Christopher Alexander – Fundamental Property 7: Local Symmetries

“… Where a living center forms, it is often necessary to have some local symmetry.
… Living things, though often symmetrical, rarely have perfect symmetry. Indeed, perfect symmetry is often a mark of death in things, rather than life. I believe the lack of clarity on the subject has arisen because of a failure to distinguish overall symmetry from local symmetries.
… The Rorschach ink-blot, for instance, is a rather weak whole; it has relatively little life as a structure; its centers are poorly developed. The one large symmetry it has, by itself, gets you very little.
… over simplified symmetry in a building is mot often naive and even brutal … Albert Speer’s design for Zeppelinfeld … is [an] example …
In general, a large symmetry of the simplified neoclassicist type rarely contributes to the life of a thing, because in any complex whole in the world, there are nearly always complex, asymmetrical forces at work – matter of location, and context, and function – which require that symmetry be broken.
We see this clearly in the Alhambra … a marvel of living wholeness. It has no overall symmetry at all, but an amazing number of minor symmetries, which hold within limited pieces of the design, leaving the whole to be organic, flexible, adapted to the site.
… the real binding force which symmetry contributes to the formation of life is … in the binding together and local symmetry of smaller centers within the whole.
… an experiment I did … at Harvard Center for Cognitive Studies … I compared a number of black and white paper strips, and measured their coherence as felt, experienced, perceived, remembered, by different subjects.
… The experiments were performed with 35 black-and-white strips seen on a neutral gray background. Each strip was 7 squares long, and was composed of 3 black squares and 4 white squares, arranged in different arrangements …
First, we established that the relative coherence of the different patterns … is not an idiosyncratic subjective feature of the patterns seen differently by different people. It is an objective measure of cognitive processing, roughly the same for everyone.
Second, we were then able to identify the structural feature of these patterns which caused this perceived ‘coherence.’ It turned out that [it] … depends on the number of local symmetries present in the pattern. However since most of the symmetries are hidden, this feature is far from obvious …
… For three or four years after completing the experiment, I worked almost continuously to find some structural feature of the 35 black and white patterns which would explain the rank order of coherence of the different patterns …
… it was quite unclear how to unite the idea of symmetry with the idea of large lumps. It was this that finally gave me the key, when I realized that both overall symmetries and large lumps actually contain more local symmetries inside them.
.. the strips which are most coherent experimentally also have the highest number of subsymmetries to within a high degree of correlation … The number of local symmetries the pattern contains essentially predicts how ‘good’ it is.
… It is as if the symmetrical segments act as a kind of glue … which holds the space together. The more glue there is, the more the space is one, solid, unified, coherent. And … for the glue to be effective, it seems that many of the symmetrical segments must overlap.
… the local symmetries … though hidden from view … essentially control the way the pattern is seen and the way it works.”