Turing machine

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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, Bletchley Park, British Empire, cellular automata, Charles Babbage, Claude Shannon: information theory, complexity theory, Computing Machinery and Intelligence, 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, Ken Thompson, Norbert Wiener, Paul Erdős, Reflections on Trusting Trust, Turing complete, Turing machine, Turing test, Von Neumann architecture

Fortunately, it doesn’t require much more work to obtain some undecidable questions that are much more relevant. Does a Turing Machine Diverge on Its Encoding? Is Undecidable When we run a Turing machine on an input string there are three possible outcomes: it halts in the accept state; it halts in the reject state; or it never halts. Let us look at three questions related to this. Is it possible to construct a Turing machine that receives encodings of Turing machines as input and halts in the accept state only if the encoded Turing machine accepts its encoding? Is it possible to construct a Turing machine that receives encodings of Turing machines as input and halts in the accept state only if the encoded Turing machine rejects its encoding?

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However, this gives a contradiction, as we have shown that there is no Turing machine with this property. The conclusion is that there is no Turing machine that receives encodings of Turing machines as input and halts in the accept state only if the encoded Turing machine diverges on its its encoding. This shows that the question Does a Turing machine diverge on its encoding? is undecidable. Again, the negation will also be undecidable, so we know that the question Does a Turing machine halt on its encoding? is undecidable. The Acceptance, Halting, and Blank Tape Problems We now have two undecidable questions: Does a Turing machine accept its encoding?

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In the last section we proved that the barber could not live in town, but this leads to the question, does he live elsewhere? We can ask the corresponding question. Could MFA be a Turing machine? The answer is, of course, yes. We have shown that there is an algorithm for deciding whether or not finite automata accept their encodings. Consequently, there is a Turing machine that does this. Turing Machines That Do Not Accept Their Encodings We now turn our attention to Turing machines and look at whether or not they accept their encodings. Just as with finite automata, there are Turing machines that accept their encodings and there are Turing machines that don’t. One difference from the previous case is that we know that if a finite automaton does not accept its encoding, then it has rejected its encoding, but with Turing machines there are three possible outcomes.

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, algorithmic management, 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, Eddington experiment, en.wikipedia.org, epigenetics, From Mathematics to the Technologies of Life and Death, Garrett Hardin, Geoffrey West, Santa Fe Institute, Gregor Mendel, Gödel, Escher, Bach, Hacker News, Hans Moravec, 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, power law, Ray Kurzweil, reversible computing, scientific worldview, stem cell, Stuart Kauffman, synthetic biology, The Wealth of Nations by Adam Smith, Thomas Malthus, Tragedy of the Commons, Turing machine

The idea is that, given a particular problem to solve, you can construct a definite procedure for solving it by designing a Turing machine that solves it. Turing machines were put forth as the definition of “definite procedure,” hitherto a vague and ill-defined notion. When formulating these ideas, Turing didn’t build any actual machines (though he built significant ones later on). Instead, all his thinking about Turing machines was done with pencil and paper alone. Universal Turing Machines Next, Turing proved an amazing fact about Turing machines: one can design a special universal Turing machine (let’s call it U) that can emulate the workings of any other Turing machine. For U to emulate a Turing machine M running on an input I, U starts with part of its tape containing a sequence of 0s, 1s, and blanks that encodes input I, and part of its tape containing a sequence of 0s, 1s, and blanks that encodes machine M.

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Von Neumann also was able to show that his cellular automaton was equivalent to a universal Turing machine (cf. chapter 4). The cell update rule plays the role of the rules for the Turing machine tape head, and the configuration of states plays the role of the Turing machine tape—that is, it encodes the program and data for the universal machine to run. The step-by-step updates of the cells correspond to the step-by-step iteration of the universal Turing machine. Systems that are equivalent in power to universal Turing machines (i.e., can compute anything that a universal Turing machine can) are more generally called universal computers, or are said to be capable of universal computation or to support universal computation.

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Following the intuition of Leibniz of more than two centuries earlier, Turing formulated his definition by thinking about a powerful calculating machine—one that could not only perform arithmetic but also could manipulate symbols in order to prove mathematical statements. By thinking about how humans might calculate, he constructed a mental design of such a machine, which is now called a Turing machine. The Turing machine turned out to be a blueprint for the invention of the electronic programmable computer. Alan Turing, 1912–1954 (Photograph copyright ©2003 by Photo Researchers Inc. Reproduced by permission.) A QUICK INTRODUCTION TO TURING MACHINES As illustrated in figure 4.1, a Turing machine consists of three parts: (1) A tape, divided into squares (or “cells”), on which symbols can be written and from which symbols can be read.

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, Bletchley Park, British Empire, carbon-based life, cellular automata, Charles Babbage, Claude Shannon: information theory, combinatorial explosion, computer age, Computing Machinery and Intelligence, 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, launch on warning, low earth orbit, machine readable, 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, synthetic biology, the scientific method, The Wealth of Nations by Adam Smith, Turing machine, Von Neumann architecture, zero-sum game

The key was added modulo 2 to the plaintext message (counting by two the way we count hours by twelve, so that 0 + 1 = 1 and 1 + 1 = 0), with 1 and 0 represented by the presence or absence of a hole in the tape. Adding the key to the enciphered text a second time would return the original text. Each Fish was a species of Turing machine, and the process by which the Colossi were used to break the various species of Fish was a textbook example of the process by which the function (or partial function) of one Turing machine could be encoded as a subsidiary function of another Turing machine to produce simulated results. The problem, of course, was that the British didn’t know the constantly changing state of the Fish; they had to guess. Colossus was programmed, in Boolean logic mode, by a plugboard and toggle switches at the back of the machine.

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A similar principle of distributed intelligence (enforced by need-to-know security rules) led to successful code breaking at Bletchley Park. The Turing machine, as a universal representation of the relations between patterns in space and sequences in time, has given these intuitive models of intelligence a common language that translates freely between concrete and theoretical domains. Turing’s machine has grown progressively more universal for sixty years. From McCulloch and Pitts’s demonstration of the equivalence between Turing machines and neural nets in 1943 to John von Neumann’s statement that “as far as the machine is concerned, let the whole outside world consist of a long paper tape,”51 the Turing machine has established the measure by which all models of computation have been defined.

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In Alan Turing’s minimal example, translation between structure and sequence is executed one bit at a time. The Turing machine scans one square on its tape, reads one bit of information, makes a corresponding change in its state of mind, and, in accordance with its instructions, writes or erases one bit of information on its tape. When the next moment arrives, it goes through this process again. The Turing machine and its visible universe cross paths one symbol at a time. As bandwidth measures the capacity to communicate information from one place to another, so it is possible to assign a magnitude to the amount of information that a Turing machine, or other organism, is able to scan as it moves from one moment to the next.

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

air gap, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Charles Babbage, Claude Shannon: information theory, Computing Machinery and Intelligence, 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

A companion demonstration shows that if one uses enough states, then, for any computable function, there exists a Turing machine using just two symbols. And second, one of the most astonishing results in Turing’s 1936 paper is that we do not have to build a different Turing machine for every new function we wish to compute. He showed that there exists a so-called Universal Turing Machine (UTM) that accepts as its input (that is, what’s initially written on its tape) a description of any other specific Turing machine (that description includes the state-transition table and the initial tape of the specific Turing machine) and then the UTM simulates the specific machine.

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—Claude Shannon, in a March 1952 talk at Bell Labs on creativity, during which he explained how he arrived at the logic circuitry for a machine that plays a perfect game of Nim 9.1 THE FIRST MODERN COMPUTER A Turing machine is the combination of a sequential, finite-state machine plus an external read/write memory storage medium called the tape (think of a ribbon of magnetic tape). The tape is a linear sequence of squares, with each square holding one of several possible symbols. Most generally, a Turing machine can have any number of different symbols it can recognize, but I’ll assume here that we are discussing the 2-symbol case (0 or 1). In 1956, Shannon showed that this in no way limits the power of what a Turing machine can do. The tape is arbitrarily long in at least one, perhaps both, directions.

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The finite-state machine and the read/write head then move along the tape (we imagine the tape is motionless) according to the internal details of the finite-state machine and the particular sequence of symbols encountered on the tape. At some time after we turn the Turing machine on, it presumably completes its task (whatever that might be), and the finite-state machine enters state 0 (called the halting state) and stops. Figure 9.1.1. A Turing machine. As far as I know, nobody has ever actually constructed a Turing machine. It is a purely theoretical concept. Described in 1936 by the English mathematician Alan Turing (see Shannon’s mini-biography in Chapter 3)— that is, ten years before the first actual electronic computers began to be constructed—Turing’s machines are nevertheless as powerful as any modern machine in what they can compute.

In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William J. Cook

Bletchley Park, complexity theory, computer age, Computer Numeric Control, financial engineering, four colour theorem, index card, John von Neumann, linear programming, NP-complete, P = NP, p-value, RAND corporation, Richard Feynman, traveling salesman, Turing machine

This is something we take for granted, but the creation of programmable machines was an intellectual leap, made by Turing in his original paper. A Turing machine is a great model for describing what we mean by an algorithm, but a Turing machine is designed for a single task, such as adding two numbers. In this sense, Turing machines are closer to a pair of shoes than to an iPhone. A crucial point made by Turing, however, is that one can design a Universal Turing machine capable of simulating every Turing machine. It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with a tape on the beginning of which is written the S.D of some computing machine M, then U will compute the same sequence as M.

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Such multiple-tape Turing machines are defined in a natural way, with separate read/write heads for each tape. Although extra tapes are convenient, anything we can compute on a multiple-tape machine can also be computed on a machine with a single tape, albeit a bit more slowly. This last point, about simulating a multiple-tape machine with a single tape, is important. We would like to define an algorithm as something that can be carried out on a single-tape Turing machine, but does this capture everything we might want in an algorithm? All we can say is that, so far, Turing machines have been able to handle everything that has been thrown at them.

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If something is computable on a modern-day computer, then a lightning-fast Turing machine could also carry out the computation. The working assumption that we can equate algorithms and Turing machines is known as the Church-Turing Thesis.3 This thesis is widely Complexity accepted and it gives the formal model of an algorithm that is used to make precise P vs. N P and other complexity questions. Perhaps, one day, exotic computing capabilities will come along to cause us to consider an expanded definition of an algorithm, but for over seventy years Turing has served up just what the research community has needed. Universal Turing Machines There is a fundamental difference between a modern telephone, such as the iPhone, and, say, a pair of shoes.

The Road to Conscious Machines by Michael Wooldridge

Ada Lovelace, AI winter, algorithmic bias, AlphaGo, Andrew Wiles, Anthropocene, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, backpropagation, basic income, Bletchley Park, Boeing 747, British Empire, call centre, Charles Babbage, combinatorial explosion, computer vision, Computing Machinery and Intelligence, DARPA: Urban Challenge, deep learning, deepfake, DeepMind, Demis Hassabis, don't be evil, Donald Trump, driverless car, Elaine Herzberg, Elon Musk, Eratosthenes, factory automation, fake news, future of work, gamification, general purpose technology, Geoffrey Hinton, gig economy, Google Glasses, intangible asset, James Watt: steam engine, job automation, John von Neumann, Loebner Prize, Minecraft, Mustafa Suleyman, Nash equilibrium, Nick Bostrom, Norbert Wiener, NP-complete, P = NP, P vs NP, paperclip maximiser, pattern recognition, Philippa Foot, RAND corporation, Ray Kurzweil, Rodney Brooks, self-driving car, Silicon Valley, Stephen Hawking, Steven Pinker, strong AI, technological singularity, telemarketer, Tesla Model S, The Coming Technological Singularity, The Future of Employment, the scientific method, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, trolley problem, Turing machine, Turing test, universal basic income, Von Neumann architecture, warehouse robotics

Any kind of mathematical recipe that you might care to think of can be encoded as a Turing machine. And, if all mathematical decision problems can be solved by following a recipe, then for any decision problem, you should be able to design a Turing machine to solve it. To settle Hilbert’s problem, all you had to do was show that there was some decision problem that could not be answered by any Turing machine. And that is what Turing did. His next trick was to show that his machines could be turned into general-purpose problem-solving machines. He designed a Turing machine that will follow any recipe that you give it. We now call these general-purpose Turing machines Universal Turing Machines:4 and a computer, when stripped down to its bare essentials, is simply a Universal Turing Machine made real.

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Dealing with uncertainty is therefore a fundamental topic in AI. See also Bayes’ Theorem and Appendix C. undecidable problem A problem that we know, in a precise mathematical sense, cannot be solved by a computer (or, more exactly, by a Turing machine). Universal Turing Machine A general type of Turing machine, which provided the template for the modern computer. While a Turing machine encodes just one specific recipe/algorithm, a Universal Turing Machine can be given any recipe/algorithm. (unsound) reasoning In logic, where we derive conclusions that are not warranted by the premises. See also (sound) reasoning. Urban Challenge A 2007 follow-on to the DARPA Grand Challenge, in which autonomous vehicles were required to autonomously traverse a built-up urban environment.

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To do this, he invented a mathematical problem-solving machine – nowadays, we call these Turing machines in his honour. A Turing machine is a mathematical description of a recipe, like the one for checking prime numbers mentioned above. All a Turing machine does is to follow the recipe it was designed for. I should emphasize that, although Turing called them ‘machines’, at this point they were nothing more than an abstract mathematical idea. The idea of solving a deep mathematical problem by inventing a machine was unconventional, to say the least – I suspect many mathematicians of the day were mystified. Turing machines are very powerful beasts. Any kind of mathematical recipe that you might care to think of can be encoded as a Turing machine.

What Algorithms Want: Imagination in the Age of Computing by Ed Finn

Airbnb, Albert Einstein, algorithmic bias, algorithmic management, algorithmic trading, AlphaGo, Amazon Mechanical Turk, Amazon Web Services, bitcoin, blockchain, business logic, Charles Babbage, Chuck Templeton: OpenTable:, Claude Shannon: information theory, commoditize, Computing Machinery and Intelligence, Credit Default Swap, crowdsourcing, cryptocurrency, data science, DeepMind, disruptive innovation, Donald Knuth, Donald Shoup, Douglas Engelbart, Douglas Engelbart, Elon Musk, Evgeny Morozov, factory automation, fiat currency, Filter Bubble, Flash crash, game design, gamification, Google Glasses, Google X / Alphabet X, Hacker Conference 1984, High speed trading, hiring and firing, Ian Bogost, industrial research laboratory, invisible hand, Isaac Newton, iterative process, Jaron Lanier, Jeff Bezos, job automation, John Conway, John Markoff, Just-in-time delivery, Kickstarter, Kiva Systems, late fees, lifelogging, Loebner Prize, lolcat, Lyft, machine readable, Mother of all demos, Nate Silver, natural language processing, Neal Stephenson, Netflix Prize, new economy, Nicholas Carr, Nick Bostrom, Norbert Wiener, PageRank, peer-to-peer, Peter Thiel, power law, Ray Kurzweil, recommendation engine, Republic of Letters, ride hailing / ride sharing, Satoshi Nakamoto, self-driving car, sharing economy, Silicon Valley, Silicon Valley billionaire, Silicon Valley ideology, Silicon Valley startup, SimCity, Skinner box, Snow Crash, social graph, software studies, speech recognition, statistical model, Steve Jobs, Steven Levy, Stewart Brand, supply-chain management, tacit knowledge, TaskRabbit, technological singularity, technological solutionism, technoutopianism, the Cathedral and the Bazaar, The Coming Technological Singularity, the scientific method, The Signal and the Noise by Nate Silver, The Structural Transformation of the Public Sphere, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, Turing machine, Turing test, Uber and Lyft, Uber for X, uber lyft, urban planning, Vannevar Bush, Vernor Vinge, wage slave

Their responses to Hilbert, now called the Church–Turing thesis, define algorithms for theorists in a way that is widely accepted but ultimately unprovable: a calculation with natural numbers, or what most of us know as whole numbers, is “effectively computable” (that is, given enough time and pencils, a human could do it) only if the Universal Turing Machine can do it. The thesis uses this informal definition to unite three different rigorous mathematical theses about computation (Turing machines, Church’s lambda calculus, and mathematician Kurt Gödel’s concept of recursive functions), translating their specific mathematical claims into a more general boundary statement about the limits of computational abstraction.

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Church grappled with this problem and developed the lambda calculus, a masterful demonstration of abstraction that served as the philosophical foundation for numerous programming languages decades after his work.21 As Berlinski puts it, Turing had “an uncanny and almost unfailing ability to sift through the work of his time and in the sifting discern the outlines of something far simpler than the things that other men saw.”22 In other words, he possessed a genius for abstraction, and his greatest achievement in this regard was the Turing machine. Turing’s simple imaginary machine is an elegant mathematical proof for universal computation, but it is also an ur-algorithm, an abstraction generator. The mathematical equivalence of Church and Turing’s work quickly suggested that varying proofs of effective computability (there are now over thirty) all gesture toward some fundamental universal truth. But every abstraction has a shadow, a puddled remainder of context and specificity left behind in the act of lifting some idea to a higher plane of thought. The Turing machine leaves open the question of what “effectively computable” might really mean in material reality, where we leave elegance and infinite tapes behind.

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As Hayles argues in How We Became Posthuman, theoretical models of biophysical reality like the early McCulloch–Pitts Neuron (which the logician Walter Pitts proved to be computationally equivalent to a Turing machine) allowed cybernetics to establish correlations between computational and biological processes at paradigmatic and operational levels and lay claim to being what informatics scholar Geoffrey Bowker calls a “universal discipline.”33 Via cybernetics, information was the banner under which “effective computability” expanded to vast new territories, first presenting the tantalizing prospect that Wolfram and others would later reach for as universal computation.34 As early as The Human Use of Human Beings, Wiener popularized these links between the Turing machine, neural networks, and learning in biological organisms, work that is now coming to startling life in the stream of machine learning breakthroughs announced by the Google subsidiary DeepMind over the past few years.

Turing's Cathedral by George Dyson

1919 Motor Transport Corps convoy, Abraham Wald, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Benoit Mandelbrot, Bletchley Park, British Empire, Brownian motion, cellular automata, Charles Babbage, cloud computing, computer age, Computing Machinery and Intelligence, Danny Hillis, dark matter, double helix, Dr. Strangelove, fault tolerance, Fellow of the Royal Society, finite state, Ford Model T, Georg Cantor, Henri Poincaré, Herman Kahn, housing crisis, IFF: identification friend or foe, indoor plumbing, Isaac Newton, Jacquard loom, John von Neumann, machine readable, mandelbrot fractal, Menlo Park, Murray Gell-Mann, Neal Stephenson, 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

The tape is not infinite, but if more tape is needed, the supply can be counted on never to run out. Each step in the relationship between tape and Turing machine is determined by an instruction table listing all possible internal states, all possible external symbols, and, for every possible combination, what to do (write or erase a symbol, move right or left, change the internal state) in the event that combination comes up. The Turing machine follows instructions and never makes mistakes. Complicated behavior does not require complicated states of mind. By taking copious notes, the Turing machine can function with as few as two internal states. Behavioral complexity is equivalent whether embodied in complex states of mind (m-configurations) or complex symbols (or strings of simple symbols) encoded on the tape.

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At this stage there was a close synergy between man, woman, and machine.”33 As a step toward the modern computer, Colossus represented as great a leap as the ENIAC, and was both running and replicated while the one-of-a-kind ENIAC was still being built. Each Fish was a form of Turing machine, and the process by which the Colossi were used to break the various species of Fish demonstrated how the function (or partial function) of one Turing machine could be encoded for execution by another Turing machine. Since the British did not know the constantly changing state of the Fish, they had to guess. Colossus, trained to sense the direction of extremely faint gradients that distinguished enciphered German from random alphabetic noise, was the distant progenitor of the search engine: scanning the Precambrian digital universe for fragments of the missing key, until the pieces fit.

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Gödel was well aware that Turing’s Universal Machine and von Neumann’s implementation of it were demonstrations, if not the direct offspring, of his, Gödel’s, ideas. “What von Neumann perhaps had in mind appears more clearly from the universal Turing machine,” he later explained to Arthur Burks. “There it might be said that the complete description of its behavior is infinite because, in view of the non existence of a decision procedure predicting its behavior, the complete description could be given only by an enumeration of all instances. The universal Turing machine, where the ratio of the two complexities is infinity, might then be considered to be a limiting case.”53 Leibniz’s belief in a universal digital coding embodied his principle of maximum diversity: infinite complexity from finite rules.

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, Bletchley Park, British Empire, business process, carbon-based life, cellular automata, Charles Babbage, Claude Shannon: information theory, combinatorial explosion, complexity theory, Computing Machinery and Intelligence, continuous integration, Conway's Game of Life, cosmological principle, dark matter, data science, deep learning, DeepMind, dematerialisation, double helix, Douglas Hofstadter, driverless car, Edward Snowden, epigenetics, Flash crash, Google Glasses, Gödel, Escher, Bach, Hans Moravec, income inequality, index card, industrial robot, intentional community, 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, machine translation, millennium bug, mirror neurons, Moravec's paradox, natural language processing, Nick Bostrom, Norbert Wiener, off grid, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, Paul Erdős, Plato's cave, post-industrial society, power law, precautionary principle, prediction markets, Ray Kurzweil, Recombinant DNA, Rodney Brooks, Second Machine Age, self-driving car, seminal paper, Silicon Valley, social intelligence, speech recognition, stem cell, Stephen Hawking, Steven Pinker, Strategic Defense Initiative, strong AI, Stuart Kauffman, synthetic biology, systems thinking, technological singularity, The Coming Technological Singularity, The Future of Employment, the scientific method, theory of mind, Turing complete, Turing machine, Turing test, Tyler Cowen, Tyler Cowen: Great Stagnation, Vernor Vinge, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Y2K

He then took Gödel’s theorem and reformulated it by replacing Gödel’s arithmetic-based notation with simple, hypothetical devices that became known as ‘Turing machines’. A Turing machine is like a tape recorder. The tape can move in both directions, back and forth, and the machine can record symbols on the tape by following simple instructions. There is also a ‘state register’, something we would today call ‘memory’, which keeps track of what the Turing machine has been up to. Remember Gödel’s genius idea of substituting logical operations and expressions with numbers? In turn, Turing substituted logical operations and expressions with Turing machines. A Turing machine took a statement as its input, applied a logical expression (or ‘formula’) that was written as a set of instructions, and produced a binary result: the statement was either true or false.

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To build this computer model in practice Turing suggested that classical, algorithmic machines should be augmented with ‘oracles’: these are machines that can decide what is undecidable by a normal Turing machine, for instance the halting problem. But what would an oracle machine look like? And how would it function? In theory, oracle machines are just like Turing machines, with the additional ability to answer ‘yes’ or ‘no’ whenever the normal Turing machine cannot find the answer. This, effectively, transforms an improvable theorem into an axiom. Nesting Turing machines with oracles produces a hypercomputer. You can go beyond that too: you can start nesting hypercomputers together, all the way to infinity.

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Von Neumann realised that, in essence, this meant the Universal Turing Machine could also code itself. Indeed, modern computers, which are Universal Turing Machines, have exactly this ability. All software stored in your computer can be copied to another computer, by your computer. In fact, copying is what takes place whenever you perform any transaction using a computer. When you ‘send’ an email, for example, nothing actually moves from one place to another: an exact copy of your email is reproduced in the computer of the person you want to communicate with. Von Neumann was fascinated with this self-copying property of the Universal Turing Machine. In true cybernetic fashion, he set off to formulate a general theory of self-reproduction that would include living organisms as well as machines.

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, Bletchley Park, card file, cellular automata, Charles Babbage, Claude Shannon: information theory, combinatorial explosion, Compatible Time-Sharing System, computer age, Computer Lib, Computing Machinery and Intelligence, conceptual framework, Conway's Game of Life, Douglas Engelbart, Dynabook, experimental subject, Hacker Ethic, heat death of the universe, Howard Rheingold, human-factors engineering, interchangeable parts, invention of movable type, invention of the printing press, Ivan Sutherland, Jacquard loom, John von Neumann, knowledge worker, machine readable, Marshall McLuhan, Menlo Park, Neil Armstrong, Norbert Wiener, packet switching, pattern recognition, popular electronics, post-industrial society, Project Xanadu, RAND corporation, Robert Metcalfe, Silicon Valley, speech recognition, Steve Jobs, Steve Wozniak, Stewart Brand, Ted Nelson, telemarketer, The Home Computer Revolution, Turing machine, Turing test, Vannevar Bush, Von Neumann architecture

The instructions, not the symbols that keep track of the way they are carried out -- the rules, not the markers -- are what make the Turing machine work. Universal Turing machines are primarily symbol manipulators. And digital computers are universal Turing machines. It isn't easy to think of the rules of a game as a kind of machine. The task is somewhat easier if you think about "mechanical processes" that are so clearly and specifically defined that a machine can perform them by referring to an instruction table. All universal Turing machines are functionally identical devices for following the program specified by an instruction table.

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All universal Turing machines are functionally identical devices for following the program specified by an instruction table. The instruction tables can differ, and they can turn the universal Turing machine into many different kinds of machine. For this reason, the programs are sometimes called "virtual machines." The distinction between a universal Turing machine and the many different Turing machines it is able to imitate is a direct analogy to digital computers. Like universal Turing machines, all digital computers are functionally identical. At the most basic level, every digital computer operates in the way our doubling machine did with the squares and Os and Xs. Instead of building a different physical machine to solve different problems, it is more practical to describe to an instruction-following machine different virtual machines (programs) that use this one-square-at-a-time mechanical instruction-following process to solve complicated problems through a pattern of simple operations.

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The moves of the game are the changing states of the machine that correspond to the specified steps of the computation. 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.

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, Bletchley Park, Brownian motion, butterfly effect, Charles Babbage, citation needed, classic study, Claude Shannon: information theory, clockwork universe, computer age, Computing Machinery and Intelligence, conceptual framework, crowdsourcing, death of newspapers, discovery of DNA, Donald Knuth, double helix, Douglas Hofstadter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Gregor Mendel, 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, Lewis Mumford, lifelogging, Louis Daguerre, machine translation, 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, quantum cryptography, 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, yottabyte

Chaitin was not thinking about telegraphs. The device he could not get out of his head was the Turing machine—that impossibly elegant abstraction, marching back and forth along its infinite paper tape, reading and writing symbols. Free from all the real world’s messiness, free from creaking wheel-work and finical electricity, free from any need for speed, the Turing machine was the ideal computer. Von Neumann, too, had kept coming back to Turing machines. They were the ever-handy lab mice of computer theory. Turing’s U had a transcendent power: a universal Turing machine can simulate any other digital computer, so computer scientists can disregard the messy details of any particular make or model.

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Turing’s U had a transcendent power: a universal Turing machine can simulate any other digital computer, so computer scientists can disregard the messy details of any particular make or model. This is liberating. Claude Shannon, having moved from Bell Labs to MIT, reanalyzed the Turing machine in 1956. He stripped it down to the smallest possible skeleton, proving that the universal computer could be constructed with just two internal states, or with just two symbols, 0 and 1, or blank and nonblank. He wrote his proof in words more pragmatic than mathematical: he described exactly how the two-state Turing machine would step left and right, “bouncing” back and forth to keep track of the larger numbers of states in a more complex computer. It was all very intricate and specific, redolent of Babbage.

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In 1965 Chaitin was an undergraduate at the City College of New York, writing up a discovery he hoped to submit to a journal; it would be his first publication. He began, “In this paper the Turing machine is regarded as a general purpose computer and some practical questions are asked about programming it.” Chaitin, as a high-school student in the Columbia Science Honors Program, had the opportunity to practice programming in machine language on giant IBM mainframes, using decks of punched cards—one card for each line of a program. He would leave his card deck in the computer center and come back the next day for the program’s output. He could run Turing machines in his head, too: write 0, write 1, write blank, shift tape left, shift tape right.… The universal computer gave him a nice way to distinguish between numbers like Alice and Bob’s A and B.

