NOTES

CHAPTER ONE: MAGIC THAT WORKS

  1. 1. James Clerk Maxwell, quoted in Basil Mahon, The Man Who Changed Everything: The Life of James Clerk Maxwell (Chichester: Wiley, 2004), 48.
  2. 2. Aristotle, quoted in Kitty Ferguson, Pythagoras: His Lives and the Legacy of a Rational Universe (London: Icon Books, 2010), 108.
  3. 3. W. K. C. Guthrie, quoted in ibid., 74.
  4. 4. Richard P. Feynman, as told to Ralph Leighton, “Surely You’re Joking Mr. Feynman!”: Adventures of a Curious Character, ed. Edward Hutchings (New York: W. W. Norton, 1997), 132.
  5. 5. David Hume, An Enquiry Concerning Human Understanding, ed. Peter Millican (Oxford: Oxford University Press, 2008), 5.
  6. 6. Ibid., 6.
  7. 7. David Hume to “Jemmy” Birch, 1785, letter, quoted in E. C. Mossner, The Life of David Hume (Oxford: Oxford University Press, 2011), 626.
  8. 8. David Hume, An Enquiry Concerning Human Understanding, ed. Peter Millican (Oxford: Oxford University Press, 2008), 12.
  9. 9. Ibid., 45.
  10. 10. Ibid., 120.
  11. 11. Ibid., 45.
  12. 12. See, for example, “Geometry and Experience,” Albert Einstein’s address to the Prussian Academy of Sciences, Berlin, January 27, 1921, in Sidelights on Relativity., trans. G. B. Jeffery and W. Perrett (1922; repr., Mineola, NY: Dover, 1983), 8–16.
  13. 13. Leonardo da Vinci, Selections from the Notebooks of Leonardo da Vinci, ed. Irma Richter (London: Oxford University Press, 1971), 2.
  14. 14. Ibid., 7.
  15. 15. The Notebooks of Leonardo da Vinci, vol. 1, Wikisource, accessed July 4, 2012, http://en.wikisource.org/wiki/The_Notebooks_of_Leonardo_Da_Vinci/I.
  16. 16. Albert Einstein, “Geometry and Experience” (address to the Prussian Academy of Sciences, Berlin, January 27, 1921), in Sidelights on Relativity, trans. G. B Jeffery and W. Perrett (1922; repr., Mineola, NY: Dover, 1983), 8.
  17. 17. Wikipedia, s.v. “Mathematical Beauty,” accessed July 3, 2012, http://en.wikipedia.org/wiki/Mathematical_beauty.
  18. 18. For an interesting discussion of this, see Eugene P. Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (Richard Courant Lecture in Mathematical Sciences, New York University, May 11, 1959), Communications on Pure and Applied Mathematics 13, no. 1 (1960):1–14.
  19. 19. Albert Einstein, quoted in Dava Sobel, Galileo’s Daughter: A Historical Memoir of Science, Faith, and Love (New York: Walker, 1999), 326.
  20. 20. John Maynard Keynes, “Newton the Man,” speech prepared for the Royal Society, 1946. See http://www-history.mcs.st-and.ac.uk/Extras/Keynes_Newton.html.
  21. 21. Arthur Herman, How the Scots Invented the Modern World: The True Story of How Western Europe’s Poorest Nation Created Our World and Everything in It (New York: Three Rivers, 2001), 190.
  22. 22. George Elder Davie, The Democratic Intellect: Scotland and Her Universities in the Nineteenth Century (Edinburgh: Edinburgh University Press, 1964), 150.
  23. 23. J. Forbes, quoted in P. Harman, ed., The Scientific Letters and Papers of James Clerk Maxwell, vol. 1, 1846–1862 (Cambridge: Cambridge University Press, 1990), 8.
  24. 24. Alan Hirshfeld, The Electric Life of Michael Faraday (New York: Walker, 2006), 185.
  25. 25. John Meurig Thomas, “The Genius of Michael Faraday,” lecture given at the University of Waterloo, 27 March 2012.
  26. 26. These are Cartesian coordinates, invented by the French philosopher René Descartes.
  27. 27. Michael Faraday to J. C. Maxwell, letter, 25 March 1857, in
    P. Harman, ed., The Scientific Letters and Papers of James Clerk Maxwell, vol. 1, 1846–1862 (Cambridge: Cambridge University Press, 1990), 548.
  28. 28. Alan Hirshfeld, The Electric Life of Michael Faraday (New York: Walker, 2006), 185.
  29. 29. J. C. Maxwell to Michael Faraday, letter, 19 October 1861, in P. Harman, ed., The Scientific Letters and Papers of James Clerk Maxwell, vol. 1, 1846–1862 (Cambridge: Cambridge University Press, 1990), 684–86.

