Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem

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pages: 210 words: 62,771

Turing's Vision: The Birth of Computer Science by Chris Bernhardt

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, British Empire, cellular automata, Claude Shannon: information theory, complexity theory, Conway's Game of Life, discrete time, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Internet Archive, Jacquard loom, John Conway, John von Neumann, Joseph-Marie Jacquard, Norbert Wiener, Paul Erdős, Turing complete, Turing machine, Turing test, Von Neumann architecture

The answer is that he wrote a remarkable paper in 1936, when he was just twenty four years old. This paper is Turing’s most important intellectual contribution. However, this paper and its groundbreaking ideas are not widely known. This book is about that paper. The paper has the rather uninviting title, On Computable Numbers, with an Application to the Entscheidungsproblem. But don’t be discouraged by the title, because it contains a wealth of elegant and powerful results. It also contains some remarkably beautiful proofs. Turing wants to show that a leading mathematician’s view of mathematics is wrong. To do this he needs to study computation: What exactly is computation?

This idea is then extended to Turing machines: there are some Turing machines that accept their encodings and some that do not, but there is no Turing machine that can distinguish these two classes. This, in turn, leads to the the proofs that certain decision problems are undecidable. In particular, we prove that the halting problem and the acceptance problem are both undecidable. Chapter 8 The title of Turing’s paper is On Computable Numbers, with an Application to the Entscheidungsproblem. The connection to the Entscheidungsproblem has now been explained, but computable numbers have not. In this chapter we explain what these numbers are and the basic result concerning them. The chapter starts with Cantor’s idea of cardinality. We look at some basic, but surprising facts, about infinite cardinal numbers.

The only conclusion is that the list of computable numbers is not something that can be constructed by a computer. If the list could be constructed by a computer, then b would be computable and we would have a contradiction. If it is not possible to construct the list by a computer, then there is no contradiction, so that must be the case. The title of Turing’s paper is “On Computable Numbers, with An application to the Entscheidungsproblem.” This title should now make sense. Turing wanted to show that Hilbert’s view of the Entscheidungsproblem was not correct. To recap: He first needed to give a definition of an effective procedure, or algorithm. This he did through his definition of what we now call Turing machines.


Turing's Cathedral by George Dyson

1919 Motor Transport Corps convoy, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Benoit Mandelbrot, British Empire, Brownian motion, cellular automata, cloud computing, computer age, Danny Hillis, dark matter, double helix, fault tolerance, Fellow of the Royal Society, finite state, Georg Cantor, Henri Poincaré, housing crisis, IFF: identification friend or foe, indoor plumbing, Isaac Newton, Jacquard loom, John von Neumann, mandelbrot fractal, Menlo Park, Murray Gell-Mann, Norbert Wiener, Norman Macrae, packet switching, pattern recognition, Paul Erdős, Paul Samuelson, phenotype, planetary scale, RAND corporation, random walk, Richard Feynman, SETI@home, social graph, speech recognition, The Theory of the Leisure Class by Thorstein Veblen, Thorstein Veblen, Turing complete, Turing machine, Von Neumann architecture

Even in a perfectly deterministic universe, there is no consistent method to predict the ending in advance. To an observer in our universe, the digital universe appears to be speeding up. To an observer in the digital universe, our universe appears to be slowing down. Universal codes and universal machines, introduced by Alan Turing in his “On Computable Numbers, with an Application to the Entscheidungsproblem” of 1936, have prospered to such an extent that Turing’s underlying interest in the “decision problem” is easily overlooked. In answering the Entscheidungsproblem, Turing proved that there is no systematic way to tell, by looking at a code, what that code will do.

“There is mighty little room for putting things in one’s cabin, but nothing else that worries me,” he reported to his mother on September 28. “The mass of canaille with which one is herded can easily be ignored.”2 Turing’s arrival in Princeton was followed, five days later, by the proofs of his “On Computable Numbers, with an Application to the Entscheidungsproblem.” These thirty-five pages would lead the way from logic to machines. Alan Mathison Turing was born at Warrington Lodge, London, on June 23, 1912, to Julius Mathison Turing, who worked for the Indian Civil Service, and Ethel Sara Turing (née Stoney), whose family included George Johnstone Stoney, who named the electron, in advance of its 1894 discovery, in 1874.

After a full year of work, Turing gave Newman a draft of his paper in April of 1936. “Max’s first sight of Alan’s masterpiece must have been a breathtaking experience, and from this day forth Alan became one of Max’s principle protégés,” says William Newman, Max’s son. Max Newman lobbied for the publication of “On Computable Numbers, with an Application to the Entscheidungsproblem,” in the Proceedings of the London Mathematical Society, and arranged for Turing to go to Princeton to work with Alonzo Church. “This makes it all the more important that he should come into contact as soon as possible with the leading workers on this line, so that he should not develop into a confirmed solitary,” Newman wrote to Church.15 Turing arrived in Princeton carrying his sextant, and stretching his resources to survive on his King’s College fellowship (of £300) for the year.


pages: 362 words: 97,862

Physics in Mind: A Quantum View of the Brain by Werner Loewenstein

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, complexity theory, dematerialisation, discovery of DNA, Gödel, Escher, Bach, Henri Poincaré, informal economy, information trail, Isaac Newton, Murray Gell-Mann, Necker cube, Norbert Wiener, Richard Feynman, stem cell, trade route, Turing machine

R. 1980. Gödel, Escher, Bach: An Eternal Braid. New York: Vintage Books, Random House. Trakhtenbrot, B. A. 1963. Algorithms and Automatic Computing Machines. Boston: D.C. Heath & Co. Turing, A. 1936. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society (2nd Series) 42:230–265. Turing, A. 1937. On computable numbers, with an application to the Entscheidungsproblem: A correction. Proceedings of the London Mathematical Society 43:544–546. Rendering the World by Computer Deutsch, D. 1985. Quantum theory, the Church-Turing principle and the universal quantum computer.

Gödel, K. 1931. On formally undecidable propositions of Principia Mathematica and related systems I. Monatsschrift für Mathematik und Physik 38:131–198. Prigogine, I. 1980. From Being to Becoming: Time and Complexity in Physical Sciences. San Francisco: Freeman. Turing, A. M. 1936/1937. On computable numbers, with an application to the entscheidungsproblem. Proceedings of the London Mathematical Society Series 2 42:230–265 and 43:544–546. A Note about Reality Carroll, Lewis. (1871) 1982. Through the Looking Glass and What Alice Found There, Chapter VII. New York: Avenel Books. 14. Information Processing in the Brain Cell Organization in the Brain Braak, H. 1976.


pages: 523 words: 143,139

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic bias, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Bayesian statistics, Berlin Wall, Bill Duvall, bitcoin, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, David Heinemeier Hansson, delayed gratification, dematerialisation, diversification, Donald Knuth, double helix, Elon Musk, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, Garrett Hardin, George Akerlof, global supply chain, Google Chrome, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, Johannes Kepler, John Nash: game theory, John von Neumann, Kickstarter, knapsack problem, Lao Tzu, Leonard Kleinrock, linear programming, martingale, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, Sam Altman, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, Stanford marshmallow experiment, Steve Jobs, stochastic process, Thomas Bayes, Thomas Malthus, Tragedy of the Commons, traveling salesman, Turing machine, urban planning, Vickrey auction, Vilfredo Pareto, Walter Mischel, Y Combinator, zero-sum game

“a clever man would put the poison into his own goblet”: The Princess Bride, screenplay by William Goldman; 20th Century Fox, 1987. “anticipating the anticipations of others”: Attributed to Keynes in Gregory Bergman, Isms, Adams Media, 2006. it was the halting problem that inspired Turing: Alan Turing considers the halting problem and proposes the Turing machine in “On Computable Numbers, with an Application to the Entscheidungsproblem” and “On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction.” “poker players call it ‘leveling’”: Dan Smith, personal interview, September 11, 2014. “You don’t have deuce–seven”: This took place at the “Full Tilt Poker Durrrr Million Dollar Challenge,” held at Les Ambassadeurs Club in London, November 17–19, 2009, and was televised on Sky Sports.

Journal of Pragmatics 70 (2014): 152–164. Tracy, Brian. Eat That Frog! 21 Great Ways to Stop Procrastinating and Get More Done in Less Time. Oakland, CA: Berrett-Koehler, 2007. Turing, Alan M. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Read November 12, 1936. Proceedings of the London Mathematical Society s2-42, no. 1 (1937): 230–265. ______. “On Computable Numbers, with an Application to the Entscheidungsproblem: A Correction.” Proceedings of the London Mathematical Society s2-43, no. 1 (1938): 544–546. Tversky, Amos, and Ward Edwards. “Information Versus Reward in Binary Choices.”


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Einstein's Fridge: How the Difference Between Hot and Cold Explains the Universe by Paul Sen

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, anti-communist, British Empire, Brownian motion, Claude Shannon: information theory, cosmic microwave background, cosmological constant, Ernest Rutherford, invention of radio, Isaac Newton, James Watt: steam engine, John von Neumann, Khan Academy, Kickstarter, Richard Feynman, Stephen Hawking, traveling salesman, Turing complete, Turing test

He graduated three years later with a first-class degree and was chosen to be a “fellow” of the college, which meant an annual stipend of £300 (worth around £11,000 [$14,000] today) and the freedom to pursue his many mathematical interests. During this time Turing wrote the paper that, along with his wartime work as a code breaker, is the achievement he’s best known for. Published in 1936, the paper has the daunting title “On Computable Numbers, with an Application to the Entscheidungsproblem.” The Entscheidungsproblem is a mathematical challenge that had been stated in its modern form in 1928 by David Hilbert, Emmy Noether’s mentor at the University of Göttingen. In simple terms, the problem asks if there is an automatic way of determining if any mathematical statement is true.

About a Microscope: See above. Natural Wonders Every Child Should Know: A book by Edwin Tenney Brewster. “How they find out when”: From above. “Hockey, or Watching the Daisies Grow”: Sara Turing drew the picture and sent it to the matron at Turing’s school in 1923. “On Computable Numbers”: “On Computable Numbers, with an Application to the Entscheidungsproblem” by Alan Turing, first published in Proceedings of the London Mathematical Society, ser. 2, 42 (1936–37). Most historians now regard Turing’s Universal Machine: See chapter 6 of The Turing Guide by B. Jack Copeland. a fifteen-year-old Jewish refugee named Robert Augenfeld: See Alan Turing by Hodges and a brief essay by Augenfeld that was written shortly before he died.

Carnot), 21 nuclear bombs, 152 nuclear power, 109, 241, 244 Nüsslein-Volhard, Christiane, 215 “On a Heuristic Point of View Concerning the Production and Transformation of Light” (Einstein), 145–48 “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy” (Thomson), 59–61 “On Computable Numbers, with an Application to the Entscheidungsproblem” (Turing), 201 “On the Conservation of ‘Kraft,’ ” (Helmholtz), 47–49 Origin of Species, The (Darwin), 71 origins of universe. See creation of universe Ostwald, Wilhelm, 125, 151 ourworldindata website, 241 Oxford University, 5, 229 particle physics, 159 pattern analysis in information flow, 175, 177–80 letter frequency in, 177–79 letter pairs in, 179 single-letter frequency in, 177–79 spoken word statistical analysis in, 180 pattern formation in morphogenesis hair follicles example of, 215–16 hand shapes and, 217 sand dune example of, 210 Turing’s cannibal-missionary model in, 208, 216–17 Turing’s research on, 207–10, 214, 215, 217 Wolpert’s PI model of, 214–16, 217 Pauli, Wolfgang, 160 Penrose, Roger, 229 Penzias, Arno, 158 perpetual motion machine Carnot’s concept of an ideal engine as, 18, 46 Helmholtz’s research on steam engine efficiency and, 46–47 Szilard on possibility of, 191, 192 Perrin, Jean, 150–51 phase changes refrigeration and, 109–12 thermodynamic maps tracking, 109 phenomenalism, 124–25 photoelectric effect of light, 146 photon, first use of word, 146 photosynthesis, 121–23, 199 phyllotaxis, Turing’s formulas for, 212 physics Bekenstein on career in, 231 black hole entropy and radiation’s domination of, 236 Boltzmann’s education in, 95, 97, 98 Boltzmann’s entropy equation and, 117 Clausius’s statement of laws of thermodynamics and, 70 grand unified theory and, 236 Helmholtz’s paper on the conservation of Kraft (energy) and, 47–49 laws of thermodynamics and, ix, 219 Maxwell’s introduction of probability into, 86 Noether’s theorem on laws of, 157–59 Planck’s discoveries and eras in, 142 teaching of, in eighteenth-century universities, 5 Thomson’s work with Regnault on research in, 34–35 physics laboratory, Cambridge University, 93–94 Pilot ACE computer, 204 PI (positional information) model, in morphogenesis, 214–16, 217 Planck, Max, 137–42 background and education of, 125 Boltzmann’s contribution to discovery of quanta and, 142 Boltzmann’s work with early criticism from, 125, 133, 137, 140, 145 Boltzmann’s work with later support from, 133, 140, 141, 142 cavity radiators measurements and, 138–42 Einstein’s paper on work of, 145 heat radiation research of, 133, 137–38 probability and statistics used by, 140 quanta discovery and naming by, 142 plants formulas phyllotaxis in, 212 photosynthesis in, 121–23, 199 Polytechnic School, Paris, 8, 9, 20, 34 positional information (PI) model, in morphogenesis, 214–16, 217 potential energy, 48, 52 power generation, thermodynamic maps on efficiency of, 109 Priestley, Joseph, 5 principle of equivalence, 221, 223 Principles of Geology (Lyell), 70 probabilistic explanations Boltzmann’s research on entropy and, 124 Boltzmann’s theory on second law of thermodynamics using, 137 phenomenalism debate and, 124 probabilistic nature of quantum theory, 161 probabilities Einstein’s use of, to grasp underlying reality of molecules, 160–61 Herschel’s use of, in astronomy, 86 Maxwell’s use of, 86–88 Planck’s use of, 140 Prussia, steam engines in, 41–42, 43 Prussian Academy of Sciences, Berlin, 224 quanta Boltzmann’s role in discovery of, 142 Einstein’s research on, 147, 160, 161, 233 Planck’s naming of, 142 Planck’s paper on, 142 quantum mechanics, 160, 236 quantum physics birth of, 142 Boltzmann’s contribution to, 142 Einstein’s paper on light and, 146 Planck’s research and birth of, 142 quantum theory Einstein’s contributions to, 146, 159–61 Hawking’s investigation of black holes and, 235–36 radiation cavity radiators measurements in, 138–41 heat transfer using, 133–34, 137–38 radioactive dating, 72–73 radio communications systems, Turing’s experience with, 206 radio waves, Maxwell’s discovery of, 136, 187 railways, Gibbs’s early interest in, 105 random fluctuation hypothesis on creation of the universe, 129–30 Rayleigh, John William Strutt, 3rd Baron, 138–40 redundancies data networks with, 182 spoken language with, 181–82 written language degeneration and, 182–83 Reflections on the Motive Power of Fire (S.


