Local symmetries

One of the 15 fundamental properties.

Local symmetries is the way that the intensity of a given center is increased by the extent to which other smaller centers which it contains are themselves arranged in locally symmetrical groups.

The existence of a center and the existence of local symmetry are closely related. Wherever there is a local symmetry, there tends to be a center. 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. […] Overall symmetry in a system, by itself, is not a strong source of life or wholeness. […] Over-simplified overall symmetry in buildings is most often naive and even brutal.

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 — matters of location, and context, and function — which require that symmetry be broken.

Thus the real binding force which symmetry contributes to the formulation of life is not in the overall symmetry of a building, but in the binding together and local symmetry of smaller centers within the whole.

Apparently large symmetries do little to contribute extra coherence to a pattern: what matters more is the number of smaller — i.e., local — symmetries. Why does the presence of many local symmetries in the design make it coherent and memorable? It is as if the symmetrical segments act as a kind of glue — the glue which holds the space together. The more glue there is, the more the space is one, solid, unified, coherent. And notice one more detail: for the glue to be effective, it seems that many of the symmetrical segments must overlap. They are by no means discrete or disjoint. One symmetrical segment overlaps another — and it is not only the number of symmetrical segments, but also their continuous overlapping which makes the glue that makes the design “whole”.

What is essential is that the local symmetries in these patterns play a decisive and quite unexpected role. Though hidden from view, they essentially control the way the pattern is seen and the way it works.

What is the relation between symmetries and centers? How do symmetries allow centers to intensify each other? In many cases, a symmetry is used to establish an elementary center. Indeed, an overwhelming majority of centers are locally symmetrical. Each local symmetry establishes a symmetry between two smaller centers to create a larger center. Indeed, one might almost say, “When in doubt, make it symmetrical.” Most centers become stronger when symmetrical, except, of course, that symmetries must not be used to smooth out real asymmetries in external conditions, and must always be true to the local conditions.

Evidently there is a deep connection between the presence of local symmetries in a field and the occurrence of a center. In empirical studies of wholeness symmetry has always played a role. Symmetry is one of the powerful ways that space is made whole. When a part of space is symmetrical it is internally consistent.

In nature

In general these symmetries occur in nature because there is no reason for asymmetry; an asymmetry only occurs when it is forced. […] In short, things tend to be “equal” unless there are particular forces making them unequal. In addition, the existence of local symmetries in nature corresponds to the existence of minimum energy and least-action principles.

In the majority of these cases, it is also the presence of layer upon layer of subsymmetry at smaller scales which is important. A Rorschach blot is symmetrical as a whole, but possesses no significant symmetries at lower scales. This kind of form, random at lower levels but symmetrical in the large, is relatively uncommon in nature. Contrast it with snow crystals which display symmetries at many levels. They are symmetrical in the large, but the smaller symmetries, nested within the whole, give them their structure.

The appearance of symmetry in nature is possibly the most widely noticed of the fifteen properties.

In the case of this property, we do have the beginnings of a general theory which predicts that locally symmetric structures and nested symmetries will arise, in general, throughout the range of natural systems.

#book/The Nature of Order/1 The Phenomenon of Life/5 Fifteen fundamental properties#

#book/The Nature of Order/1 The Phenomenon of Life/6 The fifteen properties in nature#

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