing to pay. Serlio’s concern was the average quality of building, not the artistic value of a few outstanding monuments. This was a most unusual choice for an artist of the Italian Renaissance – an iconoclastic, almost revolutionary stance. Serlio’s worldview was not one in which the misery of the many was contrasted by the magnificence of a few. Serlio pursued the uniform, slightly boring repetitiveness of a productive, “mediocre” multitude. This was an ideological project, but also a social project, ripened in the cultural context of the early protestant Reformation. It is a position that evokes and preludes well-known categories of modernity.

Sebastiano Serlio, Livre Extraordinaire de Architecture [...] (Lyon: Jean de Tournes, 1551), plate 18.
Sebastiano Serlio, Livre Extraordinaire de Architecture […] (Lyon: Jean de Tournes, 1551), plate 18.

* Footnote to this translation

This is a translation of the introduction to my book Metodo e Ordini nella Teoria Architettonica dei Primi Moderni (Geneva: Droz, Travaux d’Humanisme et Renaissance, 1993), edited, abridged, and adapted for clarity, but not updated. That book in turn derived from my PhD dissertation, supervised by Joseph Rykwert, researched and written between 1984 and 1989, and defended in the spring of 1990. Heavily influenced by Françoise Choay’s La Règle et le Modèle and by works of literary criticism by Terence Cave (The Cornucopian Text), Antoine Compagnon (La seconde main ou le travail de la citation), and Marc Fumaroli (L’âge de l’éloquence), all published between 1979 and 1980, my enquiry on the use of visual citations in Renaissance architectural design was evidently in the spirit of the time: post-modern architects in the 80s were passionate about citations (or the recycling of precedent, otherwise known as reference, allusion, collage and cut-and-paste); they were equally devoted to architectural history, and particularly to the history of Renaissance classicism. My aim then was to bridge the gap between those two sources of PoMo inspiration, showing that Renaissance architecture was itself, quintessentially, citationist. How could it have been otherwise, since the main purpose of Renaissance architects was to revive, literally, the buildings of classical antiquity – piece by piece? Thanks to the first studies of Lina Bolzoni on the sulphurous Renaissance philosopher and magician Giulio Camillo, and to my then girlfriend, who was studying Renaissance Neoplatonism (and is today a known specialist of that arcane science), I soon found evidence of an extraordinary link – biographical, ideological, and theoretical – between Giulio Camillo and Sebastiano Serlio, and I wrote a PhD dissertation to explain the transference of the citationist method from Bembo’s Prose to Camillo’s Theatre to Serlio’s Seven Books – and ultimately to Serlio’s architecture.

Unfortunately, in the process, I also found out that the citationist method in the 16th century was a tool and vector of modernity. It was a mechanical method, made to measure for the new technology of printing; it was also in many ways a harbinger of the scientific revolution that would soon follow. Besides, the citationist method was more frequently adopted by Evangelical and Protestant thinkers (particularly Calvinist), and it was condemned by the Counter-Reformation. None of this would have pleased the PoMo architects and theoreticians who were then my main interlocutors.

Fortunately for me, they never found out. When my book was published, in 1993, the tide of PoMo citationism was already receding. Investigating the sources of citationism was no longer an urgent matter for architects and designers. My book was published in Italian, in an austere collection of Renaissance studies – few architects would have known about it, let alone read it. It received some brutally disparaging reviews, as due, by some of Tafuri’s acolytes, because they thought, without reading my book, or misreading it, that I was bringing water to the PoMo mill. I wasn’t. But at that point that was irrelevant. We had all already moved on.

I was pleasantly surprised when, a few years ago, Jack Self commissioned this translation for publication in Real Review (the translation, by Fabrizio Ballabio, was soon thereafter partially republished in Scroope, the journal of the Cambridge School of Architecture, at the request of Yasmina Chami and Savia Palate); and I was of course more than happy when my colleague Alessandro Bava asked me to review it for publication in the B-Pro journal of Bartlett School of Architecture. As we all know, collage and citation are becoming trendy again in some architectural circles – for reasons quite different from those of the late structuralists and early PoMos that were my mentors when I was a student. I have somewhat mixed feelings about the current, post-digital revival of collaging, but I would be happy to restart a discussion we briefly adjourned a generation ago.

Mario Carpo (March 2022)

Publication history:

Metodo e Ordini nella Teoria Architettonica dei Primi Moderni. Alberti, Raffaello, Serlio e Camillo (Geneva: Droz, 1993). 226 pages. Travaux d’Humanisme et Renaissance, 271

“Citations, Method, and the Archaeology of Collage”. Real Review, 7 (2018): 22-30, transl. by Fabrizio Ballabio and by the author; partly republished in Scroope, Cambridge Architectural Journal, 28 (2019): 112-119

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Figure 5 - Exhibition 'Architettura Parametrica e di Ricerca Matematica e Operativa nell’Urbanistica', Milano, XII Triennale, 1960. View of the exhibition space (Archivio Moretti Magnifico)
Figure 5 – Exhibition ‘Architettura Parametrica e di Ricerca Matematica e Operativa nell’Urbanistica’, Milano, XII Triennale, 1960. View of the exhibition space (Archivio Moretti Magnifico)
Luigi Moretti: The Unity of Algorithmic Language
algorithmic fitness, Algorithmic Language, critique to empiricism, generative algorithms, Luigi Moretti, parameters, probabilistic outcomes, search space
Marco Vanucci, Marco Vanucci
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“The new art must be based upon science, in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.” Albert Durer

In the newfound spirit that emerged at the end of the Second World War, Rome became the epicentre of a cultural renaissance. Beside the swinging high life impeccably captured by Fellini in La Dolce Vita, the Eternal City shone as a cultural hub, not just attracting actors and film makers to Cinecittà but, rather, gathering artists, scientists, philosophers, architects and engineers.

The Valadieresque Piazza del Popolo was one of the epicentres of the city’s cultural life. At number 18, next to Antonio Canova’s studio and in front of Caffe Rosati, home to the literati, were the headquarters of Civiltà delle Macchine, a magazine directed by Leonardo Sinisgalli and house organ of Finmeccanica (an Italian company specialising in aerospace, defence and security), promoting the new technological and scientific zeitgeist. Nearby, in via Sistina, L’Obelisco gallery hosted Giorgio Morandi and Alberto Burri’s shows as well as the first exhibitions in Italy of René Magritte and Robert Rauschenberg. The second wave of La Scuola Romana (or Scuola di via Cavour) was also in full swing: the Caffè Aragno, on via del Corso, and the art gallery Cometa hosted discussions and exhibitions that challenged classicism in favour of new art forms, such as expressionism. The Italian “economic miracle” was thriving under the pressure of industrial development and the prosperous growth of the real estate market. The development of new infrastructure went hand-in-hand with the expansions of the cities through the construction of entire new neighbourhoods for the affluent working class. The deployment of a new apartment block typology, la palazzina [1], stretched far and wide in many parts of Rome and, beyond, across the country. Many notable examples were designed by the protagonists of a new generation of architects and engineers who, while promoting the ideas of modernism, were keen to establish a link between the new city and its architectural history. In the work of Ugo e Amedeo Luccichenti, Vincenzo Monaco, Pier Luigi Nervi, Mario Ridolfi and Luigi Moretti, the formal principals of Mannerism and Baroque evolved using reinforced concrete. They experimented with a new formal approach and often expressed new structural possibilities: the autonomous articulation of the façade, its depth, the expressive qualities of exposed concrete, as well as the daring structural solutions, were some of the characteristics of this new repertoire.

It is within this context, characterised by the productive tension between the innovative language of the modern avant-garde and the tradition of humanism, that Luigi Moretti became a central figure in the cultural landscape of the Italian post-war period, certainly one of its brightest interpreters.

Besides its lively cultural scene, Rome remained a place filled with traditional values, rituals, and multiple contradictions. The Italian novelist and Federico Fellini’s long-time screenwriter, Ennio Flaiano, described Italy as “the country where the shortest line between two points is an arabesque”. The paradox and inconsistencies of the Italian bureaucracy proved daunting to foreigners and newcomers, however, they were daily routine to the Roman citizens. Moretti navigated this intricate context with pleasure and ease. Many traits of his persona reflected this contradictory environment: he was physically imposing but elegant and refined; eloquent, charismatic and capable of attracting strong feeling of love and hatred; extroverted yet reserved, egocentric but generous with youngsters; an artist with a passion for science, coherent and multifaceted; a keen student of human nature with a strong temperament, which made discussions with him difficult and intimidating.

Moretti, however, had an eccentric side to his character. He rode with his chauffeur through the narrow street of Rome in a black and white convertible Chevrolet with bright red upholstery. One of his collaborators recalled that “he would enter the Roman trattoria like a Renaissance prince, … give precise instructions to waiter and chef…[and] unilaterally decide the menu for all”. [2]

Luigi Walter Moretti was born in via Napoleone III, on the Esquiline Hill, in the same apartment where he lived almost his entire life. He was the son of Luigi Rolland (1852-1921), an architect and engineer of Belgian origins. Having graduated in 1929 from the Royal School of Architecture in Rome, while assisting Professor Vincenzo Fasolo at the chair of restoration, Moretti won a scholarship for Roman Studies. He then worked with archaeologist and art historian Corrado Ricci at the Trajan’s Market, not far from via Panisperna, in Rione Monti, where he later established his first studio. Born one year before the publication of Marinetti’s Manifesto of Futurism, [3] Moretti absorbed the futurists’ conviction in the “magnificent and progressive fate” of technological innovation and translated it into his own theory and practice. His intellectual approach reflected the profile of a nineteenth-century polymath, a mixture of positivistic idealism and passion for the opportunities offered by the new technologies. He paired creativity with methodological rigour; he rooted his knowledge in the humanistic tradition, drawings inspiration from the late Renaissance and the Baroque, while cultivating a sensibility for mathematics and science. [4] For him, mathematics was the field of “purest contemplations” and “applicative wonders”, [5] so art was “to make humans rise to contemplation, to a sort of vivid bewilderment”. [6]

A New Humanism

Unlike the Futurists, who saw history as too heavy a burden to carry, Moretti considered the history of art and architecture as primary sustenance. He understood history as a continuum and Modernism as part of this long narrative. Luigi Moretti thought of himself as the epigon of that ‘mathematical humanism’ that flourished between Urbino and Florence in the quattrocento [7] Seminal figures such as Luca Pacioli and Piero Della Francesca were from San Sepolcro, half way between the Medici court and the Montefeltro, and each authored treatises on mathematics. Pacioli studied mathematical and artistic proportion, the golden ratio and its application to architecture. He taught math to Leonardo da Vinci who, in turn, drew the illustrations of the regular solids in De Divina Proportione [8] . History has it that Pacioli also introduced Albrecht Dürer to the study of the human body which, in the 20th century, inspired D’Arcy

Thompson’ series on the morphogenesis of forms. On the other hand, Piero Della Francesca was trained in mathematics and wrote three treatises [9], covering subjects such as arithmetic, algebra, geometry, solid geometry and perspective. As a young scholar, Piero visited Florence to study Masaccio’s crucifixion in Santa Maria Novella, where Brunelleschi drew the perspective. This collaboration possibly inspired his work for the Madonna di Senigallia where he sought the collaboration of Bramante to help with the perspective. It is not a chance if Piero Della Francesca’s Flagellation of Christ is considered the first ‘scientific’ perspective ever realised. It was still in Urbino where Francesco di Giorgio Martini mastered the art and science of fortifications, designed following the ballistic trajectories of the new firearms technology [10]. In Rome, this tradition spanned from Apollodorus of Damascus to Michelangelo, all the way to Borromini’s divine geometry where the influence of mathematicians such as Kepler and Leibniz cannot be confirmed but it’s likely have played a role. Moretti considered himself to be the incarnation of the baroque spirit. His passion for and study of the Baroque was deeply rooted in the cultural climate in Rome following the First World War, which was the result of a broader re-discovery of baroque architecture, especially by German and Austrian historians [11]. He also had the chance to study with Fasolo and Giovannoni, who were renown scholars of the Baroque. Moretti considered Michelangelo Buonarroti as his spiritual father. Particularly interesting are Moretti’s studies of one of his less known but most emblematic works: the Sforza chapel in Santa Maria Maggiore, which, according to Moretti, was configured as “the fullest expression of [his] architectural genius”, a “living archetype of architecture [in which] the constructive feeling is one with the construction [and where] the material, in every aspect of its nature, is … folded, transformed into a work of art, since … it is ‘felt’ by the architect as something of his own blood”.[12]

In 1964, at the 25th edition of the Venice Film Festival, while Deserto Rosso [13] won the Golden Lion as best movie, the Art Film section (boasting a jury presided over by Giulio Carlo Argan and including Gio Ponti) awarded the 50-minute long Michelangelo [14], directed by Charles Conrad and Luigi Moretti. In the movie, the work of Michelangelo is analysed through a series of unusual shots and points of view on his art and buildings. Moretti explained that “the first purpose [of] it is the right figurative reading of the work, above all to shake from the eyes those thin, abstract and now worn images of Michelangelo’s masterpieces; images [which are] already false in themselves, since photographs [taken] with wide angle [lens … present] images that are almost always impossible in real life. The second purpose … is that of reading according to a true order that illuminates the compositional spirit of the works … [This] is of course the most arduous, and the commentary of the film [is to] try to facilitate it”.[15] In the documentary, Moretti made use of dramatic lighting, in the manner of Caravaggio’s paintings, to accentuate the theatrical atmosphere, and avoided symmetric shots to render the work from an unusual angle. Particularly interesting is his reading of the Cappella Medicea in Florence, where he placed the camera on the ceiling, offering the opportunity to view the compressed interior spaces. Here, the director seems to be influenced by his professor Vincenzo Fasolo, who used to work through axonometric sectional views to unveil the tectonic character and planimetric sequences of space. A similar critical approach would be used by Bruno Zevi, a few years later, to produce the models and the drawings that punctuated Michelangelo’s exhibition at Palazzo delle Esposizioni [16].

Figure 1 - Study on visibility - Studies on visibility for the football stadium (Archivio Moretti Magnifico)
Figure 1 – Study on visibility – Studies on visibility for the football stadium (Archivio Moretti Magnifico)
Figure 2 - Study on visibility - Studies on visibility for the tennis stadium (Archivio Moretti Magnifico)
Figure 2 – Study on visibility – Studies on visibility for the tennis stadium (Archivio Moretti Magnifico)

The New Century of Science

Moretti’s work and approach can be understood by examining the cultural context within which he operated and where a new alliance between art and science was being defined.

At the turn of the century, the proliferation of new scientific theories challenged the axioms of modern physics and introduced ideas of complexity and chaos. Babbage’s first programmable calculator, Ada Lovelace’s first computer programs , and Boole’s binary code, together with the dissemination of Hollerith’s punched card tabulating machine, marked the beginning of the new era of mechanized binary code and semiautomatic data processing systems. In 1936, Alan Turing published On Computable Numbers,[17] describing what will become the Turing machine, and, in turn, his focus on neurology and physiology will eventually pave the way for artificial intelligence. On the back of this experimentation with the first computational machines, multiple applications became possible: fractals, theory of complexity, chaos theory, thermodynamics, neural networks, generative algorithms, etc.

Moretti was also aware of the evolutionary theory of Charles Darwin and, on the pages of the USL Paris Review [18], among a collage of images of Antonelli, Guarini and Botticelli, he laid out images of the morphological evolution of biological specimens taken from D’Arcy Thompson’s On Growth and Form.[19] Moretti’s fascination for biology and natural systems supported his ideas that form can be mathematically described and computed, which became a founding principle in his further search for a new aesthetic in architecture and the arts. These scientific breakthroughs deeply influenced Moretti, who was searching for a more objective approach to the problem of architecture and city planning in the context of the post-war reconstruction.

In 1951, in the pages of Civiltà delle Macchine, Sinisgalli synthesises the new spirit [20]:

“Today, science comes to draw the skeleton of a crystal and to identify the weak points of a beam … These surveys beyond the visible, these searches for comparative phenomena in tools and materials, they allowed us to clarify the meaning of certain provisions which only seemed owned [by] the spirit, and are instead virtues of matter. Art must retain control of the truth, and the truth of our times is of a subtle quality, it is a truth that is of an elusive nature, probable more than certain, a truth “on the edge” which borders on the ultimate reasons … Science and Poetry cannot walk on divergent roads. Poets must not have [a] suspicion of contamination. Lucretius, Dante and Goethe drew abundantly [on] the scientific and philosophical culture of their times without clouding their vein. Piero della Francesca, Leonardo and Dürer, Cardano and della Porta and Galilei always … benefited from a very fruitful symbiosis between logic and fantasy.”

Moretti shared with the futurists his political views, which were aligned with the fascist ideology. At the end of his university career, in 1932, he met Renato Ricci, then the president of the Opera Nazionale Balilla [21] (ONB), who appointed him ONB’s technical director, succeeding architect Enrico Del Debbio. In this role, Moretti designed several youth centres in Piacenza, Rome (Trastevere), Trecate, and Urbino. In 1937, he took over the design and masterplan for Foro Mussolini (now renamed Foro Italico), where he created one of his masterpieces, Casa della Armi (1933), a rationalist structure subverted by the elegant use of curved lines and the masterful control of natural light. In 1938, Moretti participated in the design of the EUR (Esposizione Universale Romana), a planned (but never completed) development in the Southern part of the city, intended to host Rome’s world fair.

In 1942, Moretti disappeared from public life. Once he reappeared, he was briefly imprisoned in 1945 for his collaboration with the regime. In the prison of San Vittore, in Milan, he met Alfonso Fossataro, an entrepreneur and builder with whom he partnered to build several developments, right after the war. Fossataro and Moretti established the developing company Cofimprese, under which Moretti worked on a series of hotel buildings, and realised the Corso Italia complex in in Milan. The il Girasole house , in the Parioli neighbourhood in Rome, belongs to this period (1949) and is considered an early example of postmodern architecture. [22] The Roman palazzina captured the attention of Robert Venturi, who included it in Complexity and Contradictions as an example of ambiguous architecture, halfway between tradition and innovation. In turn, years later, the Swiss architectural theorist Stanislaus von Moos argued that the broken pediment of Vanna Venturi House is a clear reference to Moretti’s project. [23] In the same period, Moretti designed some villas along the Tirrenic coastline: the most famous of which, La Saracena and the nearby La Califfa, are fine examples of mid-century modernism.

During those years, Moretti entertained a relationship with the Roman aristocracy, the cultural elite, and the Vatican. Studio Moretti was in Palazzo Colonna, in Piazza Santi Apostoli, a regal palace in the heart of Rome which housed the famous Galleria Colonna. Prince Colonna occupied the most important secular position in the Vatican, and he constantly received important visitors: from monarchs to cardinals to prime ministers. Moretti’s office overlooked the main cortile of the palace, so that he and his staff (mostly architects and geometri) would enjoy a daily parade of celebrities and authorities, some of who would become clients.

Figure 3 - Architettura parametrica 1960. Football stadium: Diagrams of the curves identifying optimal lines of sight (Archivio Moretti Magnifico)
Figure 3 – Architettura parametrica 1960. Football stadium: Diagrams of the curves identifying optimal lines of sight (Archivio Moretti Magnifico)
Figure 4 - Architettura parametrica 1960. Cinema hall: Diagrams of the curves identifying optimal lines of sight (Archivio Moretti Magnifico)
Figure 4 – Architettura parametrica 1960. Cinema hall: Diagrams of the curves identifying optimal lines of sight (Archivio Moretti Magnifico)


The post-war period was the golden age for Moretti: his architectural production blossomed in the context of a striving economy which propelled real estate developments across the country. This is also the period of his intellectual maturity, where Moretti developed his sharpest and most relevant reflections on architectural theory.

Moretti’s reputation with the Roman intelligentsia was compromised by his right-wing political views. Bruno Zevi was probably the one who best understood his talent, but he was also his harshest critic. The world of architecture in Rome was dominated by these two figures, so distant and yet so very close. On the one hand, Zevi:

a Jew and a socialist, exiled during the war by Mussolini; an academic historian, an acute scholar and supporter of the Modern Movement with a predilection for Frank Lloyd Wright and Alvar Aalto. On the other hand, Moretti: a conservative catholic, a supporter of the Fascist regime and an active practitioner banned from academia. They each edited an architectural journal which they used as a means to trumpet their architectural ideas. Zevi was, at one time, Moretti’s best interlocutor and strongest enemy. Despite their rivalry, their relationship could be, at times, relaxed and even civil. What is certain is that they probably shared more than they were ready to publicly admit: Zevi secretly hoped that Moretti would join the Association for Organic Architecture (APAO), a movement founded in 1945 by Zevi himself, Luigi Piccinato, Mario Ridolfi, Pier Luigi Nervi and others, aiming at creating a new school of thought, in open opposition to the reactionary model of the Faculty of Architecture of Rome. Legend has it that Zevi tried to convince Moretti to join APAO, promising to make him the greatest Italian living architect. Moretti refused and was for many years condemned to oblivion by the cultural elite. Despite the antagonism of his many detractors, in 1950, Moretti founded the magazine Spazio, [24] with a clear mission to find connections between different forms of art: from painting to architecture, from sculpture to film and theatre. Spazio burned bright in the Roman intellectual scene and, despite the stigma surrounding Moretti, became a beacon for the visual culture of the time, an elegant cultural project that nobody could dare ignore.

Spazio represents one of the most important moments in Luigi Moretti’s theoretical output. Although the magazine only published seven issues (ceasing publications in 1953), his writings published in the magazine represent his most relevant critical framework and constitute the heart of his theoretical production and cultural legacy.

Moretti was editor, editorial director and writer of most of the articles in the magazine. The opening editorial of the first issue of the magazine is titled “Eclettismo e unità di linguaggio” [25] (eclecticism and unity of language) and can be considered Moretti’s programmatic manifesto. The “Unity of Language” was not intended as a fusion of different artistic languages but rather their consonance: Moretti was aware of the differences between artistic languages, and he knew that, despite some emerging points of contact, they remained separate due to their “algorithmic and close” nature. He used the term algorithmic to describe the tendency of different systems to form the general structure of a building or piece of art. The way, for instance, a particular building deals with the modulation of light, the organisation of space and its bearing was considered by Moretti the algorithmic DNA of that structure. In other words, he conceived of architecture as a “reality of pure interrelations”.[26] Moretti believed that the algorithmic nature of the various artistic languages could finally converge and speak in unison.

“There are some periods of civilization that take shape and character from the splendour of a single language; others, very rare, in which the various expressive languages find harmony (…) and together they reach a dense maturity; they are the happy times of Pericles or of the early Renaissance or of the extraordinary seventeenth century. A unitary language is born, formal process of sorting and classification of the infinite parameters of reality and their relationships. Space thus becomes unitary, resolvable, and expressible in every point, and [a] mirror of a new balanced unity of mankind”. [27] [28]

Then in “Genesi di Forme dalla Figura Umana”,[29] in Spazio’s second issue, Moretti described the role of the human figure in the history of art. While these first two articles for Spazio were concerned with general topics, from the third issue onwards he started to explore more specific aspects that would unveil his operational approach to architecture. In “Forme Astratte nella Scultura Barocca”,[30] Moretti discusses how the non-figurative elements of baroque sculptures present a formal richness that could be subtracted from the composition and yet retain their autonomous aesthetic value as abstract forms. Analysing the Baroque sculptures, he noted that “they reveal some areas of their plastic application resolved in purely formal terms, far from any pre-eminent reference to an objective reality, so that it does not seem arbitrary to know that they belong to the abstract formal world”. A case in point is the sculptural palimpsest accompanying the four figures in Bernini’s Fontana dei Fiumi in Piazza Navona, where the landscape surrounding the human figure retains an autonomous aesthetic value.

The contemporaneity of historical art forms and the relevance of history in the world of today was often questioned and studied by Luigi Moretti. In “Trasfigurazioni di strutture murarie”[31] and “Valori della modanatura”[32] he presented a “close reading” of architectural elements: in the first article he tackles the figurative abstraction of mouldings in Romanic architecture, which he considered to be the most abstract in their pictorial simplicity, and yet very concrete in their constructive logic. Moretti juxtaposed on the same page the images of the Duomo di Pisa and Mondrian’s paintings. Signs, traces, geometric textures used in the pictorial compositions become, therefore, precious matrices to compose architectural plans, sections, and elevations. In the second article, Moretti questioned how cornices and profilescould be considered, rather than decorative elements, as pure form, as the only non-figurative elements of architecture that determine its plasticity and volumetric articulation. In “Discontinuità dello Spazio in Caravaggio”[33] and “Spazi-Luce ell’Architettura Religiosa” he continued to explore the role of light in the dynamic articulation of space. He argued that Caravaggio’s figures are always portrayed from the side, never frontal nor symmetrical, deconstructing mass and space through the interplay of light and shadows, with dynamic results. Here, Moretti made a subtle reference to his project for Corso Italia in Milan where he grafted a cantilevering mass protruding sideways from the urban street front.

Perhaps it is with “Strutture e Sequenze di Spazi”[34] that Moretti produced one of the most relevant critical studies for the culture of his time. In it, Moretti delved into the problem of reading and describing space. If the focus in considering Caravaggio was on perceptive glimpses of space, here the aim was to precisely investigate the relationship between the parts and the whole by studying the sequence of rooms articulated through the compressions and dilations of space. He systematically studies and analyses these aspects through a series of

historical examples: Villa Adriana, Guarino Guarini’s church of San Filippo Neri in Casale Monferrato, Laurana’s Palazzo Ducale in Urbino, and many others. For each of these projects, Moretti produced a series of models where the interior space is represented as a volumetric extrusion. With these, he developed an autonomous spatial reading of architecture not dissimilar to what Eisenman developed in the 1960s and 1970s, with the study of forms as pure architectural syntax. Alongside the models are a series of drawings and diagrams describing the density of the different spaces. Here, the form, the structure and the space itself are represented as a dynamic tension between the immaterial nature of space and its material representation.

It is, however, in “Struttura come Forma”[35] that Moretti elaborated the relationship between structure and form (critiquing the approach that prioritises form over structure) and, for the first time, talked about parametric architecture. Starting from the Vitruvian triad (stability, utility, beauty), Moretti argued that, historically, architecture oscillated between prioritising structure (Brunelleschi, Gothic and Roman architecture) or form (Baroque, Renaissance and 19th Century architecture). He then reflected on the direction function>form, pursed by the Rationalists and the Bauhaus. He considered the “function” as parameters determining the space and its concatenation. These parameters are either very limited, so that space can be easily deduced with scientific rigour, leading to the realm of pure technique (an extreme case of what he called parametric architecture); or these parameters are multiple and not clearly definable, so that the function is necessarily approximate, and only further articulation of the structure can define it more precisely. Here we return to the structure>form approach, where structure is, once again, understood as a complex set of relationships. The text is accompanied by an illustration by a young architect, Guido Figus, who worked on an iterative series of roof structures articulated through folded plates resembling origami. Figus’ drawings are fascinating: rather than proposing an optimum solution, they are exploring a series of possible (parametric) permutations for the structure.

Figure 5 - Exhibition 'Architettura Parametrica e di Ricerca Matematica e Operativa nell’Urbanistica', Milano, XII Triennale, 1960. View of the exhibition space (Archivio Moretti Magnifico)
Figure 5 – Exhibition ‘Architettura Parametrica e di Ricerca Matematica e Operativa nell’Urbanistica’, Milano, XII Triennale, 1960. View of the exhibition space (Archivio Moretti Magnifico)
Figure 6 - Exhibition 'Architettura Parametrica e di Ricerca Matematica e Operativa nell’Urbanistica', Milano, XII Triennale, 1960. View of the exhibition space (Archivio Moretti Magnifico)
Figure 6 – Exhibition ‘Architettura Parametrica e di Ricerca Matematica e Operativa nell’Urbanistica’, Milano, XII Triennale, 1960. View of the exhibition space (Archivio Moretti Magnifico)

An Other Art

The movement initiated with Spazio continued after the magazine ceased publication. On June 26 1954, in via Cadone, Rome, Galleria Spazio opened its doors with its first exhibition titled Caratteri della Pittura d’Oggi (Characters of Today’s Painting). The gallery was established through a collaboration between Luigi Moretti and the French art critic Michel Tapié de Celeyran. Jazz musician, curator, art critic and all-round cultural agitator, Tapié entertained close relationships with art galleries across Europe and North America that allowed him to promote and showcase his roaster of artists. He was also the author of Un Art Autre[36], a compendium about a “new art” of signs and matter, where he promoted and gave wide currency to the French style of abstract painting popular in the 1940s and 1950s called Tachisme. This movement was developed as a reaction to Cubism and was characterised by informality and an absence of premeditated structure, conception or approach (sans cérémonie).

The turning point in Tapié’s career was his friendship with artist George Mathieu. This would soon lead to his meeting with Moretti, through the Roman artist Giuseppe Capogrossi, whose large canvases filled with cryptic glyphs and dynamic forms were disseminated across Moretti’s studio and acted as an inspiration to his architecture. [37]

Moretti was seduced by Tapié; he comprehended his great potential and, with him, he seized the opportunity to promote contemporary art, pursuing the unity of languages and his eclectic vision. Under Moretti’s directorship, the art critic became “artistic consultant” of Spazio gallery. For the first exhibition at the gallery, among the large group of selected artists there were some on the brink of becoming internationally acclaimed: Pollock, Francis and Tobey from the States; Capogrossi and Dova from Italy; Appel and Jorn who, with Wols, formed the CoBrA Group; and Mathieu and Riopelle from France. In the catalogue of the exhibition Moretti wrote:[38] “The intensity, the splendour, the explosion of signs given to the surfaces, the brightness and power of relations, the pure relations these signs compose, are its justification”. He also wrote of “The dramatic beauty, the desperate egoism of these adventurous facts that today occur in art”.

Here, Moretti claimed that painting was of importance only to itself, “only tied to the personal algorithm, to the personality of the artist”. The joint venture between Moretti and Tapié, together with artists such as Mathieu and Capogrossi, represented a clear attempt to find new aesthetic and philosophical ways to make art and science converge.

In 1954, in the pages of the US Lines Paris Review,[39] Tapié claims:

It is time to reconsider the notion of rhythm, no longer by way of the only possible system of whole numbers, but rather by way of real and hypercomplex numbers; the notion of structure, no longer bound irrevocably to the ruler and compass, but to the richer and more general notions of continuity and contingency of present topology, within which classical geometry is now only an extremely specialised little chapter; the notion of content, no longer as a more or less theatrical subject-pretext, but as complying with the norms of scientific psychoanalysis; the notion of space and composition, no longer tied to a static formalistic logic and to an “equilibrium” of the same order, but rather to Galois’ Theory of Groups, to Cantor’s Theory of Wholes, to the present metalogic and to Lupasco’s dynamic logic of the contradictory.

Moretti and Tapié would often wander through the streets of Rome searching for artists and “new voices”. Among them was artist Carla Accardi who, years later, recalled visiting villa Saracena in Santa Marinella with Moretti, Tapié and the American artist Claire Falkenstein who was commissioned to design the villa’s gate.

The Roman architect and the French critic shared a common vision and a commitment to evolve the artistic language. After Spazio, they continued to collaborate for many years, far beyond the closure of the gallery, each of them following their artistic language, but sharing a precise vision: the critic called it Morfologie Autre, while the architect refers to Strutture di Insiemi, a term that Moretti borrowed from the study of Galois’ theory of groups[40]. In 1960, they co-founded the International Centre of Aesthetic Research in Turin, Italy, a facility for the study and exhibition of art, as well as for the publication and dissemination of critical, investigative, or theoretical works on art.

In 1965, they co-authored the book Le Baroque Generalisé: Manifeste du Baroque Ensembliste[41], a beautiful and rare publication where the language of the Baroque is articulated through mathematical formulas. This book synthesises Moretti’s fascination for a more scientific approach to architecture with his love for art, the Baroque and the unity of language.

However, Moretti continued to foster collaboration and intellectual exchange. One such association was with French poet Pierre Pascal, son of chemist Paul Pascal, anti-Gaullist and collaborator with the Vichy government, sentenced in absentia to life imprisonment. Pascal left France in 1944 and took refuge in Italy, where Mussolini initially offered him hospitality at the Vittoriale on Lake Garda before he later moved to Rome. There, he found accommodation at Palazzo Caetani, which became the seat of the Éditions du Cœur Fidèle, a publishing company that Pascal co-founded with Moretti. The Cœur Fidèle would publish a forest of hendecasyllabic and alexandrine verse, and rhythmic prose; from the Persian quatrains of Omar Khayyam to Le Corbeau by Poe (deciphered in his arithmetic, geometric and gematric keys), from the Livre de Job to the Apocalypse of St. John[42]. The last is certainly the most significant: it is an interpretation in French Alexandrine, with sixteen prints of Albrecht Dürer’s Apocalypsis cum figuris[43] taken from the original woodcuts used for the prints of 1498 and 1511. The book is of exquisite quality and it represents the apex of Moretti’s erudition which borders into exoterism, a testament to the belief that his intellectual work was rooted in the line drawn by the great masters of the past. Ricerca Operativa Moretti’s passion for science and mathematics led to a friendship with the engineer and mathematician Bruni De Finetti. They may have first met in Via Panisperna, in Rome, where Moretti, as a young graduate from the school of architecture, opened his studio and where De Finetti, enfant prodige and graduate in applied math from the University of Milan, attended the seminars at the Institute of Statistics. At the time, Enrico Fermi was there leading the ‘Panisperna boys’: Edoardo Amaldi, Ettore Majorana, Bruno Pontecorvo, Franco Rasetti, Emilio Segre [44], a group of bright and young scientists who opened the door to nuclear reaction and, later, to the atomic bomb.

Before collaborating with Moretti, De Finetti had been involved in studies on the economic viability of construction. In the magazine La Città,[45] the architect Giuseppe De Finetti (Bruno’s cousin), invites him to develop a mathematical approach where, thanks to a series of formulas and by establishing a relationship between land value, cost of construction and rental value, they calculated the optimum composition of the building. Such an approach would be further investigated by De Finetti in his collaboration with Moretti. Having spent many years at the University of Trieste, De Finetti arrived in Rome in 1954 as a professor of Mathematics at the Faculty of Economics. was one of the first scholars to lecture on Ricerca Operativa, [46]

(operational research), a branch of applied mathematics which was making its way into the Italian academia and intellectual environment. It consisted of analysing and resolving complex decisional problems through the development of mathematical models and quantitative methods (simulation, optimization, etc.) to provide supporting insights in the decision-making process. It is worth noting that, around the same period and with different purposes, Bruno Zevi was elaborating his theory on Critica Operativa[47], a pedagogic and cultural enterprise which aimed to create a bridge between history and modern architecture. Zevi was advocating the actualisation of those immutable characteristics of historical architecture, read and reinterpreted in a contemporary key. [48].

The problem of establishing a link between theory and practice, between thinking and making, was clearly a defining trait of the Italian culture in the post-war era.

During those years, Moretti was developing his studies on parametric architecture, an approach that consisted in the application of mathematical theory to architecture and urbanism. However, having asked De Finetti to bring his collaboration to this new field of research, Moretti wanted to go beyond the declaration of theoretical principles and, in 1957, they became respectively president and vice-president of the newly founded Institute of Mathematical and Operations Research for Urbanism (IRMOU). With them were a group of young mathematicians, architects and engineers: Anna Cuzzer (then married to Paolo Portoghesi), Giovanni Cordella, and Cristoforo Sergio Bertuglia. Moretti’s idea was to apply a more scientific approach to the challenges of post-war reconstruction in Italy. IRMOU, in turn, aimed at employing mathematical and statistical methodologies to provide solutions that were considered quantitatively and qualitatively more effective for a truly modern country. Bruno De Finetti played a particularly important role, not just as a prestigious scholar but also because he introduced the Institute to the use of computational machines, such as the IBM 610, a fixed-point decimal electronic calculator used for probabilistic computation. De Finetti purchased the machine for the University and installed it in via Ripetta, establishing the institution’s first computing centre. At the time, Moretti was involved in some of the most important commissions of his career. In 1958 he led the team involved in creating the new Olympic Village for the XVII Olympics in Rome (1960).[49] Between 1960 and 1966, following up on the masterplan developed for the Olympics, together with Cafiero, Guidi and Libera, Moretti designed and built the housing project Quartiere INCIS Decima, where the buildings were arranged following the roman castrum.

Abroad, Moretti built the Watergate Complex in Washington (which would become infamous in the wake of the 1972 political scandal) and Montreal’s Stock Exchange Tower, both projects commissioned by the insurance company Generale Immobiliare.

In 1968, he was commissioned to design a sanctuary at Tagbha, on Lake Tiberias in Israel. The project was approved by the Vatican, but was never built due to the outbreak of war between Israel and Palestine. Moretti also had commissions in Kuwait (including the headquarters of the Bedouin Engineers’ Club and Bedouin Houses s) and in Algeria (Hotel El Aurassi, the Club des Pines and a series of schools and residential projects).

Moretti was also involved in the new masterplan for the city of Rome and, with IRMOU, carried out studies to analyse and alleviate traffic in the capital. These projects led to the plan for the new subway branch Termini-Risorgimento, which culminated in the realisation of the Pietro Nenni bridge over the river Tiber, as well as the new carpark under Villa Borghese which opened in 1973. Around the same period, he also realised the project for the Thermal Bath in Fiuggi, where he mastered the used of reinforced concrete.

Figure 7 - Study on Borromini: Sant’Ivo alla Sapienza Roma, 1967. Spatial interpretation: Juxtaposition interior and exterior space. (Archivio Moretti Magnifico)
Figure 7 – Study on Borromini: Sant’Ivo alla Sapienza Roma, 1967. Spatial interpretation: Juxtaposition interior and exterior space. (Archivio Moretti Magnifico)
Figure 8 - Study on Borromini: San Carlino alle Quattro Fontane Roma, 1967. Spatial interpretation: Juxtaposition interior and exterior space. (Archivio Moretti Magnifico)
Figure 8 – Study on Borromini: San Carlino alle Quattro Fontane Roma, 1967. Spatial interpretation: Juxtaposition interior and exterior space. (Archivio Moretti Magnifico)

Architettura Parametrica

Having spent about 20 years searching for the new relationship between architecture and mathematics, in 1960, Luigi Moretti was invited to the Milan Triennale to present the work and studies carried out with IRMOU on Parametric Architecture. While IRMOU’s work mostly focused on urbanism (urban planning, urban flows, etc.), for the exhibition in Triennale, Moretti developed parametric studies on sport and leisure facilities: a football stadium, an aquatic centre, a tennis arena and a cinema. At the time, football stadiums andsports arenas in general were relatively new typologies. In addition, unlike many of today’s venues, they were mono-functional. For this reason, stadia were the perfect typology to establish parametric relationships between different components: the position of the spectators in relation with the goals, the sightlines between every seat and different areas of the pitch, etc. Moretti and his collaborators elaborated mathematical formulas to describe these dependencies. The mathematical models produced data points representing the optimum viewing areas of the stadium. The data points were elaborated using an IBM 610 Auto-Point computer.

