Chapter 28. The View from the Crow’s Nest
169 “I believe that if a hundred”: Bertrand Russell, The Scientific Outlook, p. 34.
170 “a way of bewitching”: Quoted in de Santillana, The Crime of Galileo, p. 115.
170 Galileo put the book away: Ibid., pp. 106fn., 168.
171 “He discourses often amid fifteen”: Ibid., p. 112.
171 “If reasoning were like hauling”: Galileo, The Assayer.
175 “Shut yourself up with some friend”: Galileo, Dialogue Concerning the Two Chief World Systems. This discussion takes place on day two.
175 “A company of chessmen”: Locke, Essay Concerning Human Understanding, p. 98.
Chapter 29. Sputnik in Orbit, 1687
179 “It has been observed that missiles”: The passage is from Galileo’s Two New Sciences, quoted in David Goodstein and Judith Goodstein, Feynman’s Lost Lecture, p. 38.
181 Newton pictured it all: Newton drew the diagram in the 1680s, but it was first published after his death, in A Treatise of the System of the World, a less mathematical treatment of the Principia. See John Roche, “Newton’s Principia,” in Fauvel et al., eds., Let Newton Be!, p. 58.
Chapter 30. Hidden in Plain Sight
182 “My aim is to show”: Shapin, The Scientific Revolution, p. 33.
183fn “Music,” Leibniz wrote: Kline, Mathematics in Western Culture, p. 287.
183 “Galileo spent twenty years”: Gillispie, The Edge of Objectivity, p. 42.
Chapter 31. Two Rocks and a Rope
187 Unlike most legends: Crease, The Prism and the Pendulum, p. 31.
188 “In performing the experiment”: Ibid., p. 32.
188 When television shows a diver: Barry Newman, “Now Diving: Sir Isaac Newton,” Wall Street Journal, August 13, 2008.
Chapter 32. A Fly on the Wall
190 “I sleep ten hours”: Alfred Hooper, Makers of Mathematics (Vintage, 1948), p. 209.
192fn One prominent historian calls it: The historian was Salomon Bochner, in The Role of Mathematics in the Rise of Science (Princeton, NJ: Princeton University Press, 1966), p. 40. For more on the invention of the musical staff, see Alfred Crosby, The Measure of Reality: Quantification and Western Society, 1250–1600 (New York: Cambridge University Press, 1997), pp. 142–44.
193 “the greatest single step ever”: Livio, Is God a Mathematician?, p. 86.
Chapter 33. “Euclid Alone Has Looked on Beauty Bare”
194 known today as Cartesian coordinates: Descartes’ original presentation differed from the treatment that would become standard, but all the future changes were implicit in his version.
195 “I do not enjoy speaking in praise”: E. T. Bell, The Development of Mathematics, p. 139.
195 “a notable advance in the history”: Alfred North Whitehead, Science and the Modern World, p. 20. Scientists have now found that human infants and various nonhuman animals can count (they can distinguish between two M&Ms and three, for instance), but Whitehead’s point was that it took a breakthrough to see that such concepts as “twoness” were worth identifying.
195 “The point about zero”: Newman, ed., The World of Mathematics, vol. 1, p. 442.
196 Descartes wrestled to make sense: Helena M. Pycior, Symbols, Impossible Numbers, and Geometric Entanglements (New York: Cambridge University Press, 2006), p. 82.
197 Nor did it matter if the rock: Eugene Wigner makes this point in his pathbreaking essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”
198 If there were vacuums: Butterfield, The Origins of Modern Science, p. 3.
198fn The question of whether vacuums: Russell Shorto, Descartes’ Bones (New York: Doubleday, 2008), p. 25.
198 “Only by imagining an impossible”: A. Rupert Hall, From Galileo to Newton, p. 63. Hall cites the two passages from Galileo that I quote in his brilliant discussion of abstraction in science. See ibid., pp. 63–64. My comment about mathematics and abstraction in the final sentence of this chapter is also a paraphrase of Hall’s argument on his p. 63.
Chapter 34. Here Be Monsters!
202 Albert of Saxony, a logician: My discussion follows the one on pp. 52–55 of John Barrow’s admirably lucid The Infinite Book.
Chapter 35. Barricaded Against the Beast
210 For decades mathematicians had all tried: Struik, A Concise History of Mathematics, pp. 101–9.
Chapter 37. All Men Are Created Equal
219 Abraham Lincoln asked his listeners: Lincoln made his remark on October 15, 1858 (and in at least one earlier speech) in his last debate with Stephen Douglas. The complete text is at http://www.bartleby.com/251/72.html.
222 “The planet Mars comes close”: Kline, Mathematics in Western Culture, p. 230.
