Abstract
Dan Shechtman was the first to discover an actual quasicrystal (on April 8, 1982). 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 fivefold symmetry) for crystals have been discovered. Medieval Islamic artists as well as Albrecht Dürer, Johannes Kepler, Roger Penrose, Mackay himself, and other pioneer crystallographers raised important contributions to the theoretical discovery of pure crystalline possibilities long before or independently of the discovery of their actual existence. Shechtman, however, was not the first to discover the individual pure possibility of this novel structure (the theoretical discovery), which had been excluded from the range of the possibilities of crystals (as it had been fixed by both theoretical and empirical means at the beginning of the twentieth century). Penrose and Mackay, in particular, had contributed to the discovery of the individual pure possibilities of quasicrystals, which are merely structural, and, like purely mathematical entities, they do not exist spatiotemporally and causally, whereas actual quasicrystals exist only spatiotemporally and causally. The individual pure possibilities of quasicrystals do not depend on their actualities, and without these possibilities, those actualities would have been theoretically groundless, meaningless, and could not be correctly identified, if at all. Hence, Mackay’s contribution to the meaning and theoretical basis of the discovery of actual quasicrystals is indispensable.
In this Chapter, 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.
The first versions of this chapter were published in Structural Chemistry 28:1 (2017), pp. 249–256 and Foundations of Chemistry (2018).
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Notes
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URL: http://www.wolffund.org.il/full.asp?id=17 (2004)
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Cf. Hargittai 2017, p. 8: “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.”
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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?”
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“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).
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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).
References
Cartwright, J. H. E., & Mackay, A. (2012). Beyond crystals: The dialectic of materials and information. Philos Trans A Math Phys Eng Sci, 370, 2807–2822.
Deutsch, D. (2004). It from Qubit. In J. D. Barrow, P. C. Davis, & C. L. Harper (Eds.), Science and ultimate reality: Quantum theory, cosmology, and complexity (pp. 90–102). Cambridge: Cambridge University Press.
Dyson, F. J. (2002). Random matrices, neutron capture levels, Quasicrystals and Zeta-functions Zero. http://www.msri.org/realvideo/ln/msri/2002/rmt/dyson/1/
Eddington, A. S. (1928). The deviation of stellar material from a perfect gas. Monthly Notices of the Royal Astronomical Society, 88, 352–369.
Gilead, A. (2005a). A Possibilist metaphysical reconsideration of the identity of indiscernibles and free will. Metaphysica, 6, 25–51.
Gilead, A. (2013). Shechtman’s three question marks: Impossibility, possibility, and quasicrystals. Foundations of Chemistry, 15, 209–224.
Gilead, A. (2014a). Pure possibilities and some striking scientific discoveries. Foundations of Chemistry, 16, 149–163.
Gilead, A. (2014c). Chain reactions, ‘impossible’ reactions, and panenmentalist possibilities. Foundations of Chemistry, 16, 201–214.
Gilead, A. (2016). Eka-elements as chemical pure possibilities. Foundations of Chemistry, 18, 1–16. https://doi.org/10.1007/s10698-016-9250-7.
Hargittai, I. (Ed.). (1992). Fivefold Symmetry. Singapore: World Scientific.
Hargittai, I. (1997). Quasicrystals discovery: A personal account. The Chemical Intelligencer, 3, 26–34.
Hargittai, I. (2010a). Structures beyond crystals. Journal of Molecular Structure, 976, 81–86.
Hargittai, I. (2011a). ‘There is no such animal (אין חיה כזו)’—Lessons of a discovery. Structural Chemistry, 22, 745–748.
Hargittai, I. (2011b). Geometry and models in chemistry. Structural Chemistry, 22, 3–10.
Hargittai, I. (2011c). Stubbornness: ‘Impossible’ matter. In Drive and Curiosity: What Fuels the Passion for Science (pp. 155–172). Amherst: Prometheus Books.
Hargittai, I. (2011d). Dan Shechtman’s Quasicrystal discovery in perspective. Israel Journal of Chemistry, 51, 1–9. https://doi.org/10.1002/ijch.201100137.
Hargittai, I. (2017). Generalizing crystallography: A tribute to Alan L. Mackay at 90. Structural Chemistry, 28, 1–16.
Hargittai, I., & Hargittai, M. (2000). In our own image. In Personal symmetry in discovery (Vol. 8, pp. 151–157). New York: Kluwer Academic/Plenum.
Hargittai, I., & Hargittai, M. (2009). Symmetry through the eyes of a chemist (p. 16). Berlin: Springer.
Lapidus, M. L. (2008). In search of the Riemann Zeros: Strings, fractal membranes and noncommutative Spacetimes. Providence: American Mathematical Society.
Levine, D., & Steinhardt, P. (1984). Quasicrystals: A new class of ordered structures. Physical Review Letters, 53, 2477–2480.
Lord, E. A., Mackay, A. L., & Ranganathan, S. (2006). New geometries for new materials. Cambridge: Cambridge University Press.
Mackay, A. L. (1976). Crystal symmetry. Physics Bulletin, 27, 495–498.
Mackay, A. L. (1981). De Nive Quinquangula: On the pentagonal snowflake. Soviet Physics, Crystallography, 26, 517–522.
Mackay, A. L. (1982). Crystallography and the Penrose pattern. Physica A: Theoretical and Statistical Physics, 114, 609–613.
Mackay, A. L. (1990). Crystals and fivefold symmetry. In I. Hargittai (Ed.), Quasicrystals, networks, and molecules of fivefold symmetry (pp. 1–18). New York: VCH Publishers.
Mackay, A. L. (1997). Lucretius or the philosophy of chemistry. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 129–130, 305–310.
Mackay, A. L. (2002). Generalized crystallography. Structural Chemistry, 13, 215–220.
Mislow, K., & Rickart. (1976). An epistemological note on chirality. Israel Journal of Chemistry, 15, 1–6.
Poole, C. P. (Ed.). (2004). Encyclopedic dictionary of condensed matter physics, Vol 1. Amsterdam: Elsevier.
Shechtman, D., Blech, I., Gratias, D., & Cahn, J. W. (1984). Metallic phase with long range orientational order and no translation symmetry. Physical Review Letters, 53, 1951–1954.
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Gilead, A. (2020). The Philosophical Significance of Alan Mackay’s Theoretical Discovery of Quasicrystals. In: The Panenmentalist Philosophy of Science. Synthese Library, vol 424. Springer, Cham. https://doi.org/10.1007/978-3-030-41124-4_8
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