Think Complexity by Allen B. Downey

Benoit Mandelbrot, cellular automata, Conway's Game of Life, Craig Reynolds: boids flock, discrete time, en.wikipedia.org, Frank Gehry, Gini coefficient, Guggenheim Bilbao, Laplace demon, mandelbrot fractal, Occupy movement, Paul Erdős, peer-to-peer, Pierre-Simon Laplace, power law, seminal paper, sorting algorithm, stochastic process, strong AI, Thomas Kuhn: the structure of scientific revolutions, Turing complete, Turing machine, Vilfredo Pareto, We are the 99%

Actions include modifying the cell the head is over, and moving one cell to the left or right. A Turing machine is not a practical design for a computer, but it models common computer architectures. For a given program running on a real computer, it is possible (at least in principle) to construct a Turing machine that performs an equivalent computation. The Turing machine is useful because it is possible to characterize the set of functions that can be computed by a Turing machine, which is what Turing did. Functions in this set are called Turing computable. To say that a Turing machine can compute any Turing-computable function is a tautology: it is true by definition.

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So Wolfram’s claim is that Class 4 behavior is common in the natural world and almost all of the systems that manifest it are computationally equivalent. Example 6-4. The goal of this exercise is to implement a Turing machine. See http://en.wikipedia.org/wiki/Turing_machine. Start with a copy of CA.py named TM.py. Add attributes to represent the location of the head, the action table, and the state register. Override step to implement a Turing machine update. For the action table, use the rules for a three-state busy beaver. Write a class named TMDrawer that generates an image that represents the state of the tape and the position and state of the head.

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What is the biggest spaceship you can find? Universality To understand universality, we have to understand computability theory, which is about models of computation and what they compute. One of the most general models of computation is the Turing machine, which is an abstract computer proposed by Alan Turing in 1936. A Turing machine is a 1-D CA, infinite in both directions, augmented with a read-write head. At any time, the head is positioned over a single cell. It can read the state of that cell (usually there are only two states), and it can write a new value into the cell. In addition, the machine has a register, which records the state of the machine (one of a finite number of states), and a table of rules.

The Man From the Future: The Visionary Life of John Von Neumann by Ananyo Bhattacharya

Ada Lovelace, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Alvin Roth, Andrew Wiles, Benoit Mandelbrot, business cycle, cellular automata, Charles Babbage, Claude Shannon: information theory, clockwork universe, cloud computing, Conway's Game of Life, cuban missile crisis, Daniel Kahneman / Amos Tversky, DeepMind, deferred acceptance, double helix, Douglas Hofstadter, Dr. Strangelove, From Mathematics to the Technologies of Life and Death, Georg Cantor, Greta Thunberg, Gödel, Escher, Bach, haute cuisine, Herman Kahn, indoor plumbing, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jacquard loom, Jean Tirole, John Conway, John Nash: game theory, John von Neumann, Kenneth Arrow, Kickstarter, linear programming, mandelbrot fractal, meta-analysis, mutually assured destruction, Nash equilibrium, Norbert Wiener, Norman Macrae, P = NP, Paul Samuelson, quantum entanglement, RAND corporation, Ray Kurzweil, Richard Feynman, Ronald Reagan, Schrödinger's Cat, second-price auction, side project, Silicon Valley, spectrum auction, Steven Levy, Strategic Defense Initiative, technological singularity, Turing machine, Von Neumann architecture, zero-sum game

Three hundred years earlier, when the philosopher René Descartes declared ‘the body to be nothing but a machine’ his student, the twenty-three-year-old Queen Christina of Sweden, is said to have challenged him: ‘I never saw my clock making babies’.8 Von Neumann was not the first person to ask the question ‘can machines reproduce?’ but he would be the first to answer it. At the heart of von Neumann’s theory is the Universal Turing machine. Furnished with a description of any other Turing machine and a list of instructions, the universal machine can imitate it. Von Neumann begins by considering what a Turing-machine-like automaton would need to make copies of itself, rather than just compute. He argues that three things are necessary and sufficient. First, the machine requires a set of instructions that describe how to build another like it – like Turing’s paper tape but made of the same ‘stuff’ as the machine itself.

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‘Bertus’ 22, 149, 150 Budapest anti-Semitism 2, 5 Jewish population 2 Kann-Heller 2 Lenin Boys 13 Romanian occupation 13–14 von Neumann’s life in 1–9, 5, 7 Budapest, University of 6–7, 11, 25, 65 Burks, Arthur 125, 130, 231, 235, 243, 258, 265 Burroughs, William S. xiv Bush, Vannevar 77, 107 California Institute of Technology 184, 245 Cambridge, University of, King’s College 70 Cantor, Georg 20, 20–21 carbon dioxide emissions 283 cardinality 23 Carleton University, Ottawa 225 Carter, Jimmy 264 causality 29, 48–9, 51, 60, 76, 298n63 Cayley, Arthur 32 cellular automata see self-reproducing automata Cellular Automata Machine 245 chain reaction, nuclears, Monte Carlo bomb simulations 8, 80, 81–2, 87–8, 133–4 Champernowne, David 151 Champlain, SS 77 chance 144–5 Chandrasekhar, Subrahmanyan 79 Chebyshev polynomials 12–13, 295n32 chess 4, 142–3, 144, 162–3, 164, 257, 289–90n8, 313n51 China 209 Church, Alonzo 118–9 Churchill, Winston 80, 90 cities, segregation 270, 271, 272 ‘clanking replicators’ 261–3, 262 Clauser, John 57 Cliff, Rodger 2654 climate change 283, 284 Clippinger, Richard 135 closed subroutine, the 138 Cockcroft, John 301n23 Codd, Edgar 258 Cold War 218–20183, 203, 208–12 counterforce strategy 222 doctrine of preventive war 208–10 game theory analysis 212–16 ICBM threat 216–18 kill-or-be-killed paranoia 203 little wars strategy 222–4 nuclear deterrence 212–16, 221–224 paranoia 203 preventive war 208–10 Soviet aggression 222 Soviet Union hydrogen bomb test 216–17 VNs view of 208–9 Collbohm, Frank 185–6, 217 Columbia University 78, 213, 214 Communist Party of Germany (KPD) 99 Compleat Strategyst, The (Williams) 189 Computer and the Brain, The (von Neumann) 275–6 computer programmer job born 131–2 ‘low class individuals’ 278 Neumann, Klára Dán von, as one of the first 133, 135, 136–138 computer science, foundations of 70, 121 computers xiii approach to programming 134–5 Atanasoff–Berry 127 Automatic Computing Engine (ACE) 121, 125 Automatic Sequence Controlled Calculator (ASCC) see Harvard Mark I birth of 16, 28, 102–40 closed subroutine 138 coding 115–16 comparison to the brain 273–6 delay-lines 124–5 differential analysers 107–8 earliest 73 quantum 59 women’s role 85–6, 108–9, 120–1 differential analyser 107–8 EDVAC patent dispute 125–6, 127–8 EDVAC report 121–7 see First Draft of a Report on the EDVAC (von Neumann) ENIAC xi, 1054–11, 106, 120, 123, 124, 126, 127–8 ENIAC conversion 130–5, 309–10n68 First Draft of a Report on the EDVAC (von Neumann) 111, 121–7111 for-loops 116 Gödel’s contribution 111–18 Harvard Mark I 104 human 120–1 IAS project 127, 128–30, 131, 138–9, 140, 193 IBM 701 14039 JOHNNIAC 193, 194 Manchester Baby 138 MANIAC I 137, 139, 310n77 origin of 28 program-controlled 119–20 Project PY 1101 proliferation 272–3 RAND Corporation and 192–3 size 106 Small-Scale Experimental Machine (SSEM) see Manchester Baby 138 storage capacity 123 stored-program 120, 121, 122 see also First Draft of a Report on the EDVAC subroutines 119 Turing’s contribution 118–21 the universal Turing machine 118–21, 306–7n35, 307n37 virus, first 236 VNs contribution 122, 125–76, 129–130, 131, 139–140, 308n48 VNs early interests in 79–80, 103–5 von Neumann architecture 123, 128, 275 von Neumann bottleneck 123 Conan Doyle, Arthur, ‘The Final Problem’ 153–4, 165–6, 165, 314n52 Conferences on Cybernetics 227 Connes, Alain 62 Conus textile sea snail 249 Conway, John Horton 237–41, 243 hexagonal packing of circles 237, 238 Life 239–41, 239, 240, 242, 243, 244, 245, 257 Universal Turing Machine within 241, 243 survey of life forms 240 Universal Turing machine 241, 243 cooperative game theory 172–3, 176, 178, 196–7 Copeland, B.

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Later in the paper, he uses these to help build a ‘universal computing machine’ that is capable of simulating any other Turing machine. Computer programmers today would recognize Turing’s strategy: modern programmes make use of libraries of simpler programmes known as ‘subroutines’. Subroutines simplify the structure of programs, and simpler programs are easier to understand, improve and troubleshoot. Though Turing describes his computing machine in purely abstract terms, it is quite easy to imagine building one. A Turing machine that can execute a single task might comprise a scanner, print head (erasing characters is admittedly a little trickier) and a motor that moves a ‘limitless’ roll of tape backwards and forwards.

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, Charles Babbage, Claude Shannon: information theory, cloud computing, computer age, Computing Machinery and Intelligence, Dean Kamen, discovery of DNA, double helix, driverless car, en.wikipedia.org, epigenetics, George Gilder, Google Earth, Hans Moravec, Isaac Newton, iterative process, Jacquard loom, Jeff Hawkins, John von Neumann, Law of Accelerating Returns, linear programming, Loebner Prize, mandelbrot fractal, Nick Bostrom, Norbert Wiener, optical character recognition, PalmPilot, 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

A famous unsolvable problem called the busy beaver problem is stated as follows: Find the maximum number of 1s that a Turing machine with a certain number of states can write on its tape. So to determine the busy beaver of the number n, we build all of the Turing machines that have n states (which will be a finite number if n is finite) and then determine the largest number of 1s that these machines write on their tapes, excluding those Turing machines that get into an infinite loop. This is unsolvable because as we seek to simulate all of these n-state Turing machines, our simulator will get into an infinite loop when it attempts to simulate one of the Turing machines that does get into an infinite loop.

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Turing and Alonzo Church (1903–1995), his former professor, went on to develop the Church-Turing thesis, which states that if a problem that can be presented to a Turing machine is not solvable by it, it is also not solvable by any machine, following natural law. Even though the Turing machine has only a handful of commands and processes only one bit at a time, it can compute anything that any computer can compute. Another way to say this is that any machine that is “Turing complete” (that is, that has equivalent capabilities to a Turing machine) can compute any algorithm (any procedure that we can define). A block diagram of a Turing machine with a head that reads and writes the tape and an internal program consisting of state transitions.

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Each state will then specify the number of the next state that the machine should be in. The input to the Turing machine is presented on the tape. The program runs, and when the machine halts, it has completed its algorithm, and the output of the process is left on the tape. Note that even though the tape is theoretically infinite in length, any actual program that does not get into an infinite loop will use only a finite portion of the tape, so if we limit ourselves to a finite tape, the machine will still solve a useful set of problems. If the Turing machine sounds simple, it is because that was its inventor’s objective. Turing wanted his machine to be as simple as possible (but no simpler, to paraphrase Einstein).

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, James Webb Space Telescope, Johannes Kepler, John von Neumann, Large Hadron Collider, linear programming, new economy, NP-complete, Occam's razor, P = NP, Paul Erdős, quantum cryptography, quantum entanglement, Richard Feynman, Rubik’s Cube, seminal paper, smart grid, Stephen Hawking, traveling salesman, Turing machine, Turing test, Watson beat the top human players on Jeopardy!, William of Occam

Turing used this intuition to create a formal model of computation we now call the Turing machine. Figure 5-1. Turing Machine. Though the machine was a very simple model, Turing stated that everything computable was computable by his machine. Alonzo Church at about the same time made a similar claim based on his Lambda Calculus, a rudimentary programming language. This Church-Turing thesis, developed before the invention of modern computers, has stood the test of time. Everything computable, now or in the future, is indeed computable by a Turing machine. This means we don’t have to worry about the specifics of the Turing machine; other models of computers give us no more computational power.

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This means we don’t have to worry about the specifics of the Turing machine; other models of computers give us no more computational power. You don’t really need to understand exactly what a Turing machine is to understand computation. Just think of any programming language that has access to an unlimited amount of memory. All programming languages are functionally equivalent, and all can compute exactly what can be computed by the simple Turing machine. Turing back in 1936 showed that a Turing machine cannot in fact compute everything. The most famous example, the halting problem, says that no computer can look at some code of a program and determine whether that code will run forever or eventually halt.

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Of course, we don’t have a Martian civilization to compare ourselves with, so we have to use our imagination. The Martians would have an Exigius machine of computation that would be different from the Turing machine but have the same computational ability. The Martians would have their own version of the Church-Turing thesis that everything computable is computable by an Exigius machine. So the Turing machine itself is not natural, but computation is. For P versus NP we have some non-Martian evidence. Researchers in Russia and North America with limited communication ended up developing the same P versus NP question and NP-complete problems.

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

Ada Lovelace, Alan Greenspan, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Alvin Toffler, Any sufficiently advanced technology is indistinguishable from magic, backpropagation, Buckminster Fuller, call centre, cellular automata, Charles Babbage, classic study, combinatorial explosion, complexity theory, computer age, computer vision, Computing Machinery and Intelligence, cosmological constant, cosmological principle, Danny Hillis, double helix, Douglas Hofstadter, Everything should be made as simple as possible, financial engineering, first square of the chessboard / second half of the chessboard, flying shuttle, fudge factor, functional programming, George Gilder, Gödel, Escher, Bach, Hans Moravec, I think there is a world market for maybe five computers, information retrieval, invention of movable type, Isaac Newton, iterative process, Jacquard loom, John Gilmore, 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, punch-card reader, quantum entanglement, 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, Stuart Kauffman, technological singularity, Ted Kaczynski, telepresence, the medium is the message, The Soul of a New Machine, 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, world market for maybe five computers, Y2K

Perhaps the most interesting unsolvable problem is called the Busy Beaver, which may be stated as follows: Each Turing machine has a certain number of commands in its program. Given a positive integer n, we construct all of the Turing machines that have n states (i.e., n commands). Next we eliminate those n-state Turing machines that get into an infinite loop (i.e., never halt). Finally, we select the machine (one that halts) that writes the largest number of 1s on its tape. The number of 1s that this Turing machine writes is called busy beaver of n. Tibor Rado, a mathematician and admirer of Turing, showed that there is no algorithm (that is, no Turing machine) that can compute the busy beaver function for all n’s.

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Because of their hexagonal and pentagonal shape, the molecules were dubbed “buckyballs” in reference to R. Buckminster Fuller’s building designs. Busy beaver One example of a class of noncomputational functions; an unsolvable problem in mathematics. Being a “Turing machine unsolvable problem,” the busy beaver function cannot be computed by a Turing machine. To compute busy beaver of n, one creates all the n-state Turing machines that do not write an infinite number of Is on their tape. The largest number of Is written by the Turing machine in this set that writes the largest number of Is is busy beaver of n. BWA See Biowarfare Agency Byte A contraction for “by eight.” A group of eight bits clustered together to store one unit of information on a computer.

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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. It has also persisted as our primary theoretical model of a computer because of its combination of simplicity and power.The Turing machine is one example of the simplicity of the foundations of intelligence. A Turing machine consists of two primary (theoretical) units: a tape drive and a computation unit. The tape drive has a tape of infinite length on which it can write, and (subsequently) read, a series of two symbols: zero and one.

Silence on the Wire: A Field Guide to Passive Reconnaissance and Indirect Attacks by Michal Zalewski

active measures, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, AltaVista, Charles Babbage, complexity theory, dark matter, data acquisition, Donald Knuth, fault tolerance, information security, MITM: man-in-the-middle, NP-complete, OSI model, Silicon Valley, speech recognition, Turing complete, Turing machine, Vannevar Bush

In fact, it implements the same algorithm: bits on the tape, starting at the rightmost position, are inverted until after 0 is encountered (and also inverted). This is, naturally, just the tip of the iceberg. A proper Turing machine can implement any algorithm ever conceived. The only problem is that every algorithm requires the implementation of a separate set of transition rules and internal states; in other words, we need to build a new Turing machine for every new task, which is not quite practical in the long run. Thankfully, a special type of such a machine, a Universal Turing Machine (UTM), has an instruction set that is advanced enough to implement all specific Turing machines and to execute any algorithm without the need to alter the transition table.

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Its existence is guaranteed because a specific Turing machine can be devised to perform any finite algorithm (according to the aforementioned Church-Turing thesis). Because the method for “running” a Turing machine is itself a finite algorithm, a machine can be devised to execute it. As to the complexity of this machine, a one-bit, two-element alphabet machine (the smallest UTM devised) requires 22 internal states and instructions describing state transitions, in order to execute algorithms on a sequential infinite memory tape.[52] That’s not that big a deal. Holy Grail: The Programmable Computer The Turing machine is also far more than just a hypothetical abstract device that mathematicians use to entertain themselves.

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Turing and Instruction Set Complexity As it turns out, the processor does not have to be complex. In fact, the set of instructions required for a chip to be able to execute just about any task is surprisingly small. The Church-Turing thesis states that every real-world computation can be carried out by a Turing machine, which is a primitive model of a computer. The Turing machine, named after its inventor, is a trivial device that operates on a potentially infinite tape consisting of single cells, a hypothetical, purely abstract storage medium. Each cell can store a single character from a machine “alphabet,” which is simply a name for a finite ordered set of possible values.

The Diamond Age by Neal Stephenson

British Empire, clean water, dark matter, defense in depth, digital map, edge city, Just-in-time delivery, low earth orbit, Mason jar, Neal Stephenson, pattern recognition, pneumatic tube, sensible shoes, Silicon Valley, Socratic dialogue, South China Sea, the scientific method, Turing machine, wage slave

"To discover whether it was, in fact, a Turing machine." "Well, you have your answer. Wizard 0.2 is most certainly a Turing machine-the most powerful ever built." "And the Land Beyond?" "All grown from seeds. Seeds that I invented." "And it is also a Turing machine, then? All controlled by Wizard 0.2?" "No," said King Coyote. "Managed by Wizard. Controlled by me." "But the messages in the Cipherers' Market control all the events in the Land Beyond, do they not?" "You are most perceptive, Princess Nell." "Those messages came to Wizard-just another Turing machine." "Open the altar," said King Coyote, pointing to a large brass plate with a keyhole in the middle.

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He had plans for whole armies of Turing machines made to run in parallel, and for chains with links that could be set in more than two positions, and for machines that would read and write on two-dimensional sheets of chain mail instead of one-dimensional chains, and for a three-dimensional Turing grid a mile on a side, through which a mobile Turing machine would climb about, computing as it went. No matter how complicated his designs became, the Duke always found a way to simulate their behavior by putting a sufficiently long chain into one of the traditional Turing machines. That is to say that while the parallel and multidimensional machines worked more quickly than the original model, they didn't really do anything different.

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They were written in the same special language used at the previous two castles. In other words, once Princess Nell had deciphered the messages, her stall functioned like another Turing machine. It would have been easy enough to conclude that this whole castle was, like the others, a Turing machine. But the Primer had taught Nell to be very careful about making unwarranted assumptions. Just because her stall functioned according to Turing rules did not mean that all of the others did. And even if every stall in this castle was, in fact, a Turing machine, she still could not come to any fixed conclusions. She had seen riders carrying books to and from the castle, which meant that cipherers must be at work elsewhere in this kingdom.

The Cultural Logic of Computation by David Golumbia

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, American ideology, Benoit Mandelbrot, Bletchley Park, borderless world, business process, cellular automata, citizen journalism, Claude Shannon: information theory, computer age, Computing Machinery and Intelligence, corporate governance, creative destruction, digital capitalism, digital divide, en.wikipedia.org, finite state, folksonomy, future of work, Google Earth, Howard Zinn, IBM and the Holocaust, iterative process, Jaron Lanier, jimmy wales, John von Neumann, Joseph Schumpeter, late capitalism, Lewis Mumford, machine readable, machine translation, means of production, natural language processing, Norbert Wiener, One Laptop per Child (OLPC), 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, technological determinism, Ted Nelson, telemarketer, The Wisdom of Crowds, theory of mind, Turing machine, Turing test, Vannevar Bush, web application, Yochai Benkler

A term with application in nearly every academic discourse, functionalism has a specific meaning within contemporary analytic philosophy: as proposed by Hilary Putnam and subsequently adopted by other writers, functionalism is a “model of the mind” according to which “psychological states (‘believing that p,’ ‘desiring that p,’ ‘considering whether p,’ etc.) are simply ‘computational states’ of the brain. The proper way to think of the brain is as a digital computer.” This is not simply a metaphor: “according to the version of functionalism that I originally proposed, mental states can be defined in terms of Turing machine states and loadings of the memory (the paper tape of the Turing machine)” (Putnam 1988, 73). Many of its advocates give this view the straightforward name “the computer model of the mind” (e.g., Block 1990; Schank 1973). According to functionalism, the brain just is a digital computer, or something similar enough to one such that if we could discern its physical structure in sufficient detail, we would discover a binary mechanism, probably electrochemical in nature, that constitutes mental representations, exactly as a computer can be said to create representations.

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And materialists believe that a human body is just a living body. So . . . materialists are committed to the view that the human body is—at least metaphorically—a machine. It is understandable that the notion of a Turing machine might be seen as just a way of making this materialist idea precise. Understandable, but hardly well thought out. The problem is the following: a “machine” in the sense of a physical system obeying the laws of Newtonian physics need not be a Turing machine. (4) Putnam offers some intriguing logical results to support this conclusion, but in a sense it is clearly available to empirical investigation, since many sorts of extremely sophisticated cellular and molecular “machines” are in no sense capable of universal computation in Turing’s sense (instead, they are properly analog machines, devoted to one or several tasks but not generally applicable to others).

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In its received (sometimes called its “classical”) form, computationalism is the view that not just human minds are computers but that mind itself must be a computer—that our notion of intellect is, at bottom, identical with abstract computation, and that in discovering the principles of algorithmic computation via the Turing Machine human beings have, in fact, discovered the essence not just of human thought in practice but all thought in principle (see especially Kurzweil 1990, 1999, 2006). Today, few philosophers can accept any of the straightforward versions of computationalism (although there are certainly exceptions to this rule), generally because, as Scheutz writes, “computation, assumed to be defined in abstract syntactic terms, necessarily neglects the real-time, embodied, realworld constraints with which cognitive systems intrinsically cope” (Scheutz 2002, ix).

The Fabric of Reality by David Deutsch

Any sufficiently advanced technology is indistinguishable from magic, Arthur Eddington, Boeing 747, butterfly effect, coherent worldview, complexity theory, Computing Machinery and Intelligence, conceptual framework, cosmological principle, different worldview, Donald Knuth, Douglas Hofstadter, Eddington experiment, Georg Cantor, Gödel, Escher, Bach, Johannes Kepler, Occam's razor, phenotype, quantum cryptography, Richard Feynman, scientific worldview, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, time dilation, Turing machine

Cantgotu environments Logically possible environments which cannot be rendered by any physically possible virtual-reality generator. diagonal argument A form of proof in which one imagines listing a set of entities, and then uses the list to construct a related entity that cannot be on the list. {139} Turing machine One of the first abstract models of computation. universal Turing machine A Turing machine with the combined repertoire of all other Turing machines. Turing principle (in its strongest form) It is physically possible to build a universal virtual-reality generator. On the assumptions I have been making, this implies that there is no upper bound on the universality of virtual-reality generators that will actually be built somewhere in the multiverse.

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Turing's model of computation, and his conception of the nature of the problem he was solving, was the closest to being physical. His abstract computer, the Turing machine, was abstracted from the idea of a paper tape divided into squares, with one of a finite {131} number of easily distinguishable symbols written on each square Computation was performed by examining one square at a time moving the tape backwards or forwards, and erasing or writing one of the symbols according to simple, unambiguous rules. Turing proved that one particular computer of this type, the universal Turing machine, had the combined repertoire of all other Turing machines. He conjectured that this repertoire consisted precisely of 'every function that would naturally be regarded as computable'.

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That is to say, even the lowliest of today's home computers can be programmed to solve any problem, or render any environment, that our most powerful computers can, provided only that it is given additional memory, allowed to run for long enough, and given appropriate hardware for displaying its results. {194} Quantum computation is more than just a faster, more miniaturized technology for implementing Turing machines. A quantum computer is a machine that uses uniquely quantum-mechanical effects, especially interference, to perform wholly new types of computation that would be impossible, even in principle, on any Turing machine and hence on any classical computer. Quantum computation is therefore nothing less than a distinctively new way of harnessing nature. Let me elaborate that claim. The earliest inventions for harnessing nature were tools powered by human muscles.

The Music of the Primes by Marcus Du Sautoy

Ada Lovelace, Andrew Wiles, Arthur Eddington, Augustin-Louis Cauchy, Bletchley Park, Charles Babbage, computer age, Computing Machinery and Intelligence, Dava Sobel, Dmitri Mendeleev, Eddington experiment, Eratosthenes, Erdős number, Georg Cantor, German hyperinflation, global village, Henri Poincaré, Isaac Newton, Jacquard loom, lateral thinking, Leo Hollis, music of the spheres, Neal Stephenson, New Journalism, P = NP, Paul Erdős, Richard Feynman, Rubik’s Cube, Search for Extraterrestrial Intelligence, seminal paper, Simon Singh, Stephen Hawking, Turing machine, William of Occam, Wolfskehl Prize, Y2K

Robinson felt sure that there should be a way to exploit the groundwork laid by Turing. She understood that each Turing machine gives rise to a sequence of numbers. For example, one of the Turing machines could be made to produce a list of the square numbers 1, 4, 9, 16, …, whilst another generated the primes. One of the steps in Turing’s solution of Hilbert’s Decision Problem had been to prove that no program existed that could decide whether, given a Turing machine and a number, that number is the output of the machine. Robinson was looking for a connection between equations and Turing machines. Each Turing machine, she believed, would correspond to a particular equation.

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If there were such a connection, Robinson hoped that asking whether a number was the output of a particular Turing machine would translate into asking whether the equation corresponding to that machine had a solution. So if she could establish such a connection, she would be home. If there existed a program to test equations for solutions, as Hilbert was hoping for when he posed his tenth problem, then the same program could be used, via Robinson’s as yet hypothetical connection between equations and Turing machines, to check which numbers were outputs of Turing machines. But Turing had shown that no such program – one that could decide about the outputs of Turing machines – existed. Therefore there could be no program that could decide whether equations had solutions.

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They would later be known as Turing machines. Hilbert had been rather vague about what he meant by a machine that could tell whether statements could be proved. Now, thanks to Turing, Hilbert’s question had been put into focus. If one of Turing’s machines could not distinguish the provable from the unprovable, then no other machine could. So were his machines powerful enough to meet the challenge of Hilbert’s Decision Problem? While he was out one day, running along the banks of the River Cam, Turing experienced the second flash of enlightenment that told him why none of these Turing machines could be made to distinguish between statements that had proofs and those that didn’t.

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, Bletchley Park, complexity theory, dematerialisation, discovery of DNA, Great Leap Forward, Gregor Mendel, 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

.), 33, 35 Tononi, Giulio, 303 Top-down processing, 179 Transducers, 49–51 Transmogrification. See Protein transmogrification Trellis. See Neuron trellis Tunnel diodes, 103 Tunneling, electron, 125–126 Turing, Alan, 137, 138, 140, 250 Turing machines. See Universal Turing Machines Twain, Mark, 107 Ultraviolet rays, 22, 50, 59 (fig.), 109–110, 111 Unconscious thinking, 219–221 Unification theories, 13, 156 Universal computers, 108, 140, 252, 257 Universal Turing Machines, 137–140, 142n, 143, 206, 250 Universe developmental time chart of, 17, 18 (fig.) expansion of the, 6–7, 17, 20 (fig.), 21, 155 initial information state of the, 20, 21, 23 (fig.)