Moretti explains the “necessity to formulate new logical chains aimed at identifying new architectural forms and their concatenation, dependent on various and complex functions”.[50] For Moretti, “each logical area that makes up the sequence of this new formulation of architectural thought must be the receptor and projective of mathematical thought, that is to say, it needs to be quantifiable … The solution is based on the determination of the elements conditioning the forms as a consequence of the functions that are required of it. That is to say: solutions based on qualifiable parameters, parameters that, one by one and in their quantifiable interrelation, fix the limits within which we identify and draw the forms that fulfil those functions”. And again, “the definition of the parameters must be called upon to assist the techniques and instruments of the most current scientific thought; mathematical logic, operational research and computers. To the study of this approach and to the new method and theory specified in its schemes and verified by the first exciting results, I gave the name of Parametric Architecture”. Moretti elaborated his parametric manifesto on the pages of Moebius magazine, in an axiomatic text which established the heuristic principles of parametric architecture.[51]

Bruno Zevi was intrigued by this new approach. However, confirming his opposition to Moretti, he was far from being convinced. Following the opening of the exhibition, Zevi wrote a sceptical review of it on the pages of L’Architettura Cronaca e Storia:

“Everything that serves to give us distance from empiricism and rationalism in design should be applauded. Especially in a moment like the current one in which the characteristic of the [working method] of most Italian architects is careless … A parametric method encompasses the tools, procedures, and objectives, but to what end? For these questions, electronic brains are barely useful, brains are needed. If parametric architecture is not to remain a brilliant intellectual exercise, it is indispensable that research is sustained by a high moral inspiration. For now, the idea surprises and fascinates us; tomorrow, it may convince”. [52]

Here, Zevi aired a certain dissatisfaction for the unfulfilled promises of parametric architecture. A scepticism that, beside the great advances in parametric and algorithmic design, many still share today.

However, Luigi Moretti was aware of the “high moral inspiration” required to pursue the new course of architecture. In a lecture at the Accademia Nazionale di San Luca, in 1964, he claims that “the new basic meaning” of making architecture must be identified with the “genius of a new morality, of an interior commitment to working in accordance with justice, in a superior economy, for our fellow men. This imposes a dedication, a seriousness in research and investigations and, above all, an underlying humility”. [53]

Figure 9 - Spazio, n. 7 Rome, December 1952 – April 1953 - Michelangelo. Model of the church of S. Giovanni dei Fiorentini in Rome. Representation of the internal volumes (Archivio Moretti Magnifico)
Figure 9 – Spazio, n. 7 Rome, December 1952 – April 1953 – Michelangelo. Model of the church of S. Giovanni dei Fiorentini in Rome. Representation of the internal volumes (Archivio Moretti Magnifico)
Figure 10 - Spazio, n. 7 Roma, December 1952 – April 1953 from 'Strutture e sequenze di spazi', article by Luigi Moretti. Model of Guarino Guarini's church of S. Filippo Neri in Casale Monferrato. Representation of the internal volumes (Archivio Moretti Magnifico)
Figure 10 – Spazio, n. 7 Roma, December 1952 – April 1953 from ‘Strutture e sequenze di spazi’, article by Luigi Moretti. Model of Guarino Guarini’s church of S. Filippo Neri in Casale Monferrato. Representation of the internal volumes (Archivio Moretti Magnifico)


Moretti passed away suddenly in 1973. In his obituary, Zevi didn’t spare words of either admiration or criticism for his beloved enemy: “He possessed an authentic artistic temperament integrated with a notable if non-methodical culture and an extraordinary professional capacity. He could have assumed a determining role in the depressed Italian atmosphere; but a spasmodic desire for individual affirmation associated with an intellectualism like that of D’Annunzio, greedy for refinements and luxuries, reduced his creativity to insufferable conventionality. A waste in civil and human terms”.[54]

Moretti remained a controversial figure for many years after his passing. His legacy was long ignored or undervalued. However, much of the research and many of the questions raised by Moretti during his architectural life remained relevant and some still haunt architects today. What is the role of history in designing the city of today? What is the relationship between architects and technology? Is technology merely a tool to make or also a tool to think?

Moretti was aware of the necessity to not parametrise all things. He warned against “the dictatorship of the algorithm”. The Roman architect knew that his research was still far from the government of complex phenomena with suitable complex algorithms. He knew that architects “will have to educate the mind to scientific rigor knowing how to leave [their] imagination and expressive freedom intact, since free formal expression, personal lyricism, will always find a place in the spaces that the parametric functions will leave free”.[55]

One year before his departure, Luigi Moretti offered an interesting insight. In this brief excerpt from a conference titled “Technology and the ecological problem”,[56] he warned about the uncritical endorsement of new technologies, exposing the limits of his own thinking. While he seemed to have no doubt regarding the computational turn in architecture, he seemed to distance himself from any technocratic orthodoxy.

The authentic humanism in ancient civilization … was indeed a synthesis and integral consciousness of abstract thought … It is with the Enlightenment that an approximate rationality has entered, the production of algorithmic thought as something absolutely proper, acceptable, indeed dutiful and characteristic of man. … The whole critical situation of today’s world, from ecology to ethics, economy, politics, religion and spirituality is the result of two errors … Precisely:

1) the logic of algorithmic developments without limits;

2) [the validity of] this logic …, whatever the dimensions of the empirical field on which it operates.

Technologies produce mechanisms [that are] expressions of particular logical chains, dependent [on] or aroused by other logical chains. … Everyone now feels that it is not possible to continue with them indefinitely. This is obvious; … in the laws of technological development there is a need for a limit. … There is an asymptotic point for any technology beyond which it is in vain, it is foolish to proceed. … The limit of a technology is always inherent in it; it is equivalent to its death and death is an inseparable moment of the vital process in every organism …: we take logic and its algorithmic developments as valid whatever the dimensions of the empirical field on which they operate. This is false: the logical structures are NOT valid for each dimension of the field on which they are affected.

When I was preparing the exhibition of parametric architecture, which had this statement as a conducting background, Prof. De Finetti, one of the most acute intellects in today’s world, suggested to me as a slogan and introduction a stupendous step by Galileo, which roughly says: “if you want to make an animal fifty times bigger you will not have to enlarge the bones and structures fifty times, you will have to change material and study another completely different structure, otherwise you will make a fantasy monster” …

Now, in today’s world, the dimensions are enormously changed; … we continue to use concepts and logic, in the empirical life of our global community … and mustn’t the exceptional dimension of our empirical world lead to a completely new formation of knowledge (of thought)? How can we have logical chains that conclude with certainty as a good old syllogism? As we know, they will be only probable conclusions and consequent statistically verifiable situations. This concept of truth according to probability and statistics has for some time now come alive in every beat of our thought. [57]

On the one hand, he warns against the application of algorithmic processes to all the dimensions of knowledge, establishing boundaries to what can be known through algorithms and what should be left in the hand of the architect. On the other hand, the critique to empiricism leads Moretti to re-affirm a new form of scientific thought that advances by probabilistic attempts rather than by absolute truths. Thus, not dissimilarly from the logic of generative algorithms, Moretti understood that, in the new world, the algorithmic fitness of different parameters is to be found within the boundaries of a “search space” where truth is constantly fluctuant and, far from being univocal, has multiple probabilistic outcomes.


1 “Palazzina. This term, which came into use in the Renaissance as a term of endearment for palazzo, originally designated small buildings located within parks and gardens intended to offer asylum during parties and hunting parties … La Palazzina … thus began its disruptive parable towards the city in the 1920s, replacing the continuous fabric typical of the ancient city [with] a discontinuous fabric in which the building volumes are placed side by side without any formal relationship connecting them, divided only by a thin strip of green, usually divided by the high walls erected on the boundaries of the lots.” (P. Portoghesi, The Angel of History, [Bari: Laterza, 1982])

2 Adrian Sheppard, “Luigi Moretti: a testimony” (Montreal: 2008)

3 Marinetti wrote the manifesto in the autumn of 1908 and it first appeared as a preface to a volume of his poems, published in Milan in January 1909. It was published in the Italian newspaper Gazzetta dell’Emilia in Bologna on 5 February 1909, then in French as Manifeste du futurisme (Manifesto of Futurism) in the newspaper Le Figaro on 20 February 1909. Luigi Moretti was born in Rome on 2 January 1907.

4 “To develop a complete mind: Study the science of art; Study the art of science. Learn how to see. Realize that everything connects to everything else.” Leonardo Da Vinci

5 B.Baldi, Le Vite de’ Matematici, 1587–1595, cit. in F.Abbri, E.Bellone, W.Bernardi, U.Bottazzini, P.Rossi (eds), Storia Della Scienza Moderna e Contemporanea. Dalla Rivoluzione Scientifica all’eta’ dei Lumi 1, 136, TEA, 2000

6 Luigi Moretti, Forme Astratte Nella Scultura Barocca, Spazio n.3, 20, October 1950

7 Andre Chastel introduced the notion of “mathematical humanism” in his book Centri del Rinascimento: Arte italiana 1460-1500 (Milan: Feltrinelli, 1965). Chastel identifies three strands of humanism and specifies that the mathematical one “finds its most important base in Urbino” (41), noting that “the case of Luca Pacioli is not isolated: on the contrary, it well represents the intellectual environment of the quattrocento, an environment in which theory and practice walk hand in hand without, however, adapting themselves to one another perfectly” (47, 49).

8 Luca Pacioli, De Divina Proportione, Aboca Museum, San Sepolcro, 2009

9 Trattato d’Abaco (Abacus Treatise), De quinque corporibus regularibus (On the Five Regular Solids) and De Prospectiva pingendi (On Perspective in painting).

10 Scaglia, Gustina, Francesco Di Giorgio: Checklist and History of Manuscripts and Drawings in Autographs and Copies from Ca. 1470 to 1687 and Renewed Copies, Lehigh Univ Pr, 1992

11 Literary works of architectural history such as Der Cicero by Jacob Burckhardt (1855), Studien zur Architektur geschichte des 17. und 18. Jahrhunderts by Robert Dohme (1878), Renaissance and Baroque by Heinrich Wölfflin (1888), and Barock und Rococo by Auguste Schmarsow (1897), prepare the ground; added to them at the beginning of the twentieth century were Michelangelo als Architekt by Heinrich von Geymüller (1904) and Die Entstehung der Ba rokkunst in Rome by Alois Riegl (1908). In the aftermath of the Great War, came Michelangelo-Studien by Dagobert Frey (1920) and the volume on Borromini by Eberhard Hempel (1924).

12 L. Moretti, op. cit. in Casabella LXX (2006), .78-79.

13 Red Desert, director M.Antognoni, written by M.Antognoni, T.Guerra, starring M.Vitti, R.Harris, C.Chionetti, Italy, 1964

14 Michelangelo: The Man with Four Souls, directors: L.Morfetti, C.Conrad, Italy, 1964

15 L. Moretti e Charles Conrad, presentation to the premier of the movie ’Michelangelo‘ at Circolo del P Greco, Roma, Hotel Hilton, 14 Luglio 1964 (Archivio Moretti Magnifico).

16 P. Portoghesi, B. Zevi (eds.), Michelangiolo architetto (Torino: Einaudi, 1964), with Giulio Carlo Argan, Franco Barbieri, Aldo Bertini, Sergio Bettini, Renato Bonelli, Decio Gioseffi, Roberto Pane, Paolo Portoghesi, Bruno Zevi, and Lionello Puppi.

17 A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, proceedings of the London Mathematical Society 1937

18 A.Imperiale, “An ‘Other’ aesthetic: Moretti’s Parametric Architecture”, Log 44 (2018)

19 D’Arcy Thompson, On Growth and Form, Cambridge University Press, 1917

20 L. Sinisgalli, “Natura, Calcolo, Fantasia”, Pirelli 3 (1951) 54-55.

21 Opera Nazionale Balilla (ONB) was an Italian Fascist youth organization functioning between 1926 and 1937, when it was absorbed into the Gioventù Italiana del Littorio (GIL), a youth section of the National Fascist Party.

22 Robert Venturi, Complexity and Contradiction in Architecture, The Museum of Modern Art, New York, 1966.

23 Stanislaus von Moo, Venturi, Rauch, & Scott Brown: Buildings and Projects (New York: Rizzoli, 1987),244-246

24 Spazio made its debut in July 1950 taking the form of a grandiose project, capable of combining typographic and contributor quality, investments (editorial staff in Milan, Rome, and later Florence and Paris), international screening (abstract in English, French and Castilian). The director’s writings are numerous and of absolute importance. The editor-in-chief, Agnoldomenico Pica, is the author of several texts and is flanked by recurring collaborators: Umberto Bernasconi, Angelo Canevari, Gino Severini, Sisto Villa, Ugo Diamare. Over the course of 7 issues the magazine has promoted artists and architects such as Carlo Mollino, Giuseppe Capogrossi, Alberto Burri, Renzo Zanella, Antonio Gaudi, Adalberto Libera, Ugo Carrà, Vico Magistretti, Carlo De Carli, Ettore Sottsass, Atanasio Soldati, Gianni Monnet, Vittoriano Viganò, Franco Albini, Carlo Pagani, and Luciano Baldessari. The layout was masterful, governed with skilful technique, taste and originality by the director himself

25 L.Moretti, “Ecclecttismo e Unità dei Linguaggi”, Spazio1 (1950)

26 “For me personally, the search for this secret fabric as a link between the various elements of a work, which renders, or attempts to render, the single forms as interrelated parts to the others, in a consciously inseparable fabric, is the habitual way of consider a work (descendant) above all from the eighteen pages of Galois that opened the new objective world to us as a reality of pure interrelations”. “Ultime Testimoninaze di Giuseppe Vaccaro”, L’Architettura Cronaca e Storia,201(1972).

28 L.Moretti, “Ecclecttismo e Unità dei Linguaggi”, Spazio 1, (1950).

29 L.Moretti, “Genesi di Forme dalla Figura Umana”, Spazio 2 (1950).

30 L.Moretti, “Forme Astratte nella Scultura Barocca”, Spazio 3 (1950).

31 L.Moretti, “Trasfigurazioni di strutture murarie”, Spazio 4 (1951).

32 L.Moretti, “Valori della modanatura”, Spazio 6 (1952).

33 L.Moretti, “Discontinuità dello Spazio in Caravaggio”, Spazio 5 (1951).

34 L.Moretti ”Strutture e sequenze di spazi”, Spazio 7 (1953)

35 L.Moretti, “Struttura come Forma”, Spazio 6 (1952)

36 Un Art Autre Ou il s’Agit de Noveaux Dévidages du Reel (Paris: 1952).

37 In the article “Structure comme forme”, published on the United States Line Paris Review, Moretti defines the mathematical equivalent of what he sees in Capogrossi paintings as the theory of differences, which he develops into a method to design dynamic architectural forms.

42 Pierre Pascal (curated by) Apokalypsis Ioannoy ou la Revelation de Notre Seigneur Jesus-Christ a Saint Jean, more often titled Apocalypsis Iesu Xristi / for the first time paraphrased in Alexandrian verse by Pierre Pascal (A l’enseigne du Coeur Fidele, Roma 1963)

43 The Apocalypse (Latin: Apocalipsis cum figuris) is a series of fifteen woodcuts by Albrecht Dürer published in 1498, depicting various scenes from the Book of Revelation, which rapidly brought him fame across Europe.

44 The Via Panisperna boys (Italian: I ragazzi di Via Panisperna) were a group of young scientists led by physicist Enrico Fermi. In Rome, in 1934, they made the famous discovery of slow neutrons, which later made possible the nuclear reactor and subsequently the construction of the first atomic bomb.

45 The magazine La Città: Architettura e Politica was founded and directed by Giuseppe De Finetti in 1945. Only four issues were published between 1945 and 1946. The aim was to discuss “the study of the future city”. The magazine mainly discusses the problems of reconstruction, the fate of the cities destroyed by the two wars, and the problems of traffic; “the task of rebuilding the city, of giving it back its usefulness and beauty”.

46 B. De Finetti, “Gli strumenti calcolatori nella Ricerca Operativa”, Civiltà delle Macchine, 5, 1 (1957), 18–21.

47 B. Zevi exposed his ideas regarding the relationship between architectural history and contemporary design in the opening lecture of the
academic year, held in the Aula Magna of the Rectorate of the University of Rome, on the 18th of December 1963.

48 In addition to Moretti, the team for the new Olympic Village in Rome was formed by Vittorio Cafiero, Adalberto Libera, Amedeo Luccichenti and
Vincenzo Monaco

49 L. Moretti, “Ricerca Matematica in Architettura e Urbanistica”, letter to Giulio Roisecco, director of Moebius magazine

50 L. Moretti, Moebius, IV, 1 (1971), 30–53.

51 B. Zevi, “Cervelli Elettronici? No Macchine Calcolatrici”, in L’architettura Cronaca e Storia VI, 62 (1960), 508-509, (translation A. Imperiale)

52 L. Moretti, “Significato attuale della dizione Architettura”, in Spazio, Fascicoli(1964). See also: Luigi Moretti, “L’Applicazione dei metodi della
Ricerca Operativa nel campo dell’urbanistica”, in Spazio, Fascicoli, (1960); Luigi Moretti, “Strumentazione scientifica per l’urbanistica”, in : Cultura
e realizzazioni urbanistiche, Convergenze e divergenze, conference proceedings, held at Fondazione Aldo Della Rocca, Campidoglio, Consiglio
Nazionale delle Ricerche, (Rome: 1965).

53 B. Zevi, “Computer inceppato dal dannunzianesimo,” L’Espresso (July 29, 1973), reprinted in Cronache di Architettura 2, 982 (Bari: Laterza,
1979), 145.

54 L. Moretti, “Architecture 1965: Évolution ou Révolution”, L’Architecture d’Aujourd’hui, 119 (1965), 48.

55 “Tecnologia e problema ecologico”, round table with the participation of V.Bettini, S. Lombardini, L.Moretti and P.Prini. Civilta delle Macchine 3-
4 (1972)

56 Ibidem

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Daniel Koehler, 2020.
Editorial Note
Editorial Note, Mereologies, Mereology, The Bartlett
Mollie Claypool
University College London
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Welcome to Prospectives.

Prospectives is an open-access online journal dedicated to the promotion of innovative historical, theoretical and design research around architectural computation, automation and fabrication technologies published by B–Pro at The Bartlett School of Architecture, UCL. It brings the most exciting, cutting-edge exploration and research in this area onto a global stage. It also aims to generate cross-industry and cross-disciplinary dialogue, exchange and debate about the future of computational architectural design and theoretical research, linking academic research with practice and industry. 

Featuring emerging talent and established scholars, as well as making all content free to read online, with very low and accessible prices for purchasing issues, Prospectives aims to unravel the traditional hierarchies and boundaries of architectural publishing. The Bartlett supports a rich stream of theoretical and applied research in computational design, theory and fabrication. We are proud to be leading this initiative via an innovative, flexible and agile website. Computation has changed the way we practice, and the theoretical constructs we use – as well as the way we publish.

Prospectives has been designed to be a part-automated, part-human, multiplicitous platform. You may come across things when using it that do not feel, well, quite human. You may not realise at first that you are looking at something produced by automation. And because every issue is unique yet sitting within a generative framework this may mean you see the automation behind Prospectives do things that humans may not do.

Furthermore how you engage with Prospectives is largely left up to the reader. You can read our guest-curated issue, and use the tags to generate your own unique issue – an ‘issue within an issue’ – or read individual articles. You can also suggest new tags to be adopted by articles. We hope this provokes new ways of thinking about the role that participation, digitisation and automation can play in architectural publishing. Prospectives in a work-in-progress, and its launch is the first step towards fulfilling a vision for new kinds of publishing platforms for architecture that play with, and provoke, the discourse on computation and automation in architectural design and theory research.

Issue 01: Mereologies

“Mereologies”, or the plural form of being ‘partly’, drives the explorations bundled in the first issue of Prospectives, guest curated by Daniel Koehler, Assistant Professor at University of Texas at Austin, previously a Teaching Fellow at The Bartlett School of Architecture from 2016 to 2019.

Today, architects can design directly with the plurality of parts that a building is made of due to increased computational power. What are the opportunities when built space is computed part-to-part? Partly philosophy, computation, sociology ecology and partly architecture, each text – or “mereology” – contributes a particular insight on part relations, linking mereology to peer-to-peer approaches in computation, cultural thought, and built space. First substantiated in his PhD at the University of Innsbruck, published in 2016 as The Mereological City: A Reading of the Works of Ludwig Hilberseimer (transcript), Daniel’s work on mereology and part-hood – as an nuanced interplay and blurring between theory and design – has been pivotal in breeding the ground for an emerging generation of architects interested in pursuing a new ethical and social project for the digital in architecture. The collection of writings curated here included postgraduate architecture and urban design students (both his own, and others), architecture theorists, designers, philosophers, computer scientists and sociologists. The interdisciplinary nature of this issue demonstrates how mereology as a subject area can further broaden the field of architecture’s boundaries. It also serves as a means of encapsulating a contemporary cultural moment by embedding that expanding field in core disciplinary concerns.

The contributions were informed by research and discussions in the Bartlett Prospectives (B-Pro) at The Bartlett School of Architecture, UCL London, from 2016 to 2019, culminating in an Open Seminar on mereologies, which took place on 24 April 2019 as part of the Prospectives Lecture Series in B-Pro. Contributors to this issue include: Jordi Vivaldi, Daniel Koehler, Giorgio Lando, Herman Hertzberger, Anna Galika, Hao Chen Huang, Sheghaf Abo Saleh, David Rozas, Anthony Alvidrez, Shivang Bansal and Ziming He.


Prospectives has been a work-in-progress for almost 10 years. The dream of Professor Frédéric Migayrou (Chair of School and Director of B–Pro at The Bartlett School of Architecture) when he arrived at The Bartlett in 2011, I became involved in the project when I joined the School 1 year later. It has been a labour of love and perseverance since. It is due to the fervent and ardent support of Frédéric, Professor Bob Sheil (Director of School), and Andrew Porter (Deputy Director of B–Pro) that this project later received funding in 2018 to formalise the development of Prospectives. To the B–Pro Programme Directors Professor Mario Carpo, Professor Marcos Cruz, Roberto Bottazzi, Gilles Retsin and Manuel Jimenez: I am thankful for your guidance, advice and friendship which has been paramount to this project. Colleagues such as Barbara Penner, Yeoryia Manolopoulou, Barbara Campbell-Lange, Matthew Butcher, Jane Rendell, Claire McAndrew, Clara Jaschke and Sara Shafei have all given me an ear (or a talking to!) at various stages when this project most needed it.

Finally, it is important to say that schools of architecture like the Bartlett have cross-departmental and cross-faculty teams who are often the ones who breed the ground for projects such as Prospectives to be possible. The research, expertise and support of Laura Cherry, Ruth Evison, Therese Johns, Professor Penelope Haralambidou, Manpreet Dhesi, Professor Laura Allen, Andy O’Reilly, Gill Peacock, Sian Lunt and Emer Girling has been vital – thank you.

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Mereologies Open Seminar: Round Table Discussion
Architecture, Composition, Discussions & Conversations, Mereologies, Mereology, Open Seminars
Daniel Koehler, Mario Carpo, Emmanuelle Chiappone-Piriou, Giorgio Lando, Philippe Morel, Casey Rehm, David Rozas, Jose Sanchez, Jordi Vivaldi
University of Texas at Austin
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Participants: Emmanuelle Chiappone-Piriou, Jose Sanchez, Casey Rehm, Jordi Vivaldi, David Rozas, Giorgio Lando, Daniel Koehler with questions from the audience including Mario Carpo and Philippe Morel.

Daniel Koehler: The talks of the symposium were diverse and rich but also abstract, and intentionally external to architecture. At such a point it can be asked if, how, and what role Mereologies can play in architecture? For the discussion we are joined by additional architects with unique angles on composition and part-thinking in their work. Casey Rehm, a computational designer, Jose Sanchez, who is working actively with digital models of participation and Emmanuelle Chiappone-Piriou, an ecological thinker, experienced in the history of architecture. 

José Sanchez: My first reaction to the presentations is controversial. I think it presents well much of the work that is happening in architecture at the moment showing an interest in Mereology and discrete architecture. However, looking at the issue of parts is fundamentally a project where the idea of composition and the idea of structure is relevant as well. Patterns organised by parts can potentially deal with different forms of value. So, in a way, I find a surprising rejection in some of the ideas. 
Mereology seems to be giving us a framework for many different positions to coexist, and I think that we did an excellent presentation of a much clearer advocacy for a form of relations that we might desire that has to do with pre-production, more like an agnostic framework that allows to give us a vocabulary. Are we interested in having advocacy, in having that intentionality, or are we more interested in what the ontology should be or the framework that we are going to work in?

Daniel: I have learnt something from Giorgio’s book that when we define Mereology, it comes in different notions and ranges. On the one hand, you can see it as a distinct theory, as a specific project that has its own agenda. But also, and more crucial in the first place: you can take Mereology as a larger framework to talk about the relations of parts to wholes – simply compositions. OK, but you might ask: why don’t we use the term composition directly? Because, composition has a specific connotation in architecture and refers to the Ecole des Beaux Arts, classical means of relating objects. It was rejected by the Bauhaus, which promoted a different form of composition with modern means. We could continue this through the history of architecture. In architecture, composition is a specific style but not a history. How could we compare those different modes of architectural composition? Can we think of something parallel to morphology or typology which would allow us to compare a plurality of relations between parts and wholes without defending a certain style? When the formal readings of parts turn into their own project, it might be quite valuable that one can figure a figuration without predefining its value by imposing a structure. That might be Mereology as a project. But first of all, the question is how can we intentionally speak about parts? That would be Mereology as a methodology.

Giorgio Lando: I agree with Daniel that it is very important to distinguish various ways in which the word “Mereology” can be legitimately meant. In particular, the word “Mereology” stands in some cases for a specific theory of parthood and composition, and this theory may be such that structure has a role in it, or such that structure has no role in it. A historically important kind of mereological theory, Classical Mereology, is of the latter kind: it is deliberately blind to structure in providing existence and identity conditions for complex entities. In other cases, however, the word “Mereology” stands for an entire field of research, within which competing theories disagree about the role which structure should – or should not – play. If Mereology is seen as a field of research, then it is misleading to say that structure plays no role in it. This equivocation may explain some of José’s perplexities. 
However, some other perplexities are likely to persist even once we disambiguate the word “Mereology”, and we focus on Classical Mereology. Classical Mereology indeed includes some highly counterintuitive principles, and the usual reaction of the layman to these principles is to dismiss them rather quickly. For example, it might seem prima facie incredible that the order of the parts of something does not matter for the identity conditions of complex entities. However, this quick dismissal is usually determined by an equivocation: what is actually incredible is that the order of the parts of a building, or of a village, or of a car does not matter for its nature, for what that building, that village or that car is. However, this is not what Classical Mereology claims. What Classical Mereology claims is weaker and more reasonable: it says that the order of the parts does not matter for the identity conditions of complex entities, such as buildings, villages and cars. 
According to Classical Mereology, it never happens that there are two distinct entities which only differ because of their structure. Classical Mereology is not committed to the frankly incredible claim that structure has no impact on the nature of complex entities, but only to the more reasonable claim that complex entities are never distinct only in virtue of their structure. 
Moreover, this claim of Classical Mereology is restricted to single concrete entities. This might make the confrontation between Classical Mereology and other disciplines, such as architecture, troublesome, inasmuch as these disciplines are more interested in abstract types than in concrete tokens, more interested in repeatable entities than in their single, concrete instantiations. As far as I understand, when architects speak about the parts of a building or of a city, in most cases they are not speaking about a single piece of material and the way in which it is composed, but about a type of building and the fact that there are different types of buildings which result from the combination of the same types of architectural elements, differently combined. 
Once you move from this level of types and abstract entities to the level of concrete entities, the claim of Classical Mereology that structure has no role in the identity conditions of complex entities is much less incredible: consider a single, concrete building (not a type of a building) in a certain moment in time. In that moment, its parts are structured only in one way: the parts of a single, concrete building cannot be structured in two different ways at the same time.
Architects might legitimately retort that architecture is about repeatable types of buildings, about projects which can be applied several times. Given this approach, Classical Mereology is probably not the best tool for modelling repeatable types, and it is indeed desirable to look at different theories, which are not deliberately blind to structure. Mathematics is full of tools which can be employed to this purpose, including set theory and various kinds of algebras. Architects may legitimately wonder why philosophers focus on Classical Mereology instead, which is a serious candidate for the role of sound and exhaustive theory of parthood and composition for single concrete entities, but not for abstract types. The reason is probably a sort of deep-seated philosophical skepticism towards abstract entities, and the idea that fundamental reality consists of concrete entities, while abstract entities are less fundamental, or even a mere construct of the human mind.list or minimalistic inclinations
However, it is not the case that all the philosophers working on Mereology endorse the claims of Classical Mereology. In particular, in the literature of the last ten years, many prominent philosophers (such as Karen Bennett, Aaron Cotnoir and Katherine Hawley) have by contrast argued that Classical Mereology is completely misguided, and that we should also pay attention to structure within the realm of concrete entities. In my book I have defended the claim that, by contrast, Classical Mereology is a perfectly adequate theory of parthood and composition for concrete entities, but many other mereologists disagree with me. More in general, there is virtually no claim about parthood and philosophy about which every philosopher agrees! 

Mario Carpo: Giorgio, you have said that at some point Mereology merges with set theory. What exactly is here the overlay or intersection between Mereology and set theory? In reverse, where is Mereology separating itself from set theory, and where are the core differences?

Emmanuelle Chiappone-Piriou: Is there any way that relates Mereology to category theory?

Giorgio: For what concerns the relation between set theory and Classical Mereology (which, as we have seen, is a specific theory, which is mainly designed to characterise the realm of concrete entities and the way in which they are part one of another), the deepest difference consists in the transitivity of the relation: the relation of parthood in Classical Mereology is transitive, while the relation of elementhood in set theory is not transitive. Thus, if a first entity is part of a second entity and the second entity is part of a third entity, then – according to Classical Mereology – the first entity is part of the third entity. By contrast, it can happen that something is an element of a set, which in turn is an element of a second set, while that something is not an element of the second set. Sets are stratified: you have typically sets of sets of sets. In Classical Mereology, as a consequence of the transitivity of parthood, there are no stratified complex entities. 
While there are many interesting ties between set theory and Mereology, I am unaware of any connection between Mereology and category theory.

Mario: Can you give us maybe an example, like three inclusions in set theory and three inclusions in Mereology?

Giorgio: Consider the set of Italians. I am a member of this set. The set of Italians is also a member of the set of European people. However, I am not a member of this latter set, inasmuch as I am not a European people (I am not a people at all!). We thereby obtain a failure of transitivity of elementhood among sets. Nothing similar is admitted by Classical Mereology: I am part of the fusion of Italians, the fusion of Italians is part of the fusion of Europeans, and I am part of the fusion of Europeans as well.

Mario: So, in set theory, these don’t happen?

Giorgio: It does not happen in the sense that it does not always happen. There are indeed cases in which the same elements appear at different levels of the set-theoretical hierarchy, but this does not happen in general, and is not warranted by any principle of set theory. There are actually many varieties of set Theory, but in no variety of set Theory is elementhood transitive.

Philippe Morel: My feeling is that Mereology is a matter of “technicalities” about a relationship that exists in set theory. If you look at the inclusion as the property you are also looking for in Mereology, I don’t really get what Mereology brings on top of the purely mathematical “canonical” set theory. It gives me the feeling that Mereology is foremost a way (or a “trick”) for philosophers to take control of a theory that escapes them because it is a fully mathematical theory… So, this is why I have a bit of a problem with this notion because again, technically speaking, I still can’t make a clear distinction between the philosophical property and the mathematical property. It is like a layer of metaphysics that is brought on top of the mathematical theory and of course I can’t consider this as a great addition. My second issue is more of a general remark. Why don’t you speak about relational databases like SQL databases? At some point, to my understanding, it is a very practical implementation of what describes Mereology, because it is all about belonging, etc.
Though, I find the mereological approach interesting, especially if it prevents a reintroduction of composition, as I see a danger of bringing back this concept of composition in architectural discourse.

Giorgio: You are right: set-theoretical inclusion (i.e., the relation of being a subset) has precisely the same formal feature of mereological parthood. However, set-theoretical inclusion is not the fundamental relation of set theory: it is definable in terms of set-theoretical elementhood, while set-theoretical elementhood is not definable in terms of set-theoretical inclusion. Thus, the fundamental relation of set theory is elementhood and is not transitive, while the fundamental relation of Classical Mereology is parthood, which is transitive. 
There have been several attempts (for example in Parts of Classes, a book by David Lewis) to exploit the formal analogy between mereological parthood and set-theoretical inclusion in order to reduce set theory to Classical Mereology. The biggest obstacle for this project are set-theoretical singletons, i.e. sets with a single element. The relation between these single elements and their singletons is not easily reducible to Mereology: it is a kind of brute stratification (a form of structure), which has no place in Classical Mereology.
I agree with Philippe’s remark that Classical Mereology is nowadays a mathematically uninteresting theory, in spite of the fact that it has been originally elaborated by great mathematicians such as Stanisław Leśniewski and Alfred Tarski: it is simply a complete algebra without a zero object. The reason why philosophers discuss Classical Mereology does not depend on its alleged mathematical originality: some philosophers (including me) think that this very simple and unoriginal mathematical theory is the sound and complete theory of parthood and composition, at least in the realm of concrete entities. Thus, the reason to be interested in Classical Mereology is not its mathematical originality, but its plausible correspondence with the way in which parthood and composition really work.
As far as datasets are concerned, I think that it is prima facie preferable to construe them as sets rather than as mereological wholes. Indeed, the distinction between inclusion and elementhood is pivotal for datasets. This distinction characterises set theory, while there is no analogous distinction in Classical Mereology.

Daniel: I would like to extend on Giorgio’s point that Mereology offers mathematically an algebra without a zero object. Mereology starts with individuals without defining a set in the first place. In Mereology, you can’t have an empty set, a null set, a zero object. You can’t have a building without building parts. You need parts for thinking a building. This will become more dominant in future because with higher computing capabilities we are able to compute more and more without the need of abstract models. Take as an example the Internet of Things: a building environment where every building part has sensors and is connected. That means that very literally building parts can talk with each other. Such a building environment also participates, and will offer its own economy. Here, value begins with a building part as an active participant in the market. Already in daily BIM practice it is impossible to think of a building without its parts. So, we should also stop thinking of buildings as predefined sets.
To my understanding, a database is constructed on a very specific ontological worldview. Today’s databases take Composition-as-Identity. This principle says that everything is included in the distribution of data points. Nothing above the distribution of atoms exists, not any compound meaning. Whereas, compounds are fundamental to architecture. Just think of a typology; you can’t reduce a façade to windows. What does a courtyard actually exist of? This of course does not relate to math but to philosophy. It is controversial, otherwise it would not be philosophical. Every building is controversy, or call it multiplicitous, because architecture is pre-logical in a sense. We can’t reduce architecture to math. It is also the point where the discussions on beauty depart in architecture. With ease you can describe a building in the first instance through the distribution of its cells. You can describe a housing project just through the part-relation of a shared wall between two flats only. But how do you describe the mountain which Moshe Safdie designed by stitching together the shared walls of flats in such a way that their roofs turn into terraces? Architecture starts where it exceeds simplicity. Yes, we can design buildings with the use of databases with ease. We are able today to compute buildings without structures. But where are their compound meanings? It will be fundamental to find a way to compute what is common, what is collective between the parts. Therefore, I think we should be suspicious of databases or any kind of structural models which were thought without any compound meaning, so to say, without architecture in the first place.

Jose: I’ll re-bring some of the points that Jordi made to the conversation. Jordi, you brought up Graham Harman’s concept of a radical present. I find it kind of controversial that it seems to eradicate a form of speculation, a form of potential, a form of endless abstractness. If we’re moving from the classic Mereology towards a more abstract sense, I think that a lot of architecture production that we discuss especially with discrete projects – that has to do with parts – has to do with potential encounters of entities in that list and is not purely defined by the actual instantiation of the actual encounter of entities. So, we evaluate and design, also thinking that encounters might never happen. So, under the umbrella of that radical present, I wonder what do you see in them?

Jordi Vivaldi Piera: I would say that the term “potential” is misleading. Its meaning generally refers to its capacity to produce other realities, but at the same time it undermines the possibility of novelty because it assumes that an object already contains what it will become. In this sense, I emphasise radical presence in order to understand which object’s “actualities” permit the production of novelty, rather than understanding which are the hypothetical novelties that it contains and therefore at the same time undermines. In this sense, I interpret potentiality as a particular type of actuality.

Casey: I was interested in Daniel’s point; it reminds me of a recent article by Luciana Parisi called “Reprogramming Decisionism”, where she’s talking about machine learning, neural networks and that these technologies in essence assemble. With this, fact is accumulated, which says that something is probably something else. I’m interested in this relative to Mereology and also the statement that a human deals with abstraction but a machine deals with simple facts. How does the mereological project deal with probability? Is that something probably something rather than not? How does the part, certainly something like, you know, the models that you have shown us rely on clear logic? As I nearly understood there is a kind of model that you’re describing, but how does Mereology deal with improbability? I think it is also something that is going to face the design profession in relationship to the kinds of machines which deal with things. 

