M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765), страница 5
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Anabsolutist geometrical approach would allow us to distinguish onlybetween symmetrical and asymmetrical possibly with dissymmetricalthrown in for good measure. So there must be a range of criteriaaccording to which one can decide whether something is symmetrical, and to what degree. These criteria may very well change withtime. A case in point is the question as to whether or not moleculespreserve their symmetry upon entering a crystal structure or uponthe crystal undergoing phase transition. Our notion about structuresand symmetries may evolve as more accurate data become available1 Introduction17(though their structures and symmetries are unchanged, of course,by our notions). A whole new approach is developing to analyzesymmetry properties in terms of a continuous scale rather than of adiscrete “yes/no” [58].Recognizing structural and other kinds of regularities has alwaysbeen important in chemistry.
Above we quoted Wigner in connectionwith the tasks of the physical sciences. He stressed the importance ofobserving regularities. He learned this from his mentor in preparinghis doctoral research, Michael Polanyi. Wigner mentioned this inhis two-minute speech at the Nobel award banquett in Stockholm in1963:I do wish to mention the inspiration receivedfrom Polanyi. He taught me, among other things,that science begins when a body of phenomenais available which shows some coherence andregularities, that science consists in assimilatingthese regularities and in creating concepts whichpermit expressing these regularities in a naturalway.
He also taught me that it is this method ofscience rather than the concepts themselves (suchas energy) which should be applied to other fieldsof learning [59].Linus Pauling was a master in noticing regularities among largeamounts of data. It has been argued, for example, that at the time of thefirst edition of The Nature of the Chemical Bond [60], Linus Paulinghad access to less than 0.01% of the structural information of 50 yearslater, yet his ideas on structure and bonding have stood the test oftime [61].The history of periodic tables and especially Dmitrii I.
Mendeleev’sseminal discovery, also demonstrates chemists’ never-ending questfor beauty and harmony [62]. He was looking for a simple systemfor presenting the elements as he was writing a general chemistrytext for his students. The Soviet stamp block, issued for the centennial of the Periodic Table, depicts its earliest version (Figure 1-17a).Approximately 700 periodic tables were published during the first onehundred years after the original discovery in 1869. E. G. Mazurs [63]collected, systematized, and analyzed them in a unique study.
Classification of all the tables reduced their number to 146 different types181 IntroductionFigure 1-17. (a) Soviet stamp block issued to the centenary of Mendeleev’s Periodic System; (b) The Periodic Table of the Elements as a fresco at what is today theMendeleev Institute of Metrology in St. Petersburg and was the Board of Weightsand Measures in Mendeleev’s time (photograph by and courtesy of AlexanderBelyakov, St. Petersburg) [65].and subtypes which are described by such terms as “helices, spacelemniscates, space concentric circles, space squares, spirals, seriestables, zigzags, parallel lines, step tables, tables symmetrical abouta vertical line, mirror image tables, tables of one revolution and ofone row, tables of planes, revolutions, cycles, right side as well as leftside electronic configuration tables, tables of concentric circles andparallel lines, right side as well as left side shell and subshell tables.”Figure 1-17b shows the traditional, rectangular-shaped table in formof a wall-decoration displayed on the facade of the St.
Petersburgcollege building where Mendeleev used to work. The characteristicsymmetry of this arrangement is periodicity itself. Figure 1-18 is aspiral representation of the Periodic System (drawn proportionallyto the increasing mass of the elements, prior to the understandingof the foundation of the system in the electronic structure of theelements) [64].The quest for symmetry and harmony has, of course, contributedmore than mere aesthetics in establishing the Periodic Table of1 Introduction19Figure 1-18.
Spiral periodic system, after H. Erdmann [66] (computer graphics byJudit Molnár, Budapest).the elements. Beauty and reason blend in it in a natural fashion.C. A. Coulson, theoretical chemist and professor of mathematics,concluded his Faraday lecture on symmetry with the words:Man’s sense of shape—his feeling for form—thefact that he exists in three dimensions—these musthave conditioned his mind to thinking of structure,and sometimes encouraged him to dream dreamsabout it. I recall that it was Kekulé himself whosaid: “Let us learn to dream, gentlemen, and thenwe shall learn the truth.” Yet we must not carrythis policy too far.
Symmetry is important, but it isnot everything. To quote Michael Faraday writingof his childhood: “Do not suppose that I was avery deep thinker and was marked as a precociousperson. I was a lively imaginative person, andcould believe in the Arabian Nights as easily asin the Encyclopedia. But facts were important tome, and saved me.” It is when symmetry interpretsfacts that it serves its purpose: and then it delightsus because it links our study of chemistry withanother world of the human spirit—the world of201 Introductionorder, pattern, beauty, satisfaction.
But facts comefirst. Symmetry encompasses much—but not quiteall! [67]References1. A. Koestler, Insight and Outlook, Macmillan, London and New York, 1949.2. E. Lendvai, in Module, Proportion, Symmetry, Rhythm, G. Kepes, ed., GeorgeBraziller, New York, 1966.3. N. Angier, “Why Birds and Bees, Too, Like Good Looks.” The New York Times,February 8, 1994, p.
C1. The title of the article can be taken as referring to oneof Cole Porter’s most popular songs “Let’s Do It” (“Let’s Fall in Love”) thatstarts with the words, “that’s why birds do it, bees do it,. . .”4. V. Prelog, “Chirality in Chemistry.” Science 1976, 193, 17–24.5. Quoted in C. A. Coulson, “Symmetry.” Chem. Britain 1968, 4, 113–120.6. Nobel Foundation Directory.7.
