Holistic and non-holistic sets
Most traditional architecture uses a hybrid approach between discrete and continuous techniques: metal beams and bolts (discrete) or concrete (continuous). Most available materials come from a serialized chain of industrial production, allowing designers and architects to mix and match to develop cohesive wholes out of thousands of parts. Utilizing digital information models, the current design paradigm conceives of architecture in an abstract, pre-material state. It is only through a process of iterative post-rationalization that the architect, together with many other specialists, breaks this model and defines the constituent parts. The "whole" reaches its completion in abstraction usually through digital means and starts to be actualized through a process of decomposition where every part is fully detailed to fit into the larger model of the whole, what is denominated as a process of postrationalization. As we have pointed out in Chapter 2, such a model resembles a jigsaw puzzle, meaning that each part only fits into one unique role in the assembly, serving a subservient role to the whole. Under this paradigm of post-rationalization, the topology of the system, the way in which parts connect to one another, is a rigid body map. We will define the model as "holistic sets," or collections of parts
FIGURE 3.3 Holistic set (jigsaw puzzle) vs non-holistic set (LEGO).
that operate under the ruling of the whole. In this model, the whole is fixed and unalterable.
Parametric software allows for the manipulation of the formal whole, emphasizing the "one-off" condition of an architectural proposition at every scale. Holistic sets define the capability of the whole to completely reinvent the parts in each architectural commission, if necessary. While this model offers great opportunity for performative geometries, it dismisses the opportunity for the reusability of building elements in different contexts. All architects develop their own vocabulary and do not engage with the vocabulary of others. There is no common language.
On the other hand, we can understand non-holistic sets as sets of parts that have a multiplicity of topological configurations. From this description, a non-holistic set also redefines the characteristics of the whole as remaining in a state of openness.These new emergent assemblies could be denominated "open-wholes" in their resistance of a static totality. A non-holistic set can be assimilated to a "kit of parts," which is in opposition to the jigsaw puzzle model discussed earlier under the paradigm of parametric design. Kits of parts have been popularized with products such as LEGO. While a particular LEGO product will contain the specific pieces to be assembled into one final structure, LEGO as a system is a non-holistic set. Parts are not designed to describe a unique whole, but rather to establish a systemic relationship with one another. The value of a non-holistic set is not defined by the materialization or actualization of the units but by their combinatorial capability. In this way, a discrete set defines a form of "combinatorial surplus" that is encapsulated in the potential encounters and degree of compatibility from one part with other parts.
MIT Professor and Director of the Center for Bits and Atoms Neil Gershenfeld has pioneered an understanding of discrete systems in his search for a universal building machine that can arrange units at a microscopic level. His interest in systems that could both assemble and disassemble objects follows principles of discrete reversibility. He has argued that while the reality of fabrication has embraced digital technologies to reach what we call today "digital fabrication," materials themselves have remained analog, as they still operate under the continuous paradigm of infinitesimal degrees of error. Gershenfeld would go ahead and describe and patent what he calls "digital materials." He explains:
Digital parts are error correcting and self-aligning, which allows them to be assembled into structures with higher accuracy than the placement accuracy of the assembling person or machine. For example, a Lego™ set consists of discrete parts that have a finite number of joints. The male/female pin joints on the top and bottom of the Lego™ block are discrete connections, which either make or do not make a connection to another block. By contrast, a masonry construction is a continuous (analog) material; While the masonry brick is a discrete unit, the mortar in its fluid state allow one brick to be placed on top of another in an infinite number of positions. Because the joint is not discrete, masonry construction is analog while Lego1 M construction is digital.14
Gershenfeld's research on digital materials points to a future where form can be patterned by "discrete assemblers,"15 e.g., 3-D printing machines that do not extrude plastic but rather place small units of material together. Gershenfeld's work demonstrates how technologies that have transitioned from analog to digital, starting with communications based on Claude Shannon's seminal work, "A Mathematical Theory of Communication." Computation also experiences this transition from analog to digital during the 1950s. Gershenfeld explains how materiality, when controlled by digital fabrication, has remained analog, and that it is only the advent of digital materials that can establish a breakthrough toward a true digital architecture.
The supremacy of wholes and totalities is a mereological problem, as has been stated by architects Daniel Kohler and Rasa Navasaityte, who understand the
FIGURE 3.4 3-D model of hierarchical hexagonal press-fit structure, in "Additive Assembly of Digital Materials," by Jonathan Ward. MIT Center for Bits and Atoms.
FIGURE 3.5 Digital material structure case studies. Configurations in the form of a bridge, boat and shelter. Drawings presented in axonometric, top and side view. Research project by Benjamin Jenett, Daniel Cellucci, Christine Gregg and Kenneth Cheung.
FIGURE 3.6 Logic Matter by Skylar Tibbits, MIT. Logic Matter is a system of passive mechanical digital logic modules for self-guided assembly of large-scale structures.
necessity to study buildings as part-to-whole relationships. Köhler and Navasaityte argue that "mereology, as opposed to typology, is a methodological framework for designing an architectural object not through a reference to its content or form, but through the resonance of its parts."16
Within a discrete framework, the autonomy of units increases, assemblies of multiple units start exhibiting differences from the wholes defined within holistic sets and wholes become more flexible and imbued with uncertainty. If units are designed with an awareness of systemic relations with one another, but not defining a unique topological diagram, parts acquire a degree of autonomy, as they could belong to a multiplicity of assemblies (perhaps the term "whole" loses its meaning). Units only need to be aware of their possible interface with other parts through a standard connection or link. The assembly of a multiplicity of parts could define the whole, but here again, the whole needs to be understood not as a final state but as a transient state of equilibrium, value or meaning. The organization of parts describing such an assembly defines a pattern, described by the information that determines the arrangement of a discrete set of parts.