223 Perhaps infinitesimals were real but: Carl Boyer, The History of the Calculus and Its Conceptual Development, p. 213.
223 Leibniz tried to explain: William Dunham, The Calculus Gallery, p. 24.
223 “an enigma rather than”: Leibniz’s puzzled disciples were James and John Bernoulli, quoted in Kline, Mathematics: The Loss of Certainty, p. 137.
223 “the ultimate ratio”: Ibid., p. 135.
223 “In mathematics the minutest”: Ibid., p. 134.
223 calculus is the Latin: Donald Benson, A Smoother Pebble: Mathematical Explorations, p. 167.
224 “For science it cannot be”: George Berkeley, The Analyst: or A Discourse Addressed to an Infidel Mathematician (London, 1754), p. 34.
224 Leibniz, boundlessly optimistic: Dunham, The Calculus Gallery, p. 24, and Kline, Mathematics: The Loss of Certainty, p. 140.
224 “Persist,” d’Alembert advised: Kline, Mathematics: The Loss of Certainty, p. 162.
Chapter 38. The Miracle Years
226 Calculus was in the air: Most Newtonian scholars, including Newton’s most careful biographer, Richard Westfall, and the preeminent expert on Newton’s mathematical work, D. T. Whiteside, argue emphatically that Newton achieved his mathematical breakthroughs essentially on his own. For a contrary point of view, arguing that the influence of the Cambridge mathematician Isaac Barrow on Newton has been downplayed, see Mordechai Feingold’s “Newton, Leibniz, and Barrow, Too: An Attempt at a Reinterpretation,” Isis 84, no. 2 (June 1993), pp. 310–38.
226 market called Stourbridge Fair: Stourbridge Fair served as Bunyan’s inspiration for Vanity Fair in A Pilgrim’s Progress. See Edmund Venables, Life of John Bunyan (London: Walter Scott, 1888), p. 173.
226 “The way to chastity”: Gale Christianson, In the Presence of the Creator: Isaac Newton and his Times, p. 258.
227 Newton “read it ’til”: D. T. Whiteside, “Isaac Newton: Birth of a Mathematician,” p. 58.
227 “Read only the titles”: Westfall, Never at Rest, p. 98.
228 “The same year in May”: Ibid., p. 143.
229 “All this,” he wrote: Ibid.
229 “If you haven’t done”: Author interview, in Edward Dolnick, “New Ideas and Young Minds,” Boston Globe, April 23, 1984.
230 “Age is, of course, a fever chill”: Quoted in Dean Simonton, Creativity in Science (New York: Cambridge University Press, 2004), p. 68.
230 “I know that when”: Barrow, Pi in the Sky, p. 165.
230 “Look at a composer”: Author interview, in Dolnick, “New Ideas.”
231 “no old Men (excepting Dr. Wallis)”: Westfall, Never at Rest, p. 139.
231 From his earliest youth: Gale Christianson, “Newton the Man—Again.”
231 “difficulty & ill success”: Christianson, In the Presence of the Creator, p. 260.
232 He took the Latin form: Ackroyd, Newton, p. 39.
232 “I will give thee the treasures”: Christianson, Isaac Newton, p. 58. The verse is Isaiah 45:3.
232 “The fact that he was unknown”: Westfall, Never at Rest, p. 137.
232 “In 1665, as he realized”: Ibid., p. 138.
Chapter 39. All Mystery Banished
234 In fact, though, Leibniz felt: Sinc
e God was infinite, His creation was infinite as well, which meant that the process of finding new things to understand was never-ending. But this was a virtue, not a defect, because human happiness consisted in constantly finding new aspects of God’s perfection to admire.
234 “I don’t know what I may seem”: Westfall, Never at Rest, p. 863.
234 “As a blind man has no idea”: I. Bernard Cohen’s translation of Principia (Berkeley: University of California Press, 1999), p. 428.
236 “perhaps the most resolute champion”: Ernst Cassirer, “Newton and Leibniz,” p. 379.
Chapter 40. Talking Dogs and Unsuspected Powers
237 “In the century of Kepler”: C. H. Edwards, Jr., The Historical Development of the Calculus, p. 231.
237 “an aptitude that was hard to find”: Leibniz’s letter can be found at www.leibniz-translations.com, a marvelous website run by the English philosopher Lloyd Strickland. See http://www.leibniz-translations.com/dog.htm, “Account of a Letter from Mr. Leibniz to the Abbé de St. Pierre, on a Talking Dog.”
237 “a museum of everything”: Wiener, “Leibniz’s Project.”
238 “I have so much that is new”: Stewart, The Courtier and the Heretic, p. 256.