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Geek Sublime: The Beauty of Code, the Code of Beauty by Vikram Chandra

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Apple II, barriers to entry, Berlin Wall, British Empire, business process, conceptual framework, create, read, update, delete, crowdsourcing, don't repeat yourself, Donald Knuth, East Village, European colonialism, finite state, Firefox, Flash crash, functional programming, glass ceiling, Grace Hopper, haute couture, iterative process, Jaron Lanier, John von Neumann, land reform, London Whale, Norman Mailer, Paul Graham, pink-collar, revision control, Silicon Valley, Silicon Valley ideology, Skype, Steve Jobs, Steve Wozniak, supercomputer in your pocket, theory of mind, Therac-25, Turing machine, wikimedia commons, women in the workforce

Chapter 10: Application.Restart() 1. Muller-Ortega, “Seal of Sambhu,” 574. 2. “Fwd: Amar Chitra Katha Comics in Samskritam: Participate in Readership Survey—Google Groups.” 3. Singh, “New Life, Old Death for Sanskrit in Uttarakhand.” 4. Toole, Ada, the Enchantress of Numbers, loc. 2867–870. 5. Turing, “On Computable Numbers, with an Application to the Entscheidungs-problem (1936).” 6. Toole, Ada, the Enchantress of Numbers, loc. 2131–133. 7. Gleick, The Information, loc. 2048–052. 8. Cabanne, Dialogues with Marcel Duchamp, 18–19. 9. Fishwick, “Aesthetic Computing.” 10. Hessel, Goodman, and Kotler, “Hacking the President’s DNA.” 11.

Accessed February 3, 2013. http://www.ioccc.org/. Toole, Betty Alexandra. Ada, the Enchantress of Numbers: Poetical Science. Sausalito: Critical Connection, 2010. Kindle Edition. Torvalds, Linus. “Re: Stable Linux 2.6.25.10.” Gmane.org, July 15, 2008. http://article.gmane.org/gmane.linux.kernel/706950. Turing, Alan. “On Computable Numbers, with an Application to the Entscheidungs-problem (1936).” In The Annotated Turing: A Guided Tour through Alan Turing’s Historic Paper on Computability and the Turing Machine, by Charles Petzold. Indianapolis: Wiley, 2008. Urban, Hugh B. The Economics of Ecstasy: Tantra, Secrecy, and Power in Colonial Bengal.


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Possible Minds: Twenty-Five Ways of Looking at AI by John Brockman

AI winter, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, artificial general intelligence, Asilomar, autonomous vehicles, basic income, Benoit Mandelbrot, Bill Joy: nanobots, Buckminster Fuller, cellular automata, Claude Shannon: information theory, Daniel Kahneman / Amos Tversky, Danny Hillis, David Graeber, easy for humans, difficult for computers, Elon Musk, Eratosthenes, Ernest Rutherford, finite state, friendly AI, future of work, Geoffrey West, Santa Fe Institute, gig economy, income inequality, industrial robot, information retrieval, invention of writing, James Watt: steam engine, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, Kickstarter, Laplace demon, Loebner Prize, market fundamentalism, Marshall McLuhan, Menlo Park, Norbert Wiener, optical character recognition, pattern recognition, personalized medicine, Picturephone, profit maximization, profit motive, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Rodney Brooks, salary depends on his not understanding it, self-driving car, sexual politics, Silicon Valley, Skype, social graph, speech recognition, statistical model, Stephen Hawking, Steven Pinker, Stewart Brand, strong AI, superintelligent machines, supervolcano, technological singularity, technoutopianism, telemarketer, telerobotics, The future is already here, the scientific method, theory of mind, Turing machine, Turing test, universal basic income, Upton Sinclair, Von Neumann architecture, Whole Earth Catalog, Y2K, you are the product, zero-sum game

One can imagine a different contingent version of our intellectual and technological history had Alan Turing and John von Neumann, both of whom made major contributions to the foundations of computing, not appeared on the scene. Turing contributed a fundamental model of computation—now known as a Turing Machine—in his paper “On Computable Numbers with an Application to the Entscheidungsproblem,” written and revised in 1936 and published in 1937. In these machines, a linear tape of symbols from a finite alphabet encodes the input for a computational problem and also provides the working space for the computation. A different machine was required for each separate computational problem; later work by others would show that in one particular machine, now known as a Universal Turing Machine, an arbitrary set of computing instructions could be encoded on that same tape.

., 222 Minsky, Marvin, 7, 262, 271 Mithen, Steven, 17 model-blind mode of learning, 16–17, 19 Moore, Gordon, 169 Moore’s Law, 8, 9–11 “More Is Different” (Anderson), 68 Müller, Vincent, 80 Musk, Elon, xxvi, 9 NAO, 250 nation-state superintelligences, 172–75 neural networks, 270–71 New Cinema (Expanded Cinema Festival), xvi Newell, Allen, 130 new perceptions arising from new technologies, xvi–xviii Ng, Andrew, 26 non-imminence of human-level AI argument against AI risk, 27 Norvig, Peter, 141 “no smarter than humans” argument against AI risk, 28 objective (algorist) method of prediction, 233–35 scientific objectivity, 235–39 Obrist, Hans Ulrich, 206–18 AI visualization programs, 211–13 art and science, relation between, 209–10, 214–16 art as alarm system for new development, 208 artificial stupidity, 210–11 background and overview of work of, 206–7 computers as creativity aids, 213–14 simulations, and AI, 216–18 obsolescent, reasons behind rush to make humans, 82–84 Odd John (Stapledon), 75 Omohundro, Steve, 25 “On Computable Numbers with an Application to the Entscheidungsproblem” (Turing), 57 open algorithms, 204 Oppenheimer, J. Robert, 96 optimistic AI scenario, in relation of machine superintelligences to hybrid superintelligences, 177 Orwell, George, 105, 106 Pagels, Heinz, xxiii Paglen, Trevor, 212 Paik, Nam June, 208, 259 Papert, Seymour, 271 parallel computing, xxiii–xxiv Pareto-topia, 98 Parreno, Philippe, 263–64 Pask, Gordon, 259 Pavlov, Ivan, 222 Peano, Giuseppe, 275–76 Pearl, Judea, xx, 13–19 background and overview of work of, 13–14 causal reasoning, 17–19 deep-learning, on lack of transparency in and limitations of, 15–19 human brain as nontransparent system argument, 15–16 on model-blind modes of learning, 16–17, 19 Pentland, Alex, 192–205 background and overview of work of, 192–93 credit-assignment function, applied to humans, 197–200 credit-assignment function, for AI, 196–97 culture in evolution, selecting for, 198–99 data used by AI, control over and review of, 203–4 human-AI ecologies, development of, 195–96 income inequality, 201–2 networks/ecosystems, working with, 194–95 next-generation AI, designing, 204–5 social sampling, 198–99 trust networks, building, 200–201 perception, and new technologies, xvi–xviii perceptron, 271 Perceptrons (Minsky and Papert), 271 Pinker, Steven, 100–112, 118 on AI dystopias, 108–12 background and overview of work of, 100–101 on computational theory of mind, 102–3 dystopian futures, flaws in, 105 on subjugation fear in AI scenarios, 108–10 on surveillance state dystopias, 105–7 on value alignment threat of AI, 110–11 on Wiener, 103–5, 112 Pitts, Walter, 270–71, 274 Plato, 222–23, 226 Poggio, Tomaso, 10 Popper, Karl, 116 Possible Minds Project, goal of, xxiv–xxv Principia Mathematica (Whitehead and Russell), 275 provably beneficial AI, templates for, 29–32 purposefulness, identifying, 281–84 putting purpose into machines, 23–25.


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The Information: A History, a Theory, a Flood by James Gleick

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, bank run, bioinformatics, Brownian motion, butterfly effect, citation needed, Claude Shannon: information theory, clockwork universe, computer age, conceptual framework, crowdsourcing, death of newspapers, discovery of DNA, Donald Knuth, double helix, Douglas Hofstadter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Gödel, Escher, Bach, Henri Poincaré, Honoré de Balzac, index card, informal economy, information retrieval, invention of the printing press, invention of writing, Isaac Newton, Jacquard loom, Jaron Lanier, jimmy wales, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, lifelogging, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, Norman Macrae, On the Economy of Machinery and Manufactures, PageRank, pattern recognition, phenotype, Pierre-Simon Laplace, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Rubik’s Cube, Simon Singh, Socratic dialogue, Stephen Hawking, Steven Pinker, stochastic process, talking drums, the High Line, The Wisdom of Crowds, transcontinental railway, Turing machine, Turing test, women in the workforce

The twentieth century gave algorithms a central role—beginning here. Turing was a fellow and a recent graduate at King’s College, Cambridge, when he presented his computable-numbers paper to his professor in 1936. The full title finished with a flourish in fancy German: it was “On Computable Numbers, with an Application to the Entscheidungsproblem.” The “decision problem” was a challenge that had been posed by David Hilbert at the 1928 International Congress of Mathematicians. As perhaps the most influential mathematician of his time, Hilbert, like Russell and Whitehead, believed fervently in the mission of rooting all mathematics in a solid logical foundation—“In der Mathematik gibt es kein Ignorabimus,” he declared.

♦ “NO, I’M NOT INTERESTED IN DEVELOPING A POWERFUL BRAIN”: Andrew Hodges, Alan Turing: The Enigma (London: Vintage, 1992), 251. ♦ “A CONFIRMED SOLITARY”: Max H. A. Newman to Alonzo Church, 31 May 1936, quoted in Andrew Hodges, Alan Turing, 113. ♦ “THE JUSTIFICATION … LIES IN THE FACT”: Alan M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society 42 (1936): 230–65. ♦ “IT WAS ONLY BY TURING’S WORK”: Kurt Gödel to Ernest Nagel, 1957, in Kurt Gödel: Collected Works, vol. 5, ed. Solomon Feferman (New York: Oxford University Press, 1986), 147. ♦ “YOU SEE … THE FUNNY LITTLE ROUNDS”: letter from Alan Turing to his mother and father, summer 1923, AMT/K/1/3, Turing Digital Archive, http://www.turingarchive.org

IEEE Annals of the History of Computing 18, no. 3 (1996): 4–12. ———. Ada, the Enchantress of Numbers: Prophet of the Computer Age. Mill Valley, Calif.: Strawberry Press, 1998. Tufte, Edward R. “The Cognitive Style of PowerPoint.” Cheshire, Conn.: Graphics Press, 2003. Turing, Alan M. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society 42 (1936): 230–65. ———. “Computing Machinery and Intelligence.” Minds and Machines 59, no. 236 (1950): 433–60. ———. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society of London, Series B 237, no. 641 (1952): 37–72.


