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Church Sainte Geneviève, Clovis, 502. Drawing by Jean-Baptiste Rondelet, 1810. Image: Thomas Thibaut, 2018.
Matter versus Parts: The Immaterialist Basis of Architectural Part-Thinking
Architecture, Discrete Architecture, Form, Matter, Mereologies, Mereology
Jordi Vivaldi
Institute for Advanced Architecture of Catalonia, University College London and University of Innsbruck
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“Digital Matter”; “Intelligent Matter”’; “Behavioural Matter”; “Informed Matter”; “Living Matter”, “Feeling Matter”; “Vibrant Matter”; “Mediated Matter”; “Responsive Matter”; “Robotic Matter”; “Self-Organised Matter”; “Ecological Matter”; “Programmable Matter”; “Active Matter”; “Energetic Matter”. There is no term enjoying better reputation in today’s experimental architectural discourse. Gently provided by a myriad of studios hosted in pioneer universities around the world, the previous expressions illustrate the redemption of a notion that has traditionally been dazzled by form’s radiance. After centuries of irrelevance, “Matter” has recently become a decisive term; it illuminates not just the field of experimental architecture, but the whole spectrum of our cultural landscape: several streams in philosophy, art and science have vigorously embraced it, operating under the gravitational field of its holistic and non-binary constitution.

However, another Copernican Revolution is flipping today’s experimental academic architecture from a different flank. In parallel to matter’s redemption and after the labyrinthic continuums characteristic of the ’90s, discreteness claims to be the core of a new formal paradigm. Beside its Promethean vocation and renewed cosmetics, the discrete design model restores the relevance of a term that traditionally has been fundamental in architecture: the notion of part. However, in opposition to previous architectural modulations, part’s current celebration is traversed by a Faustian desire for spatial and ontological agency, which severely precludes any reverential servitude to its whole.

The singular coincidence of matter’s revival on the one side and the discrete turn on the other opens a debate in relation to its possible conflicts and compatibilities in the field of experimental architecture. In this essay, the discussion gravitates around one single statement: the impossibility of a materialist architectural part-thinking. The argument unfolds by approaching a set of questions and analysing the consequences of its possible answers: how matter’s revival contributes to architectural part thinking? Is matter’s revival a mere importation of formal attributes? Which are the requirements for a radical part-thinking in architecture? Is matter well equipped for this endeavour? In short, are the notions of matter and part-thinking compatible in an architectural environment?

Pre-Socratic philosophy defined matter as a formless primordial substratum that constitutes all physical beings. Its irrevocable condition is that of being “ultimate”: matter lies in the depth of reality as more fundamental than any definite thing.[1] Under this umbrella, pre-Socratic philosophy ramifies in two branches: the first one associates matter with continuity, the second one associates matter with discretism.

Anaximander is the standard-bearer of the first type: the world is pre-individual in character and it is fueled by the apeiron, a continuum to which all specific structures can be reduced. We can find traces of this sort of materialism in Gilles Deleuze’s “plane of immanence”, Bruno Latour’s “plasma”, or Jane Bennett’s “vibrant matter”. Democritus is the figurehead of the second type: the world is composed by sets of atoms, that is, privileged discrete physical elements whose distinct combinations constitute the specific entities that populate the world. Resonances of this sort of materialism can be found in the “quanta” of contemporaneous quantum mechanics. Independently of their continuous or discrete nature, both types of materialisms are underpinned by an ontological assumption: the identification of matter with an ultimate cosmic whole. To this purpose, matter’s generic condition is decisive: its lack of specificity is precisely what grants matter the status of “ultimate”, which logically and chronologically precedes distinction.

Architecture’s conceptualisation of matter has not been impermeable to these philosophical discourses. In spite of the negative reputation that the Aristotelian hylomorphism projected on matter by converting it into the reverential servant of form – absent in pre-Socrátic philosophy and being introduced, in different ways, by Plato and Aristotle – in the last centuries many architectural projects opposed this status quo by capitalising on both types of materialism. Since the Enlightenment and still under form’s reign, matter has been recovering its pre-Socratic positive character by absorbing all the attributes traditionally ascribed to form. However, it also operated a conceptual replacement that is crucial in this discussion: matter moved from a marginal role in a hylomorphic dualist scheme to the solitary leadership of an ultimate holism. As we will see below, in architecture and particularly since the Enlightenment, matter’s relevance has been gradually recovered through its association with two key concepts: truthfulness, emphasised by authors of the late 18th and 19th century such as Viollet le Duc or Gottfried Semper, and vitalism, underlined by authors of the 19th century and early 20th century such as Henry Bergson or Henri Focillon.[2] Today this process has culminated with Eric Sadin’s notion of antrobology, that is, the “increasingly dense intertwining between organic bodies and ‘immaterial elfs’ (digital codes), that sketches a complex and singular composition which is determined to evolve continually, contributing to the instauration of a condition which is inextricably mixed ‘human/artificial.”[3]

In this technological framework and through the notions of information, platform and performance, matter’s traditional attributes have been replaced by those of form. Despite keeping the term “matter” as a signifier, the disorder, passivity and homogeneity that conventionally characterised its significance have been substituted by form’s structure, activity and heterogeneity. However, one crucial feature that is absent in the dualistic hylomorphic model has been reintroduced: matter’s pre-Socratic condition of being ultimate.

This incorporation is decisive when it comes to architectural part-thinking. In spite of the great popularity that matter has achieved within contemporary experimental architecture, its ultimate condition precludes any engagement with architectural part-thinking: either as a single continuous field or as a set of discrete particles, matter exalts a single holistic medium that lies at the core of reality, that is, a fundamental substrata (whole) in which all specific entities (parts) can be reduced. In a context in which designers use the power of today’s super computation to notate the inherent discreteness of reality instead of reducing it to simplified mathematical formulas,[4] or field, reality’s approach through generic and Euclidean points (particles) rather than distinct elements (parts) constitutes an unnecessary process of reduction that dissolves part’s autonomy.  

