SET MEREOLOGY

Mereology } architecture } computational design | 2017

In this rather strange architectural ‘mereology’, to borrow a term from Levi Bryant, I have considered the asymptotic use of Set Theory as a computational design method to enlist the possibilities arising from parts and their exo- and endo-relations with one another all agglomerating into a massive architectural object. For example, an object A contained parts X, Y, Z can be expressed in the following axiom:

A = [X, Y, Z]

Now consider the following, the set of configurations that can emerge from object 'A' is a subset of all possible configurations, mathematically describable of a set A. In mathematics a set A is a considered a subset of a set B,  if A is ‘contained’ inside B, that is, all elements of A are also elements of B. A and B may coincide. Likewise, in the axioms of set theory, particularly the 'power-set' axiom allows us to render all possible subsets of a set, accreting a new set out of this collection

.

A = { } {X} {Y} {Z} {X, Y,} {X, Z} {Y, Z} {X, Y. Z}

The 'power set' can then be applied yet again to generate an even broader set and so on. Each configuration is offering a new object, outside the probability of human correlate, where even the objects qua parts are autonomous from another. These arrangements do not consist of their relations but lie in the fact that the subsets of their set, the smaller objects comprising larger objects are simultaneously necessary conditions for that more massive object while being sovereign of that object. Likewise, the large object formed of these smaller objects is itself independent of these smaller objects.