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Complex and simple cells in cortex, 193, 194–196 Computation, parallel. See Parallel computation Computation process classical versus quantum, 256–258 of Universal Turing Machines, 138–140 Computation time for gestalt recognition, 229 as a measure of complexity, 205, 206 saving, 273 See also Logical depth Computer-generated images, 140–142, 165 Computers and consciousness, 217 operational mode of, versus the brain’s, 184–185, 186, 187 protein demons as computers, 147–148 See also Universal Turing Machines Computing operations, 257 Conditional gate, 260, 261 Cones, 68, 72, 73 (fig.), 165, 166 (fig.) Conscious experience feelings and emotions, 223–226 gut feelings, 226–227 holistic aspects of, 221–223 and memory, 216, 218–219 multicellular involvement in, 159, 247 neural synchrony and, 227–228 and the passing of time, 216, 217–218 unconscious thinking, 219–221 Consciousness, xiii, 2–3, 95n, 184, 216 and the brain hemispheres, 184 competition for access to, 231–232, 233 (fig.)

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3The Second Coming The Demons for Fast Information Transmission The Sensory Demons A Generalized Sensory Scheme The Demon Tandem How the Demon Tandems Censor Incoming Information 4The Sensors The Sensory Transducer Unit A Lesson in Economics from a Master The Silent Partner How Electrical Sensory Signals Are Generated 5Quantum Sensing The Quantum World Our Windows to the Quantum World Coherent Quantum Information Transmission The Advantages of Being Stable Why We See the Rainbow The Demons Behind Our Pictures in the Mind: A Darwinistic Physics View Why White Is White The Quantum View Again, Why White Is White Lady Evolution’s Quantum Game Plan Quantum Particles That Don’t Cut the Mustard 6Quantum into Molecular Information Boosting the Quantum A Consummate Sleight of Hand The Ubiquitous Membrane Demon 7Molecular Sensing A Direct Line from Nose to Cortex A Thousand Information Channels of Smell Mapping, Coding, and Synonymity Molecular Sensory Synonymity Why Sensory Synonymity Quantum Synonymity Harmless Double Entendres 8Electronic Transmission of Biological Information Evolution’s Favorite Leptons Electronic Information Transmission: A Development Stumped Two Old Batteries 9The Random Generators of Biomolecular Complexity Genuine Transmogrification A Quantum Random Generator of Molecular Form The Heuristics of Transmogrification The Random Generator and Our Genetic Heritage An Algorithm Is No Substitute for a Demon The Second Generator of Biomolecular Form Complexity as a Windfall Ikats 10The Ascent of the Digital Demons Quantum Electron Tunneling The Electronic Cul-de-Sac The Rise of the Digital Demons Do Plants Have Digital Demons, Too? 11The Second Information Arrow and Its Astonishing Dénouement: Consciousness The Structure of Time The Evolutionary Niche in the Structure of Time: A Hypothesis Forecognition 12How to Represent the World The Universal Turing Machine Rendering the World by Computer The Neuronal Virtual-Reality Generator Our Biased World Picture Computing by Neurons Correcting Our World Picture Flying the Coop of Our Senses 13Expanded Reality A Fine Bouquet Mathematics and Reality The Neuron Circuitry of Language The Feathers of the Brain Mathematics and Forecognition The Reluctant Sensory Brain The Limits of Knowledge A Note About Reality 14Information Processing in the Brain Cell Organization in the Brain Cortical Information-Processing Units Cortical-Cell Topography and Worldview A Last-Minute Change in Worldview Retrieving a Lost Dimension Information Processing in the Brain from the Bottom Up Being of One Mind Two Minds in One Body?

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, AlphaGo, AltaVista, Amazon Web Services, AOL-Time Warner, Asilomar, augmented reality, Ben Horowitz, bitcoin, Bitcoin Ponzi scheme, Bletchley Park, 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, decentralized internet, deep learning, DeepMind, Demis Hassabis, disintermediation, distributed ledger, don't be evil, Donald Knuth, Donald Trump, double entry bookkeeping, driverless car, Elon Musk, Erik Brynjolfsson, Ethereum, ethereum blockchain, fake news, 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, Geoffrey Hinton, George Gilder, Google Earth, Google Glasses, Google Hangouts, index fund, inflation targeting, informal economy, initial coin offering, Internet of things, Isaac Newton, iterative process, Jaron Lanier, Jeff Bezos, Jim Simons, Joan Didion, John Markoff, John von Neumann, Julian Assange, Kevin Kelly, Law of Accelerating Returns, machine translation, Marc Andreessen, Mark Zuckerberg, Mary Meeker, 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, Neal Stephenson, Network effects, new economy, Nick Bostrom, Norbert Wiener, Oculus Rift, OSI model, PageRank, pattern recognition, Paul Graham, peer-to-peer, Peter Thiel, Ponzi scheme, prediction markets, quantitative easing, random walk, ransomware, Ray Kurzweil, reality distortion field, Recombinant DNA, 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, Snow Crash, software is eating the world, sorting algorithm, South Sea Bubble, speech recognition, Stephen Hawking, Steve Jobs, Steven Levy, Stewart Brand, stochastic process, Susan Wojcicki, TED Talk, telepresence, Tesla Model S, The Soul of a New Machine, theory of mind, Tim Cook: Apple, transaction costs, tulip mania, Turing complete, Turing machine, Vernor Vinge, Vitalik Buterin, Von Neumann architecture, Watson beat the top human players on Jeopardy!, WikiLeaks, Y Combinator, zero-sum game

Tegmark makes the case as well as it can be made that the attainments of AI programs—“Watson” the quiz-show winner and occasionally superior medical diagnostician; Big Blue the chess champion; Google’s DeepMind game players, which learned to outperform human players from scratch in dozens of electronic games; the face-recognizers; the natural language translators; the self-driving car programs—portend a super-intelligence that will someday be so superior to the human mind that we will no more comprehend its depths than a dog grasps the meaning of our own cerebrations. It is just a matter of time. Although shunning the dystopian interpretation, Kurzweil boldly offers a date: 2049. Tegmark likes to quote Edward Robert Harrison: “Hydrogen, given enough time, turns into people.” People, given enough time, presumably turn into Turing machines, and Turing machines are essentially what people used to call “God.” He isn’t shy about the godlike powers this super-AI will have: “Whatever form matter is in, advanced technology can rearrange it into any desired substances or objects, including power plants, computers, and advanced life forms.” Life 3.0 and Asilomar are declarations of principles for a post-human age.

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The new vision ultimately led to a new information theory of biology, anticipated in principle by von Neumann and developed most fully by Hubert Yockey,10 in which human beings might eventually reprogram parts of their own DNA. More immediately, Gödel’s proof prompted Alan Turing’s invention in 1936 of the Turing machine—the universal computing architecture with which he showed that computer programs, like other logical schemes, not only were incomplete but could not even be proved to reach any conclusion. Any particular program might cause it to churn away forever. This was the “halting problem.” Computers required what Turing called “oracles” to give them instructions and judge their outputs.11 Turing showed that just as the uncertainties of physics stem from using electrons and photons to measure themselves, the limitations of computers stem from recursive self-reference.

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He pointed out that the company had amassed some $50 billion in cash at the time and was allowing it to sit in the bank at near-zero interest rates while its vast data centers still could not identify cats as well as a three-year-old could.7 Thiel is the leading critic of Silicon Valley’s prevailing philosophy of “inevitable” innovation. Page, on the other hand, is a machine-learning maximalist who believes that silicon will soon outperform human beings, however you want to define the difference. If the haphazard Turing machine of evolution could produce human brains, just imagine what could be accomplished by Google’s constellation of eminent academics devoting entire data centers full of multi-gigahertz silicon to training machines on petabytes of data. In 2012, though, the results seemed underwhelming. Simultaneously with the dogs and cats crisis in 2012, the leader of the Google Brain research team, Jeff Dean, raised the stakes by telling Urs Hölzle, Google’s data center dynamo, “We need another Google.”

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, Charles Babbage, 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, digital divide, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, functional programming, George Gilder, Gödel, Escher, Bach, Hans Moravec, hype cycle, informal economy, information retrieval, information security, 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, Nick Bostrom, Norbert Wiener, oil shale / tar sands, optical character recognition, PalmPilot, pattern recognition, phenotype, power law, precautionary principle, premature optimization, punch-card reader, quantum cryptography, quantum entanglement, radical life extension, 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, seminal paper, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, Stuart Kauffman, 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

Finally, we select the machine (one that does halt) that writes the largest number of 1s on its tape. The number of 1s that this Turing machine writes is called the busy beaver of n. Rado showed that there is no algorithm—that is, no Turing machine—that can compute this function for all ns. The crux of the problem is sorting out those n-state machines that get into infinite loops. If we program a Turing machine to generate and simulate all possible n-state Turing machines, this simulator itself gets into an infinite loop when it attempts to simulate one of the n-state machines that gets into an infinite loop.

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., "Competition in the Retinogenicu1ate Patterning Driven by Spontaneous Activity," Science 279.5359 (March 27, 1998): 2108–12. 73. The seven commands of a Turing machine are: (1) Read Tape, (2) Move Tape Left, (3) Move Tape Right, (4) Write 0 on the Tape, (5) Write 1 on the Tape, (6) Jump to Another Command, and (7) Halt. 74. In what is perhaps the most impressive analysis in his book, Wolfram shows how a Turing machine with only two states and five possible colors can be a universal Turing machine. For forty years, we've thought that a universal Turing machine had to be more complex than this. Also impressive is Wolfram's demonstration that rule 110 is capable of universal computation, given the right software.

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The complexity of Babbage's invention stemmed only from the details of its design, which indeed proved too difficult for Babbage to implement using the technology available to him. The Turing machine, Alan Turing's theoretical conception of a universal computer in 1950, provides only seven very basic commands, yet can be organized to perform any possible computation.73 The existence of a "universal Turing machine," which can simulate any possible Turing machine that is described on its tape memory, is a further demonstration of the universality and simplicity of information.74 In The Age of Intelligent Machines, I showed how any computer could be constructed from "a suitable number of [a] very simple device," namely, the "nor" gate.75 This is not exactly the same demonstration as a universal Turing machine, but it does demonstrate that any computation can be performed by a cascade of this very simple device (which is simpler than rule 110), given the right software (which would include the connection description of the nor gates).76 Although we need additional concepts to describe an evolutionary process that create intelligent solutions to problems, Wolfram's demonstration of the simplicity an ubiquity of computation is an important contribution in our understanding of the fundamental significance of information in the world.

The Computer Boys Take Over: Computers, Programmers, and the Politics of Technical Expertise by Nathan L. Ensmenger

barriers to entry, business process, Charles Babbage, Claude Shannon: information theory, computer age, deskilling, Donald Knuth, Firefox, Frederick Winslow Taylor, functional programming, future of work, Grace Hopper, informal economy, information retrieval, interchangeable parts, Isaac Newton, Jacquard loom, job satisfaction, John von Neumann, knowledge worker, Larry Ellison, loose coupling, machine readable, new economy, no silver bullet, Norbert Wiener, pattern recognition, performance metric, Philip Mirowski, post-industrial society, Productivity paradox, RAND corporation, Robert Gordon, scientific management, Shoshana Zuboff, sorting algorithm, Steve Jobs, Steven Levy, systems thinking, tacit knowledge, technological determinism, the market place, The Theory of the Leisure Class by Thorstein Veblen, Thomas Kuhn: the structure of scientific revolutions, Thorstein Veblen, Turing machine, Von Neumann architecture, world market for maybe five computers, Y2K

In order to facilitate his exploration, Turing invented a new tool, an imaginary device capable of performing simple mechanical computations. Each Turing Machine, which consisted of only a long paper tape along with a mechanism for reading from and writing to that tape, contained a table of instructions that allowed it to perform a single computation. As a computing device, the Turing Machine is deceptively simple; as a conceptual abstraction, it is extraordinarily powerful. As it turns out, the table of instructions for any Turing Machine can be rewritten to contain the instructions for building any other Turing Machine. The implication, as articulated in the Church-Turing thesis, is that every Turing Machine is a Universal Turing Machine, and by extension, every computing machine is essentially equivalent.

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By abstracting the logical design of the digital computer from any particular physical implementation, von Neumann took a crucial first step in the development of a modern theory of computation.55 His was not the only contribution; in 1937, for example, Turing had described, for the purposes of demonstrating the limits of computation, what would become known as the Universal Turing Machine. Eventually, the Universal Turing Machine would become an even more fundamental construct of modern computer science. According to the Church-Turing thesis, first articulated in 1943 by the mathematician Stephen Kleene, any function that can be physically computed can be computed by a Universal Turing Machine. The abstraction of the technology of computing in the theoretical construct of the Turing Machine mirrored the shift toward software that was occurring in the larger commercial computing industry.

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This means that in theory at least, all computers are functionally equivalent: any given computer is but a specific implementation of a more general abstraction known as a Universal Turing Machine. It is the Platonic ideal of the Universal Turing Machine, and not the messy reality of actual physical computers, that is the true subject of modern theoretical computer science; it is only by treating the computer as an abstraction, a mathematical construct, that theoretical computer scientists lay claim to their field being a legitimate scientific, rather than merely a technical or engineering, discipline. The story of this remarkable self-construction and its consequences is the subject of chapter 5. The idealized Universal Turing Machine is, of course, only a conceptual device, a convenient fiction concocted by the mathematician Alan Turing in the late 1930s as a means of exploring a long-standing puzzle in theoretical mathematics known as the Entscheidungsproblem.

When Einstein Walked With Gödel: Excursions to the Edge of Thought by Jim Holt

Ada Lovelace, Albert Einstein, Andrew Wiles, anthropic principle, anti-communist, Arthur Eddington, Benoit Mandelbrot, Bletchley Park, Brownian motion, cellular automata, Charles Babbage, classic study, computer age, CRISPR, dark matter, David Brooks, Donald Trump, Dr. Strangelove, Eddington experiment, Edmond Halley, everywhere but in the productivity statistics, Fellow of the Royal Society, four colour theorem, Georg Cantor, George Santayana, Gregor Mendel, haute couture, heat death of the universe, Henri Poincaré, Higgs boson, inventory management, Isaac Newton, Jacquard loom, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, Large Hadron Collider, Long Term Capital Management, Louis Bachelier, luminiferous ether, Mahatma Gandhi, mandelbrot fractal, Monty Hall problem, Murray Gell-Mann, new economy, Nicholas Carr, Norbert Wiener, Norman Macrae, Paradox of Choice, Paul Erdős, Peter Singer: altruism, Plato's cave, power law, probability theory / Blaise Pascal / Pierre de Fermat, quantum entanglement, random walk, Richard Feynman, Robert Solow, Schrödinger's Cat, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, Skype, stakhanovite, Stephen Hawking, Steven Pinker, Thorstein Veblen, Turing complete, Turing machine, Turing test, union organizing, Vilfredo Pareto, Von Neumann architecture, wage slave

The code number of one special-purpose Turing machine could even be fed as an input onto the tape of another Turing machine. This led Turing to the idea of a universal machine: one that, if fed the code number of any special-purpose Turing machine, would function as if it actually were that special-purpose machine. For instance, if a universal Turing machine were fed the code number of the Turing machine that performed addition, the universal machine would temporarily turn into an adding machine. That is exactly what happens when your laptop, which is a physical embodiment of Turing’s universal machine, runs a word-processing program or when your smartphone runs an app.

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In doing so, he came up with an idealized machine that defined the limits of computability: what is now known as a Turing machine. The genius of Turing’s imaginary machine lay in its stunning simplicity. (“Let us praise the uncluttered mind,” exulted one of Turing’s colleagues.) It consisted of a scanner that moved back and forth over an infinite tape reading and writing 0s and 1s according to a certain set of instructions—0s and 1s being capable of expressing all letters and numerals. A Turing machine designed for some special purpose—like adding two numbers together—could itself be described by a single number that coded its action. The code number of one special-purpose Turing machine could even be fed as an input onto the tape of another Turing machine.

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Each machine’s functioning, moreover, could be encapsulated in a single number (typically, a very long one), so that one machine could be made to operate on another by putting the number of the second machine on the tape of the first as a sequence of 0s and 1s. If a machine were fed its own number, then it could operate on itself. Turing was thereby able to exploit something akin to the paradoxes of self-reference (“I am lying”) and show that certain sorts of Turing machines could not exist. For instance, there could be no Turing machine that, when fed with the program number of another machine, would decide whether that machine would eventually come to a halt in its computation or would grind on forever. (If there were such a machine, it could be tweaked into a Hamlet-like variant that would decide, in effect, “I will come to a halt if and only if I never come to a halt.”)

Darwin's Dangerous Idea: Evolution and the Meanings of Life by Daniel C. Dennett

Albert Einstein, Alfred Russel Wallace, anthropic principle, assortative mating, buy low sell high, cellular automata, Charles Babbage, classic study, combinatorial explosion, complexity theory, computer age, Computing Machinery and Intelligence, conceptual framework, Conway's Game of Life, Danny Hillis, double helix, Douglas Hofstadter, Drosophila, finite state, Garrett Hardin, Gregor Mendel, Gödel, Escher, Bach, heat death of the universe, In Cold Blood by Truman Capote, invention of writing, Isaac Newton, Johann Wolfgang von Goethe, John von Neumann, junk bonds, language acquisition, Murray Gell-Mann, New Journalism, non-fiction novel, Peter Singer: altruism, phenotype, price mechanism, prisoner's dilemma, QWERTY keyboard, random walk, Recombinant DNA, Richard Feynman, Rodney Brooks, Schrödinger's Cat, selection bias, Stephen Hawking, Steven Pinker, strong AI, Stuart Kauffman, the scientific method, theory of mind, Thomas Malthus, Tragedy of the Commons, Turing machine, Turing test

Turing devised just such a system, and in it every computer — from your laptop to the grandest parallel supercomputer that will ever be built — has a unique description as what we now call a Turing machine. The Turing machines can each be given a unique identification number — its Library of Babel Number, if you like. Gödel's Theorem can then be reinterpreted to say that each of those Turing machines that happens to be a consistent algorithm for proving truths of arithmetic (and, not surprisingly, these are a Vast but Vanishing subset of all the possible Turing machines) has associated with it a Gödel sentence — a truth of arithmetic it cannot prove. So that is what Gödel, anchored by Turing to the world of computers, tells us: every computer that is a consistent truth-of-arithmetic-prover has an Achilles' heel, a truth it can never prove, even if it runs till doomsday.

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They wanted something dead simple, easy to visualize and easy to calculate, so they not only dropped from three dimensions to two; they also "digitized" both space and time — all times and distances, as we saw, are in whole numbers of "instants" and "cells." It was von Neumann who had taken Alan Turing's abstract conception of a mechanical computer (now called a "Turing machine") and engineered it into the specification for a general-purpose stored-program serial-processing computer (now called a "von Neumann machine"); in his brilliant explorations of the spatial and structural requirements for such a computer, he had realized — and proved — that a Universal Turing machine (a Turing machine that can compute any computable function at all) could in principle be "built" in a two-dimensional world.6 Conway and his students also set out to confirm this with their own exercise in two-dimensional engineering.7 It was far from easy, but they showed how they could "build" a working computer out of simpler Life forms.

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Of all the possible moves available, he saw that there was a good reason for this move, so this is what would be discovered. We can get a sense of the magnitude of the leap that such an inference takes by comparing it with a parallel leap that we can make in the Game of Life. Recall that one of the possible denizens of the Life world is a Universal Turing machine composed of trillions of pixels. Since a Universal Turing machine can compute any computable function, it can play chess — simply by mimicking the program of any chess-playing computer you like. Suppose, then, that such an entity occupies the Life plane, playing chess against itself, in the fashion of Samuel's computer playing checkers against itself.

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, Alignment Problem, AlphaGo, artificial general intelligence, Asilomar, autonomous vehicles, basic income, Benoit Mandelbrot, Bill Joy: nanobots, Bletchley Park, Buckminster Fuller, cellular automata, Claude Shannon: information theory, Computing Machinery and Intelligence, CRISPR, Daniel Kahneman / Amos Tversky, Danny Hillis, data science, David Graeber, deep learning, DeepMind, Demis Hassabis, easy for humans, difficult for computers, Elon Musk, Eratosthenes, Ernest Rutherford, fake news, finite state, friendly AI, future of work, Geoffrey Hinton, Geoffrey West, Santa Fe Institute, gig economy, Hans Moravec, heat death of the universe, hype cycle, income inequality, industrial robot, information retrieval, invention of writing, it is difficult to get a man to understand something, when his salary depends on his not understanding it, James Watt: steam engine, Jeff Hawkins, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, Kickstarter, Laplace demon, Large Hadron Collider, Loebner Prize, machine translation, market fundamentalism, Marshall McLuhan, Menlo Park, military-industrial complex, mirror neurons, Nick Bostrom, Norbert Wiener, OpenAI, optical character recognition, paperclip maximiser, pattern recognition, personalized medicine, Picturephone, profit maximization, profit motive, public intellectual, quantum cryptography, RAND corporation, random walk, Ray Kurzweil, Recombinant DNA, Richard Feynman, Rodney Brooks, 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, synthetic biology, systems thinking, technological determinism, technological singularity, technoutopianism, TED Talk, telemarketer, telerobotics, The future is already here, the long tail, the scientific method, theory of mind, trolley problem, Turing machine, Turing test, universal basic income, Upton Sinclair, Von Neumann architecture, Whole Earth Catalog, Y2K, you are the product, zero-sum game

Von Neumann’s digital-computer architecture is conceptually the same generalization—from early digital computers constructed with electromagnetic relays at both Harvard University and Bletchley Park—that occurs in going from a special-purpose Turing Machine to a Universal Turing Machine. Furthermore, his self-replicating automata share a fundamental similarity with both the construction of a Turing Machine and the mechanism of DNA-based reproducing biological cells. There is to this day scholarly debate over whether von Neumann saw the cross connections between these three pieces of work, Turing’s and his two. Turing’s revision of his paper was done while he and von Neumann were both at Princeton; indeed, after getting his PhD, Turing almost stayed on as von Neumann’s postdoc.

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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.

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In 1943, Warren McCulloch and Walter Pitts came up with a model for how brains conceptually, formally, might work—an artificial neural network. They saw that their brainlike model would do computations in the same way as Turing Machines. From their work, it emerged that we could make brainlike neural networks that would act as general computers. And in fact, the practical work done by the ENIAC folks and John von Neumann and others on computers came directly not from Turing Machines but through this bypath of neural networks. But simple neural networks didn’t do much. Frank Rosenblatt invented a learning device he called the perceptron, which was a one-layer neural network.

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World by Pedro Domingos

Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, backpropagation, basic income, Bayesian statistics, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Charles Babbage, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, creative destruction, crowdsourcing, Danny Hillis, data is not the new oil, data is the new oil, data science, deep learning, DeepMind, double helix, Douglas Hofstadter, driverless car, Erik Brynjolfsson, experimental subject, Filter Bubble, future of work, Geoffrey Hinton, global village, Google Glasses, Gödel, Escher, Bach, Hans Moravec, incognito mode, information retrieval, Jeff Hawkins, job automation, John Markoff, John Snow's cholera map, John von Neumann, Joseph Schumpeter, Kevin Kelly, large language model, lone genius, machine translation, mandelbrot fractal, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, Narrative Science, Nate Silver, natural language processing, Netflix Prize, Network effects, Nick Bostrom, NP-complete, off grid, P = NP, PageRank, pattern recognition, phenotype, planetary scale, power law, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, scientific worldview, Second Machine Age, self-driving car, Silicon Valley, social intelligence, speech recognition, Stanford marshmallow experiment, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the long tail, the scientific method, The Signal and the Noise by Nate Silver, theory of mind, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, white flight, yottabyte, zero-sum game

Then in 1936 Alan Turing imagined a curious contraption with a tape and a head that read and wrote symbols on it, now known as a Turing machine. Every conceivable problem that can be solved by logical deduction can be solved by a Turing machine. Furthermore, a so-called universal Turing machine can simulate any other by reading its specification from the tape—in other words, it can be programmed to do anything. The Master Algorithm is for induction, the process of learning, what the Turing machine is for deduction. It can learn to simulate any other algorithm by reading examples of its input-output behavior. Just as there are many models of computation equivalent to a Turing machine, there are probably many different equivalent formulations of a universal learner.

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., 91, 94–95 decision tree induction, 85–89 further reading, 300–302 hill climbing and, 135 Hume and, 58–59 induction and, 80–83 intelligence and, 52, 89 inverse deduction and, 52, 82–85, 91 Master Algorithm and, 240–241, 242–243 nature and, 141 “no free lunch” theorem, 62–65 overfitting, 70–75 probability and, 173 problem of induction, 59–62 sets of rules, 68–70 Taleb, Nassim, 38, 158 Tamagotchi, 285 Technology machine learning as, 236–237 sex and evolution of, 136–137 trends in, 21–22 Terrorists, data mining to catch, 232–233 Test set accuracy, 75–76, 78–79 Tetris, 32–33 Text classification, support vector machines and, 195–196 Thalamus, 27 Theory, defined, 46 Theory of cognition, 226 Theory of everything, Master Algorithm and, 46–48 Theory of intelligence, 35 Theory of problem solving, 225 Thinking, Fast and Slow (Kahneman), 141 Thorndike, Edward, 218 Through the Looking Glass (Carroll), 135 Tic-tac-toe, algorithm for, 3–4 Time, as principal component of memory, 217 Time complexity, 5 The Tipping Point (Gladwell), 105–106 Tolstoy, Leo, 66 Training set accuracy, 75–76, 79 Transistors, 1–2 Treaty banning robot warfare, 281 Truth, Bayesians and, 167 Turing, Alan, 34, 35, 286 Turing Award, 75, 156 Turing machine, 34, 250 Turing point, Singularity and, 286, 288 Turing test, 133–134 “Turning the Bayesian crank,” 149 UCI repository of data sets, 76 Uncertainty, 52, 90, 143–175 Unconstrained optimization, 193–194. See also Gradient descent Underwood, Ben, 26, 299 Unemployment, machine learning and, 278–279 Unified inference algorithm, 256 United Nations, 281 US Patent and Trademark Office, 133 Universal learning algorithm. See Master Algorithm Universal Turing machine, 34 Uplift modeling, 309 Valiant, Leslie, 75 Value of states, 219–221 Vapnik, Vladimir, 190, 192, 193, 195 Variance, 78–79 Variational inference, 164, 170 Venter, Craig, 289 Vinge, Vernor, 286 Virtual machines, 236 Visual cortex, 26 Viterbi algorithm, 165, 305 Voronoi diagrams, 181, 183 Wake-sleep algorithm, 103–104 Walmart, 11, 69–70 War, cyber-, 19–21, 279–282, 299, 310 War of the Worlds (radio program), 156 Watkins, Chris, 221, 223 Watson, James, 122, 236 Watson, Thomas J., Sr., 219 Watson (computer), 37, 42–43, 219, 237, 238 Wave equation, 30 Web 2.0, 21 Web advertising, 10–11, 160, 305 Weighted k-nearest-neighbor algorithm, 183–185, 190 Weights attribute, 189 backpropagation and, 111 Master Algorithm and, 242 meta-learning and, 237–238 perceptron’s, 97–99 relational learning and, 229 of support vectors, 192–193 Welles, Orson, 156 Werbos, Paul, 113 Wigner, Eugene, 29 Will, George F., 276 Williams, Ronald, 112 Wilson, E.