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The Big Nine: How the Tech Titans and Their Thinking Machines Could Warp Humanity by Amy Webb

Ada Lovelace, AI winter, Airbnb, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic bias, artificial general intelligence, Asilomar, autonomous vehicles, backpropagation, Bayesian statistics, Bernie Sanders, bioinformatics, blockchain, Bretton Woods, business intelligence, Cass Sunstein, Claude Shannon: information theory, cloud computing, cognitive bias, complexity theory, computer vision, crowdsourcing, cryptocurrency, Daniel Kahneman / Amos Tversky, Deng Xiaoping, disinformation, distributed ledger, don't be evil, Donald Trump, Elon Musk, Filter Bubble, Flynn Effect, gig economy, Google Glasses, Grace Hopper, Gödel, Escher, Bach, Inbox Zero, Internet of things, Jacques de Vaucanson, Jeff Bezos, Joan Didion, job automation, John von Neumann, knowledge worker, Lyft, Mark Zuckerberg, Menlo Park, move fast and break things, move fast and break things, natural language processing, New Urbanism, one-China policy, optical character recognition, packet switching, pattern recognition, personalized medicine, RAND corporation, Ray Kurzweil, ride hailing / ride sharing, Rodney Brooks, Rubik’s Cube, Sand Hill Road, Second Machine Age, self-driving car, SETI@home, side project, Silicon Valley, Silicon Valley startup, skunkworks, Skype, smart cities, South China Sea, sovereign wealth fund, speech recognition, Stephen Hawking, strong AI, superintelligent machines, surveillance capitalism, technological singularity, The Coming Technological Singularity, theory of mind, Tim Cook: Apple, trade route, Turing machine, Turing test, uber lyft, Von Neumann architecture, Watson beat the top human players on Jeopardy!, zero day

There wasn’t a way to build a thinking machine—the processes, materials, and power weren’t yet available—and so the theory couldn’t be tested. The leap from theoretical thinking machines to computers that began to mimic human thought happened in the 1930s with the publication of two seminal papers: Claude Shannon’s “A Symbolic Analysis of Switching and Relay Circuits” and Alan Turing’s “On Computable Numbers, with an Application to the Entscheidungsproblem.” As an electrical engineering student at MIT, Shannon took an elective course in philosophy—an unusual diversion. Boole’s An Investigation of the Laws of Thought became the primary reference for Shannon’s thesis. His advisor, Vannevar Bush, encouraged him to map Boolean logic to physical circuits.

See also Transparency standards Transparency standards: establishment of for Big Nine, 251; establishment of global, 252 Tribes, AI: anti-humanistic bias in, 57; characteristics, 56; groupthink, 53; homogeneity, 52; lack of diversity, 56; leaders, 53–65; need to address diversity within, 57–58; sexual assault and harassment by members, 55–56; unconscious bias training programs and, 56; unconscious biases of members, 52; university education and homogeneity of members, 58–61, 64 Trudeau, Justin, 236 TrueNorth neuromorphic chip, 92 Trump, Donald: administration, 70, 75, 85; campaign climate change comments, 75; science and technology research budget cuts, 243 Turing, Alan, 24–25, 26, 27–29, 30, 31, 35, 259; morphogenesis theory, 204; neural network concept, 27–29;“On Computable Numbers, With an Application to the Entscheidungsproblem,” 24. See also Turing Test Turing test, 27–28, 50, 146, 169, 184 Turriano, Juanelo: mechanical monk creation of, 18, 25 Tversky, Amos, 108 2000 HUB5 English, 181 2001: A Space Odyssey, 2, 35: HAL 9000, 2, 35, 39 U.S. Army: ENIAC, 27; Futures Command, 212 U.S.


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How to Create a Mind: The Secret of Human Thought Revealed by Ray Kurzweil

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Albert Michelson, anesthesia awareness, anthropic principle, brain emulation, cellular automata, Claude Shannon: information theory, cloud computing, computer age, Dean Kamen, discovery of DNA, double helix, en.wikipedia.org, epigenetics, George Gilder, Google Earth, Isaac Newton, iterative process, Jacquard loom, John von Neumann, Law of Accelerating Returns, linear programming, Loebner Prize, mandelbrot fractal, Norbert Wiener, optical character recognition, pattern recognition, Peter Thiel, Ralph Waldo Emerson, random walk, Ray Kurzweil, reversible computing, selective serotonin reuptake inhibitor (SSRI), self-driving car, speech recognition, Steven Pinker, strong AI, the scientific method, theory of mind, Turing complete, Turing machine, Turing test, Wall-E, Watson beat the top human players on Jeopardy!, X Prize

Chapter 8: The Mind as Computer 1. Salomon Bochner, A Biographical Memoir of John von Neumann (Washington, DC: National Academy of Sciences, 1958). 2. A. M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society Series 2, vol. 42 (1936–37): 230–65, http://www.comlab.ox.ac.uk/activities/ieg/e-library/sources/tp2-ie.pdf. A. M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem: A Correction,” Proceedings of the London Mathematical Society 43 (1938): 544–46. 3. John von Neumann, “First Draft of a Report on the EDVAC,” Moore School of Electrical Engineering, University of Pennsylvania, June 30, 1945.


God Created the Integers: The Mathematical Breakthroughs That Changed History by Stephen Hawking

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Antoine Gombaud: Chevalier de Méré, Augustin-Louis Cauchy, British Empire, Edmond Halley, Eratosthenes, Fellow of the Royal Society, G4S, Georg Cantor, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, p-value, Pierre-Simon Laplace, Richard Feynman, Stephen Hawking, Turing machine

Suppose that in a certain complete configuration the numbers representing the successive symbols on the tape are s1 s2 . . . sn, that the m-th symbol is scanned, and that the m-configuration has the number t; then we may represent this complete configuration by the formula ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM. A CORRECTION In a paper entitled “On computable numbers, with an application to the Entscheidungsproblem”[1] the author gave a proof of the insolubility of the Entscheidungsproblem of the “engere Funktionenkalkül”. This proof contained some formal errors[2] which will be corrected here: there are also some other statements in the same paper which should be modified, although they are not actually false as they stand.

Selections from Henri Lebesgue’s Integrale, Longeur, Aire reprinted from Annali di Matematica, Pura ed Applicata, 1902, Ser. 3, vol. 7, pp. 231–359. Kurt Gödel’s On Formally Undecidable Propositions of Principia Mathematica and Related Systems, trans. B. Meltzer, courtesy of Dover Publications. Alan Turing’s On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society courtesy of the London Mathematical Society. Picture Credits: Euclid: Getty Images. Archimedes: Getty Images. Diophantus: Title page of Diophanti Alexandrini Arthimeticorum libri sex. . . ., 1621: Library of Congress, call number QA31.D5, Rare Book/Special Collections Reading Room, (Jefferson LJ239).

CONTENTS Introduction EUCLID (C. 325BC–265BC) His Life and Work Selections from Euclid’s Elements Book I: Basic Geometry—Definitions, Postulates, Common Notions; and Proposition 47, (leading up to the Pythagorean Theorem) Book V: The Eudoxian Theory of Proportion—Definitions & Propositions Book VII: Elementary Number Theory—Definitions & Propositions Book IX: Proposition 20: The Infinitude of Prime Numbers Book IX: Proposition 36: Even Perfect Numbers Book X: Commensurable and Incommensurable Magnitudes ARCHIMEDES (287BC–212BC) His Life and Work Selections from The Works of Archimedes On the Sphere and Cylinder, Books I and II Measurement of a Circle The Sand Reckoner The Methods DIOPHANTUS (C. 200–284) His Life and Work Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra Book II Problems 8–35 Book III Problems 5–21 Book V Problems 1–29 RENÉ DESCARTES (1596–1650) His Life and Work The Geometry of Rene Descartes ISAAC NEWTON (1642–1727) His Life and Work Selections from Principia On First and Last Ratios of Quantities LEONHARD EULER (1707–1783) His Life and Work On the sums of series of reciprocals (De summis serierum reciprocarum) The Seven Bridges of Konigsberg Proof that Every Integer is A Sum of Four Squares PIERRE SIMON LAPLACE (1749–1827) His Life and Work A Philosophical Essay on Probabilities JEAN BAPTISTE JOSEPH FOURIER (1768–1830) His Life and Work Selection from The Analytical Theory of Heat Chapter III: Propagation of Heat in an Infinite Rectangular Solid (The Fourier series) CARL FRIEDRICH GAUSS (1777–1855) His Life and Work Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions) Section III Residues of Powers Section IV Congruences of the Second Degree AUGUSTIN-LOUIS CAUCHY (1789–1857) His Life and Work Selections from Oeuvres complètes d’Augustin Cauchy Résumé des leçons données à l’École Royale Polytechnique sur le calcul infinitésimal (1823), series 2, vol. 4 Lessons 3–4 on differential calculus Lessons 21–24 on the integral NIKOLAI IVANOVICH LOBACHEVSKY (1792–1856) His Life and Work Geometrical Researches on the Theory of Parallels JÁNOS BOLYAI (1802–1860) His Life and Work The Science of Absolute Space ÉVARISTE GALOIS (1811–1832) His Life and Work On the conditions that an equation be soluble by radicals Of the primitive equations which are soluble by radicals On Groups and Equations and Abelian Integrals GEORGE BOOLE (1815–1864) His Life and Work An Investigation of the Laws of Thought BERNHARD RIEMANN (1826–1866) His Life and Work On the Representability of a Function by Means of a Trigonometric Series (Ueber die Darstellbarkeit eine Function durch einer trigonometrische Reihe) On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypothesen, welche der Geometrie zu Grunde liegen) On the Number of Prime Numbers Less than a Given Quantity (Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse) KARL WEIERSTRASS (1815–1897) His Life and Work Selected Chapters on the Theory of Functions, Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857 § 7 Gleichmässige Stetigkeit (Uniform Continuity) RICHARD DEDEKIND (1831–1916) His Life and Work Essays on the Theory of Numbers GEORG CANTOR (1848–1918) His Life and Work Selections from Contributions to the Founding of the Theory of Transfinite Numbers Articles I and II HENRI LEBESGUE (1875–1941) His Life and Work Selections from Integrale, Longeur, Aire (Intergral, Length, Area) Preliminaries and Integral KURT GÖDEL (1906–1978) His Life and Work On Formally Undecidable Propositions of Principia Mathematica and Related Systems ALAN TURING (1912–1954) His Life and Work On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society INTRODUCTION WE ARE LUCKY TO LIVE IN AN AGE LN WHICH WE ARE STILL MAKING DISCOVERIES. IT IS LIKE THE DISCOVERY OF AMERICA-YOU ONLY DISCOVER IT ONCE. THE AGE IN WHICH WE LIVE IS THE AGE IN WHICH WE ARE DISCOVERING THE FUNDAMENTAL LAWS OF NATURE . . .


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Complexity: A Guided Tour by Melanie Mitchell

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Albert Michelson, Alfred Russel Wallace, anti-communist, Arthur Eddington, Benoit Mandelbrot, bioinformatics, cellular automata, Claude Shannon: information theory, clockwork universe, complexity theory, computer age, conceptual framework, Conway's Game of Life, dark matter, discrete time, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, From Mathematics to the Technologies of Life and Death, Garrett Hardin, Geoffrey West, Santa Fe Institute, Gödel, Escher, Bach, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John von Neumann, Long Term Capital Management, mandelbrot fractal, market bubble, Menlo Park, Murray Gell-Mann, Network effects, Norbert Wiener, Norman Macrae, Paul Erdős, peer-to-peer, phenotype, Pierre-Simon Laplace, Ray Kurzweil, reversible computing, scientific worldview, stem cell, The Wealth of Nations by Adam Smith, Thomas Malthus, Tragedy of the Commons, Turing machine

., Alan Turing: The Enigma. New York: Simon & Schuster, 1983, p. 92. “Turing killed off the third”: Another mathematician, Alonzo Church, also proved that there are undecidable statements in mathematics, but Turing’s results ended up being more influential. “his answer, again, was ‘no’ ”: Turing, A. M., On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 2(42), 1936, pp. 230–265. “According to his biographer Hao Wang”: Wang, H., Reflections on Kurt Gödel. Cambridge, MA: MIT Press, 1987. Chapter 5 “All great truths begin as blasphemies”: Shaw, G.

On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. Zeitschrift fuer Physik, 53, 1929, pp. 840–856. Tattersall, I. Becoming Human: Evolution and Human Uniqueness. New York: Harvest Books, 1999. Travis, J. Eye-opening gene. Science News Online, May 10, 1997. Turing, A. M. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 2(42), 1936, pp. 230–265. Ulam, S. M. and von Neumann, J. On combination of stochastic and deterministic processes (abstract). Bulletin of the American Mathematical Society, 53, 1947, 1120. Varn, D.


