The Universe Within (28 page)

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).
    

FURTHER READING

Albert, David.
Quantum Mechanics and Experience
. Cambridge, MA: Harvard University Press, 1994.

Deutsch, David.
The Beginning of Infinity
. New York: Viking, 2011.

Diamandis, Peter H., and Steven Kotler.
Abundance: The Future is Better Than You Think
. New York: Free Press, 2012.

Falk, Dan.
In Search of Time: Journeys Along a Curious Dimension.
Toronto: McClelland & Stewart, 2008.

Gowers, Timothy.
Mathematics
. New York: Sterling, 2010.

Greene, Brian.
The Fabric of the Cosmos: Space, Time and the Texture of Reality.
New York: Vintage, 2005.

Guth, Alan.
The Inflationary Universe: The Quest for a New Theory of Cosmic Origins
. New York: Basic Books, 1998.

Hawking, Stephen.
A Brief History of Time
. New York: Bantam, 1998.

Penrose, Roger.
The Road to Reality: A Complete Guide to the Laws of the Universe
. New York: Vintage, 2007.

Sagan, Carl.
Cosmos
. New York: Ballantine, 1985.

Steinhardt, Paul J., and Neil Turok.
Endless Universe: Beyond the Big Bang — Rewriting Cosmic History.
New York: Broadway, 2008.

Weinberg, Steven.
The First Three Minutes: A Modern View of the Origin of the Universe
. New York: Basic Books, 1993.

Zeilinger
,
Anton.
Dance of the Photons: From Einstein to Quantum Teleportation
. New York: Farrar, Straus & Giroux, 2010.

PERMISSIONS

Permission is gratefully acknowledged to reprint the following images:

Glenlair © Courtesy of Cavendish Laboratory, Cambridge

Force Field © Neil Turok

Raphael (Raffaello Sanzio) (1483–1520).
The School of Athens.
ca. 1510–1512. Fresco. © Scala/Art Resource, NY

Fifth Solvay Conference 1927 © Photograph by Benjamin Couprie, Institut International de Physique Solvay, courtesy
AIP
Emilio Segre Visual Archives

Double-Slit Experiment © Neil Turok

Big bang © Neil Turok

COBE
Temperature Fluctuations ©
NASA

Dark Matter ©
NASA

AIMS South Africa © African Institute for Mathematical Sciences

AIMS
South Africa Students © Neil Turok

All Known Physics Equation © Neil Turok

ATLAS
Experiment © 2012
CERN

“God Particle” ©
Fabrice Coffrini/Getty Images

 

ACKNOWLEDGEMENTS

I WOULD LIKE TO
express my heartfelt thanks to my friends and colleagues at the Perimeter Institute for Theoretical Physics, a place for quantum leaps in space and time. Their constant encouragement and steadfast support kept me going as I struggled to prepare this manuscript. Once again, they made me realize how fortunate I am to be a part of this unique community. A special thanks is due to Mike Lazaridis, Perimeter's founder and the most visionary supporter our field ever had, and to those who ensure the institute maintains the highest standards of management and communications, including Michael Duschenes and John Matlock.

Throughout this project, Alexandra Castell lent me continuous assistance. Natasha Waxman played a major role researching and helping to prepare early drafts, ably assisted by Erin Bow and Ross Diener. Daniel Gottesman, Lucien Hardy, Adrian Kent, Rob Myers, Lee Smolin, and Paul Steinhardt generously read drafts and provided invaluable comments. I have benefitted from discussions with many scientific colleagues on these topics, including Itzhak Bars, Laurent Freidel, Stephen Hawking, Ray Laflamme, Sandu Popescu, and Xiao-Gang Wen. Malcolm Longair very kindly shared with me the proofs of his fascinating new book on the historical origins of quantum mechanics,
Quantum Concepts in Physics.
Thank you for your enthusiasm and your wisdom. Naturally, whatever errors and misconceptions remain in this book are entirely my own. Many thanks to Chris Fach and Erick Schnetter for help preparing the illustrations.