238 “If controversies were to arise”: Umberto Eco, The Search for the Perfect Language, p. 281. (See Chapter 14, “From Leibniz to the Encyclopédie.”)
238 Today a diligent team: Author interview with Lawrencc Carlin, philosophy department at the University of Wisconsin at Oshkosh, July 15, 2008.
238 “Leibniz was one of the supreme”: Russell, History of Western Philosophy, p. 581.
239fn Unbeknownst to Leibniz: Harriot’s work on the telescope is discussed by Albert Van Helden in his “Introduction” to Galileo’s Sidereal Messenger, p. 9, and his mathematical work is discussed in the online journal Plus. See Anna Faherty, “Thomas Harriot, A Lost Pioneer,” at http://plus.maths.org/issue50/features/faherty/.
239 “A container shall be provided”: George Dyson, Darwin Among the Machines, p. 37.
240 Leibniz’s knowledge of mathematics: Joseph E. Hofmann, Leibniz in Paris 1672–1676: His Growth to Mathematical Maturity, p.2.
240 “I read [mathematics] almost”: Dunham, The Calculus Gallery, p. 21.
241 his correspondence alone consisted: Stewart, The Courtier and the Heretic, p. 138.
242 At an elegant dinner party: A. Rupert Hall, Philosophers at War, p. 54.
242 Or perhaps he decided: The suggestions in this sentence and the next are from email correspondence with Simon Schaffer, a distinguished historian of science at Cambridge University, on September 27, 2009.
243 “6accdae13eff7i319n4o4qrr4s8t12ux”: Westfall, Never at Rest, p. 265.
243 Leibniz made no mention: Hall, Philosophers at War, p. 77.
Chapter 41. The World in Close-Up
252 “the philosopher’s stone that changed”: Bell, The Development of Mathematics, p. 134.
Chapter 42. When the Cable Snaps
254 We find good news: My discussion here of position, speed, and acceleration draws heavily on Ian Stewart’s elegantly written account in Nature’s Numbers, pp. 50–52.
256 “You can work out distances”: Stewart, Nature’s Numbers, p. 15.
257 Proust’s “little pieces of paper”: Marcel Proust, Swann’s Way, trans. Lydia Davis (New York: Viking, 2003), p. 51.
257 Of all the ways to fire a cannon: Paul Nahin, When Least is Best, p. 165. Nahin also discusses the physics of shooting a basketball.
258 “as dawn compares to the bright”: Dunham, The Calculus Gallery, p. 19, quoting James Gregory.
Chapter 43. The Best of All Possible Feuds
259 “one of the chief geometers”: Hall, Philosophers at War, p. 111. For any student of the Newton-Leibniz feud, Hall’s book is the essential text.
259 “I value my friends”: Ibid., p. 112.
259 “Taking Mathematicks from the beginning”: Westfall, Never at Rest, p. 721.
260 “the spectacle of the century”: Boorstin, The Discoverers, p. 413.
261 “round his brains such a thick crust”: William Henry Wilkins, The Love of an Uncrowned Queen: Sophia Dorothea, Consort of George I (New York: Duffield, 1906), p. 72.
262 “When in good humour Queen Anne”: Macaulay, History of England, vol. 5, p. 190.
262 the king’s only cultural interests: Plumb, The First Four Georges, p. 41.
262 The problems rose out of: The best source for the tangled affairs of the Hanover court is www.gwleibniz.com, a website maintained by the University of Houston philosopher Gregory Brown. See http://www.gwleibniz.com/sophie_dorothea_celle/sophie_dorothea_celle.html.
264 “I dare say,” Leibniz wrote: Gregory Brown, “Personal, Political, and Philosophical Dimensions of the Leibniz-Caroline Correspondence,” p. 271.
264 “The king has joked”: Ibid., p. 292.
265 “perhaps the most famous”: Ibid., p. 262.
265 The princess scolded her ex-tutor: Ibid., p. 282.
265 “the great men of our century”: Quoted at http://www.gwleibniz.com/caro oline_ansbach/caroline.html.
265 “What difference does it make”: Brown, “Leibniz-Caroline Correspondence,” p. 282.
Chapter 44. Battle’s End
266 “attempted to rob me”: Cited in Robert Merton’s classic essay “Priorities in Scientific Discovery: A Chapter in the Sociology of Science,” p. 635. Galileo’s charge comes at the very beginning of The Assayer.
266 “I certainly should be vexed”: Merton, “Priorities in Scientific Discovery,” p. 648.
267 “Almost no one is capable”: Alfred Adler, “Mathematics and Creativity,” New Yorker, February 19, 1972.
269 “I throw myself”: Westfall, Never at Rest, p. 724.
269 “numerous and skilful”: Ibid., p. 725.