This essay develops this argument in two steps. First, it states that the current culmination of matter’s revival process in experimental architecture is, paradoxically, nothing but the exaltation of form; under the same signifier, matter’s signification has been replaced by form’s signification: all attributes that in the hylomorphic model were associated with the latter have now moved to the former, converting matter’s signifier into just another term to conjure up the significance of form. However, there is a crucial pre-Socratic introduction in relation to the hylomorphic model: matter is now understood as being also the ultimate single substance of reality, and not just the compliant serf of another element (form). This holistic vocation can be traced in contemporaneous experimental architecture in parallel to matter’s pre-Socratic distinction between a continuous field (Anaximander’s apeiron) and a discrete set of particles (Democritus’s atoms).

Second, this essay argues that current materialism, in any of its twofold registers, is incompatible with architectural part-thinking. The argument first identifies and evaluates three groups of architectural parts (topological, corpuscular and ecological) in the current experimental architectural landscape and second proposes a fourth speculative architectural part based on the notion of limit. If the idea of part demands a certain degree of autonomy from the whole, it cannot be reducible to any ultimate substrata, and therefore matter’s holistic condition becomes problematic both in its continuous and discrete register. However, the latter demands particular attention: discretism’s spatial countability might lead us to confuse the notion of particle with that of part. However, they significantly differ: while particles are discrete only from a mathematical perspective (countable), parts are discrete as well from an ontological perspective (distinct). Parts require at least both dimensions of discreteness in order to be considered autonomous from any exteriority, while simultaneously keeping its capacity to participate in it.

Architectural part-thinking demands then a radical formal approach. It requires a notion of form that operates at every level of scale, that is, an immaterialist model that recursively avoids any continuous (field) or discrete (particle) ultimate substrata in which parts could be reduced. This pan-formalism would imply then the presence of a form beyond any given form, understanding the term “form” as an autonomous spatio-temporal structure. 

Matter’s Recovery Process in Architecture: Truthfulness, Vitalism and Antrobology

Since Ancient Greece, architecture has interpreted the notion of matter through Aristotle’s hylomorphic scheme: matter is a disordered, passive and homogenous mass (matter) in attendance for a structured, active and heterogeneous pattern (form). According to this framework the architect is constituted as a demiurge: they operate from a transcendent plane in order to inform matter, that is, in order to structure its constitution through a defined pattern. However, since the Enlightenment, matter’s signifier has gradually replaced its signification with that of form through three concatenated strategies: truthfulness, vitalism and antrobology.

The concept of truthfulness in architecture should be read in opposition to the idealism of authors like Alberti or Palladio. In his De Re-aedificatoria, Alberti claimed that “architecture is not about artisan techniques but about ‘cose mentale’.”[5] What concerned him was not material attributes such as colour or texture, but the geometrical proportions of the forms that he produced with matter. This statement becomes evident in his façade for the Malatesta Temple in 1450.

Figure 1 – Malatesta Temple, Alberti, c. 1450. Image: Paolo Monti, Servizio fotografico, Rimini, 1972.

Conversely, some centuries later authors like Ruskin, Viollet-le-Duc or Semper defended the relevance of matter in architecture, asserting that the choice of a material should depend on the laws dictated by its nature, such that “brick should look like brick; wood, wood; iron, iron, each according to its own mechanical laws.”[6] Rondelet and Choissy also gave importance to the truth of the material, particularly throughout their exhaustive constructive drawings.

Figure 2 – Church Sainte Geneviève, Clovis, 502. Drawing by Jean-Baptiste Rondelet, 1810. Image: Thomas Thibaut, 2018.

However, this group of authors still remained idealistic: the use of materials was determined by the idea that the architectural object was intended to express. In that sense, and although its internal structure was recognised, matter was still subordinate to an external idea, that is, to an external form. 
Some decades later, in his Life of Forms in Art (1881) Henri Focillon dignified matter through a strategy based on a different concept: vitalism. Although arguing that the development of art is inextricably linked to external socio-politic and economic characteristics, Focillon associated an autonomous formal mutation to it through underlining matter’s inherent capacity of movement and metamorphosis. Already present in the Baroque and empowered by the Enlightenment’s idea of “natura naturans”, concepts like the “Bildungstrieb”, the “Thatkraft” or the “Urpflanze” articulated a vitalist approach to matter closely related to German Expressionism. Ruskin and Semper’s seminal materialism based on material’s truth gave way to a radical pragmatism in which architects used hybridised materials in order to relate to natural metamorphosis. Many glass-based projects from the early 20th century replicate these morphogenetic processes, an attitude already present in the gothic. In resonance with Bergson’s élan vital, a hypothetical force that explains the evolution and development of organisms, certain uses of concrete imitated the formal exuberance of some morphogenetic natural processes, as can be seen in the Goetheanum from Rudolph Steiner in 1928 or Einstein Tower from Erich Mendelsohn in 1921, but also with different materials in the Großes Schauspielhaus from Hans Poelzig in 1919.

Figure 3 – Großes Schauspielhaus, Poelzig, 1919. Image: Image on paper 18,5 x 24,2, Architekturmuseum der Technischen Universität Berlin, 1919.

Moreover, the use of concrete established a continuity between form and structure characteristic of the organic beings that were so greatly admired at that time. As a consequence, a progressive material vitalism was thus constituted through an hylozoic approach based on Einstein’s theories of matter and energy interconvertibility, which suggested a comprehension of matter as a set of energetical perturbations instead of mere inert mass. In this sense and according to Henry van de Velde, matter had not only a mechanical value, but an active dispositionality that was the consequence of its “formal vocation”. However, vitalism had also its conservative reverse. Fueled by the phenomenological work of Rasmussen and Norberg-Schulz, architects such as Herzog & Meuron, Steven Holl or Peter Zumthor propose a haptic approach to architecture that relies on materials as symbolic shapers of architectural space. Under this scenario and in close relation to Merleau-Ponty’s notion of “flesh”, matter is still understood as a holistic repository of tactile and cultural memory.