See, e.g., M. Veltman, Facts and Mysteries in Elementary Particle Physics.World Scientific, Singapore, 2003; L. Lederman (with D. Teresi), The GodParticle: If the Universe Is the Answer, What Is the Question? Mariner Books,2006; F. Wilczek, Fantastic Realities: 49 Mind Journeys and a Trip to Stockholm. World Scientific, Singapore, 2006.8. J. D.
Watson, F. H. C. Crick, “A Structure for Deoxyribose Nucleic Acid.”Nature 1953, April 25, 737–738.9. See, e.g., I. Hargittai, The DNA Doctor: Candid Conversations with JamesD.Watson. World Scientific, Singapore, 2007, pp. 10, 169, 173–174.10. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, R. E. Smalley, “C60 : Buckminsterfullerene.” Nature 1985, 318, 162–163.11. D. Shechtman, I. Blech, D. Gratias, J. W. Cahn, “Metallic Phase with LongRange Orientational Order and No Translational Symmetry.” Phys. Rev. Lett.1984, 53, 1951–1953.12.
R. B. Fuller, Synergetics: Explorations in the Geometry of Thinking,Macmillan, New York, 1975, p. 4.13. D. E. H. Jones, “Dreams in a Charcoal Fire—Predictions about Giant Fullerenesand Graphite Nanotubes.” Phil. Trans. R. Soc. London 1993, 343, 9–18.14. D. E.
H. Jones, “Ariadne.” New Scientist 1966, 35, 245.15. D. W. Thompson, On Growth and Form, Cambridge University Press, 1961.16. Ibid.17. E. Osawa, “Superaromacity” (in Japanese). Kagaku (Kyoto) 1970, 25, 854–863.18. D. A. Bochvar, E. G. Gal’pern, “Hypothetical Systems: Carbododecahedron,s-Icosahedron, and Carbo-s-Icosahedron.” Dokl.
Akad. Nauk S. S. S. R. 1973,209, 610–612.References2119. See, e.g., H. W. Kroto, “C60 B Buckminsterfullerene, Other Fullerenes and theIcospiral Shell.” In Symmetry 2, Unifying Human Understanding, I. Hargittai,ed., Pergamon Press, Oxford and New York, 1989, pp. 417–423.20. I. Hargittai, “Buckminsterfullerene in the Sarayi.” Chem. Intell. 1996, 2(4), 4.21. P. C.
Gasson, Geometry of Spacial Forms, Ellis Horwood, Chichester, 1983,pp. ix–x.22. I. Hargittai, “Fullerene geometry under the lion’s paw.” Math. Intell. 1995,17(3), 34–36.23. I. Hargittai, “Japanese symmetries.” Forma 1994, 8, 327–333.24. Hargittai, Math. Intell. 34–36.25. W. Krätschmer, L. D. Lamb, K. Fostiropoulos, D. R.
Huffman, “Solid C60 : anew form of carbon.” Nature 1990, 347, 354–358.26. H. Aldersey-Williams, Perfect Symmetry: The Discovery of the Buckyball.Wiley, New York, 1995; J. Baggott, Perfect Symmetry: The AccidentalDiscovery of Buckminsterfullerene. Oxford University Press, 1994.27. B. Hargittai, I. Hargittai, “Rising to New Heights.” Chem. Intell. 2000, 6(3),42–43. This article is a pictorial report about the experiment at the Department of Physics at the University of Arizona on August 30, 1999, in whichDonald Huffman and Wolfgang Krätschmer re-enacted the first ever production of buckminsterfullerene.28.
A. L. Mackay, “Crystallography and the Penrose Pattern.” Physica 1982, 114A,609–613.29. D. W. Crowe, in Fivefold Symmetry, I. Hargittai, ed., World Scientific,Singapore, 1992, p. 465; L. Danzer, B. Grünbaum and G. C. Shephard, “CanAll Tiles of a Tiling Have Five-fold Symmetry?” Am. Math. Monthly 1982, 89,568–570 and 583–585; A. L. Mackay, “De Nive Quinquangula: On the Pentagonal Snowflake.” Kristallografiya (Sov.
Phys. Crystallogr.) 1981, 26, 910–919(517–522).30. R. Penrose, “Pentaplexity.” Math. Intell. 1979/80, 2, 32–37.31. Mackay, Physica, 609–613.32. D. W. Crowe, “Albrecht Dürer and the Regular Pentagon.” In FivefoldSymmetry, ed. I. Hargittai, World Scientific, Singapore, 1992, pp.
465–487,p. 483.33. L. Danzer, B. Grünbaum, G. C. Shephard, “Can All Tiles of a Tiling Have Fivefold Symmetry?” Am. Math. Monthly 1982, 89, 568–570 and 583–585.34. Mackay, Kristallografiya (Sov. Phys. Crystallogr.) 910–919 (517–522).35. E. P. Wigner, Nobel lecture. In Nobel Lectures Including Presentation Speechesand Laureates’ Biographies: Physics 1963–1970. World Scientific, Singapore,1998, pp. 6–17.36. D. J. Gross, “Symmetry in Physics: Wigner’s Legacy,” Physics TodayDecember 1995, 46–50.221 Introduction37. Wigner, Nobel Lectures Including Presentation Speeches and Laureates’Biographies: Physics 1963–1970, pp. 6–17, pp. 6–7.38.
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