A huge thank you to all my partners in the African Institute for Mathematical Sciences (
AIMS
) project, and to all our wonderful students. Let me mention in particular Barry Green and Thierry Zomahoun. It is a constant pleasure to work with you and for you. I thank you for your patience and understanding during the writing of this book, and for your tireless commitment to our shared cause.

Philip Coulter at the
CBC
and Janie Yoon at House of Anansi Press deserve special gratitude for stepping in with inspirational advice at a critical time. Janie in particular found the right combination of praise and tough love to keep me on track. If this manuscript is at all readable, it is due to your heroic efforts.

And last but first, big hugs to Corinne and Ruby without whom I would be lost.

 

INDEX

 

Aberdeen, University of, 31, 36, 251

Africa, 7, 31; mathematics/science in, 8, 159; need for scientific education in, 156–67

African Institute for Mathematical Sciences (
AIMS
), 160–67; success stories of, 163, 164–65

African National Congress (
ANC
), 160

Albert, David, 247

Aldini, Giovanni, 241

Alexander the Great, 55

algebra, 32, 197; complex numbers in, 74–77, 168–69, 170; and Euler's formula, 75–76, 170; and inclusion of
i
, 73–74, 93, 170; Noether's work in, 181; Renaissance books on, 73, 74

Alhazen (Ibn al-Haytham):
Book of Optics
, 17

Alpher, Ralph, 127–28, 130

Amazon.com, 204

Ampère, André-Marie, 44–45

analog vs digital technology, 203, 230–33, 237–39

Anaximander, 9, 52–55, 153, 202, 205, 207

Anderson, Carl D., 173

Anderson, Philip, 174

Andromeda Galaxy, 105

apartheid, in South Africa, 1–3, 21–22, 157–58; end of, 3, 160

Apollo 11 mission, 22, 129

Apollo 13 mission, 23

Archimedes, 18, 98

Aristotle, 25, 52

arithmetic, 8, 10, 74, 269n9

Armstrong, Neil, 22

art: and geometry, 16, 17.
See also
Leonardo da Vinci; Raphael

Aspect, Alain, 90

astronomers, 25, 122, 126, 123–24, 134–35, 157, 245

astronomy, 8, 10, 98, 129; and discovery of dark matter, 134–35; and heliocentric universe, 20–21, 25, 100; Hubble's work in, 123–24; Maxwell's work and, 36; Newton's work and, 24–25, 29–30

AT&T
, 128, 214.
See also
Bell Labs

atomic bomb, 10, 116, 125–26

Australian National University, 137

 

Babylon, 8, 18

background radiation.
See
radiation, cosmic microwave

Bardeen, John, 216–17

Bayes, Thomas, 32

Bell, Alexander Graham, 35, 213–14

Bell, John, 51.
See also
Bell's Theorem

Bell Labs (New Jersey), 128, 129, 214–16, 220, 234

Bell Rock Lighthouse (Scotland), 32

Bell's Theorem, 83–91, 233–34; illustration of, 85–90

Bible, 1–2, 24

big bang theory, 103–6, 136, 200–1, 228, 236; background radiation and, 127–30, 214; dark matter and, 134–35, 138; Lemaître's proposal of, 124–25, 228; singularity and, 97, 122–25, 142–50, 200, 207–9; theory of inflation and, 106–10, 136, 139–52; Weinberg's book on, 247–48.
See also
singularity, at moment of big bang

Biot-Savart law, 44

Bohm, David: hidden variable theory of, 83–84

Bohr, Niels, 58–59, 76, 126, 197, 199; on Dirac, 185; and quantization of atomic structure, 58, 70–72, 76, 124;
at Solvay Conference, 58–59, 80–81; and wave-particle duality, 80