In parallel to the general disdain that Modernism showed for materiality during the first half of the 20th century, according to Eduardo Prieto truthfulness and vitalism have gradually contributed to the reconsideration of matter as a substance with a certain agency.[7] This process was based not on the exaltation of the passivity, neutrality and homogeneity that originally characterised matter, but on the importation of attributes from the notion of form. Ruskin’s truthfulness is based precisely on the understanding that matter has a specific inner character that makes it heterogeneous, while the vitalism of Steiner alludes to the metamorphic capacities of living beings.

However, both cases remain idealistic. Truthfulness asserts the need for an external form to choose the matter that best suits its purposes. Vitalism claims that matter should be seen as a material of organic expression that still needs an artist or architect to unveil its aesthetic potentialities of metamorphosis. In both cases, matter is still seen not just in opposition to an external form, but also under its control. In this sense, the vitalism defended by Bergson differs from the vitalism of Deleuze: for the former, matter is still a generic substance that needs an artist to particularise it, that is, needs an élan vital to form it. Conversely, for Deleuze, matter is an immanent reality: it provides form to itself and does not require any transcendental agent. This Deleuzian conception of matter has been emphasised today through New Materialism, whose statements in relation to the problem matter-form are based “on the idea that matter has morphogenetic capacities of its own and does not need to be commanded into generating form.”[8] In this sense, matter is no longer seen in opposition to form, that is, “it is not a substrate or a medium for the flow of desire, but it is always already a desiring dynamism, a reiterative reconfiguring, energised and energising, enlivened and enlivening.”[9] 

This philosophical approach reverberates with our current technological condition. After the stages of truthfulness and vitalism, Sadin’s antrobology culminates an architectural recovery of matter that paradoxically is based in the replacement of its signification by that of form. Faced with a dual ontology that is no longer alluding to Heideggerian human nudity but to a planet inhabited by algorithmic beings that live with and against us, Eric Sadin defines our technological scenario as Antrobological. This notion expresses the “increasingly dense intertwining between organic bodies and ‘immaterial elfs’ (digital codes).”[10] The propagation of artificial intelligence and the multi-scalar robotisation of the organic establishes, in addition to a change of medium, a change of condition: its algorithmic power does not merely offer itself as an automatic pilot for daily life, but it also triggers a radical transformation of our human nature, setting up a perennial and universal intertwining in between bodies and information. In this sense, the multidisciplinary generalisation of machine learning, progress in genetic engineering or the robotisation of the mundane no longer refer to a humanity that is merely improved or enriched, but to a humanity that is intertwined: it is unfolded through a physiological platform that is woven by algorithmic, organic, robotic and ecologic agents whose symbiosis is not metaphorical or narrative, but strictly performative. It is precisely under this scenario that “artificial extelligence” becomes “artificial intelligence”: it executes an exercise of incorporation in which the intelligence, eidos, or what has traditionally been understood as form is no longer an external entity that articulates matter from outside, but is its immanent circumstance.

The historical and incremental process of matter legitimation, based initially on the truthfulness of Ruskin and the vitalism of Steiner, culminates today with the celebration of the notions of platform, information and performance that singularise Sadin’s antrobology. Recent theorisations on concepts related to computation and design such as Keller Easterling’s “medium”[11] or Benjamin Bratton’s “stack”[12] are as well deeply underpinned by these three expressions. However, it is crucial to note that the term “form” is present in all of them, associating each expression to one of the three main form’s attributes: structure (information), activity (performance) and heterogeneity (platform). 

While matter “is that which resists taking any definite contour”,[13] form refers to the active presence of a distinguished and qualified non-ultimate structure containing other forms at every level of scale and that can occasionally change and establish relationships. It is under this framework that the previous terms should be read in relation to experimental architecture. To provide a platform means to provide the conditions for an evolving intertwining in between forms that permits the promiscuous co-existence of difference, that is, of heterogeneity. Thus, a platform is not a field: in opposition to the latter, the former doesn’t permit any sort of reductionism, that is, its elements are not mere emergences, as occurs with fields, but singularities with distinct origins. To provide information means to provide structure: it precludes disorder by establishing a spatio-temporal non-ultimate organisation. However, given that every entity already has a form and we cannot imagine a formless element, to inform means actually to transform. To provide performance, in contrast, means to present rather than represent: it produces an operative impact on the set of conditions in which it is placed, instead of merely representing an absent entity, as would be the case of a metaphor.

Under Sadin’s antrobology, the disorder, passivity and homogeneity that traditionally identified matter are replaced by those characteristics that qualified form in the hylomorphic model: structure (information), activity (performance) and heterogeneity (platform). However, if the process of legitimation of matter is rooted in replacing its attributes by those of form, it is increasingly more unsustainable to keep referring to it as “matter”, when actually, especially in Sadin’s antrobology and from a hylomorphic point of view, matter is actually empty of matter and full of form.

Matter’s Ultimate Condition and Part-Thinking

However, the rupture of the hylomorphic dichotomy caused by matter’s absorption of form has implied the introduction of a pre-Socratic matter’s condition: that of being ultimate. Matter is not understood anymore as one of the components of a dualistic model, but as a single holistic substance whose structure, activity and heterogeneity underlies the emergence of any specific entity. This model, technologically underpinned by Sadin’s antrobology, has been articulated by contemporaneous experimental architecture according to the two types of materialism that differentiate pre-Socratic philosophy: as a continuous field (Anaximander’s apeiron) or as discrete particles (Democritus’s atoms). However, its common “ultimate” condition obstructs architectural part-thinking: if the notion of part demands an autonomy that cannot be exhausted neither in its outer participation in a bigger ensemble nor in its inner constitution through a smaller ensemble, matter’s holism becomes problematic. Indeed, if any entity (part) can be deduced from a privilege underlying substrata (whole), its autonomy is called into question.

