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. In “Synthesizing 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.

Acknowledgments

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.

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.

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 25^th 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]

Guifi.net: 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 Guifi.net as an illustrative example. Guifi.net[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 Guifi.net project, instead, manages this infrastructure as a commons. In other words, Guifi.net 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 Guifi.net 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 Guifi.net, 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, Guifi.net provides a large and complex case of governance of shared infrastructure. The growth experienced by Guifi.net’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 Guifi.net, 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 Guifi.net 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, Guifi.net 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]

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 Guifi.net.

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 Guifi.net? First of all, we need to identify the relationship between Ostrom’s principles and Guifi.net. We can find, indeed, a wide exploration of the relationship between Ostrom’s principles and the evolution in the self-organisational processes of Guifi.net in the work of Baig et al..[30] They document in detail how Guifi.net 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 Guifi.net. 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 Guifi.net 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 Guifi.net: the Guifi.net 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 Guifi.net, 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. 

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: Guifi.net. 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.

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.

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.

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.

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.

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. 

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.

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.

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.

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.

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.

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.

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.

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]

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. 

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. 

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.

Fusion

“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.

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.

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. 

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.

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.

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.

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 important. This is something that is completely lost. It is also considered nostalgic. But look to New York. In New York, you have these high skyscrapers, but you also have very nice streets. When I am in Manhattan, I feel quite enclosed. That is because of the very strict system of the grid, and the building lines by which the streets are defined, and the blocks in between are open.

In one of your articles [Open City, 2011], you rightly point out that most of today’s housing projects consciously exclude communal spaces, and focus only on the assembly of private areas without any spatial linkages between them. Private areas are protected to one another rather than connected. A common – and I think dangerous – justification for such a design refers to changed economic circumstances, and most cynically, to the death of the welfare state. Would you say architecture is so dependent on economics?

Every square meter is supposed to generate a fee, so public space will be reduced to a minimum. Architecture has become business. And that makes the position of the architects to contribute to better spaces and towns very difficult.

But then architects are even more important.

Important as long as you are able to be aware of what sort of culture you are living in. I cannot give you the answer what to do. You have to explain and fight. But you need clients who believe in the architect. Things are very materialistic today. But there are also very interesting initiatives. For example, in Rotterdam, you have these old industrial halls which could be reused without high costs. Add a little paint, and it works. There are ways today that are contradicting this idea of architecture as economics. There is a lot for you to invent.

When I told a friend that we will visit you as one of the main protagonists of structuralism, his response was: ‘Wait a moment! Herman Hertzberger is not a structuralist; he is a humanist.’

Can you not be a structuralist and a humanist at the same time? Is this contradictory?

I think what my friend was pointing at is that there is a difference between structuralism as a style and structuralism as modus operandi, as a form of organisation and composition.

Style has to do with aesthetics, but aesthetics is a pitfall. Most architects think making something beautiful is all that architecture is about. But you can’t make something beautiful, it is impossible. That doesn’t work. What you can do is make a painting which is striking, and shows you something you never saw before that makes you happy or fall in love with the painting, and then we decide this is a beautiful painting. But in architecture, don’t spend energy on trying to make something beautiful. Make it work. Then you may hope that someone says this is beautiful. For instance, the composer of music Arnold Schönberg said, “Do not do what others consider beautiful, but just what is necessary to you.” I like a building because it works. When someone if I think it is beautiful, then I say, when you are in love it is going to be beautiful. Beauty comes as a result. But you cannot say, now I am going to make it beautiful. Beauty is a pitfall for architects.
Structuralism means there are simple rules that enlarge the amount of free space that you can achieve. I took the grid as an example earlier. The very rigid system of the grid allows you to be more free in the blocks in between. All of the blocks can be different; some high, some low. It is an enormous mosaic of possibilities that is held together by the grid. When you know what rules you have to use, you can be creative. It is a misunderstanding that the one contradicts the other.

It is interesting that you describe a rule as a form of enclosure, as a form of an inside.

If something is not limited you create chaos. Rules prevent you from chaos, and within rules you can be creative. Noam Chomsky [the linguist] uses the words competence and performance. The structure of language is its competence, it is its capacity to express. And performance is what you are actually expressing with it. In language you have grammar, but every individual talks in his or her personal way using the same rules.

Would you say that you have a grammar and vocabulary then? Do you have certain elements that you are frequently using? You were talking earlier about balconies and streets. In your work do you consider elements repeat structurally, which can re-emerge in different styles, but with similar performance? Or do you begin each project with a new grammar?

I do not use the same grammar for every building. I could, but I want to try different things. There are many people who thought housing should be produced in a factory, like cars. It is such a simple idea. But it doesn’t work, because every location has its own needs, whereas a car is the same everywhere. So, you can not use the same grammar. I use another grammar for a school and another for housing for instance. Some things have a similar grammar, like how you make a door, which works in most cases. 

Do you have a particular vocabulary of elements that reappear during your career in different articulations and styles?

Architecture should accommodate people and things that people are concerned with. I use this everywhere. To give you a simple example: when I make a column, most of the time I design it with a base for people to be able sit on it. This is for me an accommodating device. It always works. This sort of thing is universal in my opinion: the idea of accommodation. Another example is the handrail of a stair. I always make a handrail that guides you where to go, making the end of it in such a way that even without looking you have the feeling that this is the end of the stairs. Everything I do tries to consider how it works for people. However the point is that it should be friendly to people, but not soft.

Friendly architecture! This is a wonderful conclusion. Thank you, Herman Hertzberger for sharing your time and thoughts with us.