Ockham's Razor and chemistry

Hyle

Volumn 3, Issue , 1997, Pages 3-28

  Hoffmann, Roald ^a   Minkin, Vladimir I ^b   Carpenter, Barry K ^a  

^a Department of Molecular Biology and Genetics   (United States)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Bayesian analysis; Ockham's Razor; Principal component analysis; Principle of least action; Principle of least motion; Reaction mechanism

Indexed keywords

EID: 53249154750     PISSN: 14335158     EISSN: 14335158     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (99)

1. The definitive edition of Ockham's work is published by the Franciscan Institute at St. Bonaventure/NY, 1967-1988 (Opera philosophica et theologica); and by Manchester University Press 1940ff.
2. (Opera politica). An English translation of his philosophical work is provided by P. Boehner (ed.), Ockham. Philosophical Writings, Nelson, Edinburgh 1957.
3. The authoritative work on Ockham's life remains L. Baudry, Guillaume d'Occam. Sa vie, ses oeuvres, ses idées sociales et politiques, Librairie Philosophique Vrin, Paris, 1950.
4. There is a substantial literature on his philosophy - here we cite only four leading references: H. Junghaus, Ockham im Lichte der neueren Forschung, Lutherisches Verlagshaus, Berlin, 1968;
5. G. Leff, William of Ockham: The Metamorphosis of Scholastic Discourse, Manchester University, Manchester, 1975;
6. M.M. Adams, William Ockham, 2 vols., University of Notre Dame, Notre Dame, 1987;
7. W. Vossenkuhl, R. Schönberger (eds.), Die Gegenwart Ockhams, VCH Acta Humaniora, Weinheim, 1990.
8. P. Boehner, Die Gegenwart Ockhams, op. cit. (Note 1), pp. xxx-xxxix.
9. These are quoted from M.M. Adams, Die Gegenwart Ockhams, op. cit. (Note 1), vol. 1, pp. 156-157, who provides the citations from Ockham where the formulations quoted may be found.
10. For instance, Odo Rigaldus, Commentatorium super sententias, MS Bruges 208, fol. 150a, has "Frustra fit per plura quod potest fieri per unum."
11. (P. Boehner, Commentatorium super sententias, op. cit. (Note 1), p. xx).
12. Odo Rigaldus was Archbishop of Rouen from 1248 to 1275. Aristotle in De Caelo writes: "Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be proved. This is the common demand of the mathematicians who assume as principles things finite either in kind or in number." (The Works of Aristotle Translated into English, vol. II, De Caelo, trans, by J.L. Stocks, ed. by W.D. Ross, Clarendon, Oxford, 1930, III, c. 4, 302b)
13. . And Thomas Aquinas (1225-1274), in Summa Contra Gentiles: "If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices."
14. (Basic Writings of St. Thomas Aquinas, trans. A.C. Pegis, Random House, New York, 1945, p. 129.).
15. We owe these last two references to R. Ariew, Franciscan Studies, 37 (1977), 5-17.
16. See also G. Leff, William of Ockham, Manchester University, Manchester, 1975, p. 35, note 141;
17. and the spirited account of W.M. Thorburn, Mind (NS), 27 (1918), 345-53.
18. M.M. Adams, Mind (NS), op. cit. (Note 1), vol. 1, p. 157.
19. Rasoir des Nominaux: E.B. de Condillac, Essai sur l'Origine des Connaissances Humaines, 1746, p. 214.
20. The English variant (Occam's Razor) apparently appears first in W.R. Hamilton, Discussions, 1852, 590.
21. We owe these citations to Thorburn, Discussions, op. cit. (Note 4). But we may need a Mertonian analysis of the origins of this term...
22. For further discussions of Ockham's Razor, its utilization by Ockham and others, and its utility in philosophy, see: C.K. Brampton, Modern Schoolman, 41 (1964), no. 3, 273-82;
23. A.A. Maurer, Monist, 61 (1978), no. 3, 426-43;
24. J. Boler, Franciscan Studies, 45 (1985), 119-44;
25. K. Menger, Synthese, 13 (1961), 331-49;
26. G. O'Hara, Philosophical Studies, 12 (1963), 125-39 (particularly good in discussing Bertrand Russell's use of Ockham's Razor).
27. P.L.M. de Maupertuis, Mémoires de l'Académie Royale, 423 (1744).
28. L. de Broglie, Annales de Physique, 3/10 (1925), 22-128;
29. R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. II, Addison-Wesley, Reading, 1964, Chap. 19.
30. A. Muller, Bulletin de Société Chimique, Paris, 45 (1886), 438.
31. W. Hückel, Theoretische Grundlagen der Organischen Chemie, Akademische Verlagsgesellschaft, Leipzig, 1934.
32. See also G.W. Wheland, Advanced Organic Chemistry, Wiley, New York, 1960.
33. F. Rice, E. Teller, Journal of Chemical Physics, 6 (1936), 489.
34. See the comprehensive reviews of J. Hine, Advances in Physical Organic Chemistry 15 (1977), 1-19;
35. and M.L. Sinnott, Advances in Physical Organic Chemistry, 24 (1986), 113-204.