Developed by philosopher and computer scientist Ian Bogost, the concept of "unit operations" can offer a powerful framework for conceptualizing parts as autonomous units operating as multitudes, acquiring meaning and value and acquiring unique patterns. For Bogost, the interplay of units is not necessarily tied to a holistic totality. Units are, and should, remain autonomous, allowing for spontaneous couplings that acquire meaning and value. As Bogost explains:
I will suggest that any medium—poetic, literary, cinematic, computational— can be read as a configurative system, an arrangement of discrete, interlocking units of expressive meaning. I call these general instances of procedural expression unit operations.17
For Bogost, meaning emerges from the coupling of units without belonging to a larger holistic system. He describes units through their autonomy to a larger structure rather than parts of a whole. His distinction between wholes and multitudes allows for the existence of units without any overarching structure. Bogost writes:
| A] world of unit operations hardly means the end of systems. Systems seem to play an even more crucial role now more than ever, but they are a new kind of system: the spontaneous and complex result of multitudes rather than singular and absolute holisms.18
The patterns that define such configurations are described as a temporal condition, e.g., one of a contingent of performative configurations. Bogost also explains the struggle that units need to maintain their individuation:
Unit-operational systems are only systems in the sense they describe collections of units, structured in relation to one another. However, as Heidegger's suggestion advises, such operational structures must struggle to maintain their openness, to avoid collapsing into totalizing systems.19
The tectonic aggregate that is defined by unit operations can be described as a granular assembly, one that lives in opposition to the seamless continuity of a parametric style. Granular assemblies celebrate a collective condition that originated out of a multiplicity of origins. Architecture projects that have advanced the notion of discrete granular assemblies include Bloom by Jose Sanchez and Alisa Andrasek (Figures 3.7 and 3.8) and the Tallinn 2017 Architecture Biennial Pavilion by Gilles Retsin (Figures 3.9 and 3.10).These projects are defined by autonomous units that can be arranged in a multiplicity of configurations.
The visible granularity is a result of operating with the geometry of flatness; flatness offers a geometrical common language among units that have not been designed as a holistic system. Parts within a project are often only compatible with each other, defining a rigid protocol for compatibility. This protocol defines a limitation that has been circumvented through a number of design strategies. In the case of Bloom, units are slightly flexible, allowing for larger organizations to bend the rules of aggregation. Retsin, in his project Blockhut (Figure 3.11), envisions a hybrid model, where 90% of units are serially repeated discrete tectonics, while 10% of units can follow a logic of mass customization.21' Finally, designers Golan Levin and Shawn Sims detected the incompatibility issues between different discrete building toys such as LEGO, DUPLO or Fischertechnik. Their design of the "Free Universal Construction Kit" (Figures 3.12 and 3.13) defines a matrix of connectors that establish compatibilities between otherwise incompatible sets. His
FIGURE 3.7 Bloom the Game by Jose Sanchez and Alisa Andrasek. The project is an open-ended building system made out of identical units. The formations of the project are created by the crowds that engage with them.
FIGURE 3.8 Bloom the Game by Jose Sanchez and Alisa Andrasek. Kids interacting with the piece for the London 2012 Olympic Games.
FIGURE 3.9 Diagram of discrete parts and proposals for a multiplicity of design assemblies based on the combinatorics of the system. Gilles Retsin Architecture, Tallinn Architecture Biennale Installation, 2017.
FIGURE 3.10 Tallinn Architecture Biennale installation composed of discrete units by Gilles Retsin Architecture, 2017.
Photo credit by NAAR.O.
FIGURE 3.11 Diagram of hybrid model with discrete identical units (white) and bespoke units (gray).
Source: Gilles Retsin Architecture, Blokhut, 2015.
FIGURE 3.12 "Free Universal Construction Kit" by Golan Levin and Shawn Sims. Matrix of connections between different families of discrete units.
FIGURE 3.13 "Free Universal Construction Kit" by Golan Levin and Shawn Sims. Assembly connecting units from multiple sets.
project reflects on the open-ended nature of discrete granular assemblies, where new actors in the economy are able to expand on the universe of parts and increase the possibility space of combinations.
Granular assemblies also resist a tendency toward coalescence that would consolidate an assembly into a totality. Only by maintaining principles of reversibility as has been understood in the tradition of dismountable architecture, can design patterns remain adaptable and flexible to the ever-changing landscape of the built environment.
Discrete design seeks to allow for such a condition of granular assemblies, or open-wholes that do not need to engage with systemic relations conforming to a performative state.This granularity is both literal and metaphorical, as it determines an architectural tectonic condition of units designed to exist in a multiplicity of contexts, and the result respects the provenance of contributions of all the agencies that took part in its production without pointing to a singular hierarchical author.