The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries)

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The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries) Page 27

by David Leavitt


  on AT’s work, 113–14, 121–22, 124–26, 127, 135, 201

  background of, 110, 113, 116

  Entscheidungsproblem addressed by, 106–7, 108, 109–10, 112–14, 124, 136, 137

  as formalist, 138

  personality of, 110–12, 122, 137, 138

  teaching style of, 111, 144

  Church, Mary, 121

  Churchill, Winston, 176n

  Church of England, 120–21

  cillis (sillies), 184

  ciphers:

  Fish traffic, 188, 191–92

  keywords of, 161, 162, 164

  machine scrambling of, 165–76, 191–92; see also Enigma encipherment machine

  monoalphabetic, 159–60, 164, 174

  polyalphabetic, 160–64, 173–74

  randomly generated key sequences in, 164–65

  spoken messages rendered in, 192–93, 194–95, 198

  statistical analysis of letter repetitions in, 162–64

  circle-free machines, 82

  Civil War, U.S., 165

  Clarke, Joan, 177–78, 196

  Clayton, Fred (Frank Clare), 15, 20n

  Clayton, Mrs., (AT’s housekeeper), 265, 275–76, 277

  cloning, 245–46

  Cloven Pine, The (Clare), 20n

  Code Book, The (Singh), 162, 163n

  coding systems:

  in computing machines, 79–80, 232–33

  see also ciphers

  Cohen, A. M., 131

  Colles, W. M. “Bill,” 190

  Colossus cryptanalysis machine, 192, 194, 199, 219

  common sense, 147, 156

  complete configuration, 59, 83

  complex numbers, 129n

  compound symbols, 61

  computable numbers, 57–58, 61, 77, 99, 105, 106, 108, 112, 114, 125

  computation, human efforts of, 54–55, 60–66

  computer development:

  application proposals in, 208–9, 220, 226–27, 258–59

  AT’s contributions to, 6–7, 83, 86, 202, 215–16; see also “On Computable Numbers”

  Babbage’s analytical engine, 55–56, 59, 201–2

  beginnings of, 54–56

  at Manchester University, 219–20, 221, 231–35, 235, 236–39, 255, 259–60

  Mersenne primes verified in, 233–34, 239

  at NPL, 199, 211, 212–15, 219, 220, 221

  speed as principal objective in, 199, 208, 209, 220

  U.S. vs. British, 199, 212–14, 215

  computers:

  ACE design, 201–17, 219, 221, 223, 224, 227, 263, 264

  binary notation used in, 29n, 69–72, 134, 208

  cathode-ray tube technology and, 209–10, 219, 231–32, 237

  digital nature of, 142, 208, 209

  EDSAC, 214–15, 219, 220

  EDVAC, 200–201, 202, 208, 209, 213, 214, 215

  ENIAC, 199–200, 201, 202, 208, 213, 214, 220, 223, 224

  hardware vs. software in, 200, 202–4, 208

  intelligence attributed to, 5, 94, 193, 203, 204–7, 221–30, 236–59, 261–64

  literal-mindedness of, 204–5

  memory storage in, 203–4, 209–10, 219

  reading mechanisms and, 204

  technical workers vs. masters of, 207, 210–11

  as threat to humanity, 207, 239

  Turing test of, 229–30, 241–47

  “Computing Machinery and Intelligence” (Turing), 240–59

  consciousness, intelligence vs., 237, 247, 250

  Constitution, U.S., 258

  contradiction, logical, 25–27, 32, 94, 152–56

  Courant, Richard, 115

  creativity, intelligence vs., 236, 237, 238, 240, 254

  cribs, 179, 182, 183

  Curtis, Tony, 252

  Cybernetics (Wiener), 235–36

  Daly, Joseph, 123

  Darwin, Charles (grandfather), 198, 216

  Darwin, Sir Charles Galton (grandson), 198–99, 211, 212–13, 216, 217, 221

  Davis, Martin, 6n, 55n, 81, 215, 216

  decision problem, see Entscheidungsproblem

  delay lines, 209, 210, 219

  Delilah speech encipherment machine, 194–95, 198, 217, 263

  denary (Arabic) system, 67, 69–70

  Denniston, Alastair, 139

  DePauli, Werner, 108n, 146

  description number (D.N.), 80, 83

  diagonal method, 91–93

  Dickens, Charles, 60, 250

  digital machines, 142, 208, 209

  see also computer development; computers

  Disney, Walt, 5, 47, 140, 280

  Douglas, James, 18

  Doxiadis, Apostolos, 45n

  Dummett, Michael, 30n

  Eckert, J. Prosper,199

  Eddington, Arthur Stanley, 24, 278n

  EDSAC (electronic delay storage automatic computer), 214–15, 219, 220

  EDVAC (electronic discrete variable automatic computer), 200–201, 202, 208, 209, 213, 214, 215

