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# Combinatorial design

As we shift our attention toward discrete design, operating with kits of parts and explicit linkages between them, the design process is altered. In the parametric design paradigm, design could be understood as a search function that operates moving in degree along an infinitesimal domain. Designing with discrete units doesn’t allow a gradient flow between variables but combinatorial patterning instead. While a parametric definition can offer a multiplicity of designs, those alternatives offer difference in degree. A discrete methodology on the other hand, with its open-ended combinatorial possibilities, offers difference in kind. The Braun Lectron kit that we discussed earlier serves as a good example; different configurations of the units do not create variants of a radio but different functionalities altogether.

Coming from mathematics, the term combinatorics describes the studies of the structures allowed by a finite set of discrete units. In its definition, the term demarcates a difference from nonstandard calculus, identifying that it operates in the realm of the discrete rather than the continuous. It also denotes the use of“finite,” countable units, as opposed to the variable units described by a parametric model.

The degree of differentiation of a parametric model can only operate by stretching and shrinking a fixed topological diagram. A combinatorial model lacks a topological diagram. One only arises as a contingent proposition unique to the pattern of arrangement. This is what can be called “the missing topolog}' mechanic.”23 A pattern establishes the linkages and relations between units, defining the topological diagram of the model. These patterns are immaterial, as they are defined by the indexical information that links units. This information density stored in a design pattern can be characterized as a metric of order that differentiates the aggregation from pure randomness. The challenge of combinatorics is that of negative entropy, the creation of information-rich patterns.

It’s important to be clear that combinatorial design is not just the study of possible permutations of parameters, or what Kostas Terzidis calls “permutation design,”24 where any given variable of a design problem establishes a degree of freedom that can be catalogued and cross-referenced to other variables, yielding the solution space of a given system. In fact, Terzidis rejects how intuition and experience can play a role in the design process, favoring a framework of optimization performed by a deep search of algorithms over the permutation space. He explains:

Traditionally, such arrangements are done by human designers who base their decision making either on intuition (from the point of view of the designer) or on random sampling until a valid solution is found. However, in both cases the solution found may be an acceptable one but cannot be labeled as “the best possible solution” due to the subjective or arbitrary nature of the selection process. In contrast, an exhaustive list of permutation-based arrangements will eventually reveal the “best solution” since it will exclude all other possible solutions.25

In comparison to Terzidis, combinatorial design is a design strategy that starts from the definition and individuation of parts, describing an open-ended series of relations with one another. These parts are coupled and aggregated to generate larger assemblies, describing meaning, performance and function at different scales of configuration. The system always remains open-ended and malleable, allowing for the replacement of parts within it.The open-endedness of the system implies that there is no possible optimization, as the solution space of permutations grows with each unit added at an exponential rate, becoming computationally impossible to search for an optimum. The malleability of a combinatorial system implies a temporal relevance and the contingent emergence of a pattern out of contextual conditions. No pattern might be the optimal one for a long period of time but rather an ad hoc solution harvested by designers or as we will see in the following chapter, crowds.

Combinatorial design can define a broader scope for a design agenda that is interested in developing a common repository of architectural units with potential compatibilities. A discrete combinatorial methodology is a project of coordination between different design entities aiming to generate positive externalities from the contribution of a publicly accessible catalog of architectural knowledge.

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