Bolt, Usain, 49

Boltzmann, Ludwig: equipartition principle of, 65–66

Bombelli, Rafael:
Algebra
, 74

Borges, Jorge Luis, 223

Born, Max, 57, 58, 59, 180, 199; on general relativity, 119; and matrix mechanics, 58; on Planck, 61; on Schrödinger's wavefunction, 76–77

Brahe, Tycho, 25

Brattain, Walter, 216

Brin, Sergey, 166

Brout, Robert, 174

Bryn Mawr College, 180

 

calculus, 26, 43, 101

California, University of: at Berkeley, 133, 137; at Santa Barbara, 219

Cambridge University, 31; author's tenure at, 96–97, 98, 143, 151–52, 160, 161; cosmology workshop at, 106, 136; Dirac at, 182; Gamow at, 126; Maxwell at, 35, 42, 251; Newton at, 24, 223.
See also
Hawking, Stephen

Cape Town: and
AIMS
, 160–67; University of, 160

Cardano, Gerolamo:
Ars Magna
(
The Great Art
), 73, 74

Carnie, Margaret, 22, 97–99

cellphones, 47, 160, 214.
See also
smartphones

CERN
(European Organization for Nuclear Research), 84, 192.
See also
Large Hadron Collider

Cicero:
On the Nature of the Gods
, 153

classical physics/universe: Newton and, 20, 25–26, 30, 48, 56–95, 112, 118–19, 206, 210; quantum theory and, 48, 56–95, 115–16, 168, 171, 179–80, 183–85, 196, 206, 210, 234–35, 256.
See also
quantum theory

communication/information technology, 5, 56, 91, 209–39; Bell/Bell Labs and, 35, 213–14, 215; and democratic movements, 203; and information overload, 68–69, 203, 209–11; McLuhan on, 225–27, 230; as problematic, 198, 203, 209; satellites and, 128–29, 151–52, 205, 236, 237; Teilhard de Chardin on, 227–28, 230; transistor and, 215–17, 218, 235; vacuum tubes and, 212–13, 215

complex numbers, 74–75, 168–71; and Euler's formula, 75–76, 170–71; and Schrödinger's wave equation, 76–77, 168–70, 171

computers, 68–69, 167–68, 170, 203, 209, 212, 213, 214; digital nature of, 230–33, 237–38; predictions about, 227–28, 230; quantum, 218–25, 233, 238–39; storage capacity of, 217–18.
See also
quantum computers

conserved quantities, Noether's theorem on, 176–78, 179–80

Copenhagen, University of, 59, 126

Copernicus, and concept of heliocentric universe, 20, 21, 25, 100

Cosmic Background Explorer (
COBE
), 130–36; and
DMR
experiment, 132–36; and
FIRAS
experiment, 131–32

“cosmological term” (Einstein), 120–21, 122; and vacuum energy, 136–37

cosmology, historical: of ancient Greece, 8–9, 20, 25, 52–53, 99–100, 102, 118, 152–53, 205; of Newtonian universe, 20, 25–26, 30, 48, 56–95, 112, 118–19, 206, 210; of Renaissance Italy, 18, 20–21, 25, 28–29, 100–1, 205

cosmology, modern, 96–155; background radiation and, 127–33, 214; complex numbers and, 75, 95; cyclic universe theory of, 149–54; dark matter and, 134–35, 138; Einstein and, 110–13, 118–22; Friedmann and, 121–23; Gamow and, 125–28; inflationary theory of, 106–10, 136, 139–54; Lemaître and, 123–25; vacuum energy and, 136–38.
See also
big bang theory; singularity, at moment of big bang

Cosmos
(television series), 157

Coulomb, Charles Augustin de, 44

Croton (southern Italy): Pythagoreans and, 9

Curie, Marie, 58, 59, 70, 91, 126

Curie, Pierre, 58, 70

cyclic universe, theory of, 149–52; precursors of, 153–54.
See also
inflation, theory of