CHAPTER TWO: OUR IMAGINARY REALITY

  1. 30. John Bell, “Introduction to the Hidden-Variable Question” (1971), in Quantum Mechanics, High Energy Physics and Accelerators: Selected Papers of John S. Bell (with Commentary), ed. M. Bell, K. Gottfried, and M. Veltman (Singapore: World Scientific, 1995), 716.
  2. 31. Albert Einstein, “How I Created the Theory of Relativity,” trans. Yoshimasa A. Ono, Physics Today 35, no. 8 (1982): 45–7.
  3. 32. Carlo Rovelli, The First Scientist: Anaximander and His Legacy (Yardley, PA: Westholme, 2011).
  4. 33. Wikipedia, s.v. “Anaximander,” accessed April 15, 2012, http://en.wikipedia.org/wiki/Anaximander, and “Suda,” accessed April 15, 2012, http://en.wikipedia.org/wiki/Suda.
  5. 34. Werner Heisenberg, “Quantum-Mechanical Re-interpretation of Kinematic and Mechanical Relations,” in Sources of Quantum Mechanics, ed. B. L. van der Waerden (Amsterdam: North-Holland, 1967), 261–76.
  6. 35. Werner Heisenberg, quoted in J. C. Taylor, Hidden Unity in Nature’s Laws (Cambridge: Cambridge University Press, 2001), 225.
  7. 36. Lauren Redniss, Radioactive: Marie and Pierre Curie: A Tale of Love and Fallout (HarperCollins, 2010), 17.
  8. 37. Werner Heisenberg, quoted in F. Selleri, Quantum Paradoxes and Physical Reality (Dordrecht, Netherlands: Kluwer, 1990), 21.
  9. 38. Wikipedia, s.v., “Max Planck,” accessed July 10, 2012, http://en.wikipedia.org/wiki/Max_Planck.
  10. 39. Ibid.
  11. 40. Ibid.
  12. 41. Albert Einstein, quoted in Abraham Pais, Inward Bound: Of Matter and Forces in the Physical World (New York: Oxford University Press, 1986), 134.
  13. 42. Susan K. Lewis and Neil de Grasse Tyson, “Picturing Atoms” (transcript from NOVA ScienceNOW), PBS, accessed July 4, 2012, http://www.pbs.org/wgbh/nova/physics/atoms-electrons.html.
  14. 43. Clifford Pickover, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (New York: Sterling, 2009), 118–24.
  15. >44. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, vol. 1 (Reading, MA: Addison-Wesley, 1964), 22.
  16. 45. Werner Heisenberg, “Ueber den anschaulichen Inhalt der quantentheoretischen Kinematik and Mechanik,” Zeitschrift für Physik 43 (1927), 172–98. English translation in John Archibald Wheeler and Wojciech H. Zurek, eds., Quantum Theory and Measurement (Princeton, NJ: Princeton University Press, 1983), 62–84.
  17. 46. There is a beautiful animation of diffraction and interference from two slits on Wikipedia, s.v. “Diffraction,” accessed July 2, 2012, http://en.wikipedia.org/wiki/Diffraction.
  18. 47. F. Scott Fitzgerald, The Crack-Up (New York: New Directions, 1993), 69.
  19. 48. Werner Heisenberg, Physics and Beyond: Encounters and Conversations (New York: Harper & Row, 1971), 81.
  20. 49. Irene Born, trans., The Born-Einstein Letters, 1916–1955: Friendship, Politics and Physics in Uncertain Times (New York: Walker, 1971), 223.
  21. 50. My discussion here is a simplified version of David Mermin’s simplified version of Bell’s Theorem, presented in N. D. Mermin, “Bringing Home the Atomic World: Quantum Mysteries for Anybody,” American Journal of Physics 49, no. 10 (1981): 940. See also Gary Felder, “Spooky Action at a Distance ” (1999), North Carolina University, accessed July 4, 2012, http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html.
  22. 51. H. Minkowski, “Space and Time,” in H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, The Principle of Relativity, trans. W. Perrett and G. B. Jeffery (1923; repr., Mineola, NY: Dover Publications, 1952), 75–91.

CHAPTER THREE: WHAT BANGED?