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In Our Own Image: Savior or Destroyer? The History and Future of Artificial Intelligence by George Zarkadakis

3D printing, Ada Lovelace, agricultural Revolution, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, animal electricity, anthropic principle, Asperger Syndrome, autonomous vehicles, barriers to entry, battle of ideas, Berlin Wall, bioinformatics, British Empire, business process, carbon-based life, cellular automata, Claude Shannon: information theory, combinatorial explosion, complexity theory, continuous integration, Conway's Game of Life, cosmological principle, dark matter, dematerialisation, double helix, Douglas Hofstadter, Edward Snowden, epigenetics, Flash crash, Google Glasses, Gödel, Escher, Bach, income inequality, index card, industrial robot, Internet of things, invention of agriculture, invention of the steam engine, invisible hand, Isaac Newton, Jacquard loom, Jacques de Vaucanson, James Watt: steam engine, job automation, John von Neumann, Joseph-Marie Jacquard, Kickstarter, liberal capitalism, lifelogging, millennium bug, Moravec's paradox, natural language processing, Norbert Wiener, off grid, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, Paul Erdős, post-industrial society, prediction markets, Ray Kurzweil, Rodney Brooks, Second Machine Age, self-driving car, Silicon Valley, social intelligence, speech recognition, stem cell, Stephen Hawking, Steven Pinker, strong AI, technological singularity, The Coming Technological Singularity, The Future of Employment, the scientific method, theory of mind, Turing complete, Turing machine, Turing test, Tyler Cowen: Great Stagnation, Vernor Vinge, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Y2K

., and Naccache, L. (2001), ‘Towards a cognitive neuroscience of consciousness: basic evidence of a workspace framework’, in: Cognition, 79 (1–2), pp. 1-37. 7Artificial Intelligence split from cybernetics in the summer of 1956 with its inaugural conference in Dartmouth, New Hampshire, one year before von Neumann’s death. 8Turing, A. M. (1936), ‘On Computable Numbers, with an Application to the Entscheidungsproblem’, Proceedings of the London Mathematical Society, 2 (1937), 42, pp. 230–65. 9To be more accurate, Gödel encoded metamathematical statements within ordinary arithmetic. 10The incomplete manuscript and notes based on a series of lectures given by von Neumann at the University of Illinois in 1949 was assembled and edited by Arthur Burks and published ten years after von Neumann’s death. 11New findings in epigenetics show that the mechanism of passing hereditary features to future generations is more complex than previously thought, and probably involves other systems in the cell beyond DNA replication. 12The human mind may be beyond logical coding (as Gödel has indirectly showed) but it is not beyond computation.

That was the actual statement that Gödel ‘formalised’. 14To be more precise, Gödel proved that for any computable axiomatic system that is powerful enough to describe arithmetic of the natural numbers (e.g. the Peano axioms) the consistency of the axioms cannot be proven within the system. 15Heisenberg’s uncertainty principle essentially states that we can never know everything about a quantum phenomenon. Therefore, nature will remain forever at least partially unknown to us. 16Turing, A. M. (1936), ‘On Computable Numbers, with an Application to the Entscheidungsproblem’, in: Proceedings of the London Mathematical Society, 1937, Vol. 2, No. 42, pp. 230–65. 17The American mathematician Alonzo Church independently published his proof of the Entscheidungsproblem for the American Mathematical Society using a method called ‘lamda calculus’, and therefore the solution is known as the Turing-Church theorem.


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Deep Medicine: How Artificial Intelligence Can Make Healthcare Human Again by Eric Topol

23andMe, Affordable Care Act / Obamacare, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic bias, artificial general intelligence, augmented reality, autonomous vehicles, backpropagation, bioinformatics, blockchain, cloud computing, cognitive bias, Colonization of Mars, computer age, computer vision, conceptual framework, creative destruction, crowdsourcing, Daniel Kahneman / Amos Tversky, dark matter, David Brooks, digital twin, Elon Musk, en.wikipedia.org, epigenetics, Erik Brynjolfsson, fault tolerance, George Santayana, Google Glasses, ImageNet competition, Jeff Bezos, job automation, job satisfaction, Joi Ito, Mark Zuckerberg, medical residency, meta-analysis, microbiome, natural language processing, new economy, Nicholas Carr, nudge unit, pattern recognition, performance metric, personalized medicine, phenotype, placebo effect, randomized controlled trial, recommendation engine, Rubik’s Cube, Sam Altman, self-driving car, Silicon Valley, speech recognition, Stephen Hawking, text mining, the scientific method, Tim Cook: Apple, War on Poverty, Watson beat the top human players on Jeopardy!, working-age population

A BRIEF HISTORY With all the chatter and buzz about AI these days, it would be easy to think it was some kind of new invention, but, conceptually, it goes back at least eighty years. In 1936 Alan Turing published a paper on powerful, automated, intelligent systems—a universal computer—titled “On Computable Numbers, with an Application to the Entscheidungsproblem.”13 I don’t understand the multitude of equations in this thirty-six-page gem, but I must agree with his statement, “We are now in a position to show that the Entscheidungsproblem cannot be solved,” both because I can’t say it and still don’t have a clue what it is!

., “Algorithmic Life,” Los Angeles Review of Books. 2017. 10. Harari, Y. N., Homo Deus. 2016. New York: HarperCollins, p. 348. 11. Harari, Homo Deus. 12. Beam, A. L., and I. S. Kohane, “Big Data and Machine Learning in Health Care.” JAMA, 2018. 319(13): pp. 1317–1318. 13. Turing, A. M., “On Computable Numbers with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, 1936. 42(1): pp. 230–265. doi: 10.1112/plms/s2-42.1.230. 14. Turing, A. M., “Computing Machinery and Intelligence.” Mind, 1950. 49: pp. 433–460. https://www.csee.umbc.edu/courses/471/papers/turing.pdf. 15.


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Tools for Thought: The History and Future of Mind-Expanding Technology by Howard Rheingold

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, card file, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer age, conceptual framework, Conway's Game of Life, Douglas Engelbart, Dynabook, experimental subject, Hacker Ethic, Howard Rheingold, interchangeable parts, invention of movable type, invention of the printing press, Jacquard loom, John von Neumann, knowledge worker, Marshall McLuhan, Menlo Park, Norbert Wiener, packet switching, pattern recognition, popular electronics, post-industrial society, RAND corporation, Robert Metcalfe, Silicon Valley, speech recognition, Steve Jobs, Steve Wozniak, Stewart Brand, Ted Nelson, telemarketer, Turing machine, Turing test, Vannevar Bush, Von Neumann architecture

Turing then proved that for any formal system, there exists a Turing machine that can be programmed to imitate it. This kind of general formal system with the ability to imitate any other formal system was what Turing was getting at. These systems are now known as "universal Turing machines." The theory was first stated in a paper with the forbidding title "On Computable Numbers, with an application to the Entscheidungsproblem." The Turing Machine was a hypothetical device Turing invented on the way to settling a critical question about the foundations of mathematics as a formalized means of thinking. He showed that his device could solve infinitely many problems, but that there are some problems that cannot be solved because there is no way of predicting in advance whether or when the machine is going to stop.

[10] George Boole, An investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities (London: Macmillan, 1854; reprint, New York: Dover Publications, 1958), 1-3 [11]Leon E Truesdell, The Development of Punch Card Tabulation in the Bureau of the Census, 1890-1940 (Washington: U.S. Government Printing Office, 1965), 30-31. [12] Ibid., 31. Chapter Three: The First Hacker and his Imaginary Machine [1] Alan M. Turing, "On Computable Numbers, with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society, second series, vol. 42, part 3, November 12, 1936, 230-265. [2] An amusing example of an easily constructed Turing machine, using pebbles and toilet paper, is given in the third chapter of Joseph Weizenbaum, Computer Power and Human Reason (San Francisco: W.


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Infinite Ascent: A Short History of Mathematics by David Berlinski

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Douglas Hofstadter, Eratosthenes, four colour theorem, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, Murray Gell-Mann, Stephen Hawking, Turing machine, William of Occam

Some years after Gödel presented his results, the American logician Alonzo Church defined what he called the lambda-computable functions. And to roughly the same point since the recursive and the lambda-computable functions, although quite different, did the same thing and carried on in the same way. In 1936, Alan Turing published the first of his papers on computability, “On Computable Numbers with an Application to the Entscheidungsproblem,” and so gave the idea of an algorithm a vivid and unforgettable metaphor. An effective calculation is any calculation that could be undertaken, Turing argued, by an exceptionally simple imaginary machine, or even a human computer, someone who has, like a clerk in the department of motor vehicles or a college dean, been stripped of all cognitive powers and can as a result execute only a few primitive acts.


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The Golden Ticket: P, NP, and the Search for the Impossible by Lance Fortnow

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Claude Shannon: information theory, cloud computing, complexity theory, Donald Knuth, Erdős number, four colour theorem, Gerolamo Cardano, Isaac Newton, Johannes Kepler, John von Neumann, linear programming, new economy, NP-complete, Occam's razor, P = NP, Paul Erdős, Richard Feynman, Rubik’s Cube, smart grid, Stephen Hawking, traveling salesman, Turing machine, Turing test, Watson beat the top human players on Jeopardy!, William of Occam

Trakhtenbrot, “A Survey of Russian Approaches to Prebor (Brute-Force Search) Algorithms,” Annals of the History of Computing 6, no. 4 (October 1984): 384–400. Warren McCulloch and Walter Pitts, “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Bulletin of Mathematical Biology 5, no. 4 (1943): 115–33. Panel discussion, Complexity of Computer Computations 40, no. 4 (1972): 169–85. Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society 42 (1936): 230–65. S. Yablonsky, “On the Impossibility of Eliminating PEREBOR in Solving Some Problems of Circuit Theory,” Doklady Akademii Nauk SSSR 124 (1959): 44–47. Y. Zhuravlev, “On the Impossibility of Constructing Minimal Disjunctive Normal Forms for Boolean Functions by Algorithms of a Certain Class, Doklady Akademii Nauk SSSR 132 (1960): 504–6.


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Computer: A History of the Information Machine by Martin Campbell-Kelly, William Aspray, Nathan L. Ensmenger, Jeffrey R. Yost

Ada Lovelace, air freight, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Apple's 1984 Super Bowl advert, barriers to entry, Bill Gates: Altair 8800, borderless world, Buckminster Fuller, Build a better mousetrap, Byte Shop, card file, cashless society, cloud computing, combinatorial explosion, computer age, deskilling, don't be evil, Donald Davies, Douglas Engelbart, Douglas Engelbart, Dynabook, fault tolerance, Fellow of the Royal Society, financial independence, Frederick Winslow Taylor, game design, garden city movement, Grace Hopper, hockey-stick growth, Ian Bogost, informal economy, interchangeable parts, invention of the wheel, Jacquard loom, Jeff Bezos, jimmy wales, John Markoff, John von Neumann, Kickstarter, light touch regulation, linked data, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Menlo Park, Mitch Kapor, natural language processing, Network effects, New Journalism, Norbert Wiener, Occupy movement, optical character recognition, packet switching, PageRank, pattern recognition, Pierre-Simon Laplace, pirate software, popular electronics, prediction markets, pre–internet, QWERTY keyboard, RAND corporation, Robert X Cringely, Silicon Valley, Silicon Valley startup, Steve Jobs, Steven Levy, Stewart Brand, Ted Nelson, the market place, Turing machine, Vannevar Bush, Von Neumann architecture, Whole Earth Catalog, William Shockley: the traitorous eight, women in the workforce, young professional

Alan Turing was born in 1912 and at school he was drawn to science and practical experimenting. He won a scholarship to King’s College, Cambridge University, and graduated in mathematics with the highest honors in 1934. He became a Fellow of King’s College and, in 1936, published his classic paper “On Computable Numbers with an Application to the Entscheidungsproblem” in which he described the Turing Machine. Turing showed that not all mathematical questions were decidable, and that one could not always determine whether or not a mathematical function was computable. For nonmathematicians this was an obscure concept to grasp, although later—after World War II—Turing explained the idea in an article in Science News.