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“All humans are mortal” is much more succinct than seven billion statements of mortality, one for each human. Memorization gives us none of these things. Another candidate Master Algorithm is the microprocessor. After all, the one in your computer can be viewed as a single algorithm whose job is to execute other algorithms, like a universal Turing machine; and it can run any imaginable algorithm, up to its limits of memory and speed. In effect, to a microprocessor an algorithm is just another kind of data. The problem here is that, by itself, the microprocessor doesn’t know how to do anything; it just sits there idle all day. Where do the algorithms it runs come from?

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

At any given moment, the reading head may occupy one of a number of internal states. These, too, are finite and correspond in an unspecified way to various internal configurations of the reading head, so that what the Turing machine does is a function not only of what at any moment it sees, but what at any moment it is. There is not much else. A Turing machine is a deterministic device, and like an ordinary machine, it does what it must do. Turing machines can nonetheless do rather an astonishing variety of intellectual tasks. Addition is an example, as with a few notational elaborations the logician may be observed constructing a calculating device out of thin air.

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No matter where logicians begin in defining the algorithm, they always end up in the same place. Gödel regarded this circumstance as a miracle. FIG. 10.1 And so it is. In virtue of its elegance and obviousness, the definition of an algorithm in terms of Turing machines has become the standard. The usual operations of arithmetic are all Turing-computable. So, too, most algorithms. So, too, Church argued, any algorithm, the concept of a Turing machine exhausting completely the idea of an effective calculation. This last claim is known as Church’s thesis, and in the seventy years since it was advanced, it has passed progressively from a conjecture, to a persuasive definition, to a law of nature, to an unbudgeable fixture in contemporary thought.

…

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. A Turing machine consists of a tape divided into squares and a reading head. Although finite, the tape may be extended in both directions. The reading head, as its name might suggest, is designed to recognize and manipulate a finite set of symbols—0 and 1, for most purposes. Beginning at an initial square, the reading head is capable of moving to the left or to the right on the tape, one square at a time, and it is capable of writing symbols on the tape or erasing the symbols that it is scanning.

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, Alignment Problem, AlphaGo, Amazon Mechanical Turk, artificial general intelligence, autonomous vehicles, Big Tech, Black Swan, Bletchley Park, Boeing 737 MAX, business intelligence, Charles Babbage, Claude Shannon: information theory, Computing Machinery and Intelligence, conceptual framework, correlation does not imply causation, data science, deep learning, DeepMind, driverless car, Elon Musk, Ernest Rutherford, Filter Bubble, Geoffrey Hinton, Georg Cantor, Higgs boson, hive mind, ImageNet competition, information retrieval, invention of the printing press, invention of the wheel, Isaac Newton, Jaron Lanier, Jeff Hawkins, John von Neumann, Kevin Kelly, Large Hadron Collider, Law of Accelerating Returns, Lewis Mumford, Loebner Prize, machine readable, machine translation, Nate Silver, natural language processing, Nick Bostrom, Norbert Wiener, PageRank, PalmPilot, paperclip maximiser, pattern recognition, Peter Thiel, public intellectual, Ray Kurzweil, retrograde motion, self-driving car, semantic web, Silicon Valley, social intelligence, speech recognition, statistical model, Stephen Hawking, superintelligent machines, tacit knowledge, technological singularity, TED Talk, The Coming Technological Singularity, the long tail, 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

Hilbert was wrong.6 I M PLICAT IONS FOR A I What is impor­tant to AI ­here is this: Turing disproved that mathe­ matics was decidable by inventing a machine, a deterministic machine, requiring no insight or intelligence to solve prob­lems. ­Today, we refer to his abstract formulation of a machine as a Turing machine. I am typing on one right now. Turing machines are computers. It is one of the ­g reat ironies of intellectual history that the theoretical framework for computation was put in place as a side-­thought, a means to another end. While working to disprove that mathe­matics itself was decidable, Turing first in­ven­ted something precise and mechanical, the computer.

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His thesis considered the powers of ingenuity, by creating ever more complicated systems of rules. (Ingenuity, it turned out, could become universal—­ there are machines that can take as input other machines, and thus run all the machines that can be built. This insight, technically a universal Turing machine and not a s­ imple Turing machine, was to become the digital computer.) But in his formal work on computing, Turing had (perhaps inadvertently) let the cat out of the bag. By allowing for intuition as distinct from and outside of the operations of a purely formal system like a computer, Turing in effect suggested that ­there may be differences between computer programs that do math and mathematicians.

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(In a moment of sheer panic, it occurs to her that this logic jeopardizes the entire enterprise of getting to superintelligence, but she manages to suppress this concern quickly.) Alice decides, in deference to AI’s founder and to the eager-­beaver marketing department of her com­pany, Ultra++, that ­she’ll instead focus on designing a machine as intelligent as Alan Turing, called the Turing-­Machine. Now, assuming that Turing was smarter than Alice (though who is to say?), she c­ an’t just design a Turing-­Machine directly, and anyway 40 T he S implified W orld she already ran into a brick wall puzzling out how to design a Bob-­ Machine. She decides to begin with a machine that’s as smart as Hugh Alexander—­Turing’s colleague at Bletchley Park and a one-­time chess champion of Cambridge.

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, Bletchley Park, Boeing 747, Byte Shop, Charles Babbage, Claude Shannon: information theory, Compatible Time-Sharing System, computer age, Computing Machinery and Intelligence, conceptual framework, cuban missile crisis, Dennis Ritchie, do well by doing good, Donald Davies, double helix, Douglas Engelbart, Douglas Engelbart, Dynabook, experimental subject, Fairchild Semiconductor, fault tolerance, Frederick Winslow Taylor, friendly fire, From Mathematics to the Technologies of Life and Death, functional programming, Gary Kildall, Haight Ashbury, Howard Rheingold, information retrieval, invisible hand, Isaac Newton, Ivan Sutherland, James Watt: steam engine, Jeff Rulifson, John von Neumann, Ken Thompson, Leonard Kleinrock, machine translation, Marc Andreessen, Menlo Park, Multics, New Journalism, Norbert Wiener, packet switching, pink-collar, pneumatic tube, popular electronics, RAND corporation, RFC: Request For Comment, Robert Metcalfe, Silicon Valley, Skinner box, Steve Crocker, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, Ted Nelson, The Soul of a New Machine, Turing machine, Turing test, Vannevar Bush, Von Neumann architecture, Wiener process, zero-sum game

Their own paper, published in 1943 as "A Logical Calculus of the Ideas Immanent in Nervous Activity," was essentially a demonstration that their idealized neural networks were functionally equivalent to Turing machines. That is, any problem that a Turing machine could solve, an appropriately designed network could also solve. And conversely, anything that was beyond a Turing machine's power-such as the decidability problem-was likewise beyond a network's power. As the science historian William Aspray has written, "With the Turing machines providing an abstract characterization of thinking in the machine world and McCulloch and Pitts's neuron nets providing one in the biological world, the equivalence result suggested a unified theory of thought that broke down barriers between the physical and biological worlds."14 Or, as McCulloch himself would put it in his 1965 autobiography Embodiments of Mind, he and Pitts had proved the equivalence of all general Turing machines, whether "man-made or begotten."

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And to enable transformations between sentence structures-the sort of thing we do all the time when we go from, say, active voice Oohn kissed Mary) to passive (Mary was kissed by John) or to a question (Whom did John kiss?)- you need a grammar from the most powerful class of all, the one that is mathe- matically equivalent to a Turing machine. To put it another way, the very fact that we human beings use language in the way we do is proof that, in some sense, our brains have the computational power of a Turing machine. Or to express it still another way, the pinnacle of all possi- ble mathematical machines-the Turing machine-is also the baseline, the mini- mum needed for human cognition. Anybody who seriously wants to understand the workings of the mind had better start from there, because nothing less will do.

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In at least one instance, moreover, his theory proved to be spectacularly prescien t. In the case of, say, a factory machine tool, von Neumann observed, you have an automaton that can turn out very complex parts but not another machine tool. Likewise, a universal Turing machine can output an arbitrarily complex tape but not another Turing machine. However, in almost any biological organ- ism, you have an automaton that can not only reproduce identical copies of it- self but also (through evolution) give rise to organisms that are more complex than itself. So von Neumann asked, What are the essential features required for an automaton to reproduce itself and to evolve?

The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction by Richard Bookstaber

asset allocation, bank run, Bear Stearns, behavioural economics, bitcoin, business cycle, butterfly effect, buy and hold, capital asset pricing model, cellular automata, collateralized debt obligation, conceptual framework, constrained optimization, Craig Reynolds: boids flock, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, dark matter, data science, disintermediation, Edward Lorenz: Chaos theory, epigenetics, feminist movement, financial engineering, financial innovation, fixed income, Flash crash, geopolitical risk, Henri Poincaré, impact investing, information asymmetry, invisible hand, Isaac Newton, John Conway, John Meriwether, John von Neumann, Joseph Schumpeter, Long Term Capital Management, margin call, market clearing, market microstructure, money market fund, Paul Samuelson, Pierre-Simon Laplace, Piper Alpha, Ponzi scheme, quantitative trading / quantitative finance, railway mania, Ralph Waldo Emerson, Richard Feynman, risk/return, Robert Solow, Saturday Night Live, self-driving car, seminal paper, sovereign wealth fund, the map is not the territory, The Predators' Ball, the scientific method, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, tulip mania, Turing machine, Turing test, yield curve

., 85 Sharpe, William, 85 Shereshevsky, Solomon, 76–77 Simon, Herbert, 110 SIVs, 161, 165 Slick, Grace, 50 Smith, Adam, 3–4, 188 Societie Generale (SocGen), 164 Solow, Robert, 92 Soros, George, 83, 115, 137; and reflexivity, 58–59 stampede: and emergence, 35–36; Hajj, example of, 34–36 Standard & Poor’s, 160 stock market crash (October 1987): and the New York Stock Exchange (NYSE), 145–147; and portfolio insurance, 145–147 (see also portfolio insurance); and the S&P 500, 145–147 subprime mortgages, 160–161 Sun Pin, 117 Syll, Lars, 138 Thomas Theorem, 108 tight coupling, 112 Turing, Alan: and David Hilbert’s program, 54 (see also halting problem); and the halting problem, 31, 55; and the printing problem, 55; and Turing test, 196; and the universal Turing machine (UTM), 54 (see also universal Turing machine) Tversky, Amos, 45–47 Unbearable Lightness of Being, The, 60–61 uncertainty principle, 56–57; and the limits to knowledge, 51 universal Turing machine (UTM), 32, 54–56 University of Chicago, 3 Victorian England, 3–4 Volcker Rule, 156, 158 Walras, Leon, 194 Washington Mutual, 11 white night, 131 Whitehead, Alfred North, 52–53 Wittgenstein, Ludwig, 40 Wolfram, Stephen, 26–27 A NOTE ON THE TYPE This book has been composed in Adobe Text and Gotham.

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Turing’s colleague Alonzo Church (who, independently of Turing, had also demonstrated the impossibility of Hilbert’s program) called this the Turing machine. Turing went a step further, and added to the machine a set of instructions that were internal to the machine and were not altered over the course of execution. The instruction set could be for any computation we can envision, and so this became known as the universal computing machine, or the universal Turing machine (UTM). The UTM is a momentous achievement; it is the foundation for modern computers. It allows for the essential elements of computing—reading, writing, a database (in Turing’s conception, held on an infinitely long tape), short-term memory of the state of the computation, and the instructions to execute held internally as part of the database.

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See MGonz Chernobyl, nuclear accident of, 112 Church, Alonzo, 54 Citigroup, 11, 166 Clower, Robert, 85 cockroach, 68, 74; defense mechanism of, 66; and omniscient planner, 66–67 Coleman, Henry, 5 collateral: haircuts and, 131; risk reduction of, 204; transformations of, 131 commercial paper, 136 Commodity Futures Trading Commission (CFTC), 147–148 complexity: and chaos theory, 110–111; in comparison to computational irreducibility, 108, 122; description of, 109–112; and emergence, 108, 122; and ergodicity, 111, 122; and financial crises, 112 (see also financial crises); and informational irreducibility, 109–110; investigation of by Gotfried Wilhelm Leibniz, 109; and neoclassical economics, 123–124 (see also neoclassical economics); and network theory, 110; and nonlinear systems, 110–111; and the OODA loop, 122 (see also OODA Loop); and radical uncertainty, 112, 122; and strategic complexity, 122–124 computational irreducibility, 12, 18, 33; crises and, 105; and heuristics, 65; and the Library of Babel, 62–63; and maps, 26; and mathematical shortcuts, 26; and neoclassical economics, 83 (see also neoclassical economics); and three-body problem, 27–28 (see also three-body problem); and Turing’s halting problem, 55 computers, and the universal Turing machine, 54. See also universal Turing machine Conway, John, 30. See also Conway’s Game of Life Conway’s Game of Life: as an agent-based model, 32–33, 122–123; and boids, 37; and computational irreducibility, 32; and context, 122–124; in the context of radical uncertainty, 123–124; emergence in, 32; rules of, 30–31; self-replication features of, 32; and Turing’s halting problem, 55 credit default swaps, 163–165 Cruise, Tom, 94 Darwin, Charles, 72–73 Dawkins, Richard, 181 decimalization, 149 deduction, 15, 107, 124, 180–183, 188–189 degenerative research program, 90–91 Demon of Our Own Design, A, 108, 157 Department of Defense, 158 Deutsche Bank, 165 diversification, 15–16 Dodd-Frank Act, 156–157 Dostoyevsky, Fyodor, 116 Duffie, Darrell, 152–153 dynamic stochastic general equilibrium model, 92 efficient market hypothesis, 116 emergence, 12; and boids, 37; and complexity, 38; and crises, 105; flock of birds movement, example of, 37; and Hajj stampede, 35–36; and heuristics, 65; and limits to knowledge, 52; and neoclassical economics, 83 (see also neoclassical economics); school of fish movement, example of, 36; and stability, 39; stampedes, example of 127–128; traffic example, 95, 97–98; and traffic flow, 17, 94 enclosures, 5 equilibrium, crises of, 104–105 ergodicity, 12, 17–18, 41, 196; context of, 40; history of, 40; and limits to knowledge, 52; and MGonz, 44; and neoclassical economics, 84 (see also neoclassical economics); in physical systems, 40; in physical versus social sciences, 85; testing models of, 177 essayism, 178 eternal recurrence, 60 fallibility, 59, 115, 117; and the rational expectations hypothesis, 175 Feynman, Richard, 54, 90 financial crises: fire marshal analogy, 127–129; financial crisis of 1987, 90; financial crisis of 2008, 92 (see also financial crisis of 2008); structure of, 129 financial crisis of 2008, 157; an agent-based view, 160; contagion during, 160; leverage and, 156, 176; liquidity and, 156; market-to-market difficulties and, 159–164; regulation and, 156; role of AIG in, 163–165; role of Bear Stearns Asset Management (BSAM) in, 161–162 (see also Bear Stearns Asset Management); role of Goldman Sachs in, 163–164 financial institutions: agents of, 99, 106; interactions between, 128–131 financial markets: complexity of, 108–109, 157; crisis in, 14–16, 108–109; environment of, 100–101; fire marshal analogy, 127–128; and Flash Crash, 147–151; and liquidity, 206; and reflexivity, 59; structure of, 128; weather analogy 113, 185–186 Financial Stability Oversight Council, 158 financial system: fire marshal analogy, 129; flows of, 131; multilayer schematic of, 131, 134; schematic system of, 129; structure of, 129, 131 fire sale, 107; asset-based, 138; funding-based, 139 Flash Crash, 147; effect of decimalization on, 149–150; effect of high-frequency trading on, 150; The Price is Right analogy, 148–150 Flaubert, Gustave, 116 Freudianism, 58 Frydman, Roman, 175 funding, 131, 134; cash providers of, 136; and collateral, 137; flows within financial system, 137; and hedge funds, 136; securities lenders for, 136 funding runs, 138–139 Funes, the Memorious, 75–78 Game of Life.

Ways of Being: Beyond Human Intelligence by James Bridle

Ada Lovelace, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Anthropocene, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, behavioural economics, Benoit Mandelbrot, Berlin Wall, Big Tech, Black Lives Matter, blockchain, Californian Ideology, Cambridge Analytica, carbon tax, Charles Babbage, cloud computing, coastline paradox / Richardson effect, Computing Machinery and Intelligence, corporate personhood, COVID-19, cryptocurrency, DeepMind, Donald Trump, Douglas Hofstadter, Elon Musk, experimental subject, factory automation, fake news, friendly AI, gig economy, global pandemic, Gödel, Escher, Bach, impulse control, James Bridle, James Webb Space Telescope, John von Neumann, Kickstarter, Kim Stanley Robinson, language acquisition, life extension, mandelbrot fractal, Marshall McLuhan, microbiome, music of the spheres, negative emissions, Nick Bostrom, Norbert Wiener, paperclip maximiser, pattern recognition, peer-to-peer, planetary scale, RAND corporation, random walk, recommendation engine, self-driving car, SETI@home, shareholder value, Silicon Valley, Silicon Valley ideology, speech recognition, statistical model, surveillance capitalism, techno-determinism, technological determinism, technoutopianism, the long tail, the scientific method, The Soul of a New Machine, theory of mind, traveling salesman, trolley problem, Turing complete, Turing machine, Turing test, UNCLOS, undersea cable, urban planning, Von Neumann architecture, wikimedia commons, zero-sum game

One of the most interesting of those branches is to be found budding on the eve of the Second World War, at the very moment the modern computer was conceived. The kind of computer I am using – that we are all using – is based on something called a Turing machine. This is the model of a computer described theoretically by Alan Turing in 1936. It’s what’s called an ideal machine – ideal as in imaginary, but not necessarily perfect. The Turing machine was a thought experiment, but because it came to form the basis for all future forms of computation, it also altered the way we think. Turing’s imaginary machine consisted of a long strip of paper and a tool for reading and writing onto it, like a tape recorder.

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Almost every computer in the world is just a more elaborate version of a strip of paper and a read/write head. Every time you open an email, type on a keyboard, take money out of an ATM, play a digital song, stream a movie or see through a satellite, you are working with an incarnation of a Turing machine: symbols read and written from the equivalent of a strip of tape. I am writing this on a Turing machine; there’s also a chance you’re reading it on one (and if not, many were still necessary to produce what you hold in your hands). These Turing-imagined computers are in some way responsible for almost every aspect of our lives. But their sheer ubiquity masks a powerful realization: almost every computer working today represents only a tiny fraction of what computers might be.

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This was the focus of a question laid down by the German mathematician David Hilbert in his influential Entscheidungsproblem of 1928, which asked whether it was possible to construct a step-by-step, algorithmic process to solve what are called ‘decision problems’. Given a yes/no question, could you write a set of instructions which would be guaranteed to give a yes/no answer? Turing concluded that it was not, but in doing so he created a novel framework for computing decision problems in general – the Turing machine – which gave us the modern computer. So decidability has a very specific and technical definition in computer science, and Turing’s machine gave us a method for dealing with it. But what I am interested in is undecidability. Undecidability has a technical meaning too – but it also has a real meaning, a literal meaning, referring to that which we cannot know for certain.

Diaspora by Greg Egan

conceptual framework, cosmic abundance, cosmic microwave background, Fermat's Last Theorem, gravity well, Jacquard loom, stem cell, telepresence, telepresence robot, Turing machine

Think of a row of Wang Tiles as being like the data tape of a Turing Machine." Paolo had the library grant him knowledge of the term; it was the original conceptual form of a generalized computing device, an imaginary machine which moved hack and forth along a limitless one-dimensional data tape, reading and writing symbols according to a given set of rules. "With the right set of tiles, to force the right pattern, the next row of the tiling will look like the data tape after the Turing Machine has performed one step of its computation. And the row after that will be the data tape after two steps, and so on. For any given Turing Machine, there's a set of Wang Tiles that can imitate it."

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You've found a pattern? Don't tell me: our set of twenty thousand polysaccharide Wang Tiles just happens to form the Turing Machine for calculating pi." "No. What they form is a universal Turing Machine. They can calculate anything at all-depending on the data they start with. Every daughter fragment is like a program being fed to a chemical computer. Growth executes the program." "Ah." Paolo's curiosity was roused-but he was having some trouble picturing where the hypothetical Turing Machine put its read/write head. "Are you telling me only one tile changes between any two rows, where thèmachine' leaves its mark on thèdata tape' ... .

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"Are you telling me only one tile changes between any two rows, where thèmachine' leaves its mark on thèdata tape' ... . The mosaics he'd seen were a riot of complexity, with no two rows remotely the same. Karpal said, "No, no. Wang's original example worked exactly like a standard Turing Machine, to simplify the argument ... but the carpets are more like an arbitrary number of different computers with overlapping data, all working in parallel. This is biology, not a designed machine-it's as messy and wild as, say, a mammalian genome. In fact, there are mathematical similarities with gene regulation: I've identified Kauffman networks at every level, from the tiling rules up; the whole system's poised on the hyperadaptive edge between frozen and chaotic behavior."

The Fourth Age: Smart Robots, Conscious Computers, and the Future of Humanity by Byron Reese

"World Economic Forum" Davos, agricultural Revolution, AI winter, Apollo 11, artificial general intelligence, basic income, bread and circuses, Buckminster Fuller, business cycle, business process, Charles Babbage, Claude Shannon: information theory, clean water, cognitive bias, computer age, CRISPR, crowdsourcing, dark matter, DeepMind, Edward Jenner, Elon Musk, Eratosthenes, estate planning, financial independence, first square of the chessboard, first square of the chessboard / second half of the chessboard, flying shuttle, full employment, Hans Moravec, Hans Rosling, income inequality, invention of agriculture, invention of movable type, invention of the printing press, invention of writing, Isaac Newton, Islamic Golden Age, James Hargreaves, job automation, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, lateral thinking, life extension, Louis Pasteur, low interest rates, low skilled workers, manufacturing employment, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Mary Lou Jepsen, Moravec's paradox, Nick Bostrom, On the Revolutions of the Heavenly Spheres, OpenAI, pattern recognition, profit motive, quantum entanglement, radical life extension, Ray Kurzweil, recommendation engine, Rodney Brooks, Sam Altman, self-driving car, seminal paper, Silicon Valley, Skype, spinning jenny, Stephen Hawking, Steve Wozniak, Steven Pinker, strong AI, technological singularity, TED Talk, telepresence, telepresence robot, The Future of Employment, the scientific method, Timothy McVeigh, Turing machine, Turing test, universal basic income, Von Neumann architecture, Wall-E, warehouse robotics, Watson beat the top human players on Jeopardy!, women in the workforce, working poor, Works Progress Administration, Y Combinator

Almost all of them.” In fact, anything a computer can do today, you could theoretically do on a Turing machine. And Turing not only conceived of the machine but figured all this out. Consider that simple machine, that thought experiment with just a handful of parts: Everything Apollo 11 needed to do to make it to the moon and back could be programmed on a Turing Machine. Everything your smartphone can do can be programmed on a Turing machine, and everything IBM Watson can do can be programmed on a Turing machine. Who could have guessed that such a humble little device could do all that? Well, Turing could, of course.

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Turing’s contribution at this point in our tale came in 1936, when he first described what we now call a Turing machine. Turing conceived of a hypothetical machine that could perform complex mathematical problems. The machine is made up of a narrow strip of graph paper, which, in theory, is infinitely long. On the graph paper there is always a single active cell, and above that cell hovers a head. The head can read and write to the paper and move around a bit, based on the instructions it receives or the programs it runs. The point of the Turing machine was not “Here’s how you build a computer” but rather, “This simple imaginary device can solve an enormous range of computational problems.

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Well, Turing could, of course. But no one else seems to have had that singular idea. Exit Turing. Enter John von Neumann, whom we call the father of modern computing. In 1945, he developed the von Neumann architecture for computers. While Turing machines are purely theoretical, designed to frame the question of what computers can do, the von Neumann architecture is about how to build actual computers. He suggested an internal processor and computer memory that holds both programs and data. In addition to the computer’s memory, there might also be external storage to hold data and information not currently needed.

Quantum Computing for Everyone by Chris Bernhardt

Albert Einstein, complexity theory, correlation does not imply causation, discrete time, John von Neumann, low earth orbit, P = NP, quantum cryptography, quantum entanglement, reversible computing, Richard Feynman, selection bias, Turing machine, Von Neumann architecture

This is what Peter Shor achieved in his 1994 landmark paper, in which he showed (among other things) how quantum computing could be used to break the codes that are currently used for Internet security. We will briefly discuss Shor’s algorithm in the next chapter, where we look at the impact of quantum computing. * NP comes from nondeterministic polynomial, which in turn refers to certain types of Turing machines that are called nondeterministic Turing machines. ** “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proceedings of the Royal Society A 400 (1818): 97–117. *** You may have seen systems of linear equations before and remember that you need n equations to solve a system with n unknowns.

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The point of this is that we don’t have to worry about how to write an algorithm that emulates the function, so we don’t have to calculate the number of steps that function takes to evaluate the input. We just keep track of the number of questions. This is much simpler. To illustrate, we begin with the most elementary example. Deutsch’s Algorithm David Deutsch is one of the founders of quantum computing. In 1985, he published a landmark paper that described quantum Turing machines and quantum computation.** This paper also includes the following algorithm—the first to show that a quantum algorithm could be faster than a classical one. The problem concerns functions of just one variable. The input can be either 0 or 1. The output also just takes the values of 0 or 1. There are four of these functions that we will denote , , and : The function sends both inputs to 0; i.e., and .

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Computation Alan Turing is one of the fathers of the theory of computation. In his landmark paper of 1936 he carefully thought about computation. He considered what humans did as they performed computations and broke it down to its most elemental level. He showed that a simple theoretical machine, which we now call a Turing machine, could carry out any algorithm. Turing’s theoretical machines evolved into our modern day computers. They are universal computers. Turing’s analysis showed us the most elemental operations. These involve the manipulation of bits. But remember, Turing was analyzing computation based on what humans do.

On Intelligence by Jeff Hawkins, Sandra Blakeslee

airport security, Albert Einstein, backpropagation, computer age, Computing Machinery and Intelligence, conceptual framework, Jeff Hawkins, Johannes Kepler, Necker cube, PalmPilot, pattern recognition, Paul Erdős, Ray Kurzweil, Silicon Valley, Silicon Valley startup, speech recognition, superintelligent machines, the scientific method, Thomas Bayes, Turing machine, Turing test

Turing proved, mathematically, that if you choose the right set of rules for the CPU and give it an indefinitely long tape to work with, it can perform any definable set of operations in the universe. It would be one of many equivalent machines now called Universal Turing Machines. Whether the problem is to compute square roots, calculate ballistic trajectories, play games, edit pictures, or reconcile bank transactions, it is all 1's and 0's underneath, and any Turing Machine can be programmed to handle it. Information processing is information processing is information processing. All digital computers are logically equivalent. Turing's conclusion was indisputably true and phenomenally fruitful.

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Nor did he think he could define intelligence formally, so he didn't even try. Instead, he proposed an existence proof for intelligence, the famous Turing Test: if a computer can fool a human interrogator into thinking that it too is a person, then by definition the computer must be intelligent. And so, with the Turing Test as his measuring stick and the Turing Machine as his medium, Turing helped launch the field of AI. Its central dogma: the brain is just another kind of computer. It doesn't matter how you design an artificially intelligent system, it just has to produce humanlike behavior. The AI proponents saw parallels between computation and thinking.

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Sure, people do all this with brains and not with the kinds of computers we build, but Turing has shown that it doesn't matter how you implement or manipulate the symbols. You can do it with an assembly of cogs and gears, with a system of electronic switches, or with the brain's network of neurons— whatever, as long as your medium can realize the functional equivalent of a Universal Turing Machine." This assumption was bolstered by an influential scientific paper published in 1943 by the neurophysiologist Warren McCulloch and the mathematician Walter Pitts. They described how neurons could perform digital functions— that is, how nerve cells could conceivably replicate the formal logic at the heart of computers.

