Natural symmetries
The geometry of living structure — what comes from the fifteen transformations — is the result of a process in which a complex system becomes at one and the same time both richer and simpler. Each new bit of structure, each new center, adds new differentiations. But each time, as soon as we get the new differentiations, we at once try to boil the garbage away so that the structure is simplified and concentrated. We try to keep it continuously simple, even while we fill it with more and more structure. The ultimate aim of this process is to find a perfectly simple structure which contains an immense wealth of structure.
We are constantly trying to simplify, to produce a system of centers and symmetries which is the simplest possible. The more we keep to simple symmetries when there is no reason for anything else, the more the whole thing gets purified. When we can, we remove smaller local symmetries, and simplify them even further, by enlarging the symmetries. We aim, by the end, to remove all extraneous structure. What we want is to cut and cut and cut until there is almost nothing left.
Sounds a lot like refactoring. I wonder if in software symmetries are replacing code that is similar to other code with generalizations, similar to the DRY principle…?
To clarify the connection between symmetries and simplicity: Complexity (in the bad sense) consists of distinctions which unnecessarily complicate a structure. To get simplicity, on the other hand, we need a process which questions every distinction. Any distinction which is not necessary is removed. To remove a distinction we replace it by a symmetry. During this process the building gets simpler. Gradually we get just that syncopated system of local symmetries, rough but regular, symmetrical in details but syncopated in the large, that is typical of all life.
Since each step will be most structure-preserving when it adds only the simplest symmetries, we may then expect that the end-result of a long sequence of such steps will be almost entirely made up of local symmetries. This means that the geometry of a wholesome living structure will be almost entirely made up of local symmetries, while yet being mainly asymmetrical in the large.
The structure of local symmetries may be nearly all there is, and this is the most fundamental way of understanding living structure.
I claim that everything is made up of parts which are roughly symmetrical.
But, you may argue, if we divide the world up fine enough, any design at all can be composed of symmetrical elements. For example, if we go down to the level of pixels or photographic grain, we know that we can represent any object simply as a pattern of black and white dots of various size. And each dot, within this array, is symmetrical, no matter what the large-scale design is like.
But I am talking about higher level symmetries than that. I am talking about the fact that all the discernible pieces, the natural “wholes” of which the thing is made, are themselves either symmetrical or made up of symmetrical parts.
A few asymmetries here and there are quite all right. What matters is that the maker tried to make each part symmetrical wherever he could, and a few times he missed. […]
What is remarkable is that most of the relatively larger pieces of the locomotive are almost symmetrical, or at least distortions from symmetry made under a continual attempt to be symmetrical.
In such 20th-century industrial structures, we often find the same loose agglomeration of symmetries. But many more recent designed modern structures (buildings and other things) possess an immense number of asymmetries — and there the overwhelming feeling is that the asymmetries are arbitrary, not forced by necessity.
#book/The Nature of Order/2 The process of creating life/17 Simplicity#