## Quasicrystal and Information

Consequently, a universe where time is real must be loveless. I don’t like that idea.Impressions from the PI workshop on the Laws of Nature

Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. Classical theory of crystals allows only 2, 3, 4, and 6-fold rotational symmetries, but quasicrystals display symmetry of other orders (folds). They can be said to be in a state intermediate between crystal and glass. Just like crystals, quasicrystals produce modified Bragg diffraction, but where crystals have a simple repeating structure, quasicrystals are more complex.

Aperiodic tilings were discovered by mathematicians in the early 1960s, but some twenty years later they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography and solid state physics. Quasicrystals had been investigated and observed earlier[1] but until the 80s they were disregarded in favor of the prevailing views about the atomic structure of matter.

Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled; i.e. the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than 2, 3, 4, or 6. The first officially reported case of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1984.[2] The distinction between quasicrystals and their corresponding mathematical models (e.g. the three-dimensional version of the Penrose tiling) need not be emphasized.

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What Is Information? by Stuart Kauffman

Put briefly — and Schrodinger did not say so guessing his intuition is up to us — I think his intuition was that an aperiodic crystal breaks a lot of symmetries, therefore contains a lot of (micro) constraints that can enable an enormous diversity of real and organized processes to happen physically. This idea of organized processes seems to be hinted at in his statement that the aperiodic crystal would contain a microcode for (generating) the organism. I have inserted “generating”, and this is the set of specific processes aspect of information that I think we need to incorporate into our idea of what information IS.  I think Schrodinger is telling us both a deeper meaning of what information “is”, and part of how the universe got complex — by repeatedly breaking symmetries that enabled organized processes to happen that both provided new sources of free energy and enabled the breaking of further symmetries.

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