Anaximander’s apeiron model is the most popular representative of pre-Socratic continuous approaches to matter. For the greek philosopher, apeiron refers to the notions of indefinite and unlimited, alluding explicitly to the origin (arché) of all forms of reality. Precisely because apeiron, as suggested by its etymology, is that which cannot be limited, it doesn’t have in itself any specific form, that is, it is not definable. It is therefore a continuous material substrata, vague and boundaryless, capable of supporting the opposites from which all the world’s differentiation emerges. Besides Bruno Latour’s ‘plasma’, described by its author as that unknown and material hinterland which is not yet formatted, measured or subjectified, one of the most popular contemporaneous elaborations of this apeiron’s holistic theory is Jane Bennett’s “throbbling whole”. For the American philosopher, objects would be “those swirls of matter, energy, and incipience that hold themselves together long enough to vie with the strivings of other objects, including the indeterminate momentum of the throbbing whole”, something that according to Harman “we already encountered, in germ, in the pre-Socratic apeiron”.[14] Beside pure formal continuities such as Alejandro Zaera’s Yokohama (2000) or François Roche Asphalt Spot (2002), we can find a similar holistic vocation in projects such as Neri Oxman’s BitMap Printing (2012), Mette Ramsgard Thomsen’s Slow Furl (2008), and Poletto-Pasquero’s Urban Algae Follies (2016). Its renovated notion of matter is usually referred to as behavioural matter, living matter, ecological matter, digital matter, expanded matter, data-driven matter or intelligent matter. 

Paradoxically, what is relevant in all these expressions is not the term matter, but its qualifier, which systematically refers to spatio-temporal formal arrangements rather than hylomorphic matter attributes, emphasising the relevance of form as identifier over matter. Nery Oxman’s “material ecology” is an emblematic example of this phenomena. Oxman defines this expression as “an emerging field in design denoting informed relations between products, buildings, systems and their environment”.[15] The architect uses the term “informed” referring to information and therefore alluding to matter’s inner structure. However, if “matter” is informed, it is no longer a homogeneous and amorphous substance, but it contains a digital or a physical structure that operates at every level of scale. Her project Bitmap Printing (2012) acts as a platform that intertwines between natural, human and algorithmic agents, whose activity has performative consequences rather than symbolic references. In this sense, given that the project is informed, acts as a platform and performs, it is hardly understandable why, under a hylomorphic scheme, we refer to them as specific configurations of matter rather than as a particular type of form.

However, these three projects, together with the work of authors such as Marcos Cruz, Phillip Beesley or Areti Markopoulou, introduce a pre-Socratic’s matter attribute absent in the hylomorphic scheme: matter’s condition of being ultimate. In particular, we can find this pre-Socratic’s matter attribute in the continuous version developed by Anaximander through the notion of apeiron. As we can see in projects such as the Hylozoic Garden (2010) by Philip Beesley, full relationality and complete interconnectedness are the basis of a systemic approach to architecture in which the conceptual idea of field articulates Delanda’s “continuous heterogeneity”. 

The project is based on the ancient belief that matter has life and should be understood, according to its author, as an active environment of processes rather than as an accumulation of objects. Unlike hylomorphic matter, the anti-maternalistic matter evoked by the Hylozoic Garden does not contain an Aristotelian pattern that provides structure to it, but is instead self-formed, that is, structured, active and heterogeneous. However, specific parts are always an emergence from an underlying holistic field, that is, a whole. Indeed, continuity is actually capable of producing objects, that is, continuity on one level creates episodic variation on the next that may be presented as discrete elements, but they are always dependent on this first gradual variation. Under this scheme, part-thinking is very limited because specificity is always a deduction from a privilege underlying substrata. Parts are then prevented from its autonomy, being instead exhausted in its participation as subsidiary members of a whole. As Daniel Koehler suggests, “departing from parts a preconceived whole or any kind of structure does not exist. Parts do not establish wholes, but measure quantities.”[16] And quantities, indeed, begin with individuals, that is, with discreteness.

However, the notion of “discreteness” needs differentiation: not all the interpretations of this term permit to understand its individuals as parts. In this sense, it is crucial to note that pre-Socratic philosophy articulates as well a type of materialism based on discreteness: beside the continuity emphasised by Anaximander’s apeiron, Democritus’s atomic model is the most popular representative of this discrete approach to matter. For the Greek philosopher, atoms are not just eternal and indivisible, but also homogeneous, that is, generic. Although atoms differ in form and size, its internal qualities are constant in all of them, producing difference only through its grouping modes. Atoms are then particles: generic individuals whose variable conglomerates produce the difference that we observe in the world. As Graham Harman affirms, this form of materialism is “based in ultimate material elements that are the root of everything and higher-level entities are merely secondary mystifications that partake of the real only insofar as they emerge from the ultimate material substrate.”[17] 

The atomic model is thus a reductionist model: the different specificities that conform the world are mere composites of a privileged and ultimate physical element. In opposition to the continuous form of materialism, the discrete atomic type is easily misunderstood when it comes to considering its part-thinking capacities due to a frequent confusion: that between “part” and “particle”. This association is especially present nowadays in architectural experimental design, particularly under the notion of “digital” and its inherent discrete nature. Computation’s power of today has been aligned with this position through the recognition that “designers use the power of today’s computation to notate reality as it appears at any chosen scale, without converting it into simplified and scalable mathematical formulas or laws.”[18] It assumes “the inherent discreteness of nature”,[19] where the abstract continuity of the spline doesn’t exist. However, this process of architectural discretisation needs differentiation in order to be understood in relation to the notion of part, defined here as an interactive and autonomous element which is not just countable (mathematically discrete) but also distinct (ontologically discrete). Within the contemporaneous discrete project, three groups of architectural approaches to the notion of part, together with a speculative proposition, need to be distinguished according to its relation with matter’s ultimate condition: topological parts, corpuscular parts, ecological parts and limital parts.