The Secret Life of Bletchley Park: The WWII Codebreaking Centre and the Men and Women Who Worked There by Sinclair McKay

Beeching cuts, Bletchley Park, British Empire, Charles Babbage, computer age, Desert Island Discs, Etonian, pneumatic tube, Turing machine

Yet he was a more radical, open, honest soul than the accounts suggest. Turing became a Fellow of King’s College before, in the late 1930s, heading for the United States, to Princeton. Building bridges between the two disciplines of mathematics and applied physics, he threw himself into the construction of a ‘Turing machine’, a machine that could carry out logical binary calculations. Having seen a tide-predicting machine some years back in Liverpool, it occurred to him that the principle of this device could be applied to his own machine, greatly speeding its function. By 1938, when it was increasingly clear that war was coming to the whole of Europe, Turing returned to England, and to King’s, with his electric multiplier machine mounted on a bread-board.

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Even in the years that followed the war, with all the technological progress that had been made, Turing’s devices tended to fulfil the stereotype of the mad scientist’s invention: a labyrinth of wires trailing everywhere, held together with sticking plaster. Prior to his premature death in 1954, his home in Manchester was filled with extraordinary and sometimes pungent chemical experiments. Turing had fixed upon the idea of a ‘Universal Turing Machine’ in the 1930s; the inspiration had been provided by a mathematical problem posed in Cambridge, concerning the provability of any given mathematical assertion. Turing had the idea of developing a machine that could carry out this task. When first trying to envisage the form of such a machine, Turing thought of typewriters, how they were built to carry out a certain sort of function.

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According to his biographer Andrew Hodges, he had in his head an idea of a super-typewriter: a machine that could identify symbols; that could write, but could also erase. A machine that could be configured in many ways to carry out many tasks, and yet would be automatic, requiring little or no intervention from a human operator. His argument was that any calculation that a human could perform, a machine could perform as well. The bombes were not Universal Turing Machines. Far from it. Nor were they an extension of the Polish ‘bomba’ machines, from which their name was taken. The British bombe was quite a different thing. In one sense, it was a philosophical response to the nature of Enigma. Despite the daunting number of combinations thrown up by Enigma, it none the less worked via a mechanical process.

When Things Start to Think by Neil A. Gershenfeld

3D printing, Ada Lovelace, Bretton Woods, cellular automata, Charles Babbage, Claude Shannon: information theory, Computing Machinery and Intelligence, disinformation, Dynabook, Hedy Lamarr / George Antheil, I think there is a world market for maybe five computers, information security, invention of movable type, Iridium satellite, Isaac Newton, Jacquard loom, Johannes Kepler, John von Neumann, low earth orbit, means of production, new economy, Nick Leeson, packet switching, RFID, speech recognition, Stephen Hawking, Steve Jobs, telemarketer, the medium is the message, Turing machine, Turing test, Vannevar Bush, world market for maybe five computers

In 1936 Turing proved the latter. To do this, he had to bring some kind of order to the notion of a smart machine. Since he couldn't anticipate all the kinds of machines people might build, he had to find a general way to describe their capabilities. He did this by introducing the concept of a Universal Turing Machine. This was a simple machine that had a tape (possibly infinitely long), and a head that could move along it, reading and writing marks based on what was already on the tape. Turing showed that this machine could perform any computation that could be done by any other machine, by preparing it first with a program giving the rules for interpreting the instructions for the other machine.

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With this result he could then prove or disprove the Entscheidungsproblem for his one machine and have it apply to all of the rest. He did this by showing that it was impossible for a program to exist that could determine whether another program would eventually halt or keep running forever. Although a Turing machine was a theoretical construction, in the period after World War II a number of laboratories turned to successfully making electronic computers to replace the human "computers" who followed written instructions to carry out calculations. These machines prompted Turing to pose a more elusive question: 128 + WHEN THINGS START TO THINK could a computer be intelligent?

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This idea has come to be known as Cellular Automata (CAs). From the 1970s onward, the group of Ed Fredkin, Tomaso Toffoli, and Norm Margolus at MIT started to make special-purpose computers designed for CAs. Because these machines entirely dispense with approximations of continuous functions, they can be much simpler and faster. And because a Turing machine can be described this way, a CA can do anything that can be done with a conventional computer. A cellular automata model of the universe is no less fundamental than one based on calculus. It's a much more natural description if a computer instead of a pencil is used to work with the model. BIT BELIEFS + 133 And the discretization solves another problem: a continuous quantity can represent an infinite amount of information.

Paper Machines: About Cards & Catalogs, 1548-1929 by Markus Krajewski, Peter Krapp

Apollo 11, business process, Charles Babbage, continuation of politics by other means, double entry bookkeeping, Frederick Winslow Taylor, Gödel, Escher, Bach, index card, Index librorum prohibitorum, information retrieval, invention of movable type, invention of the printing press, Jacques de Vaucanson, Johann Wolfgang von Goethe, Joseph-Marie Jacquard, knowledge worker, means of production, new economy, paper trading, Turing machine, work culture

This comparison is not to claim that the index catalog is already a Turing machine. Comparisons, transfers, and analogies are not that simple. If the elements of a universal discrete machine are present, they still lack the computational logic of an operating system, the development of which constitutes Turing’s foundational achievement. What is described here is merely the fact that the card catalog is literally a paper machine, similar to a nontrivial Turing machine only in having similar components—no more, no less. 16. See for instance note 15 regarding the limits of the Turing machine analogy, note 1 of chapter 2 for the book flood metaphor, and notes 62 of chapter 2 and 42 of chapter 4 for the business card and bank note comparisons, respectively.

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This epistemological payoff is contained in the description—in short, the necessary catachresis of historiography activates insights that are called forth by the various connotations of the metaphors chosen. 8 Chapter 1 Thus, readers ought not be too surprised by references that may appear peculiar at first. They will find correspondences between index cards and bank notes, house numbers and book shelving, card catalogs and Turing machines, masses of books and their description as waves of a flood. These images are called upon consciously, at times by way of historical quotations. Even if it is clear that a card catalog does not perfectly resemble the digital calculator or computer, I maintain that the card catalog is one precursor of computing.14 On the software side, the components of the catalog and its function correspond to the theoretical concept of a universal discrete machine as developed by Turing in 1936, with a writing/reading head (or scriptor), an infinite paper band partitioned into discrete steps (or slips), and an unambiguous set of instructions for reading and writing data.15 Moreover, on the hardware side there is a line of industrial development from library technology directly to the producers of early computing installations, pointing to the technology transfer from the catalog card to the punch card and on to modern storage media.

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Boyd Rayward, and Oliver Simons for their assistance and cooperation; last but not least, and particularly for the time in between the two books, thanks to Frau V. Weimar, May 2010 Markus Krajewski Notes Chapter 1 1. From the catalog copy in figure 1.1. 2. Turing 1987, pp. 20, 91 and also in this connection, Dotzler 1996, esp. p. 7. For the structural analogy between card catalog and Turing machine, see above all note 15 in this chapter. 3. “For the duration of a state,” as Müller 1995, p. 45 put it. 4. See Kittler 1986, pp. 244f., and Kittler 1993, pp. 170ff. 5. Translator’s note: The author uses the German word verzetteln in a double sense: putting notes and quotes down on paper slips, and sorting individual notes in an index; but also disseminating, releasing them.

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, Bletchley Park, British Empire, c2.com, Charles Babbage, computer age, Computing Machinery and Intelligence, Fellow of the Royal Society, Ford Model T, Henri Poincaré, IBM and the Holocaust, Isaac Newton, John von Neumann, Karl Jansky, machine translation, Norbert Wiener, Norman Macrae, Pierre-Simon Laplace, punch-card reader, RAND corporation, Turing machine, Vannevar Bush, Von Neumann architecture

The lambda calculus “represented an elegant and powerful symbolism for mathematical processes of abstraction and variation,” but the Turing machine was a thought experiment that posited a mechanical operation, to be done by either a mechanism or by a human mind. 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.”

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In spring 1945, right around the time that the order was going out for the ten Colossus machines to be destroyed, Womersley went to the United States and was shown ENIAC (before, in fact, it was unveiled to the general public). When Womersley got back to the UK, he was eager to build a UK version. Since, unlike Mauchly and Eckert, he happened to be quite familiar with “On Computable Numbers” and had even toyed with designing a mechanical version of a Turing machine before the war (his partner, like Mauchly and Eckert’s original partner, was in the horse-racing pari-mutuel totalizer business), he offered Turing £800 per year—£200 more than he had received at Bletchley Park—to come to the NPL. Turing began work on October 1, 1945, and he was ready with plenty of ideas.

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Turing thought that if the hardware was fast enough and the program detailed and complex enough, roomfuls of processor units could be avoided. However, such a machine would have had difficulties of its own, according to John Gustafson, who maintains, It is clear that what he had in mind building was something very like the theoretical model in his Computability paper, the model we now call a Turing machine. It worked on one bit at a time, but used a huge amount of memory to do anything of consequence. Since he had proved that anything that was computable could be theoretically computed on such a simple device, why not build one? The CPU would only have required a handful of vacuum tubes. But such a machine is horrendously difficult to program, and even at electronic speeds, it would have been painfully slow for many simple things like floating-point arithmetic.2 One of Turing’s difficulties (or Womersley’s, as his director) was that he didn’t mind talking to the press (either the general press or journals of particular groups, such as the Institution of Radio Engineers), but when he did talk, he raised hopes that did not seem realistically capable of fulfillment, and he was often met with skepticism.

The Code Book: The Science of Secrecy From Ancient Egypt to Quantum Cryptography by Simon Singh

Bletchley Park, Charles Babbage, Donald Davies, friendly fire, information security, Leo Hollis, Mikhail Gorbachev, old-boy network, operational security, quantum cryptography, Ronald Reagan, Schrödinger's Cat, Simon Singh, Turing machine, unbiased observer, undersea cable, Zimmermann PGP

Turing imagined a whole series of these so-called Turing machines, each specially designed to tackle a particular task, such as dividing, squaring or factoring. Then Turing took a more radical step. He imagined a machine whose internal workings could be altered so that it could perform all the functions of all conceivable Turing machines. The alterations would be made by inserting carefully selected tapes, which transformed the single flexible machine into a dividing machine, a multiplying machine, or any other type of machine. Turing called this hypothetical device a universal Turing machine because it would be capable of answering any question that could logically be answered.

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Unfortunately, it turned out that it is not always logically possible to answer a question about the undecidability of another question, and so even the universal Turing machine was unable to identify every undecidable question. Mathematicians who read Turing’s paper were disappointed that Gödel’s monster had not been subdued but, as a consolation prize, Turing had given them the blueprint for the modern programmable computer. Turing knew of Babbage’s work, and the universal Turing machine can be seen as a reincarnation of Difference Engine No. 2. In fact, Turing had gone much further, and provided computing with a solid theoretical basis, imbuing the computer with a hitherto unimaginable potential.

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In fact, Turing had gone much further, and provided computing with a solid theoretical basis, imbuing the computer with a hitherto unimaginable potential. It was still the 1930s though, and the technology did not exist to turn the universal Turing machine into a reality. However, Turing was not at all dismayed that his theories were ahead of what was technically feasible. He merely wanted recognition from within the mathematical community, who indeed applauded his paper as one of the most important breakthroughs of the century. He was still only twenty-six. This was a particularly happy and successful period for Turing. During the 1930s he rose through the ranks to become a fellow of King’s College, home of the world’s intellectual elite.

The Deep Learning Revolution (The MIT Press) by Terrence J. Sejnowski

AI winter, Albert Einstein, algorithmic bias, algorithmic trading, AlphaGo, Amazon Web Services, Any sufficiently advanced technology is indistinguishable from magic, augmented reality, autonomous vehicles, backpropagation, Baxter: Rethink Robotics, behavioural economics, bioinformatics, cellular automata, Claude Shannon: information theory, cloud computing, complexity theory, computer vision, conceptual framework, constrained optimization, Conway's Game of Life, correlation does not imply causation, crowdsourcing, Danny Hillis, data science, deep learning, DeepMind, delayed gratification, Demis Hassabis, Dennis Ritchie, discovery of DNA, Donald Trump, Douglas Engelbart, driverless car, Drosophila, Elon Musk, en.wikipedia.org, epigenetics, Flynn Effect, Frank Gehry, future of work, Geoffrey Hinton, Google Glasses, Google X / Alphabet X, Guggenheim Bilbao, Gödel, Escher, Bach, haute couture, Henri Poincaré, I think there is a world market for maybe five computers, industrial robot, informal economy, Internet of things, Isaac Newton, Jim Simons, John Conway, John Markoff, John von Neumann, language acquisition, Large Hadron Collider, machine readable, Mark Zuckerberg, Minecraft, natural language processing, Neil Armstrong, Netflix Prize, Norbert Wiener, OpenAI, orbital mechanics / astrodynamics, PageRank, pattern recognition, pneumatic tube, prediction markets, randomized controlled trial, Recombinant DNA, recommendation engine, Renaissance Technologies, Rodney Brooks, self-driving car, Silicon Valley, Silicon Valley startup, Socratic dialogue, speech recognition, statistical model, Stephen Hawking, Stuart Kauffman, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Von Neumann architecture, Watson beat the top human players on Jeopardy!, world market for maybe five computers, X Prize, Yogi Berra

When data sets are small, a single sample left out of the training set can be used to test the performance of the network trained on the remaining examples, and the process repeated for every sample to get an average test performance. This is a special case of cross-validation where n = 1, in which n subsamples are held out. 284 Glossary Turing machine Hypothetical computer invented by Alan Turing (1937) as a simple model for mathematical calculation. A Turing machine consists of a “tape” that can be moved back and forth, a “head” that has a “state” that can change the property of the active cell beneath it, and a set of instructions for how the head should modify the active cell and move the tape.

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(The Department of Defense had recently poured $600 million into its Strategic Computing Initiative, a program that ran from 1983 to 1993 but came up short on building a vision system to guide a self-driving tank.)9 “Good luck with that,” was my reply. Gerald Sussman, who made several important applications of AI to real-world problems, including a system for high-precision integration for orbital mechanics, defended the honor of MIT’s approach to AI with an appeal to the classic work of Alan Turing, who had proven that the Turing machine, a thought experiment, could compute any computable function. “And how long would that take?” I asked. “You had better compute quickly or you will be eaten,” I added, then walked across the room to pour myself a cup of coffee. And that was the end of the dialogue with the faculty. 34 Chapter 2 “What is wrong with this picture?”

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This suggests that, for solutions to the hard problems in artificial intelligence, we should be looking into computers with massively parallel architectures rather than those with von Neumann digital architectures through which data and instructions are fetched and executed one at a time. Yes, it is true that a Turing machine can compute any computable function given enough memory and enough time, but nature had to solve problems in real The Dawn of Neural Networks 39 time. To do this, it made use of the brain’s neural networks that, like the most powerful computers on the planet, have massively parallel processors.

Rage Inside the Machine: The Prejudice of Algorithms, and How to Stop the Internet Making Bigots of Us All by Robert Elliott Smith

"World Economic Forum" Davos, Ada Lovelace, adjacent possible, affirmative action, AI winter, Alfred Russel Wallace, algorithmic bias, algorithmic management, AlphaGo, Amazon Mechanical Turk, animal electricity, autonomous vehicles, behavioural economics, Black Swan, Brexit referendum, British Empire, Cambridge Analytica, cellular automata, Charles Babbage, citizen journalism, Claude Shannon: information theory, combinatorial explosion, Computing Machinery and Intelligence, corporate personhood, correlation coefficient, crowdsourcing, Daniel Kahneman / Amos Tversky, data science, deep learning, DeepMind, desegregation, discovery of DNA, disinformation, Douglas Hofstadter, Elon Musk, fake news, Fellow of the Royal Society, feminist movement, Filter Bubble, Flash crash, Geoffrey Hinton, Gerolamo Cardano, gig economy, Gödel, Escher, Bach, invention of the wheel, invisible hand, Jacquard loom, Jacques de Vaucanson, John Harrison: Longitude, John von Neumann, Kenneth Arrow, Linda problem, low skilled workers, Mark Zuckerberg, mass immigration, meta-analysis, mutually assured destruction, natural language processing, new economy, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, On the Economy of Machinery and Manufactures, p-value, pattern recognition, Paul Samuelson, performance metric, Pierre-Simon Laplace, post-truth, precariat, profit maximization, profit motive, Silicon Valley, social intelligence, statistical model, Stephen Hawking, stochastic process, Stuart Kauffman, telemarketer, The Bell Curve by Richard Herrnstein and Charles Murray, The Future of Employment, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Thomas Malthus, traveling salesman, Turing machine, Turing test, twin studies, Vilfredo Pareto, Von Neumann architecture, warehouse robotics, women in the workforce, Yochai Benkler

In 1936, British mathematician (and later war hero) Alan Turing designed a theoretical mechanical device, and a mathematical proof that it could do any mechanical procedure, that could be implemented on any computer, ever. This device, which we now call a Turing Machine, involved configurations of mechanical ‘states’, and the ability to write to and read from memory (in the form of symbols written on an infinitely long roll of tape). In every way, the Turing Machine is like Babbage’s Engine, if that Engine had infinite memory in its ‘store’. In fact, the whole point of Turing’s proof was that this machine was equivalent to any general-purpose computer, and therefore any general-purpose computer is just like any other.

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In fact, the whole point of Turing’s proof was that this machine was equivalent to any general-purpose computer, and therefore any general-purpose computer is just like any other. That is to say, Turing proved that regardless of whether it was built on a substrate of brass gears and levers, vacuum tubes, as-yet-uninvented semiconductor chips, or even biological cells, the Turing Machine could implement any algorithm10 that could be implemented on any other computer. It defined the range of what could be computed by algorithms. This is known as the theory of universal computation, and is a basis upon which many believers in AI feel that the brain is just a kind of computer. After all, they theorize, everything that can possibly be built must follow the mechanical rules of physics.

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Turing showed that all such devices that compute, regardless of the substrate they are built on, have the same ultimate algorithmic capabilities. The theory concludes that the brain is just another mechanical device, a built ‘machine’ that must follow the rules of physics. Therefore, the brain can’t do anything that a Turing machine, and thus any other computer, can’t do. By this argument, the brain is just a computer. Of course, the ultimate ‘capabilities’ assumed in this line of reasoning are the execution of Hilbert’s ‘mechanical procedures’ (algorithms). Whether this is all brains do is a debatable question that is philosophically central to AI.

I Am a Strange Loop by Douglas R. Hofstadter

Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Brownian motion, Charles Babbage, double helix, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Hans Moravec, Isaac Newton, James Watt: steam engine, John Conway, John von Neumann, language acquisition, mandelbrot fractal, pattern recognition, Paul Erdős, place-making, probability theory / Blaise Pascal / Pierre de Fermat, publish or perish, random walk, Ronald Reagan, self-driving car, Silicon Valley, telepresence, Turing machine

For instance, consider the case of John Searle, a philosopher who has spent much of his career heaping scorn on artificial-intelligence research and computational models of thinking, taking special delight in mocking Turing machines. A momentary digression… Turing machines are extremely simple idealized computers whose memory consists of an infinitely long (i.e., arbitrarily extensible) “tape” of so-called “cells”, each of which is just a square that either is blank or has a dot inside it. A Turing machine comes with a movable “head”, which looks at any one square at a time, and can “read” the cell (i.e., tell if it has a dot or not) and “write” on it (i.e., put a dot there, or erase a dot). Lastly, a Turing machine has, stored in its “head”, a fixed list of instructions telling the head under which conditions to move left one cell or right one cell, or to make a new dot or to erase an old dot.

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Lastly, a Turing machine has, stored in its “head”, a fixed list of instructions telling the head under which conditions to move left one cell or right one cell, or to make a new dot or to erase an old dot. Though the basic operations of all Turing machines are supremely trivial, any computation of any sort can be carried out by an appropriate Turing machine (numbers being represented by adjacent dot-filled cells, so that “•••” flanked by blanks would represent the integer 3). Back now to philosopher John Searle. He has gotten a lot of mileage out of the fact that a Turing machine is an abstract machine, and therefore could, in principle, be built out of any materials whatsoever. In a ploy that, in my opinion, should fool only third-graders but that unfortunately takes in great multitudes of his professional colleagues, he pokes merciless fun at the idea that thinking could ever be implemented in a system made of such far-fetched physical substrates as toilet paper and pebbles (the tape would be an infinite roll of toilet paper, and a pebble on a square of paper would act as the dot in a cell), or Tinkertoys, or a vast assemblage of beer cans and ping-pong balls bashing together.

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Page 26 abstractions are central…in the study of the brain… See [Treisman], [Minsky 1986], [Schank], [Hofstadter and FARG], [Kanerva], [Fauconnier], [Dawkins], [Blackmore], and [Wheelis] for spellings-out of these abstract ideas. Page 27 Just as the notion of “gene” as an invisible entity that enabled… See [ Judson]. Page 27 and just as the notion of “atoms” as the building blocks… See [Pais 1986], [Pais 1991], [Hoffmann], and [Pullman]. Page 28 Turing machines are…idealized computers… See [Hennie] and [Boolos and Jeffrey]. Page 29 In his vivid writings, Searle gives… See Chapter 22 of [Hofstadter and Dennett]. Page 29 one particular can that would “pop up”… In his smugly dismissive review [Searle] of [Hofstadter and Dennett], Searle states: “So let us imagine our thirst-simulating program running on a computer made entirely of old beer cans, millions (or billions) of old beer cans that are rigged up to levers and powered by windmills.

How the Mind Works by Steven Pinker

affirmative action, agricultural Revolution, Alfred Russel Wallace, Apple Newton, backpropagation, Buckminster Fuller, cognitive dissonance, Columbine, combinatorial explosion, complexity theory, computer age, computer vision, Computing Machinery and Intelligence, Daniel Kahneman / Amos Tversky, delayed gratification, disinformation, double helix, Dr. Strangelove, experimental subject, feminist movement, four colour theorem, Geoffrey Hinton, Gordon Gekko, Great Leap Forward, greed is good, Gregor Mendel, hedonic treadmill, Henri Poincaré, Herman Kahn, income per capita, information retrieval, invention of agriculture, invention of the wheel, Johannes Kepler, John von Neumann, lake wobegon effect, language acquisition, lateral thinking, Linda problem, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, Mikhail Gorbachev, Murray Gell-Mann, mutually assured destruction, Necker cube, out of africa, Parents Music Resource Center, pattern recognition, phenotype, Plato's cave, plutocrats, random walk, Richard Feynman, Ronald Reagan, Rubik’s Cube, Saturday Night Live, scientific worldview, Search for Extraterrestrial Intelligence, sexual politics, social intelligence, Steven Pinker, Stuart Kauffman, tacit knowledge, theory of mind, Thorstein Veblen, Tipper Gore, Turing machine, urban decay, Yogi Berra

In fact, one doesn’t even need a huge warehouse of these machines, one to do sums, another to do square roots, a third to print English sentences, and so on. One kind of Turing machine is called a universal Turing machine. It can take in a description of any other Turing machine printed on its tape and thereafter mimic that machine exactly. A single machine can be programmed to do anything that any set of rules can do. Does this mean that the human brain is a Turing machine? Certainly not. There are no Turing machines in use anywhere, let alone in our heads. They are useless in practice: too clumsy, too hard to program, too big, and too slow.

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It can apply the rules of any useful logical system to derive true statements from other true statements. It can apply the rules of any grammar to derive well-formed sentences. The equivalence among Turing machines, calculable mathematical functions, logics, and grammars, led the logician Alonzo Church to conjecture that any well-defined recipe or set of steps that is guaranteed to produce the solution to some problem in a finite amount of time (that is, any algorithm) can be implemented on a Turing machine. What does this mean? It means that to the extent that the world obeys mathematical equations that can be solved step by step, a machine can be built that simulates the world and makes predictions about it.

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The machine consists of a tape divided into squares, a read-write head that can print or read a symbol on a square and move the tape in either direction, a pointer that can point to a fixed number of tickmarks on the machine, and a set of mechanical reflexes. Each reflex is triggered by the symbol being read and the current position of the pointer, and it prints a symbol on the tape, moves the tape, and/or shifts the pointer. The machine is allowed as much tape as it needs. This design is called a Turing machine. What can this simple machine do? It can take in symbols standing for a number or a set of numbers, and print out symbols standing for new numbers that are the corresponding value for any mathematical function that can be solved by a step-by-step sequence of operations (addition, multiplication, exponentiation, factoring, and so on—I am being imprecise to convey the importance of Turing’s discovery without the technicalities).

Speaking Code: Coding as Aesthetic and Political Expression by Geoff Cox, Alex McLean

4chan, Amazon Mechanical Turk, augmented reality, bash_history, bitcoin, Charles Babbage, cloud computing, commons-based peer production, computer age, computer vision, Computing Machinery and Intelligence, crowdsourcing, dematerialisation, Donald Knuth, Douglas Hofstadter, en.wikipedia.org, Everything should be made as simple as possible, finite state, Free Software Foundation, Gabriella Coleman, Gödel, Escher, Bach, Hacker Conference 1984, Ian Bogost, Jacques de Vaucanson, language acquisition, Larry Wall, late capitalism, means of production, natural language processing, Neal Stephenson, new economy, Norbert Wiener, Occupy movement, packet switching, peer-to-peer, power law, Richard Stallman, Ronald Coase, Slavoj Žižek, social software, social web, software studies, speech recognition, SQL injection, stem cell, Stewart Brand, systems thinking, The Nature of the Firm, Turing machine, Turing test, Vilfredo Pareto, We are Anonymous. We are Legion, We are the 99%, WikiLeaks, Yochai Benkler

As far as the Chinese is concerned, I simply behave like a computer; I perform computational operations on formally specified elements. For the purposes of the Chinese, I am simply an instantiation of the computer program.”51 Searle’s position is based on the linguistic distinction between syntax and semantics as applied to the digital computer or Turing machine as a “symbol-manipulating device,” where the units have no meaning in themselves (a position that follows from semiotics). Even if it is argued that there is some sense of intentionality in the program or a degree of meaning in the unit, it is not the same as human information processing, and this sense of agency is what Searle calls “as-if intentionality.”

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The “grain of the voice” is what Barthes calls the individual “voice-magic,” imparted by the “very precise space of the encounter between a language and a voice.” Roland Barthes, “The Grain of the Voice,” in Image, Music, Text, 181. The music industry tries to commodify this “grain.” 54. It is interesting to note that a function to calculate pi can be written; the issue is that it would never return the value. If running indefinitely, a Turing machine would be able to output it all, as it has infinite memory. 55. Groys, The Communist Postscript, xvii. 56. Nick Couldry, Why Voice Matters: Culture and Politics after Neoliberalism (London: Sage, 2010), 3. 57. Echoed in the phrase “words made flesh,” the title of Florian Cramer’s Words Made Flesh: Code, Culture, Imagination (Rotterdam: Piet Zwart Institute, 2005), 125 (available at http:// pzwart.wdka.hro.nl/mdr/research/fcramer/wordsmadeflesh/). 58.

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., 168–169, citing Wittgenstein’s Philosophical Investigations (1953). 54. Proudfoot, “Wittgenstein’s Anticipation of the Chinese Room,” 177–178. 55. John R. Searle, “Twenty-One Years in the Chinese Room,” in Preston and Bishop, Views into the Chinese Room, 56. 56. Ibid. With this statement, Searle is arguing that Turing machines rely on abstract mathematical processes but not on energy transfer like some other machines; and one might extrapolate that the discourse around artificial life reinvigorates the fantasies of artificial intelligence in this way. Merely increasing computer capacity does not mean machine consciousness is any closer but perhaps only that the fantasies become stronger, as artificial intelligence morphs into the discourse around artificial life and the messier biocomputational “wet” realm of living cells. 57.

