Parts, chunks, stacks and aggregates are the bits of computational architecture today. Why do mereologies – or buildings designed from part-to-whole – matter? All too classical, the roughness of parts seems nostalgic for a project of the digital that aims for dissolving building parts towards a virtual whole. Yet if parts shrink down to computable particles and matter, and there exists a hyper-resolution of a close to an infinite number of building parts, architecture would dissolve its boundaries and the capacity to frame social encounters. Within fluidity, and without the capacity to separate, architecture would not be an instrument of control. Ultimately, freed from matter, the virtual would transcend from the real and form finally would be dead. Therein is the prospect of a fluid, virtual whole.

The Claustrophobia of a City that Transcends its Architecture

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

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 Detached from the architecture of the city, with no belonging left, urban speculation has withdrawn into the private sphere.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

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

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

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

Hyper-parts: Spatial Practices of representations

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

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

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

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

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

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

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

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

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

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

The Poiesis of a Virtual Whole

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

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

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

Partitioning Architectures

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

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

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

Replicating: A Spatial Practice of Representations

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

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

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

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

From Partitioning to Partaking

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

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

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

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

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

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

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