Giorgio: As far as probability is concerned, I do not envisage any specific, direct problem stemming from the interaction of probability and Mereology. A mereological claim can have a certain degree of probability, and the probability at stake can be either objective/statistical or subjective. In neither case are there specific problems: mereological claims are, from this viewpoint, on a par with other claims. 
While probability is not directly troublesome, there are some potential problems in the vicinity: Classical Mereology does not countenance the hypothesis that an entity is part of another, but only at a certain degree. Consider a cloud in the sky: the water molecules in the centre of the cloud are definitely parts of the cloud, and the molecules far away from the cloud definitely are not parts of the cloud. However, there seems to be a grey zone of molecules, which are neither definitely within the cloud nor definitely out of it. 
These scenarios can be treated in various ways, and the approach depends on the adoption of a certain theory of vagueness. According to the so-called epistemic theory of vagueness (set forth for example by Timothy Williamson), the fact that we are unable to identify the boundaries of a cloud depends on our epistemic limitations (we are unable to identify the boundaries of the cloud, but this does not show that the cloud has in itself no definite boundaries). According to the semantic theory of vagueness (in the version adopted for example by David Lewis), there are actually myriads of clouds and each cloud has precise boundaries; however, our discourses about the cloud are semantically underdetermined, inasmuch as we have not decided which among the myriads of clouds in the sky we are speaking about. Both the epistemic theory of vagueness and the semantic theory of vagueness are perfectly compatible with Classical Mereology, because they locate vagueness in our language or in our epistemic practices and not in reality: in reality, given two entities, either the former definitely is part of the latter, or the former definitely is not part of the latter.  
However, recently also the so-called ontological theory of vagueness (Michael Tye is one of the most ardent advocates of this approach to vagueness) has gained some traction. According to the ontological theory of vagueness, vagueness is in reality, and this happens also in the mereological case of the cloud: the molecules at the periphery of the cloud are neither definitely parts nor definitely non-parts of the cloud. The adoption of the ontological theory of vagueness indeed requires a revision of Classical Mereology. According to Classical Mereology, for example, two complex entities are identical if and only if they have the same proper parts (the proper parts of something are those parts of it which are not identical to it): but this principle is not applicable to entities which have no definite domain of proper parts. According to the ontological theory of vagueness, this is what happens in the case of the clouds and in similar cases. To sum up: probability and various theories of vagueness (such as the epistemic theory and the semantic theory) do not require any departure from Classical Mereology; only the ontological theory of vagueness requires a departure. 

Emmanuelle: It appears we are navigating and combining different sets of discourses that may or may not be consistent with one another, nor with Mereology as it appears here to be merge into a compositional paradigm: we are simultaneously addressing materiality and formal systems, social coherences and principles of governance, all at once.
I believe that, as in the 1950s and 1960s, architecture faces the risk of talking itself into an impasse, by resorting to certain languages and positions that may induce, and reproduce, a reification of social patterns. 
In this context I often think of a remark from Michel Ragon, the French architecture critic who wrote about and promoted experimental architecture in the 1960s. Looking back at those projects, twenty years later, he asked himself how a “life-like” macro-structure could be designed in advance, and if it could be designed at all, considering life is “rightly made of chance and unpredictability”. This remains a valid and important question, which is updated by our resort to instruments that allow us to think of, and manipulate, the world in terms of particles and parts. Quantum physics teaches us that there is irreducible uncertainty in our physical existence, an inherent contingency, and that there is a fundamental limit of precision with which you can actually measure a particle, hence a limit to the precision with which you can grasp the world. How is it that this uncertainty can be taken into account when dealing with matter or with information; and, when dealing with parts, how can we do so without first defining them? How can we account for interactions and relationality? How is it that we can account for change, for performance and transformation, all at once?
This brings me to a second point that stems from this a priori impossibility to capture the image of life without “to some extent captur[ing] life itself” (Ragon). I understand that Mereology makes a claim for exhaustibility and generality. But what if we take this claim into the architectural project? Do we think that we can actually design a system, a structure or a whole whose formal principles allow for it to be exhaustive? Following Gödel, I understand that you either have exhaustibility or consistency, but not both. 

Mario: Can I go back to the branch of theoretical philosophy to cover things? We more or less know why we in the design profession became interested in particles, and the relation between particles, in recent years. It seems he (Daniel) came across the term Mereology. He hijacked it and imported it into the architectural discourse. Like we always do. We take a more refined tool which comes from another discipline, and then we appropriate it and give it another meaning which means nothing to you (Giorgio). This we have been doing for a long time. This part of the story we know. The part of the story that we don’t know, that you can tell us in two lines is, does this happen with Mereology? Can you give us an outline of the history of analysis of Mereology in contemporary philosophical discourse? Because when I was a student nobody mentioned Mereology, and now everyone does? When did that happen? Where does this come from? And from a distance, from a critical point of view, why is it that you right now are talking about Mereology while many years ago nobody talked about it?

Giorgio: The word ‘Mereology’ is rather new and was made relatively popular by Stanisław Leśniewski at the beginning of the 20th century (according to Leśniewski, Mereology was more properly a branch of logic). However, philosophers (and in particular metaphysicians) have always used the notion of part and set forth theories about it. Plato’s theory of parthood has been recently analysed and defended by Verity Harte, while Aristotle’s theory of parthood is considered by several neo-Aristotelian metaphysicians a viable option in the contemporary mereological debate.

Mario: But, in math, there are fractions, proportions, modularity. These are all today discussed as mereological questions.

Giorgio: An important difference between many past theories of parthood (in particular in Ancient and Medieval philosophy) and contemporary Mereology concerns the expected domain of application: Plato, Aristotle, Abelard and Ockham were for example mainly interested in the parthood relation which connects a property with an individual instantiating those properties, or two properties one with another. These instances of parthood were important within metaphysics itself, for example when a theory of ideas or universals was elaborated. By contrast, contemporary Mereology is more focused on the concrete, spatio-temporal parts of concrete entities.
However, no matter what the original domain of application of the parthood relation was, the theories of parthood became progressively more abstract and formal: in some works of Leibniz (17th century), for example, it is possible to find a formally complex and highly abstract theory of parthood, whose principles are expected to hold irrespective of the domain of application. This is also the case of the theory of parthood developed by Bernard Bolzano in the 19th century. Thus, in spite of the fact that the word ‘Mereology’ became popular only in the 20th century, contemporary Mereology has solid roots in the history of philosophy. 
Nonetheless, it is true that – for example – forty years ago Mereology was much less popular than nowadays. This may have depended on the alternating fortunes of metaphysics (the wider branch of philosophy to which Mereology belongs) in analytic philosophy. Forty years ago analytic philosophers, in continuity with logical positivism, often despised metaphysics as an obsolete leftover from the past. This has changed dramatically in the later decades, thanks to the influence of thinkers such as David Lewis and Saul Kripke, and metaphysics is now back at the centre stage of contemporary analytic philosophy. The renewed popularity of Mereology is an aspect of the renewed popularity of metaphysics in general. This also depends on the fact that contemporary metaphysicians often attach great importance to the concepts of existence and identity. Classical Mereology has the ambition to provide existence and identity conditions for every complex entity. This makes Classical Mereology highly interesting for contemporary metaphysicians. 

Philippe: Let’s make a comparison with the discipline of architecture. In architecture, this last trend could be compared to what happened with Christopher Alexander, or before with Mies and then Peter Eisenman. The challenge for me is that I don’t consider Mereology an uninteresting philosophy in architecture, I just see it as a highly modernist theory.
My question is the following. According to you (Giorgio), in the field of philosophy, do you consider Mereology as a modernist philosophical trend or something that has nothing to do with philosophical modernism? Because in architecture, my feeling is that it directly corresponds to a highly modernist attitude, and the fact is that this modernist attitude is highly reductionist. It is defining what is the most elemental aspect of things, so it’s pure reductionism, and it’s still based on some concept of – maybe not order, but at least some attempt at bringing order into things (though sometimes “unpredictable order”).
For me, that is super modernist and my feeling is that we are living in a world built on this reductionist modernity. Right after this reduction – and we already had it in some form a hundred years ago –, let’s say after 1950 we were already going into the opposite direction: an explosion of models… That one is now based on statistical methods, on big data, as related by Mario in his book. So again, I’m not saying Mereology can’t be an important or at least a useful platform for debate, I am just wondering about the inherent nostalgia of going backward in the ordering of reality – in History. Maybe we can – and should – just accept absolute chaos and trillions of trillions of terabytes of data as a fact, without trying to put some order into that. So, my question finally on a purely philosophical level is: do you consider Mereology as modernist, or maybe as a new modern or late modern philosophical theory, or as something which has nothing to do with that?

Giorgio: There is indeed a modernist component in Mereology: the deliberate blindness to structure, which characterises Classical Mereology, is motivated by a form of “taste for desert landscapes”, which in turn might be seen as the outcome of a modernist appetite for order. However, it should also be considered that Classical Mereology includes either as an axiom or as a theorem (according to the way in which Classical Mereology is axiomatised) the principle of Unrestricted Composition, according to which – given some entities, no matter how sparse and gerrymandered they are – they compose something. Due to Unrestricted Composition, Classical Mereology is committed to the existence of all sorts of awkward entities, such as the fusion of my left arm, Barack Obama’s nose and the Great Pyramid of Giza!
On the other hand, a rather “modernist” thesis, which is often associated with Classical Mereology, is the thesis of Composition as Identity. According to the thesis of Composition as Identity, any whole is strictly speaking identical to its parts and is – so to say – no addition to being, with respect to them. This mereological thesis is expected to warrant a form of ontological economy, and can be seen, as a consequence, as the outcome of an appetite for order. 
However, Composition as Identity is not derivable from Classical Mereology, and is a highly problematic thesis in itself. A whole (for example, a chair) and its parts (the four legs, the back and the seat) are mutually discernible, inasmuch as – for example – the chair is one entity, while the four legs, the back and the seat are six entities. If they are discernible (i.e., if they have different properties), then it is not easy to make sense of the claim (entailed by Composition as Identity) that they are identical.

Casey: I think you have covered everything I want to say. Based on this I don’t think there is anything suggestively reductive about composition. I think that it is a ridiculous idea that unrestricted composition suggests that this property could be part of something.
My colleague Daniel is doing the mereological project, but it is certainly nothing reductive. I think it’s more that there is a very explicitness and straightforwardness about the roles and function of the thing, i.e. the function isn’t the exclusive part of the composition, especially according to the kind of lectures we saw today.

Mario: I have a suspicion. I see one main point of this symposium is that in the theory of parts of  today’s computation the parts we are dealing with are new in the history of architecture theory because they don’t need rules of application. These parts are different from Alberti’s or Eisenman’s because for the first time ever in the history of humankind or the history of design we can deal with parts without any rules or orders in them whether it is proportions, fractions, modules, geometrical symmetry, proportional symmetry, etc.
In the history of design, all these tricks and tools were needed to make sense out of parthood. We had to invent structures, like reductionism or data compression, to put some order into the chaos generated by the random accumulation of parts–to make order out of chaos; to manage parts in a “rational”, ie intelligible way: a way that made sense for the limited data-management skills of our own mind.  And now for the first time ever in many practical instances we are getting particles just as they are. We can put them flat on the table and each one of them stands, and that is all that we need. This the nobility of the parts that you’re dealing with. This is the novelty: parts without anthropocentric reduction and human-made intelligibility. 

Casey: Do you say that there are no rules for these parts or is it just that the rules are inherited in the parts and not applied to the total? I’m suspicious of saying that (the former) in dealing with parts. And again, we still have rules because we have generated something that is mereological. There are still rules but the rules are in the parts rather than trying to be imposed on them. And so actually, it is just where the rules are located in the design process. 

Mario: There must be rules of some sort somewhere, but the main difference, and again, I follow my suspicion, we no longer need rules to manage the accumulation of parts beyond the limit of computational (ie machinic) retrieval.  We don’t need to structure them in symmetrical parthood or any other strategy for part retrieval. We always needed some superposition over the structure to reduce the complexity of what was so big that we couldn’t deal with it. Now when dealing with something so big, we can just let the machines deal with it.  The generation process must have some rules somewhere, but my suspicion is these are no longer needed for any practical human purpose. Now we are capable of managing any messy random heap of disconnected parts–because if fact we don’t have to deal with that mess any more: we have machine to do it in our stead.

Emmanuelle: One simple question would be: what kind of parts are we dealing with? Are they not themselves wholes composed of other parts, entering into larger or different wholes? Are we talking solely about human-made parts, which designers can generate, craft and master, or we are considering opening up these wholes to other domains; thus, to what degree and within which limit are they potentially extendable?
You’ll excuse me for coming back to my previous point, regarding the notion of uncertainty and how it can be taken into account, and let’s hypothesise the wholes we consider are governmental ensembles. The researcher in philosophy of law Antoinette Rouvroy identifies how uncertainty and unpredictability are systematically considered as risk. She analyses how the cybernetic and algorithmic order that underlie our contemporary forms of governance attempt to systematically and preemptively tackle risk in order to eradicate it. On the other side, there is a reverse relationship to risk that, against risk management, consists in exploiting it and profiting from it, as you can see in high frequency trading. Risk here appears to be the motor of speculation, it plays with the asymmetric distribution of information within a system.
But if you consider chance, and hence uncertainty and unpredictability, as being not epistemic – as in both aforementioned cases – but objective, and furthermore, if you consider it to be at the source of all life in the biosphere – as Biology Nobel Prize Jacques Monod showed – how can it be taken into account and integrated in the elaboration of hybrid parts and wholes? Embracing this objectivity could allow us to conceptualise a commonality based on an open, decentralised notion of whole that is not subjected to social constructivism.

Giorgio: I owe an answer to Emmanuelle about unpredictability. Unpredictability can be either an epistemic phenomenon (it happens when some human subjects are de facto unable to foresee how things will go, and their inability to do so might be due to their contingent cognitive limitations), or a metaphysical phenomenon (there is metaphysical unpredictability when something is objectively indeterminate, independently of any fact concerning human subjects). If unpredictability is seen as an epistemic phenomenon, then it does not require any modification of Mereology: the fact that some human subjects are unable to determine whether x is part of y has no impact on the circumstance whether objectively x is part of y
The philosophical consequences of quantum indeterminacy are hard to interpret: according to some interpretations, it is indeed a kind of objective, metaphysical indeterminacy. However, as far as I can see, quantum indeterminacy does not concern mereological relations. Thus, it seems to me that neither epistemic nor metaphysical unpredictability have any specific bearing on Mereology.

Daniel: Unpredicted and indeterminant like a good building, it seems to me that Emmanuelle and Giorgio overcame the boundaries of the round table. I would like to use the moment to thank you all for your insights, contributions, and round up the discussion with an open ending.

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Daniel Koehler, 2020
Introduction to Issue 01: Mereologies
Architecture, Architecture Theory, Discrete Architecture, Mereologies, Mereology, Philosophy
Daniel Koehler
University of Texas at Austin
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Part relationships play an important role in architecture. Whether an aspect of a Classical order, a harmonious joining of building components, a representation of space, a partition of spaces, or as a body that separates us and identifies us as individuals. From the very outset, every form of architecture begins with an idea of how parts come together to become a whole and an understanding of how this whole relates to other parts. Architecture first composes a space as a part of a partitioning process well before defining a purpose, and before using any geometry.

The sheer performance of today’s computational power makes it possible to form a world without a whole, without any third party or a third object. Ubiquitous computing fosters peer-to-peer or better part-to-part exchange. It is not surprising then that today’s sharing represents an unfamiliar kind of partiality. From distributive manufacturing to the Internet of Things, new concepts of sharing promise systematic shifts, from mass-customisation to mass-individualisation: the computational enabled participations are foundational. It is no longer the performance or mode of an algorithm that drives change but its participatory capacities. From counting links, to likes, to seats, to rooms: tools for sharing have become omnipresent in our everyday lives. Thus, that which is common is no longer negotiated but computed. New codes – not laws or ideologies – are transforming our cities at a rapid pace, but what kind of parthood is being described? How does one describe something only through its parts today? To what extent do the automated processes of sharing differ from the partitioning of physical space? How can we add, intervene and design such parts through architecture?

The relationship between parts and their whole is called Mereology. In this issue of Prospectives, mereology’s theories and the specifics of part-relations are explored. The differences between parts and the whole, the sharing of machines and their aesthetics, the differences between distributive and collective, their ethical commitments, and the possibilities of building mereologies are discussed in the included articles and interviews.

Just as mereology describes objects from their parts, this issue is partial. It is not a holistic proposal, but a collection of positions. Between philosophy, computation, ecology and architecture, the texts are reminders that mereologies have always been part of architecture. Mereology is broadly a domain that deals with compositional possibilities, relationships between parts. Such an umbrella – analogue to morphology, typology, or topology – is still missing in architecture. Design strategies that depart part-to-part or peer-to-peer are uncommon in architecture, also because there is (almost) no literature that explores these topics for architectural design. This issue hopes to make the extra-disciplinary knowledge of mereology accessible to architects and designers, but also wishes to identify links between distributive approaches in computation, cultural thought and built space.

The contributions gathered here were informed by research and discussions in the Bartlett Prospectives (B-Pro) at The Bartlett School of Architecture, UCL London from 2016 to 2019, culminating in an Open Seminar on mereologies which took place on 24 April 2019 as part of the Prospectives Lecture Series. The contributions are intended as a vehicle to inject foundational topics such as mereology into architectural design discourse.

The Contributions

This compilation starts with Giorgio Lando’s text “Mereology and Structure”. Lando introduces what mereology is for philosophers, and why philosophers discuss mereological theses, as well as disagree one with another about them. His text focuses in particular on the role of structure in mereology outlining that from a formal point of view part relations are freed from structure. He argues that independence from structure might be the identifying link between mereology and architecture. The second article “From Partitioning to Partaking” is a plea for re-thinking the city. Daniel Koehler’s essay points to the differences between virtual and real parts. Koehler observes a new spatial practice of virtual representations that render previous models of urban governance obsolete. He argues that the hyper-dimensional spaces of a big data-driven economy demand a shift from a partitioning practice of governance to more distributed forms of urban design. In “Matter versus Parts: The Immaterialist Basis of Architectural Part-Thinking” Jordi Vivaldi Piera highlights the revival of matter in parallel to the discrete turn in contemporary discourses on experimental architecture. The essay gravitates around the notion of part-thinking in association with the notion of form. Fluctuating between continuous and discrete, the text sets out requirements for radical part-thinking in architecture. As a computational sociologist, David Rozas illustrates the potential of decentralised technologies for democratic processes at the scale of neighborhood communities. After an introduction to models of distributed computation, “Affordances of Decentralised Technologies for Commons-based Governance of Shared Technical Infrastructure” draws analogies to Elinor Ostrom’s principles of commons governance and how those can be computationally translated, turning community governance into fully decentralised autonomous organisations.

Departing from the Corbusian notion of a ‘machine for living’, Sheghaf Abo Saleh defines a machine for thinking. In “When Architecture Thinks! Architectural Compositions as a Mode of Thinking in the Digital Age” Abo Saleh states that the tectonics of a machine that thinks is brutal and rough. As a computational dialogue, she shows how roughness can enable posthumanism which, in her case, turns “tempered” parts into a well-tempered environment. Ziming He’s entry point for “The Ultimate Parts” is the notion of form as the relations between parts and wholes. He’s essay sorts architectural history through a mereological analysis, proposing a new model of part-to-part without wholes. Shivang Bansal’s “Towards a Sympoietic Architecture: Codividual Sympoiesis as an Architectural Model” investigates the potential of sympoiesis. By extending Donna Haraway‘s argument of “tentacular thinking” into architecture, the text shifts focus from object-oriented thinking to parts. Bansal argues for the limits of autopoiesis as a system and conceptualises spatial expressions of sympoiesis as a necessity for an adaptive and networked existence through “continued complex interactions” among parts.

Merging aspects of ‘collective’ and ‘individuality,’ in “Codividual Architecture within Decentralised Autonomous System” Hao Chen Huang proposes a new spatial characteristic that she coins as the “codividual”. Through an architectural analysis of individual and shared building precedents, Huang identifies aspects of buildings that merge shared and private features into physical form. Anthony Alviraz’s paper “Computation Within Codividual Architecture” investigates the history and outlook of computational models into architecture. From discrete to distributed computation, Alviraz speculates on the implications of physical computation where physics interactions overcome the limits of automata thinking. InSynthesizing Hyperumwelten”, Anna Galika transposes the eco-philosophical concept of an HyperObject into a “Hyperumwelt”. While the Hyperobject is a closed whole that cannot be altered, a Hyperumwelt is an open whole that uses objects as its parts. The multiple of a Hyperumwelt offers a shift from one object’s design towards the impact of multiple objects within an environment.

Challenging the notion of discreteness and parts, Peter Eisenman asks in the interview “Big Data and the End of Architecture Being Distant from Power” for a definition of the cultural role of the mereological project. Pointing to close readings of postmodern architecture that were accelerated by the digital project, Eisenman highlights that the demand for a close reading is distanced from the mainstream of power. The discussion asks: ultimately, what can an architecture of mereology critique? The works of Herman Hertzberger are an immense resource on part-thinking. In the interview “Friendly Architecture: In the Footsteps of Structuralism”, Herman Hertzberger explains his principle of accommodation. When building parts turn into accommodating devices, buildings turn into open systems for staging ambiguity.**

The issue concludes with a transcript from the round table discussion at the Mereologies Open Seminar at The Bartlett School of Architecture on 24 April 2019.


The contributions evolved within the framework of Bartlett Prospectives (B-Pro) at The Bartlett School of Architecture, UCL. I want to thank Frédéric Migayrou for his vision, commitment and long years of building up a research program, not only by architecture but through computation. I would like to thank Roberto Bottazzi for the years of co-organising the Prospectives Lecture Series, where plenty of the discussions that form the backbone of this issue took place. Thanks to Mario Carpo for raising the right question at the right time for so many people within the program, thanks to Andrew Porter for enabling so many events, to Gilles Retsin, for without the discrete there are no parts, Mollie Claypool for the editing and development of Prospectives journal, and Vera Buehlmann, Luciana Parisi, Alisa Andrasek, Keller Easterling, Matthew Fuller, John Frazer, Philippe Morel, Ludger Hovestadt, Emmanuelle Chiappone-Piriou, Jose Sanchez, Casey Rehm, Tyson Hosmer, and Jordi Vivaldi Piera for discussions and insights. 

I want to thank Rasa Navasaityte, my partner in Research Cluster 17 at B-Pro, for driving the design research. Thank you for the research contributed by the researchers and tutors: Christoph Zimmel, Ziming He, Anqi Su, Sheghaf Abo Saleh, and to all participants, specifically to highlight: Genmao Li, Zixuan Wang, Chen Chen, Qiming Li, Anna Galika, Silu Meng, Ruohan Xu, Junyi Bai, Qiuru Pu, Anthony Alviraz, Shivang Bansal, Hao-Chen Huang, Dongxin Mei, Peiwen Zhan, Mengshi Fu, Ren Wang, Leyla El Sayed Hussein, Zhaoyue Zhang, Yao Chen, and Guangyan Zhu.

The issue includes articles that evolved from thesis reports conducted in the following clusters: Ziming He from Research Cluster 3 tutored by Tyson Hosmer, David Reeves, Octavian Gheorghiu, and Jordi Vivaldi in architecture theory. Sheghaf Abo Saleh, Anthony Alvidrez, Shivang Bansal, Anna Galika, Hao Chen Huang from Research Cluster 17 tutored by Daniel Koehler and Rasa Navasaityte. If not indicated directly, the featured images, graphics of this issue are by Daniel Koehler, 2020.

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When Architecture Thinks! Architectural Compositions as a Mode of Thinking in the Digital Age
Architecture, Building, Environmental Design, Mereologies, Mereology
Sheghaf Abo Saleh
University College London
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“One must turn the task of thinking into a mode of education in how to think.”[1]

These words from the philosopher Martin Heidegger point towards new modes of thinking. As architects, one can mention Mario Carpo’s remark about the huge amounts of data that are available for everyone nowadays: most of it is underused.[2] As this essay will argue, this new condition of Big Data, and the digital tools used to comprehend and utilise it, can trigger an entirely new way of thinking about architecture. It is a way to both open doors for testing, and an opportunity to look back into history and re-evaluate certain moments in new ways. As an example one can take Brutalism, which emerged as a post-war period solution in the 1950s. It was a new mode of thinking about architecture that was influenced by Le Corbusier’s Unité d’Habitation de Grandeur Conforme, Marseilles (1948–54), the Industrial Revolution and the age of the mechanical machine. Brutalism can be read as the representation of reading the building as a machine at that time. Luciana Parisi has expanded on this idea, writing that Brutalism can be considered as the start of thinking about architecture as a digital machine, having removed any notion of emotion from the architectural product, leaving a rough mass of materials and inhabitable structures.[3] In Parisi’s sense, brutal architecture can then be read as a discrete system of autonomous architectural parts brought together with a set of rules: symmetry, asymmetry, scales, proportions, harmony, etc. These rules, materials and structures act autonomously using collective behaviours to produce data. The data can then be translated into concrete compositional elements which form a building, a city or a whole territory. The adjacencies between each discrete compositional element creates the relations between those parts.

Figure 1 – Thinking parts interacting to produce a building. Image: Espen Dietrichson, Hard Edges, Cloudy Cities, Galleri Haaken, 2018.

The Building Thinking Machine  

The building as a machine departs from Le Corbusier’s claim for a functional architecture.[4] Today, the use of machine learning and artificial intelligence means that machines are no longer used only for making. They are thinking machines.[5] This allows a new translation of Le Corbusier’s understanding of function, asking the questions: what if architecture acts as a mode of thinking? How would a building as a thinking machine perform? 

The generation following Le Corbusier progressed the building machine. Regner Banham linked the building machine to comfort and the environment,[6] seeing the building as a kit of tools that provide comfort. In other studies, Reyner Banham proposed the building as a package which is totally enclosed and isolated from the external environment, referring to this as “the environmental bubble”. He proposed that surrounding the building with one thick layer that protected the internal space was the best solution to provide a well-tempered environment. Yet Banham presents a clear separation between the interior and exterior spaces which no longer matches the complexity of interior-exterior relationships at both urban and architectural scales. 

Mereological Reading of Architectural Precedents

Different types of systems that provide for a well-tempered environment inside the building distinguish difference between inside and outside as the difference between a well- and non-tempered environment. Mereology, or the study of parts-relations,[7] can be used as a methodology to read a building in terms of its compositional aspects. 

One historical example is the Rasoulian House (1904) which was designed to provide a state of comfort for its users throughout the year. A basic architectural element known as the wind catcher tower, or Malqaf, provided the building with breeze. As Sarinaz Suleiman described, the Malqaf is a composition of architectural elements that work together to create air flow. These elements include walls, doors, rooms and include the basement and the courtyard, organised in a specific order, proportions and orientation to create specific relationships between the inside and the outside.[8] 

The Malgaf is the first point at which air flow enters the building. It then travels down a shaft which is the first interior space that the wind interacts with. The air continues to a second interior space through a window-like opening into a room, and then is moved through an opening in the room’s floor to a cellar space under the building. This third interior space is the coolest space in the building. The cellar is connected to the courtyard through an opening that facilitates air circulation and absorbs wind. For this to happen, two kinds of relationships need to exist: the exterior relation formed by the geometry of two elements, e.g. the height of the Malqaf and the width of the courtyard which help to create a high difference in air pressure, and an internal relation which is controlled by the openings between the interior spaces and between interior and exterior spaces as well. Ventilation is not only a void space, but another level of interiority inside the building. 

Figure 2 – An architectural precedent for ventilation, Rasolian house in Yazd city, Iran, 19th century. Image: Sheghaf Abo Saleh, 2020.

Another example of a complex ventilation system is a data centre building.[9] Data centres usually produce vast thermal exhaust which requires constant air movement, requiring large depths to ceilings and floors which may be as big as the building itself. Servers are positioned in the room with a certain distance between each other. This distance is related to the degree of temperature and the air circulation speed. Higher temperatures inside the room are used to decrease air pressure and create a pressure difference that enables air circulation naturally in the room. The path that the air travels allows the air the time it needs to cool down naturally.

Computational Ventilation

Hundreds of years ago, Vitruvius described wind, saying that “wind is a flowing wave of air with an excess of irregular movements. It is produced when heat collides with moisture, and the shock of the crash expels its force in a gust of air.”[10] Vitruvius’ definition can be deconstructed into two parts, the first of which deals with the dominant wind direction and its relation to the outer envelope of the building. This concept was emphasised by Vitruvius’ example of the Octagon Marble Tower (15th century BC). The second part relates to the process of creating wind flow in nature. Vitruvius explains that air circulation occurs when two different air pressures encounter each other. The difference in the air pressure always happens as a result of changes in temperature and moisture. High temperature heats up the air causing low density and consequently low pressure areas, and lower temperature will create a high pressure area. This concept is the logic that has been followed in all passive ventilation systems throughout history. These systems tend to create two points with a high difference in pressure, connecting these two points with a path that needs to be ventilated. This path would then move through the building accelerating air movement from the high pressure area to the low pressure area creating air flow inside the building.

Figure 3 – The Octagon Marble Tower, Athens, Greece. Image: Included in Vitruvius’ Ten Books on Architecture, 15th century BC.

A traditional building from the Middle East can be taken as a case study for applying thermodynamic logic to create natural air circulation in a building. In the previous example of  Rasolian House, the side that is exposed to the sun is heated up by the sun. Consequently, air pressure decreases. The geometry that is exposed to the sun creates shadowed areas inside and outside of the building. These shadowed areas are much colder and have high air pressure. Air circulates from the high pressure to low pressure areas. That means air can move from a cooler courtyard to an upper space located above it. This air movement absorbs the air from inside the building to fill in the void in the courtyard that the high pressure air had left behind when it moves upwards. Due to the opening at the top of the shaft, air will enter the building to fill in the void that the inner air has left behind as well. This air replacement creates the air circulation inside the building. The creation of wind is dependent on the design of the inner space and its relation to the outer space through openings. This means that, by closing and allowing openings, wind can be created or stopped, and by changing some openings, the wind flow path can be changed, and wind speed could increase or decrease. This follows a logic of discrete, combinatorial air flow.

Figure 4 – Section in a wind catcher shows the path of the wind as a binary system controlled by switching circuits. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.

Computation Ventilation on the Urban and Architectural Scale

The building can be seen as a machine for creating an environmental condition through compositional thinking. This way of thinking turns the building, in the case of the Malgarf, into a switch that can turn the air flow on and off.  In this instance, the creation of wind is entirely dependent on a series of elements that are well- organised and ordered. From this combinatorial thinking, wind can be read as a form of pre-digital computation considering the inside-outside sequences as what causes the air flow.

The order of inside-outside also plays an important role in disrupting air flow. A single element that has been extracted from a building can serve as an example. It is a corridor, but at the same time this element plays a crucial role in creating wind. The way that the walls are arranged produces a contrast between the inside-outside spaces. Moreover, the design and arrangement of the openings turns the corridor into a path for air. Taking this element as a discrete part, and rearranging its parts within the same local rules that have been set over the ventilation logic, another version of the element emerges. Following this same logic would give different versions of different elements. Further on, each version of each element has its discreteness and can be upscaled. With this upscaling strategy, more complex interiors emerge.

Figure 5 – (clockwise, from upper left) Extracted element from a church in Finland; new version of the element with mereological changes; arrangement of ten elements combined in a way that ensures the wind flow runs through the whole system; the path that wind flow draws. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.

By integrating an environmental aspect within the design process, a new type of building that embraces another wind geometry can be created. This provides an opportunity to design highly dense architectural forms that can reassure the qualities of the internal space. By nesting interiors one can create different low and high pressure areas over inside-outside sequences.

Figure 6 – Different arrangements of [-][+] situations and what they create as wind patterns, the discreteness of the wind flow, wind-geometry. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.

This allows a rethinking of the inside-outside arrangement in the city according to what positive or negative sequences are created. For example, for more similar interiors less contrast in air pressure needs to be produced. For more variation between the interiors, the contrast in the air pressure needs to increase and more air will flow. An air circulation concept can be used as a means to arrange both interior and exterior spaces in the building and in the city.

Figure 7 – A range of building fragments with the same number of elements but different [-][+] sequences, by more to less wind flow. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.

Achieving Banham’s Campfire

At an architectural scale the interior-exterior relation can also be managed by the building façade. The façade tends to be used to provide separation between indoor and outdoor spaces as well as between a tempered and non-tempered environment in order to achieve comfort. However, a new understanding of wind circulation can provide a well-tempered environment regardless of the façade. In other words, façade here can be seen as the tools or the elements that provide comfort and facilitate air circulation inside the building.

A façade needs to meet specific criteria in order to generate a difference in air pressure just like the inside-outside arrangement in the city scale. Three design parameters can support this: the orientation of the elevation in relation to the sun, the number of layers that are needed to create more or less tempered areas and the degree of translucency of the façade that helps to prevent or allow sunlight which helps in its turn to reach the preferred temperature. The facade is not any more the envelope of the building, it is the layers that are responsible for providing the comfort inside the building.

Figure 8 – Building fragments. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.

Indeed, thinking about architecture through architecture’s interiors can expose low-tech computation that starts from a thermodynamic discreteness. This enables the understanding of spatial sequence that can support different levels of space in a building and the notion of layers of building-in-buildings. If this concept is upscaled to the scale of the city it could be an opportunity to study the kinds of patterns that mereology can create utilising environmental thinking. This means that a building, or even a city, could become an example of the campfire that Banham aimed to reach many years ago.[11]

Figure 10 – Building fragment implemented with the façade concept. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.
Figure 11 – Building fragment implemented with the façade concept. Image: Sheghaf Abo Saleh, RC17, The Bartlett School of Architecture, UCL, 2018.


[1] M. Heidegger, The End of Philosophy, trans. Joan Stambaugh (Cambridge University Press, 2003).

[2] M. Carpo, The Second Digital Turn: Design Beyond Intelligence, (Cambridge, Massachusetts: MIT Press, 2017).

[3] L. Parisi, “Reprogramming Decisionism,” e-flux, 85 (2017).

[4] Le Corbusier, Eyes That Do Not See  in Towards a New Architecture, (London: The Architectural Press, 1927), 107.

[5] M. Carpo, “Excessive Resolution: Artificial Intelligence and Machine Learning in Architectural Design,” Journal of Architectural Record (2018),, last accessed 3 May 2019.

[6] R. Banham, “Machines A habiter”, The Architecture of the Well-tempered Environment, (Chicago: Chicago Press, 1969).

[7] A. Varzi, “Mereology Then and Now”, Journal of Logic and Logical Philosophy, 24 (2015), 409-427.

[8] S. Suleiman, “Direct comfort ventilation: Wisdom of the past and technology of the future (wind-catcher),” Journal of Sustainable Cities and Society, 5, 1 (2012 ), 8-15.

[9] M. de Jong, “Air Circulation in Data Centres: rethinking your design” , Data Centre Knowledge, (2014),, last accessed 5 May 2019.

[10] M. P. Vitruvius, “First Principles and The Layout of Cities,” Ten Books on Architecture, ed. Ingrid D. Rowland (Cambridge: Cambridge University Press, 1999), 21-32.

[11] R. Banham, “The kit of parts: heat and light,” The Architecture of the Well-tempered Environment (Chicago: Chicago Press, 1969).

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Penrose block simulation allowing objects to interact with on a large scale and within three dimensions, forming a single whole object. Image: Anthony Alvidrez, Large City Architecture, RC17, The Bartlett School of Architecture, UCL, 2018.
Architectural Computation Within Codividual Architecture
Architecture, City Architecture, Composition, Computational Design, Mereologies, Mereology, Urban Design
Anthony Alvidrez
University College London
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The design research presented here aims to develop a design methodology that can compute an architecture that participates within the new digital economy. As technology advances, the world needs to quickly adapt to each new advancement. Since the turn of the last century, technology has integrated itself within our everyday lives and deeply impacted the way in which we live. This relationship has been defined by TM Tsai et al. as “Online to Offline” or “O2O” for short.[1] What O2O means is defining virtually while executing physically, such as platform-based companies like Uber, AirBnb, and Groupon do. O2O allows for impact or disruption of the physical world to be made within the digital world. This has significantly affected economies around the world. 

Paul Mason outlined in Post Capitalism: A Guide to our Future (2015) that developments in technology and the rise of the internet have created a decline in capitalism, which is being replaced by a new socio-economic system called “Post Capitalism”. As Mason describes,“technologies we’ve created are not compatible with capitalism […] once capitalism can no longer adapt to technological change”.[2] Traditional capitalism is being replaced by the digital economy, changing the way products are produced, sold and purchased. There is a new type of good which can be bought or sold: the digital product. Digital products can be copied, downloaded and moved an infinite number of times. Mason states that it is almost impossible to produce a digital product through a capitalist economy due to the nature of the digital product. An example he uses is a program or software that can be changed throughout time and copied with little to no cost.[3] The original producer of the product cannot regain their cost as one can with a physical good, leading to traditional manufacturers losing income from digital products. With the increase in digital products, the economy must be adapted. 

In The Second Digital Turn (2017) Mario Carpo describes this phenomenon, stating that digital technologies are creating a new economy where production and transactions are done entirely algorithmically, and as a result are no longer time-consuming, labour intensive or costly. This leads to an economy which is constantly changing and adapting to the current status of the context in which it is in. Carpo describes the benefits of the digital economy as the following: “[…] it would appear that digital tools may help us to recreate some degree of the organic, spontaneous adaptivity that allowed traditional societies to function, albeit messily by our standards, before the rise of modern task specialisation.”[4]

Computational Machines

It is useful to look at the work of Kurt Gödel and his theorems for mathematical logic, which are the basis for computational logic. In his first theorem the term “axioms” is presented, which are true statements that can be proven as true. The theorem states that “If axioms do not contradict each other and are ‘listable’ some statements are true but cannot be proved.”[5] This means that any system based on mathematical statements, axioms, cannot prove everything unless additional axioms are added to the list. From this Gödel describes his second theorem, “A system of axioms cannot show its inconsistency.”[6] To relate this to programming, axioms can be seen as similar to code, yet everything cannot be proven from a single system of code. 

Allen Turing’s work on computable numbers is a result of these two theorems by Gödel. Turing was designing a rigorous notion of effective computability based on the “Turing Machine”. The Turing Machine was to process any given information based on a set of rules, or a programme the machine follows, provided by the user for a specified intention. The machine is fed with an infinitely long tape, divided into squares, which contains a sequence of information. The machine would “scan” a symbol, “read” the given rules, “write” an output symbol, and then move to the next symbol. As Turning described, the “read” process refers back to the rule set provided: the machine would look through the rules, find the scanned symbol, then proceed to follow the instructions of the scanned symbol. The machine then writes a new symbol and moves to a new location, repeating the process over and over until it is told to by the ruleset to halt or stop the procedure and deliver an output.[7] Turing’s theories laid down the foundation for the idea of a programmable machine able to interpret given information based on a given programme. 