Topological Parts, Corpuscular Parts, Ecological Parts, Limital Parts

There is a first group of proposals in which parts are topological parts; in spite of the granular appearance of its architectural ensembles, its vocation is still derivative from the parametric project: the continuity of its splines has reduced its resolution through a process of “pixelisation”, but it still operates under the material logic of an ultimate field. The notion of topology should be read here under the umbrella of the Aristotelian concept of topos. While Plato’s term chora refers to a flat and neutral receptacle, the term topos refers to a variable and specific place. In contrast to the flat spaces of modernity, the three-dimensional variability of 1990s spaces produces topographic surfaces in which every point is singular. This results in “a constant modification of the space that leads to a changing reading of the place,”[20] implying the shift from Plato’s chora to Aristotle’s topos. Unlike the universal abstraction of the former, in the Physics, Aristotle “identifies the generic concept of space with another more empirical concept, that of ‘place’, always referred to with the term topos. In other words, Aristotle looks at space from the point of view of place. Every body occupies its specific place, and place is a fundamental and physical property of bodies.”[21]

This is very clear in the following text by the Stagirite: 

“Again, place (topos) belongs to the quantities which are continuous. For the parts of a body which join together at a common boundary occupy a certain place. Therefore, also the parts of place which are occupied by the several parts of the body join together at the same boundary at which the parts of the body do.”[22]

Aristotle defines topos as a continuous and three-dimensional underlying substratum, but above all as an empirical and localised substratum.

The rhizomatic twists associated with these projects and underpinned by the intensive use of computational tools seem to oppose the homogeneity of its parts. According to Peter Eisenman, “while Alberti’s notational systems transcribed a single design by a single author, computation has the capacity to produce multiple iterations that the designer must choose from.”[23] Computers function as generators of variability, a fact that seems to promote Eisenman’s inconsistent multiples, calling into question Alberti’s homogeneous spatiality. However, in spite of being countable and distinct, the constitution of the parts associated with projects such as BIG’s Serpentine’s Pavilion (2016) and The Mountain (2008) or Eisenman’s Berlin Memorial (2005) is reducible to one single formula or equation, that is, a consistent and calculable single medium (parametricism). Its discrete look is provided by a set of elements which are countable, distinct and interactive, but that cannot be read as parts because its autonomy is restricted for a twofold reason: both its distinction and position depend on an ultimate system of relations which is external to the logics of its individuals, evoking therefore apeiron’s type of materialism. In this sense, parts here should be read as components: the location and form of them is subordinated to the topological bending of a general surface, precluding any type of part’s autonomy.

There is a second group of experimental projects in which parts are corpuscular parts. In these parts architectural ensembles are formalised through countable and qualitatively identical corpusculi, that is, individual entities which are not systematised by any external and preconceived structure. Its advocates follow a path similar – even if this is not their conscious intention – to that of Walter Gropius, Mies van der Rohe and Le Corbusier when they freed themselves from the straitjackets of the symmetry characteristic of 19th century’s Beaux-Arts, championed by architects such as Henri Labrouste or Felix Duban. However, corpuscular parts differ from modern parts in the fact that they are formally identical in between them despite performing different functions. Mario Carpo relates some of this work with Kengo Kuma’s Yure Pavilion (2015) and GC Prostho Museum Research Center (2010) under the expression “particlised.”[24] The term relates to the non-figural, aggregational or atomised way of producing architecture, in which Kuma states that “each element needs to be relieved from contact or structure beforehand, and placed under free conditions.”[25] 

Experimental projects such as Bloom (2012) by Alisa Andrasek and José Sánchez or Flow (2016) by Calvin Fung and Victor Huynh participate as well in this process of “particalisation” by relying on an ultimate, generic and privileged element: in opposition to modernist assemblies and in resonance with some of the early work of Miguel Fisac, “the buildings blocks are not predefined, geometric types – like columns or slabs – that only operate for a specific function,”[26] and unlike parametricism they do not derive from a predefined whole. 

Instead, the particle’s specific function is an emergent attribute of its interaction. In this sense, what gives specificity to these generic particles is not an a priori and fixed structure as modernism, but a posteriori and evolving relationality with the world. This is problematic with the requirement of autonomy demanded by parts for two reasons. On the one side, if part’s specificity is exhausted with its outer relationality, its nomos is coming from outside and we are therefore in Kant’s heteronomy rather than autonomy. On the other side, if parts are originally generic, they refer to an original standard type which is holistic precisely because it is shared by default by all its members. The fact that specificity is an emergent property in which parts are defined exclusively by their relationships with other parts has been interpreted as their emancipation with respect to the notion of whole. Timothy Morton describes this type of relational process as “simply the last philosophical reflex of modernity”.[27] 

Indeed, the instrumental reason characteristic of modernity is still behind this type of operation because emergent processes are teleological processes. “Emergence is always emergence for”[28] because there is always a holistic target that subjugates the parts to the benefit of the whole. As such, we are not dealing with a mereology of parts, but rather a mereology of particles: each element is not an incomplete piece that is unique in its identity and therefore irreducible (part), but rather a generic ultimate element that becomes specific at the price of being relationally dissolved into the whole of which it belongs (particle). Its being is defined precisely by the relationships it establishes with other elements, and those relationships are the way they are because they are beneficial to a whole. 

