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In Japanese culture the concept of katachi has special
significance, connoting relationships and connectedness. Although
katachi cannot be translated precisely, it corresponds most closely
to "form," "shape," "pattern," or "Gestalt." The contemporary study
of katachi is interdisciplinary and encompasses virtually all
scientific and aesthetic endeavors. Katachi research seeks to
bridge the gap between cultures - whether the "two cultures" of
C.P. Snow or the contrasting cultures of East and West. To help
achieve this aim and to foster international cooperation, the
interdisciplinary symposium titled "Katachi "U" Symmetry" was
convened in Tsukuba, Japan, November 21 - 25, 1994. With many
participants from differing backgrounds and cultural perspectives,
the symposium was the culmination of 15 years of work in the field.
Like-minded researchers and philosophers came together from two
movements in interdisciplinary studies of katachi and symmetry that
arose in the 1980s, one in Japan, the other in Hungary. The
proceedings of the symposium will stimulate and provoke the
interest of scientists and mathematicians, engineers and
architects, philosophers and semioticians - indeed, all those with
a lively sense of curiosity and a wide-ranging intellect.
This volume contains papers presented at the Twelfth Taniguchi
Symposium on the Theory of Condensed Matter, which was held at
Kashikojima (in Ise Shima National Park), Japan, November 14-19,
1989. The general purpose of the Taniguchi Symposia is to encourage
important developing, rather than established, fields in condensed
matter theory. The topic of the present sym posium, Quasicrystais,
is quite typical. In 1984, Shechtman, Blech, Gratias and Cahn
discovered the icosahedral symmetry of a diffraction pattern and
Levine and Steinhardt independently presented the notion of
quasicrystals. Before these discoveries, Roger Penrose of Oxford
University had invented a space-filling non-periodic tiling, now
called Penrose tiling. These factors form a new field that had
become mathematically viable by the end of 1984, and many important
new ideas are still being created. In standard textbooks of
solid-state science, the first chapter used to be devoted to
symmetry and periodicity in crystals. Now, the textbooks should be
revised; quasi-periodicity and its physical properties should be
added in several chapters and almost all standard conceptions
should be reconsidered. However, the facts that are known about
quasiperiodicity are not enough to complete even an introductory
chapter of a textbook. Revision should be extended to generalized
crystallography, defects, crystal growth, electronic structure,
spectral theory and localization, electron transport, spin
statistics, etc. These are all topics treated in this volume.
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