Einstein's Clocks and Poincare's Maps

by Peter Galison

  20. Goroff, Introduction, in Poincaré, New Methods (1993), I9, from Poincaré, “Mémoire sur les courbes” [1881], 376–77. Emphasis added.

  21. Poincaré, “Sur les courbes définies par les équations différentielles” [1885], 90; cited and translated in Barrow-Green, “Poincaré” (1997), 34.

  22. Barrow-Green, “Poincaré” (1997), 51–59.

  23. Poincaré, “La Logique et l’intuition” [1889], 132.

  24. Mittag-Leffler to Poincaré, 16 July 1889, letter 89, in La Correspondance entre Poincaré et Mittag-Leffler (1999).

  25. “I had thought that all these asymptotic curves, having moved away from a closed curve representing a periodic solution, would then asymptotically approach the same curve.” Poincaré to Mittag-Leffler, 1 December 1889, letter 90, in La Correspondance entre Poincaré et Mittag-Leffler (1999).

  26. Poincaré to Mittag-Leffler, 1 December 1889, letter 90, in La Correspondance entre Poincaré et Mittag-Leffler (1999).

  27. Mittag-Leffler to Poincaré, and attached notes, 4 December 1889, letter 92, in La Correspondance entre Poincaré et Mittag-Leffler (1999).

  28. Weierstrass to Mittag-Leffler, 8 March 1890, note to letter 92, in La Correspondance entre Poincaré et Mittag-Leffler (1999).

  29. For an accessible discussion of chaotic phenomena, see Ekeland, Mathematics (1988), and Diacu and Holmes, Celestial Encounters (1996), from which the following figures are drawn; more technical discussions in Barrow-Green, “Poincaré” (1997); and Goroff, Introduction, in Poincaré, New Methods (1993).

  30. Poincaré, New Methods (1993), part 3, section 397, 1059.

  31. On the postmodern interpretation of chaos, see, for example, Hayles, Chaos and Order (1991); Wise and Brock, “The Culture of Quantum Chaos” (1998); for physics and the connection of chaotic physics and art, see Eric J. Heller, www.ericjhellergallery.com (accessed June 19, 2002).

  32. Poincaré, “Sur le problème des trois corps” [1890], 490; Poincaré, Preface to the French Edition [1892], in idem, New Methods (1993), xxiv.

  33. Poincaré, Preface to the French Edition [1892], in idem, New Methods (1993), xxiv.

  34. Poincaré, “Sur les hypothèses fondamentales” [1887], 91.

  35. Poincaré, “Non-Euclidean Geometries” [1891], in idem, Science and Hypothesis (1902), 50, 41–43.

  36. Giedymin, Science and Convention (1982), 21–23, on 23.

  37. On Riemann, for example, cf. A. Gruenbaum, “Carnap’s Views” (1963); and his Geometry and Chronometry (1968). On Helmholtz as a source for Poincaré, Gerhard Heinzmann, “Foundations of Geometry,” Science in Context 14 (2001), 457–70. On reading sources of Poincaré’s mathematical conventionalism from more contemporary sources such as Jordan or Hermite, see Gray and Walter, Introduction, in Henri Poincaré (1997), 20.

  38. Poincaré, “Non-Euclidean Geometries” [1891], in idem, Science and Hypothesis (1902), on 50, emphasis added.

  CHAPTER 3

  1. Duc Louis Decazes, in Documents diplomatiques (1875), see 36. For an excellent introduction to the joint moral and technical history of standardization, see Wise, ed., Precision (1995), and further references in the rich essays by Simon Schaffer, M. Norton Wise, Graham Gooday, Ken Alder, Andrew Warwick, Frederic Holmes, and Kathryn Olesko. On the original mission to fix the meter see Alder, Measure (2002).

  2. J.B.A. Dumas, in Documents diplomatiques (1875), 121–30, esp. 126–27.

  3. Guillaume, “Travaux du Bureau International des Poids et Mesures” (1890).

  4. Comptes rendus des séances de la première conférence générale des poids et mesures, Poincaré, “Rapport” (1897). After the burial of M, metrological work moved toward the adoption of a different sort of procedure, one in which the wavelength of light became the standard of length—and so replacing that particular bar with a certain number of cesium wavelengths. This amalgamation of metrologists and spectroscopists, astrophysicists, and optical physicists is tracked by two fine pieces: Charlotte Bigg, Behind the Lines. Spectroscopic Enterprises in Early Twentieth Century Europe, unpublished doctoral dissertation, esp. Part II, University of Cambridge, 2002; and Staley, “Traveling Light” (2002).