 

dark matter, 134–35, 138, 187, 200

Darwin, Charles: library of, 223; and theory of evolution, 228, 229, 246–47

Davy, Sir Humphrey: Bakerian Lecture by, 240–41; and Faraday, 36–37, 251

Dawkins, Richard, 246–47

Dicke, Robert, 130, 131

Differential Microwave Radiator (
DMR
), 132–36

digital vs analog technology, 203, 230–33, 237–39

diodes, 213, 215

Dirac, Paul, 58, 59, 60, 181–87, 197; “bra-ket” notation of, 181; education of, 181–82; and Feynman's formulation, 92, 183–84; on mathematics, 156, 183, 185–87; matter particle equation of, 92, 172–73, 174, 175–76, 182–83, 196, 199; and prediction of positron, 92, 173, 182; and quantum electrodynamics, 92, 183; and quantum theory, 182, 183–85; on Schrödinger's wave equation, 186; unassuming personality of, 182, 185, 187

Dirac field (
ψ
), 173, 174, 175–76

DNA
, 200, 201, 231–33, 239

“double-slit experiment,” 78–80, 93

 

e
(Euler's number), 75, 92, 170–71

Echo 1 (balloon satellite), 128, 129

Eda, Abonnema (fictional character), 157, 167

Eddington, Arthur, 121, 124

Edinburgh, 31–32, 185

Edinburgh, University of, 11, 31, 32, 35, 213

education, scientific: in Africa, 156–67; in ancient Greece, 51–53, 211; of Dirac, 181–82; in internet age, 5, 203, 211–12, 255; of Maxwell, 34–35; in medieval universities, 10; Noether's contribution to, 178–81; of Scottish Enlightenment, 32, 34, 211, 213

Ehrenfest, Paul, 59

Einstein, Albert, 18, 21, 49, 51, 59, 99, 106, 109, 186, 197, 199, 204, 206, 210; and confirmation of Planck's work, 64–70, 72; “cosmological term” of, 120–21, 122, 136–39; Dirac on, 184; Hume's influence on, 14; and initial unease over quantum theory, 70, 77, 80–81, 91; as invoked by
AIMS
, 164–65; and mass-energy equivalence, 113–16; and Maxwell's theory, 47–48, 101–2, 110–12; on Noether, 180–81; and photoelectric effect, 58, 69; at Solvay Conference, 58, 59, 80–81; and theory of general relativity, 116–25, 133, 147, 165, 172, 174, 179, 189–90, 193, 195, 196, 199; and theory of special relativity, 47, 94, 101–2, 110–16, 138–39; and “ultraviolet catastrophe,” 68–69, 196

Einstein–Poldolsky–Rosen critique of quantum theory, 81–82, 233–34; and Bell's Theorem, 83–91, 234; Pauli
on, 82

ekpyrosis
(Stoic concept of cosmology), 153

electricity: Faraday's work on,
37–39; and modern electro­nics, 212–18; and plot of
Frankenstein
, 37, 240–42; public experiments using, 37, 241; quantum theory and, 92, 214–18

electromagnetic waves: and background radiation, 127–30; and big bang theory, 103–6, 123–24, 127–30; and colour of light, 47, 61–62, 64, 68, 123–24; length of, 47, 61–62, 65–68, 71–72, 190, 210, 265n7; and mass-energy equivalence, 114–15; and quantum theory, 61–72; speed of, 45–46; types/applications of, 47, 111

electromagnetism, 39–40; and big bang theory, 103–6, 123–24, 127–30; and electroweak theory, 172, 174; Faraday's work on, 38, 40–42, 45, 84; Maxwell's work on, 34, 36, 39, 42–48, 56, 61, 63, 84, 92, 101, 110–12, 115, 172, 174, 175, 210; and Newton's theories, 33, 40–41, 43, 47; previous work related to, 44–45; and quantum theory, 46, 48, 61–72, 101–2

electroweak theory, 107, 172, 173, 174, 178, 188, 196

Englert, François, 174

Epicurus, 253

Erlangen, University of, 178

ethics: Hume on, 14–15; of reciprocity, 253

Euclid, 52, 269n9

Euler, Leonhard, 75, 170, 192; beta function formula of, 192

Euler's formula (complex analysis), 75, 170–71; Heisenberg's use of, 75–78; and number
e
, 75, 92, 170–71; and number
i
, 75, 170