See NCR National Defense Research Committee (NDRC), 66, 72, 74, 145 National Science Foundation (NSF), 292 National Semiconductor, 221 Nature, 41, 59, 299–300 Nautical Almanac, 4, 7, 47, 52–53 Navigation tables, 4, 47, 53 NCR accounting machines, 31, 38, 53, 117 acquisition of CRC, 117 business software, 122 business strategies of, 30, 34, 123–124, 132 cash registers, 31–32 computer industry and, 98 digital computing machines, 54 as IBM competitor, 133 non-IBM-compatible computers of, 132 postwar business challenges, 103 punched-card systems, 21, 38 role in computer industry, 21, 117 sales strategies of, 30, 31–32, 36 scanning technology, 164 as software contractors, 177 technical innovation by, 31 user training, 30 Nelson, Ted, 234–235, 237, 279, 286 Netiquette, 285 Netscape Communications Corporation, 289–290 Network analyzers, 48, 50 Network protocols, 285 Networks, 275 New Communalists, 234 New Deal projects, 39 New Product Line (IBM), 126–128, 129 Newman, Max, 82 Nokia, 297, 298 Non-IBM-compatible computers, 132 Norris, William, 99, 124, 249 Northrop Aircraft Corporation, 101, 102, 105, 116 Notation, programming, 168 Notebook computers, 296, 298 Noyce, Robert, 219–221, 222, 231, 249 Noyes, Eliot, 120 Nuclear weapons, 65, 74, 78, 109, 127, 149 Numerical meteorology, 50–52 Office machine industry. See Business machine industry Office of Naval Research (ONR), 147–148, 150 Office of Scientific Research and Development (OSRD), 49, 65–66, 74 Office systematizers, 19, 134 Olivetti, 197, 251 Olsen, Kenneth, 217–218 Omidyar, Pierre, 295 “On Computable Numbers with an Application to the Entscheidungsproblem” (Turing), 60 Opel, John, 246 Open-source software, 215, 288, 296 Operating systems for mainframe computers, 179–182, 205, 206, 210, 212–215 for mobile devices, 297, 298 for personal computers, 242–243, 246–247, 253–254, 257–258, 264–267 See also specific operating systems Optical character recognition, 164 OS/2 operating system, 265, 266 OS/360 operating system, 179–182, 183, 212 Osborne 1 computer, 198 (photo), 296 Outsourcing of components and software, 245–246, 247 Oxford English Dictionary, 3 Packaged software programs, 186–188, 254 Packard, David, 249 Packet-switching technology, 281–282 Page, Larry, 294 Palm, Inc., 297, 298 Palo Alto Research Center (PARC), 260, 261, 280, 296 Papian, Bill, 150 Parker, Sean, 301 Pascal programming language, 185 Passages from the Life of a Philosopher (C.


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The Age of Spiritual Machines: When Computers Exceed Human Intelligence by Ray Kurzweil

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, backpropagation, Buckminster Fuller, call centre, cellular automata, combinatorial explosion, complexity theory, computer age, computer vision, cosmological constant, cosmological principle, Danny Hillis, double helix, Douglas Hofstadter, Everything should be made as simple as possible, first square of the chessboard / second half of the chessboard, fudge factor, functional programming, George Gilder, Gödel, Escher, Bach, I think there is a world market for maybe five computers, information retrieval, invention of movable type, Isaac Newton, iterative process, Jacquard loom, John Markoff, John von Neumann, Lao Tzu, Law of Accelerating Returns, mandelbrot fractal, Marshall McLuhan, Menlo Park, natural language processing, Norbert Wiener, optical character recognition, ought to be enough for anybody, pattern recognition, phenotype, Ralph Waldo Emerson, Ray Kurzweil, Richard Feynman, Robert Metcalfe, Schrödinger's Cat, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, social intelligence, speech recognition, Steven Pinker, Stewart Brand, stochastic process, technological singularity, Ted Kaczynski, telepresence, the medium is the message, There's no reason for any individual to have a computer in his home - Ken Olsen, traveling salesman, Turing machine, Turing test, Whole Earth Review, Y2K

Fatmi and R. W Young, “A Definition of Intelligence,” Nature 228 (1970): 97. 16 Alan Turing showed that the essential basis of computation could be modeled with a very simple theoretical machine. He created the first theoretical computer in 1936 (first introduced in Alan M. Turing, “On Computable Numbers with an Application to the Entscheinungs Problem,” Proc. London Math. Soc. 42 [1936]: 230-265) in an eponymous conception called the Turing machine. As with a number of Turing’s breakthroughs, he would have both the first and last word. The Turing machine represented the founding of modern computational theory.

_______. Visual Explanations: Images and Quantities, Evidence and Narrative. Cheshire, CT: Graphics Press, 1997. Turing, Alan. “Computing Machinery and Intelligence.” Reprinted in Minds and Machines, edited by Alan Ross Anderson. Englewood Cliffs, NJ: Prentice-Hall, 1964. ________. “On Computable Numbers, with an Application to the Entscheidungsproblem ” Proceedings, London Mathematical Society, 2, no. 42 (1936). Turkle, Sherry. The Second Self: Computers and the Human Spirit. New York: Simon and Schuster, 1984. Tye, Michael. Ten Problems of Consciousness: A Representational Theory of the Phenomenal Mind.


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The Stack: On Software and Sovereignty by Benjamin H. Bratton

1960s counterculture, 3D printing, 4chan, Ada Lovelace, additive manufacturing, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, Amazon Mechanical Turk, Amazon Web Services, augmented reality, autonomous vehicles, basic income, Benevolent Dictator For Life (BDFL), Berlin Wall, bioinformatics, Biosphere 2, bitcoin, blockchain, Buckminster Fuller, Burning Man, call centre, carbon footprint, carbon-based life, Cass Sunstein, Celebration, Florida, charter city, clean water, cloud computing, connected car, corporate governance, crowdsourcing, cryptocurrency, dark matter, David Graeber, deglobalization, dematerialisation, disintermediation, distributed generation, don't be evil, Douglas Engelbart, Douglas Engelbart, Edward Snowden, Elon Musk, en.wikipedia.org, Eratosthenes, Ethereum, ethereum blockchain, facts on the ground, Flash crash, Frank Gehry, Frederick Winslow Taylor, functional programming, future of work, Georg Cantor, gig economy, global supply chain, Google Earth, Google Glasses, Guggenheim Bilbao, High speed trading, Hyperloop, Ian Bogost, illegal immigration, industrial robot, information retrieval, Intergovernmental Panel on Climate Change (IPCC), intermodal, Internet of things, invisible hand, Jacob Appelbaum, Jaron Lanier, Joan Didion, John Markoff, Joi Ito, Jony Ive, Julian Assange, Khan Academy, Kim Stanley Robinson, liberal capitalism, lifelogging, linked data, Mark Zuckerberg, market fundamentalism, Marshall McLuhan, Masdar, McMansion, means of production, megacity, megastructure, Menlo Park, Minecraft, MITM: man-in-the-middle, Monroe Doctrine, Network effects, new economy, offshore financial centre, oil shale / tar sands, packet switching, PageRank, pattern recognition, peak oil, peer-to-peer, performance metric, personalized medicine, Peter Eisenman, Peter Thiel, phenotype, Philip Mirowski, Pierre-Simon Laplace, place-making, planetary scale, RAND corporation, recommendation engine, reserve currency, RFID, Robert Bork, Sand Hill Road, self-driving car, semantic web, sharing economy, Silicon Valley, Silicon Valley ideology, Slavoj Žižek, smart cities, smart grid, smart meter, social graph, software studies, South China Sea, sovereign wealth fund, special economic zone, spectrum auction, Startup school, statistical arbitrage, Steve Jobs, Steven Levy, Stewart Brand, Stuxnet, Superbowl ad, supply-chain management, supply-chain management software, TaskRabbit, the built environment, The Chicago School, the scientific method, Torches of Freedom, transaction costs, Turing complete, Turing machine, Turing test, undersea cable, universal basic income, urban planning, Vernor Vinge, Washington Consensus, web application, Westphalian system, WikiLeaks, working poor, Y Combinator

Later, the formalization of logic within the philosophy mathematics (from Pierre-Simon Laplace, to Gottlob Frege, Georg Cantor, David Hilbert, and so many others) helped to introduce, inform, and ultimately disprove a version of the Enlightenment as the expression of universal deterministic processes (of both thought and physics). In 1936, with his now-famous paper, “On Computable Numbers, with an Application to the Entscheidungsproblem,” a very young Alan Turing at once introduced the theoretical basis of modern computing and demonstrated the limits of what could and could not ever be calculated and computed by a universal technology. Turing envisioned his famous “machine” according to the tools of his time to involve an infinite amount of “tape” divided into cells that can store symbols, moved along a stationary read-write “head” that can alter those symbols, a “state register” that can map the current arrangement of symbols along the tape, and a “table” of instructions that tells the machine to rewrite or erase the symbol and to move the “head,” assuming a new state for the “register” to map.

Readers may reference the image at this book's companion website, thestack.org. 5.  Originally conceived in 1936 by twenty-four-year-old Alan Turing and called an “a-machine” (for “automatic machine”), it describes a hypothetical universal computer, which, given enough time and energy, would be capable of calculating any “computable” problem. In that paper, “On Computable Numbers, with an Application to the Entscheidungs Problem,” Proceedings of the London Mathematical Society, Ser. 2 42 (1937), Turing demonstrates the range of problems that in fact are not computable. The figure of the Turing machine, as a philosophical and machinic hypothesis, stands for the technology of universal computation and for the ultimate limits of computation within mathematics. 6. 

See also User AI User, 277–279 algorithmic hardware, 348–349 animal User, 274–277 as co-User, 276–277, 349 designing for, 339 enrollment and motivation, 297–298 identifying, 345 machine User, 279–284 rights of, 345 nonpersonhood, 173–175 nonplace, end of, 16 non-state actors with nation-state functions, 10–11 nonvisual interfaces, 341, 424n41 Nortel patent bid, 134 North American Free Trade Agreement, 443n23 North Sea wind farms proposal (OMA), 181 No-Stop City project (Archizoom), 149–151, 160, 178–179 notational systems, 383n4 NSA/CSS Threat Operations Center, US, 441n8 Obama, Barack, 98, 180, 322 Obi-Wan Kenobi, 176 object identifiers, universal, 214–215 object-instruments, computational, 227 objects addressability, 214–215 agency of, 131 defined, 402n59 essentials of, 260 identifiers, digital, 207, 214–215 interface design, 230–235 memory of, 212, 215 non-citizen User, 188 object-to-object communication, 197, 210, 212, 216, 338 object-to-object spam, 216 reordering by, 206 semantic relations, 202–203 SPIME designation for, 201–204 as symbolic artifacts, 212 ocean exploration, 30 oceanic data centers, 113–114, 140 Oculus, 127 Office of Metropolitan Architecture (OMA), 53, 99, 170, 178, 180–181 offshoring, 443n23 oil geopolity, 99 Oklahoma City Bombing guidelines, 322 “On Computable Numbers, with an Application to the Entscheidungsproblem” (Turing), 78 One57, New York, 311 One Riverside Park, New York, 311 OOZ (Jeremijenko), 276 Open, The (Agamben), 273 OpenFlow, 437n58 open government movement, 121 Open Stack, 174 open systems interconnection (OSI) network model, 61–63 Operation Centurion, Dr.


pages: 333 words: 64,581

Clean Agile: Back to Basics by Robert C. Martin

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, c2.com, continuous integration, DevOps, disinformation, double entry bookkeeping, en.wikipedia.org, failed state, Frederick Winslow Taylor, index card, iterative process, Kubernetes, loose coupling, microservices, remote working, revision control, Turing machine

I wish I could have been a fly on the wall when Alan Turing was writing his 1936 paper.1 My guess is that the many “programs” he wrote in that book were developed in small steps with plenty of desk checking. I also imagine that the first code he wrote for the Automatic Computing Engine, in 1946, was written in small steps, with lots of desk checking, and even some real testing. 1. Turing, A. M. 1936. On computable numbers, with an application to the Entscheidungsproblem [proof]. Proceedings of the London Mathematical Society, 2 (published 1937), 42(1):230–65. The best way to understand this paper is to read Charles Petzold’s masterpiece: Petzold, C. 2008. The Annotated Turing: A Guided Tour through Alan Turing’s Historic Paper on Computability and the Turing Machine.


pages: 229 words: 67,599

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age by Paul J. Nahin

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Claude Shannon: information theory, conceptual framework, Edward Thorp, Fellow of the Royal Society, finite state, four colour theorem, Georg Cantor, Grace Hopper, Isaac Newton, John von Neumann, knapsack problem, New Journalism, Pierre-Simon Laplace, reversible computing, Richard Feynman, Schrödinger's Cat, Steve Jobs, Steve Wozniak, thinkpad, Thomas Bayes, Turing machine, Turing test, V2 rocket

In developing this view of a computing machine, Turing was not suggesting it as a practical design for an actual machine. Rather, as a mathematician he used his machines as a conceptual framework in which to study the limits on just what mechanistic devices can actually compute. Indeed, the title of his 1936 paper, “On Computable Numbers, with an Application to the Entscheidungsproblem’’—that final tongue-twister translates as “the decision problem’’—clearly shows Turing’s intent. His great accomplishment was to show that not all the numbers we can imagine are in fact actually computable. That is, Turing showed there are limits to what a computer—any computer—can do.