  Edward VIII, King of Great Britain, 120–21

  effective calculability, 108, 112, 136

  Einstein, Albert, 6, 47, 115, 117, 123, 126n

  Eisenhart, Katherine, 127

  Eisenhart, Luther, 127

  electronic automatic computer, see EDSAC

  electronic discrete variable automatic computer, see EDVAC

  Eliot, George, 28

  Emigrants, The (Sebald), 231

  emotion:

  as criterion of intelligence, 236–37, 251–52, 262–63

  mechanistic view of, 229

  ENIAC (electronic numerical integrator and calculator), 199–200, 201, 202, 208, 213, 214, 220, 223, 224

  Enigma (film), 158n

  Enigma encipherment machine:

  bombe machines used in decoding of, 175, 180–83, 181, 186, 188, 189, 193–94, 198

  British cryptanalysis work on, 158, 171, 174, 176–86, 188–90, 193–94, 196, 208, 232

  design of, 166–76, 168, 179, 184–85, 193

  invention of, 165–66

  military adoption of, 132–33, 166, 169

  multitude of permutations furnished by, 171

  naval version of, 184–85, 191, 193, 208

  Polish cryptanalysis work on, 169, 172, 174–76, 178, 186, 190

  reversibility of, 167, 170, 173, 182

  security improvements on, 173–76, 184–85

  stecker board of, 170, 171, 176, 179, 181–82

  Entscheidungsproblem (decision problem), 25, 49–56, 115

  AT’s computability in disproof of, 52–54, 56, 82, 90–99, 104, 105–8, 112–14, 124–26, 136–37, 152, 178, 205, 242, 249

  Church’s lambda calculus applied to, 106–7, 112–14, 124, 125, 136, 137

  defined, 36

  as example of undecidable problem, 105

  medieval roots of, 49

  Epimenides, 25–26, 94

  “Equivalence of Left and Right Almost Periodicity” (Turing), 24

  Erewhon (Butler), 20, 239

  Eubulides, 26

  Euclid, 128

  Euclid’s algorithm, 50–51

  Euler, Leonhard, 132

  exclusion principle, 279

  extra-sensory perception (ESP), 255–56

  Feferman, Solomon, 105–6, 122–23, 137

  females (cipher repetitions), 175, 178

  Fermat, Pierre de, 132

  Fine Hall, 115, 116–17, 118

  finite-1 process, 108–9

  first-order logic, 49n–50n,51

  Fish cipher traffic, 188, 191–92

  Flowers, Tommy, 192

  Forster, E. M.:

  Cambridge novel of, 19, 217

  on friendship vs. patriotism, 23, 269–70

  homosexual protagonist of, 4–5, 17–18, 102, 196–97, 265

  on human connection, 102, 137, 274

  at King’s College, 6, 17, 20

  on public school, 12

  Foundations of Arithmetic, The (Die Grundlagen der Arithmetik) (Frege), 30–31

  four-color
theorem, 220

  free will, 99–100, 102

  Frege, Gottlob, 29, 30–33, 34, 39, 94, 143, 144, 154, 181

  Friedman, William, 163

  friendship, patriotism vs., 23, 269–70

  Furbank, P. N., 17n

  games, computer, 226, 227

  of chess, 209, 229–30

  Gandy, Robin, 197, 217, 265, 275

  on AT’s final months, 278, 279

  on AT’s work process, 54, 108

  cryptanalysis work of, 194, 195

  on Turing machine, 54, 55n–56n

  Gauss, Karl, 128–29, 131, 132, 223, 224

  Germany:

  Enigma encipherment machine used by, 132–33, 158, 159, 166–86, 168, 188–90, 193–94, 196, 208

  interwar period in, 37, 38

  Lorenz encipherment machine developed by, 191–92

  Gödel, Kurt, 115, 201

  as antiformalist, 104–5, 138

  on AT’s work, 137

  on lambda calculus, 136, 137, 138

  on limitations of machines, 222, 249

  mathematics consistency/completeness refuted by, 33–34, 39, 41–48, 52, 53, 104, 122–23, 130, 135–36