  1. 52. Thomas Huxley, “On the Reception of the Origin of Species” (1887), in Francis Darwin, ed., The Life and Letters of Charles Darwin, vol. 1 (New York: Appleton, 1904), accessed online at http://www.gutenberg.org/files/2089/2089-h/2089-h.htm.
  2. 53. John Archibald Wheeler, “How Come the Quantum?” Annals of the New York Academy of Sciences 480, no. 1 (1986): 304–16.
  3. 54. Albert Einstein, quoted in Antonina Vallentin, Einstein: A Biography (Weidenfeld & Nicolson, 1954), 24.
  4. 55. Luc Ferry, A Brief History of Thought: A Philosophical Guide to Living (New York: Harper Perennial, 2011), 19.
  5. 56. Albert Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunk,” Annalen der Physik 17, no. 6 (1905), 132–48. A good Wikisource translation is available online at http://en.wikisource.org/wiki/On_a_Heuristic_Point_of_View_about_the_Creation_and_Conversion_of_Light.
  6. 57. Albert Einstein, “Maxwell’s Influence on the Development of the Conception of Physical Reality,” in James Clerk Maxwell: A Commemorative Volume (New York: Macmillan, 1931), 71.
  7. 58. Max Planck invented so-called Planck units when thinking of how to combine gravity with quantum theory. The Planck scale is Lp = (hG/c3)1/2 = 4 × 10−35 metres, a combination of Newton’s gravitational constant; Planck’s constant, h; and the speed of light, c. Below the Planck length, the effects of quantum fluctuations become so large that any classical notion of space and time becomes meaningless. The Planck energy is the energy associated with a quantum of radiation with a wavelength equal to the Planck length, Ep = (hc5/G)1/2 = 1.4 MWh.
  8. 59. Albert Einstein, quoted in Frederick Seitz, “James Clerk Maxwell (1831–1879), Member APS 1875,” Proceedings of the American Philosophical Society 145, no. 1 (2001): 35. Available online at: http://www.amphilsoc.org/sites/default/files/Seitz.pdf.
  9. 60. Albert Einstein and Leopold Infeld, The Evolution of Physics (New York: Simon & Schuster, 1938), 197–8.
  10. 61. John Archibald Wheeler and Kenneth William Ford, Geons, Black Holes, and Quantum Foam: A Life in Physics (New York: W. W. Norton, 2000), 235.
  11. 62. George Bernard Shaw, “You Have Broken Newton’s Back,” in The Book of the Cosmos: Imagining the Universe from Heraclitus to Hawking, ed. D. R. Danielson (New York: Perseus, 2000), 392−3.
  12. 63. Irene Born, trans., The Born-Einstein Letters, 1916–1955: Friendship, Politics and Physics in Uncertain Times (New York: Walker, 1971), 223.
  13. 64. John Farrell, The Day Without Yesterday: Lemaître, Einstein, and the Birth of Modern Cosmology (New York: Basic Books, 2010), 10.
  14. 65. Ibid, 207.
  15. 66. Abbé G. Lemaître, “Contributions to a British Association Discussion on the Evolution of the Universe,” Nature 128 (October 24, 1931), 704–6.
  16. 67. Duncan Aikman, “Lemaître Follows Two Paths to Truth,” New York Times Magazine, February 19, 1933.
  17. 68. Gino Segrè, Ordinary Geniuses: Max Delbrück, George Gamow, and the Origins of Genomics and Big Bang Cosmology (London: Viking, 2011), 146.
  18. 69. U.S. Space Objects Registry, accessed July 4, 2012, http://usspaceobjectsregistry.state.gov/registry/dsp_DetailView.cfm.
  19. 70. Adam Frank, About Time: Cosmology and Culture at the Twilight of the Big Bang (New York: Free Press, 2011), 196–201.
  20. 71. Technically, this means that the cosmological constant is the unique type of matter that is Lorentz-invariant.
  21. 72. See Paul J. Steinhardt and Neil Turok, Endless Universe: Beyond the Big Bang (London: Weidenfeld & Nicolson, 2007).
  22. 73. Cicero, On the Nature of the Gods, Book II, Chapter 46, quoted in ibid., 171.
  23. 74. G. Lemaître, “L’Univers en expansion,” Annales de la Société Scientifique de Bruxelles A21 (1933): 51.

CHAPTER FOUR: THE WORLD IN AN EQUATION

  1. 75. Paul Dirac, quoted in Graham Farmelo, The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (New York: Basic Books, 2010), 435.
  2. 76. H. Weyl, “Emmy Noether,” Scripta Mathematica 3 (1935): 201–20, quoted in Peter Roquette, “Emmy Noether and Hermann Weyl” (2008), an extended manuscript of a talk given at the Hermann Weyl Conference, Bielefield, Germany, September 10, 2006 (see http://www.rzuser.uni-heidelberg.de/~ci3/weyl+noether.pdf), 22.
  3. 77. Albert Einstein, “The Late Emmy Noether,” letter to the editor of the New York Times, published May 4, 1935.
  4. 78. Helge Kragh, “Paul Dirac: The Purest Soul in an Atomic Age,” in Kevin C. Knox and Richard Noakes, eds., From Newton to Hawking: A History of Cambridge University’s Lucasian Professors of Mathematics (Cambridge: Cambridge University Press, 2003), 387.
  5. 79. John Wheeler, quoted by Sir Michael Berry in an obituary of Dirac. Available online at http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry130.pdf .
  6. 80. P. A. M. Dirac, “The Evolution of the Physicist’s Picture of Nature,” Scientific American 208, no. 5 (May 1963): 45–53.