When applying computational thinking to architecture, it becomes evident that a problem based in the physical requires a type of physical computation. By examining the work of John von Neumann in comparison with Lionel Sharples Penrose the difference between the idea of a physical computational machine and a traditional automata computation can be explored. In Arthur W. Burks’s essay ‘Von Neumann’s Self-Reproducing Automata’ (1969) he describes von Neumann’s idea of automata, or the way in which computers think and the logic to how they process data. Von Neumann developed simple computer automata that functioned on simple switches of “and”, “or”, and “not”, in order to explore how automata can be created that are similar to natural automata, like cells and a cellular nervous system, making the process highly organic and with it the ability to compute using physical elements and physical data. Von Neumann theorised of a kinetic computational machine that would contain more elements than the standard automata, functioning in a simulated environment. As Burks describes, the elements are “floating on the surface, […] moving back and forth in random motion, after the manner of molecules of a gas.”[8] As Burks states, von Neumann utilised this for “the control, organisational, programming, and logical aspects of both man-made automata […] and natural systems.”[9] 

However this poses issues around difficulty of control, as the set of rules are simple but incomplete. To address this von Neumann experimented with the idea of cellular automata. Within cellular automata he constructs a series of grids that act as a framework for events to take place, or a finite list of states in which the cell can be. Each cell’s state has a relation to its neighbours. As states change in each cell, this affects the states of each cell’s neighbour.[10] This form of automata constructs itself entirely on a gridded and highly strict logical system.

Von Neumann’s concept for kinetic computation was modelled on experiments done by Lionel Sharples Penrose in 1957. Penrose experimented with the intention of understanding how DNA and cells self-replicate. He built physical machines that connected using hooks, slots and notches. Once connected the machines would act as a single entity, moving together forming more connections and creating a larger whole. Penrose experimented with multiple types of designs for these machines. He began with creating a single shape from wood, with notches at both ends and an angled base, allowing the object to rock on each side. He placed these objects along a rail, and by moving the rail forwards and backwards the objects interacted, and, at certain moments, connected. He designed another object with two identical hooks facing in opposite directions on a hinge. As one object would move into another, the hook would move up and interlock with a notch in the other element. This also allowed for the objects to be separated. If three of these objects were joined, and a fourth interlocked at the end, the objects would split into two equal parts. This enabled Penrose to create a machine which would self-assemble, then when it was too large, it would divide, replicating the behaviours of cellular mitosis.[11] These early physical computing machines would operate entirely on kinetic behaviour, encoding behaviours within the design of the machine itself, transmitting data physically.   

Experimenting with Penrose: Physical Computation

The images included here are of design research into taking Penrose objects into a physics engine and testing them at a larger scale. By modifying the elements to work within multiple dimensions, certain patterns and groupings can be achieved which were not accessible to Penrose. Small changes to an element, as well as other elements in the field, affect each other in terms of how they connect and form different types of clusters. 

Figure 1 – Modified Penrose object simulation testing how individual objects interact and join together, forming patterns and connections through fusion. Image: Anthony Alvidrez, Large City Architecture, RC17, The Bartlett School of Architecture, UCL, 2018.

In Figure X, there is a spiralling hook. Within the simulations the element can grow in size, occupying more area. It is also given a positive or negative rotation. The size of the growth represents larger architectural elements, and thus takes more of the given space within the field. This leads to a higher density of elements clustering. The rotation of the spin provides control over what particular elements will hook together. Positive and positive rotations will hook, as well as negative and negative ones, but opposite spins will repeal each other as they spin.

Figure 2 – Penrose block simulation allowing objects to interact with on a large scale and within three dimensions, forming a single whole object. Image: Anthony Alvidrez, Large City Architecture, RC17, The Bartlett School of Architecture, UCL, 2018.

Through testing different scenarios, formations begin to emerge, continuously adapting as each object is moving. At a larger scale, how the elements will interact with each other can be planned for spatially. In larger simulations certain groupings can be combined together to create larger formations of elements connected through strings of hooked elements. This experimentation leads towards a new form of architecture referred to as “codividual architecture”, or a computable architectural space created using the interaction and continuous adaptation of spatial elements. The computation of space occurs when individual spaces fuse together, therefore becoming one new space indistinguishable from the original parts. This process continues, allowing codividual architecture of constant change and adaptability.

Codividual Automata

Codividual spaces can be further supported by utilising machine learning, which computes parts at the moment they fuse with other parts, the connection of spaces, the spaces that change, and how parts act as a single element once fused together. This leads to almost scaleless spatial types of infinite variations. Architectural elements move in a given field and through encoded functions – connect, move, change and fuse. In contrast to what von Neumann was proposing, where the elements move randomly similar to gaseous molecules, these elements can move and join based on an encoded set of rules.

Figure 3 – Codividual architecture using machine learning. Image: COMATA, Anthony Alvidrez, Hazel Huang, and Shivang Bansal, Large City Architecture, RC17, The Bartlett School of Architecture, UCL, 2019.

Within this type of system that merges together principles of von Neumann’s automata with codividuality, traditional automata and state machines can be radically rethought by giving architectural elements the capacity for decision making by using machine learning. The elements follow a set of given instructions but also have additional knowledge allowing them to assess the environment in which they are placed. Early experiments, shown here in images of the thesis project COMATA, consisted of orthogonal elements that varied in scale, creating larger programmatic spaces that were designed to create overlaps, and interlock, with the movement of the element. The design allowed for the elements to create a higher density of clustering when they would interlock in comparison to a linear, end-to-end connection.

Figure 4 – Barcelona super block simulation. Image: COMATA, Anthony Alvidrez, Anthony Alvidrez, Hazel Huang, and Shivang Bansal, Large City Architecture, RC17, The Bartlett School of Architecture, UCL, 2019.

This approach offers a design methodology which takes into consideration not only the internal programme, structure and navigation of elements, but the environmental factors of where they are placed. Scale is undefined and unbounded: each part can be added to create new parts, with each new part created as the scale grows. Systems adapt to the contexts in they are placed, creating a continuous changing of space, allowing for an understanding of the digital economics of space in real time.


[1] T. M. Tsai, P. C. Yang, W. N. Wang, “Pilot Study toward Realizing Social Effect in O2O Commerce Services,” eds. Jatowt A. et al., Social Informatics, 8238 (2013).

[2] P. Mason, Postcapitalism: A Guide to Our Future, (Penguin Books, 2016), xiii.

[3] Ibid, 163.

[4] M. Carpo, The Second Digital Turn: Design Beyond Intelligence (Cambridge, Massachusetts: MIT Press, 2017), 154.

[5] P. Millican, Hilbert, Gödel, and Turing [Online] (2019),, last accessed May 2 2019.

[6] Ibid.

[7] A. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, 1, 2-42, (1937), 231-232.

[8] A. W. Burks, Von Neumann's Self-Reproducing Automata; Technical Report (Ann Arbor: The University of Michigan, 1969), 1.

[9] A. W. Burks, Essay on Cellular Automata, Technical Report (Urbana: The University of Illinois Press, 1970), 5.

[10] A. W. Burks, Essay on Cellular Automata, Technical Report (Urbana: The University of Illinois Press, 1970), 7-8.

[11] L. S. Penrose, “Self-Reproducing Machines,” Scientific American, 200 (1959), 105-114.

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Mereology, WanderYards, Genmao Li, Chen Chen and Xixuan Wang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2017.
From Partitioning to Partaking, or Why Mereologies Matter
Architecture, Building, Digital, Digital Architecture, Discrete Architecture, Mereologies, Mereology, Participatory Design, Virtual
Daniel Koehler
University of Texas at Austin
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Parts, chunks, stacks and aggregates are the bits of computational architecture today. Why do mereologies – or buildings designed from part-to-whole – matter? All too classical, the roughness of parts seems nostalgic for a project of the digital that aims for dissolving building parts towards a virtual whole. Yet if parts shrink down to computable particles and matter, and there exists a hyper-resolution of a close to an infinite number of building parts, architecture would dissolve its boundaries and the capacity to frame social encounters. Within fluidity, and without the capacity to separate, architecture would not be an instrument of control. Ultimately, freed from matter, the virtual would transcend from the real and form finally would be dead. Therein is the prospect of a fluid, virtual whole.

The Claustrophobia of a City that Transcends its Architecture

In the acceleration from Data to Big Data, cities have become more and more virtual. Massive databases have liquefied urban form. Virtual communication today plays freely across the material boundaries of our cities. In its most rudimentary form virtuality is within the digital transactions of numbers, interests and rents. Until a few years ago,  financial investments in architectural form were equatable according to size and audience, e.g. as owner-occupied flats, as privately rented houses or as lease holding.[1] Today capital flows freely scatter across the city at the scale of the single luxury apartment. Beyond a certain threshold in computational access, data becomes big. By computing aggregated phone signal patterns or geotagged posts, virtual cities can emerge from the traces of individuals. These hyperlocal patterns are more representative of a city than its physical twin. Until recently, architecture staged the urban through shared physical forms: the sidewalk, lane or boulevard. Adjacent to cars, walkable for pedestrians or together as citizens, each form of being urban included an ideology of a commons, and grounded with that particular parts of encountering.

Figure 1 – (left to right) Floor area comparisons between housing projects from the Brutalist era (top) and today (bottom): Previ, Atelier 5 vs Seguro, Kerez La Sainte-Baume, Le Corbusier vs The Mountain, BIG; La Muralla Roja Calpe, Bofill vs Communal Villa, Dogma. Image: Daniel Koehler.

In contrast, a hyper-local urban transcends lanes and sidewalks. Detached from the architecture of the city, with no belonging left, urban speculation has withdrawn into the private sphere. Today, urban value is estimated by counting private belongings only, with claustrophobic consequences. An apartment that is speculatively invested displaces residents. The housing shortage in the big cities today is not so much a problem of lack of housing, but instead of vacant space, accessible not to residents but to interests they hold in the hyper-urban.[2] The profit from rent and use of space itself is marginal compared to the profit an embodied urban speculation adds to the property. The possibility of mapping every single home as data not only adds interest, like a pension to a home but literally turns a home into a pension.[3] However this is not for its residents but for those with access to resources. Currently, computing Big Data expands and optimises stakeholders’ portfolios by identifying undervalued building assets.[4] However, the notion of ‘undervalued’ is not an accurate representation of assets.

Hyper-localities increase real estate’s value in terms of how their inhabitants thrive in a neighbourhood through their encounters with one another and their surrounding architecture. The residents themselves then unknowingly produce extra value. The undervaluing of an asset is the product of its residents, and like housework, is unpaid labour. In terms of the exchange of capital, additional revenue from a property is usually paid out as a return to the shareholders who invested in its value. Putting big data-driven real estate into that equation would then mean that they would have to pay revenues to their residents. If properties create surplus value from the data generated by their residents, then property without its residents has less worth and is indeed over-, but not under-, valued.

Figure 2 – (left to right) City in a Building, City as a Building and City as an Element of Architecture. Image: University of Innsbruck, Daniel Koehler with Martin Danigel and Jordi Vivaldi, 2016-2018.

The city uses vehicles for creating public revenue by governing the width of a street’s section or the height of a building. Architecture’s role was to provide a stage for that revenue to be created. For example the Seagram Building (van der Rohe, Johnson, 1958) created a “public” plaza by setting back its envelope in exchange for a little extra height. By limiting form, architecture could create space for not only one voice, but many voices. Today, however, the city’s new parameters hidden in the fluidity of digital traces cannot be governed by the boundaries of architecture anymore. Outlined already 40 years ago, when the personal computer became available, Gilles Deleuze forecasted that “Man is not anymore man enclosed”.[5] At that time, and written as a “Postscript on the Societies of Control”, the fluid modulation of space prospected a desirable proposition. By liquefying enclosures, the framework of the disciplinary societies of Foucault’s writings would disappear. In modern industrial societies, Deleuze writes, enclosures were moulds for casting distinct environments, and in these vessels, individuals became masses of the mass society.[6] For example, inside a factory, individuals were cast as workers, inside schools as students. Man without a cast and without an enclosure seemed to be freed from class and struggle. The freedom of an individual was interlinked with their transcendence from physical enclosures.

Figure 3 – The Hyper-Nollie Plan, Daniel Koehler, 2019. Image: Daniel Koehler, 2019.

During the last forty years, the relation between a single individual and the interior framed architecture rightly aimed to dissolve the institutional forms of enclosures that represented social exclusion at their exterior. Yet, in this ambition alternative forms for the plural condition of what it means to be part of a city were not developed. Reading Deleuze further, a state without enclosures also does not put an end to history. The enclosures of control dissolve only to be replaced. Capitalism would shift to another mode of production. When industrial exchange bought raw materials and sold finished products, now it would buy the finished products and profit from the assemblies of those parts. The enclosure is then exchanged with codes that mark access to information. Individuals would not be moulded into masses but considered as individuals: accessed as data, divided into proper parts for markets, “counted by a computer that tracks each person’s position enabling universal modulation.”[7] Forty years in, Deleuze’s postscript has become the screenplay for today’s reality.

Hyper-parts: Spatial Practices of representations

A house is no longer just a neutral space, an enclosing interior where value is created, realised and shared. A home is the product of social labour; it is itself the object of production and, consequently, the creation of surplus value. By shifting from enclosure to asset, the big data-driven economy has also replaced the project behind modernism: humanism. Architecture today is post-human. As Rosi Braidotti writes, “what constitutes capital value  today is the informational power of living matter itself”.[8] The human being as a whole is displaced from the centre of architecture. Only parts of it, such as its “immanent capacities to form surplus-value”, are parts of a larger aggregation of architecture. Beyond the human, the Hyper-city transcends the humane. A virtual city is freed from its institutions and constituent forms of governance. Economists such as Thomas Piketty describe in painstaking detail how data-driven financial flows undermine common processes of governance, whether urban, regional, or national, in both speed and scale. Their analysis shows that property transactions shelled in virtual value-creation-bonds are opaque to taxation. Transcending regulatory forms of governance, one can observe the increase of inequalities on a global scale. Comparable to the extreme wealth accumulation at the end of the nineteenth century, Piketty identifies similar neo-proprietarian conditions today, seeing the economy shifting into a new state he coins as “hypercapitalism”.[9] From Timothy Morton’s “hyper-objects” to hypercapitalism,  hyper replaces the Kantian notion of transcendence. It expresses not the absorption of objects into humanism, but its withdrawal. In contrast to transcendence, which subordinates things to man’s will, the hyper accentuates the despair of the partial worlds of parts – in the case of Morton in a given object and in the case of Piketty in a constructed ecology.

When a fully automated architecture emerged, objects oriented towards themselves, and non-human programs began to refuse the organs of the human body. Just as the proportions of a data center are no longer walkable, the human eye can no longer look out of a plus-energy window, because it tempers the house, but not its user. These moments are hyper-parts: when objects no longer transcend into the virtual but despair in physical space. More and more, with increasing computational performance, following the acronym O2O (from online to offline),[10] virtual value machines articulate physical space. Hyper-parts place spatial requirements. A prominent example is Katerra, the unicorn start-up promising to take over building construction using full automation. In its first year of running factories, Katerra advertises that it will build 125,000 mid-rise units in the United States alone. If this occurred, Katerra would take around 30% of the mid-rise construction market in the company’s local area. Yet its building platform consists of only twelve apartment types. Katerra may see the physical homogeneity as an enormous advantage as it increases the sustainability of its projects. This choice facilitates financial speculation, as the repetition of similar flats reduces the number of factors in the valuing of apartments and allows quicker monetary exchange, freed from many variables. Sustainability refers not to any materiality but to the predictability of its investments. Variability is still desired, but oriented towards finance and not to inhabitants. Beyond the financialisation of a home, digital value machines create their own realities purely through the practice of virtual operations.

Figure 4 – The hyper-dimensional spaces of the digital economy are incompatible with cellular architecture. With every dimension added, the hull will gain weight until it absorbs more space than its content. From pure mathematical calculations, the dividends associated with the living cell and count more than its inhabitants. Image: Daniel Koehler, 2019.

Here one encounters a new type of spatial production: the spatial practice of representations. At the beginning of what was referred to as “late capitalism”, the sociologist and philosopher Henri Lefebvre proposed three spatialities which described modes of exchange through capitalism.[11] The first mode, a spatial practice referred to a premodern condition, which by the use of analogies interlinked objects without any forms of representation—the second, representations of space linked directly to production, the organic schemes of modernism. The third representational spaces express the conscious trade with representations, the politics of postmodernism, and their interest in virtual ideas above the pure value of production. Though not limited to three only, Lefebvre’s intention was to describe capitalism as “an indefinite multitude of spaces, each one piled upon, or perhaps contained within, the next”.[12] Lefebvre differentiated the stages in terms of their spatial abstraction. Incrementally, virtual practices transcended from real-to-real to virtual-to-real to virtual-to-virtual. But today, decoupled from the real, a virtual economy computes physically within spatial practices of representations. Closing the loop, the real-virtual-real, or new hyper-parts, do not subordinate the physical into a virtual representation, instead, the virtual representation itself acts in physical space.

This reverses the intention of modernism orientated towards an organic architecture by representing the organic relationships of nature in geometric thought. The organicism of today’s hypercomputation projects geometric axioms at an organic resolution. What was once a representation and a geometry distant from human activity, now controls the preservation of financial predictability.

The Inequalities Between the Parts of the Virtual and the Parts of the Real

Beyond the human body, this new spatial practice of virtual parts today transcends the digital project that was limited to a sensorial interaction of space. This earlier understanding of the digital project reduced human activity to organic reflexes only, thus depriving architecture of the possibility of higher forms of reflection, thought and criticism. Often argued through links to phenomenology and Gestalt theory, the simplification of architectural form to sensual perception has little to do with phenomenology itself. Edmund Husserl, arguably the first phenomenologist, begins his work with considering the perception of objects, not as an end, but to examine the modes of human thinking. Examining the logical investigations, Husserl shows that thought can build a relation to an object only after having classified it, and therefore, partitioned it. By observing an object before considering its meaning, one classifies an object, which means identifying it as a whole. Closer observations recursively partition objects into more unaffected parts, which again can be classified as different wholes.[13] Husserl places parts before both thought and meaning.

Figure 5 – Mereologies, 2016. Image(s): (top) Genmao Li, RC17, MArch Urban Design, B-Pro, The Bartlett School of Architecture, UCL, 2016; (bottom) Zhiyuan Wan, Chen Chen, Mengshi Fu, RC17, MArch Urban Design, B-Pro, The Bartlett School of Architecture, UCL, 2016.

Derived from aesthetic observations, Husserl’s mereology was the basisof his ethics, and was therefore concluded in societal conceptions. In his later work, Husserl’s analysis is an early critique of the modern sciences.[14] For Husserl, in their efforts to grasp the world objectively, the sciences have lost their role in enquiring into the meaning of life. In a double tragedy, the sciences also alienated human beings from the world. Husserl thus urged the sciences to recall that they ground their origins in the human condition, as for Husserl humanism was ultimately trapped in distancing itself further from reality.

One hundred years later, Husserl’s projections resonate in “speculative realism”. Coined By Levi Bryant as “strange mereology”,[15] objects, their belongings, and inclusions are increasingly strange to us. The term “strange” stages the surprise that one is only left with speculative access. However, ten years in, speculation is not distant anymore. That which transcends does not only lurk in the physical realm. Hyper-parts figurate ordinary scales today, namely housing, and by this transcend the human(e) occupation.

Virtual and physical space are compositionally comparable. They both consist of the same number of parts, yet they do not. If physical elements belong to a whole, then they are also part of that to which their whole belongs. In less abstract terms, if a room is part of an apartment, the room is also part of the building to which the apartment belongs. Materially bound part relationships are always transitive, hierarchically nested within each other. In virtual space and the mathematical models with which computers are structured today, elements can be included within several independent entities. A room can be part of an apartment, but it can also be part of a rental contract for an embassy. A room is then also part of a house in the country in which the house is located. But as part of an embassy, the room is at the same time part of a geographically different country on an entirely different continent than the building that houses the embassy. Thus, for example, Julian Assange, rather than boarding a plane, only needed to enter a door on a street in London to land in Ecuador. Just with a little set theory, in the virtual space of law, one can override the theory of relativity with ease.

Parts are not equal. Physical parts belong to their physical wholes, whereas virtual parts can be included in physical parts but don’t necessarily belong to their wholes.  Far more parts can be included in a virtual whole than parts that can belong to a real whole. When the philosopher Timothy Morton says “the whole is always less than the sum of its parts”,[16] he reflects the cultural awareness that reality breaks due to asymmetries between the virtual and the real. A science that sets out to imitate the world is constructing its own. The distance which Husserl spoke of is not a relative distance between a strange object and its observer, but a mereological distance, when two wholes distance each other because they consist of different parts. In its effort to reconstruct the world in ever higher resolution, modernism, and in its extension the digital project, has overlooked the issue that the relationship between the virtual and the real is not a dialogue. In a play of dialectics between thought and built environment, modernism understood design as a dialogue. In extending modern thought, the digital project has sought to fulfill the promise of performance, that a safe future could be calculated and pre-simulated in a parallel, parametric space. Parametricism, and more generally what is understood as digital architecture, stands not only for algorithms, bits, and rams but for the far more fundamental belief that in a virtual space, one can rebuild reality. However, with each resolution that science seeks to mimic the world, the more parts it adds to it.

Figure 6 – Illustrations of exemplary stairs constructed through cubes, Sebastiano Serlio, 1566. Image: public domain.

The Poiesis of a Virtual Whole

The asymmetry between physical and virtual parts is rooted in Western classicism. In early classical sciences, Aristotle divided thinking into the trinity of practical action, observational theory and designing poiesis. Since the division in Aristotle’s Nicomachean Ethics, design is a part of thought and not part of objects. Design is thus a knowledge, literally something that must first be thought. Extending this contradiction to the real object, design is not even concerned with practice, with the actions of making or using, but with the metalogic of these actions, the in-between between the actions themselves, or the art of dividing an object into a chain of steps with which it can be created. In this definition, design does not mean to anticipate activities through the properties of an object (function), nor to observe its properties (materiality), but through the art of partitioning, structuring and organising an object in such a way that it can be manufactured, reproduced and traded.

To illustrate poiesis, Aristotle made use of architecture.[17] No other discipline exposes the poetic gap so greatly between theory, activity and making. Architecture first deals with the coordination of the construction of buildings. As the architecture historian Mario Carpo outlines in detail, revived interest in classicism and the humanistic discourse on architecture began in the Renaissance with Alberti’s treatise: a manual that defines built space, and ideas about it solely through word. Once thought and coded into words, the alphabet enabled the architect to physically distance from the building site and the built object.[18] Architecture as a discipline then does not start with buildings, but with the first instructions written by architects used to delegate the building.

A building is then anticipated by a virtual whole that enables one to subordinate its parts. This is what we usually refer to as architecture: a set of ideas that preempt the buildings they comprehend. The role of the architect is to imagine a virtual whole drawn as a diagram, sketch, structure, model or any kind of representation that connotates the axes of symmetries and transformations necessary to derive a sufficient number of parts from it. Architectural skill is then valued by the coherence between the virtual and the real, the whole and its parts, the intention and the executed building. Today’s discourse on architecture is the surplus of an idea. You might call it the autopoiesis of architecture – or merely a virtual reality. Discourse on architecture is a commentary on the real.

Adrian Bowyer (left) and Vik Olliver (right) with a parent RepRap machine, and the first child machine, made by the RepRap on the left. Image in public domain.
Figure 7 – Adrian Bowyer (left) and Vik Olliver (right) with a parent RepRap machine, and the first child machine, made by the RepRap on the left. Image: public domain.

Partitioning Architectures

From the very outset, architecture distanced itself from the building, yet also aimed to represent reality. Virtual codes were never autonomous from instruments of production. The alphabet and the technology of the printing press allowed Alberti to describe a whole ensemble distinct from a real building. Coded in writing, printing allowed for the theoretically infinite copies of an original design. Over time, the matrices of letters became the moulds of the modern production lines. However, as Mario Carpo points out, the principle remained the same.[19] Any medium that incorporates and duplicates an original idea is more architecture than the built environment itself. Belonging to a mould, innovation in architecture research could be valued in two ways. Quantitatively, in its capacity to partition a building in increasing resolution. Qualitatively, in its capacity to represent a variety of contents with the same form. By this, architecture faced the dilemma that one would have to design a reproducible standard that could partition as many different forms as possible to build non-standard figurations.[20]

The dilemma of the non-standard standard moulds is found in Sebastiano Serlio’s transcription of Alberti’s codes into drawings. In the first book of his treatise, Serlio introduces a descriptive geometry to reproduce any contour and shape of a given object through a sequence of rectangles.[21] For Serlio, the skill of the architect is to simplify the given world of shapes further until rectangles become squares. The reduction finally enables the representation of physical reality in architectural space using an additive assembly of either empty or full cubes. By building a parallel space of cubes, architecture can be partitioned into a reproducible code. In Serlio’s case, architecture could be coded through a set of proportional ratios. However, from that moment on, stairs do not consist only of steps, and have to be built with invisible squares and cubes too.

Today, Serlio’s architectural cubes are rendered obsolete by 3D printed sand. By shrinking parts to the size of a particle of dust, any imaginable shape can be approximated by adding one kind of part only. 3D printing offers a non-standard standard, and with this, five hundred years of architectural development comes to an end.

Figure 8 – Von Neumann’s illustrations describing automata as a set of linkages between nodes. Image: Arthur W. Burks, 1969, public domain.

Replicating: A Spatial Practice of Representations

3D printing dissolved existing partitioning parts to particles and dust. A 3D-printer can not only print any shape but can also print at any place, at any time. The development of 3D printing was mainly driven by DIY hobbyists in the Open Source area. One of the pioneering projects here is the RepRap project, initiated by Adrian Bowyer.[22] RepRap is short for replicating rapid prototyping machine. The idea behind it is that if you can print any kind of objects, you can also print the parts of the machine itself. This breaks with the production methods of the Modern Age. Since the Renaissance, designers have crafted originals and used these to build a mould from those so that they can print as many copies as possible. This also explains the economic valuation of the original and why authorship is so vehemently protected in legal terms. Since Alberti’s renunciation of drawings for a more accurate production of his original idea through textual encoding, the value of an architectural work consisted primarily in the coherence of a representation with a building: a play of virtual and real. Consequently, an original representation that cast a building was more valued than its physical presentation. Architecture design was oriented to reduce the amount of information needed to cast. This top-down compositional thinking of original and copy becomes obsolete with the idea of replication.

Since the invention of the printing press, the framework of how things are produced has not changed significantly. However, with a book press, you can press a book, but with a book, you can’t press a book. Yet with a 3D printer, you can print a printer. A 3D printer does not print copies of an original, not even in endless variations, but replicates objects. The produced objects are not duplicates because they are not imprints that would be of lower quality. Printed objects are replicas, objects with the same, similar, or even additional characteristics as their replicator.

Figure 9 – Lionel R. Penrose, drawing for a physical implementation of a self-replicating chain of 3 units in length. Image: Photograph f40v, Galton Laboratory Archive, University College London, 1955.

A 3D printer is a groundbreaking digital object because it manifests the foundational principle of the digital – replication – on the scale of architecture. The autonomy of the digital is based not only on the difference between 0 and 1 but on the differences in their sequencing. In mathematics in the 1930s, the modernist project of a formal mimicry of reality collapsed through Godel’s proof of the necessary incompleteness of all formal systems. Mathematicians then understood that perhaps far more precious knowledge could be gained if we could only learn to distance ourselves from its production. The circle of scientists around John von Neumann, who developed the basis of today’s computation, departed from one of the smallest capabilities in biology: to reproduce. Bits, as a concatenation of simple building blocks and the integrated possibility of replication, made it possible, just by sequencing links, to build first logical operations, and connecting those programs to today’s artificial networks.[23] Artificial intelligence is artificial but it is also alive intelligence.

To this day, computerialisation, not computation is at work in architecture. By pursuing the modern project of reconstructing the world as completely as possible, the digital project computerised a projective cast[24] in high resolution. Yet this was done without transferring the fundamental principles of interlinking and replication to the dimensions of the built space.

Figure 10 – (left to right) Mereologies: WanderYards, 2016, Genmao Li, Chen Chen, and Xixuan Wang, 2016; Enframes, Kexin Cao, Yue Jin, Qiming Li, 2017; iiOOOI, Sheghaf Abo Saleh, Hua Li, Chuwei Ye, Yaonaijia Zhou, 2018 (right). Image(s): RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2016-2018.

From Partitioning to Partaking

The printing press depends on a mould to duplicate objects. The original mould was far more expensive to manufacture than its copies, so the casting of objects had to bundle available resources. This required high investments in order to start production, leading to an increasing centralisation of resources in order to scale the mass-fabrication of standard objects for production on an assembly line. Contrarily, digital objects do not need a mould. Self-replication provided by 3D printing means that resources do not have to be centralised. In this, digital production shifts to distributed manufacturing.[25]

Independent from any mould, digital objects as programs reproduce themselves seamlessly at zero marginal costs.[26] As computation progresses, a copy will then have less and less value. Books, music and films fill fewer and fewer shelves because it no longer has value to own a copy when they are ubiquitously available online. And the internet does not copy; it links. Although not fully yet integrated into its current TCP-IP protocol,[27] the basic premise of hyperlinking is that linked data adds value.[28] Links refer to new content, further readings, etc. With a close to infinite possibility to self-reproduce, the number of objects that can be delegated and repeated becomes meaningless. What then counts is hyper-, is the difference in kind between data, programs and, eventually, building parts. In his identification of the formal foundations of computation, the mathematician Nelson Goodman pointed out that beyond a specific performance of computation, difference, and thus value, can only be generated when a new part is added to the fusion of parts.[29] What is essential for machine intelligence is the dimensionality of its models, e.g., the number of its parts. Big data refers less to the amount of data, but more to the number of dimensions of data.[30]

Figure 11 – Enframes, 2017. Image: Kexin Cao, Yue Jin, Qiming Lim, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2017.

With increasing computation, architecture shifted from an aesthetic of smoothness that celebrated the mastership of an infinite number of building parts to roughness. Roughness demands to be thought (brute). The architecture historian Mario Carpo is right to frame this as nostalgic, as “digital brutalism”.[31] Similar to brutalism that wanted to stimulate thought, digital roughness aims to extend spatial computability, the capability to extend thinking, and the architecture of a computational hyper-dimensionality. Automated intelligent machines can accomplish singular goals but are alien to common reasoning. Limited around a ratio of a reality, a dimension, a filter, or a perspective, machines obtain partial realities only. Taking them whole excludes those who are not yet included and that which can’t be divided: it is the absolute of being human(e).

A whole economy evolved from the partial particularity of automated assets ahead of the architectural discipline. It would be a mistake to understand the ‘sharing’ of the sharing economy as having something “in common”. On the contrary, computational “sharing” does not partition a common use, but enables access to multiple, complementary value systems in parallel.

Figure 12 – Physical model, WanderYards, 2017. Image: Genmao Li, Chen Chen and Xixuan Wang, RC8, MArch Architecture Design, The Bartlett School of Architecture, UCL, 2017.

Cities now behave more and more like computers. Buildings are increasingly automated. They use fewer materials and can be built in a shorter time, at lower costs. More buildings are being built than ever before, but fewer people can afford to live in them. The current housing crisis has unveiled that buildings no longer necessarily need to house humans or objects. Smart homes can optimise material, airflow, temperature or profit, but they are blind to the trivial.

Figure 13 – Physical model, Slabrose, 2019. Image: Dongxin Mei, Zhiyuan Wan, Peiwen Zhan, and Chi Zhou, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

It is a mistake to compute buildings as though they are repositories or enclosures, no matter how fine-grain their resolution is. The value of a building is no longer derived only from the amount of rent for a slot of space, but from its capacities to partake with. By this, the core function of a building changes from inhabitation to participation. Buildings do not anymore frame and contain: they bind, blend, bond, brace, catch, chain, chunk, clamp, clasp, cleave, clench, clinch, clutch, cohere, combine, compose, connect, embrace, fasten, federate, fix, flap, fuse, glue, grip, gum, handle, hold, hook, hug, integrate, interlace, interlock, intermingle, interweave, involve, jam, join, keep, kink, lap, lock, mat, merge, mesh, mingle, overlay, palm, perplex, shingle, stick, stitch, tangle, tie, unit, weld, wield, and wring.

In daily practice, BIM models do not highlight resolution but linkages, integration and collaboration. With further computation, distributed manufacturing, automated design, smart contracts and distributed ledgers, building parts will literally compute the Internet of Things and eventually our built environment, peer-to-peer, or better, part-to-part – via the distributive relationships between their parts. For the Internet of Things, what else should be its hubs besides buildings? Part-to-part habitats can shape values through an ecology of linkages, through a forest of participatory capacities. So, what if we can participate in the capacities of a house? What if we no longer have to place every brick, if we no longer have to delegate structures, but rather let parts follow their paths and take their own decisions, and let them participate amongst us together in architecture?

Figure 14 – Interior view of physical model, NPoche, 2018. Image: Silu Meng, Ruohan Xu, and Qianying Zhou. RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018.
Figure 15 – Seggregational section, WanderYards, 2017. Image: Genmao Li, Chen Chen and Xixuan Wang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2017.


[1] S. Kostof, The City Assembled: The Elements of Urban Form Through History (Boston: Little, Brown and Company, 1992).

[2] J. Aspen, "Oslo – the triumph of zombie urbanism." Edward Robbins, ed., Shaping the city, (New York: Routledge, 2004).

[3] The World Bank actively promotes housing as an investment opportunity for pension funds, see: The World Bank Group, Housing finance: Investment opportunities for pension funds (Washington: The World Bank Group, 2018).

[4] G. M. Asaftei, S. Doshi, J. Means, S. Aditya, “Getting ahead of the market: How big data is transforming real estate”, McKinsey and Company (2018).

[5] G. Deleuze, “Postscript on the societies of control,” October, 59: 3–7 (1992), 6.

[6] Ibid, 4.

[7] Ibid, 6.

[8] R. Braidotti, Posthuman Knowledge (Medford, Mass: Polity, 2019).

[9] T. Piketty, Capital and Ideology (Cambridge, Mass: Harvard University Press, 2020).

[10] A. McAfee, E. Brynjolfsson, Machine, platform, crowd: Harnessing our digital future (New York: W.W. Norton & Company, 2017).

[11] H. Lefebvre, The Production of Space (Oxford: Basil Blackwell, 1991), 33.

[12] Ibid, 8.

[13] E. Husserl, Logische Untersuchungen: Zweiter Teil Untersuchungen zur Phänomenologie und Theorie der Erkenntnis.trans. "Logical investigations: Part Two Investigations into the phenomenology and theory of knowledge" (Halle an der Saale: Max Niemeyer, 1901).

[14] E. Husserl, Cartesianische Meditationen und Pariser Vortraege. trans. "Cartesian meditations and Parisian lectures" (Haag: Martinus Nijhoff, Husserliana edition, 1950).

[15] L. Bryant, The Democracy of Objects (Ann Arbor: University of Michigan Library, 2011).

[16] T. Morton, Being Ecological (London: Penguin Books Limited, 2018), 93.

[17] Aristotle, Nicomachean Ethics 14, 1139 a 5-10.

[18] M. Carpo, Architecture in the Age of Printing (Cambridge, Mass: MIT Press, 2001).

[19] M. Carpo, The Alphabet and the Algorithm (Cambridge, Mass: MIT Press, 2011).

[20] F. Migayrou, Architectures non standard (Editions du Centre Pompidou, Paris, 2003).

[21] S. Serlio, V. Hart, P. Hicks, Sebastiano Serlio on architecture (New Haven and London: Yale University Press, 1996).

[22] R. Jones, P. Haufe, E. Sells, I. Pejman, O. Vik, C. Palmer, A. Bowyer, “RepRap – the Replicating Rapid Prototyper,” Robotica 29, 1 (2011), 177–91.

[23] A. W. Burks, Von Neumann's self-reproducing automata: Technical Report (Ann Arbor: The University of Michigan, 1969).

[24] R. Evans, The Projective Cast: Architecture and Its Three Geometries (Cambridge, Massachusetts: MIT Press, 1995).

[25] N. Gershenfeld, “How to make almost anything: The digital fabrication revolution,” Foreign Affairs, 91 (2012), 43–57.

[26] J. Rifkin. The Zero Marginal Cost Society: The Internet of Things, the Collaborative Commons, and the Eclipse of Capitalism (New York: Palgrave Macmillan, 2014).

[27] B. Bratton, The Stack: On Software and Sovereignty (Cambridge, Massachusetts: MIT Press, 2016).

[28] J. Lanier, Who Owns the Future? (New York: Simon and Schuster, 2013).

[29] N. Goodman, H. S. Leonard, “The calculus of individuals and its uses,” The Journal of Symbolic Logic, 5, 2 (1940), 45–55.

[30] P. Domingos, The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World (London: Penguin Books, 2015).

[31] M. Carpo, “Rise of the Machines,” Artforum, 3 (2020).

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Church Sainte Geneviève, Clovis, 502. Drawing by Jean-Baptiste Rondelet, 1810. Image: Thomas Thibaut, 2018.
Matter versus Parts: The Immaterialist Basis of Architectural Part-Thinking
Architecture, Discrete Architecture, Form, Matter, Mereologies, Mereology
Jordi Vivaldi
Institute for Advanced Architecture of Catalonia, University College London and University of Innsbruck
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“Digital Matter”; “Intelligent Matter”’; “Behavioural Matter”; “Informed Matter”; “Living Matter”, “Feeling Matter”; “Vibrant Matter”; “Mediated Matter”; “Responsive Matter”; “Robotic Matter”; “Self-Organised Matter”; “Ecological Matter”; “Programmable Matter”; “Active Matter”; “Energetic Matter”. There is no term enjoying better reputation in today’s experimental architectural discourse. Gently provided by a myriad of studios hosted in pioneer universities around the world, the previous expressions illustrate the redemption of a notion that has traditionally been dazzled by form’s radiance. After centuries of irrelevance, “Matter” has recently become a decisive term; it illuminates not just the field of experimental architecture, but the whole spectrum of our cultural landscape: several streams in philosophy, art and science have vigorously embraced it, operating under the gravitational field of its holistic and non-binary constitution.

However, another Copernican Revolution is flipping today’s experimental academic architecture from a different flank. In parallel to matter’s redemption and after the labyrinthic continuums characteristic of the ’90s, discreteness claims to be the core of a new formal paradigm. Beside its Promethean vocation and renewed cosmetics, the discrete design model restores the relevance of a term that traditionally has been fundamental in architecture: the notion of part. However, in opposition to previous architectural modulations, part’s current celebration is traversed by a Faustian desire for spatial and ontological agency, which severely precludes any reverential servitude to its whole.

The singular coincidence of matter’s revival on the one side and the discrete turn on the other opens a debate in relation to its possible conflicts and compatibilities in the field of experimental architecture. In this essay, the discussion gravitates around one single statement: the impossibility of a materialist architectural part-thinking. The argument unfolds by approaching a set of questions and analysing the consequences of its possible answers: how matter’s revival contributes to architectural part thinking? Is matter’s revival a mere importation of formal attributes? Which are the requirements for a radical part-thinking in architecture? Is matter well equipped for this endeavour? In short, are the notions of matter and part-thinking compatible in an architectural environment?