Timothy Morton affirms that moving past modernity implies the need for a “philosophy of sparkling unicities; quantised units that are irreducible to their parts or to some larger whole; sharp, specific units that are not dependent on an observer to make them real.”[29] Despite their local character, the relations that regulate individuals undervalue the parts on the one hand and overvalue the whole on the other. They undervalue the parts by fully determining their specific behaviour according to external factors, its original character being generic. They overestimate the whole by varying individual’s specific behaviour according to the benefit of the whole. This position facilitates the emergence of a framework in which bits are associated literally with parts and the act of counting is frequently confused with an act of discretisation. It is then crucial to differentiate mathematical discreteness from ontological discreteness. While the first one alludes to countable elements (particles), the second one alludes to distinct elements (parts). 

Figure 4 – Mathematical Discreteness, Ontological Discreteness, 2020. Image: Jordi Vivaldi, 2020.

The lack of distinction characteristic of generic particles prevents its approach through an exercise of architectural “part-thinking”. Instead, we are confronted with the discrete type of materialism elaborated by pre-Socratic philosophy. Although its ultimate condition permits individual’s participation, it ignores its autonomy’s requirement for part-thinking under a masked heteronomy, which provides specificity to generic particles at the cost of its exhaustion under external relationality.

There is a third group of recent experimental architectural proposals in which parts are ecological parts; they operate as a set of distinct objects that intertwine with one another under the gravitational field of different systems. The notion of ecology should be interpreted here in keeping with the etymology of the Greek term oikos. Its meaning is that of “house” understood as the set of people and objects forming a domestic space and being regulated by the economy (the nomos of the oikos).  

However, the term oikos has traditionally been associated with another very similar one: oikia. Both have been translated as “house”, in the most general sense of the word. Nonetheless, Xenophon outlines a distinction[30] that, although not entirely accepted by all Greek authors, is very useful in approaching the question at hand. The Greek philosopher asserts that the expression oikos refers to a house in the strict sense of a place of residence, whereas the expression oikia denotes not only the house but also the property it contains and its inhabitants. 

Based on this distinction, the word oikia would refer to a collection of elements of different natures and sizes whose coexistence and eventual interlacement would give rise to a specific spatial conception. It is formed not only by the house itself, but also by the property it contains (animals, instruments, jewellery, furniture, etc.) and its inhabitants. It would therefore be a large composite of objects whose eventual interlacements over time would form what Xenophon defines as domestic space. In that sense, these spaces not only contain and are contained by other spaces simultaneously, they also never appear as completely closed elements, despite remaining identifiable and extractable. Oikia is then not produced from a passive Platonic receptacle (chora) or an active Aristotelian substrate (topos); it is constructed instead from the multi-scalar co-existence of various groups and subgroups of systems. The ecological parts characteristic of this branch of experimental architectural projects represent, in different ways, a departure from the materialism analysed in previous cases. They find an example avant la lettre in the work of Jean Renaudie, particularly in his two housing complexes in Ivry sur Seine (1975) and Givors (1974).

Although not all parts fully coincide with the definition provided here, the discreteness of the projects operates with autonomous discrete entities that cannot be interpreted under a materialistic framework; there is no ultimate element acting as an underlying substrata (continuous or discrete) to which entities can be reduced. However, as we have seen, the notion of ecology implies the presence of oikia, that is, a house, a common denominator whose presence can be traced in these projects by a formal homogeneity that traverses the whole composition.

We can find a wide range of experimental architectural formal strategies working in this direction. Daniel Kohler’s Hyper-Nollie (2019) develops a complicit discreteness with more than 40 different parts that are always cooperative and incomplete, never single entities, never fully defined, never identical. However, the continuous connection of its spaces and the fact that each one of them is accessible from each part seem to formally evoke the logics of a relational field, particularly through the homogeneous granularity revealed by a general overview. Nevertheless, the project’s tension between the distinct discreteness of its close view and the texturised continuity of its far-view precludes any attempt to simply reduce its parts to an underlying material substrata: each part positions its own context’s interpretation through a complex balance in between identity (inherent distinction) and relationality (local complicities).

Although its assumption of the voxel as a standard unit and its complicity with Christopher Alexander’s notion of structure, Jose Sánchez’s Block’hood (2016) tends as well to avoid the possibility of any full material reductionism to any ultimate being. In spite of its underlying 3D grid, the project provides each voxel with a specific performative behaviour whose specificity is not merely underpinned by relationality, but is partly inherent to its constitution. In this sense, each unit approaches our definition of part because despite its underlying common framework, voxel’s singularity cannot be merely reduced to it or to its relations. Rasa Navasaityte’s Urban Interiorities (2015) approaches the notion of part through a recursive structure of groups inside groups: there is not any ultimate element from which the rest of compositions can be derived, but a recursive process.This partly acts as a holistic system of form production, at the same time permitting the presence of distinction beyond countability. 

These projects represent the different nuances of a part: they operate through the tension established in between part’s autonomy and part’s participation, e.g. the part’s capacity to be inherently distinct and at the same time the part’s capacity to retain something in common with other parts in order to permit local and ephemeral complicities. This type of mereology resonates with what Levi Bryant has defined as a “strange mereology”: “one object is simultaneously part of another object and an independent object in its own right.”[31] Indeed, on the one side, the parts that we have seen in this last group of projects are autonomous beings in the world that cannot be reduced to other parts. But at the same time, parts are composed by other parts, compose other parts, and relate with other parts. In synthesis, part-thinking demands parts execute what seems to be a paradox: its constitution as a countable and distinct entity that is both independent and relational.