36. See as well the comment, in the context of concerted reactions, by J.A. Berson, in: P. de Mayo (ed.), Rearrangements in Ground and Excited States, vol. 1, Academic, New York, 1980, p. 375-76.
37. M.S. Korobov et al., Journal of the Chemical Society - Chemical Communications, (1982) 169-170.
38. M.S. Korobov et al., Journal of Molecular Structure - Theochem, 200 (1989), 61-72.
39. A.J. Boulton, C.S. Prado, Journal of the Chemical Society - Chemical Communications, (1982), 1008-9.
40. R.A. Jackson, Mechanism: An Introduction to the Study of Organic Reactions, Clarendon, Oxford, 1972.
41. B.K. Carpenter, Determination of Organic Reaction Mechanism, Wiley-Interscience, New York, 1984.
42. B. Russell, The Problems of Philosophy, Oxford University, Oxford, 1980, p. 97.
43. N. Oreskes, K. Shrader-Frechette, K. Belitz, Science, 263 (1994), 641-646, endnote 25.
44. V.I. Minkin, L.E. Nivoroshkin, M.S. Korobov, Russian Chemical Reviews, Uspekhi Khimii, (1994), 303.
45. According to the original definition, pericyclic reactions are those "in which all first order changes in bonding relationships take place in concert on a closed curve" (R.B. Woodward, R. Hoffmann, The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim, 1970).
46. K.N. Houk, Y. Li, J.D. Evanseck, Angewandte Chemie International Edition English, 31 (1992), 682-707;
47. M.J.S. Dewar, C. Jie, Accounts of Chemical Research, 25 (1992), 537-543.
48. Of special interest are the contradictory conclusions (in some cases) arising from ab initio vs. or semiempirical methods of calculation. For an up-to-date and most readable account of this neverending story see K.N. Houk, J. González, Y. Li, Accounts of Chemical Research, 28 (1995), 81-90.
49. For a leading reference see H. Schwarz, Angewandte Chemie International Edition English, 32 (1993), 1412-15.
50. R.E. Smalley, Accounts of Chemical Research, 25 (1992), 98-105;
51. J.M. Hunter et al., Journal of Physical Chemistry, 98 (1994), 1810;
52. G. von Helden et al., Nature, 363 (1993), 60-63;
53. J. Hunter et al., Science, 260 (1993), 784-6;
54. J.M. Hunter et al., Journal of Physical Chemistry, 98 (1994), 1810;
55. R.L. Murry et al., Nature, 366 (1993), 665;
56. C. Xu, G.E. Scuseria, Physical Review Letters, 72(1993), 669.
57. See also Note 24 and the work of T. Belz et al., Angewandte Chemie International Edition English, 33 (1994), 1866.
58. See R.E. Smalley (Note 25).
59. Quantum mechanical tunnelling is a widespread reaction mechanism responsible for occurrence of many proton and electron transfer reactions. Tunnelling also occurs, as we have only recently learned, for heavier atoms; B.K. Carpenter, Journal of the American Chemical Society, 105 (1983), 1700-1.
60. J. Platt, Science, 146 (1964), 4642.
61. Of course it takes six for sex: L.B. Bjostad et al., Journal of Chemical Ecology, 10 (1984), 1309-23;
62. W.L. Roelofs, T. Glover, in: C.J. Wysocki, M.R. Kare (eds.), Chemical Senses, vol. 3, Dekker, New York, 1991;
63. C.E. Linn, W.L. Roelofs, to be published.
64. The provisional nature of Ockham's Razor based arguments has been stressed by R.O. Kapp, The British Journal for the Philosophy of Science, 81 (1958), 265-81.
65. The definition of the term 'degrees of freedom' here differs from that commonly used in statistical mechanics.
66. The choice becomes a little less clear-cut when one starts to inquire about models for which the line comes close to, but does not pass exactly through all of the points. In statistical practice, this situation is dealt with by applying the Fisher F test (see, for example, J.C. Miller, J.N. Miller, Statistics for Analytical Chemistry, 2nd edn., Ellis Horwood, Chichester, 1988, p. 60). The sum of the squares of the deviations (y - ym)2 is computed for each model (y is the experimentally measured response of the system under study to a given value of x; ym is the response predicted by the model) and then divided by the appropriate number of degrees of freedom. This calculation provides the variance for each model. The ratio of the variances is compared with tabulated values that allow one to decide, with a specified level of confidence, whether the more complex model has made a statistically significant improvement to the fit. If it has not, one will generally opt for the simpler model because, again, it has the larger number of degrees of freedom.
67. See also the clear arguments here of H. Jeffreys, Theory of Probability, Oxford University, Oxford, 1939;
68. W.H. Jefferys, J.O. Berger, American Scientist, 80 (1992), 64-72.