Pre-Socratic philosophy defined matter as a formless primordial substratum that constitutes all physical beings. Its irrevocable condition is that of being “ultimate”: matter lies in the depth of reality as more fundamental than any definite thing.[1] Under this umbrella, pre-Socratic philosophy ramifies in two branches: the first one associates matter with continuity, the second one associates matter with discretism.

Anaximander is the standard-bearer of the first type: the world is pre-individual in character and it is fueled by the apeiron, a continuum to which all specific structures can be reduced. We can find traces of this sort of materialism in Gilles Deleuze’s “plane of immanence”, Bruno Latour’s “plasma”, or Jane Bennett’s “vibrant matter”. Democritus is the figurehead of the second type: the world is composed by sets of atoms, that is, privileged discrete physical elements whose distinct combinations constitute the specific entities that populate the world. Resonances of this sort of materialism can be found in the “quanta” of contemporaneous quantum mechanics. Independently of their continuous or discrete nature, both types of materialisms are underpinned by an ontological assumption: the identification of matter with an ultimate cosmic whole. To this purpose, matter’s generic condition is decisive: its lack of specificity is precisely what grants matter the status of “ultimate”, which logically and chronologically precedes distinction.

Architecture’s conceptualisation of matter has not been impermeable to these philosophical discourses. In spite of the negative reputation that the Aristotelian hylomorphism projected on matter by converting it into the reverential servant of form – absent in pre-Socrátic philosophy and being introduced, in different ways, by Plato and Aristotle – in the last centuries many architectural projects opposed this status quo by capitalising on both types of materialism. Since the Enlightenment and still under form’s reign, matter has been recovering its pre-Socratic positive character by absorbing all the attributes traditionally ascribed to form. However, it also operated a conceptual replacement that is crucial in this discussion: matter moved from a marginal role in a hylomorphic dualist scheme to the solitary leadership of an ultimate holism. As we will see below, in architecture and particularly since the Enlightenment, matter’s relevance has been gradually recovered through its association with two key concepts: truthfulness, emphasised by authors of the late 18th and 19th century such as Viollet le Duc or Gottfried Semper, and vitalism, underlined by authors of the 19th century and early 20th century such as Henry Bergson or Henri Focillon.[2] Today this process has culminated with Eric Sadin’s notion of antrobology, that is, the “increasingly dense intertwining between organic bodies and ‘immaterial elfs’ (digital codes), that sketches a complex and singular composition which is determined to evolve continually, contributing to the instauration of a condition which is inextricably mixed ‘human/artificial.”[3]

In this technological framework and through the notions of information, platform and performance, matter’s traditional attributes have been replaced by those of form. Despite keeping the term “matter” as a signifier, the disorder, passivity and homogeneity that conventionally characterised its significance have been substituted by form’s structure, activity and heterogeneity. However, one crucial feature that is absent in the dualistic hylomorphic model has been reintroduced: matter’s pre-Socratic condition of being ultimate.

This incorporation is decisive when it comes to architectural part-thinking. In spite of the great popularity that matter has achieved within contemporary experimental architecture, its ultimate condition precludes any engagement with architectural part-thinking: either as a single continuous field or as a set of discrete particles, matter exalts a single holistic medium that lies at the core of reality, that is, a fundamental substrata (whole) in which all specific entities (parts) can be reduced. In a context in which designers use the power of today’s super computation to notate the inherent discreteness of reality instead of reducing it to simplified mathematical formulas,[4] or field, reality’s approach through generic and Euclidean points (particles) rather than distinct elements (parts) constitutes an unnecessary process of reduction that dissolves part’s autonomy.  

This essay develops this argument in two steps. First, it states that the current culmination of matter’s revival process in experimental architecture is, paradoxically, nothing but the exaltation of form; under the same signifier, matter’s signification has been replaced by form’s signification: all attributes that in the hylomorphic model were associated with the latter have now moved to the former, converting matter’s signifier into just another term to conjure up the significance of form. However, there is a crucial pre-Socratic introduction in relation to the hylomorphic model: matter is now understood as being also the ultimate single substance of reality, and not just the compliant serf of another element (form). This holistic vocation can be traced in contemporaneous experimental architecture in parallel to matter’s pre-Socratic distinction between a continuous field (Anaximander’s apeiron) and a discrete set of particles (Democritus’s atoms).

Second, this essay argues that current materialism, in any of its twofold registers, is incompatible with architectural part-thinking. The argument first identifies and evaluates three groups of architectural parts (topological, corpuscular and ecological) in the current experimental architectural landscape and second proposes a fourth speculative architectural part based on the notion of limit. If the idea of part demands a certain degree of autonomy from the whole, it cannot be reducible to any ultimate substrata, and therefore matter’s holistic condition becomes problematic both in its continuous and discrete register. However, the latter demands particular attention: discretism’s spatial countability might lead us to confuse the notion of particle with that of part. However, they significantly differ: while particles are discrete only from a mathematical perspective (countable), parts are discrete as well from an ontological perspective (distinct). Parts require at least both dimensions of discreteness in order to be considered autonomous from any exteriority, while simultaneously keeping its capacity to participate in it.

Architectural part-thinking demands then a radical formal approach. It requires a notion of form that operates at every level of scale, that is, an immaterialist model that recursively avoids any continuous (field) or discrete (particle) ultimate substrata in which parts could be reduced. This pan-formalism would imply then the presence of a form beyond any given form, understanding the term “form” as an autonomous spatio-temporal structure. 

Matter’s Recovery Process in Architecture: Truthfulness, Vitalism and Antrobology

Since Ancient Greece, architecture has interpreted the notion of matter through Aristotle’s hylomorphic scheme: matter is a disordered, passive and homogenous mass (matter) in attendance for a structured, active and heterogeneous pattern (form). According to this framework the architect is constituted as a demiurge: they operate from a transcendent plane in order to inform matter, that is, in order to structure its constitution through a defined pattern. However, since the Enlightenment, matter’s signifier has gradually replaced its signification with that of form through three concatenated strategies: truthfulness, vitalism and antrobology.

The concept of truthfulness in architecture should be read in opposition to the idealism of authors like Alberti or Palladio. In his De Re-aedificatoria, Alberti claimed that “architecture is not about artisan techniques but about ‘cose mentale’.”[5] What concerned him was not material attributes such as colour or texture, but the geometrical proportions of the forms that he produced with matter. This statement becomes evident in his façade for the Malatesta Temple in 1450.

Figure 1 – Malatesta Temple, Alberti, c. 1450. Image: Paolo Monti, Servizio fotografico, Rimini, 1972.

Conversely, some centuries later authors like Ruskin, Viollet-le-Duc or Semper defended the relevance of matter in architecture, asserting that the choice of a material should depend on the laws dictated by its nature, such that “brick should look like brick; wood, wood; iron, iron, each according to its own mechanical laws.”[6] Rondelet and Choissy also gave importance to the truth of the material, particularly throughout their exhaustive constructive drawings.

Figure 2 – Church Sainte Geneviève, Clovis, 502. Drawing by Jean-Baptiste Rondelet, 1810. Image: Thomas Thibaut, 2018.

However, this group of authors still remained idealistic: the use of materials was determined by the idea that the architectural object was intended to express. In that sense, and although its internal structure was recognised, matter was still subordinate to an external idea, that is, to an external form. 
Some decades later, in his Life of Forms in Art (1881) Henri Focillon dignified matter through a strategy based on a different concept: vitalism. Although arguing that the development of art is inextricably linked to external socio-politic and economic characteristics, Focillon associated an autonomous formal mutation to it through underlining matter’s inherent capacity of movement and metamorphosis. Already present in the Baroque and empowered by the Enlightenment’s idea of “natura naturans”, concepts like the “Bildungstrieb”, the “Thatkraft” or the “Urpflanze” articulated a vitalist approach to matter closely related to German Expressionism. Ruskin and Semper’s seminal materialism based on material’s truth gave way to a radical pragmatism in which architects used hybridised materials in order to relate to natural metamorphosis. Many glass-based projects from the early 20th century replicate these morphogenetic processes, an attitude already present in the gothic. In resonance with Bergson’s élan vital, a hypothetical force that explains the evolution and development of organisms, certain uses of concrete imitated the formal exuberance of some morphogenetic natural processes, as can be seen in the Goetheanum from Rudolph Steiner in 1928 or Einstein Tower from Erich Mendelsohn in 1921, but also with different materials in the Großes Schauspielhaus from Hans Poelzig in 1919.

Figure 3 – Großes Schauspielhaus, Poelzig, 1919. Image: Image on paper 18,5 x 24,2, Architekturmuseum der Technischen Universität Berlin, 1919.

Moreover, the use of concrete established a continuity between form and structure characteristic of the organic beings that were so greatly admired at that time. As a consequence, a progressive material vitalism was thus constituted through an hylozoic approach based on Einstein’s theories of matter and energy interconvertibility, which suggested a comprehension of matter as a set of energetical perturbations instead of mere inert mass. In this sense and according to Henry van de Velde, matter had not only a mechanical value, but an active dispositionality that was the consequence of its “formal vocation”. However, vitalism had also its conservative reverse. Fueled by the phenomenological work of Rasmussen and Norberg-Schulz, architects such as Herzog & Meuron, Steven Holl or Peter Zumthor propose a haptic approach to architecture that relies on materials as symbolic shapers of architectural space. Under this scenario and in close relation to Merleau-Ponty’s notion of “flesh”, matter is still understood as a holistic repository of tactile and cultural memory.

In parallel to the general disdain that Modernism showed for materiality during the first half of the 20th century, according to Eduardo Prieto truthfulness and vitalism have gradually contributed to the reconsideration of matter as a substance with a certain agency.[7] This process was based not on the exaltation of the passivity, neutrality and homogeneity that originally characterised matter, but on the importation of attributes from the notion of form. Ruskin’s truthfulness is based precisely on the understanding that matter has a specific inner character that makes it heterogeneous, while the vitalism of Steiner alludes to the metamorphic capacities of living beings.

However, both cases remain idealistic. Truthfulness asserts the need for an external form to choose the matter that best suits its purposes. Vitalism claims that matter should be seen as a material of organic expression that still needs an artist or architect to unveil its aesthetic potentialities of metamorphosis. In both cases, matter is still seen not just in opposition to an external form, but also under its control. In this sense, the vitalism defended by Bergson differs from the vitalism of Deleuze: for the former, matter is still a generic substance that needs an artist to particularise it, that is, needs an élan vital to form it. Conversely, for Deleuze, matter is an immanent reality: it provides form to itself and does not require any transcendental agent. This Deleuzian conception of matter has been emphasised today through New Materialism, whose statements in relation to the problem matter-form are based “on the idea that matter has morphogenetic capacities of its own and does not need to be commanded into generating form.”[8] In this sense, matter is no longer seen in opposition to form, that is, “it is not a substrate or a medium for the flow of desire, but it is always already a desiring dynamism, a reiterative reconfiguring, energised and energising, enlivened and enlivening.”[9] 

This philosophical approach reverberates with our current technological condition. After the stages of truthfulness and vitalism, Sadin’s antrobology culminates an architectural recovery of matter that paradoxically is based in the replacement of its signification by that of form. Faced with a dual ontology that is no longer alluding to Heideggerian human nudity but to a planet inhabited by algorithmic beings that live with and against us, Eric Sadin defines our technological scenario as Antrobological. This notion expresses the “increasingly dense intertwining between organic bodies and ‘immaterial elfs’ (digital codes).”[10] The propagation of artificial intelligence and the multi-scalar robotisation of the organic establishes, in addition to a change of medium, a change of condition: its algorithmic power does not merely offer itself as an automatic pilot for daily life, but it also triggers a radical transformation of our human nature, setting up a perennial and universal intertwining in between bodies and information. In this sense, the multidisciplinary generalisation of machine learning, progress in genetic engineering or the robotisation of the mundane no longer refer to a humanity that is merely improved or enriched, but to a humanity that is intertwined: it is unfolded through a physiological platform that is woven by algorithmic, organic, robotic and ecologic agents whose symbiosis is not metaphorical or narrative, but strictly performative. It is precisely under this scenario that “artificial extelligence” becomes “artificial intelligence”: it executes an exercise of incorporation in which the intelligence, eidos, or what has traditionally been understood as form is no longer an external entity that articulates matter from outside, but is its immanent circumstance.

The historical and incremental process of matter legitimation, based initially on the truthfulness of Ruskin and the vitalism of Steiner, culminates today with the celebration of the notions of platform, information and performance that singularise Sadin’s antrobology. Recent theorisations on concepts related to computation and design such as Keller Easterling’s “medium”[11] or Benjamin Bratton’s “stack”[12] are as well deeply underpinned by these three expressions. However, it is crucial to note that the term “form” is present in all of them, associating each expression to one of the three main form’s attributes: structure (information), activity (performance) and heterogeneity (platform). 

While matter “is that which resists taking any definite contour”,[13] form refers to the active presence of a distinguished and qualified non-ultimate structure containing other forms at every level of scale and that can occasionally change and establish relationships. It is under this framework that the previous terms should be read in relation to experimental architecture. To provide a platform means to provide the conditions for an evolving intertwining in between forms that permits the promiscuous co-existence of difference, that is, of heterogeneity. Thus, a platform is not a field: in opposition to the latter, the former doesn’t permit any sort of reductionism, that is, its elements are not mere emergences, as occurs with fields, but singularities with distinct origins. To provide information means to provide structure: it precludes disorder by establishing a spatio-temporal non-ultimate organisation. However, given that every entity already has a form and we cannot imagine a formless element, to inform means actually to transform. To provide performance, in contrast, means to present rather than represent: it produces an operative impact on the set of conditions in which it is placed, instead of merely representing an absent entity, as would be the case of a metaphor.

Under Sadin’s antrobology, the disorder, passivity and homogeneity that traditionally identified matter are replaced by those characteristics that qualified form in the hylomorphic model: structure (information), activity (performance) and heterogeneity (platform). However, if the process of legitimation of matter is rooted in replacing its attributes by those of form, it is increasingly more unsustainable to keep referring to it as “matter”, when actually, especially in Sadin’s antrobology and from a hylomorphic point of view, matter is actually empty of matter and full of form.

Matter’s Ultimate Condition and Part-Thinking

However, the rupture of the hylomorphic dichotomy caused by matter’s absorption of form has implied the introduction of a pre-Socratic matter’s condition: that of being ultimate. Matter is not understood anymore as one of the components of a dualistic model, but as a single holistic substance whose structure, activity and heterogeneity underlies the emergence of any specific entity. This model, technologically underpinned by Sadin’s antrobology, has been articulated by contemporaneous experimental architecture according to the two types of materialism that differentiate pre-Socratic philosophy: as a continuous field (Anaximander’s apeiron) or as discrete particles (Democritus’s atoms). However, its common “ultimate” condition obstructs architectural part-thinking: if the notion of part demands an autonomy that cannot be exhausted neither in its outer participation in a bigger ensemble nor in its inner constitution through a smaller ensemble, matter’s holism becomes problematic. Indeed, if any entity (part) can be deduced from a privilege underlying substrata (whole), its autonomy is called into question.

Anaximander’s apeiron model is the most popular representative of pre-Socratic continuous approaches to matter. For the greek philosopher, apeiron refers to the notions of indefinite and unlimited, alluding explicitly to the origin (arché) of all forms of reality. Precisely because apeiron, as suggested by its etymology, is that which cannot be limited, it doesn’t have in itself any specific form, that is, it is not definable. It is therefore a continuous material substrata, vague and boundaryless, capable of supporting the opposites from which all the world’s differentiation emerges. Besides Bruno Latour’s ‘plasma’, described by its author as that unknown and material hinterland which is not yet formatted, measured or subjectified, one of the most popular contemporaneous elaborations of this apeiron’s holistic theory is Jane Bennett’s “throbbling whole”. For the American philosopher, objects would be “those swirls of matter, energy, and incipience that hold themselves together long enough to vie with the strivings of other objects, including the indeterminate momentum of the throbbing whole”, something that according to Harman “we already encountered, in germ, in the pre-Socratic apeiron”.[14] Beside pure formal continuities such as Alejandro Zaera’s Yokohama (2000) or François Roche Asphalt Spot (2002), we can find a similar holistic vocation in projects such as Neri Oxman’s BitMap Printing (2012), Mette Ramsgard Thomsen’s Slow Furl (2008), and Poletto-Pasquero’s Urban Algae Follies (2016). Its renovated notion of matter is usually referred to as behavioural matter, living matter, ecological matter, digital matter, expanded matter, data-driven matter or intelligent matter. 

Paradoxically, what is relevant in all these expressions is not the term matter, but its qualifier, which systematically refers to spatio-temporal formal arrangements rather than hylomorphic matter attributes, emphasising the relevance of form as identifier over matter. Nery Oxman’s “material ecology” is an emblematic example of this phenomena. Oxman defines this expression as “an emerging field in design denoting informed relations between products, buildings, systems and their environment”.[15] The architect uses the term “informed” referring to information and therefore alluding to matter’s inner structure. However, if “matter” is informed, it is no longer a homogeneous and amorphous substance, but it contains a digital or a physical structure that operates at every level of scale. Her project Bitmap Printing (2012) acts as a platform that intertwines between natural, human and algorithmic agents, whose activity has performative consequences rather than symbolic references. In this sense, given that the project is informed, acts as a platform and performs, it is hardly understandable why, under a hylomorphic scheme, we refer to them as specific configurations of matter rather than as a particular type of form.

However, these three projects, together with the work of authors such as Marcos Cruz, Phillip Beesley or Areti Markopoulou, introduce a pre-Socratic’s matter attribute absent in the hylomorphic scheme: matter’s condition of being ultimate. In particular, we can find this pre-Socratic’s matter attribute in the continuous version developed by Anaximander through the notion of apeiron. As we can see in projects such as the Hylozoic Garden (2010) by Philip Beesley, full relationality and complete interconnectedness are the basis of a systemic approach to architecture in which the conceptual idea of field articulates Delanda’s “continuous heterogeneity”. 

The project is based on the ancient belief that matter has life and should be understood, according to its author, as an active environment of processes rather than as an accumulation of objects. Unlike hylomorphic matter, the anti-maternalistic matter evoked by the Hylozoic Garden does not contain an Aristotelian pattern that provides structure to it, but is instead self-formed, that is, structured, active and heterogeneous. However, specific parts are always an emergence from an underlying holistic field, that is, a whole. Indeed, continuity is actually capable of producing objects, that is, continuity on one level creates episodic variation on the next that may be presented as discrete elements, but they are always dependent on this first gradual variation. Under this scheme, part-thinking is very limited because specificity is always a deduction from a privilege underlying substrata. Parts are then prevented from its autonomy, being instead exhausted in its participation as subsidiary members of a whole. As Daniel Koehler suggests, “departing from parts a preconceived whole or any kind of structure does not exist. Parts do not establish wholes, but measure quantities.”[16] And quantities, indeed, begin with individuals, that is, with discreteness.

However, the notion of “discreteness” needs differentiation: not all the interpretations of this term permit to understand its individuals as parts. In this sense, it is crucial to note that pre-Socratic philosophy articulates as well a type of materialism based on discreteness: beside the continuity emphasised by Anaximander’s apeiron, Democritus’s atomic model is the most popular representative of this discrete approach to matter. For the Greek philosopher, atoms are not just eternal and indivisible, but also homogeneous, that is, generic. Although atoms differ in form and size, its internal qualities are constant in all of them, producing difference only through its grouping modes. Atoms are then particles: generic individuals whose variable conglomerates produce the difference that we observe in the world. As Graham Harman affirms, this form of materialism is “based in ultimate material elements that are the root of everything and higher-level entities are merely secondary mystifications that partake of the real only insofar as they emerge from the ultimate material substrate.”[17] 

The atomic model is thus a reductionist model: the different specificities that conform the world are mere composites of a privileged and ultimate physical element. In opposition to the continuous form of materialism, the discrete atomic type is easily misunderstood when it comes to considering its part-thinking capacities due to a frequent confusion: that between “part” and “particle”. This association is especially present nowadays in architectural experimental design, particularly under the notion of “digital” and its inherent discrete nature. Computation’s power of today has been aligned with this position through the recognition that “designers use the power of today’s computation to notate reality as it appears at any chosen scale, without converting it into simplified and scalable mathematical formulas or laws.”[18] It assumes “the inherent discreteness of nature”,[19] where the abstract continuity of the spline doesn’t exist. However, this process of architectural discretisation needs differentiation in order to be understood in relation to the notion of part, defined here as an interactive and autonomous element which is not just countable (mathematically discrete) but also distinct (ontologically discrete). Within the contemporaneous discrete project, three groups of architectural approaches to the notion of part, together with a speculative proposition, need to be distinguished according to its relation with matter’s ultimate condition: topological parts, corpuscular parts, ecological parts and limital parts.

Topological Parts, Corpuscular Parts, Ecological Parts, Limital Parts

There is a first group of proposals in which parts are topological parts; in spite of the granular appearance of its architectural ensembles, its vocation is still derivative from the parametric project: the continuity of its splines has reduced its resolution through a process of “pixelisation”, but it still operates under the material logic of an ultimate field. The notion of topology should be read here under the umbrella of the Aristotelian concept of topos. While Plato’s term chora refers to a flat and neutral receptacle, the term topos refers to a variable and specific place. In contrast to the flat spaces of modernity, the three-dimensional variability of 1990s spaces produces topographic surfaces in which every point is singular. This results in “a constant modification of the space that leads to a changing reading of the place,”[20] implying the shift from Plato’s chora to Aristotle’s topos. Unlike the universal abstraction of the former, in the Physics, Aristotle “identifies the generic concept of space with another more empirical concept, that of ‘place’, always referred to with the term topos. In other words, Aristotle looks at space from the point of view of place. Every body occupies its specific place, and place is a fundamental and physical property of bodies.”[21]

This is very clear in the following text by the Stagirite: 

“Again, place (topos) belongs to the quantities which are continuous. For the parts of a body which join together at a common boundary occupy a certain place. Therefore, also the parts of place which are occupied by the several parts of the body join together at the same boundary at which the parts of the body do.”[22]

Aristotle defines topos as a continuous and three-dimensional underlying substratum, but above all as an empirical and localised substratum.

The rhizomatic twists associated with these projects and underpinned by the intensive use of computational tools seem to oppose the homogeneity of its parts. According to Peter Eisenman, “while Alberti’s notational systems transcribed a single design by a single author, computation has the capacity to produce multiple iterations that the designer must choose from.”[23] Computers function as generators of variability, a fact that seems to promote Eisenman’s inconsistent multiples, calling into question Alberti’s homogeneous spatiality. However, in spite of being countable and distinct, the constitution of the parts associated with projects such as BIG’s Serpentine’s Pavilion (2016) and The Mountain (2008) or Eisenman’s Berlin Memorial (2005) is reducible to one single formula or equation, that is, a consistent and calculable single medium (parametricism). Its discrete look is provided by a set of elements which are countable, distinct and interactive, but that cannot be read as parts because its autonomy is restricted for a twofold reason: both its distinction and position depend on an ultimate system of relations which is external to the logics of its individuals, evoking therefore apeiron’s type of materialism. In this sense, parts here should be read as components: the location and form of them is subordinated to the topological bending of a general surface, precluding any type of part’s autonomy.

There is a second group of experimental projects in which parts are corpuscular parts. In these parts architectural ensembles are formalised through countable and qualitatively identical corpusculi, that is, individual entities which are not systematised by any external and preconceived structure. Its advocates follow a path similar – even if this is not their conscious intention – to that of Walter Gropius, Mies van der Rohe and Le Corbusier when they freed themselves from the straitjackets of the symmetry characteristic of 19th century’s Beaux-Arts, championed by architects such as Henri Labrouste or Felix Duban. However, corpuscular parts differ from modern parts in the fact that they are formally identical in between them despite performing different functions. Mario Carpo relates some of this work with Kengo Kuma’s Yure Pavilion (2015) and GC Prostho Museum Research Center (2010) under the expression “particlised.”[24] The term relates to the non-figural, aggregational or atomised way of producing architecture, in which Kuma states that “each element needs to be relieved from contact or structure beforehand, and placed under free conditions.”[25] 

Experimental projects such as Bloom (2012) by Alisa Andrasek and José Sánchez or Flow (2016) by Calvin Fung and Victor Huynh participate as well in this process of “particalisation” by relying on an ultimate, generic and privileged element: in opposition to modernist assemblies and in resonance with some of the early work of Miguel Fisac, “the buildings blocks are not predefined, geometric types – like columns or slabs – that only operate for a specific function,”[26] and unlike parametricism they do not derive from a predefined whole. 

Instead, the particle’s specific function is an emergent attribute of its interaction. In this sense, what gives specificity to these generic particles is not an a priori and fixed structure as modernism, but a posteriori and evolving relationality with the world. This is problematic with the requirement of autonomy demanded by parts for two reasons. On the one side, if part’s specificity is exhausted with its outer relationality, its nomos is coming from outside and we are therefore in Kant’s heteronomy rather than autonomy. On the other side, if parts are originally generic, they refer to an original standard type which is holistic precisely because it is shared by default by all its members. The fact that specificity is an emergent property in which parts are defined exclusively by their relationships with other parts has been interpreted as their emancipation with respect to the notion of whole. Timothy Morton describes this type of relational process as “simply the last philosophical reflex of modernity”.[27] 

Indeed, the instrumental reason characteristic of modernity is still behind this type of operation because emergent processes are teleological processes. “Emergence is always emergence for”[28] because there is always a holistic target that subjugates the parts to the benefit of the whole. As such, we are not dealing with a mereology of parts, but rather a mereology of particles: each element is not an incomplete piece that is unique in its identity and therefore irreducible (part), but rather a generic ultimate element that becomes specific at the price of being relationally dissolved into the whole of which it belongs (particle). Its being is defined precisely by the relationships it establishes with other elements, and those relationships are the way they are because they are beneficial to a whole. 

Timothy Morton affirms that moving past modernity implies the need for a “philosophy of sparkling unicities; quantised units that are irreducible to their parts or to some larger whole; sharp, specific units that are not dependent on an observer to make them real.”[29] Despite their local character, the relations that regulate individuals undervalue the parts on the one hand and overvalue the whole on the other. They undervalue the parts by fully determining their specific behaviour according to external factors, its original character being generic. They overestimate the whole by varying individual’s specific behaviour according to the benefit of the whole. This position facilitates the emergence of a framework in which bits are associated literally with parts and the act of counting is frequently confused with an act of discretisation. It is then crucial to differentiate mathematical discreteness from ontological discreteness. While the first one alludes to countable elements (particles), the second one alludes to distinct elements (parts). 

Figure 4 – Mathematical Discreteness, Ontological Discreteness, 2020. Image: Jordi Vivaldi, 2020.

The lack of distinction characteristic of generic particles prevents its approach through an exercise of architectural “part-thinking”. Instead, we are confronted with the discrete type of materialism elaborated by pre-Socratic philosophy. Although its ultimate condition permits individual’s participation, it ignores its autonomy’s requirement for part-thinking under a masked heteronomy, which provides specificity to generic particles at the cost of its exhaustion under external relationality.

There is a third group of recent experimental architectural proposals in which parts are ecological parts; they operate as a set of distinct objects that intertwine with one another under the gravitational field of different systems. The notion of ecology should be interpreted here in keeping with the etymology of the Greek term oikos. Its meaning is that of “house” understood as the set of people and objects forming a domestic space and being regulated by the economy (the nomos of the oikos).  

However, the term oikos has traditionally been associated with another very similar one: oikia. Both have been translated as “house”, in the most general sense of the word. Nonetheless, Xenophon outlines a distinction[30] that, although not entirely accepted by all Greek authors, is very useful in approaching the question at hand. The Greek philosopher asserts that the expression oikos refers to a house in the strict sense of a place of residence, whereas the expression oikia denotes not only the house but also the property it contains and its inhabitants. 

Based on this distinction, the word oikia would refer to a collection of elements of different natures and sizes whose coexistence and eventual interlacement would give rise to a specific spatial conception. It is formed not only by the house itself, but also by the property it contains (animals, instruments, jewellery, furniture, etc.) and its inhabitants. It would therefore be a large composite of objects whose eventual interlacements over time would form what Xenophon defines as domestic space. In that sense, these spaces not only contain and are contained by other spaces simultaneously, they also never appear as completely closed elements, despite remaining identifiable and extractable. Oikia is then not produced from a passive Platonic receptacle (chora) or an active Aristotelian substrate (topos); it is constructed instead from the multi-scalar co-existence of various groups and subgroups of systems. The ecological parts characteristic of this branch of experimental architectural projects represent, in different ways, a departure from the materialism analysed in previous cases. They find an example avant la lettre in the work of Jean Renaudie, particularly in his two housing complexes in Ivry sur Seine (1975) and Givors (1974).

Although not all parts fully coincide with the definition provided here, the discreteness of the projects operates with autonomous discrete entities that cannot be interpreted under a materialistic framework; there is no ultimate element acting as an underlying substrata (continuous or discrete) to which entities can be reduced. However, as we have seen, the notion of ecology implies the presence of oikia, that is, a house, a common denominator whose presence can be traced in these projects by a formal homogeneity that traverses the whole composition.

We can find a wide range of experimental architectural formal strategies working in this direction. Daniel Kohler’s Hyper-Nollie (2019) develops a complicit discreteness with more than 40 different parts that are always cooperative and incomplete, never single entities, never fully defined, never identical. However, the continuous connection of its spaces and the fact that each one of them is accessible from each part seem to formally evoke the logics of a relational field, particularly through the homogeneous granularity revealed by a general overview. Nevertheless, the project’s tension between the distinct discreteness of its close view and the texturised continuity of its far-view precludes any attempt to simply reduce its parts to an underlying material substrata: each part positions its own context’s interpretation through a complex balance in between identity (inherent distinction) and relationality (local complicities).

Although its assumption of the voxel as a standard unit and its complicity with Christopher Alexander’s notion of structure, Jose Sánchez’s Block’hood (2016) tends as well to avoid the possibility of any full material reductionism to any ultimate being. In spite of its underlying 3D grid, the project provides each voxel with a specific performative behaviour whose specificity is not merely underpinned by relationality, but is partly inherent to its constitution. In this sense, each unit approaches our definition of part because despite its underlying common framework, voxel’s singularity cannot be merely reduced to it or to its relations. Rasa Navasaityte’s Urban Interiorities (2015) approaches the notion of part through a recursive structure of groups inside groups: there is not any ultimate element from which the rest of compositions can be derived, but a recursive process.This partly acts as a holistic system of form production, at the same time permitting the presence of distinction beyond countability. 

These projects represent the different nuances of a part: they operate through the tension established in between part’s autonomy and part’s participation, e.g. the part’s capacity to be inherently distinct and at the same time the part’s capacity to retain something in common with other parts in order to permit local and ephemeral complicities. This type of mereology resonates with what Levi Bryant has defined as a “strange mereology”: “one object is simultaneously part of another object and an independent object in its own right.”[31] Indeed, on the one side, the parts that we have seen in this last group of projects are autonomous beings in the world that cannot be reduced to other parts. But at the same time, parts are composed by other parts, compose other parts, and relate with other parts. In synthesis, part-thinking demands parts execute what seems to be a paradox: its constitution as a countable and distinct entity that is both independent and relational.

We could synthesise the different approaches towards the definition of part presented here as follows: the first group of projects, constituted by what we have defined as topological parts, leaves aside part’s autonomy in favour of an underlying field of relations. The second group, whose parts are defined as corpuscular parts, emphasises part’s countability (mathematical discreteness) instead of part’s inherent distinction (ontological discreteness). The third group, composed by ecological parts, still retains a vague remainder of a general background (oikia) that vectorises part’s distribution. In all of them, matter’s ultimate condition is still present, although in a blurry and definitely weakened version, particularly in the last one. However, we could briefly speculate with a fourth group of architectural parts, associated with the notion of limit, that would emerge from the radical limitation of matter’s ultimate condition.

Figure 5 – Topological, Corpsular, Ecological and Limital Parts, 2020. Image: Jordi Vivaldi, 2020.

The notion of limit is at the core of architecture. If we understand the architectural practice as the production of interiorities, that is, as the production of spaces within spaces, the idea of a border distinguishing them is decisive. In this sense, the etymology of the term “temple” is particularly revealing: its root “-tem”, present also in the terms témenos, templum, and “time”, indicates the idea of a cutout, a demarcation, a frontier, a limit instrumentalised in order to separate the sacred realm of the gods from the profane territory of humans. In ancient Rome, the construction of a temple began with the cumtemplatio, the contemplative observation of a demarcated zone of the sky by the augurs. Through the attentive observation of birds, the sun and the clouds’ trajectories within the selected celestial area, the augurs interpreted the auspices of the city that was about to be founded. Once the observation was completed, the demarcated zone of the sky was projected onto the ground in order to trace the contours of the future temple, the germinal cell of the coming city. Cumtemplatio was thus cum-tem-platio: the tracing of the limits through which the cosmos took on meaning and signification by being projected onto the earth and establishing the ambit in which the humans could purposively inhabit the world. Thus, the temple instrumentalised the limit not just as a border between what is sacred and what is profane, that is, between inside and outside, but also as a space in itself, as a frontier territory mediating between the celestial realm of the gods and the terrestrial realm of humanity.

The spatialised register of the limit evoked by the temple and aligned with notions such as the Christian limbo or the Roman limes, lays the foundation for the type of immaterialist parts hypothesised here with the expression limital parts. They expand the decreasingly shy immaterialism present in topological parts, corpuscular parts and ecological parts by limiting the reduction to any sort of matter’s ultimate condition. In order to do so, limital parts are liminal, limited, and limitrophe, three decisive attributes aligned with supercomputation’s capacity to avoid parametric reductionism.

First, limital parts are liminal, that is, they are the locus of junction and disjunction. The notion of liminality should be read under its instrumentalisation by Arnold van Gennep and Victor Turner: the limit is not the Euclidean divider line that is at the core of the Modern Movement’s programmatic zonification, but, the limit is, in its anthropological register, the frontier territory that in a rite of passage mediates between the old and new identity of its participants. Parts’s liminality constitutes a daimonic space whose nature is that of “differential sameness and autoreferential difference,”[32] if the limit is in itself and by itself internal differentiation, if in its re-flection the limit separates and divides, then limital parts should necessarily join and disjoin, or, more accurately, limital parts should join what they disjoin. The liminality of limital parts does not mean that its composition is simply the random juxtaposition of a litany of solipsistic monades: in their symbiotic intertwinings, the different liminal parts establish clusters and sub-clusters of performative transfers that are constantly sewing and resewing the limit’s limits: their operativity is not always structured by harmonic consensus, but they engage in constant resistance and deviation. They produce spontaneous symbiotic interlacements that overlap without any preconceived agreement and certainly not without décalages, displacements and misfits.

Second, limital parts are limited, that is, they are distinct and determined. The notion of limitation should be read under its Hegelian instrumentalisation: “The limit is the essentiality of something, it is its determination.”[33] Thus, to limit means to define; the latin term definire signifies to trace the borders of something in order to separate it from its neighbours. Definire is the establishment of finis, ends. However, the term finis should not be read here only under the light of its topological or chronological sense, but it should also be approached in its ontological register: to define means to specify the qualities of a part that make a part this part and not that part, avoiding its reduction to any ultimate material substrata. It traces an ontological contour in order to limit the part’s infinite possible variability. A limited part refers thus to a distinct part; it is determined, but not predetermined, that is, it is not determined avant la lettre. It contrasts with what is open, flexible and generic; in a context where the power of today’s supercomputation makes it possible to notate the inherent discreteness of reality, it is no more necessary to design with simplified spatial formulas (fields), or repetitive spatial blocks (particles). Today’s computational power applied to architectural design allows an emancipation from reductive laws, whose standardisation is at the core of the material remanences of topological parts, corpuscular parts and ecological parts. Thus, rather than formulative and open parts, the unprecedented power unfolded by supercomputation lets us operate with massive sets and sub-sets of distinct parts. The limited condition of limital parts does not align with the notion of the generic, nor with derivative concepts such as flexibility, adaptability or resilience, so common in the three previous groups of architectural parts. Thus, rather than flexible, limital parts are plastic (plastiquer, plastiquage, associated in French to the notion of explosion): they vary, but at the price of gaining a new specificity and cancelling the previous one.

Third, limital parts are limitrophe, that is, they are foliated. The notion of limitrophy should be read in light of its instrumentalisation by Jacques Derrida. Rather than effacing or ignoring the limit, Derrida attempts, through his use of the term “limitrophy”, “to multiply its figures, to complicate, thicken, delinearize, fold, and divide the line precisely by making it increase and multiply.”[34] Limital parts are thus thickened, which is the literal sense of the Greek term trepho, that is, to nurture. Under this umbrella, a limitrophe part is not a solipsistic monade or a fragment referring to an absent whole. Limital parts produce inconsistent multiplicities by acquiring a foliated consistency and becoming an edgy, plural and repeatedly folded frontier. Limital parts shouldn’t orchestrate thus an abyssal and discontinuous limit: the latter does not form the single and indivisible line characteristic of modernity, rather, it produces “more than one internally divided line.”[35] Thus, limital parts grow and multiply into a plethora of edges. Precisely because of their liminal, limited and limitrophe condition, limital parts are immaterialist: they are not reducible to one, as is the case, with decreasing intensity, of topological parts, corpuscular parts or ecological parts. 

Ending Considerations

Avoiding matter’s ultimate condition requires understanding form as a spatio-temporal structure that operates at every level of scale. It demands the assumption that there is always a form beyond any given form, avoiding any continuous (field) or discrete (particle) ultimate background in which parts could be reduced. In this sense and as Graham Harman affirms, “although what is admirable in materialism is its sense that any visible situation contains a deeper surplus able to subvert or surprise it,”[36] the kind of formalism approached here does not deny this surplus, it merely states that this surplus is also formed.

The impossibility of conjugating matter’s ultimate condition with a radical part-thinking would suggest a pan-formalism based on a Matryoshka logic, a multiscalar recursivity that doesn’t rely on an ultimate and maternal underlying substrata. Under this framework and building on the German and Russian formalist traditions later developed by figures such as Colin Rowe, Alan Colquhoun, Alexander Tzonis or Liane Lefaivre, the formalism that could emerge from these statements shouldn’t be understood in the sense that there is no excess beneath the architectural forms that are given, rather, in the sense that “the excess is itself always formed.”[37] 

The constant and multiscalar presence of form and the avoidance of any ultimate substrata are posited as the two conditions that a radical part-thinking would require; they represent the only way in which the notion of part can be understood in its full radicality, that is, as an interactive and autonomous element which is not just countable (mathematically discrete) but also distinct (ontologically discrete). As we have seen, this approach is incompatible with matter’s understanding: despite matter’s revival has paradoxically imported all the attributes associated with the hylomorphic understanding of form, the re-introduction of pre-Socratic’s ultimate condition represents the clandestine re-introduction of the notion of whole and therefore an unsurpassable obstacle for part-thinking.