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

1960s counterculture, 3D printing, 4chan, Ada Lovelace, Adam Curtis, additive manufacturing, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, Amazon Mechanical Turk, Amazon Robotics, Amazon Web Services, Andy Rubin, Anthropocene, augmented reality, autonomous vehicles, basic income, Benevolent Dictator For Life (BDFL), Berlin Wall, bioinformatics, Biosphere 2, bitcoin, blockchain, Buckminster Fuller, Burning Man, call centre, capitalist realism, carbon credits, carbon footprint, carbon tax, carbon-based life, Cass Sunstein, Celebration, Florida, Charles Babbage, charter city, clean water, cloud computing, company town, congestion pricing, connected car, Conway's law, corporate governance, crowdsourcing, cryptocurrency, dark matter, David Graeber, deglobalization, dematerialisation, digital capitalism, digital divide, disintermediation, distributed generation, don't be evil, Douglas Engelbart, Douglas Engelbart, driverless car, Edward Snowden, Elon Musk, en.wikipedia.org, Eratosthenes, Ethereum, ethereum blockchain, Evgeny Morozov, facts on the ground, Flash crash, Frank Gehry, Frederick Winslow Taylor, fulfillment center, functional programming, future of work, Georg Cantor, gig economy, global supply chain, Google Earth, Google Glasses, Guggenheim Bilbao, High speed trading, high-speed rail, Hyperloop, Ian Bogost, illegal immigration, industrial robot, information retrieval, Intergovernmental Panel on Climate Change (IPCC), intermodal, Internet of things, invisible hand, Jacob Appelbaum, James Bridle, Jaron Lanier, Joan Didion, John Markoff, John Perry Barlow, Joi Ito, Jony Ive, Julian Assange, Khan Academy, Kim Stanley Robinson, Kiva Systems, Laura Poitras, liberal capitalism, lifelogging, linked data, lolcat, Mark Zuckerberg, market fundamentalism, Marshall McLuhan, Masdar, McMansion, means of production, megacity, megaproject, megastructure, Menlo Park, Minecraft, MITM: man-in-the-middle, Monroe Doctrine, Neal Stephenson, Network effects, new economy, Nick Bostrom, ocean acidification, off-the-grid, offshore financial centre, oil shale / tar sands, Oklahoma City bombing, OSI model, 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, pneumatic tube, post-Fordism, precautionary principle, RAND corporation, recommendation engine, reserve currency, rewilding, RFID, Robert Bork, Sand Hill Road, scientific management, self-driving car, semantic web, sharing economy, Silicon Valley, Silicon Valley ideology, skeuomorphism, Slavoj Žižek, smart cities, smart grid, smart meter, Snow Crash, 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, synthetic biology, TaskRabbit, technological determinism, TED Talk, the built environment, The Chicago School, the long tail, the scientific method, Torches of Freedom, transaction costs, Turing complete, Turing machine, Turing test, undersea cable, universal basic income, urban planning, Vernor Vinge, vertical integration, warehouse automation, warehouse robotics, Washington Consensus, web application, Westphalian system, WikiLeaks, working poor, Y Combinator, yottabyte

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. The Church-Turing thesis (developed through the 1940s and 1950s) would demonstrate that Turing's “machine” not only could simulate algorithms, but that a universal Turing machine, containing all possible such machines, could, in theory, calculate all logical problems that are in fact computable (a limit that Turing's paper sought to identify). The philosophical implications are thorny and paradoxical. At the same moment that Turing demonstrates the mechanical basis for synthetic logic by machines (suggesting real artificial intelligence), he partially delinks the correlation between philosophical thought and machinic calculation.

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For me these are conjoined, and not just by their geographic proximity: Deleuze on the beach contemplating (we might assume) what he called “the plane of immanence,” the field from which all potential forms emerge, and Intel's initial approximations of microprocessor technology for universal computation, putting a mini-Turing machine on a silicon wafer.5 In different ways and for different ends, both grapple with matter as vibrant, contingent, and mutable, as reproduced in the careful calculation of sets of differences drawn from particular virtual possibilities. At the end of the day, Deleuze's philosophy is more about chemistry than computation, continuities more than discrete digitalizations, but his philosophical imagery of worlds appearing from the multiplication of imminent processes and generic diagrams, on oscillations of the physical and the virtual, is not unfamiliar to the projects of information realism.

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So irrespective of the mathematical limits of algorithmic reason, The Stack is interested instead in the limited and sufficient compositional capacities of a megastructure already under construction, the thresholds of which are geological, sociological, economic, chemical, and geopolitical as much as they are calculative. This chapter draws on those limits and on the risks that come with positioning the Earth as a layer in a synthetic machine, and for this Earth is the Earth—a physical planet—not a metaphor for “nature.” There is no planetary-scale computation, now a vast network of many billions of little Turing machines, that does not intake and absorb the Earth's chemistry in order to function. The Stack is a hungry machine, and while its curated population of algorithms may be all but massless, their processing of Earthly material is a physical event, and therefore the range of possible translations between information and mechanical appetites has another limit that is not mathematical but defined by the real finitude of substances that can force communication between both sides of this encounter.20 Furthermore, like any megamachine the Earth layer is as socially constrained as it is technologically configured, and so there are political economies of Turing machines that are only accessible through misaligned and uneven hierarchies of geography, energy, and programmability.21 This is made clear by unpacking and sifting through the hardware on which The Stack depends.

The Secret War Between Downloading and Uploading: Tales of the Computer as Culture Machine by Peter Lunenfeld

Albert Einstein, Andrew Keen, anti-globalists, Apple II, Berlin Wall, British Empire, Brownian motion, Buckminster Fuller, Burning Man, business cycle, business logic, butterfly effect, Charles Babbage, computer age, Computing Machinery and Intelligence, creative destruction, crowdsourcing, cuban missile crisis, Dissolution of the Soviet Union, don't be evil, Douglas Engelbart, Douglas Engelbart, Dynabook, East Village, Edward Lorenz: Chaos theory, Fairchild Semiconductor, Fall of the Berlin Wall, folksonomy, Francis Fukuyama: the end of history, Frank Gehry, Free Software Foundation, Grace Hopper, gravity well, Guggenheim Bilbao, Herman Kahn, Honoré de Balzac, Howard Rheingold, Ian Bogost, invention of movable type, Isaac Newton, Ivan Sutherland, Jacquard loom, Jane Jacobs, Jeff Bezos, John Markoff, John von Neumann, Jon Ronson, Kickstarter, Mark Zuckerberg, Marshall McLuhan, Mercator projection, Metcalfe’s law, Mother of all demos, mutually assured destruction, Neal Stephenson, Nelson Mandela, Network effects, new economy, Norbert Wiener, PageRank, pattern recognition, peer-to-peer, planetary scale, plutocrats, post-materialism, Potemkin village, RFID, Richard Feynman, Richard Stallman, Robert Metcalfe, Robert X Cringely, Schrödinger's Cat, Search for Extraterrestrial Intelligence, seminal paper, SETI@home, Silicon Valley, Skype, social bookmarking, social software, spaced repetition, Steve Ballmer, Steve Jobs, Steve Wozniak, technological determinism, Ted Nelson, the built environment, the Cathedral and the Bazaar, The Death and Life of Great American Cities, the medium is the message, Thomas L Friedman, Turing machine, Turing test, urban planning, urban renewal, Vannevar Bush, walkable city, Watson beat the top human players on Jeopardy!, William Shockley: the traitorous eight

In it, he proposed the questions that still remain central to the discipline decades later. Turing suggested that it should be possible to make a “Universal Machine,” a computer that could simulate the performance of any other device. The fact that the analog machines of the late 1930s and early 1940s were far too slow to function as Universal Turing Machines did not affect his faith that such devices would come into existence. And with the stimulus of the war effort, they did. Within a decade, Turing was working on the Manchester Mark I computer—one of the first machines recognized as being a direct antecedent to the computers we use now. Turing proposed a universal machine that functioned as a stored program computer; in this setup, the programs, or software, could be swapped and modified, improved and abandoned, just as the hardware could and would be.

…

He assisted Christopher Strachey in producing what was probably the first artwork made with a computer: the love letter generator of 1952. 5 Strachey, working from a thousand-line piece of software (the longest yet written for the Mark I), created a program that randomly produced such sentimental and vaguely meaningless missives as: 18 STICK Y Darling Sweetheart, You are my avid fellow feeling. My affection curiously clings to your passionate wish. My liking yearns for your heart. You are my wistful sympathy: my tender liking. Yours beautifully M. U. C. Here, the Universal Turing Machine simulates mawkish Victorian sentimentality by choosing from a database of prewritten phrases that it then arranges into syntactically correct but stilted English. This trifle, inspired at least in part by the renown of Christopher’s uncle Lytton Strachey’s 1918 portrait of a generation, Eminent Victorians, is the product of a stored program computer, and as such may well be the first aesthetic object produced by the ancestors of the culture machine.

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Congress and, 90 violations of, 92–93, 95 Web n.0 and, 88–95 Corian, 64 Creative Commons, 173, 189n12 bespoke futures and, 123 Mickey Mouse Protection Act and, 90 Computers (continued) Aquarians and, xv, 24, 144, 152, 157, 159–169 challenge to television of, 2 as culture machine, xiv, xvi, xv–xvi, 5 (see also Culture machine) distribution and, xiii dominance of, xii–xiii, xiv as dream machines, xiii emergence of, xii–xiii first, 146 hackers and, 22–23, 54, 67, 69, 162, 170–173 historical perspective on, 143–178 Hosts and, xv, 144, 167, 175 Hustlers and, xv, 144, 156, 162–167 intelligence test for, 19 as “Man of the Year,” xii Moore’s law and, 156, 195n13 mouse for, 158–159 participation and, xvi, 15–17, 27–35, 54, 66–67, 74–80, 98–99, 120– 121, 129, 143–147, 151, 156–165, 170, 175–178 Patriarchs and, xv, 143–144, 147–153, 156–157, 162–163, 166–168 personal, 152, 161–167 Plutocrats and, xv, 144, 152–159, 163–166, 170 production and, xiii relationship with data and, 32 Searchers and, xv–xvi, 144, 167, 174–178 simulation and, xvi, 2 (see also Simulation) Sterling on, 101–102 symbiosis and, 151–152 systems theory and, 151 ubiquity and, xiii, 22–23, 39, 57–59, 62, 74, 81–82, 87, 92–93, 125, 128, 144, 166, 177–178 Universal Turing Machine and, 18–19 201 INDEX Creative Commons (continued) open source and, 90–93, 123, 173 purpose of, 91 Web n.0 and, 90–93 Creatives, 30 Credit cards, 76 Crenshaw district, 105 Critical inquiry, 14 Cuban Missile Crisis, xi Cubism, 44, 79, 117 Cultural issues commercialism and, 4–5, 8 (see also Commercial culture) diabetic technologies and, 3–5 dominance of television and, xii, 2–5, 7–10 fan culture and, 28–32, 48, 49, 87 free culture and, 75, 92, 98–99 Freud and, 43–44 hierarchies and, 1, 24, 29, 93, 114 junk culture and, 5–10 mass/pop culture and, 13, 31, 39–40, 47–48, 53, 56–58, 61–63, 107, 109, 184n16 mechanization and, 44–45 open source and, 36, 61, 69, 74–75, 91–92, 116, 121–126, 144, 170– 173, 177, 189n12 psychology and, 16, 21–22, 42–44, 56, 151, 161 secular culture and, 133–139 Slow Food and, 5–7 stickiness and, 28–32 (see also Stickiness) Culture machine, 5 Aquarians and, xv, 24, 144, 152, 157, 159–169 bespoke futures and, 97–101, 116, 123–133, 137–138 design and, 139, 150, 160, 165, 167, 171–172, 176 development of, 143–178 downloading and, 143, 168 gaming and, 70–74 Hosts and, xv, 144, 167, 175 Hustlers and, xv, 144, 156, 162–167 information and, 46, 143–149, 152– 153, 163, 167–168, 172, 176–178 networks and, 143–144, 152, 167– 168, 172–175, 178 participation and, 15–17, 143–147, 151, 156–165, 170, 175–178 Patriarchs and, xv, 143–144, 147–153, 156–157, 162–163, 166–168 Plutocrats and, xv, 144, 152–159, 163–166, 170 postmodernism and, 39–40 Searchers and, xv–xvi, 144, 167, 174–178 simulation and, 15–17, 143–144, 147– 152, 156–160, 166–168, 175–178 stickiness and, 15–19, 27, 32, 35 technology and, 143–163, 173–174 unimodernism and, 39, 42, 46–60, 67–76 uploading and, 143, 168, 173, 175 Warriors and, 146–147 Web n.0 and, 79–85, 90–93 Cut-up fiction, 52 Cyberpunk, 68, 87, 110 Czechoslovakia, 104 Dada, 79, 186n8 Danger Mouse, 54–55 Dare, Dan, 108 Darth Vader, 90 Darwin, Charles, 133 Davis, Miles, 25–26 Dawkins, Richard, 143 Death and Life of Great American Cities, The (Jacobs), 84–85 Deconstruction, 29–31 DeLanda, Manuel, 189n8 De.lic.ious, 75 202 INDEX Design bespoke futures and, 102, 105–106, 110–111, 115–116, 119–120, 124–125, 137 control over form and, 111 culture machine and, 139, 150, 160, 165, 167, 171–172, 176 future as client and, 110–113 futurists on, 101–102 graphic, 31, 45, 64, 102, 181n7 Gropius and, 36–37 isotypes and, 44, 125, 193n34 mechanization and, 44–45 Moore’s law and, 156 open source, 36, 61, 69, 74–75, 91–92, 116, 121–126, 144, 170– 173, 177, 189n12 play and, 32–34 postmodernism and, 29–30, 39–41, 74, 79, 130, 135 power and, 32–34 tweaking and, 32–35 unimodernism and, 39, 43–46, 49, 55–56, 60, 64–8, 71–74 Design of Everyday Things, The (Norman), 16 Design Within Reach, 46 Desk jobs, 3 Dewey, John, 129 Dewey, Melvil, 80 Diabetes, 3–5, 8 “Diamond Dogs” (Bowie), 62 Dick, Philip K., 9 Difference engine, 149 Digg, 34 Digital Equipment Corporation (DEC), 71, 149, 153, 163, 170 Digital video discs (DVDs), 2, 7–8, 15, 58 Digital video recorders (DVRs), 2, 7, 15, 23, 181n3 Disco, 63 Disney Concert Hall, 39 DIY (do-it-yourself) movements, 67–70 203 Dot-com bubble, 79, 145, 174 Doubleclick, 177 Downloading, xiii–xiv, 180nn1,2 animal kingdom and, 1 bespoke futures and, 97, 123, 132, 138 best use and, 13–14 commercial networks and, 4–5 communication devices and, 15–16 cultural hierarchy of, 1–2 culture machine and, 143, 168 dangers of overabundance and, 7–10 defined, 1 diabetic responses to, 3–5 disrupting flow and, 23–24 figure/ground and, xvi, 42–43, 46, 102 Freedom software and, 22–23 habits of mind and, 9–10 humans and, 1–2 information overload and, 22, 149 info-triage and, xvi, 20–23, 121, 132, 143 as intake, 5 mindfulness and, xvi, 14, 17, 20–24, 27–29, 42, 77, 79, 123, 129, 183n6 patio potato and, 9–10, 13 peer-to-peer networks and, 15, 54, 92, 116, 126 stickiness and, 13–17, 20–23, 27–29, 184n15 surfing and, 20, 80, 180n2 television and, 2 unimodernism and, 41–42, 49, 54–57, 66–67, 76–77 viral distribution and, 30, 56, 169 wants vs. needs and, 13, 37, 57 Web n.0 and, 79, 82–83, 86–87 Duchamp, Marcel, 44, 48, 94 Dymaxion map, 73 Dynabook, 161–162, 196n17 Dynamic equilibrium, 117–120 EBay, 68 Eckert, J.

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, Bletchley Park, borderless world, Buckminster Fuller, Build a better mousetrap, Byte Shop, card file, cashless society, Charles Babbage, cloud computing, combinatorial explosion, Compatible Time-Sharing System, computer age, Computer Lib, deskilling, don't be evil, Donald Davies, Douglas Engelbart, Douglas Engelbart, Dynabook, Edward Jenner, Evgeny Morozov, Fairchild Semiconductor, fault tolerance, Fellow of the Royal Society, financial independence, Frederick Winslow Taylor, game design, garden city movement, Gary Kildall, Grace Hopper, Herman Kahn, hockey-stick growth, Ian Bogost, industrial research laboratory, informal economy, interchangeable parts, invention of the wheel, Ivan Sutherland, Jacquard loom, Jeff Bezos, jimmy wales, John Markoff, John Perry Barlow, John von Neumann, Ken Thompson, Kickstarter, light touch regulation, linked data, machine readable, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Menlo Park, Mitch Kapor, Multics, natural language processing, Network effects, New Journalism, Norbert Wiener, Occupy movement, optical character recognition, packet switching, PageRank, PalmPilot, pattern recognition, Pierre-Simon Laplace, pirate software, popular electronics, prediction markets, pre–internet, QWERTY keyboard, RAND corporation, Robert X Cringely, Salesforce, scientific management, Silicon Valley, Silicon Valley startup, Steve Jobs, Steven Levy, Stewart Brand, Ted Nelson, the market place, Turing machine, Twitter Arab Spring, Vannevar Bush, vertical integration, Von Neumann architecture, Whole Earth Catalog, William Shockley: the traitorous eight, women in the workforce, young professional

This question, known as the Entscheidungsproblem, asked: “Did there exist a definite method or process by which all mathematical questions could be decided?” Turing and Church came up with equivalent results in the mid-1930s. Turing’s approach, however, was one of startling originality. Whereas Church relied on conventional mathematics to make his arguments, Turing used a conceptual computer, later known as the Turing Machine. The Turing Machine was a thought experiment rather than a realistic computer: the “machine” consisted of a scanning head that could read and write symbols on a tape of potentially infinite length, controlled by an “instruction table” (which we would now call a program). It was computing reduced to its simplest form.

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Turing made a much stronger claim: that a universal computer could tackle problems not just in mathematics but in any tractable area of human knowledge. In short, the Turing Machine embodied all the logical capabilities of a modern computer. 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.

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., 108–109 GUI (graphical user interface), 253, 257–261, 264–267, 273, 297 Handwriting recognition technology, 297, 298 Harvard Business Review, 134 Harvard Mark I, 54–59, 73, 80, 83, 91 (photo), 104 Harvard Mark II, 83–84 Harvard University, 83–84, 104 Hewlett, William, 239, 249 Hewlett-Packard (HP), 219, 239, 249 High-speed broadband, 274 Hilbert, David, 59 Hitachi, 251 Hobbyists, 230, 231, 232–238, 239–241, 242 Hock, Dee, 158–161 Hoerni, Jean, 221 Hoff, Ted, 231–232 Hollerith, Herman, 13–18, 27, 33–36 Hollerith Electric Tabulating System, 15–18, 27, 33–34, 38 Home computing, 211–212 Homebrew Computer Club, 237, 240 Home-built computers, 219 Honeywell competitive strategies of, 132 computer recession and, 133 FACT programming language, 175 IBM-compatible computers, 128–129, 131 mainframe computers, 98, 116, 117, 124 minicomputers, 219 Hopper, Grace Murray, 59, 110, 171, 173, 174–175, 192 (photo) Human computers, 3–6, 50–51, 52–54, 65, 67–68, 71 Human Factors Research Center, 199, 258–259, 282 Human knowledge, 275–278 Human-computer interaction, 207–210, 243, 258–259 Human-factors design, 208 Hypertext, 200, 234–235, 279, 286–287 IBM 1401 mainframe computer, 95 (photo), 117, 120–123, 126, 128–129 accounting machines, 38, 121, 125, 130 Airline Control Program operating system, 160 airline reservation systems, 154–157 antitrust suit against, 187 Automatic Computing Plant, 57 BASE II computer system, 160 Bitnet, 292 business computers, 123–124, 130–133, 138–139 business practices, 21, 30, 39–40, 97 Commercial Translator, 175 compatible product lines and, 125 computer development and, 80 computer industry and, 21, 98, 117, 133 computer industry rank, 219 computer industry standardization, 135 core memory technology, 115, 150, 151 data processing computers, 112–116, 133–134 Defense Calculator (model 701), 107, 113, 114, 115 as defense contractor, 107, 151, 152 Eckert and Mauchly’s attempts to sell EMCC to, 108 electromechanical manufacturing and, 138 electronic technology, 103–107 Endicott Laboratory, 57 ENIAC and, 71–81, 92 (photo), 93, 99, 145 FORTRAN developed by, 171–175, 185, 191, 205–206, 214, 215 Harvard Mark I and, 54–59, 73, 80, 83, 91 (photo), 104 Hollerith and, 14 IBM PC as industry standard, 197 (photo), 245–249 as leader in computer technology, 106 Magnetic Drum Calculator (model 650), 106, 112, 115, 120–121 mainframe computers, 126, 130–131 MS-DOS development agreement and, 256 naming of company, 36 New Product Line, 126–128, 129 OS/2 operating system, 265 PC Jr. computer, 263 personal computers, 197 (photo), 229, 245–249 PL/1 programming language, 183 Program Development Laboratories, 180–182 public image of, 119–120 punched-card systems of, 21, 38–39, 53, 90 (photo) rent-and-refill nature of business, 36, 37–38 sales strategies of, 21, 36–37, 39–40, 138, 246 sales training, 39–40 scanning technology, 164 Selective Sequence Electronic Calculator, 104, 105–106 survival of Great Depression by, 36, 37 systems integration and, 138–139 System/360 computers, 96 (photo), 124–132, 138, 209, 210 Systems Network Architecture, 285 Tape Processing Machine (model 702), 106–107, 112–115 technical innovation, 21, 31, 36, 38–39 T-H-I-N-K motto, 33, 37, 106 time-sharing computers, 209–210 total-system design approach, 120–123 TopView operating system, 265 TSS/360 operating system, 212–213 unbundling, 187–188 war-related computing projects of, 74, 79 IBM-compatible personal computers developed by competitors, 128–129, 131, 138 market dominance of, 255, 261, 263 software development for, 254, 256–257, 264–267 IBM Selective Sequence Electronic Calculator (SSEC), 104–106, 117 Icons, desktop, 258, 260 iOS platform, 297 iPad tablets, 298 iPhone, 298 iPod devices, 298 iTunes stores, 298 Illustrated London News, 12, 88 (photo) Informatics, 177, 188 Information processing calculating engines for, 6–8 clearing houses for, 8–11 human computers for, 3–6 mechanical systems for, 13–19 telegraphy and, 11–13 Information Processing Techniques Office (IPTO), 208, 258–259, 280–283 Information storage, office, 21, 27 Information technology, 19, 25 Initial Orders program, 169 Institute for Advanced Study (IAS), Princeton, 73, 80, 93 (photo), 107, 147, 191 Instruction tables (Turing Machine), 60 Insurance industry, 4, 18, 101, 102, 109, 175, 187 Integrated circuits, 130, 131, 194 (photo), 215–219, 221, 222–225 Intel 8088 chip, 246, 247, 248 Fairchild origins of, 221, 222 integrated circuit technology and, 216 microprocessors and, 195 (fig.), 231–232, 251, 265 Interactive computing, 207–210, 243, 258–259 interface message processor (IMP), 282 International Business Machines.

Fancy Bear Goes Phishing: The Dark History of the Information Age, in Five Extraordinary Hacks by Scott J. Shapiro

3D printing, 4chan, active measures, address space layout randomization, air gap, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, availability heuristic, Bernie Sanders, bitcoin, blockchain, borderless world, Brian Krebs, business logic, call centre, carbon tax, Cass Sunstein, cellular automata, cloud computing, cognitive dissonance, commoditize, Compatible Time-Sharing System, Computing Machinery and Intelligence, coronavirus, COVID-19, CRISPR, cryptocurrency, cyber-physical system, Daniel Kahneman / Amos Tversky, Debian, Dennis Ritchie, disinformation, Donald Trump, double helix, Dr. Strangelove, dumpster diving, Edward Snowden, en.wikipedia.org, Evgeny Morozov, evil maid attack, facts on the ground, false flag, feminist movement, Gabriella Coleman, gig economy, Hacker News, independent contractor, information security, Internet Archive, Internet of things, invisible hand, John Markoff, John von Neumann, Julian Assange, Ken Thompson, Larry Ellison, Laura Poitras, Linda problem, loss aversion, macro virus, Marc Andreessen, Mark Zuckerberg, Menlo Park, meta-analysis, Minecraft, Morris worm, Multics, PalmPilot, Paul Graham, pirate software, pre–internet, QWERTY keyboard, Ralph Nader, RAND corporation, ransomware, Reflections on Trusting Trust, Richard Stallman, Richard Thaler, Ronald Reagan, Satoshi Nakamoto, security theater, Shoshana Zuboff, side hustle, Silicon Valley, Skype, SoftBank, SQL injection, Steve Ballmer, Steve Jobs, Steven Levy, Stuxnet, supply-chain attack, surveillance capitalism, systems thinking, TaskRabbit, tech billionaire, tech worker, technological solutionism, the Cathedral and the Bazaar, the new new thing, the payments system, Turing machine, Turing test, Unsafe at Any Speed, vertical integration, Von Neumann architecture, Wargames Reagan, WarGames: Global Thermonuclear War, Wayback Machine, web application, WikiLeaks, winner-take-all economy, young professional, zero day, éminence grise

The intelligence in computation lies not in any particular step, Turing explained, but in their sequence—just as music isn’t in the individual notes, but in their relationship to one another. Every operation the Turing Machine performs is primitive, trivial, monotonous, unintelligent, arational, stupid. Yet, by ordering many of these basic operations in just the right way, the mindless Turing Machine yields an intelligent solution. Turing’s discovery of the physicality principle was profound: he conjectured that the basic physical instructions—reading, writing, and movement—underlie all computing. Provided a machine can manipulate symbols using these three simple instructions, it can use them (if sequenced correctly) to solve any solvable problem.

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As Turing showed, computing devices need perform only three basic actions of symbol manipulation: read symbols from a paper tape, write symbols to the tape, and move along the tape. The device picks one of these actions by following an internal instruction table. As long as the instruction table sequences these primitive actions in the right order, the device (traditionally known as a Turing Machine) will physically compute the correct answer. Because our world is filled with billions of physical computing devices, we take physicality for granted. We should pause for a moment, however, to appreciate the boldness of Turing’s claim. Somehow, a series of mindless manipulations performed by a mechanical contraption obeying the witless laws of physics adds up to something intelligent.

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Provided a machine can manipulate symbols using these three simple instructions, it can use them (if sequenced correctly) to solve any solvable problem. One machine can add numbers: if you write the numbers 2 and 2 on the tape, the machine will output 4. Another machine can calculate the billionth digit in the decimal expansion of pi. One can even build a Turing Machine that can model how carbon taxes will affect global warming. Running that simulation would require trillions of symbol manipulations and would take many centuries to complete. But in principle, it can be done. In practice, however, no usable computing device can run without extensive shortcuts.