270 “Mr. Leibniz cannot be”: The entire review is reprinted as an appendix to Hall’s Philosophers at War. The quoted passage appears on p. 298.
270 It, too, was written: Charles C. Gillispie, “Isaac Newton,” in Dictionary of Scientific Biography (New York: Scribner’s, 1970–80), vol. 10.
270 “broke Leibniz’ heart”: William Whiston, Historical Memoirs of the Life and Writings of Dr. Samuel Clarke (London, 1748), p. 132.
Chapter 45. The Apple and the Moon
271 “So few went to hear Him”: Westfall, Never at Rest, p. 209.
272 “In the year 1666”: Ibid., p. 154.
272 The story, which is the one thing: Westfall discusses the evidence pro and con in Never at Rest, pp. 154–55, and is more inclined than many to give the story some credence.
272 Despite his craving: Simon Schaffer, “Somewhat Divine,” London Review of Books, November 16, 2000, reviewing I. Bernard Cohen’s translation of Newton’s Principia.
272 Historians who have scrutinized: See Cohen’s “Introduction” to his translation of the Principia, p. 15, and Schaffer, “Somewhat Divine.”
273 “I began to think”: Westfall, Never at Rest, p. 143.
275 By combining Kepler’s third law: I. Bernard Cohen, “Newton’s Third Law and Universal Gravity,” p. 572.
277 “compared the force required”: Westfall, Never at Rest, p. 143.
Chapter 46. A Visit to Cambridge
279 In crowded rooms thick: Steven Shapin, “At the Amsterdam,” London Review of Books, April 20, 2006, reviewing The Social Life of Coffee by Brian Cowan. See also Mark Girouard, Cities and People (New Haven, CT: Yale University Press, 1985), p. 207.
279 Wren, still more skilled, confessed: Merton, “Priorities in Scientific Discovery,” p. 636.
279 “Mr. Hook said that he had it”: Roche, “Newton’s Principia,” in Fauvel et al., eds., Let Newton Be!, p. 58.
280 taverns with Peter the Great: Manuel, A Portrait of Isaac Newton, p. 318.
280 he would invent a diving bell: Alan Cook, Edmond Halley: Charting the Heavens and the Seas (New York: Oxford University Press, 1998), pp. 11, 140–41, 281.
280 “Sir Isaac replied immediately”: Westfall, Never at Rest, p. 403.
Chapter 47. Newton Bears Down
282fn The statement if a planet: Bruce Pourciau, “Reading the Master: Newton and the Birth of Celestial Mechanics,” and Curtis Wilson, “Newton’s Orbit Problem.”
283 Albert Einstein kept a picture: Dudley Herschbach, “Einstein as a Student,” available at http://tinyurl.com/yjptcq8.
283 “Nature to him”: This was from Einstein’s foreword to a new edition of Newton’s Opticks, published in 1931.
283 “Now I am upon”: Westfall, Never at Rest, p. 405.
283 “I never knew him take”: Ibid., p. 192.
284 “When he has sometimes taken”: Ibid., p. 406.
284 If everything attracted everything: Kuhn, The Copernican Revolution, p. 258.
285 “To do this business right”: Westfall, Never at Rest, p. 409.
285 “That all these problems”: Chandrasekhar, “Shakespeare, Newton, and Beethoven.”
287 “swallowed up and lost”: Westfall, Never at Rest, p. 456.
Chapter 48. Trouble with Mr. Hooke
288 “a nice man to deal with”: Henry Richard Fox Bourne, The Life of John Locke, vol. 2 (New York: Harper Brothers, 1876), p. 514.
289 “There is one thing more”: Westfall, Never at Rest, p. 446.
289 “Mr Hook seems to expect”: Manuel, A Portrait of Isaac Newton, p. 154.
289 “He has done nothing”: Ibid., p. 155.
289 “Philosophy [i.e., science] is such”: Ibid., p. 155.
290 He never replied to Hooke’s letter: Westfall, Never at Rest, pp. 387–88.
290 Newton had designed a telescope: Ibid., p. 233.
291 “poore & solitary endeavours”: Ibid., p. 237.
291 “the oddest, if not the most considerable”: Ibid., p. 237.
292 “Now is not this very fine”: Ibid., p. 448.
292 Hooke stalked out of the room: Manuel, A Portrait of Isaac Newton, p. 159.
292 Even twenty years after: Ibid., p. 137.
292 In the course of the move: Christianson, Isaac Newton, p. 106.
Chapter 49. The System of the World
293 “I must now again beg you”: Westfall, Never at Rest, p. 450.
294 If the universe had been governed by a different law: Martin Rees, Just Six Numbers, p. 150. See also Schaffer, “Somewhat Divine.”
The Clockwork Universe Page 29
