Differentiation

Differentiating space

latent, half-formed structure -> coherent, fully-developed

To understand the way a living process helps us achieve living structure by differentiating space, let us consider, in detail, how space does actually get differentiated, and how a person may use the differentiating process to move steadily, again and again, from latent, half-formed structure to fully developed, coherent structure.

15 Transformations

Transform latent centers by differentiation. Nudge a system steadily towards living structure. 1. Purely mathematical / formal * have their origin in the nature of space itself * do not arise as a result of “function” * used in the service of function * but not functional in origin 2. Increase the life of the whole * cannot be applied blindly, but must be applied appropriately * must act in service of function

Latent centers may be transformed by differentiation (through the use of the fifteen transformations) in such a way that the system of centers as a whole becomes intensified or more alive.

Two things should be noticed about these transformations:
First, they are purely mathematical, that is, formal. They have their origin only in the nature of space itself, and do not arise as a result of “function”. They are used, in all real cases (buildings, biological systems, physical systems) in the service of function — but they are not functional in origin. They are pure transformations of space itself, through which the space becomes differentiated, and through which the life of the space is increased.
Second, as a result of the application of these transformations, the life of the whole is increased.
I do not mean to imply that these transformations can be applied blindly, in the hope of getting life to occur. They must always be appropriate. They must act in the service of function; they must be undertaken, always, with an eye to local adaptation, and so on.

We do have a system of transformations which are, in principle, capable of nudging a system steadily towards living structure, and these transformations are precisely those transformations which govern the life of the centers themselves — and hence the wholeness (which is the system of centers), too.

-> Emergence of beautiful geometry

#book/The Nature of Order/2 The process of creating life/7 The fundamental differentiating process#