CHAPTER FIVE: THE OPPORTUNITY OF ALL TIME

  1. 81. The sole surviving fragment of Anaximander’s works, as quoted by Simplicius (see http://www.iep.utm.edu/anaximan/#H4).
  2. 82. Louis C. K., during an appearance on Late Night with Conan O’Brien, originally aired on NBC on February 24, 2009.
  3. 83. John Gertner, The Idea Factory: Bell Labs and the Great Age of American Innovation (New York: Penguin, 2012).
  4. 84. Ibid., 149–52.
  5. 85. See the 1956 Nobel Prize lectures by Shockley, Brattain, and Bardeen, all of which are available online at http://www.nobelprize.org/nobel_prizes/physics/laureates/1956/.
  6. 86. Michael Riordan and Lillian Hoddeson, Crystal Fire: The Invention of the Transistor and the Birth of the Information Age (New York: W. W. Norton, 1997), 115–41.
  7. 87. Sebastian Loth et al., “Bistability in Atomic-Scale Antiferromagnets,” Science 335, no. 6065 (January 2012): 196. For a lay summary, see http://www.ibm.com/smarterplanet/us/en/smarter_computing/article/atomic_scale_memory.html.
  8. 88. In fact, the quantum state of a qubit is specified by two real numbers, giving the location on a two-dimensional sphere.
  9. 89. A theorem due to Euclid, called the fundamental theorem of arithmetic, shows that such a factoring is unique.
  10. 90. Marshall McLuhan, Understanding Me: Lectures and Interviews, ed. Stephanie McLuhan and David Staines (Toronto: McClelland & Stewart, 2005), 56.
  11. 91. Marshall McLuhan and Bruce Powers, Global Village: Transformations in World Life and Media in the 21st Century (New York: Oxford University Press, 1992), 143.
  12. 92. Pierre Teilhard de Chardin, quoted in Tom Wolfe’s foreword to Marshall McLuhan, Understanding Me: Lectures and Interviews, ed. Stephanie McLuhan and David Staines (Toronto: McClelland & Stewart, 2005), xvii.
  13. 93. Pierre Teilhard de Chardin, The Phenomenon of Man (Harper Colophon, 1975), 221.
  14. 94. Julian Huxley, in introduction to Pierre Teilhard de Chardin, The Phenomenon of Man (HarperCollins Canada, 1975), 28.
  15. 95. Marshall McLuhan and Quentin Fiore, The Medium Is the Massage: An Inventory of Effects (Toronto: Penguin Canada, 2003), 12.
  16. 96. Brian Aldiss, The Detached Retina: Aspects of SF and Fantasy (Liverpool: Liverpool University Press, 1995), 78.
  17. 97. Richard Holmes, The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science (London: HarperPress, 2008), 295.
  18. 98. Ibid., 317.
  19. 99. Mary Shelley, Frankenstein, 3rd ed. (1831; repr., Mineola, NY: Dover, 1994), 31–2.
  20. 100. Percy Bysshe Shelley, “A Defence of Poetry” (1821), available online at http://www.bartleby.com/27/23.html.
  21. 101. Mary Shelley, The Last Man (1826; repr., Oxford: Oxford University Press, 2008), 106.
  22. 102. Ibid., 219.
  23. 103. Ibid., 470.
  24. 104. Ibid., 220.
  25. 105. D. Albert, “On the Origin of Everything,” New York Times, March 23, 2012.
  26. 106. Steven Weinberg, The First Three Minutes: A Modern View of the Origin of the Universe (New York: Basic Books, 1977), 144.
  27. 107. Richard Feynman, The Pleasure of Finding Things Out (London: Penguin, 2007), 248.
  28. 108. Richard Feynman, “The Uncertainty of Science,” in The Meaning of It All: Thoughts of a Citizen Scientist (New York: Perseus, 1998), 3.
  29. 109. Basil Mahon, The Man Who Changed Everything: The Life of James Clerk Maxwell, (Chichester: Wiley, 2004), 45.
  30. 110. See, for example, Elizabeth Asmis, Epicurus’ Scientific Method (Ithaca, NY: Cornell University Press, 1984).