Surviving AI: The Promise and Peril of Artificial Intelligence by Calum Chace

3D printing, Ada Lovelace, AI winter, Airbnb, Alvin Toffler, artificial general intelligence, augmented reality, barriers to entry, basic income, bitcoin, Bletchley Park, blockchain, brain emulation, Buckminster Fuller, Charles Babbage, cloud computing, computer age, computer vision, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, deep learning, DeepMind, dematerialisation, Demis Hassabis, discovery of the americas, disintermediation, don't be evil, driverless car, Elon Musk, en.wikipedia.org, epigenetics, Erik Brynjolfsson, everywhere but in the productivity statistics, Flash crash, friendly AI, Geoffrey Hinton, Google Glasses, hedonic treadmill, hype cycle, industrial robot, Internet of things, invention of agriculture, job automation, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, life extension, low skilled workers, machine translation, Mahatma Gandhi, means of production, mutually assured destruction, Neil Armstrong, Nicholas Carr, Nick Bostrom, paperclip maximiser, pattern recognition, peer-to-peer, peer-to-peer model, Peter Thiel, radical life extension, Ray Kurzweil, Robert Solow, Rodney Brooks, Second Machine Age, self-driving car, Silicon Valley, Silicon Valley ideology, Skype, South Sea Bubble, speech recognition, Stanislav Petrov, Stephen Hawking, Steve Jobs, strong AI, technological singularity, TED Talk, The future is already here, The Future of Employment, theory of mind, Turing machine, Turing test, universal basic income, Vernor Vinge, wage slave, Wall-E, zero-sum game

He died two years later and it took 57 years before a British government apologised for this barbaric behaviour. Before the war, in 1936, Turing had already devised a theoretical device called a Turing machine. It consists of an infinitely long tape divided into squares, each bearing a single symbol. Operating according to the directions of an instruction table, a reader moves the tape back and forth, reading one square – and one symbol – at a time. Together with his PhD tutor Alonzo Church he formulated the Church-Turing thesis, which says that a Turing machine can simulate the logic of any computer algorithm. (That word “algorithm” crops up a lot in computer science. It simply means a set of rules, or instructions, for a computer to follow.

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Turing is also famous for inventing a test for artificial consciousness called the Turing Test, in which a machine proves that it is conscious by rendering a panel of human judges unable to determine that it is not (which is essentially the test that we humans apply to each other). The birth of computing The first design for a Turing machine was made by Charles Babbage, a Victorian academic and inventor, long before Turing’s birth. Babbage never finished the construction of his devices, although working machines have recently been built based on his designs. His Difference Engine (designed in 1822) would carry out basic mathematical functions, and the Analytical Engine (design never completed) would carry out general purpose computation.

Mastering Ethereum: Building Smart Contracts and DApps by Andreas M. Antonopoulos, Gavin Wood Ph. D.

air gap, Amazon Web Services, bitcoin, blockchain, business logic, continuous integration, cryptocurrency, Debian, digital divide, Dogecoin, domain-specific language, don't repeat yourself, Edward Snowden, en.wikipedia.org, Ethereum, ethereum blockchain, fault tolerance, fiat currency, Firefox, functional programming, Google Chrome, information security, initial coin offering, intangible asset, Internet of things, litecoin, machine readable, move fast and break things, node package manager, non-fungible token, peer-to-peer, Ponzi scheme, prediction markets, pull request, QR code, Ruby on Rails, Satoshi Nakamoto, sealed-bid auction, sharing economy, side project, smart contracts, transaction costs, Turing complete, Turing machine, Vickrey auction, Vitalik Buterin, web application, WebSocket

Specifically, he proved that the halting problem (whether it is possible, given an arbitrary program and its input, to determine whether the program will eventually stop running) is not solvable. Alan Turing further defined a system to be Turing complete if it can be used to simulate any Turing machine. Such a system is called a Universal Turing machine (UTM). Ethereum’s ability to execute a stored program, in a state machine called the Ethereum Virtual Machine, while reading and writing data to memory makes it a Turing-complete system and therefore a UTM. Ethereum can compute any algorithm that can be computed by any Turing machine, given the limitations of finite memory. Ethereum’s groundbreaking innovation is to combine the general-purpose computing architecture of a stored-program computer with a decentralized blockchain, thereby creating a distributed single-state (singleton) world computer.

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, Turing Completeness and Gas implications of, Implications of Turing Completeness Turing, Alan, Ethereum and Turing Completeness tx object, Transaction context tx.origin authentication security threatpreventative techniques, Preventative Techniques vulnerability, The Vulnerability typecasting, Variable Typecasting typographical conventions, Conventions Used in This Book U unchecked CALL return value security threat, Unchecked CALL Return Values-Real-World Example: Etherpot and King of the Etherpreventative techniques, Preventative Techniques real-world example: Etherpot and King of the Ether, Real-World Example: Etherpot and King of the Ether vulnerability, The Vulnerability underflow, Arithmetic Over/Underflows-Real-World Examples: PoWHC and Batch Transfer Overflow (CVE-2018–10299), The Vulnerability unexpected etherpreventative techniques, Preventative Techniques security threat from, Unexpected Ether-Further Examples vulnerability, The Vulnerability-The Vulnerability uninitialized storage pointers security threat, Uninitialized Storage Pointers-Real-World Examples: OpenAddressLottery and CryptoRoulette Honey Potspreventative techniques, Preventative Techniques real-world examples: OpenAddressLottery and CryptoRoulette honey pots, Real-World Examples: OpenAddressLottery and CryptoRoulette Honey Pots vulnerability, The Vulnerability-The Vulnerability Universal Turing machine (UTM), Ethereum and Turing Completeness user interface, as DApp frontend, Frontend (Web User Interface) utilities, EthereumJS helpeth: A Command-Line Utilitydapp.tools, dapp.tools EthereumJS helpeth, EthereumJS helpeth: A Command-Line Utility SputnikVM, SputnikVM utility currency, ether as, Compared to Bitcoin utility tokensdefined, Using Tokens: Utility or Equity equity tokens disguised as, It’s a Duck! issues to consider when using, Utility Tokens: Who Needs Them?-Utility Tokens: Who Needs Them? UTM (Universal Turing machine), Ethereum and Turing Completeness V value field, Transaction Value and Data-Transmitting Value to EOAs and Contracts variable declarations, ordering of, Function and Variable Ordering version pragma, Selecting a Solidity Compiler and Language Version Vickrey auctions, Vickrey auctions view (function keyword), Functions visibility specifiers, Default Visibilities-Real-World Example: Parity Multisig Wallet (First Hack) vulnerabilities, Vulnerabilities and Vyper(see also security; specific attacks/vulnerabilities) Vyper, Introduction to Ethereum High-Level Languages, Smart Contracts and Vyper-Conclusionsclass inheritance, Class Inheritance compilation, Compilation contract vulnerabilities and, Vulnerabilities and Vyper decorators, Decorators defined, Quick Glossary function ordering, Function and Variable Ordering function overloading, Function Overloading modifiers, Modifiers overflow protection, Protecting Against Overflow Errors at the Compiler Level preconditions/postconditions, Preconditions and Postconditions reading/writing data, Reading and Writing Data Solidity compared to, Comparison to Solidity-Preconditions and Postconditions variable ordering, Function and Variable Ordering variable typecasting, Variable Typecasting W wallets, Wallets-Conclusionsbest practices for, Wallet Best Practices-Navigating the HD wallet tree structure browser wallets, Browser Wallets choosing, Choosing an Ethereum Wallet cold-storage wallets, Extended public and private keys creating HD wallets from root seed, Creating an HD Wallet from the Seed defined, Quick Glossary, Choosing an Ethereum Wallet, Wallets deterministic, Wallet Technology Overview, Deterministic (Seeded) Wallets duress wallet, Optional passphrase in BIP-39 Emerald Wallet, Choosing an Ethereum Wallet HD (see hierarchical deterministic wallets) Jaxx, Choosing an Ethereum Wallet, Mobile (Smartphone) Wallets, Jaxx MetaMask (see MetaMask) Mist, Quick Glossary, Mist mnemonic codes (BIP-39), Seeds and Mnemonic Codes (BIP-39), Mnemonic Code Words (BIP-39)-Working with mnemonic codes mobile, Mobile (Smartphone) Wallets MyCrypto, MyCrypto MyEtherWallet, Choosing an Ethereum Wallet, MyEtherWallet (MEW), MyCrypto nondeterministic, Wallet Technology Overview-Nondeterministic (Random) Wallets Parity Multisig Wallet hacks, Real-World Example: Parity Multisig Wallet (Second Hack)-Real-World Example: Parity Multisig Wallet (Second Hack), Real-World Example: Parity Multisig Wallet (First Hack) remote clients compared to, Should I Run a Full Node?

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Turing complete A concept named after English mathematician and computer scientist Alan Turing: a system of data-manipulation rules (such as a computer’s instruction set, a programming language, or a cellular automaton) is said to be “Turing complete” or “computationally universal” if it can be used to simulate any Turing machine. Vitalik Buterin A Russian–Canadian programmer and writer primarily known as the cofounder of Ethereum and of Bitcoin Magazine. Vyper A high-level programming language, similar to Serpent, with Python-like syntax. Intended to get closer to a pure functional language. Created by Vitalik Buterin.

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

"Friedman doctrine" OR "shareholder theory", 4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Bertrand Russell: In Praise of Idleness, Blue Ocean Strategy, carbon footprint, cellular automata, Charles Babbage, Claude Shannon: information theory, cognitive dissonance, commoditize, complexity theory, Computing Machinery and Intelligence, 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, Kaizen: continuous improvement, Ken Thompson, l'esprit de l'escalier, language acquisition, Loebner Prize, machine translation, Menlo Park, operational security, Ray Kurzweil, RFID, Richard Feynman, Ronald Reagan, SimCity, 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

Indeed, theoretical models of the computer—the Turing machine, the von Neumann architecture—seem like reproductions of an idealized version of conscious, deliberate reasoning. As Ackley puts it, “The von Neumann machine is an image of one’s conscious mind where you tend to think: you’re doing long division, and you run this algorithm step-by-step. And that’s not how brains operate. And only in various circumstances is that how minds operate.” I spoke next with University of Massachusetts theoretical computer scientist Hava Siegelmann, who agreed. “Turing was very [mathematically] smart, and he suggested the Turing machine as a way to describe a mathematician.16 It’s [modeling] the way a person solves a problem, not the way he recognizes his mother.”

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I grew up three miles from the Atlantic Ocean; during the summer, tanning salons a block and a half from the beach would still be doing a brisk business. To see ourselves as distinct and apart from our fellow creatures is to see ourselves as distinct and apart from our bodies. The results of adopting this philosophy have been rather demonstrably weird. Turing Machines and the Corporeal IOU Wanting to get a handle on how these questions of soul and body intersect computer science, I called up the University of New Mexico’s and the Santa Fe Institute’s Dave Ackley, a professor in the field of artificial life. “To me,” he says, “and this is one of the rants that I’ve been on, that ever since von Neumann and Turing and the ENIAC guys15 built machines, the model that they’ve used is the model of the conscious mind—one thing at a time, nothing changing except by conscious thought—no interrupts, no communication from the outside world.

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This fits in nicely with our sense of an inner homunculus pulling the levers and operating our body from a control room behind our eyeballs. It fits in nicely with Aristotle’s notion that thinking is the most human thing we can do. And so we compensate accordingly. I almost wonder if micromanagement comes from the same over-biasing of deliberate conscious awareness that led, both to and out of, the Turing machine model of computation underlying all of our computers today. Aware of everything, acting logically, from the top down, step-by-step. But bodies and brains are, of course, not like that at all. Micromanagement and out-of-control executive compensation are odd in a way that dovetails precisely with what’s odd about our rationalist, disembodied, brain-in-a-vat ideas about ourselves.

A Thousand Brains: A New Theory of Intelligence by Jeff Hawkins

AI winter, Albert Einstein, artificial general intelligence, carbon-based life, clean water, cloud computing, deep learning, different worldview, discovery of DNA, Doomsday Clock, double helix, en.wikipedia.org, estate planning, Geoffrey Hinton, Jeff Hawkins, PalmPilot, Search for Extraterrestrial Intelligence, self-driving car, sensor fusion, Silicon Valley, superintelligent machines, the scientific method, Thomas Kuhn: the structure of scientific revolutions, Turing machine, Turing test

There were computers designed for specific tasks. There were analog computers, and computers that could only be repurposed by changing the wiring. There were computers that worked with decimal instead of binary numbers. Today, almost all computers are the universal form that Turing envisioned. We even refer to them as “universal Turing machines.” With the right software, today’s computers can be applied to almost any task. Market forces decided that universal, general-purpose computers were the way to go. This is despite the fact that, even today, any particular task can be performed faster or with less power using a custom solution, such as a special chip.

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Today’s computers come in many shapes and sizes, from the microcomputer in a toaster to room-size computers used for weather simulation. Despite their differences in size and speed, all these computers work on the same principles laid out by Turing and others many years ago. They are all instances of universal Turing machines. Similarly, intelligent machines of the future will come in many shapes and sizes, but almost all of them will work on a common set of principles. Most AI will be universal learning machines, similar to the brain. (Mathematicians have proven that there are some problems that cannot be solved, even in principle.

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No one can know how intelligent machines will be used fifty or sixty years from now. When Is Something Intelligent? When should we consider a machine intelligent? Is there a set of criteria we can use? This is analogous to asking, When is a machine a general-purpose computer? To qualify as a general-purpose computer—that is, a universal Turing machine—a machine needs certain components, such as memory, a CPU, and software. You can’t detect these ingredients from the outside. For example, I can’t tell if my toaster oven has a general-purpose computer inside or a custom chip. The more features my toaster oven has, the more likely it contains a general-purpose computer, but the only sure way to tell is by looking inside and seeing how it works.

Engineering Security by Peter Gutmann

active measures, address space layout randomization, air gap, algorithmic trading, Amazon Web Services, Asperger Syndrome, bank run, barriers to entry, bitcoin, Brian Krebs, business process, call centre, card file, cloud computing, cognitive bias, cognitive dissonance, cognitive load, combinatorial explosion, Credit Default Swap, crowdsourcing, cryptocurrency, Daniel Kahneman / Amos Tversky, Debian, domain-specific language, Donald Davies, Donald Knuth, double helix, Dr. Strangelove, Dunning–Kruger effect, en.wikipedia.org, endowment effect, false flag, fault tolerance, Firefox, fundamental attribution error, George Akerlof, glass ceiling, GnuPG, Google Chrome, Hacker News, information security, iterative process, Jacob Appelbaum, Jane Jacobs, Jeff Bezos, John Conway, John Gilmore, John Markoff, John von Neumann, Ken Thompson, Kickstarter, lake wobegon effect, Laplace demon, linear programming, litecoin, load shedding, MITM: man-in-the-middle, Multics, Network effects, nocebo, operational security, Paradox of Choice, Parkinson's law, pattern recognition, peer-to-peer, Pierre-Simon Laplace, place-making, post-materialism, QR code, quantum cryptography, race to the bottom, random walk, recommendation engine, RFID, risk tolerance, Robert Metcalfe, rolling blackouts, Ruby on Rails, Sapir-Whorf hypothesis, Satoshi Nakamoto, security theater, semantic web, seminal paper, Skype, slashdot, smart meter, social intelligence, speech recognition, SQL injection, statistical model, Steve Jobs, Steven Pinker, Stuxnet, sunk-cost fallacy, supply-chain attack, telemarketer, text mining, the built environment, The Death and Life of Great American Cities, The Market for Lemons, the payments system, Therac-25, too big to fail, Tragedy of the Commons, Turing complete, Turing machine, Turing test, Wayback Machine, web application, web of trust, x509 certificate, Y2K, zero day, Zimmermann PGP

To the user they’re blurred into a single “do whatever needs to be done to this object” action, to the extent that even experienced Windows and Mac users have a hard time comprehending what Unix execute permission bits are for since for them there’s no distinct concept of “program execution” [636]. Another surprising location where Turing machines turn up is during the boot process of any reasonably recent computer (via the hardware-independent ACPI machine language), in fonts (via a stripped-down Postscript interpreter, this was used for one of the iPhone jailbreaks), and in UEFI, the Universal Extensible Firmware Interface (via the EFI bytecode or EIC) [637]. One of the most unusual Turing machines is built into the RAR archiver. RAR attempts to limit what the code being interpreted by the Turing machine can do by requiring that actions like screen output run from data with a fixed CRC32 value, so that only static strings can be displayed.

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A better use of the time and effort required for user education would have been to concentrate on making the types of documents that are sent as attachments purely passive and unable to cause any action on the destination machine. A generalisation of this problem is that we have Turing machines everywhere — in the pursuit of extensibility, everything from Word documents to web site URLs has been turned 198 Psychology into a programming language [626]. There’s even a standards group that manages the creation of such embedded Turing machines [627][628]49. While a pen-tester once reported that seeing Javascript embedded in DNS results get executed on the target machine came as a considerable surprise to him, the later discovery that the same thing worked just as well with DHCP packets [629][630] and SSIDs [631][632][633][634] (complete with ready-made tools to exploit them [635]) confirmed that we really do have Turing machines in the most surprising places.

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Since CRC32 isn’t a cryptographically strong hash function and it’s relatively easy to make your data have an arbitrary CRC value [638], all that’s required in order to bypass the check is to have your code modify the data to produce the expected CRC value, whereupon the Turing machine’s interpreter processes it without further ado [639]. Further Turing machines have been discovered in the x86 architecture’s interrupt handling and memory translation tables [640] and ELF executable metadata [641], with the discovery of further Turingmachine mechanisms limited only by the imagination of security researchers. You can’t even trust hardcopy any more, since it’s a trivial task to use the programmability of printer languages like Postscript to have the screen display one thing (for example a payment value of $1,000) and the printout display another ($10,000 or $100, depending on which way you want to go) [642].

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

Adam Curtis, agricultural Revolution, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, Anthropocene, artificial general intelligence, augmented reality, autism spectrum disorder, autonomous vehicles, backpropagation, basic income, behavioural economics, bitcoin, blockchain, bread and circuses, Charles Babbage, 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, data science, deep learning, DeepMind, Demis Hassabis, digital capitalism, digital divide, digital rights, discrete time, Douglas Engelbart, driverless car, Elon Musk, Emanuel Derman, endowment effect, epigenetics, Ernest Rutherford, experimental economics, financial engineering, Flash crash, friendly AI, functional fixedness, global pandemic, Google Glasses, Great Leap Forward, Hans Moravec, hive mind, Ian Bogost, income inequality, information trail, Internet of things, invention of writing, iterative process, James Webb Space Telescope, Jaron Lanier, job automation, Johannes Kepler, John Markoff, John von Neumann, Kevin Kelly, knowledge worker, Large Hadron Collider, lolcat, loose coupling, machine translation, microbiome, mirror neurons, Moneyball by Michael Lewis explains big data, Mustafa Suleyman, natural language processing, Network effects, Nick Bostrom, Norbert Wiener, paperclip maximiser, pattern recognition, Peter Singer: altruism, phenotype, planetary scale, Ray Kurzweil, Recombinant DNA, 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, synthetic biology, systems thinking, tacit knowledge, TED Talk, 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!, We are as Gods, Y2K

These exciting modern services often camp it up with “female” vocal chat. They talk like Turing women—or, rather, they emit lines of dialog somewhat like voice-over actresses. However, they also offer swift access to vast fields of combinatorial Big Data that no human brain could ever contain, or will ever contain. These services are not stand-alone Turing Machines. They’re amorphous global networks, combing through clouds of Big Data, algorithmically cataloging responses from human users, providing real-time user response with wireless broadband, while wearing the pseudohuman mask of a fake individual so as to meet some basic interface-design needs. That’s what they are.

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In fact, natural cognition is likely much more complex and detailed than our current incarnations of artificial intelligence or cognitive computing. For example, how sophisticated do we have to imagine natural cognition, when quantum coherence at room temperature can help birds in our garden sense the magnetic field? How complex do we have to imagine embodied cognition in octopi, when it’s possible to build Turing Machines made exclusively of artificial muscles? How should we answer these questions, when we’re still far from recording in full detail what’s going on in our brains? My guess is that in 200 years our current thinking machines will look as primitive as the original Mechanical Turk. However sophisticated they may become, our machines are still primitive compared to the resolution and efficiency of natural cognition.

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KAUFFMAN Pioneer of biocomplexity research; affiliate, Institute for Systems Biology, Seattle; author, Reinventing the Sacred: A New View of Science, Reason, and Religion The advent of quantum biology, light-harvesting molecules, bird navigation, perhaps smell, suggests that sticking to classical physics in biology may turn out to be simply stubborn. Now Turing Machines are discrete state (0,1), discrete time (T, T+1) subsets of classical physics. We all know they, like Shannon information, are merely syntactic. Wonderful mathematical results such as Gregory Chaitin’s omega—the probability that a program will halt, which is totally non-computable and nonalgorithmic—tell us that the human mind, as Roger Penrose also argued, cannot be merely algorithmic.

The Art of Computer Programming: Fundamental Algorithms by Donald E. Knuth

Charles Babbage, discrete time, distributed generation, Donald Knuth, fear of failure, Fermat's Last Theorem, G4S, Gerard Salton, Isaac Newton, Ivan Sutherland, Jacquard loom, Johannes Kepler, John von Neumann, linear programming, linked data, Menlo Park, probability theory / Blaise Pascal / Pierre de Fermat, sorting algorithm, stochastic process, Turing machine

A suitable notation for coroutines in ALGOL-like languages was introduced in Dahl and Nygaard's SIMULA I [CACM 9 A966), 671-678], 230 BASIC CONCEPTS 1-4.5 and several excellent examples of coroutines (including replicated coroutines) appear in the book Structured Programming by O.-J. Dahl, E. W. Dijkstra, and C. A. R. Hoare, Chapter 3. The first interpretive routine may be said to be the "Universal Turing Machine," a Turing machine capable of simulating any other Turing machines. Turing machines are not actual computers; they are theoretical constructions used to prove that certain problems are unsolvable by algorithms. Interpretive routines in the conventional sense were mentioned by John Mauchly in his lectures at the Moore School in 1946. The most notable early interpreters, chiefly intended to provide a convenient means of doing floating point arithmetic, were certain routines for the Whirlwind I (by C.

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We must admit that, as the number n of nodes created by a linking automa- automaton approaches infinity, we don't know how to build such a device physically, since we want the machine operations to take the same amount of time regardless of the size of n; if linking is represented by using addresses as in a computer memory, it is necessary to put a bound on the number of nodes, since the link fields have a fixed size. A multitape Turing machine is therefore a more realistic model when n approaches infinity. Yet it seems reasonable to believe that a linking automaton as described above leads to a more appropriate theory of the complexity of algorithms than Turing machines do, even when asymptotic formulas for large n are considered, because the theory is more likely to be relevant for practical values of n. Furthermore when n gets bigger than 1030 or so, not even a one-tape Turing machine is realistic: It could never be built. Relevance is more important than realism.

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Some of the most interesting problems to solve for such devices would be to determine how fast they can solve certain problems, or how many nodes they need to solve certain problems (for example, to translate certain formal languages). At the time this chapter was first written, several interesting results of this kind had been obtained (notably by J. Hartmanis and R. E. Stearns) but only for special classes of Turing machines having multiple tapes and read/write heads. The Turing machine model is comparatively unrealistic, so these results tended to have little to do with practical problems. We must admit that, as the number n of nodes created by a linking automa- automaton approaches infinity, we don't know how to build such a device physically, since we want the machine operations to take the same amount of time regardless of the size of n; if linking is represented by using addresses as in a computer memory, it is necessary to put a bound on the number of nodes, since the link fields have a fixed size.

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, AlphaGo, Andrew Wiles, artificial general intelligence, Asilomar, Asilomar Conference on Recombinant DNA, augmented reality, autonomous vehicles, basic income, behavioural economics, Bletchley Park, blockchain, Boston Dynamics, brain emulation, Cass Sunstein, Charles Babbage, Claude Shannon: information theory, complexity theory, computer vision, Computing Machinery and Intelligence, connected car, CRISPR, crowdsourcing, Daniel Kahneman / Amos Tversky, data science, deep learning, deepfake, DeepMind, delayed gratification, Demis Hassabis, Elon Musk, en.wikipedia.org, Erik Brynjolfsson, Ernest Rutherford, fake news, Flash crash, full employment, future of work, Garrett Hardin, Geoffrey Hinton, Gerolamo Cardano, Goodhart's law, Hans Moravec, 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, luminiferous ether, machine readable, machine translation, Mark Zuckerberg, multi-armed bandit, Nash equilibrium, Nick Bostrom, Norbert Wiener, NP-complete, OpenAI, openstreetmap, P = NP, paperclip maximiser, Pareto efficiency, Paul Samuelson, Pierre-Simon Laplace, positional goods, probability theory / Blaise Pascal / Pierre de Fermat, profit maximization, RAND corporation, random walk, Ray Kurzweil, Recombinant DNA, recommendation engine, RFID, Richard Thaler, ride hailing / ride sharing, 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, trolley problem, Turing machine, Turing test, universal basic income, uranium enrichment, vertical integration, Von Neumann architecture, Wall-E, warehouse robotics, Watson beat the top human players on Jeopardy!, web application, zero-sum game

Modern revival of the topic in the context of global ecology: Garrett Hardin, “The tragedy of the commons,” Science 162 (1968): 1243–48. 30. It’s quite possible that even if we had tried to build intelligent machines from chemical reactions or biological cells, those assemblages would have turned out to be implementations of Turing machines in nontraditional materials. 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.

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In it, he described a simple computing device that could accept as input the description of any other computing device, together with that second device’s input, and, by simulating the operation of the second device on its input, produce the same output that the second device would have produced. We now call this first device a universal Turing machine. To prove its universality, Turing introduced precise definitions for two new kinds of mathematical objects: machines and programs. Together, the machine and program define a sequence of events—specifically, a sequence of state changes in the machine and its memory. In the history of mathematics, new kinds of objects occur quite rarely.

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See work, elimination of Tegmark, Max, 4, 114, 138 Tellex, Stephanie, 73 Tencent, 250 tensor processing units (TPUs), 35 Terminator (film), 112, 113 Tesauro, Gerry, 55 Thaler, Richard, 244 Theory of the Leisure Class, The (Veblen), 230 Thinking, Fast and Slow (Kahneman), 238 thinking, learning from, 293–95 Thornton, Richard, 133 Times, 7, 8 tool (narrow) artificial intelligence, 46, 47, 136 TPUs (tensor processing units), 35 tragedy of the commons, 31 Transcendence (film), 3–4, 141–42 transitivity of preferences, 23–24 Treatise of Human Nature, A (Hume), 167 tribalism, 150, 159–60 truck drivers, 119 TrueSkill system, 279 Tucker, Albert, 30 Turing, Alan, 32, 33, 37–38, 40–41, 124–25, 134–35, 140–41, 144, 149, 153, 160–61 Turing test, 40–41 tutoring, 100–101 tutoring systems, 70 2001: A Space Odyssey (film), 141 Uber, 57, 182 UBI (universal basic income), 121 uncertainty AI uncertainty as to human preferences, principle of, 53, 175–76 human uncertainty as to own preferences, 235–37 probability theory and, 273–84 United Nations (UN), 250 universal basic income (UBI), 121 Universal Declaration of Human Rights (1948), 107 universality, 32–33 universal Turing machine, 33, 40–41 unpredictability, 29 utilitarian AI, 217–27 Utilitarianism ((Mill), 217–18 utilitarianism/utilitarian AI, 214 challenges to, 221–27 consequentialist AI, 217–19 ideal utilitarianism, 219 interpersonal comparison of utilities, debate over, 222–24 multiple people, maximizing sum of utilities of, 219–26 preference utilitarianism, 220 social aggregation theorem and, 220 Somalia problem and, 226–27 utility comparison across populations of different sizes, debate over, 224–25 utility function, 53–54 utility monster, 223–24 utility theory, 22–26 axiomatic basis for, 23–24 objections to, 24–26 value alignment, 137–38 Vardi, Moshe, 202–3 Veblen, Thorstein, 230 video games, 45 virtual reality authoring, 101 virtue ethics, 217 visual object recognition, 6 von Neumann, John, 23 W3C Credible Web group, 109 WALL-E (film), 255 Watson, 80 wave function, 35–36 “we’re the experts” argument, 152–54 white-collar jobs, 119 Whitehead, Alfred North, 88 whole-brain emulation, 171 Wiener, Norbert, 10, 136–38, 153, 203 Wilczek, Frank, 4 Wiles, Andrew, 185 wireheading, 205–8 work, elimination of, 113–24 caring professions and, 122 compensation effects and, 114–17 historical warnings about, 113–14 income distribution and, 123 occupations at risk with adoption of AI technology, 118–20 reworking education and research institutions to focus on human world, 123–24 striving and enjoying, relation between, 121–22 universal basic income (UBI) proposals and, 121 wage stagnation and productivity increases, since 1973, 117 “work in human–machine teams” argument, 163 World Economic Forum, 250 World Wide Web, 64 Worshipful Company of Scriveners, 109 Zuckerberg, Mark, 157 ABCDEFGHIJKLMNOPQRSTUVWXYZ About the Author Stuart Russell is a professor of Computer Science and holder of the Smith-Zadeh Chair in Engineering at the University of California, Berkeley.

