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By Payne K.R.
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Extra info for Singular metrics and associated conformal groups underlying differential operators of mixed and degenerate types
Example text
109 We agree that Legendre and Lacroix played critical roles and, as far as we know, Roche is the only scholar among historians who discuss symmetry to call attention to Lacroix. 112 So far, so good. But there are a number of “missed opportunities”. Roche does not discuss passages in Greek texts where the term, symmetry, occurs; he does not mention Vitruvius and the impact of his work in early modern times; he does not explore the context for the innovations of Legendre and Lacroix (in the latter case, he only cites the English translation of 1816, not the French original); he ignores the role of Ren´e Just Ha¨uy (1743–1822), who introduced a “law of symmetry” in a paper of 1815 on crystallography; and he neglects the passage in Curie’s paper of 1894 which says that appeal to symmetry had not occurred in physics prior to 1894.
10. 111 Roche 1987, 4, n. 7. 112 Roche 1987, 20–21. 113 Roche 1987, 3. 34 1 Introduction try in the same way that Kepler’s nested regular solids and cosmic harmonies are. ” As Roche sees it, beginning with Aristotle “the commitment to a circularly symmetric astronomy . . was . . 4). Indeed, the title of Kepler’s major work is Astronomia nova AITIOΛOΓ HTOΣ, sev physica coelestis (New Astronomy Based on Causes, or Celestial Physics), and it indicates that he is concerned with causal explanations.
61 Van Fraassen 1989, 216. 62 Van Fraassen 1989, 233. 63 Ibid. , Hon and Goldstein 2005, 445, 453, 454, 457, 458, 459, 462. See also Hon and Goldstein 2006b. 65 Van Fraassen 1989, 235, 236. 66 Van Fraassen 1989, 239. 67 This is akin to the distinction Michael Redhead put forward in his seminal work on symmetry in intertheory relations. ”69 Redhead calls the former class physical symmetries as distinct from the latter which he calls mathematical. This distinction between physical and mathematical symmetry reflects a similar approach to that of van Fraassen, namely, Redhead separates symmetry as content (“substantively”) dependent, and symmetry which is free of this constraint and answers, so to speak, only to the logic of the situation; the latter being of much greater generality.