The idea of a natural system of symmetries
Thus we see systems of symmetries, which are roughly symmetrical locally and are all nested, forming a hierarchy of approximate symmetries.
This natural system of symmetries is one of the defining marks of all living structure. I cannot for the moment define what I mean by calling this natural structure a “balanced” and comfortable system of symmetries. I only draw attention to it. Look at the character of the symmetries, and pay attention to the way they work.
None of the symmetries are perfect. They are syncopated, uneven, comfortable, relaxed. That is because the symmetries only occur where they are generated, where they have to be.
It is over-simplified. The symmetries we see are perfect, very rigid, one might say almost obsessive in their perfection. […] This is a building which lacks a natural system of symmetries.
The lack of need for “image”, again makes it possible for people to do just what is required, and nothing else. There are local symmetries where they are needed and nowhere else. Some of the elements are symmetrical. Large scale symmetries are visible. On the other hand, wherever the symmetries need to be interrupted, they are interrupted. They do not suffer from an image of a controlled overall plan, which tries to tie the symmetries down. They exist where they please — that means, only where they need to exist. Again, this is comfortable.
Making a building which has life is essentially a problem of creating such a balanced system of symmetries. Whenever we manage to create a great work of art, we manage it only because we manage to discover a natural and comfortable system of balanced, nested, symmetries.
It is not an overpowering, overall symmetry. The system of symmetries have the same balance and easiness which we observe in nature.
This particular balance of symmetries, which seems like an almost accidental pleasantness or easiness, it is in fact a highly specific structure. This highly specific structure must be present in order for something to have life, and it takes very precise form because this is the structure something has when it is true.
We may summarize the relation between life and symmetry by saying simply this: Life requires a natural system of symmetries.
Or, in dynamic terms we may say this: A living process must generate a natural system of symmetries in order to make something whole.
This rule is directly related to the theory of structure-preserving transformations in which we produce living structure by unfolding the wholeness (field of centers) step by step. The unfolding of the field of centers may be considered as a process in which we introduce one symmetry at a time. The wholeness is the end-result of this dynamic process; it is the trace left by a process which produces one symmetry at a time.
Successful life which creates unity in a building and holds it together is generated by the balanced, syncopated, off-beat quality that the natural system of symmetries creates. “Balanced” and “offbeat” seem to be opposites. But the idea that a structure exists which has both these attributes at the same time is precisely one of the most important attributes of living structure.
At first sight, being tight in terms of symmetry, and being loose seem opposite. One is orderly, one is disordered. But the real unity is precisely that quality which is generated by the balance in which both exactness and looseness exist together.
#book/The Nature of Order/2 The process of creating life/17 Simplicity#