How many possible living structures are there?
In Book 1, I introduced the idea of two imaginary mathematical classes, each containing a huge number of possible configurations, one the class of all possible configurations, and the other, the smaller class of all living configurations. In a similar vein, I now define C(all), as the class of all possible buildings, and C(living) as the smaller class of all those buildings which have living structure. Of course the artificial division of all configurations into just these two classes is a convenient fiction only. As I have said repeatedly throughout these books, the degree of life in things is a matter of degree, to be placed somewhere on a continuum in relation to the life of other buildings.
I wish to emphasize that although these two classes are both almost unimaginably huge, one is much larger than the other, and they are real classes with very roughly identifiable numbers of configurations in them. More important is the relative size of these two classes. It is vital to see that C(living) is many orders of magnitude smaller than C(all), possibly as little as 1/10^12,000 of C(all). The class C(dead), on the other hand, the class of buildings which are dead, is very large, essentially the same size as C(all), as we may even see in my diagram, since it is the area of the whole disc, less only the tiny dot. Most of the possible building configurations are dead ones; they do not have life. Compared with the much huger number of all possible building configurations, there are only relatively few living buildings. What we usually call “design” then, is the task of finding instances of C(living), while looking around among the elements of the much larger class C(all).
Given the dispersal of very widely spaced, rare and precious living structures in configuration space, how then, can one ever hope to find them? How does one move around the solar-system-sized haystack, to find the few dust-sized specks which represent well adapted, living structures? The answer relies on structure-preserving paths in configuration space, ways of moving from one configuration to another within the space of all possible configurations, which home in gradually (but reliably) on “good” and well-adapted, living ones.
The buildings of C(living) form a visually recognizable class. We should not fool ourselves, by thinking that the buildings in C(living) can be made to look, any way we want. That is a fallacy, committed by too many architects. If you want to build buildings with living structure — that is, buildings with real life — then they will have definite, distinctive, recognizable morphological character. Primarily, they will have this character because they have unfolded truthfully by unfolding from the wholeness of their contexts and because this unfolding introduces the fifteen properties again and again in a definite and recognizable patterning, even though the pattern of the whole is different each time that it occurs.
There is nothing about the size of C(living) that should give an architect anything to worry about — in terms of limits on his, or her, inventiveness and creativity. There are, effectively, no limitations. But what we do need to worry about, is the much larger size of C(dead), the much larger number of possible dead buildings that are not structure-preserving to their places on Earth, and which infect and destroy the beauty of the Earth, every day, now, in this era, because people have not yet understood this simple point.
Numerical estimates of the size of different classes
A living configuration must unfold by differentiation. To visualize this unfolding process, we may conceive it as a series of forks, or decision points, along a path through the space of all possible configurations. At each decision point, we might guess that there are a thousand possible branch points or paths to chose from.
The previous very crude estimates of astronomically gigantic numbers, are only intended to draw attention to three vital points. First, the number of living buildings is a tiny, tiny, tiny fraction of the class of all possible buildings, far too tiny and hard to reach by what we nowadays call “design”. Second, the rare and hard-to-find living structures are easily reachable by the structure-preserving-processes method that nature uses millions upon millions of times per day, to generate instances of the equally tiny class of living structures in nature, throughout the natural world. Third, although there are few living buildings compared with the much larger number of dead buildings, nevertheless the number of all possible living buildings is still unimaginably huge, far larger than all human beings on Earth could ever use up, even if every one of them was to make billions of new living buildings every day, and if they wanted to go on doing it for a billion centuries. In short, staying inside the class of living buildings, and staying away from the class of dead buildings, is no restriction on an artist’s creativity, at all.
Instead of worrying about our creativity, we had better worry about the difficulty of finding the tiny scattered specks in configuration space that we call C(living), and about managing to make living buildings at all.
#book/The Nature of Order/3 A Vision of a Living World/Appendix on number#