  5. “Le Nouvel étalon du mètre” (1876).

  6. Le Temps, 28 September 1889, 1.

  7. See, for example, in Comptes rendus de l’Académie des Sciences: Violle, “Sur l’alliage du kilogramme” (1889); Larce, “Sur l’extension du système métrique” (1889); Bosscha, “Études relatives à la comparaison du mètre international” (1891); Foerster, “Remarques sur le prototype” (1891), 414.

  8. “Extrait du Rapport du Chef du Service Technique,” Ponts et Chaussées, 5 March 1881. Archives de la Ville de Paris, VONC 219.

  9. Dohrn-van Rossum, History of the Hour (1996), 272.

  10. “Conseil de l’Observatoire de Paris, Présidence de M. Le Verrier” [1875]; Le Verrier to M. le Préfet [January?, 1875?], both Archives de la Ville de Paris, VONC 219.

  11. “Projet d’Unification de l’heure dans Paris. Rapport de la Commission des horloges,” 22 January 1879. Archives de la Ville de Paris, VONC 219.

  12. Tresca, “Sur le réglage électrique de 1’heure” (1880); Ingénieur en Chef, Adjoint aux Travaux de Paris, “Quelques Observations en Réponse au Rapport du 25 Novembre, 1880.” Archives de la Ville de Paris, VONC 3184, 6.

  13. See, for example, G. Collin to M. Williot, 23 September 1882; G. Collin to M. Chrétien, 10 April 1883; both Archives de la Ville de Paris, VONC 219.

  14. Breguet, “L’unification de l’heure” (1880); on time coordination in Paris, see also David Aubin, “Fading Star,” forthcoming.

  15. M. Faye to M. le Directeur, Direction des Travaux de Paris, 16 January 1889. Archives de la Ville de Paris, VONC 219.

  16. Nordling, “L’Unification” (1888), 193.

  17. Ibid., 198, 200–201, and 202.

  18. Ibid., 211.

  19. Sobel, Longitude (1995), and Bennett, “Mr. Harrison” (2002).

  20. G. P. Bond to A. D. Bache, Supt USCS. 28 Feb. 1854. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Chronometric Expedition, letters, reports, miscellany; Box 1: Reports.

  21. W. C. Bond, “Report of the Director” (4 December 1850).

  22. W. C. Bond, “Report of the Director” (4 December 1851), clvi-clvii; G. P. Bond to A. D. Bache, Supt. USCS. 22 Oct. 1851. Both documents in Harvard University Archives, Harvard College Observatory, Cambridge, MA. Chronometric Expedition, letters, reports, miscellany; Box 1: Reports.

  23. Stephens, “Partners in Time” (1987), 378.

  24. Stephens, “‘Reliable Time’” (1989), 17; who cites, on 19, Shaw, Railroad Accidents (1978), 31–33.

  25. Bartky, Selling Time (2000), 64.

  26. “Report of the Director” (1853), clxxi.

  27. The literature on individual observatories is simply immense, and there is no better survey of their various roles in time coordination than Bartky, Selling Time (2000), which concentrates on the American case.

  28. Jones and Boyd, “The First Four Directorships” (1971), on 160; agreement with Boston & Providence Railroad, Boston & Lowell, Eastern Railroad Company, Boston and Maine Co., etc. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Observatory Time Service, 1877–92. Box 1, folder 7.

  29. “Historical Account” (1877), 22–23.

  30. Pickering, in idem, Annual Report of the Director (1877), 10–11.

  31. Report from Leonard Waldo, assistant to Prof. Edward C. Pickering, Director of the Observatory Harvard College, 20 November 1877, Appendix C in Pickering, Annual Report (1877), 28–36.

  32. George H. Clark, Proprietor, Rhode Island Card Board to Director of Cambridge Observatory, 16 May 1877. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Correspondence re: Time Signals. Folder 2.

  33. Waldo, “Appendix C” (1877), 28–29.

  34. Ibid., 33–34.

  35. Charles Teske to Leonard Waldo, 12 July, 8 Augus
t, 15 August, and 11 November 1878. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Correspondence re: Time Signals. Folder 1.

  36. Leonard Waldo, handwritten report to Director for year ending 1 Nov 1878. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Observatory Time Service, 1877–92. Box 1, folder 8.

  37. Charles Teske to Leonard Waldo, [illegible day] December 1878 and 15 April 1879. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Correspondence re: Time Signals. Folder 1; “Law of Connecticut, approved March 9, 1881,” Statutes of Conn., 1881, Ch. XXI. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Observatory Time Service, 1877–92. Box 1, folder 6; S. M. Seldon (Gen. Mgr. New York & New England RR Co.) to W. F. Allen, 23 March 1883, William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 3, book 1.