[1] G. Harman, “Materialism Is Not the Solution”, The Nordic Journal of Aesthetics, 47 (2014), 95.

[2] E. Prieto, La vida de la materia (Madrid: Ediciones Asimetricas, 2018), 28-102.

[3] E. Sadin, La humanidad aumentada (Buenos Aires: La Caja Negra, 2013), 152.

[4] M. Carpo, The Second Digital Turn: Design Beyond Intelligence (Cambrige: MIT Press, 2017), 71.

[5] Alberti, Re-Aedificatoria, (Madrid: Ediciones Asimétricas, 2012), 21.

[6] G. Semper, The Four Elements of Architecture and Other Writings (Cambridge: Cambridge University Press, 1969), 45-73.

[7] E. Prieto, La vida de la materia (Madrid: Ediciones Asimétricas, 2018), 28-102.

[8] M. Delanda, “Interview with Manuel Delanda”, New Materialism: Interviews and Cartographies, 9. 

[9] K. Barad, “Interview with Keren Barad”, New Materialism: Interviews and Cartographies, ed. Rick Dolphijn & Iris van der Tuin (London: Open Humanities Press, 2012), 59.

[10] E. Sadin, La humanidad aumentada (Buenos Aires: La Caja Negra, 2013), 152.

[11] K. Easterling, Medium Design (Kindle Edition: Strelka Press, 2018).

[12] B. Bratton, The Stack: On Software and Sovereignty (London: The MIT Press, 2016).

[13] G. Harman, “Materialism is Not the Solution”, The Nordic Journal of Aesthetics, 47 (2014), 100.

[14] Ibid, 98.

[15] N. Oxman, “Material Ecology”, Proceedings of the 32nd Annual Conference of the Association for Computer Aided Design in Architecture ACADIA (2012), 19-20.

[16] D. Koehler. Large City Architecture: The Fourth Part (London: 2018), 19.

[17] G. Harman, “Materialism is Not the Solution” The Nordic Journal of Aesthetics, 47 (2014), 100.

[18] M. Carpo, The Second Digital Turn: Design Beyond Intelligence, (Cambridge: MIT Press, 2017), 71.

[19] Ibid.

[20] A. Zaera, “Nuevas topografías. La reformulación del suelo,” Otra mirada: posiciones contra crónicas, ed. M. Gausa and R. Devesa (Barcelona: Gustavo Gili, 2010), 116-17.

[21] J. M. Montaner, La modernidad superada (Barcelona: Gustavo Gili, 2011), 32.

[22] Aristotle, Physis, trans. W.A. Pickard (Cambridge: The Internet Classics Archive, 1994).

[23] P. Eisenman, “Brief Advanced Design Studio”, last modified October 2014,

[24] M. Carpo, “Particalised”, Architectural Design, 89, 2 (2019), 86-93.

[25] K. Kuma, Materials, Structures, Details (Basel: Birkhäusser, 2004), 14.

[26] G. Retsin, “Bits and Pieces” Architectural Design, 89, 2 (2019), 43.

[27] T. Morton, Hyperobjects, (Minneapolis: University of Minnesota Press, 2013), 119.

[28] Ibid.

[29] Ibid, 41.

[30] K. Algra, Concepts of Space in Greek Thought (London: Brill, 1995), 32.

[31] L. Bryant, The Democracy of Objects (Cambridge: MIT Press, 2017), 215.

[32] E. Trías, Los límites del Mundo (Barcelona: Ariel Filosofía, 1985), 121.

[33] G. W. F. Hegel, The Science of Logic (Cambridge: Heidelberg Writings, 1996), 249.

[34] J. Derrida, “The Animal That Therefore I am (More to Follow)” trans. David Wills, Critical Inquiry, 28, 2 (2002), 398.

[35] Ibid., 398.

[36] G. Harman, “Materialism Is Not the Solution”, The Nordic Journal of Aesthetics, 47 (2014), 100.

[37] Ibid.

Suggest a Tag for this Article
Mereology and Structure
Components, Composition, Mereologies, Mereology, Philosophy
Giorgio Lando
University of L'Aquila
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In this short paper I illustrate what is mereology for philosophers, and which reasons lead philosophers to discuss mereological theses and disagree one with another about them. I will focus in particular on the role of structure in mereology and propose a rather simple account of what structure is from the viewpoint of mereology. As we are going to see, many philosophical controversies in mereology concern the issue of whether mereology should account for structure or not, and which role (if any) structure plays in mereology. I will also present some examples of philosophical controversies about mereological principles, and of the reasons which might be brought for choosing one side or the other in these controversies.

An additional purpose of the paper is to suggest that structure is a broad topic of common concern between architecture and philosophical mereology. In their discussions about structure, mereologists do often resort to examples involving buildings and villages. These examples – I am going to use some of them in what follows – are extremely simple, to the point of naïveté. The frequent usage of these examples might depend on the rough intuition that there are indeed some connections between mereology and architecture, and the concept of structure might be the link between them.

What Is Mereology About?

Let us begin by asking what is mereology. Mereology is the theory of two (mutually related) relations: parthood and composition. Parthood is a one-one relation between a part and a whole. These are some instances of parthood: 

my left hand is part of my body; 

Portugal is part of Europe; 

an atom of oxygen is part of a molecule of water; 

a handle is part of a door; 

the word ‘salad’ is part of the sentence ‘I eat a salad’.

The other relation which, together with parthood, is the subject matter of mereology is composition, a many-one relation. Composition indeed connects many entities (the components) to a single entity (the composed entity). Consider a rather simplistic house with a base, four outer walls, a roof and nothing else. The base, the four walls and the roof compose the house. Another example is the following: the Netherlands, Belgium and Luxembourg compose Benelux.

Composition is definable in terms of parthood. The composed entity is expected to include all the components as parts and not to include anything extraneous to the components. Also the latter feature of the composed entity can be expressed in terms of parthood, namely by requiring that every part of the composed entity has at least a part in common with at least one of the components. 
In order to express the resulting definition of composition in terms of parthood we can first define the relation of overlap, which holds between two entities if and only if they have at least a part in common (P is the relation of parthood; ⚬ is the defined relation of overlap):

Overlap: x ० y ≡def ∃z (z P x ⋀ z P y)  

Now, composition can be defined in terms of parthood and overlap (which has in turn been defined in terms of parthood above) as follows (C is the relation of composition; xx is a plural variable for the components; ≺ is the relation of being one of):

Composition: xx C y ≡def ∀z (z ≺ xx → z P y) ⋀ ∀z (z P y → ∃w (w ≺ xx ⋀  z ० w))

According to this definition, some entities xx compose one entity y if and only if every entity z that is one of xx is also part of y and every entity z that is part of y is such that there is an entity w that is one of xx and overlaps z.

What do mereologists say about parthood and composition? They attribute some features to these relations. The attributed features are generally expected to be formal or topic-neutral, in the sense that the features are not expected to depend on which kinds of entities are part of one another or compose one another. For example, the features of parthood and composition are expected by mereologists to be independent of whether we are considering the parts of a human body, the parts of a chemical molecule, or the parts of a town. Mereology is also formal in a more general sense, inasmuch as mereology never attempts to identify the parts of something or to establish what composes what: it is not the expected duty of mereology to establish what are the parts of a car, or of a building, or what composes a sentence. 

Mereological principles consist in attributions of some formal features to parthood and composition. Let us consider some examples of mereological principles and of formal features which these principles attribute to parthood and composition. In considering these examples, it is important to keep in mind that every mereological principle (any attribution of formal features to parthood and composition) is controversial, including the following examples. It can also be controversial whether the principles at stake are really formal: given a candidate principle, it might be objected that it holds when parthood is instantiated by, say, buildings, while it fails when parthood is instantiated by animal organisms. 

A mereological principle about parthood defended by many philosophers is for example that parthood is a transitive relation (transitivity is the formal feature which this principle attributes to parthood): if a is part of b and b is part of c, then a is part of c. Here are three more or less controversial instances of transitivity (involving various kinds of entities, in coherence with the expected topic-neutrality of mereological principles): 

if a handle is part of a door and the door is part of a building, then the handle is part of the building;

if my left hand is part of my left arm and my left arm is part of my body, then my left hand is part of my body;

if an MP is part of the Italian Parliament and the Italian Parliament is part of the Inter-Parliamentary Association, then the MP is part of the Inter-Parliamentary Association. 

Principles about parthood also concern the problem of whether the chains of parthood terminate or not. Do the chains of parthood terminate downwards? Does everything have a part that is different from itself no matter how deep you go down? Or is there a bottom layer of mereological simples (i.e. entities without further parts)? In the other direction, do the chains of parthood terminate upwards? Is everything part of something different from itself? Or is there a top layer, the mereological universe (i.e. an entity such that everything is part of it, and it is part of nothing different from itself)? Mereological principles can dictate an answer to these questions. 

These principles can be applied to matters of potential architectural or urbanistic concern. As regards downward termination, a problem of potential architectural concern is whether there is a bottom layer of parts of a building (say: the layer of bricks, or the layer of the smallest pieces which are visible to the human eye). As regards upward termination, a problem of potential urbanistic concern is whether there is a top layer of entities, over which entities stop being interesting for urbanists and are at best interesting for other kinds of scholars, such as geographists.

Other principles concern composition (the other relation, which – together with parthood – is the subject matter of mereology). The principles about composition mainly provide existence conditions and identity conditions for composed entities. Existence and identity are in general two pivotal concepts in metaphysics, i.e. in the wider branch of philosophy to which mereology belongs. As far as composition is concerned, mereology asks whether, given some entities, there exists something which they compose (in answering this question, mereologists provide existence conditions for composed entities), and whether there may exist two or more entities composed by the same entities (in answering this latter question, mereologists provide identity conditions for composed entities). 

Thus, given some components, how many things do they compose? Consider Barack Obama’s nose, my left shoe and the Great Pyramid of Giza. Do they compose anything? Is there a spatially scattered object (a bit in Washington, a bit here, a bit in Egypt) they compose? 

Consider instead a building entirely made of bricks. Those bricks compose that building. Do the bricks compose only the building? Or do they compose also a different, less structured entity, which we might dub ‘heap of bricks’? Suppose that the building collapses: after the collapse – one might say – the building stops existing, while the heap of bricks continues existing. How can this happen, if they are identical, i.e. if the bricks compose only one entity? A single entity cannot both continue existing and stop existing.

The following are two examples of two rather popular (albeit controversial) mereological principles about composition (their usual label is indicated in the parenthesis):

given some entities – no matter how sparse and heterogeneous they are – there is at least an entity composed by them (Unrestricted Composition); 

given some entities, there is at most an entity composed by them (Uniqueness of Composition). 

Unrestricted Composition provides existence conditions for composed entities, while Uniqueness of Composition provides identity conditions for composed entities.

The Role of Structure in Mereology

In the above example of the brick building and of the heap of bricks, we have seen how the temptation arises to distinguish wholes according to their being structured or non-structured, or according to their being structured in different ways. In order to appreciate the role of structure in mereology, it is very important not to misidentify the subject matter of the philosophical controversies about this kind of example. 

Indeed, no mereologist doubts that, in order to compose a building, the bricks have to be in some mutual relations and that, more in general, not any heap of bricks is a building. There is no interesting philosophical controversy on the fact that the parts of many composed entities are arranged or structured in a certain way. 

The problem mereology is concerned with is different: does structure have any impact on the existence and identity of composed entities? Do some things need to be structured in a certain way (e.g. in a building-like way, or in a car-like way, or in a person-like way, or in a mountain-like way) in order to compose something? There is obviously a difference between the parts of a car on the one hand, and Barack Obama’s nose, my left shoe and the Great Pyramid of Giza on the other. The difference is that the parts of a car are in certain mutual relations and have certain designated functional roles. The relations among the parts of a car and their functional roles are constrained by the nature of cars in general, and by the project of that specific car model. The mutual relations among parts and the roles of the parts are roughly what structure consists in. 

To repeat: nobody doubts that the parts of a car have a kind of structure which, by contrast, disparate, sparse entities lack. Mereology is not about this. The mereological problem at stake is whether, on the basis of this difference between the parts of a car on the one hand, and Barack Obama’s nose, my left shoe and the Great Pyramid of Giza on the other, we should conclude that only the parts of a car compose something, while Barack Obama’s nose, my left shoe and the Great Pyramid of Giza do not compose anything. If this were the case, then, in contrast with the above principle of Unrestricted Composition, it would not be true that, given some entities – no matter how disparate and sparse they are – there exists something they compose: there would be nothing which Barack Obama’s nose, my left shoe and the Great Pyramid of Giza compose. 

Unrestricted Composition is a mereological principle according to which structures have no bearing on the existence conditions for composed entities. According to Unrestricted Composition, composed entities exist irrespective of whether and how their components are structured. 

Another mereological problem concerning structure is: does structure have any bearing on the identity conditions of composed entities? According to Uniqueness of Composition, given some entities there is at most one entity composed by them. Thus, there cannot be two different entities composed by the same entities. This entails that two composed entities cannot have exactly the same parts. If the composed entities are different, then they have a different part, and this different part is their difference maker. The fact that these parts are in different mutual relations and have different roles is not an admissible difference maker for composed entities. If Uniqueness of Composition is true, then the identity conditions for composed entities countenance only their parts, and not their structure. Thus, both Unrestricted Composition (for what concerns the existence conditions for composed entities) and Uniqueness of Composition (for what concerns the identity conditions for composed entities) exhibit a kind of deliberate blindness to structure.

Principles of Structure Obliteration

Before considering how it is possible to argue in favour or against this blindness to structure, it is useful to be a bit more precise on how structure is construed in this context. A theory of parthood and composition can countenance or obliterate various aspects of structure. This depends on whether, in a certain theory of parthood, certain principles of structure obliteration hold or not. We will consider four principles of structure obliteration.[1] These principles are interesting because they are of help in distinguishing various aspects of structure. These aspects of structure are obliterated in the identity conditions for composed entities, if the respective obliteration principle holds. They are by contrast countenanced in the identity conditions for composed entities, if the respective principle fails. 

The first principle is Absorption and claims that the repetition of parts is not a difference maker for composed entities. If Absorption is true, then the repetition of parts has no impact on the identity conditions for composed entities. Absorption can be formalised as follows (Σ is an operation of composition, whose inputs are the components and whose output is the composed entity; the formula expresses the fact that the multiple occurrences of the inputs – expressed by the multiple occurrences of the variables x and y in the left part of the formula – make no difference for the identity conditions of the output): 

Absorption: ∑ (…, x, x, …, y, y, …) = ∑ (…, x, …, y, …)

The second and the third principles are Collapse and Levelling and jointly claim that the stratification and the groupings of parts at different levels are not difference makers for composed entities (i.e. they have no impact on the identity conditions for composed entities). 

Collapse: ∑ (x) = x

Levelling: ∑ (…, ∑(x, y, z, …), …, ∑ (u, v, w, …), …) = ∑ (…, x, y, z, …, …, u, v, w, …, …)

The fourth principle is Permutation and claims that the order of the parts is not a difference maker for composed entities (i.e. it has no impact on the identity conditions for composed entities).

Permutation: ∑ (…, x, …, y, …, z,…) = ∑ (…, y, …, z, …, x, …)

This approach manages to differentiate various theories of parthood, according to their degree of blindness with respect to structure. What is usually called (for historical reasons) Classical Mereology abides by all the above four principles of structure obliteration and is, as a result, deliberately blind with respect to the repetition, to the stratification, to the groupings at different levels and to the order of the components in a composed entity. Only the parts matter for the identity conditions of composed entities, according to Classical Mereology. By contrast, the ways in which the parts are arranged/structured (e.g. repeated, stratified, grouped or ordered) do not matter. 

It is noteworthy that the four principles of structure obliteration are mutually independent. If you adopt a Non-Classical Mereology, you are not thereby forced to reject all the four principles as a single package. You can reject one or more of them, while keeping the others. In so doing, you sometimes end up adopting a theory which is no less well-established than Classical Mereology. For example, suppose that you think that the stratification and groupings at various levels of parts matter for the identity conditions of composed entities, while their order and repetition do not matter. What you obtain is Set Theory, a well-established theory, with a pivotal role in the foundations of mathematics.

Controversies in Mereology (and How to Argue About Them)

How should we argue about the formal features of parthood and composition? What reasons can be brought in favour of or against the mereological principles which attribute formal features to parthood and composition? And what reasons can – in particular – be brought in favour of or against the principles we have introduced above, such as Transitivity of Parthood, Unrestricted Composition, Uniqueness of Composition and the four principles of structure obliteration? 

Mereologists mainly proceed either by analysing and assessing alleged counterexamples to the mereological principles, or by analysing and assessing a priori arguments in support of or against them. As far as counterexamples are concerned, let us focus on Uniqueness of Composition and on its radical blindness to structure (i.e. – as we have seen in § 3 – blindness to repetition, stratification, groupings at different levels and order of components in a composed entity). One might be tempted to dismiss Uniqueness of Composition rather quickly, on the basis of the fact that some prima facie unavoidable counterexamples might seem fatal to it. 

Consider the components of the sentence ‘Gina loves Mario’: the words ‘Gina’, ‘loves’ and ‘Mario’. The same components can also form the sentence ‘Mario loves Gina’. ‘Gina loves Mario’ and ‘Mario loves Gina’ might seem two composed entities with the same components, in contrast with Uniqueness of Composition. The order of words (an aspect of structure, which belongs to the subject matter of syntax in linguistics) in sentences seems to matter for the identity conditions of sentences, in contrast with Uniqueness of Composition and with Permutation. 

Consider also a very small village, composed by a square, two streets and four buildings. It seems prima facie plain that Uniqueness of Composition fails for those components: the disposition of the streets with respect to the square, and the location of the buildings with respect to those of the square and of the streets (in general: the way in which the components of the village are arranged) would seem to matter for the identity of the village. 

However, the evaluation of these alleged counterexamples is not as easy as it seems, and Uniqueness of Composition should not be dismissed so quickly. Why? Because whether two composed entities (two sentences, two small villages) can be different while having the same parts and whether they can – as a consequence – be different only in virtue of their structure depends on a controversial identification of the entities at stake. 

In the case of the sentence, it depends on whether the entities at stake are linguistic tokens or types. Consider only single concrete tokens or inscriptions of ‘Mario’, ‘loves’ and ‘Gina’: sequences of sounds, stains of ink or groups of pixels on a screen. These concrete tokens are always in a single, specific order. Some of these inscriptions are ordered in a way such that ‘Mario’ is the first inscription (counting from the left) and ’Gina’ is the last inscription (this is the case of the word inscriptions in ’Mario loves Gina’). Others of these inscriptions are ordered in a way such that ’Gina’ is the first inscription (counting from the left) and ’Mario’ is the last inscription (this is the case of the word inscriptions in ’Gina loves Mario’). It never happens that the same inscriptions are arranged in two ways and thereby compose two different wholes. The initial impression that it is clear that two sentences can be different simply due to the arrangement of their parts (even if they have exactly the same parts) depends on seeing words not as tokens but as abstract word types, which occur in many different sentence types. 

Consider also the case of the small village. Given a specific small village, at a specific time, the square, the two streets and the four buildings are arranged in a single way (they have a single structure). There are not two small villages composed by that square, those streets and those buildings at that time. 

These considerations about the sentence and the small village can, as a matter of fact, be generalised. Whenever we are tempted to dismiss those principles of Classical Mereology which express its deliberate blindness to structure, it turns out that the temptation depends on a controversial characterisation of the involved entities.[2]

Please note that the philosophers objecting to Uniqueness of Composition might refine their counterexamples, and the defenders of Uniqueness of Composition might refine their analysis in order to deal with these counterexamples: the purpose of the above analysis is not to resolve the philosophical disputes about the role of structure in mereology in favour of blindness to structure, but to exemplify the way in which philosophers argue one with another about mereology and structure. The exemplifications are also meant to suggest that these controversies are unlikely to be easily solvable by adducing counterexamples: the analysis of these counterexamples is often arduous and depends on controversial assumptions. 

Finally, I would like to discuss an example of the second main way of arguing about mereological principles, the one which involves general, a priori arguments in support of or against mereological principles. Let us focus in this case on Unrestricted Composition. Suppose that you deny Unrestricted Composition. This denial will be based on the intuition that there is a patent difference between – say – the parts of a car on the one hand, and Barack Obama’s nose, my left shoe and the Great Pyramid of Giza on the other. What does this difference consist in? In order to obtain an alternative to Unrestricted Composition, this difference should correspond to a general condition which a plurality of entities should satisfy in order to have a fusion. 

We might try to extract this general condition from the examples, e.g. by observing that the parts of a car are spatially close one to another, while Barack Obama’s nose, my left shoe and the Great Pyramid of Giza are not; or by observing that there are causal links among the parts of a car (e.g. a movement in the steering causes a movement in its anterior wheels), while Barack Obama’s nose, my left shoe and the Great Pyramid of Giza are in no direct causal connection. On this basis, one might propose the following criteria for the restriction of composition: only mutually close entities compose something; only entities which move together (or act together) compose something. However, these criteria are unavoidably vague. There is no such thing as being definitely close in space or as being definitely causally connected. Every two parts of the universe are at some distance and have some kind of more or less remote causal connection. 

How is it possible to fix a threshold, i.e. a minimal degree of proximity or of causal connectedness? The threshold should be such that: entities above that threshold compose something; entities below that threshold do not compose anything. For example, we should determine once and for all at which maximum distance some buildings should be in order to contribute to compose a certain town, instead of belonging to two different towns. Any such threshold would be arbitrary, and would risk making arbitrary our existence claims about composed entities (such as towns) as well. 

A famous argument in support of Unrestricted Composition is based on the thesis that existence claims cannot be either vague or arbitrary. This means that no compelling motivation for restricting composition can be satisfied, and that, as a consequence, composition cannot be restricted. Thus, composition would be unrestricted. 

The general idea behind this famous argument for Unrestricted Composition (of which I have presented a simplified version)[3] is that existence conditions for composed entities should not be constrained by structural considerations about the mutual unity of parts. Why? Because it is arbitrary to delimit the domain of what is unitary. Every plurality of entity can be seen as unitary (or as non-unitary) according to certain criteria and/or from a certain standpoint. This is a general motivation why classical mereology is deliberately blind to structure: because the attribution of roles to structure risks introducing arbitrary and hardly justifiable thresholds. Thus, also, when mereologists proceed by analysing and assessing a priori arguments – as much as when they proceed by analysing and assessing counterexamples, as we have seen above – the problem whether structure has any role in mereology is pivotal, and has no easy solution.


[1] These principles have been originally presented in K. Fine, "Towards a Theory of Part," The Journal of Philosophy, 107, 11 (2010): 559-589.

[2] 2 See G. Lando, Mereology: A Philosophical Introduction (London: Bloomsbury, 2017), chapter 8, for other applications of this defense strategy for classical mereology.

[3] The argument had been originally presented in  D. Lewis, Parts of Classes (Oxford: Blackwell, 1991) and has been later refined in T. Sider, Four-Dimensionalism: An Ontology of Persistence and Time (Oxford: Oxford University Press, 2001). See D. Korman, D. The Argument from Vagueness” Philosophy Compass, 5, 10 (2010), 891–901 for an overview of the literature on this argument.

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Affordances of Decentralised Technologies for Commons-based Governance of Shared Technical Infrastructure
Architecture Theory, Blockchain, Commons, Decentralisation, Mereologies, Mereology
David Rozas
Universidad Complutense de Madrid
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In this article I will illustrate affordances of decentralised technologies in the context of commons governance. My aim is to summarise the conversation around the lecture “When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance” I gave in the Mereologies Open Seminar organised by The Bartlett School of Architecture at University College London on 25th April 2019. I will also extend the conversation by providing a concrete example of such affordances in the context of a community network.

What is Blockchain? Three Key Concepts around Decentralised Technologies

In 2008, an anonymous paper presented Bitcoin: the first cryptocurrency based purely on a peer-to-peer system.[1] For the first time, no third parties were necessary to solve problems such as double-spending, thanks to cryptography. The solution was achieved through the introduction of a data structure known as a blockchain. In simple terms, a blockchain can be understood as a distributed ledger. Distributed refers to a technical property of a system in which certain components are located on different computers connected through a network. The blockchain, in this sense, can be thought of as a “decentralised book” in which agreed transactions can be stored in a set of distributed computers. Data, such as the history of monetary exchanges generated by using cryptocurrencies, can be stored in a blockchain. The key aspect resides in the fact that there is no need to trust a third party, such as a bank server, to store that information.

Nakamoto’s article opened what is considered to be the first generation of blockchain technologies.[2] This generation, up to approximately 2013, includes Bitcoin and a number of crypto-currencies that appeared after it. The second generation, approximately from 2014 onwards, is the extension of these blockchains with capabilities beyond currencies in the form of automatic agreements or smart contracts.[3] Smart contracts can be understood as distributed applications which encode clauses that are automatically enforced and executed without the need for a central authority. They can be employed, for example, to enable the execution of code to provide certifications, such as obtaining a diploma or a registry of lands, according to previously mutually agreed rules. Again, the novel aspect here is the fact that the execution of such rules, in the form of computer instructions, is distributed across a large number of computers without the need of a central point of control.

Complex sets of smart contracts can be developed to make it possible for multiple parties to interact with each other. This fostered the emergence of the last of the concepts I will introduce around decentralised technologies: Decentralised Autonomous Organisations (DAO). A DAO is a self-governed organisation in which interactions between the members of the organisation are mediated by the rules embedded in the DAO code. These rules are sets of smart contracts that encode such interactions. The rules embedded in the code are automatically enforced by the underlying technology, the blockchain, in a decentralised manner. DAOs could, for example, hire people to carry out certain tasks or compensate them for undertaking certain action. Overall, this can be understood as analogous to a legal organisation, with legal documents – bylaws – which define the rules of interaction among members. The development of DAOs has been, unsurprisingly, significantly popular around financial services.[4] However, DAOs could be used to provide a wide variety of services or management of resources in a more diverse range of areas. A more artistic example of a DAO is the Plantoid project,[5] a sculpture of a plant, which can hire artists to physically modify the sculpture itself according to the rules collectively agreed in the smart contracts encoded in it.

All of these potentials of decentralised technologies represent an emerging research field. Together with other colleagues of the EU project P2PModels,[6] we are exploring some of these potentials and limitations in the context of the collaborative economy and, more precisely, on some of the models emerging around Commons-Based Peer Production.

Collaborative Economy and Commons-Based Peer Production

The collaborative economy is a growing socio-economic phenomenon in which individuals produce, exchange and consume services and goods, coordinating through online software platforms. It is an umbrella concept that encompasses different initiatives and significantly different forms are emerging; there are models where large corporations control the platform, thus ensuring its technologies and the knowledge held therein are proprietary and closed. Uber, a riding service, and AirBnB, a short-term lettings service, are perhaps the most well-known examples of such initiatives. They differ from models that revolve around Commons-Based Peer Production (CBPP), where individuals produce public goods by dispensing with hierarchical corporate structures and cooperating with their peers.[7] In these models, participants of the community govern the assets, freely sharing and developing technologies.[8] Some of the most well-known examples of the initiatives around such commons-based models are Wikipedia and GNU/Linux, a Free/Libre Open Source Software (FLOSS) operating system. Commons-based models of the collaborative economy are, however, extending to areas as broad as open science, urban commons, community networks, peer funding and open design.[9]

Three main characteristics are salient in the literature on CBPP.[10] Firstly, CBPP is marked by decentralisation, since authority resides in individual agents rather than a central organiser. Secondly, it is commons-based since CBPP communities make frequent use of common resources. These resources can be material, such as in the case of 3D printers shared in small-scale workshops known as Fab Labs; or immaterial, such as the wiki pages of Wikipedia or the source code in a FLOSS project. Thirdly, non-monetary motivations are prevalent in the community. These motivations are, however, commonly intertwined with extrinsic motivations resulting in a wide spectrum of forms of value operating in CBPP communities,[11] beyond monetary value.[12] An Example of a CBPP Community in Action

In order to extend the discussion of the affordances of decentralised technologies in CBPP, I will employ as an illustrative example.[13] is a community network: a participatory project whose goal is to create a free, open and neutral telecommunications network to provide access to the Internet. If you are reading this article online, you might be accessing it through a commercial Internet Service Provider. These are the companies which control the technical infrastructure you are using to connect to the Internet. They manage this infrastructure as a private good. The project, instead, manages this infrastructure as a commons. In other words, is organised around a CBPP model,[14] in which the network infrastructure is governed as a common good. Over the past 16 years, participants of have developed communitarian rules, legal licenses, technological tools and protocols which are constantly negotiated and implemented by the participants.

I have chosen to discuss the potentialities of blockchain drawing on, a community network, for two main reasons. Firstly, the most relevant type of commons governed in this case is shared infrastructure, such as fibre optic and routers. The governance of rival material goods, in contrast to the commons governance of non-rival goods such as source code or wiki pages, better matches the scope of the conversations which emerged during the symposium around architecture of the commons and the role played by participatory platforms.[15] Secondly, provides a large and complex case of governance of shared infrastructure. The growth experienced by’s infrastructure and community since the first pair of nodes were connected in a rural region of Catalonia in 2004 is significant. In their study of the evolution of governance in, Baig et al. reported a network infrastructure consisting of more than 28,500 operational nodes which cover a total length of around 50,000 km of links that are connected to the global Internet. This study refers to the period 2005–2015.[16] The latest statistics reported by state that there are more than 35,000 operational nodes and 63,000 km of links.[17] Beyond the infrastructure, the degree of participation in the community is also significant: more than 13,000 registered participants up to 2015, according to the aforementioned study, and more than 50,000 users of this community network connect on a day to day basis, as reported by the community at present.[18] Thus, provides a suitable scenario for the analysis of the affordances of decentralised technologies for commons governance.

Ostrom’s Principles and Affordances of Decentralised Technologies for Commons Governance

How do communities of peers manage to successfully govern common resources? The study of the organisational aspects of how common goods might be governed was traditionally focussed on the study of natural resources. This commons dilemma was explored by Hardin in his influential article “The Tragedy of the Commons”, whose ideas became the dominant view. In this article, Hardin states how resources shared by individuals acting as homo economicus (out of self-interest in order to maximise their own benefit) results in the depletion of the commons. The individuals’ interests enter into conflict with the group’s, and because they act independently according to their short-term interests, the result of the collective action depletes the commons.[19] As a consequence, in order to avoid this logic – “If I do not use it, someone else will”, which is not sustainable – it was necessary to manage these commons through either private ownership or centralised public administration. 

Later on, Nobel laureate researcher Elinor Ostrom questioned and revisited “The Tragedy of the Commons”. In her work, she showed how under certain conditions commons can indeed be managed in a sustainable way by local communities of peers. Her approach took into account that individual agents do not operate in isolation, nor are they driven solely by self interest. Instead, she argued that communities communicate to build processes and rules, with different degrees of explicitation, that ensure their sustainability.[20] This hypothesis was supported by a meta-analysis of a wide range of case studies,[21] and has been confirmed in subsequent research.[22] As part of this work, she identified a set of principles for the successful management of these commons,[23] which has also been subsequently applied to the study of collaborative communities whose work is mediated by digital platforms, such as Wikipedia and FLOSS communities:[24]

1. Clearly defined community boundaries: in order to define who has rights and privileges within the community.

2. Congruence between rules and local conditions: the rules that govern behaviour or commons use in a community should be flexible and based on local conditions that may change over time. These rules should be intimately associated with the commons, rather than relying on a “one-size-fits-all” regulation.

3. Collective choice arrangements: in order to best accomplish congruence (with principle number 2), people who are affected by these rules should be able to participate in their modification, and the costs of alteration should be kept low.

4. Monitoring: some individuals within the community act as monitors of behaviour in accordance with the rules derived from collective choice arrangements, and they should be accountable to the rest of the community.

5. Graduated sanctions: community members actively monitor and sanction one another when behaviour is found to conflict with community rules. Sanctions against members who violate the rules are aligned with the perceived severity of the infraction.

6. Conflict resolution mechanisms: members of the community should have access to low-cost spaces to resolve conflicts.

7. Local enforcement of local rules: local jurisdiction to create and enforce rules should be recognised by higher authorities.

8. Multiple layers of nested enterprises: by forming multiple nested layers of organisation, communities can address issues that affect resource management differently at both broader and local levels.

What kind of affordances do decentralised technologies offer in the context of commons governance and, more concretely, with regards to Ostrom’s principles? Together with other colleagues,[25] we have identified six potential affordances to be further explored. 

Firstly, tokenisation. This refers to the process of transforming the rights to perform an action on an asset into a transferable data element (named token) on the blockchain. For example, tokens can be employed to provide authorisation to access a certain shared resource. Tokens may also be used to represent equity, decision-making power, property ownership or labour certificates.[26]

Secondly, self-enforcement and formalisation of rules. These affordances refer to the process of embedding organisational rules in the form of smart contracts. As a result, there is an affordance for the self-enforcement of communitarian rules, such as those which regulate monitoring and graduated sanctions, as reflected in Ostrom’s principles 4 and 5. This encoding of rules also implies a formalisation, since blockchain technologies require these rules to be defined in ways that are unambiguously understood by machines. In other words, the inherent process of explicitation of rules related to the use of distributed technologies also provides opportunities to make these rules more available and visible for discussion, as noted in Ostrom’s principle 2.

Thirdly, autonomous automatisation: the process of defining complex sets of smart contracts which may be set up in such a way as to make it possible for multiple parties to interact with each other without human interaction. This is analogous to software communicating with other software today, but in a decentralised manner. DAOs are an example of autonomous automatisation as they could be self-sufficient to a certain extent. For instance, they could charge users for their services.[27]

Fourthly, decentralised technologies offer an affordance for the decentralisation of power over the infrastructure. In other words, they can facilitate processes of communalising the ownership and control of the technological artefacts employed by the community. They do this through the decentralisation of the infrastructure they rely on, such as collaboration platforms employed for coordination.

Fifthly, transparency: for the opening of organisational processes and the associated data, by relying on the persistency and immutability properties of blockchain technologies.

Finally, decentralised technologies can facilitate processes of codification of a certain degree of trust into systems which facilitate agreements between agents without requiring a third party. Figure 1 below provides a summary of the relationships between Elinor Ostrom’s principles and the aforementioned affordances.[28]

Figure 1 – Summary of the relationships between the identified affordances of blockchain technologies for governance and Ostrom’s principles (Ostrom, 1990). Image credit:, identified by Rozas et al., 2018.

These congruences allow us to describe the impact that blockchain technologies could have on governance processes in these communities. These decentralised technologies could facilitate coordination, help to scale up commons governance or even be useful to share agreements and different forms of value amongst various communities in interoperable ways, as shown by Pazaitis et al..[29] An example of how such affordances might be explored in the context of CBPP can be found in community networks such as

A DAO for Commons Governance of Shared Technical Infrastructure

Would it be possible to build a DAO that might help to coordinate collaboration and scale up cooperative practices, in line with Ostrom’s principles, in a community network such as First of all, we need to identify the relationship between Ostrom’s principles and We can find, indeed, a wide exploration of the relationship between Ostrom’s principles and the evolution in the self-organisational processes of in the work of Baig et al..[30] They document in detail how governs the infrastructure as a commons drawing on these principles, and provide a detailed analysis of the different components of the commons governance of the shared infrastructure in Secondly, we need to define an initial point of analysis, and tentative interventions, in the form of one of the components of this form of commons governance. From all of these components, I will place the focus of analysis on the economic compensation system. The reason for selecting this system is twofold. On the one hand, it reflects the complexity behind commons governance and, thus, allows us to illustrate the aforementioned principles in greater depth. Secondly, it is an illustrative example of the potential of blockchain, as we shall see, to automatise and scale up various cooperative processes.

The economic compensation system of was designed as a mechanism to compensate imbalances in the uses of the shared infrastructure. Professional operators, for example, are requested to declare the expenditures and investments in the network. In alignment with Ostrom’s principle number 4, the use, expenditure and investments of operators are monitored, in this case by the most formal institution which has emerged in the Foundation. The Foundation is a legal organisation with the goal to protect the shared infrastructure and monitor compliance with the rules agreed by the members of the community. The community boundaries, as in Ostrom’s principle number 1, are clearly defined and include several stakeholders.[31] Different degrees of commitment with the commons were defined as collective choice arrangements (principle number 3). These rules are, however, open to discussion through periodic meetings organised regionally, and adapted to the local conditions, in congruence with principle number 2. If any participant, such as an operator, misuses the resources or does not fulfill the principles, the individual is subject to graduated sanctions,[32] in alignment with principle number 5. As part of the compensation system, compensation meetups are organised locally to cope with conflict resolution, in congruence with principle 6. Principles 6 and 7 are also clearly reflected in the evolution of the governance of, although they are more closely associated with scalability.[33] 

The compensation DAO could be formed by a set of local DAOs, whose rules are defined and modifiable exclusively by participants holding a token which demonstrates they belong to this node. These local DAOs could be deployed from templates, and could be modified at any point as a result of a discussion at the aforementioned periodic meetings held by local nodes and in congruence with the local conditions. Among the rules of the smart contracts composing these DAOs, participants may decide to define the different factors that are considered when discussing the local compensation system arrangements, as well as graduated sanctions in case of misuse of the common goods. These rules might be copied and adapted by some of the nodes facilitating the extension of the collaborative practices.

Some of the settings of these local DAOs could be dependent on a federal compensation DAO that defines general aspects. A mapping of the current logic could consist of reaching a certain degree of consensus between the participants in all of the nodes, but having this process approved by the members of the Foundation, who would hold a specific token.  Examples of general aspects regulated by the federal DAO are the levels of commitment towards the commons of each operator, which is currently evaluated and monitored manually by the Foundation. General aspects such as this could be automatised in several ways therefore moving from manual assignations by the Foundation, as is currently the case, to automatically assigned tokens depending on the communitarian activities tracked in the platform. This is an example of a possible intervention to automatise certain collaborative practices assuming the current structure. Figure 1 below provides an overview of a preliminary design of a DAO for a compensation system mapping the current logics. 