pages: 253 words: 80,074

The Man Who Invented the Computer by Jane Smiley

1919 Motor Transport Corps convoy, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Arthur Eddington, British Empire, c2.com, computer age, Fellow of the Royal Society, Henri Poincaré, IBM and the Holocaust, Isaac Newton, John von Neumann, Karl Jansky, Norbert Wiener, Norman Macrae, Pierre-Simon Laplace, RAND corporation, Turing machine, Vannevar Bush, Von Neumann architecture

Andrew Hodges, Turing’s biographer, points out that Turing’s idea “was not only a matter of abstract mathematics, not only a play of symbols, for it involved thinking about what people did in the physical world … His machines—soon to be called Turing Machines—offered a bridge, a connection between abstract symbols and the physical world. Indeed, his imagery was, for Cambridge, almost shockingly industrial.” In May 1936, Alan Turing submitted his paper, entitled “On Computable Numbers, with an Application to the Entscheidungsproblem,” to the Proceedings of the London Mathematical Society and then applied unsuccessfully for a Procter Fellowship at Princeton. As far as anyone in England knew, only Turing and the American Alonzo Church had come up with answers to the Entscheidungsproblem.


pages: 720 words: 197,129

The Innovators: How a Group of Inventors, Hackers, Geniuses and Geeks Created the Digital Revolution by Walter Isaacson

1960s counterculture, Ada Lovelace, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, Apple II, augmented reality, back-to-the-land, beat the dealer, Bill Atkinson, Bill Gates: Altair 8800, bitcoin, Bob Noyce, Buckminster Fuller, Byte Shop, c2.com, call centre, citizen journalism, Claude Shannon: information theory, Clayton Christensen, commoditize, computer age, crowdsourcing, cryptocurrency, Debian, desegregation, Donald Davies, Douglas Engelbart, Douglas Engelbart, Douglas Hofstadter, Dynabook, El Camino Real, Electric Kool-Aid Acid Test, en.wikipedia.org, Firefox, Google Glasses, Grace Hopper, Gödel, Escher, Bach, Hacker Ethic, Haight Ashbury, Howard Rheingold, Hush-A-Phone, HyperCard, hypertext link, index card, Internet Archive, Jacquard loom, Jaron Lanier, Jeff Bezos, jimmy wales, John Markoff, John von Neumann, Joseph-Marie Jacquard, Leonard Kleinrock, linear model of innovation, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Menlo Park, Mitch Kapor, Mother of all demos, new economy, New Journalism, Norbert Wiener, Norman Macrae, packet switching, PageRank, Paul Terrell, pirate software, popular electronics, pre–internet, RAND corporation, Ray Kurzweil, RFC: Request For Comment, Richard Feynman, Richard Stallman, Robert Metcalfe, Rubik’s Cube, Sand Hill Road, Saturday Night Live, self-driving car, Silicon Valley, Silicon Valley startup, Skype, slashdot, speech recognition, Steve Ballmer, Steve Crocker, Steve Jobs, Steve Wozniak, Steven Levy, Steven Pinker, Stewart Brand, technological singularity, technoutopianism, Ted Nelson, The Coming Technological Singularity, The Nature of the Firm, The Wisdom of Crowds, Turing complete, Turing machine, Turing test, Vannevar Bush, Vernor Vinge, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Whole Earth Catalog, Whole Earth Review, wikimedia commons, William Shockley: the traitorous eight, Yochai Benkler

Despite what Hilbert seemed to hope, no mechanical procedure can determine the provability of every mathematical statement. Gödel’s incompleteness theory, the indeterminacy of quantum mechanics, and Turing’s answer to Hilbert’s third challenge all dealt blows to a mechanical, deterministic, predictable universe. Turing’s paper was published in 1937 with the not so snappy title “On Computable Numbers, with an Application to the Entscheidungsproblem.” His answer to Hilbert’s third question was useful for the development of mathematical theory. But far more important was the by-product of Turing’s proof: his concept of a Logical Computing Machine, which soon came to be known as a Turing machine. “It is possible to invent a single machine which can be used to compute any computable sequence,” he declared.10 Such a machine would be able to read the instructions of any other machine and carry out whatever task that machine could do.

., ref1 Nelson, Ted, ref1, ref2, ref3 Netscape, ref1 networks, ref1, ref2 data blocks in, ref1 distributed, ref1, ref2, ref3, ref4 lack of centralization in, ref1, ref2, ref3 packet switched, ref1, ref2, ref3, ref4 Network Working Group, ref1 Neumann, Max, ref1 neural networks, ref1 neurons, ref1 Newman, Max, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9 newsgroups, ref1 Newton, Isaac, ref1 New Yorker, ref1 New York Times, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8 New York World’s Fair (1939), ref1, ref2, ref3 NeXT, ref1, ref2 Nishi, Kay, ref1 Nixon, Richard, ref1, ref2 NM Electronics, ref1 noncomputable numbers, ref1 North Carolina, University of, ref1 Norton, Larry, ref1 Norvig, Peter, ref1 Nova, ref1, ref2 Novack, Ken, ref1 Noyce, Robert, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13 corporate culture and, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8 Fairchild resignation of, ref1 Intel employees empowered by, ref1 Intel money raised by, ref1 Intel’s organization chart drawn by, ref1 microchip of, ref1, ref2 microprocessor and, ref1 in patent lawsuit, ref1 planar process and, ref1 resistor designed by, ref1 as Shockley’s replacement, ref1 on synergy, ref1 n-p-n junction architecture, ref1 NSFNET, ref1 n-type, ref1 Nuance Communications, ref1 nuclear weapons, ref1 Internet and, ref1 Nupedia, ref1, ref2, ref3 Nutting, Bill, ref1 Nutting Associates, ref1, ref2, ref3 Obama, Barack, ref1 Office of Defense Mobilization, ref1 Office of Scientific Research, ref1 Ohm’s Law, ref1 oil, ref1 Olsen, Ken, ref1 Olson, Judith, ref1 “On Computable Numbers, with an Application to the Entscheidungsproblem“ (Turing), ref1, ref2 On Distributed Communications (Baran), ref1 One Flew Over the Cuckoo’s Nest (Kesey), ref1 online communities, ref1 oNLine System (NLS), ref1, ref2, ref3, ref4, ref5, ref6 On the Connexion of the Physical Sciences (Somerville), ref1 Opel, John, ref1 open architecture, ref1, ref2 OpenOffice, ref1 open-sourcing, ref1, ref2 Operating Manual for Spaceship Earth (Fuller), ref1 operating systems, ref1 open-source, ref1 operations, ref1 Ordnance Department, U.S.


Know Thyself by Stephen M Fleming

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, autonomous vehicles, availability heuristic, backpropagation, citation needed, computer vision, Douglas Hofstadter, Elon Musk, Estimating the Reproducibility of Psychological Science, global pandemic, index card, Jeff Bezos, l'esprit de l'escalier, Lao Tzu, lifelogging, longitudinal study, meta-analysis, mutually assured destruction, Network effects, patient HM, Pierre-Simon Laplace, prediction markets, QWERTY keyboard, recommendation engine, replication crisis, self-driving car, side project, Skype, Stanislav Petrov, statistical model, theory of mind, Thomas Bayes

Trouche, Emmanuel, Petter Johansson, Lars Hall, and Hugo Mercier. “The Selective Laziness of Reasoning.” Cognitive Science 40, no. 8 (2016): 2122–2136. Tulving, Endel. “Memory and Consciousness.” Canadian Psychology/Psychologie canadienne 26, no. 1 (1985): 1–12. Turing, Alan Mathison. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society 42, no. 1 (1937): 230–265. Ullsperger, Markus, Helga A. Harsay, Jan R. Wessel, and K. Richard Ridderinkhof. “Conscious Perception of Errors and Its Relation to the Anterior Insula.” Brain Structure & Function 214, nos. 5–6 (2010): 629–643.


pages: 332 words: 93,672

Life After Google: The Fall of Big Data and the Rise of the Blockchain Economy by George Gilder

23andMe, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, Amazon Web Services, Asilomar, augmented reality, Ben Horowitz, bitcoin, Bitcoin Ponzi scheme, blockchain, Bob Noyce, British Empire, Brownian motion, Burning Man, business process, butterfly effect, carbon footprint, cellular automata, Claude Shannon: information theory, Clayton Christensen, cloud computing, computer age, computer vision, crony capitalism, cross-subsidies, cryptocurrency, Danny Hillis, disintermediation, distributed ledger, don't be evil, Donald Knuth, Donald Trump, double entry bookkeeping, Elon Musk, Erik Brynjolfsson, Ethereum, ethereum blockchain, fault tolerance, fiat currency, Firefox, first square of the chessboard, first square of the chessboard / second half of the chessboard, floating exchange rates, Fractional reserve banking, game design, George Gilder, Google Earth, Google Glasses, Google Hangouts, index fund, inflation targeting, informal economy, Internet of things, Isaac Newton, iterative process, Jaron Lanier, Jeff Bezos, Joan Didion, John Markoff, John von Neumann, Julian Assange, Kevin Kelly, Law of Accelerating Returns, Marc Andreessen, Mark Zuckerberg, means of production, Menlo Park, Metcalfe’s law, Money creation, money: store of value / unit of account / medium of exchange, move fast and break things, move fast and break things, Network effects, new economy, Norbert Wiener, Oculus Rift, PageRank, pattern recognition, Paul Graham, peer-to-peer, Peter Thiel, Ponzi scheme, prediction markets, quantitative easing, random walk, ransomware, Ray Kurzweil, Renaissance Technologies, Robert Mercer, Robert Metcalfe, Ronald Coase, Ross Ulbricht, Ruby on Rails, Sand Hill Road, Satoshi Nakamoto, Search for Extraterrestrial Intelligence, self-driving car, sharing economy, Silicon Valley, Silicon Valley ideology, Silicon Valley startup, Singularitarianism, Skype, smart contracts, Snapchat, software is eating the world, sorting algorithm, South Sea Bubble, speech recognition, Stephen Hawking, Steve Jobs, Steven Levy, Stewart Brand, stochastic process, telepresence, Tesla Model S, theory of mind, Tim Cook: Apple, transaction costs, tulip mania, Turing complete, Turing machine, Vernor Vinge, Von Neumann architecture, Watson beat the top human players on Jeopardy!, WikiLeaks, Y Combinator, zero-sum game

Blockchain Revolution: How the Technology behind Bitcoin is Changing Money, Business, and the World (New York: Penguin Random House, 2016). Tegmark, Max. Life 3.0: Being Human in the Age of Artificial Intelligence (New York: Alfred A. Knopf, 2017). Turner, Fred. Burning Man at Google: A Cultural Infrastructure for New Media Production (Sage Journal, 2009). Turing, Alan. “On Computable Numbers, With An Application to the Entscheidungsproblem” (Princeton: Princeton Graduate Press, 1936). Turing, Alan. Systems of Logic, edited and introduced by Andrew W. Appel (Princeton, NJ: Princeton University Press, 2012). Vigna, Paul and Michael J. Casey, The Age of Cryptocurrency: How Bitcoin and Digital Money are Challenging the Global Economic Order (New York: St.


pages: 370 words: 94,968

The Most Human Human: What Talking With Computers Teaches Us About What It Means to Be Alive by Brian Christian

4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Bertrand Russell: In Praise of Idleness, carbon footprint, cellular automata, Claude Shannon: information theory, cognitive dissonance, commoditize, complexity theory, crowdsourcing, David Heinemeier Hansson, Donald Trump, Douglas Hofstadter, George Akerlof, Gödel, Escher, Bach, high net worth, Isaac Newton, Jacques de Vaucanson, Jaron Lanier, job automation, l'esprit de l'escalier, Loebner Prize, Menlo Park, Ray Kurzweil, RFID, Richard Feynman, Ronald Reagan, Skype, Social Responsibility of Business Is to Increase Its Profits, starchitect, statistical model, Stephen Hawking, Steve Jobs, Steven Pinker, Thales of Miletus, theory of mind, Thomas Bayes, Turing machine, Turing test, Von Neumann architecture, Watson beat the top human players on Jeopardy!, zero-sum game

Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York: Basic Books, 1979). 8 Mark Humphrys, “How My Program Passed the Turing Test,” in Parsing the Turing Test, edited by Robert Epstein et al. (New York: Springer, 2008). 9 V. S. Ramachandran and Sandra Blakeslee, Phantoms in the Brain: Probing the Mysteries of the Human Mind (New York: William Morrow, 1998). 10 Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, 1937, 2nd ser., 42, no. 1 (1937), pp. 230–65. 11 Ada Lovelace’s remarks come from her translation (and notes thereupon) of Luigi Federico Menabrea’s “Sketch of the Analytical Engine Invented by Charles Babbage, Esq.,” in Scientific Memoirs, edited by Richard Taylor (London, 1843). 12 Alan Turing, “Computing Machinery and Intelligence,” Mind 59, no. 236 (October 1950), pp. 433–60. 13 For more on the idea of “radical choice,” see, e.g., Sartre, “Existentialism Is a Humanism,” especially Sartre’s discussion of a painter wondering “what painting ought he to make” and a student who came to ask Sartre’s advice about an ethical dilemma. 14 Aristotle’s arguments: See, e.g., The Nicomachean Ethics. 15 For a publicly traded company: Nobel Prize winner, and (says the Economist) “the most influential economist of the second half of the 20th century,” Milton Friedman wrote a piece in the New York Times Magazine in 1970 titled “The Social Responsibility of Business Is to Increase Its Profits.”


pages: 268 words: 109,447

The Cultural Logic of Computation by David Golumbia

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, American ideology, Benoit Mandelbrot, borderless world, business process, cellular automata, citizen journalism, Claude Shannon: information theory, computer age, corporate governance, creative destruction, en.wikipedia.org, finite state, future of work, Google Earth, Howard Zinn, IBM and the Holocaust, iterative process, Jaron Lanier, jimmy wales, John von Neumann, Joseph Schumpeter, late capitalism, means of production, natural language processing, Norbert Wiener, packet switching, RAND corporation, Ray Kurzweil, RFID, Richard Stallman, semantic web, Shoshana Zuboff, Slavoj Žižek, social web, stem cell, Stephen Hawking, Steve Ballmer, Stewart Brand, strong AI, supply-chain management, supply-chain management software, Ted Nelson, telemarketer, The Wisdom of Crowds, theory of mind, Turing machine, Turing test, Vannevar Bush, web application, Yochai Benkler

Philadelphia, PA: University of Pennsylvania Press. Taylor, R. Gregory. 1998. Models of Computation and Formal Languages. New York: Oxford University Press. Trippi, Joe. 2004. The Revolution Will Not Be Televised: Democracy, the Internet, and the Overthrow of Everything. New York: Regan Books. Turing, Alan. 1936. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society, Series 2, Volume 42 (1936–37), 230–265. ———. 1937. “Computability and λ-Definability.” The Journal of Symbolic Logic 2, 153–163. ———. 1950. “Computing Machinery and Intelligence.” Mind: A Quarterly Review of Psychology and Philosophy 59, Number 236 (October), 433–460.


The Myth of Artificial Intelligence: Why Computers Can't Think the Way We Do by Erik J. Larson

AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Amazon Mechanical Turk, artificial general intelligence, autonomous vehicles, Black Swan, Boeing 737 MAX, business intelligence, Claude Shannon: information theory, conceptual framework, correlation does not imply causation, Elon Musk, Ernest Rutherford, Filter Bubble, Georg Cantor, hive mind, ImageNet competition, information retrieval, invention of the printing press, invention of the wheel, Isaac Newton, Jaron Lanier, John von Neumann, Kevin Kelly, Law of Accelerating Returns, Loebner Prize, Nate Silver, natural language processing, Norbert Wiener, PageRank, pattern recognition, Peter Thiel, Ray Kurzweil, retrograde motion, self-driving car, semantic web, Silicon Valley, social intelligence, speech recognition, statistical model, Stephen Hawking, superintelligent machines, technological singularity, The Coming Technological Singularity, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, theory of mind, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, Yochai Benkler

Abduction in name only is not what I mean by abduction, and the systems using the name but not solving the prob­lem ­won’t help us make pro­g ress in AI. I ­w ill explain all this in pages to come. Chapter 1: The Intelligence Error 1. A. M. Turing, “Computing Machinery and Intelligence,” Mind 59, no. 236 (October 1950), 433–460. 2. A. M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, vols. 2–42, issue 1 (January 1937), 230–265. 3. A. M. Turing, Systems of Logic Based on Ordinals (PhD diss., Prince­ton University, 1938), 57. 284 N O T E S TO PA G E S 13 – 21 4. Gödel also showed that adding rules would patch up incompleteness in some systems, but that the new system, with the additional rules, would have yet other blind spots, on and on.


pages: 440 words: 109,150

The Secrets of Station X: How the Bletchley Park codebreakers helped win the war by Michael Smith

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, British Empire, Etonian, haute cuisine, QWERTY keyboard, trade route

Max Newman, one of the mathematicians working in the Testery, was a thin, bald academic from Manchester University, who like Tutte had worked in Tiltman’s research section. He had been Turing’s tutor at one stage. It was Newman’s suggestion that machines might be able to prove mathematical statements that had led Turing to write his ground-breaking paper ‘On Computable Numbers, with an Application to the Entscheidungsproblem’, and Newman who had ensured that it was published. Newman became convinced that, using similar principles to those advocated by Turing, it would be possible to build a machine that, once the patterns of the wheels had been worked out in the Testery, would find the settings of the first row of wheels, thereby making the codebreakers’ task immeasurably easier.


pages: 387 words: 111,096

Enigma by Robert Harris

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, British Empire, Columbine, index card, invention of the printing press, sensible shoes, Turing machine

The boxes she carried upstairs. One carton was full of books. A couple of Agatha Christies. A Synopsis of Elementary Results in Pure and Applied Mathematics, two volumes, by a fellow named George Shoobridge Garr. Principia Mathematical, whatever that was. A pamphlet with a suspiciously Germanic ring to it—On Computable Numbers, with an Application to the Entscheidungs problem—inscribed 'To Tom, with fond respect, Alan'. More books full of mathematics, one so repeatedly read it was almost falling to pieces and stuffed full of markers—bus and tram tickets, a beer mat, even a blade of grass. It fell open at a heavily underlined passage: there is one purpose at any rate which the real mathematics may serve in war.


pages: 416 words: 112,268

Human Compatible: Artificial Intelligence and the Problem of Control by Stuart Russell

3D printing, Ada Lovelace, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alfred Russel Wallace, algorithmic bias, Andrew Wiles, artificial general intelligence, Asilomar, Asilomar Conference on Recombinant DNA, augmented reality, autonomous vehicles, basic income, blockchain, brain emulation, Cass Sunstein, Claude Shannon: information theory, complexity theory, computer vision, connected car, crowdsourcing, Daniel Kahneman / Amos Tversky, delayed gratification, Elon Musk, en.wikipedia.org, Erik Brynjolfsson, Ernest Rutherford, Flash crash, full employment, future of work, Garrett Hardin, Gerolamo Cardano, ImageNet competition, Intergovernmental Panel on Climate Change (IPCC), Internet of things, invention of the wheel, job automation, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John Nash: game theory, John von Neumann, Kenneth Arrow, Kevin Kelly, Law of Accelerating Returns, Mark Zuckerberg, Nash equilibrium, Norbert Wiener, NP-complete, openstreetmap, P = NP, Pareto efficiency, Paul Samuelson, Pierre-Simon Laplace, positional goods, probability theory / Blaise Pascal / Pierre de Fermat, profit maximization, RAND corporation, random walk, Ray Kurzweil, recommendation engine, RFID, Richard Thaler, ride hailing / ride sharing, Robert Shiller, Robert Shiller, robotic process automation, Rodney Brooks, Second Machine Age, self-driving car, Shoshana Zuboff, Silicon Valley, smart cities, smart contracts, social intelligence, speech recognition, Stephen Hawking, Steven Pinker, superintelligent machines, surveillance capitalism, Thales of Miletus, The Future of Employment, The Theory of the Leisure Class by Thorstein Veblen, Thomas Bayes, Thorstein Veblen, Tragedy of the Commons, transport as a service, Turing machine, Turing test, universal basic income, uranium enrichment, Von Neumann architecture, Wall-E, Watson beat the top human players on Jeopardy!, web application, zero-sum game

Whether an object is a general-purpose computer has nothing to do with what it’s made of. 31. Turing’s breakthrough paper defined what is now known as the Turing machine, the basis for modern computer science. The Entscheidungsproblem, or decision problem, in the title is the problem of deciding entailment in first-order logic: Alan Turing, “On computable numbers, with an application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, 2nd ser., 42 (1936): 230–65. 32. A good survey of research on negative capacitance by one of its inventors: Sayeef Salahuddin, “Review of negative capacitance transistors,” in International Symposium on VLSI Technology, Systems and Application (IEEE Press, 2016). 33.


pages: 414 words: 109,622

Genius Makers: The Mavericks Who Brought A. I. To Google, Facebook, and the World by Cade Metz

AI winter, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, artificial general intelligence, Asilomar, autonomous vehicles, backpropagation, British Empire, carbon-based life, cloud computing, computer age, computer vision, digital map, Donald Trump, drone strike, Elon Musk, Fellow of the Royal Society, Frank Gehry, game design, Google Earth, Google X / Alphabet X, Googley, Internet Archive, Isaac Newton, Jeffrey Epstein, job automation, John Markoff, life extension, Mark Zuckerberg, means of production, Menlo Park, move fast and break things, move fast and break things, new economy, nuclear winter, PageRank, pattern recognition, Paul Graham, paypal mafia, Peter Thiel, profit motive, Richard Feynman, ride hailing / ride sharing, Ronald Reagan, Rubik’s Cube, Sam Altman, Sand Hill Road, self-driving car, side project, Silicon Valley, Silicon Valley startup, Skype, speech recognition, statistical model, stem cell, Stephen Hawking, Steve Ballmer, Steven Levy, Steven Pinker, telemarketer, The Future of Employment, Turing test, Y Combinator

Larry Page and Sergey Brin, DeepMind’s biggest supporters, announced they were retiring: Jack Nicas and Daisuke Wakabayashi, “Era Ends for Google as Founders Step Aside from a Pillar of Tech,” New York Times, December 3, 2019, https://www.nytimes.com/2019/12/03/technology/google-alphabet-ceo-larry-page-sundar-pichai.html. CHAPTER 21: X FACTOR “When I was an undergrad at King’s College Cambridge”: Geoff Hinton, tweet, March 27, 2019, https://twitter.com/geoffreyhinton/status/1110962177903640582?s=19. This was the paper that helped launch the computer age: A. M. Turing, “Article Navigation on Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, vol.s2-42, issue 1 (1937), pp. 230–265. built face recognition technology that could help track: Paul Mozur, “One Month, 500,000 Face Scans: How China Is Using AI to Profile a Minority,” New York Times, April 14, 2019, https://www.nytimes.com/2019/04/14/technology/china-surveillance-artificial-intelligence-racial-profiling.html.


pages: 463 words: 118,936

Darwin Among the Machines by George Dyson

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, backpropagation, British Empire, carbon-based life, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer age, Danny Hillis, Donald Davies, fault tolerance, Fellow of the Royal Society, finite state, IFF: identification friend or foe, independent contractor, invention of the telescope, invisible hand, Isaac Newton, Jacquard loom, James Watt: steam engine, John Nash: game theory, John von Neumann, low earth orbit, Menlo Park, Nash equilibrium, Norbert Wiener, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, phenotype, RAND corporation, Richard Feynman, spectrum auction, strong AI, the scientific method, The Wealth of Nations by Adam Smith, Turing machine, Von Neumann architecture, zero-sum game

CHAPTER 4 1.Alan Turing, “Computing Machinery and Intelligence,” Mind 59 (October 1950): 443. 2.A. K. Dewdney, The Turing Omnibus (Rockville, Md.: Computer Science Press, 1989), 389. 3.Robin Gandy, “The Confluence of Ideas in 1936,” in Rolf Herken, ed., The Universal Turing Machine: A Half-century Survey (Oxford: Oxford University Press, 1988), 85. 4.Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of the London Mathematical Society, 2d ser. 42 (1936–1937); reprinted, with corrections, in Martin Davis, ed., The Undecidable (Hewlett, N.Y.: Raven Press, 1965), 117. 5.Ibid., 136. 6.Kurt Gödel, 1946, “Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics,” reprinted in Davis, The Undecidable, 84. 7.W.


pages: 481 words: 125,946

What to Think About Machines That Think: Today's Leading Thinkers on the Age of Machine Intelligence by John Brockman

agricultural Revolution, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, artificial general intelligence, augmented reality, autonomous vehicles, backpropagation, basic income, bitcoin, blockchain, clean water, cognitive dissonance, Colonization of Mars, complexity theory, computer age, computer vision, constrained optimization, corporate personhood, cosmological principle, cryptocurrency, cuban missile crisis, Danny Hillis, dark matter, discrete time, Douglas Engelbart, Elon Musk, Emanuel Derman, endowment effect, epigenetics, Ernest Rutherford, experimental economics, Flash crash, friendly AI, functional fixedness, global pandemic, Google Glasses, hive mind, Ian Bogost, income inequality, information trail, Internet of things, invention of writing, iterative process, Jaron Lanier, job automation, Johannes Kepler, John Markoff, John von Neumann, Kevin Kelly, knowledge worker, loose coupling, microbiome, Moneyball by Michael Lewis explains big data, natural language processing, Network effects, Norbert Wiener, pattern recognition, Peter Singer: altruism, phenotype, planetary scale, Ray Kurzweil, recommendation engine, Republic of Letters, RFID, Richard Thaler, Rory Sutherland, Satyajit Das, Search for Extraterrestrial Intelligence, self-driving car, sharing economy, Silicon Valley, Skype, smart contracts, social intelligence, speech recognition, statistical model, stem cell, Stephen Hawking, Steve Jobs, Steven Pinker, Stewart Brand, strong AI, Stuxnet, superintelligent machines, supervolcano, the scientific method, The Wisdom of Crowds, theory of mind, Thorstein Veblen, too big to fail, Turing machine, Turing test, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Y2K

Chesterton, Heretics (New York: John Lane, 1905). 6. I. J. Good, “Speculation Concerning the First Ultraintelligent Machine,” Advances in Computers, vol. 6, 1965. 7. Kevin Kelly, “The Technium,” Edge, entry February 3, 2014, https://edge.org/conversation/the-technium [accessed July 21, 2015]. 8. Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proc. Lond. Math. Soc. 42, series 2 (1936–7): 230–65. 9. Steven Pinker, comment on “The Myth of AI,” Edge, entry November 14, 2014, http://edge.org/conversation/the-myth-of-ai#25987 [accessed July 21, 2015]. 10. Hannah Arendt, The Life of the Mind, vol. 1 (New York: Harcourt Brace, 1978). 11.