69. E.R. Malinowski, D.G. Howery, Factor Analysis in Chemistry, Wiley-Interscience, New York, 1990.
70. See also H.J. Gauch Jr., American Scientist, 81 (1993), 468.
71. T. Auf der Heyde, South African Journal of Chemistry, 46 (1993), 45.
72. A.R. Katritzky et al., Journal of the American Chemical Society, 111 (1989), 7-15.
73. See V.I. Minkin, M.N. Glukhovtsev, B.Y. Simkin, Aromaticity und Antiaromaticity, Wiley, New York, 1994, for leading references.
74. Recently Katritzky et al.'s conclusion has been questioned by P.v.R. Schleyer et al., Angewandte Chemie International Edition English, 34 (1995), 337-340.
75. R. Murray-Rust, W.D.S. Motherwell, Acta Crystallographica - Section B, 34 (1978) 2534.
76. T.P.E. Auf der Heyde, H.B. Bürgi, Inorganic Chemistry, 28 (1989), 3960, 3970, 3982.
77. G. Basu et al., Journal of the American Chemical Society, 116 (1994), 6307-15.
78. M.E. Fisher, personal communication.
79. See 'toughness-tenderness' and 'juiciness' separated as important Principal Components, in an analysis of 69 beef roasts by J.M. Harris, D.N. Rhodes, B.B. Chrystall, Journal of Texture Studies, 3 (1972), 101;
80. or the analysis of sensory characteristics of ham and their relationships with composition, visco-elasticity and strength: G.R. Nute et al., International Journal of Food Science and Technology, 22 (1987), 461.
81. Our source for these references on sensory properties and preferences of meat products is a perceptive overview by Einar Risvik, (Matforsk, Ås, Norway), to be published. For the use of PCA in the evaluation of 1976 Bordeaux wines see A.C. Nobel, A.A. Williams, S.P. Langdon, Journal of the Science of Food and Agriculture, 35 (1984), 88. H.K. Sivertsen, E. Risvik (to be published) have carried out a detailed multivariate study of French wine profiles. They had eight panelists rate thirty wines for 17 specific and integrated sensory attributes. Two Principal Components accounted for 65% of the variation. The first of these was a fruity aroma axis, "going from berry aromas to vegetative aromas and attributes representing a more ripened aroma, like 'animal' and 'vanilla'. PC2 could be described as a mouthfeel and color axis, going from 'suppleness' to 'astringency', 'color intensity', 'potential', and 'color tone'." Sivertsen and Risvik point to an amusing mapping of the wine varieties separating along these Principal Components onto the geography of France wineproducing regions.
82. H. Jeffreys, Theory of Probability, Oxford University Press, Oxford, 1939.
83. See also articles by S.F. Gull, in: G.J. Erickson, C.R. Smith (eds.), Maximum Entropy and Bayesian Methods in Science and Engineering, Vol. 1: Foundations, Kluwer, Dordrecht, pp. 53-74;
84. and in: J. Skilling (ed.), Maximum Entropy and Bayesian Methods, Cambridge 1988, Kluwer, Dordrecht, 1989, pp. 53-71.
85. D.J.C. MacKay, Neural Computation, 4 (1992), 415-47.
86. W.H. Jefferys, J.O. Berger, American Scientist, 80 (1992), 64-72;
87. see also H.G. Gauch Jr., American Scientist, 81 (1993), 468-77.
88. H.G. Schuster, Deterministic Chaos, Verlag Chemie, Weinheim, 1984.
89. D.A. Hrovat, K. Morokuma, W.T. Borden, Journal of the American Chemical Society, 116 (1994), 1072-1076.
90. See also P.M. Kozlowski, M. Dupuis, E.R. Davidson, Journal of the American Chemical Society, 117 (1995), 774-8;
91. H. Jiao, P.v.R. Schleyer, Angewandte Chemie International Edition English, 34 (1995), 334-7;
92. and the account of Houk, González and Li (Note 23).
93. B.K. Carpenter, Accounts of Chemical Research, 25 (1992), 520-28.
94. C.J. Suckling, R.E. Suckling, C.W. Suckling, Chemistry Through Models. Concepts and Applications of Modelling in Chemical Science, Technology and Industry, Cambridge University Press, Cambridge, 1980.
95. For a contrary view, see: H.A. Simon, The Sciences of the Artificial; 2nd edn., MIT Press, Cambridge, 1981.
96. M. Jammer, The Conceptual Development of Quantum Mechanics; 2nd edn., American Institute of Physics, New York, 1989.
97. J. Mehra, H. Rechenberg, The Historical Development of Quantum Theory, Springer, New York, 1982, vol. 1, part 1, p. 150;
98. see also T.S. Kuhn, Blackbody Theory, and the Quantum Discontinuity, Oxford University Press, New York, 1978, part 2, pp. 616-17.
99. It is not all that easy to define simplicity: "The notion of simplicity, like truth, beauty and effective process is an intuitive one calling for a more objective characterization, i.e., formalization, before we can even hope to agree about the relative complexities of different theories", J.J. Casti, Searching for Certainty, Morrow, New York, 1990.