Figure 2 – A proposal of a simple compensation DAO. The green arrows represent the extension of practices between local DAOs, including new nodes such as number 5. Black arrows represent the interactions between the local DAOs and the federal DAO, in congruence with Ostrom’s principle 8. Image credit: Rozas, et al, 2018.

More disruptive tentative interventions could consist of the implementation of more horizontal governance logics which allow modifications of the rules at a federal level or to transform the rules that regulate the monitoring. These interventions, however, should be carefully co-designed together with those who participate in the day-to-day of these collectives. Our approach states that the development of decentralised tools which support commons governance should be undertaken as a gradual process to construct situated technology, with an awareness of the cultural context and aiming to incorporate particular social practices into the design of these decentralised tools. 

This basic example of a DAO illustrates, on the one hand, the relationship with Ostrom’s principles: monitoring mechanisms, local collective choice arrangements, graduated sanctions and clear boundaries. These principles are sustained by the aforementioned affordances of blockchain for commons governance. For example, tokenisation with regards to providing permission as to who has the ability to participate in the choices locally and at a federal level and how, as well as the certification of the level of commitment to the commons; monitoring of the expenditures and reimbursements through the transparency provided by the blockchain; self-enforcement, formalisation and automatisation of the communitarian rules in the form of smart contracts. Another, more general, example of this is the increment in the degree of decentralisation of power over the platform because of the inherent decentralised properties of the technology itself. In this way, this could result in a partial shift of power over the platform from the Foundation towards the different nodes formed by the participants. Furthermore, as discussed, the fact that such rules are encoded in the form of configurations of smart contracts could facilitate the extension of practices and the development of new nodes; or even the deployment of alternative networks capable of operating as the former network, and reusing and adapting the encoded rules of the community while still using the shared infrastructure. Overall, further research of the role of decentralised technologies in commons governance offers, in this respect, a promising field of experimentation and exploration of the potential scalability of cooperative dynamics.

Discussion and Concluding Remarks

In this article I provided an overview and discussed an example of the affordances of blockchain technologies for commons governance. Concretely, I described such potentialities drawing on the example of a DAO to automatise some of the collaborative processes surrounding the compensation system of a community network: Throughout this example, I aimed to illustrate, in more detail, the affordances of blockchain for commons governance which I presented during the symposium. The aim of this example is to illustrate how blockchain may facilitate the extension and scaling up of the cooperation practices of commons governance. Further explorations, more closely related to the architecture field, could explore the discussed affordances for commons governance with discrete design approaches that provide participatory frameworks for collective production.[34] In this respect, decentralised technologies offer opportunities of exploration to tackle challenges such as those identified by Sánchez[35] to define ways to allocate ownership, authorship and distribution of value without falling into extractivist practices.

A better understanding of the capabilities of blockchain technologies for commons governance will require, however, further empirical research. Examples of research questions which need to be addressed are those with regards to the boundaries of the discussed affordances. For example, with regards to tokenisation and formalisation of rules: which aspects should remain in/off the blockchain, or furthermore completely in/out of code?

Overall, CBPP communities provide radically differing values and practices when compared with those in markets. In this respect, the study of the potentialities and limitations of blockchain technologies in the context of the governance of CBPP communities offers an inspiring opportunity to take further steps on a research journey that has only just begun.


[1] S. Nakamoto,“Bitcoin: A Peer-to-Peer Electronic Cash System” (2008).

[2] M. Swan, Blockchain: Blueprint for a New Economy (Sebastopol, CA, USA: O’Reilly, 2015).

[3] N. Szabo, ”Formalizing and Securing Relationships on Public Networks, First Monday, 2, 9 (1997).

[4] See, for example, a cryptocurrency backed by bars of gold in which the governance is mediated by a DAO, last accessed on 24th July 2019.

[5] See, last accessed on 24th July 2019.

[6] See, last accessed on 2nd July 2019.

[7] Y. Benkler, The Wealth of Networks: How Social Production Transforms Markets and Freedom (2006); M. Bauwens, “The Political Economy of Peer Production,CTheory 1, 12 (2005).

[8] M. Fuster-Morell, J. L. Salcedo, and M. Berlinguer. “Debate About the Concept of Value in Commons-Based Peer Production,” Internet Science (2016); Bauwens, Michel, and Alekos Pantazis. 2018. “The Ecosystem of Commons-Based Peer Production and Its Transformative Dynamics.” The Sociological Review, 66, 2 (2016), 302–19.

[9] V. Kostakis and M. Papachristou, “Commons-Based Peer Production and Digital Fabrication: The Case of a RepRap-Based, Lego-Built 3D Printing-Milling Machine” (2013); V. Niaros, V. Kostakis, and W. Drechsler, “Making (in) the Smart City: The Emergence of Makerspaces,” Telematics and Informatics (2017).

[10] A. Arvidsson, A. Caliandro, A. Cossu, M. Deka, A. Gandini, V. Luise, and G. Anselm, “Commons Based Peer Production in the Information Economy,” P2PValue (2016).

[11] C. Cheshire, and J. Antin, “The Social Psychological Effects of Feedback on the Production of Internet Information Pools,” Journal of Computer-Mediated Communication, 13, 1 (2008).

[12] M. Fuster-Morell, J. L. Salcedo, and M. Berlinguer, “Debate About the Concept of Value in Commons-Based Peer Production,Internet Science (2016).

[13] See, last accessed on 30th June 2019.

[14] R. Baig, R. Roca, F. Freitag, and L. Navarro, “, a Crowdsourced Network Infrastructure Held in Common,Computer Networks: The International Journal of Computer and Telecommunications Networking, 90 (2015).

[15] J. Sánchez, “Architecture for the Commons: Participatory Systems in the Age of Platforms,Architectural Design, 89, 2 (2019).

[16] R. Baig, R. Roca, F. Freitag, and L. Navarro. “, a Crowdsourced Network Infrastructure Held in Common,” Computer Networks: The International Journal of Computer and Telecommunications Networking, 90 (2015).

[17] 2019. “Node Statistics,” Node Statistics (2019).

[18] Ibid.

[19] G. Hardin, “The Tragedy of the Commons. The Population Problem Has No Technical Solution; It Requires a Fundamental Extension in Morality,Science 162, 3859 (1968), 1243–48.

[20] E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action (Cambridge University Press, 1990).

[21] Ibid.

[22] E. Ostrom, “Understanding Institutional Diversity” (2009); M. Cox, G. Arnold, and S. Villamayor Tomás, “A Review of Design Principles for Community-Based Natural Resource Management” (2010).

[23] E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action (Cambridge University Press, 1990), 88–102.

[24] F. B. Viégas, M. Wattenberg, and M. M. McKeon, “The Hidden Order of Wikipedia,” Online Communities and Social Computing, OCSC'07: Proceedings of the 2nd international conference on Online communities and social computing (2007).

[25] D. Rozas, A. Tenorio-Fornés, S. Díaz-Molina, and S. Hassan, “When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance,SSRN Electronic Journal (2018), 8–20.

[26] S. Huckle and M. White, “Socialism and the Blockchain.” Future Internet, 8, 4 (2016), 49.

[27] P. De Filippi, and S. Hassan, “Blockchain Technology as a Regulatory Technology: From Code Is Law to Law Is Code,First Monday, 21, 12 (2016).

[28] D. Rozas, A. Tenorio-Fornés, S. Díaz-Molina, and S. Hassan, “When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance,” SSRN Electronic Journal (2018), 21–22.

[29] A.  Pazaitis, P. De Filippi, and V. Kostakis, “Blockchain and Value Systems in the Sharing Economy: The Illustrative Case of Backfeed,” Technological Forecasting and Social Change, 125 (2017), 105–15.

[30] R. Baig, R. Roca, F. Freitag, and L. Navarro. “, a Crowdsourced Network Infrastructure Held in Common,” Computer Networks: The International Journal of Computer and Telecommunications Networking, 90 (2015).

[31] Ibid.

[32] Ibid.

[33] See Baig et al. (2015) for further details.

[34] J. Sánchez, “Architecture for the Commons: Participatory Systems in the Age of Platforms,” Architectural Design, 89, 2 (2019).

[35] Ibid.

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View into a codividual interiority. Physical Model, Comata at the BPro Show 2019. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.
Towards a Sympoietic Architecture: Codividual Sympoiesis as an Architectural Model
Architecture, Autopoesis, City Architecture, Computational Design, Mereologies, Mereology, Urban Design
Shivang Bansal
University College London
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“…the rigour of the architecture is concealed beneath the cunning arrangement of the disordered violences…”[1] 

This essay investigates the potential of codividual sympoiesis as a mode of thinking overlapping ecological concepts with economics, contemporary philosophy, advanced research in computation and digital architecture. By extending Donna Haraway’s argument of “tentacular thinking” into architecture, it lays emphasis on a self-organising and sympoietic approach to architecture. Shifting focus from an object-oriented thinking to parts, it uses mereology, the study of part-hoods and compositions, as a methodology to understand a building as being composed of parts. 

It argues the limits of autopoiesis as a system and conceptualises a new architectural computing system embracing spatial codividuality and sympoiesis as a necessity for an adaptive and networked existence through continued complex interactions among its components. It propagates codividual sympoiesis as a model for continuous discrete computation and automata, relevant in the present times of distributed and shared economies.

A notion of fusing parts is established to scale up the concept and to analyse the assemblages created over a steady sympoietic computational process, guided by mereology and the discrete model. It gives rise to new conceptions of space, with a multitude of situations offered by the system at any given instant. These sympoietic inter-relations between the parts can be used to steadily produce new relations and spatial knottings, going beyond the most limiting aspect of autopoiesis, enabling it to begin to produce similar patterns of relations.

Tentacular Thinking

This essay extends the conceptual idea of tentacular thinking,[2] propagated by Donna Haraway, into architecture. Tentacular thinking, as Haraway explains, is an ecological concept which is a metaphorical explanation for a nonlinear, multiple, networked existence. It elaborates on a biological idea that “we are not singular beings, but limbs in a complex, multi-species network of entwined ways of existing.” Haraway, being an ecological thinker, leads this notion of tentacular thinking to the idea of poiesis, which means the process of growth or creation and brings into discussion several ecological organisational concepts based on self-organisation and collective organisation, namely autopoiesis and sympoiesis. It propagates the notion that architecture can evolve and change within itself, be more sympoietic rather than autopoietic, and more connected and intertwined. 

With the advent of distributed and participatory technologies, tentacularity offers a completely new formal thinking, one in which there is a shift from the object and towards the autonomy of parts. This shift towards part-thinking leads to a problem about how a building can be understood not as a whole, but on the basis of the inter-relationships between its composing parts. It can be understood as a mereological shift from global compositions to part-hoods and fusions triggering compositions.

A departure from the more simplified whole-oriented thinking, tentacular thinking comes about as a new perspective, as an alternative to traditional ideologies and thinking processes. In the present economic and societal context, within a decentralised, autonomous and more transparent organisational framework, stakeholders function in a form that is akin to multiple players forming a cat’s cradle, a phenomenon which could be understood as being sympoietic. With increases in direct exchange, especially with the rise of blockchain and distributed platforms such as Airbnb, Uber, etc. in architecture, such participatory concepts push for new typologies and real estate models such as co-living and co-working spaces.

Fusion of Parts: Codividuality

In considering share-abilities and cooperative interactions between parts, the notions of a fusing part and a fused part emerge, giving rise to a multitude of possibilities spatially. Fusing parts fuse together to form a fused part which, at the same stage, behaves as another fusing part to perform more fusions with other fusing parts to form larger fused parts. The overlaps and the various assemblages of these parts gain relevance here, and this is what codividuality is all about.

As Haraway explains, it begins to matter “what relations relate relations.”[3] Codividual comes about as a spatial condition that offers cooperative, co-living, co-working, co-existing living conditions. In the mereological sense, codividuality is about how fusing parts can combine to form a fused part, which in turn, can combine to form a larger fused part and so on. Conceptually, it can be understood that codividuality looks into an alternative method for the forming and fusing of spatial parts, thereby evolving a fusion of collectivist and individualist ideologies. It evolves as a form of architecture that is created from the interactions and fusion of different types of spaces to create a more connected and integrated environment. It offers the opportunity to develop new computing systems within architecture, allowing architectural systems to organise with automaton logic and behave as a sympoietic system. It calls for a rethinking of automata and computation.

Figure 1 – Computational experiments in Tentacular Thinking. Image: Anthony Alvidrez, Shivang Bansal and Haochen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

Codividual can be perceived as a spatial condition allowing for spatial connectivities and, in the mereological sense, as a part composed of parts; a part and its parts. What is crucial is the nature of the organisation of these parts. An understanding of the meaning and history of the organisational concepts of autopoiesis and sympoiesis brings out this nature.

Autopoiesis: Towards Assemblages of Parts

The concept of autopoiesis stems from biology. A neologism introduced by Humberto Maturana and Francisco Varela in 1980, autopoiesis highlights the self-producing nature of living systems. Maturana and Varela defined an autopoietic system as one that “continuously generates and specifies its own organisation through its operation as a system of production of its own components.”[4] A union of the Greek terms – autos, meaning “self” and, poiesis, meaning “organisation” – autopoiesis came about as an answer to questions cropping up in the biological sciences pertaining to the organisation of living organisms. Autopoiesis was an attempt to resolve the confusion between biological processes that depend on history such as evolution and ontogenesis, in contrast with those that are independent of history, like individual organisation. It questioned the organisations of living systems which made them a whole.

Varela et al pointed out autonomy as the characteristic phenomenon arising from an autopoietic organisation; one that is a product of a recursive operation.[5] They described an autopoietic organisation as a unity; as a system, with an inherently invariant organisation. Autopoietic organisation can be understood as a circular organisation; as a system that is self-referential and closed. Jerome McGann, on the basis of his interpretation of Varela et al, described an autopoietic system as a “closed topological space, continuously generating and specifying its own organisation through its operation as a system of production of its own components, doing it in an endless turnover of components”.[6]

What must be noted here is that the computational concept of self-reproducing automata is classically based on an understanding of a cell and its relation to the environment. This is akin to the conceptual premise of autopoiesis, which is the recursive interaction between the structure and its environment,[7] thus forming the system. It must be noted that both the concepts start with a biological understanding of systems and then extend the concept. A direct link can be observed between the works of von Neumann, and Maturana and Varela. Automata, therefore, can be seen as an autopoietic system. 

The sociologist, Niklas Luhmann, took forward this concept into the domain of social systems. His theoretical basis for the social systems theory is that all social events depend on systems of communication. On delving into the history of social or societal differentiation, Luhmann observes that the organisation of societies is based on functional differentiation. A “functionally differentiated society”, as he explains, comprises varying parallel functional systems that co-evolve as autonomous discourses. He discovers that each of these systems, through their own specific medium, evolve over time, following what Luhmann calls “self-descriptions”, bringing out a sense of autonomy in that respective system.[8] 

Following Maturana and Varela’s explanation, an autopoietic organisation may be viewed as a composite unity, where internal interactions form the boundary through preferential neighbourhood interactions, and not external forces. It is this attribute of self-referential closure that Luhmann adopts in his framework. This closure maintains the social systems within and against an environment, culminating in order out of chaos.

The Limits of Autopoietic Thinking

Beth Dempster, as a contradiction to Maturana and Varela’s proposition of autopoiesis, proposed a new concept for self-organising systems. She argues that heuristics based on the analogy of living systems are often incongruous and lead to misleading interpretations of complex systems. Besides, autopoietic systems tend to be homeostatic and are development oriented in their nature.[9] Being self-producing autonomous units “with self-defined spatial or temporal boundaries”,[10] autopoietic systems show a centralised control system and are consequently efficient. At the same time, such systems tend to develop patterns and become foreseeable. It is this development-oriented, predictable and bounded nature of autopoietic systems that poses a problem when such systems are scaled up. 

Autopoietic systems follow a dynamic process that allows them to continually reproduce a similar pattern of relations between their components. This is also true for the case of automata. Moreover, autopoietic systems produce their own boundaries. This is the most limiting aspect of these concepts.

Autopoietic systems do not instigate the autonomy of parts, as they evolve on a prescribed logic. Instead, a more interesting proposition is one in which the interacting parts instigate a kind of feedback mechanism within the parts, leading to a response that triggers another feedback mechanism, and so on. Mario Carpo’s argument that in the domain of the digital, every consumer can be a producer, and that the state of permanent interactive variability offers endless possibilities for aggregating the judgement of many,[11] becomes relevant at this juncture. What holds true in the context of autopoiesis is Carpo’s argument that fluctuations decrease only at an infinitely large scale, when the relations converge ideally into one design.

In the sympoietic context, however, this state of permanent interactive variability Carpo describes is an offer of the digital to incorporate endless externalised inputs.[12] The need for sympoiesis comes in here. Sympoiesis maintains a form of equilibrium or moderation all along, but also, at the same time, remains open to change. The permanent interactive variability not only offers a multitude of situations but also remains flexible.


The limits to autopoietic thinking is what forms the basis for Dempster’s argument. In contradistinction to autopoiesis, she proposes a new concept that theorises on an “interpretation of ecosystems”, which she calls sympoietic systems. Literally, sympoiesis means “collective creation or organisation”. A neologism introduced by Dempster, the term, sympoiesis, explains the nature of living systems. Etymologically, it stems out from the Ancient Greek terms “σύν (sún, “together” or “collective”)” and “ποίησις (poíesis, “creation, production”)”. As Dempster explains, these are “collectively producing systems, boundaryless systems.”[13]

Sympoietic systems are boundary-less systems set apart from the autopoietic by “collective, amorphous qualities”. Sympoietic systems do not follow a linear trajectory and do not have any particular state. They are homeorhetic, i.e., these systems are dynamical systems which return to a trajectory and not to a particular state.[14] Such systems are evolution-oriented in nature and have the potential for surprising change. As a result of the dynamic and complex interactions among components, these systems are capable of self-organisation. Sympoietic systems, as Donna Haraway points out, decentralise control and information”,[15] which gets distributed over the components.

Sympoiesis can be understood simply as an act of “making-with”.[16] The notion of sympoiesis gains importance in the context of ecological thinking. Donna Haraway points out that nothing or no system can reproduce or make itself, and therefore, nothing is really absolutely autopoietic or self-organising. Sympoiesis reflects the notion of “complex, dynamic, responsive, situated, historical systems.” As Haraway explains, “sympoesis enlarges and displaces autopoesis and all other self-forming and self-sustaining system fantasies.”[17]

Haraway describes sympoietic arrangements as “ecological assemblages”.[18] In the purview of architecture, sympoiesis brings out a notion of an assemblage that could be understood as an architectural assemblage growing over sympoietic arrangements. Though sympoiesis is an ecological concept, what begins to work in the context of architecture is that the parts don’t have to be strict and they aim to think plenty; they also have ethics and synergies among each other. In sympoietic systems, components strive to create synergies amongst them through a cooperation and a feedback mechanism. It is the linkages between the components that take centre stage in a sympoietic system, and not the boundaries. Extrapolating the notion of sympoiesis into the realm of architecture, these assemblages can be conceived in Haraway’s words as “poly-spatial knottings”, held together “contingently and dynamically” in “complex patternings”.[19] What become critical are the intersections or overlaps or the areas of contact between the parts.

Sympoietic systems strategically occupy a niche between allopoiesis and autopoiesis, the two concepts proposed by Maturana and Varela. The three systems are differentiated by various degrees of organisational closure. Maturana and Varela elaborate on a binary notion of organisationally open and closed systems. Sympoiesis, as Dempster explains steps in as a system that depends on external sources, but at the same time it limits these inputs in a “self-determined manner”. It is neither closed nor open; it is “organisationally ajar”.[20] However, these systems must be understood as only idealised sketches of particular scenarios. No system in reality must be expected to strictly adhere to these descriptions but rather lie on a continuum with the two idealised situations as its extremes. 

It is this argument that is critical. In the context of architecture and urban design, what potentially fits is a hybrid model that lies on the continuum of autopoiesis and sympoiesis. While autopoiesis can guide the arrangement or growth of the system at the macro level, sympoiesis must and should step in in order to trigger a feedback or a circular mechanism within the system to respond to externalities. What can be envisaged is therefore a system wherein the autopoietic power of a system constantly attempts to optimise the system towards forming a boundary, and simultaneously the sympoietic power of the system attempts to trigger the system for a more networked, decentralised growth and existence, and therefore, creates a situation where both the powers attempt to push the system towards an equilibrium.

Towards Poly-Spatial Knottings

In sympoiesis, parts do not precede parts. There is nothing like an initial situation or a final situation. Parts begin to make each other through “semiotic material involution out of the beings of previous such entanglements”[21] or fused situations. In order to define codividuality and to identify differences, an understanding of classifying precedents is important. The first move is a simple shift from an object-oriented thinking to a parts-oriented thinking. Buildings are classified as having a dividual, individual and codividual character from the point of view of structure, navigation and program. 

Codividual is a spatial condition that promotes shared spatial connections, internally or externally, essentially portraying parts composed of parts, which behave as one fused part or multiple fused parts. The fused situations fulfil the condition for codividuality as the groupings form a new inseparable part – one that is no longer understood as two parts, but as one part, which is open to fuse with another part.

Fused Compositions

Delving into architectural history, one can see very few attempts in the past by architects and urban designers towards spatial integration by sympoietic means. However a sympoietic drive can be seen in the works of the urban planner Sir Patrick Geddes. He was against the grid-iron plan for cities and practised an approach of “conservative surgery” which involved a detailed understanding of the existing physical, social and symbolic landscapes of a site. For instance, in the plan for the city of Tel Aviv in Israel (1925–1929), Geddes stitches together the various nodes of the existing town akin to assemblages to form urban situations like boulevards, thereby activating those nodes and the connecting paths.

Fumihiko Maki and Masato Oktaka also identify three broad collective forms, namely, compositional form, megastructures and group forms. Maki underscores the importance of linkages and emphasises the need for making “comprehensible links” between discrete elements in urban design. He further explains that the urban is made from a combination of discrete forms and articulated large forms and is therefore, a collective form and “linking and disclosing linkage (articulation of the large entity)”[22] are of primary importance in the making of the collective form. He classifies these linkages into operational categories on the basis of their performance between the interacting parts.

Building upon Maki’s and Ohtaka’s theory of “collective form”, it is useful to appreciate that the architecture of a building can be thought of as a separate entity, and consequently there is an “inadequacy of spatial language to make meaningful urban environment.”[23] Sympoiesis comes out through this notion of understanding the urban environment as an interactive fabric between the building and the context. Maki and Ohtaka also make an important comment that the evolution of architectural theory has been restricted to the building and describe collective forms as a concept which goes beyond the building. Collective forms can have a sympoietic or an autopoietic nature, which is determined by the organisational principles of the collective form. Sympoietic collective forms not only can go beyond the building, but also weave a fabric of interaction with the context. Although a number of modern cases of collective forms exist, most of the traditional examples of collective forms, however, have evolved into collective forms over time, albeit unintentionally.

Figure 2 – Sympoietic urban fusion in the Uffizi corridor by Giorgio Vasari. Image: Shivang Bansal, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018-19.

The Corridor by Giorgio Vasari

An important case of an early endeavour in designing a collective form at an urban scale is Corridoio Vasariano by Giorgio Vasari in Florence, built in the year 1564. It can be understood as a spatial continuum that connects through the numerous important buildings or nodes within the city through a built corridor, resulting in a collective form. According to Michael Dennis, Vasari’s Corridor, in its absolute sense, is a Renaissance “insert” into the “fundamentally medieval fabric of central Florence”.[24]  As Dennis writes in The Uffizi: Museum as Urban Design (1980),

“…Each building has its own identity and internal logic but is also simultaneously a fragment of a larger urban organisation; thus each is both complete and incomplete. And though a
given building may be a type, it is always deformed, never a pure type. Neither pure object nor pure texture, it has characteristics of both – an ambiguous building that was, and still is, multifunctional…”[25]

Dennis’s description for the design of the Vasari’s Corridor brings out the notion of spatial fusion of buildings as parts. The Corridor succeeds as an urban insert and this is primarily for two reasons. At first, it maintains the existing conditions and is successful in acclimatising to the context it is placed in. Secondly, it simultaneously functions on several varying scales, from that of the individual using the Corridor to the larger scale of the fabric through which it passes. The Vasari’s Corridor is a sympoietic urban fusion – one that is a culmination of the effect of local conditions.

Stan Allen, in contrast to compositions, presents a completely inverted concept for urban agglomerations. His concept of field configurations reflects a bottom-up phenomena. In his view, the design must necessarily reflect the “complex and dynamic behaviours of architecture’s users”.[26] Through sympoiesis, the internal interaction of parts becomes decisive and they become relevant as they become the design drivers and the overall formation remains fluid and a result of the interactions between the internal parts.

Figure 3 – Poly-spatial knottings composed of parts. Image: Anthony Alvidrez, Shivang Bansal and Haochen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

Towards a Sympoietic Architecture

Another important aspect that forms a basis for the sympoietic argument is the relevance of information in systems. While Maturana and Varela explain that information must be irrelevant to self-producing systems since it is an extrinsically defined quantity, Dempster lays great emphasis on the relevance of information in sympoietic systems. Her explanation on the relevance of information is that it potentially carries a message or a meaning for a recipient. Information, therefore, is dependent on the context and recipient, but Stafford Beer hints that it is also “observer dependent”.[27]

In the architectural domain, it signifies that information or external data input holds no relevance in an autopoietic system. The system grows purely on the basis of the encoded logic and part-to-part organisational relations, and is unrestricted and free from any possible input. However, information or data in the sympoietic paradigm gains relevance as it activates the system as a continuous flux of information guiding its organisation. This relates to the concepts of reinforced machine learning, wherein the system learns by heuristics to evolve by adapting to changing conditions, and by also producing new ones, albeit it comes with an inherent bias.

The Economic Offer of the Codividual

From an economic lens, the concept of sympoiesis does not exist at the moment. However, with the rise in participatory processes within the economy and the advent of blockchain, it shows immense potential in architecture. Elinor Ostrom’s work on the role of commons in decision-making influences the work of David Rozas, who researches on a model of blockchain-based commons governance. He envisages a system which is decentralised, autonomous, distributed and transparent, a more democratic system where each individual plays his/her own role.[28] This idea is about bringing a more sympoietic kind of drive to blockchain. Sympoietic systems are based on a model that is akin to a commons-oriented or a blockchain-based economy that functions like a cat’s cradle with its multiple stakeholders being interdependent on each other. And as Jose Sanchez points out, it is the power of the discrete, interdependent system that makes this architecture possible. According to him, it offers a “participatory framework for collective production”.[29]

Figure 4 – Fused parthoods over sympoietic interactions. Physical model Comata, Anthony Alvidrez, Shivang Bansal and Haochen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019. Image: Rasa Navasaityte.

The fusion of parts leads to the creation of parts such that the sum of the parts becomes greater than the whole. A codividual sympoietic model can potentially resolve the housing crisis since it flips the economic model to a bottom-up approach. With tokenisation, autonomous automatisation, decentralisation of power and transparency, this blockchain-based codividual model can compete with traditional real estate models, thereby resulting in more equitable and fair-minded forms of housing. As Lohry and Bodell point out, such models can reduce personal risk and also make livelihoods more economical and “community-oriented”.[30] 


The ecological framework of the concept of poiesis, as already outlined, is based on the growth from the organisation of elements. In the context of autopoiesis and sympoiesis, it can be observed that “part-to-part” and even “part-to-whole” conditions gain significant relevance in these concepts. An appreciation of these conditions, therefore, becomes relevant to understand these kinds of notions. The idea of components, as described by Dempster and Haraway in the purview of sympoiesis, and Jerome McGann in the autopoietic context, could be extended to architecture in the form of part-thinking.

However, a mereological approach begins with existing entities or “sympoietic interactions” and proceeds further with a description of their clusters, groupings and collectives. Through codividual sympoiesis, the whole gets distributed all over the parts.[31] In this system, the discreteness of parts is never just discrete. It goes beyond the participating entities and the environment. In line with Daniel Koehler’s argument, the autonomy of the part ceases to be defined just as a self-contained object. It goes beyond it and begins to be defined “around a ratio of a reality, a point of view, a filter or a perspective”[32].

Sympoiesis evolves out of competitive or cooperative interactions of parts. As in ecology, these parts play symbionts to each other, in diverse kinds of relationalities and with varying degrees of openness to attachments and assemblages with other fusing parts depending on the number of embedded brains and the potential connectors. Traditionally, architecture is parasitic. When the aesthetic or the overall form drives the architecture, architectural elements act as a host for other architectural elements to attach to depending on composition. In sympoiesis, there is no host and no parasite. It inverts the ideology of modernism, beginning with not a composition but actually evolving a composition of “webbed patterns of situated and dynamic dilemmas” over symbiotic interaction. Furthermore, increasingly complex levels of quasi-individuality of parts come out of this process of codividual sympoiesis. It gives an outlook of a collective and still retains the identity of the individual. It can simply be called multi-species architecture or becoming-with architecture.

Figure 5 – Sympoietic Assemblages of Parts. Physical model Comata, Anthony Alvidrez, Shivang Bansal and Haochen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019. Image: Rasa Navasaityte.

Talking of transdisciplinary ecologies and architecture, we can foresee string figures tying together human and nonhuman ecologies, architecture, technologies, sustainability, and more. This also gives rise to a notion of ecological fusion of spatial conditions such as daylight and ventilation, in addition to physical fusion of parts. Codividual sympoiesis, thus, even shows potential for a nested codividual situation, in that the parts sympoietically fuse over different spatial functions.

Going over sympoiesis and mereology, it makes sense to look for parts which fuse to evolve fused parts; to look for architecture through which architecture is evolved; to look for a codividuality with which another codividuality is evolved. From a mereological point of view, in a system in which the external condition overlaps with an internal part in the search for another component, to give rise to a new spatial condition over the fusion of parts could be understood as codividual sympoiesis. Codividual sympoiesis is therefore about computing a polyphony, and not orchestrating a cacophony.


[1] M. Foucault, Madness and Civilization (New York: Random House US, 1980).

[2] D. Haraway, Staying with the Trouble: Making Kin in the Chthulucene (Durham: Duke University Press,  2016), 30–57.

[3] Ibid, 35.

[4] H. R. Maturana and F. G. Varela, Autopoiesis And Cognition (Dordrecht, Holland: D. Reidel Pub. Co., 1980).

[5] H. R. Maturana, F. G. Varela, and R. Uribe, "Autopoiesis: The Organization Of Living Systems, Its Characterization And A Model," Biosystems, 5, 4, (1974), 187–196.

[6] J. McGann, A New Republic of Letters (Cambridge, Massaschusetts: Harvard University Press, 2014).

[7] A. W. Burks, Von Neumann's Self-Reproducing Automata; Technical Report (Ann Arbor: The University of Michigan, 1969).

[8] N. Luhmann, Art as a Social System (Stanford: Stanford University Press, 2000), 232.

[9] B. Dempster, Sympoietic and Autopoietic Systems : A new distinction for self-organizing systems (Waterloo: School of Planning, University of Waterloo, 1998).

[10] Ibid, 9.

[11] M. Carpo, The Second Digital Turn: Design Beyond Intelligence (Cambridge, Massachusetts: MIT Press, 2017), 131–44.

[12] Ibid, 12.

[13] B. Dempster, Sympoietic and Autopoietic Systems : A new distinction for self-organizing systems (Waterloo: School of Planning, University of Waterloo, 1998).

[14] Ibid.

[15] D. Haraway, Staying with the Trouble: Making Kin in the Chthulucene (Durham: Duke University Press,  2016), 33.

[16] Ibid, 5.

[17] Ibid, 125.

[18] Ibid, 58.

[19] Ibid, 60.

[20] B. Dempster, Sympoietic and Autopoietic Systems : A new distinction for self-organizing systems (Waterloo: School of Planning, University of Waterloo, 1998).

[21] D. Haraway, Staying with the Trouble: Making Kin in the Chthulucene (Durham: Duke University Press, 2016), 60.

[22] F. Maki, and M. Ohtaka, Investigations in Collective Form (St. Louis: School of Architecture, Washington University, 1964), 3-17.

[23] Ibid.

[24] M. Dennis, "The Uffizi: Museum As Urban Design", Perspecta, 16, 62 (1980), 72.

[25] Ibid, 63.

[26] S. Allen, "From Object to Field,” Architectural Design, AD 67, 5-6 (1997), 24–31.

[27] S. Beer, “Preface,” Autopoiesis: The Organization of the Living, auth. H. R. Maturana and F. Varela (Dordrecht, Holland: D. Reidel Publishing Company, 1980).

[28] D. Rozas, “When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance” (2019),, last accessed 3 May 2019.

[29] J. Sánchez, “Architecture for the Commons: Participatory Systems in the Age of Platforms,” Architectural Design, 89, 2 (2019), 22–29.

[30] M. Lohry and B. Bodell, "Blockchain Enabled Co-Housing" (2015),, last accessed 3 May 2019.

[31] D. Koehler, “Mereological Thinking: Figuring Realities within Urban Form,” Architectural Design, 89, 2 (2019), 30–37.

[32] Ibid.

Suggest a Tag for this Article
TARSS. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.
The Ultimate Parts: A Mereological Approach of Form Under the Notion of Object-Oriented Ontology
Architecture, Architecture Theory, City Architecture, Form, Mereologies, Mereology, Urban Design
Ziming He
University College London
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Read Article: 3648 Words

Mereology is a formal concept which enters architecture as an additional formal category. Form is a rather ambiguous concept in architecture. So in this essay, first an investigation is conducted by contrasting two closely related concepts: shape and content.

Hans Trusack criticises the problem of shape for its shallow formalism and historical-theoretical indifference as a defensive strategy that evades the disciplines and difficulties of past and future.[1] The distinction between the terms “form” and “shape”, following Tursack’s argument, is a “matter of generative process”. Both terms point to the production of visual expression. Yet while shape refers to the appearance of an object, form reflects the logic of transformation and operation within historical and theoretical contexts such as political and religious ideology, economics and technological background. Tursack criticised the strategy of shape in architecture, stating its lack of reference, it being “plainly, and painfully, evident”,[2] and incapable of moving forward. Whereas form is difficult, disciplinary and requires historical and theoretical study, and yet promises the future. 

Form has the advantage of being able to deal with complex relations due to its deep and continuously evolving intervention with content. The term form derives from the Latin word forma, is understood as the combination of two Greek words: eidos, the conceptual form, and morphe, the physical form. The complexity of form can be attributed to these differentiated meanings, yet complexity is compatible with agencies and relations. This can emerge further by conducting a brief historical review.

Ancient Greek architecture pursues the ideality in mathematics and proportion. The efforts made by architects in designing the Parthenon provides evidence of this feature. These operations tried to approximate the physical shape of architecture to the “ideal” form. Form reflects the pursuit of ideality and perfection in this period. 

For Gothic architecture, there were more concerns about structure, and matter was pushed to its maximum capability to build as tall as possible for religious appeal. Consequently, structures were designed to be rigid and lightweight, and solid walls were replaced by glass windows, while flying buttresses supported the main structure to grow even taller. Consequently, astonishing space and fascinating transparency emerged.

Modernism claims that “form follows function”,[3] rejecting traditional architecture styles. The reality of matter and the logic of technology eschewed decorations, proportions, or any subjective distortion of matter. The emphasis on the term “function” illustrates an ideology of treating architecture as a machine. Each part is nothing more than a component that has a certain feature inside this machine, and redundant decorations and details are removed to deliver this idea clearly. Without distractions, space becomes evident.

In the shift to postmodernism, the uniformity and the lack of variety of modernist architectures were reacted against, and a great variety of approaches emerged to overcome the shortcomings of modernism. Parametricism, for instance, has been promoted by the thriving of digital technologies. Designers are capable of more complex formal production, and architectural elements have become variables that can be interdependently manipulated. In this formalism, rigidity, isolation, and separation are opposed, while softness, malleability, differentiation and continuity are praised.

From the examples above, form is the embodiment of the relations between architecture and its motive in specific historical scenarios, while for shape, only the results are accounted for – relations are ignored, and architecture is treated as isolated physical entities, incapable of producing new relations. Different methodologies of dealing with architectural form also imply the variation of ideology in compiling form with content.

Mereology – An Approach of Architectural Form

In recent philosophical texts, a third notion of form is brought forward. Contrary to a dialectic of form and content, here investigations deal with the resonance of parts: the description of objects by their ontological entanglement only. The writings of the philosopher Tristan Garcia are a strong example for such mereological considerations. In his treatise Form and Object: A Treatise on Things (2014), Garcia investigates the ontology of objects with two initial questions, “… what is everything compose of? … what do all things compose?”[4] The first question interrogates the internal, the elementary component of everything. The second interrogates the external, the totality of everything. For Garcia, the form of a thing is “the absence of the thing, its opposite, its very condition,”[5] form has two senses, the “beginning”, and the “end”, which never ends. Form begins when a thing ends, it begins with different forms; in the end, since it has “endless end”, form ultimately merges into one, which is “the world”. Garcia defines an object as “a thing limited by other things and conditioned by one or several things.”[6] The form of an object depends on what comprehends or limits this object. Every object is “embedded in a membership relation with one or several things”,[7] they can be divided by defining limits, which is also a thing distinguishing one thing from another. Garcia’s argument adapts the concept of mereology. Form has two extremes, one toward the fundamental element of matter, and the other toward the world, comprehending everything. All things can always be divided into an infinite number of parts, and they can always be parts of another thing. Identifying parts or wholes within a section we can operate on can establish a limit. The relevance between form and mereology opens a new opportunity to inspect architectural form from a different point of view.

One of the first discussions about parts and wholes in modern philosophy was posed by Edmund Husserl, in Logical Investigation (1st ed. 1900-1901, 2nd ed, 1913),[8] but the term “mereology” has not been put forward until Stanisław Leśniewski used it in 1927 from the Greek work méros (parts).[9] Mereology is considered as an alternative to set theory. A crucial distinction lies between mereology and set theory in that set theory concerns the relations between a class and its elements, while mereology describes the relations between entities. The mathematical axioms of mereology will be used as the fundamental theory of developing the method of analysing architectural form.

Figure 1 – Diagrams for Mereological Relation in Mathematics, Ziming He, 2019. Image credit: Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2019.

