An interesting question is whether symmetry with respect to translation, and indeed reflection and rotation too, is limited to the visual arts, or may be exhibited by other artistic forms, such as pieces of music. Evidently, if we refer to the sounds, rather than to the layout of the written musical score, we would have to define symmetry operations in terms other than purely geometrical, just as we did in the case of the palindromes. Once we do that, however, the answer to the question, Can we find translation-symmetric music? is a resounding yes. As Russian crystal physicist G. V. Wulff wrote in 1908: "The spirit of music is rhythm. It consists of the regular, periodic repetition of parts of the musical composition...the regular repetition of identical parts in the whole constitutes the essence of symmetry." Indeed, the recurring themes that are so common in musical composition are the temporal equivalents of Morris's designs and symmetry under translation. Even more generally, compositions are often based on a fundamental motif introduced at the beginning and then undergoing various metamorphoses.
( Mario Livio )
[ The Equation That Couldn't Be ]
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