European Space Agency, 151.
See also
Planck satellite

evolution, theory of (Darwin), 228, 229, 246–47

 

Facebook, 204

Fairchild Semiconductor, 217

Faraday, Michael, 33, 36–42, 50, 101; and concept of force field, 39, 40–42, 43, 45, 84; and Davy, 36–37, 251; and electricity, 37–39; and electromagnetism, 38, 40–42, 45, 84; Maxwell's continuation of work by, 36, 39, 42–48, 84, 101, 111; and Newton's law of gravitation, 40–41, 116–17; as non-mathematician, 39, 42; as tireless experimenter, 38–39, 42

Far Infrared Absolute Spectrophotometer (
FIRAS
), 131–32

Fermat, Pierre de, 62

Ferro, Scipione del, 73–74

Feynman, Richard, 249, 250; on Euler's formula, 75; and formulation of quantum theory (“sum over histories”), 92–93, 169–70, 171, 179, 183–84, 196; on nuclear bomb, 10; on quantum computers, 219–20; and quantum electrodynamics, 92, 183

Fifth Solvay International Conference on Electrons and Photons (1927), 56–60, 76–77, 80–81

Fitzgerald, F. Scott, 80

Fizeau, Hippolyte, 45

force fields: Faraday's concept of, 39, 40–42, 43, 45, 84; force-
carrier particles of, 148, 174–76; Maxwell's work on, 42–46, 80, 172, 174, 199.
See also
particle physics

formula for all known physics, 167–201; as analogy for society/humanity, 197–201; Dirac's equation and, 172–73, 174, 175–76, 182–83, 196, 199; Einstein's theory of gravity and, 172, 174, 189–90, 196, 199; Euler's number and, 170–71; Feynman's formulation and, 92–93, 169–71, 183–84, 196; and goal of scientific education/learning, 156–67, 199–200; Hamilton's action principle and, 171, 183; Higgs field and, 173, 174–75, 178, 189; Higgs mechanism and, 174; Higgs potential energy and, 175, 190; Maxwell–Yang–Mills force field theories and, 172, 174, 199; Noether's theorem and, 176–78, 179–80; as problematic, 187–91; Schrödinger's wavefunction and, 92–93, 168–71, 183; string theory as alternative to, 191–95; Yukawa–Kobayashi–Maskawa matter particle mass term and, 173

Fourier analysis in time, 72–73, 75

Franklin, Benjamin, 44, 177–78

Friedmann, Alexander, 121–23, 125, 127, 154

 

Galileo, 18, 23, 28–29, 100–1, 117, 205, 253;
Dialogue Concerning the Two Chief World Systems
, 13; and heliocentric universe, 20–21, 25, 100;
Two New Sciences
, 21

gamma rays, 47, 111

Gamow, George, 125–28; and concept of background radiation, 127–28; and stellar energy conference, 126; as U.S. Navy consultant, 126

Gandhi, Mohandas, 6

Gates, Bill, 166

Gauss, Carl Friedrich, 44

general relativity.
See
theory of general relativity

geometry, 7, 20, 52; in academic curriculum, 10, 32, 197; Anaximander's use of, 53; and art, 16, 17; of curved space, 118; Einstein and, 51, 118, 184; Euler's formula and, 75, 170; of four-dimensional space, 143; Leonardo's use of, 17; Pythagorean theorem of, 8; and quantum theory, 76–77, 93, 170; of universe, 143, 210, 246, 256

Glasgow, University of, 31, 34

Glashow, Sheldon Lee, 172, 174, 188

Godwin, William, 240

Google, 204, 237

Göttingen, University of, 178–79, 180