Following Roberto Casati and Achim Varzi, the four fundamental mathematical formularisations of mereology are: “Relations are reflexive, antisymmetric and transitive. (…) First, everything is part of itself. Second, two different objects cannot be part of each other. Third, each part of a part of a whole is also part of that whole. Fourth, an object can be a part of another object, if both exist.”[10] 

Mereology can be a promising approach also for the reading of architectural form, as it emphasises relationships without reducing buildings to their appearance or function. However, such philosophical descriptions consider wholes and parts as mostly abstract figures. Therefore, a supplement could be developed to properly categorise the mereological relations in the field of architecture. Having the relations between form and mereology addressed, methodologies can be developed to access the analysis of architectural form. Mereology as a specific methodology for architecture is quite new. One of the first introductions can be found in Daniel Koehler’s book The Mereological City: A Reading of the Works of Ludwig Hilberseimer (2016). Here, Koehler departs from the modern city, exemplified through the work of Ludwig Hilberseimer to illustrate mereological relations in the modernist city. From the room to the house to the city to the region, Hilberseimer canonically drew the city as a hierarchical, nested stack of cellular spaces.[11] However, through the close reading of its mereological relations it becomes clear that political, economic or social conditions are entangled in a circular composition between the parts of the city. Recalling Garcia’s discourse, and resonating with Leon Battista Alberti’s thesis, Koehler shows that the cells in Hilberseimer’s modernist city are interlocked. A house becomes the whole for rooms; a city becomes the whole for houses. By considering the city and its individual buildings equally, “the whole is a part for the part as a whole.”[12]

Architectural Relations Between Parts and Wholes

Parts are not only grouped, packed and nested through different scales, but also in different relations. Specific relationships have been developed in different architectural epochs and styles. Mathematically, four general classes of relations can be drawn: whole-to-whole, part-to-part, whole-to-parts and parts-to-whole, while more specific subclasses can be discovered from each. 

According to the mathematical definition, between wholes there exist complex relations, the whole could exist on any mereological level, and the complexity of relations between multiple levels are also accounted for. Whole-to-whole relations can become complex when considering multi-layer interaction, and more relations can be identified: juxtapose, overlap, contain, undercrossing, transitivity, partition, trans-boundary, intact juxtapose, compromised juxtapose.

Figure 2 – Whole-to-whole relations. Image credit: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

A first glance of New York, gives the impression that it is quite heterogeneous, but underneath there is a city grid underlying the heterogeneity, and while the relations displayed in the grid are rather simple, all wholes juxtapose with one another. In comparison, in Siena, an Italian city, the urban space is quite complex, where boundaries of all wholes negotiate with others, the gaps in between are carefully treated, the nesting relations are extremely rich, and multiple relations from the diagram above can be found.

Figure 3 – New York. Image: Jonathan Riley.
Figure 4 – Siena. Image: Cristina Gottardi.

The whole-to-parts relation studies what the whole does to its part, namely in terms of top-down rules. The mathematical definition does not involve specific situations that a whole-part condition holds. Distinctions within individual contexts make a significant difference in clarifying an explicit relation. The situations for the whole can generally be classified into following types: fuse, fit and combine.

Figure 5 – Whole-to-part relations. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

One of Zaha Hadid’s projects, Heydar Aliyev Centre, indicates the fusing relation. Architecture is represented as a smooth, fluid volume. The distinction between elements disappears, and this dominating power even extends to the external landscape. In order to maintain a continuous whole, parts are fabricated into a particular shape, having their unique unchangeable locations. The continuous whole excessively overwhelms the parts, yet not all parts are reshaped to fuse into the whole, and because the parts are small enough in relationship to the whole, the control from the whole is weakened, and parts are fit into the whole.

The third type is combining. An example for this relation is Palladio’s project Villa Rotonda. In this case, parts are obvious. The whole is a composition of the parts’ identities. However, the whole also holds a strong framework, in a rigorous geometric rule that decides positions and characters of parts. The arrangement of parts is the embodiment of this framework. 

Figure 5 – Heydar Aliyev Centre, designed by Zaha Hadid Architects. Image: Orxan Musayev.
Figure 6 – Diagram of fitting relation. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.
Figure 7 – Façade of Villa Rotonda. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

The parts-to-whole relation studies what the parts do to the whole, or the power of bottom-up relationships. The different situations of parts are also key parameters in validating a given relation. The classification of situations for parts are as follows: frame, intrinsic frame, extrinsic frame, bounded alliance, unbounded alliance.

Figure 8 – Part-to-whole relations. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

Emil Kaufmann thoroughly investigated the innovative works by Claude Nicholas Ledoux in Three Revolutionary Architects: Boullee, Ledoux and Lequeu (1952).[13] According to Kaufmann’s study, Ledoux’s works developed new compositional relations of elements from the Baroque. The characteristics of parts in Baroque architecture are rich, but tend to regulate the identities of all the elementary parts and fuse them together to serve the harmony of the whole, presenting the intrinsic framing. Ledoux’s work is an extrinsic framing, where the parts are relatively independent, with each element maintaining its own properties, and while consisting of the whole, they can be replaced with other identical components.

One of my projects in discrete aggregation of elements presents an unbounded alliance relation. The aggregation as a whole shows a form that is discretised (Figure 12), and does not pass any top-down instructions to its parts.

Figure 9 – Facade of Church of the Gesù. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.
Figure 10 – Façade of Château de Mauperthuis. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

Figure 11 – Discrete aggregation. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

Part-to-Part Without Whole – The Ultimate Parts

For part-to-part relations, local interactions are emphasised, and interactions occur at multiple levels of compositions, where the part-to-part relations in some cases are similar to that between wholes. It has following classifications: juxtapose, interrelate, contain, partition, overlap, trans-juxtapose, over-juxtapose, over-partition, over-overlap.

Figure 12 – Part-to-part relation. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

Architects have been working on the possibility of removing the whole by studying the part-to-part relations. Several approaches have been developed, mainly through computation. Neil Leach considers the city as a “swarm intelligence”,[14] bringing forward the potential of developing urban form with computational method. Leach encourages swarm intelligence for the interactions between agents (parts), which “offers behavioral translations of topology and geometry”,[15] while fractals, L-systems or cellular automata are all constrained by some limitation. However, although swarm intelligence is based on the interaction of individual agents, it is always treated as a whole; all cells of CA are fixed in the background grid, which is also a whole. For fractals and L-systems, they can be subdivided into infinite parts, a transcendent whole where all parts grown from still exist. In the mereological sense, none of these cases can escape the shadow of the whole – strictly speaking, they are part-to-whole relations. To discuss the part-to-part relation in more depth, more investigation is needed to clarify the concept of part.

In The Democracy of Objects (2011), Levi Bryant claims that objects constitute a larger object by establishing relations with others, but this doesn’t alter the existence of objects, as he says, “all objects equally exist, but not all objects exist equally.” In Bryant’s discourse, this independence suggests the dissolution of the whole. Bryant proposes a concept of “regimes of attraction”, that includes the “endo-relation” and the “exo-relation”. The endo-relation indicates that the proper being of an object consists of its powers or what an object can do”, not the “qualities” emerging within an exo-relation. An object possesses “volcanic powers”, the stabilisation of the regime of attraction actualises it into a specific state.[16] The concept of the whole reduces objects to this state, which displays only a section of their proper beings. The concept of regimes of attraction is against this reduction.

The regime of attraction can be linked to the notion of “assemblage” from Manuel DeLanda, however, there is a distinction between the two. Assemblage holds only the relation of exteriority, whereas regime of attraction maintains both relations of interiority and exteriority. In Assemblage Theory (2016), DeLanda reassembled the concept “assemblage”, which was originated from the French agencement. Created by Gilles Deleuze and Félix Guattari, this original term refers to the following meanings: the “action of matching or fitting together a set of components” – the process, and the “result of such an action” – the product. 

DeLanda emphasised two aspects, heterogeneity and relations. As he indicated, the “contrast between filiations and alliances”[17] can be described in other words as intrinsic and extrinsic relations. 

The nature of these relations has different influences on the components. The intrinsic relation tends to define the identities of all the parts and fix them into exact location, while the extrinsic relation connects the parts in exteriority – without interfering with their identities. DeLanda summarised four characteristics of assemblage: 1) individuality, an assemblage is an individual entity, despite different scale or different number of components; 2) heterogeneity, components of an assemblage are always heterogeneous; 3) composable, assemblages can be composed into another assemblage; 4) bilateral-interactivity, an assemblage emerges from parts interactions, it also passes influences on parts.[18]

DeLanda then moved on to the two parameters of assemblage. The first parameter is directed toward the whole, the “degree of territorialisation and deterritorialisation”, meaning how much the whole “homogenises” its component parts. The second parameter is directed toward the parts, the “degree of coding and decoding”, meaning how much the identities of parts are fixed by the rules of the whole. The concept of assemblage provides us a new lens of investigating these mereological relations. With this model, the heterogeneities and particularity of parts are fully respected. The wholes become immanent, individual entities, existing “alongside the parts in the same ontological plane”,[19] while parts in a whole are included in the whole but not belonging to it, and according to Bryant’s discourse, the absence of belonging dispelled the existence of the whole.[20]

From the study of regime of attraction and assemblage, this essay proposes a new concept – “the ultimate parts” – in which a proper “part-to-part without whole” is embedded. A part (P) horizontally interacts with its neighbouring parts (Pn), with parts of neighbouring parts (Pnp), as well as interacting downwardly with parts that compose it (Pp) and upwardly with wholes it is constituting which are also parts (Pw). This concept significantly increases the initiatives of parts and decreases the limitations and reductions of them. It doesn’t deny the utilities of the whole, but considers the whole as another independent entity, another part. It’s neither top-down, nor bottom-up, but projects all relations from a hierarchical structure to a comprehensive flattened structure. The ultimate parts concept provides a new perspective for observing relations between objects from a higher dimension.

Figure 13 – Diagram of “The Ultimate Parts”. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

One application of this concept is TARSS (Tensegrity Adaptive Robotic Structure System), my research project in MArch Architectural Design in B-Pro at The Bartlett School of Architecture in 2017–2018. This project utilises the features of tensegrity structures of rigidity, flexibility and lightweight. The difference is that rather than fixing parts into a static posture and eliminating their movements, the project contrarily tries to increase the freedom of parts as much as possible. The tensile elements have the ability to adjust their lengths collaboratively to change the general shape of the aggregation. Reinforcement learning is employed to empower the parts with objective awareness. The training sessions were set up toward multiple objectives that are related to architectural concerns, including pathfinding, transformation, balance-keeping, self-assembling and structural load distributing. This approach brings obvious benefits, as architecture design in this sense is not only about an eventual result, but about the dynamic process of constantly responding to the environmental, spatial or functional requirements. The premise is to treat parts as ultimate parts whilst retaining their objectivity and being able to actively interact at all mereological levels without limitations.

Figure 14 – Key images from the project TARSS. Image: Ziming He, Living Architecture Lab, RC3, MArch Architectural Design, The Bartlett School of Architecture, UCL, 2018.

The concept of ultimate parts brings forward a new relation of “part-to-part without whole”. This new relation belongs to a higher dimension. The details and essence of objects are simultaneously displayed, without being obscured by the compositional structure. Analogised with spatial dimensions, a 3-dimensional cube simultaneously shows all its faces and interior in 4-dimensional space. The significance is that it opens vast new perspectives and operational methodologies in the architectural design realm. Especially with the advancement in robotics and artificial intelligence, this type of new relationship enables greater opportunities by regarding machines as characters with immense potential to work with us, instead of for us. The role of designers would be very much like “breeders of virtual forms”,[21] who do not rule the form, but guide it towards the demands. This moves away from anthropocentric design by overcoming part-to-whole with part-to-part.


[1] H. Tursack, "The Problem With Shape", Log 41 (New York: Anyone Corporation, 2017), 53.

[2] Ibid, 50.

[3] L. Sullivan, "The Tall Office Building Artistically Considered", Lippincott's Magazine (1896), 403–409.

[4] T. Garcia, M. A. Ohm and J. Cogburn, Form And Object (Edinburgh: Edinburgh University Press, 2014), 19.

[5] Ibid, 48.

[6] Ibid, 77-78.

[7] Ibid, 145.

[8] E. Husserl, Logical Investigation (London: Routledge & K. Paul, 1970).

[9] Stanisław Leśniewski, O podstawach matematyki [trans. On the Foundations of Mathematics], I-V, 1927-1930, Przegląd Filozoficzny, 30 (1927), 164–206; 31 (1928), 261–291; 32 (1929), 60–101; 33 (1930), 77–105; 34 (1931), 142–170.

[10] R. Casati and A. C. Varzi, Parts and Places: The Structures of Spatial Representation (Cambridge, Massachusetts: MIT Press, 1999).

[11]  L. Hilberseimer, The New City: Principles of Planning (P. Theobald, 1944), 74-75.

[12] D. Koehler, The Mereological City: A Reading of the Works of Ludwig Hilberseimer (Transcript, Verlag, 2016), 182.

[13] E. Kaufmann, Three Revolutionary Architects, Boullée, Ledoux, And Lequeu (Philadelphia: The American Philosophical Society, 1968).

[14] N. Leach, "Swarm Urbanism", Architectural Design, 79, 4 (2009), 56-63.

[15] Ibid.

[16] L. Bryant, The Democracy Of Objects (Open Humanities Press, 2011), 290.

[17] M. DeLanda, Assemblage Theory (Edinburgh: Edinburgh University Press, 2016), 2.

[18] Ibid, 19-21.

[19] Ibid, 12.

[20] L. Bryant, The Democracy Of Objects (Open Humanities Press, 2011), 273.

[21] M. DeLanda, "Deleuze And The Use Of The Genetic Algorithm In Architecture" (2001), 3.

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Application of the Hyperumwelt concept in an urban proposal, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018, photograph by Rasa Navasaityte.
Synthesising Hyperumwelten
Architecture, Building, City Architecture, Computational Design, Hyperobjects, Mereologies, Mereology
Anna Galika
University College London
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Object-oriented programming in blockchain has been a catalyst for philosophical research on the way blocks and their nesting are perceived. While attempting a deeper investigation on the composition of blocks, as well as the environment that they are able to create, concepts like Jakob von Uexkull’s “Umwelt”[1] and Timothy Morton’s “Hyperobject”[2] can be synthesised into a new term; the “Hyperumwelt”. The Hyperumwelt is an object that is capable of creating its own environment. By upscaling this definition of the Hyperumwelt, this essay describes objects with unique and strong compositional characteristics that act as closed black boxes and are able to create large scale effects through their distribution. Hyperobjects are able to create their own Umwelt, however when they are nested and chained in big aggregations, the result is a new and unexpected environment: the Hyperumwelt. 

In his book Umwelt und die Innenwelt der Tiere (1921) Uexkull introduced the notion of subjective environments. With the term “Umwelt” Uexkull defined a new perspective for the contextualisation of experiences, where each individual organism perceives surrounding elements with their senses and reinterprets them into its own “Umwelt”, producing different results.[3] An Umwelt requires two components: an individual and its abstracted perception of its surroundings. Based on this process and parameters, notions of parthood and wholeness in spatial environments, and the relations that they produce with interacting elements, become relevant.

Space as a Social Construction

For Bill Hillier and Julienne Hanson these two parameters related to society and space, writing that “society can only have lawful relations to space if society already possesses its own intrinsic spatial dimension; and likewise space can only be lawfully related to society if it can carry those social dimensions in its very form.”[4] What Hillier and Hanson argue is that the relation between the formation of society and the space is created by the interaction between differing social environments. Hillier and Hanson essentially make use of a mereological definition of the environment that states that parts are independent of their whole, the way that society is independent from its space, but at the same time societies contain definitions of space. Space is therefore a deeply social construction.

As Hillier and Hanson outline, our understandings of space are revealed in the relations between “social structure” and “spatial structure”, or how society and space are shaped under the influence of each other. Space is a field of communication. Within a network of continuously exchanged information, space can be altered as it interacts with the people in it.[5] However, this approach can only produce limited results as it creates environments shaped by only two parameters, humans and space. At this point is where Hillier and Hanson’s theory fails, as this way of understanding the environment relies only on additive information produced by interactions. If we were to expand this theory into the kind of autonomous learning mechanism that is mandatory for processing today’s computational complexity, we would end up with a slow, repetitive operation between these two components. 

Hyperobjects to Hyperumwelt

Another perspective that is elusive from Hillier and Hanson’s understanding of the environment is how social behaviour is shaped by spatial parameters. Timothy Morton’s object-oriented ontological theory contradicts this anthropocentric understanding of the world. In The Ecological Thought (2010) Morton presents the idea that not only do we produce the environment but we are also a product of it. This means that the creation of things is not solely a human act non-human objects cannot partake in, but rather an inherent feature of any existing object.[6] For Morton, complexity is not only a component of society and space, but extends complexity to an environment that has objects as its centre and thus cannot be completely understood. He calls these entities ‘Hyperobjects”.[7]

While Morton uses the term Hyperobject to describe objects, either tangible or intangible, that are “massively distributed in time and space as to transcend spatiotemporal specificity”.[8] The term can be reinterpreted to describe an environment, rather than an object, which is neither understandable nor manageable. This environment – a Hyperumwelt – is the environment constructed by Hyperobjects. A Hyperumwelt is beyond comprehension due to its complexity.

Figure 1 – Qualities of the Hyperumwelt forming at the urban scale, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018.

The term Hyperobject is insufficient as it retains its own wholeness. This means that all components inside a  Hyperobject cannot be seen (as it acts like a black box of information) but can only be estimated. Morton described the Hyperobject as a whole without edges. This stems from Morton’s point of perception, as he puts himself inside of the object.[9] This position makes him unable to see its wholeness and thus it leaves him adrift of its impact, unable to grasp control of it. Here, also, the discussion opens about authorship inside the environments and what Morton suggests is that Hyperobjects have their own authority and there is nothing that can alter them or specify their impact on the environment.[10]

Figure 2 – Elements creating distributed patterns of information, creating their own environment, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018.

A Tree in a Forest

Yet there is also no need for the Hyperobjects to be clearly understandable. In terms of the Hyperumwelt, Hyperobjects can remain vast and uncomprehended. What is now needed are the implications of distributing nested Hyperobjects, seen as black boxes, inside an environment. An Umwelt is an environment constantly altered by the perceived information. This makes the Hyperumwelt a whole with porous edges that allows the distribution, and the addition or subtraction, of information. Another difference is the external position that the Hyperumwelt is perceived from, meaning that there is no need for it to be part of the environment. Since what is important is the distribution of the objects within the Hyperumwelt, a distant point of view is needed in order to detect the patterning of the distributed objects. While it will remain difficult to decipher and discretise the components, the patterns that are created can be seen. 

Figure 03 – Zooming in on patterns to recognise familiar qualities that provide a better understanding of the composed whole, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018, photograph by Rasa Navasaityte.

While the Hyperobject is a closed whole of parts that cannot be altered, a Hyperumwelt is an open whole of wholes that uses objects as its parts. So, while the Hyperobject gives us no authority over its consequences, the Hyperumwelt bypasses this in order for its wholeness to be controlled. Yet what is important for the Hyperumwelt is not the impact of one object, but the impact of multiple objects within the environment. This synthesis and merging of objects and their relations produces a new reality which may or may not be close to the reality of the single objects. A Hyperobject is looking at a black box – say, a tree – and knowing there is a pattern – such as a forest – and a Hyperumwelt is looking at the tree and knowing the impact that it has on the forest and the impact that the forest creates in the environment. 

Figure 4 – Application of the Hyperumwelt concept in an urban proposal, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018, photograph by Rasa Navasaityte.

[1] J. von Uexküll, Umwelt und Innenwelt der Tiere (Berlin: J. Springer, 1909), 13-200.

[2] T. Morton, Hyperobjects: Philosophy and Ecology After the End of the World (Minneapolis, Minnesota: University of Minnesota Press, 2013).

[3] J. von Uexküll, Umwelt und Innenwelt der Tiere (Berlin: J. Springer, 1909), 13-200.

[4] B. Hillier and J. Hanson, The Social Logic of Space (London: Cambridge University Press, 1984), 26.

[5] Ibid.

[6] T. Morton, The Ecological Thought (Cambridge, Massachusetts: Harvard University Press, 2010).

[7] Ibid, 110.

[8] T. Morton, Hyperobjects: Philosophy and Ecology After the End of the World (Minneapolos, Minnesota: University of Minnesota Press, 2013).

[9] T. Morton, Being Ecological (Penguin Books Limited, 2018).

[10] Ibid.

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View into a codividual interiority. Codividual aesthetics forming a plural space. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.
Codividual Architecture within Decentralised Autonomous Systems
Architecture, Autonomy, Collectivity, Computational Design, Decentralisation, Mereologies, Mereology
Hao Chen Huang
University College London
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In mereology, the distinction of “dependent” or “independent” could be used to describe the relationship between parts and wholes. Using a mereological description, individuals can be seen as self-determining entities independently identified by themselves as a whole. On the other hand, the identities of collectives are determined by their group members which participate in a whole. Therefore, based on parthood theory, an individual could be defined as a self-determined “one in a whole”; in contrast, collectives could be seen as “a part within a whole”. Following the mereological logic, this paper surveys the new term “codividuality”, a word consisting of the combined meaning of “collective” and “individuality”. Codividuality preserves the intermediate values of individualism and collectivism. It consists of the notion of share-ability benefited from collectivism, and is merged with the idea of self-existence inspired by individualism. The characterisation of codividuality starts from individuals that share features, and are grouped, merging with other groups to compose new clusters.


“Codividuals” could also be translated into “parts within parts”. Based on this part-to-part relation, codividuals in the sense of composition begin with existing individuals and then collectives of self-identified parts. Parts are discrete, but also participating entities[2] in an evolving self-organising system. Unlike individuals’ self-determination, parts’ identities contribute by participating, forming a strong correlation in-between parts but preserving autonomy of parts. In codividuality, each individualistic entity obtains the potential of state-transforming by sharing its identity with others; as such, all parts are able to translate one another, and are irreducible to their in-between relationship. From an ontological perspective, the existence of a part is not from adding a new object but by sharing features to fuse itself into a new part. A new part does not contribute by increasing an entity’s quantity but through a dynamic overlap transforming over time. Since the involved entities fuse into new collectives, the compositing group will simultaneously change its form by corresponding to sharing features; as such, codividuality could be seen as an autonomous fusion.

Figure 1 – Mereological drawings of the chosen Precedents, bringing out the individual, dividual and codividual nature of buildings. Image: Hao-Chen Huang.

Metabolism: As One in Whole

According to the definition of individualism, each individual has its own autonomous identity and the connectivity between individuals is loose. In architecture, social connectivity provides insight on the relationship of spatial sequences within cultural patterns. Metabolism, as an experimental architectural movement in post-war Japan, emerged with a noticeable individualist approach, advocating individual mobility and liberty. Looking at the configurations and spatial characteristics in Metabolist architecture, it is easy to perceive the features of “unit” and “megastructure”[3] as the major architectural elements in the composition, showing the individualistic characterisation in spatial patterns. Megastructure as an unchangeable large-scale infrastructure conceptually served to establish a comprehensible community structure. The unit as a structural boundary reinforced the identity of individuals in the whole community.

The Nakagin Capsule Tower (1970) by Kisho Kurokawa is a rare built example of Metabolism. It is a residential building consisting of two reinforced concrete towers, and the functional equipment is integrated into the megastructure forming a system of a core tower that serves its ancillary spaces. The functional programmes required for the served spaces are extended from the core where the structure and pipes are integrated. The identical, isolated units contain everything to meet basic human needs in daily life, which expresses the idea of individualism in architecture that is aimed for a large number of habitants. The independent individual capsules create a maximum amount of private space with little social connectivity to neighbours.

Constructivism: As Parts in Whole

Collectivism could be applied to a society in which individuals tie themselves together into a cohesion which obtains the attributes of dependence, sharing and collective benefit. This is aligned to the principles of constructivism, proposing the collective spatial order to encourage human interaction and generate collective consciousness. In contrast to the Metabolists, constructivist architecture underlined spatial arrangements for public space within compressed spatial functions that enable a collective identification.

The Narkomfin Building (1928–1932) by OSA Group is one of the few realised constructivist projects. The building is a six-story apartment located in a long block designed as a “social condenser”.[4] It consists of multiple social functions that correspond to specific functional and constructive norms for working and living space within whole community. The main building is a mix-use compound with one part for individual space and another designed as collective space. The private and common space are linked by an exterior walkway as a communal rooftop garden. There are 54 living units, and each of them only contain bedroom and bathroom. Each flat could be divided into two, one in which contains a playground and kitchen; the other one, a collective function area, which consists of garden, library and gymnasium. The corridors linking the flats are wide and open, appearing as an urban street to encourage inhabitants to stop and communicate with their neighbours.

Compared with the Nagakin Capsule Tower, the concept behind the spatial arrangement of Narkomfin Building is the collectivism of all needed programs. The large-scale collective was proposed as a means to replicate the concept of the village in the city. Practically this allows for a shrinking of the percentage of private space while stimulating the social interaction within the collective living space. The concept of amplifying communal space aligns to the constructivist movement through the concept of reinventing people’s daily life by new socialist experimental buildings, reinforcing the identity of collectives within the whole community.

Figure 2 – (left) the Nakagin Tower metabolized by individualist parts; (right) the Narkofim constructed with collectivist parts. Image: Hao Chen Huang.

Codividuality: As Parts in Parts

In architecture, the word “codividuality” originally emerged in the Japanese architectural exhibition House Vision (2019) to refer to collective living in terms of the sharing economy, delivering a social meaning: “creating a new response to shared-living in the age of post- individualism”.[5] Economically speaking, codividuality expresses the notion of share-ability in sense of sharing value and ownership. Moreover, it offers a participatory democracy for spatial use in relationship to changing social structures and practices. The architectural applications of codividuality are not merely about combined private space with shared public facilities but reveal a new reality that promotes accessibility and sustainability in multiple dimensions, including spatial use, economy and ecology.

Share House LT Josai (2013) is a collective-living project in Japan, offering an alternative for urban living in the twenty-first century sharing economy. Due to the change of demographic structure and rapidly rising house prices, Naruse Inokuma Architects created an opportunity to continually share spaces with unrelated people by creating an interactive living community in a two-and-a-half-story house. The 7.2 square meter individual rooms are three-dimensionally arranged across the two and a half levels. Between the bedrooms are the shared spaces, including a void area and an open plan living platform and kitchen that extend toward identical private rooms. The juxtaposition of private and communal spaces creates a new spatial configuration and an innovative living model in the sharing economy. Codividuality obtains individuals’ autonomy and, on the other hand, encourages collective interaction. It is not an opposition to individualism nor a replication of collectivism, but a merged concept starting from individualism, then juxtaposing against the notion of collectivism. 

Figure 3 – Fusion of parts. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

Autonomy of Parts

In contemporary philosophy, “Object Oriented Ontology” (OOO)[6] proposes a non-human way of thinking, unshackling objects from the burden of dominant ideologies. Objects are withdrawn from human perception, thereby containing the autonomy and irreducibility of substance. Accordingly, what this autonomy is based on is the independence of the object itself. An individual object is not reliant on any other objects, including humans. Objects exist whether we are aware of them or not. Objects do not need to passively rely on human cognition to represent themselves, but self-evidently and equally stand in the world.

OOO enables a transition in architectural meaning from architecture as autonomous objects to interactive relationships between object and field, where indirect relations between autonomous objects are observed. In an ecological sense, the reason behind this shift could be understood as an irreducibility of the architectural relationship within the environment; in other words, an architectural object cannot be withdrawn from its relation to context. As Timothy Morton writes, “all the relations between objects and within them also count as objects”,[7] and David Ruy states in his recent essay, “the strange, withdrawn interaction between objects sometimes brings forth a new object.”[8] Ruy emphasises the relation between objects based on a dynamic composition interacted with by individuals that is not a direct translation of nature.

In an object-orientated ontology, architecture is not merely an individual complete object but fused parts. This could be translated into a mereological notion of shifting from wholeness to parts. As a starting point for a design methodology, extracting elements from buildings represents loosening the more rigid system found in a modernist framework, by understanding architectural parts as autonomous and self-contained. Autonomous architectural elements cannot be reduced to the individual parts that make up the whole. This shift opens up an unprecedented territory in architectural discourse. Autonomous architectural parts now can participate in a non-linear system involving not only input or output, beginning or end, or cause or result; architecture can be understood as part of a process.

Figure 4 – Sampling of infinite codividual parts shown as yellow. Parts with different states showing the machine learning process of identifying codividual combination. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

Architecture in the Sharing Economy

The rise of the sharing economy in the past decade has provided alternatives to the traditional service economy, allowing people to share and monetise their private property and shift thinking around privacy. In this context the following question arises: how could mereological architecture reveal new potentials beyond the inhabitation of buildings by engaging with the sharing economy? Due to the financialisation of the housing market and, simultaneously, the standardisation and lowering of quality of housing standards due to deregulation of the market, this question is even more pressing. Furthermore the bureaucracy of the planning system limits the architectural designing process by slowing development down and restricting innovation. In this context the reconfiguration of housing to emphasise collective space could be an alternative living model, alongside financial solutions such as shared ownership.

Decentralised Autonomous Organisation

The notion of a Decentralised Autonomous Organisation (DAO) seems fitting for furthering this discussion. In economic and technological terms, DAO is a digital organisation based on blockchain technologies, offering a decentralised economic model. As an alternative to centralised economic structures within a capitalist system, DAO benefits from blockchain technology as a digital tool for achieving a more transparent, accessible and sustainable economic infrastructure. This involves shifting decision-making away from centralised control and giving the authority to individual agents within the system.

In the Medium article “The Meaning of Decentralisation” by Vitalik Buterin, Buterin describes a decentralised system as a collective of individual entities that operate locally and self-organise, which supports diversity. Distribution enables a whole to be discretised into parts that interact in a dynamic computing system that evaluates internal and external connectivity between parts.[9] Through continuous interaction, autonomous discrete entities occasionally form chains of connectivity. In this process the quantities of parts at junctions continuously change. Over time patterns emerge according to how entities organise both locally and globally. Local patterns internally influence a collective while global patterns influence between collectives – or externally in a field of patterns – similar to Stan Allen’s notion of a “field condition”.[10] This creates global complexity while sustaining autonomy through local connectivity.

Figure 5 – Simulations of the interlocking chains training a machine learning model. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

Distributing Codividuality

Codividuality could be seen as a post-individualism, where a diverse self-organising system withdraws power from capitalist authorities. The process of decentralisation characteristic of DAO is key to codividuality for it allows repeated patterns to form in a connected network. Architecturally, in codividual space each spatial unit consists of an open-ended program and self-contained structure, which means that architectural elements such as walls or slabs exist not for a specific function but serve a non-representational configuration.

Through computing codividual connectivity, autonomous spatial units start to overlap with other units, generating varying states of spatial use and non-linear circulation. What this distribution process offers is an expanded field of spatial iterations, using computation to respond to changes in quantity or type of inhabitants. In this open-ended system, codividual parts provide each spatial participant the capability to overcome the limitation of scalability through autonomous interconnection supported by a distributed database.

Unlike conventional planning in a modernist framework, codividual space does not aim for a module system that is used for the arrangement of programme, navigation or structure but for a non-figurative three-dimensional spatial sequence. The interconnections between parts and the field enable scalability from the smaller scale of spatial layouts towards large-scale urban formations. This large-scale fusion of codividual space generates a more fragmented, heterogeneous and interconnected spatial order, balancing collective benefit and individual freedom. In this shifting towards heterogeneity, codividuality opens a new paradigm of architecture in the age of the sharing economy.

Figure 6 – Perspective of a codividual building proposal for a site in Lisbon. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.
Figure 7 – Perspective view into a codividual space offering a 3dimensional urbanity. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.
Figure 08 – Close-up into a codividual living area. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.
Figure 09 – View into a codividual interiority. Codividual aesthetics forming a plural space. Image: Comata, Anthony Alvidrez, Shivang Bansal, and Hao-Chen Huang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

[1] H. C. Triandis, Individualism And Collectivism (Boulder: Westview Press, 1995).

[2] “Mereological Thinking: Figuring Realities within Urban Form,” Architectural Design, 89, 2 (2019), 30–37.

[3] Z. Lin, Kenzo Tange And The Metabolist Movement (London: Routledge, 2010).

[4] D. Udovicki-Selb, M. J. Ginzburg, I. F. Milinis. Narkomfin, Moscow 1928-1930 (Tübingen: Wasmuth Verlag, 2016).

[5] "HOUSE VISION", HOUSE VISION (2019),, accessed 9 May 2019.

[6] L. Bryant, The Democracy of Objects, (Open Humanities Press, 2011).

[7] T. Morton. The Ecological Thought (Cambridge: Harvard University Press, 2010).

[8] D. Ruy, “Returning to (Strange) Objects”, TARP Architecture Manual: Not Nature. (Brooklyn, New York: Pratt Institute Graduate School of Architecture, 2015).

[9] V. Buterin, “The Meaning of Decentralization” (2017),, accessed 9 May 2019.

[10] S. Allen and G. Valle, Field Conditions Revisited (Long Island City, NY: Stan Allen Architect, 2010).

Suggest a Tag for this Article
An accommodating facade, between a terrace, a stair, and a balcony. Urban redevelopment Haarlemmer Houttuinen, Amsterdam, 1982. Image by Herman Hertzberger.
Friendly Architecture – In the Footsteps of Structuralism: An Interview with Herman Hertzberger
Architecture, Architecture Theory, City Architecture, Mereologies, Mereology, Urban Design
Herman Hertzberger, Daniel Koehler
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This interview took place on April 11th, 2017 at the office of Herman Hertzberger in Amsterdam, with questions by Daniel Koehler.

Daniel Koehler: After all your years as a teacher, maybe it would be a good departure for conversation if you can tell us what is your favourite exercise for teaching architecture?

Herman Hertzberger: Well, my favourite exercise is making a housing environment, where small children could live and play outside. This is an old-fashioned thing, but I am absolutely convinced that children should play in the streets in order to find out about the world and to learn about the good and the bad things that exist. I am afraid that today in urbanism you find high-rises, and the immense distance from the living unit to the street is a problem. Consequently, cities only have playgrounds with fences around, and there children are safe to play. But the world is not only about safety, the world is about finding out how far you can go in your life.

Can you tell us a little bit about how you began to communicate as a group during the beginning of structuralism?

We started a school! We had seminars for discussion, where everyone brought in something to discuss. And then we had the Forum editorial staff. There was Aldo van Eyck, Jacob Bakema and others who are less well known (Dick Apon, Joop Hardy, Jurriaan Schrofer and Gert Boon). There was an enormous amount of communication. Every Tuesday night we saw each other with no exception, where we discussed the next issue of the magazine.

And, what was the relevant media at the time you started to develop your ideas?

Magazines were very important. We used to have three or four Dutch magazines, two French, two English, one American, two Swiss, two Italian. They were all on the table. “Did you see that building? I think it is good.” And then we had a discussion. Today we still get some magazines, but today you get all the information from around the world in one click. That is fantastic, the possibilities today are just immense. It is more information, a lot of pieces of an enormous puzzle. But is it also possible to put it together? I hope the younger generation can.
The magazine Forum was for me a sort of postgraduate study. At that moment I started to see the work, the hands and eyes of real architects. That helped me to start thinking. And there were connections to many other architects from all over. There were conferences, and there you saw people. At Delft University, where I was teaching, we invited all the architects we were interested in. We are still doing this.

When one reads the current literature, one can draw two different issues. On the one hand a common critique of functionalism in architecture, and on the other hand, the influence of new ideas coming from sociology. Would you say that this enormous explosion of ideas and diversity of projects was a response to architectural problems or were these new concepts coming from other fields prescriptive to your projects?

First of all, there is nothing coming from sociology. I have little or no connection to sociology. Sociology is the science of human relations. But you do not need to go into this science as an architect. Architecture is a matter of using your eyes and ears to look into the world and see what needs to be done. But today, architecture is driven by algorithms and rules. All the rules, saying you should do this or that, you are supposed to not do this. Architecture is then reduced to problem-solving. You must be aware of that mistake. Architecture is not problem-solving. Of course, you have to solve problems, but this is only one aspect of architecture. It starts to be architecture when it provides more freedom to people, opening the possibility that things are getting better than they were before.

Can you give an example?

A dwelling needs to have a balcony. Why? To let people go outside, and there are rules about the size of your balcony. Most architects think: well, I included a balcony. But they should base the form and dimensions of a balcony on the needs of daily life. Such as sitting in a corner without being seen by others or not being disturbed while reading your book yet with the possibility of having contact with your neighbour. Second, you may want to be able to have a meal with your family. You maybe want to have flowers and plants. In a way, this is culture. Make that list, and when you design a balcony, be sure that all the points you have listed have also been fulfilled. In this way you increase people’s freedom. Most balconies do not do that. On most balconies all you can do is sit. Most architects don’t think, they don’t look at what is going on. And then, of course, the developer says, “It should not cost more, so we have to make it small.” So I have rules independent of the developers. For me, it starts to become good when those rules are going to be met. This method works for every part of the building, from a dwelling, to a living unit, to a street, to the school. In a school, you can design where the black board in a classroom is going to be. And you have to think about what a school might be. I don’t need sociologists for that. Sometimes, sociologists can tell you some interesting things, but you have to think, and in the first place, look for yourself.

Your communal spaces are famous for their human scale, like the doorstep. I think that this down-scaling of the city to elements of a building enables you to design the building as an open system. For me, it seems you draw a difference in creating a building as a building and designing a building as a city.

For me, city, architecture, and building are very much related. Aldo van Eyck believed that making architecture is always making things more inside than before. Aldo van Eyck said, “Whatever you do, it is supposed to always increase the inside quality.” When you want to go outside, you go to the fields. There you have the horizon, you have the clouds and the openness. A city is for exchange – exchange of goods, of ideas. Cities are mostly based on trade, and on having a cinema, having shops, having communal things, being together.
Aldo van Eyck also claimed that the city should be a big house. I think that is a dangerous thing to say because the city is not the house where you are yourself, or where you are enclosed. The city should never be enclosed but always open, in connection with the whole world. It is the place where you see the airplanes flying above you. But it is an inside space in relation to the open field. And a building is, in fact, a small city. Make a building as a small city to have the emphasis lay on communication and exchange.
But most buildings are private territories with public corridors. How narrow can a public corridor be? It cannot be a centimetre larger, because this would cost money. Means of communication are considered extra. You can sell the dwellings but not the corridors. As a result, most buildings have very beautiful apartments and very small corridors. I am pleading for buildings where the corridors are streets. I try to put more emphasis on the communal spaces in a building.

When you consider a building as an open system, what role does the boundary between inside and outside have? Do you think that these open systems have an outside or do you think of them as endless? What is their relationship to the context and environment?

City is not just buildings but the space in between the buildings as well. The edge of building is forming the space of the city. You have to conceive of the edge of a building not as an end where the outside starts. You must see it the other way around, as a wall in the interior space of the city. The idea of the building as city is to put buildings in such a relation that the space in-between them is as import