Software Design for Flexibility by Chris Hanson, Gerald Sussman

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, connected car, domain-specific language, Donald Knuth, en.wikipedia.org, functional programming, Guido van Rossum, interchangeable parts, loose coupling, Magellanic Cloud, phenotype, premature optimization, Richard Stallman, stem cell, the scientific method, Turing machine, type inference

Cambridge, MA: MIT Press, 2001/2014. [122]Gerald Jay Sussman and Jack Wisdom with Will Farr; Functional Differential Geometry. Cambridge, MA: MIT Press, 2013. [123]The TTL Data Book for Design Engineers, by the Engineering Staff of Texas Instruments Incorporated, Semiconductor Group. [124]Alan M. Turing; “On Computable Numbers, with an Application to the Entscheidungsproblem,” in Proceedings of the London Mathematical Society (Series 2), 42 (1936): 230–265. [125]David L. Waltz; Generating Semantic Descriptions From Drawings of Scenes With Shadows, PhD thesis, MIT, also Artificial Intelligence Laboratory Technical Report 271, November 1972. http://hdl.handle.net/1721.1/6911 [126]Stephen A.


The Science of Language by Noam Chomsky

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alfred Russel Wallace, backpropagation, British Empire, Brownian motion, dark matter, Drosophila, epigenetics, finite state, Howard Zinn, phenotype, statistical model, stem cell, Steven Pinker, theory of mind

Tomalin, Marcus (2003) “Goodman, Quine, and Chomsky: from a grammatical point of view.” Lingua 113: 1223–1253. Tomalin, Marcus (2006) Linguistics and the Formal Sciences: The Origins of Generative Grammar. Cambridge University Press. Tomalin, Marcus (2007) “Reconsidering Recursion in Linguistic Theory.” Lingua 117: 1784–1800. Turing, Alan (1937) “On Computable Numbers, with an Application to the Entscheidungsproblem.” London Mathematical Society, Series 2 42: 230–265. Turing, Alan (1950) “Computing Machinery and Intelligence.” Mind 59: 433–460. Turing, Alan (1992) Collected Works of Alan Turing: Morphogenesis. Ed. P. T. Saunders. Amsterdam: North Holland. Tversky, Amos and Daniel Kahneman (1974) “Judgment under Uncertainty.”


pages: 759 words: 166,687

Between Human and Machine: Feedback, Control, and Computing Before Cybernetics by David A. Mindell

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Charles Lindbergh, Claude Shannon: information theory, Computer Numeric Control, discrete time, Frederick Winslow Taylor, From Mathematics to the Technologies of Life and Death, James Watt: steam engine, John von Neumann, Menlo Park, Norbert Wiener, Paul Samuelson, Ronald Reagan, Silicon Valley, Spread Networks laid a new fibre optics cable between New York and Chicago, telerobotics, Turing machine

Proceedings of the Royal Society of London 24 (1876): 269–71. Tinus, W. C., and W. H. C. Higgins. “Early Fire-Control Radars for Naval Vessels.” Bell System Technical Journal 25 (January 1946): 1–47. Tomayko, James E. “Helmut Hoelzer’s Fully Electronic Analog Computer.” Annals of the History of Computing 7 (1985): 227–40. Turing, Alan. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society 2, no. 42 (1937): 230–65. U.S. Naval Academy. Fire Control Installations . United States Naval Academy, Postgraduate School, Pub. no. 105. Annapolis, Md., [ca. 1940]. ———. Notes on Fire Control . Washington, D.C.: U.S.


pages: 573 words: 157,767

From Bacteria to Bach and Back: The Evolution of Minds by Daniel C. Dennett

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Andrew Wiles, Bayesian statistics, bioinformatics, bitcoin, Build a better mousetrap, Claude Shannon: information theory, computer age, computer vision, disinformation, double entry bookkeeping, double helix, Douglas Hofstadter, Elon Musk, epigenetics, experimental subject, Fermat's Last Theorem, Gödel, Escher, Bach, information asymmetry, information retrieval, invention of writing, Isaac Newton, iterative process, John von Neumann, Menlo Park, Murray Gell-Mann, Necker cube, Norbert Wiener, pattern recognition, phenotype, Richard Feynman, Rodney Brooks, self-driving car, social intelligence, sorting algorithm, speech recognition, Stephen Hawking, Steven Pinker, strong AI, The Wealth of Nations by Adam Smith, theory of mind, Thomas Bayes, trickle-down economics, Turing machine, Turing test, Watson beat the top human players on Jeopardy!, Y2K

A Natural History of Human Thinking. Cambridge: Harvard University Press. Tononi G. 2008. “Consciousness as Integrated Information: A Provisional Manifesto.” Biological Bulletin 215 (3): 216–42. Trivers, Robert. 1985. Social Evolution. Menlo Park, Calif.: Benjamin/Cummings. Turing, Alan M. 1936. “On Computable Numbers, with an Application to the Entscheidungs Problem.” Journal of Math 58 (345–363): 5. —. 1960. “Computing Machinery and Intelligence.” Mind: 59: 433–460. von Neumann, John, and Oskar Morgenstern. 1953 (©1944). Theory of Games and Economic Behavior. Princeton, N.J.: Princeton University Press. von Uexküll, Jakob. 1934.


pages: 761 words: 231,902

The Singularity Is Near: When Humans Transcend Biology by Ray Kurzweil

additive manufacturing, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, backpropagation, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business cycle, business intelligence, c2.com, call centre, carbon-based life, cellular automata, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, coronavirus, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, functional programming, George Gilder, Gödel, Escher, Bach, informal economy, information retrieval, invention of the telephone, invention of the telescope, invention of writing, iterative process, Jaron Lanier, Jeff Bezos, job automation, job satisfaction, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, lifelogging, linked data, Loebner Prize, Louis Pasteur, mandelbrot fractal, Marshall McLuhan, Mikhail Gorbachev, Mitch Kapor, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Norbert Wiener, oil shale / tar sands, optical character recognition, pattern recognition, phenotype, premature optimization, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Robert Metcalfe, Rodney Brooks, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, semantic web, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, Thomas Bayes, transaction costs, Turing machine, Turing test, two and twenty, Vernor Vinge, Y2K, Yogi Berra

(Cambridge, U.K.: Cambridge University Press, 1910, 1912, 1913). 27. Gödel's incompleteness theorem first appeared in his "Uberformal unenscheiderbare Satze der Principia Mathematica und verwandter Systeme I," Monatshefte für Mathematik und Physik 38 (1931): 173–98. 28. Alan M. Turing, "On Computable Numbers with an Application to the Entscheidungsproblem," Proceedings of the London Mathematical Society 42 (1936): 230-65. The "Entscheidungsproblem" is the decision or halting problem—that is, how to determine ahead of time whether an algorithm will halt (come to a decision) or continue in an infinite loop. 29.


The Dream Machine: J.C.R. Licklider and the Revolution That Made Computing Personal by M. Mitchell Waldrop

Ada Lovelace, air freight, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Apple II, battle of ideas, Berlin Wall, Bill Atkinson, Bill Duvall, Bill Gates: Altair 8800, Byte Shop, Claude Shannon: information theory, computer age, conceptual framework, cuban missile crisis, Donald Davies, double helix, Douglas Engelbart, Douglas Engelbart, Dynabook, experimental subject, fault tolerance, Frederick Winslow Taylor, friendly fire, From Mathematics to the Technologies of Life and Death, functional programming, Haight Ashbury, Howard Rheingold, information retrieval, invisible hand, Isaac Newton, James Watt: steam engine, Jeff Rulifson, John von Neumann, Leonard Kleinrock, Marc Andreessen, Menlo Park, New Journalism, Norbert Wiener, packet switching, pink-collar, popular electronics, RAND corporation, RFC: Request For Comment, Robert Metcalfe, Silicon Valley, Steve Crocker, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, Ted Nelson, Turing machine, Turing test, Vannevar Bush, Von Neumann architecture, Wiener process, zero-sum game

"A Perspective on SAGE: Discussion." Annals of the H15tory ofComputzng 5 (1983). -. "RelIabilIty of Components (Interview with Jay W. Forrester)." Annals of the H15tory ofComputzng 5 (1983). -. "Origin of the Term Bit." Annals of the History ofComputzng 6 (1984). Turing, Alan M. "On Computable Numbers, with an ApplIcation to the Entschldungsproblem." Pro- ceedzngs of the London Mathematical Soczety 2, no. 42 (1937). -. "Computing Machinery and Intelligence." Mind 59, no. 236 (1950). Reprinted In The Mznd's I: Fantaszes and ReflectIOns on Self & Soul, edited by Douglas R. Hofstadter and Daniel C. Dennett.


pages: 1,351 words: 385,579

The Better Angels of Our Nature: Why Violence Has Declined by Steven Pinker

1960s counterculture, affirmative action, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, availability heuristic, Berlin Wall, Bonfire of the Vanities, British Empire, Broken windows theory, business cycle, California gold rush, Cass Sunstein, citation needed, clean water, cognitive dissonance, colonial rule, Columbine, computer age, conceptual framework, correlation coefficient, correlation does not imply causation, crack epidemic, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Brooks, delayed gratification, demographic transition, desegregation, Doomsday Clock, Douglas Hofstadter, Edward Glaeser, en.wikipedia.org, European colonialism, experimental subject, facts on the ground, failed state, first-past-the-post, Flynn Effect, food miles, Francis Fukuyama: the end of history, fudge factor, full employment, Garrett Hardin, George Santayana, ghettoisation, Gini coefficient, global village, Henri Poincaré, Herbert Marcuse, Hobbesian trap, humanitarian revolution, impulse control, income inequality, informal economy, Intergovernmental Panel on Climate Change (IPCC), invention of the printing press, Isaac Newton, lake wobegon effect, libertarian paternalism, long peace, longitudinal study, loss aversion, Marshall McLuhan, mass incarceration, McMansion, means of production, mental accounting, meta-analysis, Mikhail Gorbachev, moral panic, mutually assured destruction, Nelson Mandela, open economy, Peace of Westphalia, Peter Singer: altruism, QWERTY keyboard, race to the bottom, Ralph Waldo Emerson, random walk, Republic of Letters, Richard Thaler, Ronald Reagan, Rosa Parks, Saturday Night Live, security theater, Skype, Slavoj Žižek, South China Sea, Stanford marshmallow experiment, Stanford prison experiment, statistical model, stem cell, Steven Levy, Steven Pinker, sunk-cost fallacy, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, theory of mind, Tragedy of the Commons, transatlantic slave trade, Turing machine, twin studies, ultimatum game, uranium enrichment, Vilfredo Pareto, Walter Mischel, WikiLeaks, women in the workforce, zero-sum game

Natural selection of parental ability to vary the sex ratio of offspring. Science, 179, 90–91. Tuchman, B. W. 1978. A distant mirror: The calamitous 14th century. New York: Knopf. Tucker, G. R. & Lambert, W. E. 1969. White and Negro listeners’ reactions to various American-English dialects. Social Forces, 47, 465–68. Turing, A. M. 1936. On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42, 230–65. Turing, A. M. 1950. Computing machinery and intelligence. Mind, 59, 433–60. Turkheimer, E. 2000. Three laws of behavior genetics and what they mean. Current Directions in Psychological Science, 5, 160–64.