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