  38. T. R. Welles to L. Waldo, 5 December 1877. Harvard University Archives, Harvard College Observatory, Cambridge, MA. Correspondence re: Time Signals. Folder 2.

  39. Proceedings of the American Metrological Society (1878), 37.

  40. Bartky, “Adoption of Standard Time” (1989), 34–39.

  41. “Report of Committee on Standard Time” (May 1879), 27.

  42. Ibid.

  43. W. F. Allen to Cleveland Abbe, 13 June 1879. William F. Allen Papers, New York Public Library Archives, New York City, NY. Outgoing Correspondence: Box 3, book VII, 1; the two Time Conventions merged in 1886 becoming American Railway Association, later Association of American Railroads. See Bartky, “Invention of Railroad Time” (1983), 13.

  44. Cleveland Abbe to W. F. Allen. 14 June, 1879. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 3, book I.

  45. Charles Dowd had in mind a system not far from what was adopted. But when in 1879 he asked Allen if he, Dowd, could prepare an article explaining his idea for “National Time” in Allen’s Railway Guide, Allen demurred, saying that there simply was no space for the intervention. Charles F. Dowd to W. F. Allen, 30 October 1879. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 3, book I; W. F. Allen to Dowd, 9 December 1879. William F. Allen Papers, New York Public Library Archives, New York City, NY. Outgoing Correspondence: Book VII. Letters reprinted in Dowd, Charles F. Dowd (1930), IX.

  46. On Fleming, see Blaise, Time Lord (2000); Creet, “Sandford Fleming” (1990); older literature includes Burpee, Sandford Fleming (1915). Quotation in Fleming, “Terrestrial Time” (1876), 1.

  47. Fleming, “Terrestrial Time” (1876), 14–15.

  48. Ibid., 31, 22, and 36–37.

  49. Fleming, “Longitude” (1879), 53–57; attack on the French position on 63.

  50. Cleveland Abbe, U.S. Signal Office, to Sandford Fleming, 10 March 1880. Barnard to Fleming, 18 March, 6 April 1880, and 29 April 1881. All Barnard to Fleming letters Sandford Fleming Papers, National Archives of Canada, Ottawa, Ontario, MG 29 B1 Vol 3. File: Baring-Barnard. For Barnard showing a watch, see Proceedings of the American Metrological Society (1883).

  51. Barnard to Fleming, 11 June 1881, Sandford Fleming Papers, National Archives of Canada, Ottawa, Ontario, MG 29 B1 Vol 3. File: Baring-Barnard; Smyth, “Report to the Board of Visitors” (1871), R12–R20, on R19; response to Smyth’s work more generally by Barnard, “The Metrology” (1884). On Smyth and his natural theological metrology, see Schaffer, Metrology (1997).

  52. Airy to Barnard, 12 July 1881, Fleming Papers, vol. 3, folder 19.

  53. Barnard to Fleming, 19 August, 3 September, and 8 September 1881, quotation from 3 September. Sandford Fleming Papers, National Archives of Canada, Ottawa, Ontario, vol. 3, folder 19. On the shambles of Thomson’s appointment: Barnard, “A Uniform System” (1882).

  54. John Rodgers to Hazen, 11 June 1881. United States Naval Observatory LS-M vol. 4.

  55. “Report of the Committee” [December 1882].

  56. Col. H. S. Haines (Gen. Mgr., Charleston & Savannah Railway) to W. F. Allen, 12 March 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 3, book I, 72.

  57. Allen, Report on Standard Time (1883), 2–6. W. F. Allen, Scrapbook, at Widener Library Harvard University.

  58. Allen, Report on Standard Time (1883), 5.

  59. Ibid., 6.

  60. Figures on the number of letters and telegrams from Allen, “History” (1884), 42; figures on the number of lines running from different cities’ times from Bartky, “Invention of Railroad Time” (1983), 20.

  61. Newspaper article, unsigned, in letter to W. F. Allen from F. C. Nunenmacher (Central Vermont Railroad), 23 November 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 5, book IV, 158; E. Richardson (for D. D. Jayne and Son, Publishers, Philadelphia) to W. F. Allen, 5 December 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 5, book V, 48.

  62. See, for example, telegram of Col. A. A Talmage (Gen. Transport. Mgr. of the Missouri Pacific Railway), in Allen, “History” (1884), 42; S.W. Cummings (Central Vermont Railroad) to W. F. Allen, 26 November 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 5, book V, 18; and George Crocker (Asst. Supt., Central Pacific R. R. San Francisco) to W. F. Allen, 8 October 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 4, book II, 97.

