Abstract
As early as 1981, about 1 year before Shechtman’s discovery of an actual quasicrystal, Alan L. Mackay discussed, in a seminal paper, the first steps for the expansion of crystallography toward its modern phase. In this phase, new possibilities of structures and order, such as the structures of five-fold symmetry, for crystals have been discovered. Medieval Islamic decorators as well as Albrecht Dürer, Johannes Kepler, Roger Penrose, Mackay himself, and other pioneer crystallographers raised important contributions to the theoretical discovery of crystalline possibilities long before or independently of the discovery of their actual existence. In this paper, I discuss further the philosophical significance of Mackay’s theoretical discovery and his contribution to the expansion of pure geometrical crystallography, biological crystallography, and generalized crystallography.
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Notes
Cf. Hargittai (2017, p. 8): “them. The search for extended structures with five-fold symmetry had been going on for centuries and involved excellent minds, such as Johannes Kepler and Albrecht Dürer, Roger Penrose came up with such a pattern in two dimensions and Mackay crucially extended it to the third dimension, and urged experimentalists to be on the lookout for such structures”.
Cf. Mackay (1976, p. 497): “We must ask as many have asked since Kepler what the rules which lead to the formation of a snowflake are. We are just beginning to see how the rules for the growth of a tree are written in the genetic code. Is there any resemblance between these two extremes of complexity? Does it make any sense to look back and ask where the program for providing a snowflake may be stored?”.
“Liquid structures … cannot be characterized by any of the 230 three-dimensional space groups and yet it is unacceptable to consider them as possessing no symmetry whatsoever. Bernal noted presciently that the major structural distinction between liquids and crystalline solids is the absence of long-range order in the former. … A generalized description should also characterize liquid structures and colloids, as well as the structures of amorphous substances. It should also account for the greater variations in their physical properties as compared with those of the crystalline solids. Bernal’s ideas have greatly encouraged further studies in this field which is usually called generalized crystallography” (Hargittai 2010, p. 485).
The electron diffraction pattern originating from a gaseous or a plasma sample is the result of intramolecular interferences and to only negligible extent to intermolecular ones, if any, in conrast to solid samples and to a lesser extent to liquid ones. Stating that all living substances are made of crystals (or, better, molecular structures), I mean to say that when wet proteins (which have the structure of crystals) are investigated, they are closer to the living matter, because they better approximate their exisence in aquaeous solution, than the”dry” crystals. Crystallization in its classical meaning leads living matter to death. I own this comment to the kindness of Istvan Hargittai. But perhaps it will be more helpful to adopt Mackay (and Hargittai’s following of him) that „crystalography” should be replaced by „structural chemistry” [see Hargittai (2017, p. 9); cf. (Hargittai 2010, p. 81): in essence, generalized crystallography is the science of structures, crystalline and otherwise].
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Gilead, A. Further light on the philosophical significance of Mackay’s theoretical discovery of crystalline pure possibilities. Found Chem 21, 285–296 (2019). https://doi.org/10.1007/s10698-018-9323-x
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DOI: https://doi.org/10.1007/s10698-018-9323-x