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Symmetry has a very wide appeal; it is of as much interest to mathematicians as it is to artists, and is as relevant to physics as it is to architecture. In fact, many other disciplines lay their own claims on the subject, each having their own ideas of what symmetry is, or should be. Clearly, whatever approach is taken, we are dealing here with a universal principle, however, in our day-to-day experience conspicuous symmetries are comparatively rare and most are far from obvious. So what is symmetry? Are there general terms for it? Can it, indeed, be clearly defined at all? On investigation, it soon becomes clear that the whole field is hedged about with paradox. To begin with, any notion of symmetry is completely entangled with that of asymmetry; we can scarcely conceive of the former without invoking thoughts of the latter (as with the related concepts of order and disorder)—and there are other dualities. Symmetry precepts are always involved with categorisation, with classification and observed regularities; in short, with limits. But in itself symmetry is unlimited; there is nowhere that its principles do not penetrate. In addition, symmetry principles are characterised by a quietude, a stillness that is somehow beyond the bustling world; yet, in one way or another, they are almost always involved with transformation, or disturbance, or movement. The more deeply one investigates this subject the more apparent it becomes that this is at the same time one of the most mundane and extensive areas of study—but that, in the final analysis, it remains one of the most mysterious.