  63. John Adams (Gen. Supt., Fitchburg Railroad) to W. F. Allen, 2 October 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 4, book II, 68; W. F. Allen to John Adams, 4 October 1883. William F. Allen Papers, New York Public Library Archives, New York City, NY. Incoming Correspondence: Box 3, book VII, 299.

  64. Proceedings of General Time Convention (11 October 1883).

  65. Ibid.

  66. For U.S. and Canada, Proceedings of the Southern Railway Time Convention (17 October 1883).

  67. Proceedings of the General Time Convention (11 October 1883).

  68. W. F. Allen to Mayor Franklin Edson requests shift of New York time to 75th meridian; followed by Edson to Alderman, 24 October 1883, in J. S. Allen, ed., Standard Time (1951), 17.

  69. 7 November 1883, in J. S. Allen, ed., Standard Time (1951), 18.

  70. Barnard to Fleming, 22 October 1883. Fleming Papers.

  71. de Bernardières, “Déterminations télégraphique” (1884). On de Bernardières: Dossier sur Octave, Marie, Gabriel, Joachim de Bernardières, November 1886. Archives of the Service historique de la marine, Vincennes, No. 2879.

  72. Figure; details from www.porthcurno.org.uk/refLibrary/Construction.html, (accessed 14 February 2002).

  73. Green, Report on Telegraphic Determination (1877), 9–10.

  74. Report of the Superintendent of Coast Survey (1861), 23.

  75. Before the Civil War, the process had a rather improvisational quality. Dudley Observatory in Albany, New York, for example, aimed to determine its relative position to New York City by lofting a wire from a small wooden building assembled on the observatory site to the private residence of astronomer Lewis M. Rutherfurd, esquire, at Second Avenue and Eleventh Street in New York City. By B. A. Gould with observers George W. Dean with Edward Goodfellow, A. E. Winslow and A. T. Mosman, appendix 18, in Report of the Superintendent of the Coast Survey (1862), 221–23.

  76. Introduction, in Report of the Superintendent of the Coast Survey (1864); also ibid. Gould, appendix 18, 154–56; Report of the Superintendent of the Coast Survey (1866), esp. 21–23.

  77. Report of the Superintendent of the Coast Survey (1867), esp. 1–8 and ibid. Gould, appendix 14, 150–51.

  78. Report of the Superintendent of the Coast Survey (1867), 60.

  79. See, for example, Prescott, History (1866), esp. ch. XIV; Finn, “Growing Pains a
t the Crossroads” (1976); and Provincial Historic Site, “Heart’s Content Cable Station” (www.lark.ieee.ca/library/hearts-content/historic/provsite.html, accessed on 8 April 2002).

  80. On Gould’s earlier American work and his adoption of British techniques, see Bartky, Selling Time (2000), 61–72. On the transatlantic work, see Gould, in Report of the Superintendent of the Coast Survey (1869), 60–67.

  81. Gould, in Report of the Superintendent of the Coast Survey (1869), 61.

  82. Gould, in Report of the Superintendent of the Coast Survey (1869), 63, 65.

  83. Report of the Superintendent of the Coast Survey (1873), 16–18; appendix 18 in Report of the Superintendent (1877), 163–64. Triangle in ibid., 164.

  84. Green, Report on the Telegraphic Determination (1877).

  85. Green, Davis, and Norris, Telegraphic Determination of Longitudes (1880).

  86. Ibid., 8.

  87. Ibid., 9.

  88. Davis, Norris, and Laird, Telegraphic Determination of Longitudes (1885), 10.

  89. Ibid., 9.

  90. de Bernardières, “Déterminations télégraphiques” (1884).

  91. La Porte, “Détermination de la longitude” (1887).

  92. Rayet and Salats, “Détermination de la longitude” (1890), B2.

  93. Annex III in International Conference at Washington (1884), 210.

  94. Septième Conférence Géodésique Internationale (1883), 8.

  95. International Conference at Washington (1884), 24.

  96. Ibid., 37.

  97. Ibid., 39–41, on 39.

  98. Ibid., 41.

  99. Ibid., 42–47, on 47.

  100. Ibid., 42, 44, and 49–50.

  101. Ibid., 51.

  102. Ibid., 52–54.

  103. Ibid., 54.

  104. Ibid., 62–64, on 64.

  105. Ibid., 65–68, quotations on 65, 67, 68.

  106. Ibid., 68–69.

  107. Ibid., 76–80.

  108. Ibid., Lefaivre on 91–92; adoption of the metric system on 92–93; Thomson on 94; the vote, see 99.