We could synthesise the different approaches towards the definition of part presented here as follows: the first group of projects, constituted by what we have defined as topological parts, leaves aside part’s autonomy in favour of an underlying field of relations. The second group, whose parts are defined as corpuscular parts, emphasises part’s countability (mathematical discreteness) instead of part’s inherent distinction (ontological discreteness). The third group, composed by ecological parts, still retains a vague remainder of a general background (oikia) that vectorises part’s distribution. In all of them, matter’s ultimate condition is still present, although in a blurry and definitely weakened version, particularly in the last one. However, we could briefly speculate with a fourth group of architectural parts, associated with the notion of limit, that would emerge from the radical limitation of matter’s ultimate condition.

Figure 5 – Topological, Corpsular, Ecological and Limital Parts, 2020. Image: Jordi Vivaldi, 2020.

The notion of limit is at the core of architecture. If we understand the architectural practice as the production of interiorities, that is, as the production of spaces within spaces, the idea of a border distinguishing them is decisive. In this sense, the etymology of the term “temple” is particularly revealing: its root “-tem”, present also in the terms témenos, templum, and “time”, indicates the idea of a cutout, a demarcation, a frontier, a limit instrumentalised in order to separate the sacred realm of the gods from the profane territory of humans. In ancient Rome, the construction of a temple began with the cumtemplatio, the contemplative observation of a demarcated zone of the sky by the augurs. Through the attentive observation of birds, the sun and the clouds’ trajectories within the selected celestial area, the augurs interpreted the auspices of the city that was about to be founded. Once the observation was completed, the demarcated zone of the sky was projected onto the ground in order to trace the contours of the future temple, the germinal cell of the coming city. Cumtemplatio was thus cum-tem-platio: the tracing of the limits through which the cosmos took on meaning and signification by being projected onto the earth and establishing the ambit in which the humans could purposively inhabit the world. Thus, the temple instrumentalised the limit not just as a border between what is sacred and what is profane, that is, between inside and outside, but also as a space in itself, as a frontier territory mediating between the celestial realm of the gods and the terrestrial realm of humanity.

The spatialised register of the limit evoked by the temple and aligned with notions such as the Christian limbo or the Roman limes, lays the foundation for the type of immaterialist parts hypothesised here with the expression limital parts. They expand the decreasingly shy immaterialism present in topological parts, corpuscular parts and ecological parts by limiting the reduction to any sort of matter’s ultimate condition. In order to do so, limital parts are liminal, limited, and limitrophe, three decisive attributes aligned with supercomputation’s capacity to avoid parametric reductionism.

First, limital parts are liminal, that is, they are the locus of junction and disjunction. The notion of liminality should be read under its instrumentalisation by Arnold van Gennep and Victor Turner: the limit is not the Euclidean divider line that is at the core of the Modern Movement’s programmatic zonification, but, the limit is, in its anthropological register, the frontier territory that in a rite of passage mediates between the old and new identity of its participants. Parts’s liminality constitutes a daimonic space whose nature is that of “differential sameness and autoreferential difference,”[32] if the limit is in itself and by itself internal differentiation, if in its re-flection the limit separates and divides, then limital parts should necessarily join and disjoin, or, more accurately, limital parts should join what they disjoin. The liminality of limital parts does not mean that its composition is simply the random juxtaposition of a litany of solipsistic monades: in their symbiotic intertwinings, the different liminal parts establish clusters and sub-clusters of performative transfers that are constantly sewing and resewing the limit’s limits: their operativity is not always structured by harmonic consensus, but they engage in constant resistance and deviation. They produce spontaneous symbiotic interlacements that overlap without any preconceived agreement and certainly not without décalages, displacements and misfits.

Second, limital parts are limited, that is, they are distinct and determined. The notion of limitation should be read under its Hegelian instrumentalisation: “The limit is the essentiality of something, it is its determination.”[33] Thus, to limit means to define; the latin term definire signifies to trace the borders of something in order to separate it from its neighbours. Definire is the establishment of finis, ends. However, the term finis should not be read here only under the light of its topological or chronological sense, but it should also be approached in its ontological register: to define means to specify the qualities of a part that make a part this part and not that part, avoiding its reduction to any ultimate material substrata. It traces an ontological contour in order to limit the part’s infinite possible variability. A limited part refers thus to a distinct part; it is determined, but not predetermined, that is, it is not determined avant la lettre. It contrasts with what is open, flexible and generic; in a context where the power of today’s supercomputation makes it possible to notate the inherent discreteness of reality, it is no more necessary to design with simplified spatial formulas (fields), or repetitive spatial blocks (particles). Today’s computational power applied to architectural design allows an emancipation from reductive laws, whose standardisation is at the core of the material remanences of topological parts, corpuscular parts and ecological parts. Thus, rather than formulative and open parts, the unprecedented power unfolded by supercomputation lets us operate with massive sets and sub-sets of distinct parts. The limited condition of limital parts does not align with the notion of the generic, nor with derivative concepts such as flexibility, adaptability or resilience, so common in the three previous groups of architectural parts. Thus, rather than flexible, limital parts are plastic (plastiquer, plastiquage, associated in French to the notion of explosion): they vary, but at the price of gaining a new specificity and cancelling the previous one.

Third, limital parts are limitrophe, that is, they are foliated. The notion of limitrophy should be read in light of its instrumentalisation by Jacques Derrida. Rather than effacing or ignoring the limit, Derrida attempts, through his use of the term “limitrophy”, “to multiply its figures, to complicate, thicken, delinearize, fold, and divide the line precisely by making it increase and multiply.”[34] Limital parts are thus thickened, which is the literal sense of the Greek term trepho, that is, to nurture. Under this umbrella, a limitrophe part is not a solipsistic monade or a fragment referring to an absent whole. Limital parts produce inconsistent multiplicities by acquiring a foliated consistency and becoming an edgy, plural and repeatedly folded frontier. Limital parts shouldn’t orchestrate thus an abyssal and discontinuous limit: the latter does not form the single and indivisible line characteristic of modernity, rather, it produces “more than one internally divided line.”[35] Thus, limital parts grow and multiply into a plethora of edges. Precisely because of their liminal, limited and limitrophe condition, limital parts are immaterialist: they are not reducible to one, as is the case, with decreasing intensity, of topological parts, corpuscular parts or ecological parts. 