  mental illness of, 47, 279

  on recursive function, 108, 125, 127–28

  Goldbach’s conjecture, 39, 44–45, 51, 90, 148n

  Good, Jack, 189

  Government Code and Cipher School, 139, 141, 158

  Gray, Jeremy J., 51n

  Greenbaum, Frank M., 271, 276

  Gregory, James, 12

  group theory, 24, 126, 127, 259

  Grundgesetze der Arithmetik, Die (The Basic Laws of Arithmetic) (Frege), 31, 32

  Grundlagen der Arithmetik, Die (The Foundations of Arithmetic) (Frege), 30–31

  Grundzüge der theoretischen Logik (Hilbert and Ackermann), 51

  Guinness, Alec, 3, 4

  Hall,Radclyffe,18

  halting problem, 82–83

  Hanslope Park, 194–95

  Hardy, G. H., 40n, 54, 141, 143, 264, 279

  on Entscheidungsproblem, 51–52

  Hilbertian formalism and, 34, 35

  on mathematical knowledge vs. belief, 148n

  on mathematics as neutral science, 132–33, 152, 172

  on national differences in mathematics, 38–39

  personality of, 20, 115

  on proofs, 148n, 195

  on Riemann hypothesis, 130–31

  on Russell, 22n, 34

  Hare and Hounds Club, 218

  Harrison, Kenneth, 20n

  Harvard University, 126n

  Hazelhurst School, 10, 11, 11

  Heath Robinson (cryptanalysis machine), 192

  Hebern, Edward, 165n

  Herbrand, Jacques, 52, 108, 125

  Hilbert, David, 33–41, 42, 54, 156

  on Entscheidungsproblem, 49, 51, 53, 57, 107, 125

  formalism of, 34–41, 46

  pacifism of, 37–38

  on paradoxes, 39–40

  students of, 110, 115, 122

  Hilton,Peter,14

  Hitchcock, Alfred, 278

  Hitler, Adolf, 139, 177, 186

  Hodges, Andrew, 6, 14, 102, 139, 186, 187, 279

  on AT’s computing machine concepts, 99, 105n, 173n, 201

  on AT’s education, 21, 23

  on AT’s homosexuality, 178, 196

  on computable numbers, 57, 66n

  on Hardy, 132

  on imitation game, 243, 244

  on von Neumann’s computer work, 201

  Home Guard, 13–14, 187

  homosexuality:

  British criminal prosecution of, 4, 5, 18, 265–66, 268–69

  “cures” for, 5, 16, 268

  government security clearance and, 269–70

  as natural vs. unnatural, 245

  in public schools, 12, 15

  secrecy on, 4–5, 18–19, 195, 244–45

  social stigma of, 4–5, 120, 190, 196–97, 238

  traditional arguments against, 222

  Howards End (Forster), 102

  hydrogen bomb, 200

  iconoscopes, 209–10

  imaginary numbers, 129n

  imitation game, 241–47, 250, 253–54, 255–56

  Infinity and the Mind (Rucker), 26n

  Institute for Advanced Study, 114–15, 123

  see also Princeton University

  intelligence, see machine intelligence

  “Intelligent Machinery” (Turing), 221–30, 256

  International Congress of Mathematicians, 36–37

  Irvine, Lyn, 8, 196, 265

  Ivy House, 212

  Jefferson, Sir Geoffrey, 236–40, 247, 248, 250, 258, 261–63, 264, 266

  Jefferson, Thomas, 165

  Jeffreys, John, 158

  Johnniacs, 208n

  Johnson, Neville, 218, 265

  Jones, Will T., 118, 277–78

  Journal of Symbolic Logic, 106, 108, 110, 124–25, 218

  Kant, Immanuel, 34, 35

  Keller, Helen, 257–58

  Kemeny, John, 33n

  Keynes, John Maynard, 6, 17, 19, 20, 21–23, 102–3, 143, 144, 203

  Khowârizmi, Muhammad ibn Mûsâ al-, 50

  Kilburn, Tom, 219, 231–32

  King’s College, 6

  athletic activities at, 20, 190, 218

  AT’s fellowships of, 25, 127, 217

  philosophical ethos of, 21–24, 102–3

  social life at, 17–18, 19–21, 117, 217–18

  Turing archive at, 142

  Kleene, Stephen, 77, 89, 106, 108, 112, 115, 125, 128, 136–37

  Knox, Dilwyn, 169

  K-ray lighting system, 15

  Kullback, Solomon, 162–63

  Labouchere amendment (1885), 18

  lambda calculus, 106, 109–10, 112, 124, 136, 138

  λ-definability, 106, 108, 112, 114, 125, 136, 137

  language:

  computer efforts at skills in, 226, 227

  mathematics and, 146–57

  Lassègue, Jean, 243n, 256n

  learning process, 203, 227–29, 256–58

  Lefschetz, Solomon, 111n, 115

  Lehman, R. S., 131

  Lehmer, D. H., 234

  Leibniz, Gottfried Wilhelm, 28–29, 46–47, 49, 52

  Leon, Sir Herbert, 157

  liar’s paradox, 25–27, 32, 52, 94, 152, 154

  lighting systems, 15

  Linolite electric strip reflector lamp, 15

  Littlewood, J. E., 130

  Liverpool calculating machine, 135, 142

  logic:

  arithmetic as branch of, 30

  first-order, 40n–50n

  of language in mathematics, 146–57

  law of contradiction in, 152–56

  liar’s paradox, 25–27, 32, 94, 152, 154

  symbolic, 29–30

  logicism, 30

  London Mathematical Society, 203, 206–7, 223

  Longest Journey, The (Forster), 19, 23, 217

  Loom of Youth, The (Waugh), 12

  Lorenz cipher machine, 191–92

  Lovelace, Ada Byron, Lady, 55, 254

  Lucas, Edouard, 234

  Ludgate, P. E., 55n

  Lullus, Raimundus, 49

  Lutman-Kokoszynska, Marya, 143

  machine intelligence, 94, 204–7, 221–30, 236–59

  anthropomorphic view of, 203, 206, 257–58

  brain function as model of, 193, 203, 218, 224–26, 237, 263–64

  categorical analysis of, 224–25

  creativity and, 236, 237, 238, 240

  educability as measure of, 203, 224, 228–29, 256–58

  emotional life and, 236–37, 251–52, 262–63

  fallibility of, 205, 223, 249, 262

  imitation game as test of, 241–47, 250, 253–54, 255–56

  public controversy on, 236–40, 261–63

  religious arguments against, 5, 222, 247–48

  as threat to humanity, 207, 239

  Mackendrick, Alexander, 3

  MacPha
il, Donald, 143, 259

  MacPhail, Malcolm, 134, 142

  Malcolm, Norman, 143, 144, 145, 146

  Manchester University, 219–20, 221, 231, 264

  Baby computer built at, 231–35, 235, 236–39, 255, 259–60

  Man in the White Suit, The, 3–5, 56, 60, 109, 207, 278

  mankind, innate superiority of, 247–49

  Massinger Society, 19

  Mathematical Laboratory, 214, 220–21

  mathematicians, political pressures on, 37–39

  Mathematician’s Apology, A (Hardy), 132, 279

  mathematics:

  completeness of, 33–34, 36, 41, 44, 53

  computer applications in, 209, 220, 226, 227, 259

  consistency of, 33–34, 36, 41, 44, 48, 53, 104

  as cure for homosexuality, 16

  decidability of, 25, 33–34, 36, 49–56, 82, 90–99; see also Entscheidungsproblem

  as discovery vs. invention, 109, 148

  formalist, 34–41, 45–46, 104, 138

  foundations of, 27–48

  logical paradoxes in, 27, 31–33, 39–40, 44–47

  metamathematics vs., 35–36, 105

  as neutral science, 132–33

  ordinary language vs. language of, 143, 146–57

  proofs in, 30, 35, 39, 90–91, 148, 149–50, 195

  see also specific mathematical problems

  Matthews, Peter, 218, 263

  Mauchley, John, 199

  Maurice (Forster), 4–5, 17–18, 21, 102, 196–97, 245n, 265, 267

  Mayhew, M. J. E., 131

  m-configurations, 58, 59, 67, 103

  Mersenne, Marin, 233–34

  Mersenne primes, 233–34, 239

  Messages from the Unseen World (Turing), 278–79

  metamathematics, 35–36, 105

  “Method for the Calculation of the Zeta-function, A” (Turing), 260

  microprogramming, 214n, 215

  Middlemarch (Eliot), 28

  “Mind of Mechanical Man, The” (Jefferson), 236

  Miss Fine’s School, 118

  Monet, Claude, 124

  monoalphabetic ciphers, 159–60, 164, 174

  Moore, G. E., 21, 102, 143

  Moore, Henry, 262

  Moore School of Engineering, 199, 214

  Moral Science Club, 20, 218, 225

  Morcom, Christopher, 16–17, 20n, 99, 100–101, 197, 246, 256, 274

  morphogenesis, mathematical model of, 263–64

  Moslem theology, 248

  Muggeridge, Malcolm, 178

  Murray, Arnold, 266–68, 272, 273

  Nagel, Ernest, 35

  Napoleonic Code, 265

  National Biscuit Company, 118

  National Physics Laboratory (NPL), 198, 217

  AT’s final report to, 221–30, 236, 240, 249

  computer development at, 199, 211, 212–15, 219, 220, 221

  Natural Wonders Every Child Should Know (Brewster), 10–11

 

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