Exploring the Idea of Order
نویسنده
چکیده
Although everyone has an intuitive perception of the concept of " order " , it is by no means obvious how to define and to characterize order in mathematical terms. As often, it is a good idea to look what Nature has to offer. In the physical world, the paradigm of order is a perfect crystal. Its regular macro-scopic features derive from an underlying lattice structure where the atoms are arranged in a periodic fashion. The lattice structure can also be probed directly by diffraction experiments, for instance with X-rays or electrons. The diffrac-tion images consist of beautiful point patterns, manifesting the long-range order and the symmetry of the atomic positions. Some twenty years ago, a surprising discovery shook the perfect world of crystals. Certain materials, so-called quasicrystals, show diffraction patterns that are as point-like as those of crystals, but with symmetries that are incompatible with lattice periodicity. Their mathematical description requires more general ordered structures than lattices. This stimulated the exploration of the vast expanse of possible manifestations of order that lie between the extremes
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