Ending Considerations

Avoiding matter’s ultimate condition requires understanding form as a spatio-temporal structure that operates at every level of scale. It demands the assumption that there is always a form beyond any given form, avoiding any continuous (field) or discrete (particle) ultimate background in which parts could be reduced. In this sense and as Graham Harman affirms, “although what is admirable in materialism is its sense that any visible situation contains a deeper surplus able to subvert or surprise it,”[36] the kind of formalism approached here does not deny this surplus, it merely states that this surplus is also formed.

The impossibility of conjugating matter’s ultimate condition with a radical part-thinking would suggest a pan-formalism based on a Matryoshka logic, a multiscalar recursivity that doesn’t rely on an ultimate and maternal underlying substrata. Under this framework and building on the German and Russian formalist traditions later developed by figures such as Colin Rowe, Alan Colquhoun, Alexander Tzonis or Liane Lefaivre, the formalism that could emerge from these statements shouldn’t be understood in the sense that there is no excess beneath the architectural forms that are given, rather, in the sense that “the excess is itself always formed.”[37] 

The constant and multiscalar presence of form and the avoidance of any ultimate substrata are posited as the two conditions that a radical part-thinking would require; they represent the only way in which the notion of part can be understood in its full radicality, that is, as an interactive and autonomous element which is not just countable (mathematically discrete) but also distinct (ontologically discrete). As we have seen, this approach is incompatible with matter’s understanding: despite matter’s revival has paradoxically imported all the attributes associated with the hylomorphic understanding of form, the re-introduction of pre-Socratic’s ultimate condition represents the clandestine re-introduction of the notion of whole and therefore an unsurpassable obstacle for part-thinking.


[1] G. Harman, “Materialism Is Not the Solution”, The Nordic Journal of Aesthetics, 47 (2014), 95.

[2] E. Prieto, La vida de la materia (Madrid: Ediciones Asimetricas, 2018), 28-102.

[3] E. Sadin, La humanidad aumentada (Buenos Aires: La Caja Negra, 2013), 152.

[4] M. Carpo, The Second Digital Turn: Design Beyond Intelligence (Cambrige: MIT Press, 2017), 71.

[5] Alberti, Re-Aedificatoria, (Madrid: Ediciones Asimétricas, 2012), 21.

[6] G. Semper, The Four Elements of Architecture and Other Writings (Cambridge: Cambridge University Press, 1969), 45-73.

[7] E. Prieto, La vida de la materia (Madrid: Ediciones Asimétricas, 2018), 28-102.

[8] M. Delanda, “Interview with Manuel Delanda”, New Materialism: Interviews and Cartographies, 9. 

[9] K. Barad, “Interview with Keren Barad”, New Materialism: Interviews and Cartographies, ed. Rick Dolphijn & Iris van der Tuin (London: Open Humanities Press, 2012), 59.

[10] E. Sadin, La humanidad aumentada (Buenos Aires: La Caja Negra, 2013), 152.

[11] K. Easterling, Medium Design (Kindle Edition: Strelka Press, 2018).

[12] B. Bratton, The Stack: On Software and Sovereignty (London: The MIT Press, 2016).

[13] G. Harman, “Materialism is Not the Solution”, The Nordic Journal of Aesthetics, 47 (2014), 100.

[14] Ibid, 98.

[15] N. Oxman, “Material Ecology”, Proceedings of the 32nd Annual Conference of the Association for Computer Aided Design in Architecture ACADIA (2012), 19-20.

[16] D. Koehler. Large City Architecture: The Fourth Part (London: 2018), 19.

[17] G. Harman, “Materialism is Not the Solution” The Nordic Journal of Aesthetics, 47 (2014), 100.

[18] M. Carpo, The Second Digital Turn: Design Beyond Intelligence, (Cambridge: MIT Press, 2017), 71.

[19] Ibid.

[20] A. Zaera, “Nuevas topografías. La reformulación del suelo,” Otra mirada: posiciones contra crónicas, ed. M. Gausa and R. Devesa (Barcelona: Gustavo Gili, 2010), 116-17.

[21] J. M. Montaner, La modernidad superada (Barcelona: Gustavo Gili, 2011), 32.

[22] Aristotle, Physis, trans. W.A. Pickard (Cambridge: The Internet Classics Archive, 1994).

[23] P. Eisenman, “Brief Advanced Design Studio”, last modified October 2014,

[24] M. Carpo, “Particalised”, Architectural Design, 89, 2 (2019), 86-93.

[25] K. Kuma, Materials, Structures, Details (Basel: Birkhäusser, 2004), 14.

[26] G. Retsin, “Bits and Pieces” Architectural Design, 89, 2 (2019), 43.

[27] T. Morton, Hyperobjects, (Minneapolis: University of Minnesota Press, 2013), 119.

[28] Ibid.

[29] Ibid, 41.

[30] K. Algra, Concepts of Space in Greek Thought (London: Brill, 1995), 32.

[31] L. Bryant, The Democracy of Objects (Cambridge: MIT Press, 2017), 215.

[32] E. Trías, Los límites del Mundo (Barcelona: Ariel Filosofía, 1985), 121.

[33] G. W. F. Hegel, The Science of Logic (Cambridge: Heidelberg Writings, 1996), 249.

[34] J. Derrida, “The Animal That Therefore I am (More to Follow)” trans. David Wills, Critical Inquiry, 28, 2 (2002), 398.

[35] Ibid., 398.

[36] G. Harman, “Materialism Is Not the Solution”, The Nordic Journal of Aesthetics, 47 (2014), 100.

[37] Ibid.

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