The Language Instinct: How the Mind Creates Language by Steven Pinker

Albert Einstein, Boeing 747, cloud computing, Computing Machinery and Intelligence, David Attenborough, double helix, Drosophila, elephant in my pajamas, finite state, Gregor Mendel, illegal immigration, Joan Didion, language acquisition, Loebner Prize, mass immigration, Maui Hawaii, meta-analysis, MITM: man-in-the-middle, natural language processing, out of africa, phenotype, rolodex, Ronald Reagan, Sapir-Whorf hypothesis, Saturday Night Live, speech recognition, Steven Pinker, Strategic Defense Initiative, tacit knowledge, theory of mind, transatlantic slave trade, Turing machine, Turing test, twin studies, Yogi Berra

It took Alan Turing, the brilliant British mathematician and philosopher, to make the idea of a mental representation scientifically respectable. Turing described a hypothetical machine that could be said to engage in reasoning. In fact this simple device, named a Turing machine in his honor, is powerful enough to solve any problem that any computer, past, present, or future, can solve. And it clearly uses an internal symbolic representation—a kind of mentalese—without requiring a little man or any occult processes. By looking at how a Turing machine works, we can get a grasp of what it would mean for a human mind to think in mentalese as opposed to English. In essence, to reason is to deduce new pieces of knowledge from old ones.

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A grammar composed of a set of phrase structure rules, which build a deep-structure tree, and one or more transformational rules, which move the phrases in the deep structure to yield a surface-structure tree. transitive. See intransitive. Turing machine. A design for a simple computer consisting of a potentially infinite strip of paper, and a processor that can move along the paper and print or erase symbols on it in a sequence that depends on which symbol the processor is currently reading and which of several states it is in. Though too clumsy for practical use, a Turing machine is thought to be capable of computing anything that any digital computer, past, present, or future, can compute. Universal Grammar.

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The neuron at the receiving end adds up any signals coming in from excitatory synapses, subtracts any signals coming in from inhibitory synapses, and if the sum exceeds a threshold, the receiving neuron becomes active itself. A network of these toy neurons, if large enough, can serve as a computer, calculating the answer to any problem that can be specified precisely, just like the page-crawling Turing machine in Chapter 3 that could deduce that Socrates is mortal. That is because toy neurons can be wired together in a few simple ways that turn them into “logic gates,” devices that can compute the logical relations “and,” “or,” and “not” that underlie deduction. The meaning of the logical relation “and” is that the statement “A and B” is true if A is true and if B is true.

Life at the Speed of Light: From the Double Helix to the Dawn of Digital Life by J. Craig Venter

Albert Einstein, Alfred Russel Wallace, Apollo 11, Asilomar, Barry Marshall: ulcers, bioinformatics, borderless world, Brownian motion, clean water, Computing Machinery and Intelligence, discovery of DNA, double helix, dual-use technology, epigenetics, experimental subject, global pandemic, Gregor Mendel, Helicobacter pylori, Isaac Newton, Islamic Golden Age, John von Neumann, Louis Pasteur, Mars Rover, Mikhail Gorbachev, phenotype, precautionary principle, Recombinant DNA, Richard Feynman, stem cell, Stuart Kauffman, synthetic biology, the scientific method, Thomas Kuhn: the structure of scientific revolutions, Turing machine

The mere making of life would only be important if we intended to allow it to evolve of itself anew.” A logical recipe to create these complex mechanisms was developed in the next decade. In 1936 Alan Turing, the cryptographer and pioneer of artificial intelligence, described what has come to be known as a Turing machine, which is described by a set of instructions written on a tape. Turing also defined a universal Turing machine, which can carry out any computation for which an instruction set can be written. This is the theoretical foundation of the digital computer. Turing’s ideas were developed further in the 1940s, by the remarkable American mathematician and polymath John von Neumann, who conceived of a self-replicating machine.

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The onset of efforts to create another kind of self-reproducing automaton, along with the beginnings of artificial-life research, date back to around this period, when the first modern computers came into use. The discovery of the coded nature of life’s genetic information system led naturally to parallels with Turing machines. Turing himself, in his key 1950 paper on artificial intelligence, discussed how survival of the fittest was “a slow method” that could possibly be given a boost, not least because an experimenter was not restricted to random mutations.26 Many began to believe that artificial life would emerge from complex logical interactions within a computer.

The Blockchain Alternative: Rethinking Macroeconomic Policy and Economic Theory by Kariappa Bheemaiah

"World Economic Forum" Davos, accounting loophole / creative accounting, Ada Lovelace, Adam Curtis, Airbnb, Alan Greenspan, algorithmic trading, asset allocation, autonomous vehicles, balance sheet recession, bank run, banks create money, Basel III, basic income, behavioural economics, Ben Bernanke: helicopter money, bitcoin, Bletchley Park, blockchain, Bretton Woods, Brexit referendum, business cycle, business process, call centre, capital controls, Capital in the Twenty-First Century by Thomas Piketty, cashless society, cellular automata, central bank independence, Charles Babbage, Claude Shannon: information theory, cloud computing, cognitive dissonance, collateralized debt obligation, commoditize, complexity theory, constrained optimization, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-border payments, crowdsourcing, cryptocurrency, data science, David Graeber, deep learning, deskilling, Diane Coyle, discrete time, disruptive innovation, distributed ledger, diversification, double entry bookkeeping, Ethereum, ethereum blockchain, fiat currency, financial engineering, financial innovation, financial intermediation, Flash crash, floating exchange rates, Fractional reserve banking, full employment, George Akerlof, Glass-Steagall Act, Higgs boson, illegal immigration, income inequality, income per capita, inflation targeting, information asymmetry, interest rate derivative, inventory management, invisible hand, John Maynard Keynes: technological unemployment, John von Neumann, joint-stock company, Joseph Schumpeter, junk bonds, Kenneth Arrow, Kenneth Rogoff, Kevin Kelly, knowledge economy, large denomination, Large Hadron Collider, Lewis Mumford, liquidity trap, London Whale, low interest rates, low skilled workers, M-Pesa, machine readable, Marc Andreessen, market bubble, market fundamentalism, Mexican peso crisis / tequila crisis, Michael Milken, MITM: man-in-the-middle, Money creation, money market fund, money: store of value / unit of account / medium of exchange, mortgage debt, natural language processing, Network effects, new economy, Nikolai Kondratiev, offshore financial centre, packet switching, Pareto efficiency, pattern recognition, peer-to-peer lending, Ponzi scheme, power law, precariat, pre–internet, price mechanism, price stability, private sector deleveraging, profit maximization, QR code, quantitative easing, quantitative trading / quantitative finance, Ray Kurzweil, Real Time Gross Settlement, rent control, rent-seeking, robo advisor, Satoshi Nakamoto, Satyajit Das, Savings and loan crisis, savings glut, seigniorage, seminal paper, Silicon Valley, Skype, smart contracts, software as a service, software is eating the world, speech recognition, statistical model, Stephen Hawking, Stuart Kauffman, supply-chain management, technology bubble, The Chicago School, The Future of Employment, The Great Moderation, the market place, The Nature of the Firm, the payments system, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, too big to fail, trade liberalization, transaction costs, Turing machine, Turing test, universal basic income, Vitalik Buterin, Von Neumann architecture, Washington Consensus

Luckily for the Allies, hope lay in the form of some work that had been done a few years earlier by another Cambridge mathematician, Alan Turing. Along with his mentor, Max Newman, Turing set about designing and building automated machines (Turing Machines) that could decrypt secret German military communications (as documented in the popular movie, ‘The Imitation Game’). However, owing to an obsession for secrecy during the war years and for several years after that, the achievements made by Turing and the team at Bletchley Park in computer development was kept hidden from view. Instead of Turing Machines, over the same time period, a machine called the ENIAC (Electronic Numerical Integrator And Computer) was being developed by John Mauchly and Presper Eckert across the Atlantic.

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As World War Two broke out, these advances in computing were adopted and developed by various militaries to communicate sensitive information by integrating the techniques of cryptography - a kind of natural selection. To combat this, pioneers such as Alan Turing and his mentor Max Newman, set about designing and building automated machines (Turing Machines) that could decrypt these camouflaged communiqués. This effectively changed the use of the computer and increased the diversity of the kinds of computers. After the war, advances by notable inventors such as John Mauchly, Presper Eckert and John von Neumann (a veritable polymath) led to the creation of the EDVAC (Electronic Discrete Variable Automatic Computer) , the first binary computer.

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See Figure 4-11. Figure 4-11.General design of the Electronic Discrete Variable Automatic Computer. Reference Source: ‘The von Neumann Architecture’, The Computing Universe, 2014 From an abstract architecture perspective, von Neumann’s design is logically equivalent to Turing’s Universal Turing Machine. In fact, von Neumann had read Turing’s theoretical papers prior to designing his machine. Ultimately it was this simple design that was built upon by successive generations of computer scientists and led to the design of computers with multiple processors and the creation of parallel computing.

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, Alvin Toffler, Apollo Guidance Computer, Apple II, augmented reality, back-to-the-land, beat the dealer, Bill Atkinson, Bill Gates: Altair 8800, bitcoin, Bletchley Park, Bob Noyce, Buckminster Fuller, Byte Shop, c2.com, call centre, Charles Babbage, citizen journalism, Claude Shannon: information theory, Clayton Christensen, commoditize, commons-based peer production, computer age, Computing Machinery and Intelligence, content marketing, crowdsourcing, cryptocurrency, Debian, desegregation, Donald Davies, Douglas Engelbart, Douglas Engelbart, Douglas Hofstadter, driverless car, Dynabook, El Camino Real, Electric Kool-Aid Acid Test, en.wikipedia.org, eternal september, Evgeny Morozov, Fairchild Semiconductor, financial engineering, Firefox, Free Software Foundation, Gary Kildall, Google Glasses, Grace Hopper, Gödel, Escher, Bach, Hacker Ethic, Haight Ashbury, Hans Moravec, Howard Rheingold, Hush-A-Phone, HyperCard, hypertext link, index card, Internet Archive, Ivan Sutherland, Jacquard loom, Jaron Lanier, Jeff Bezos, jimmy wales, John Markoff, John von Neumann, Joseph-Marie Jacquard, Leonard Kleinrock, Lewis Mumford, linear model of innovation, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Menlo Park, Mitch Kapor, Mother of all demos, Neil Armstrong, new economy, New Journalism, Norbert Wiener, Norman Macrae, packet switching, PageRank, Paul Terrell, pirate software, popular electronics, pre–internet, Project Xanadu, punch-card reader, RAND corporation, Ray Kurzweil, reality distortion field, 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, Susan Wojcicki, technological singularity, technoutopianism, Ted Nelson, Teledyne, the Cathedral and the Bazaar, The Coming Technological Singularity, The Nature of the Firm, The Wisdom of Crowds, Turing complete, Turing machine, Turing test, value engineering, 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

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. In essence, it embodied the dream of Charles Babbage and Ada Lovelace for a completely general-purpose universal machine.

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Turing asked his mother to send out reprints of it to the mathematical philosopher Bertrand Russell and a half dozen other famous scholars, but the only major review was by Alonzo Church, who could afford to be flattering because he had been ahead of Turing in solving Hilbert’s decision problem. Church was not only generous; he introduced the term Turing machine for what Turing had called a Logical Computing Machine. Thus at twenty-four, Turing’s name became indelibly stamped on one of the most important concepts of the digital age.12 CLAUDE SHANNON AND GEORGE STIBITZ AT BELL LABS There was another seminal theoretical breakthrough in 1937, similar to Turing’s in that it was purely a thought experiment.

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In 1939 Zuse began work on a third model, the Z3, that used electromechanical relays both for the arithmetic unit and for the memory and control units. When it was completed in 1941, it became the first fully working all-purpose, programmable digital computer. Even though it did not have a way to directly handle conditional jumps and branching in the programs, it could theoretically perform as a universal Turing machine. Its major difference from later computers was that it used clunky electromagnetic relays rather than electronic components such as vacuum tubes or transistors. Zuse’s friend Schreyer went on to write a doctoral thesis, “The Tube Relay and the Techniques of Its Switching,” that advocated using vacuum tubes for a powerful and fast computer.

Our Final Invention: Artificial Intelligence and the End of the Human Era by James Barrat

AI winter, air gap, AltaVista, Amazon Web Services, artificial general intelligence, Asilomar, Automated Insights, Bayesian statistics, Bernie Madoff, Bill Joy: nanobots, Bletchley Park, brain emulation, California energy crisis, cellular automata, Chuck Templeton: OpenTable:, cloud computing, cognitive bias, commoditize, computer vision, Computing Machinery and Intelligence, cuban missile crisis, Daniel Kahneman / Amos Tversky, Danny Hillis, data acquisition, don't be evil, drone strike, dual-use technology, Extropian, finite state, Flash crash, friendly AI, friendly fire, Google Glasses, Google X / Alphabet X, Hacker News, Hans Moravec, Isaac Newton, Jaron Lanier, Jeff Hawkins, John Markoff, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, Loebner Prize, lone genius, machine translation, mutually assured destruction, natural language processing, Neil Armstrong, Nicholas Carr, Nick Bostrom, optical character recognition, PageRank, PalmPilot, paperclip maximiser, pattern recognition, Peter Thiel, precautionary principle, prisoner's dilemma, Ray Kurzweil, Recombinant DNA, Rodney Brooks, rolling blackouts, Search for Extraterrestrial Intelligence, self-driving car, semantic web, Silicon Valley, Singularitarianism, Skype, smart grid, speech recognition, statistical model, stealth mode startup, stem cell, Stephen Hawking, Steve Jobs, Steve Jurvetson, Steve Wozniak, strong AI, Stuxnet, subprime mortgage crisis, superintelligent machines, technological singularity, The Coming Technological Singularity, Thomas Bayes, traveling salesman, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, zero day

Before the war, Turing had studied mathematics and encryption at Cambridge and Princeton. He had imagined an “automatic machine,” now known as a Turing machine. The automatic machine laid out the basic principles of computation itself. The Church-Turing hypothesis, which combined Turing’s work with that of his Princeton professor, mathematician Alonso Church, really puts the starch in the pants of the study of artificial intelligence. It proposes that anything that can be computed by an algorithm, or program, can be computed by a Turing machine. Therefore, if brain processes can be expressed as a series of instructions—an algorithm—then a computer can process information the same way.

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Searle, John self-awareness Self-Aware Systems self-improvement self-preservation September 11 attacks serial processing SETI (Search for Extraterrestrial Intelligence) Shostak, Seth Silicon Valley Singularitarians Singularity definitions of Kurzweil and technological Singularity Is Near, The (Kurzweil) Singularity Summit Singularity University Sir Groovy Siri 60 Minutes Skilling, Jeffrey Smart Action smart phones see also iPhone software complexity of malware see also programming solar energy space exploration “Speculations Concerning the First Ultraintelligent Machine” (Good) speech recognition SRI International stealth companies Sterrit, Roy Stibel, Jeff Stuxnet subprime mortgage crisis Symantec SyNAPSE Technological Risk (Lewis) technology journalism Terminator movies terrorism 9/11 attacks Thiel, Peter Thinking Machines, Inc. Three Mile Island tightly coupled systems Thrun, Sebastian transhumans transistors Traveller Trillion Credit Squadron Turing, Alan Turing machine Turing test Tversky, Amos two-minute problem 2001: A Space Odyssey Ulam, Stanislaw utility function Vassar, Michael Vicarious Systems Vinge, Vernor violence Virginia Tech Massacre Virtually You (Aboujaoude) voice recognition von Neumann, John Voss, Peter Wallach, Wendall Wall Street Warwick, Kevin Washington Post Watson weapons, see military Whitby, Blay “Why the Future Doesn’t Need Us” (Joy) Wired for Thought (Stibel) Wissner-Gross, Alexander D.

Superintelligence: Paths, Dangers, Strategies by Nick Bostrom

agricultural Revolution, AI winter, Albert Einstein, algorithmic trading, anthropic principle, Anthropocene, anti-communist, artificial general intelligence, autism spectrum disorder, autonomous vehicles, backpropagation, barriers to entry, Bayesian statistics, bioinformatics, brain emulation, cloud computing, combinatorial explosion, computer vision, Computing Machinery and Intelligence, cosmological constant, dark matter, DARPA: Urban Challenge, data acquisition, delayed gratification, Demis Hassabis, demographic transition, different worldview, Donald Knuth, Douglas Hofstadter, driverless car, Drosophila, Elon Musk, en.wikipedia.org, endogenous growth, epigenetics, fear of failure, Flash crash, Flynn Effect, friendly AI, general purpose technology, Geoffrey Hinton, Gödel, Escher, Bach, hallucination problem, Hans Moravec, income inequality, industrial robot, informal economy, information retrieval, interchangeable parts, iterative process, job automation, John Markoff, John von Neumann, knowledge worker, Large Hadron Collider, longitudinal study, machine translation, megaproject, Menlo Park, meta-analysis, mutually assured destruction, Nash equilibrium, Netflix Prize, new economy, Nick Bostrom, Norbert Wiener, NP-complete, nuclear winter, operational security, optical character recognition, paperclip maximiser, pattern recognition, performance metric, phenotype, prediction markets, price stability, principal–agent problem, race to the bottom, random walk, Ray Kurzweil, recommendation engine, reversible computing, search costs, social graph, speech recognition, Stanislav Petrov, statistical model, stem cell, Stephen Hawking, Strategic Defense Initiative, strong AI, superintelligent machines, supervolcano, synthetic biology, technological singularity, technoutopianism, The Coming Technological Singularity, The Nature of the Firm, Thomas Kuhn: the structure of scientific revolutions, time dilation, Tragedy of the Commons, transaction costs, trolley problem, Turing machine, Vernor Vinge, WarGames: Global Thermonuclear War, Watson beat the top human players on Jeopardy!, World Values Survey, zero-sum game

But even if a small group had always been isolated, it might still be part of a larger collective intelligence than meets the eye—namely, the collective intelligence consisting of not only the present but all ancestral generations as well, an aggregate that can function as a feed-forward information processing system. 14. By the Church–Turing thesis, all computable functions are computable by a Turing machine. Since any of the three forms of superintelligence could simulate a Turing machine (if given access to unlimited memory and allowed to operate indefinitely), they are by this formal criterion computationally equivalent. Indeed, an average human being (provided with unlimited scrap paper and unlimited time) could also implement a Turing machine, and thus is also equivalent by the same criterion. What matters for our purposes, however, is what these different systems can achieve in practice, with finite memory and in reasonable time.

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Murphy (2012). 28. Pearl (2009). 29. We suppress various technical details here in order not to unduly burden the exposition. We will have occasion to revisit some of these ignored issues in Chapter 12. 30. A program p is a description of string x if p, run on (some particular) universal Turing machine U, outputs x; we write this as U(p) = x. (The string x here represents a possible world.) The Kolmogorov complexity of x is then K(x):=minp {l(p): U(p) = x}, where l(p) is the length of p in bits. The “Solomonoff” probability of x is then defined as where the sum is defined over all (“minimal,” i.e. not necessarily halting) programs p for which U outputs a string starting with x (Hutter 2005). 31.

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What matters for our purposes, however, is what these different systems can achieve in practice, with finite memory and in reasonable time. And the efficiency variations are so great that one can readily make some distinctions. For example, a typical individual with an IQ of 85 could be taught to implement a Turing machine. (Conceivably, it might even be possible to train some particularly gifted and docile chimpanzee to do this.) Yet, for all practical intents and purposes, such an individual is presumably incapable of, say, independently developing general relativity theory or of winning a Fields medal. 15. Oral storytelling traditions can produce great works (such as the Homeric epics) but perhaps some of the contributing authors possessed uncommon gifts. 16.

Infinity in the Palm of Your Hand: Fifty Wonders That Reveal an Extraordinary Universe by Marcus Chown

Albert Einstein, Anton Chekhov, Apollo 11, Arthur Eddington, Carrington event, dark matter, Donald Trump, double helix, Eddington experiment, Edmond Halley, gravity well, horn antenna, Isaac Newton, Kickstarter, Large Hadron Collider, microbiome, Neil Armstrong, Richard Feynman, Search for Extraterrestrial Intelligence, space junk, Stephen Hawking, Turing machine

The crucial thing is that Turing’s machine can be fed a description, encoded in binary, of any other machine and will then simulate that machine. Because of this unprecedented ability, Turing called it a Universal Machine. Today, it is referred to as a Universal Turing Machine. Clearly, it is unrecognizable as a computer. But that is exactly what it is. A Universal Turing Machine is the simplest computer imaginable: the irreducible atom of computing. Ironically, Turing devised his machine-of-the-mind to show not what a computer can do but what it cannot do. As a mathematician, it was the ultimate limit of computers that interested him.

Applied Cryptography: Protocols, Algorithms, and Source Code in C by Bruce Schneier

active measures, cellular automata, Claude Shannon: information theory, complexity theory, dark matter, Donald Davies, Donald Knuth, dumpster diving, Dutch auction, end-to-end encryption, Exxon Valdez, fault tolerance, finite state, heat death of the universe, information security, invisible hand, John von Neumann, knapsack problem, MITM: man-in-the-middle, Multics, NP-complete, OSI model, P = NP, packet switching, quantum cryptography, RAND corporation, RFC: Request For Comment, seminal paper, software patent, telemarketer, traveling salesman, Turing machine, web of trust, Zimmermann PGP

Previous Table of Contents Next ----------- Complexity of Problems Complexity theory also classifies the inherent complexity of problems, not just the complexity of particular algorithms used to solve problems. (Excellent introductions to this topic are [600, 211, 1226]; see also [1096, 27, 739].) The theory looks at the minimum time and space required to solve the hardest instance of a problem on a theoretical computer known as a Turing machine . A Turing machine is a finite-state machine with an infinite read-write memory tape. It turns out that a Turing machine is a realistic model of computation. Problems that can be solved with polynomial-time algorithms are called tractable, because they can usually be solved in a reasonable amount of time for reasonable-sized inputs. (The exact definition of “reasonable” depends on the circumstance.)

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Figure 11.1 shows the more important complexity classes and their presumed relationships. (Unfortunately, not much about this material has been proved mathematically.) On the bottom, the class P consists of all problems that can be solved in polynomial time. The class NP consists of all problems that can be solved in polynomial time only on a nondeterministic Turing machine: a variant of a normal Turing machine that can make guesses. The machine guesses the solution to the problem—either by making “lucky guesses” or by trying all guesses in parallel—and checks its guess in polynomial time. NP ’s relevance to cryptography is this: Many symmetric algorithms and all public-key algorithms can be cracked in nondeterministic polynomial time.

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Furthermore, this argument is not applicable to all classes of ciphers; in particular, it is not applicable to one-time pads—for any C, there are many X, k pairs that yield C when run through the encryption algorithm, but most of these X s are nonsense, not legitimate plaintexts. Figure 11.1 Complexity classes. The class NP includes the class P, because any problem solvable in polynomial time on a deterministic Turing machine is also solvable in polynomial time on a nondeterministic Turing machine; the guessing stage can simply be omitted. If all NP problems are solvable in polynomial time on a deterministic machine, then P = NP. Although it seems obvious that some NP problems are much harder than others (a brute-force attack against an encryption algorithm versus encrypting a random block of plaintext), it has never been proven that P ` NP (or that P = NP).

The Scandal of Money by George Gilder

Affordable Care Act / Obamacare, Alan Greenspan, bank run, behavioural economics, Bernie Sanders, bitcoin, blockchain, borderless world, Bretton Woods, capital controls, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, central bank independence, Claude Shannon: information theory, Clayton Christensen, cloud computing, corporate governance, cryptocurrency, currency manipulation / currency intervention, currency risk, Daniel Kahneman / Amos Tversky, decentralized internet, Deng Xiaoping, disintermediation, Donald Trump, fiat currency, financial innovation, Fractional reserve banking, full employment, George Gilder, glass ceiling, guns versus butter model, Home mortgage interest deduction, impact investing, index fund, indoor plumbing, industrial robot, inflation targeting, informal economy, Innovator's Dilemma, Internet of things, invisible hand, Isaac Newton, James Carville said: "I would like to be reincarnated as the bond market. You can intimidate everybody.", Jeff Bezos, John Bogle, John von Neumann, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, Law of Accelerating Returns, low interest rates, Marc Andreessen, Mark Spitznagel, Mark Zuckerberg, Menlo Park, Metcalfe’s law, Money creation, money: store of value / unit of account / medium of exchange, mortgage tax deduction, Nixon triggered the end of the Bretton Woods system, obamacare, OSI model, Paul Samuelson, Peter Thiel, Ponzi scheme, price stability, Productivity paradox, proprietary trading, purchasing power parity, quantitative easing, quantitative trading / quantitative finance, Ray Kurzweil, reality distortion field, reserve currency, road to serfdom, Robert Gordon, Robert Metcalfe, Ronald Reagan, Sand Hill Road, Satoshi Nakamoto, Search for Extraterrestrial Intelligence, secular stagnation, seigniorage, Silicon Valley, Skinner box, smart grid, Solyndra, South China Sea, special drawing rights, The Great Moderation, The Rise and Fall of American Growth, The Wealth of Nations by Adam Smith, Tim Cook: Apple, time value of money, too big to fail, transaction costs, trickle-down economics, Turing machine, winner-take-all economy, yield curve, zero-sum game

Addressing pure logic as math, Gödel concluded that even arithmetic cannot constitute a complete and coherent system. All logical schemes have to move beyond self-referential circularity and invoke axioms outside themselves. Turing explored the possibility of a complete and self-sufficient logical machine and found it an impossible dream. His “Turing machine” defined the abstract logical architecture of all computers. But all computers must depend on what Turing called human “oracles” to define their symbols, instructions, and programs and to interpret their output, which as a stream of off-and-on currents or charges is ostensibly meaningless.1 Shannon set out to create a purely mathematical definition of information and ended up providing a logical scheme of communication that depends on human subjectivity and creativity for meaning and purpose.

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See also secular stagnation Stiglitz, Joseph, 89 stimulus, xiii, xviii, 14, 150, 171 Stockman, David, 40, 48, 50 Stone Age, 19, 169 Summers, Lawrence “Larry,” 3, 7, 56, 114, 134, 150 Sun Microsystems, 119 Swanson’s Law, 18 Sweden, Swedes, 5, 36 Szabo, Nick, 64, 72–76, 160 T Taiwan, Taiwanese, 30, 46–48, 106 Tamny, John, 11 tax cuts, xiv, 12, 151, 153 Taylor, John, 35 Taylor Rule, 35 technology, xi, xviii–xix, xxi–xxii, 2–3, 5–9, 12–13, 19, 41, 43, 45, 56–58, 63–67, 70, 83, 90, 92, 100, 143, 158, 171 Tel Aviv, 118 Texas, 55, 99 Thailand, 110 Thiel, Peter, xi, 14, 56 third world, the, 6, 118, 152 Tiananmen Square, 29, 43 Troubled Asset Relief Program, 55 Trump, Donald, 40, 113 Turing, Alan, 64, 138, 168, 174 Turing machine, 138 Turner, Adair, 88–96, 110 Turner-Piketty thesis, 93, 96 Tversky, Amos, xx Twilight of Sovereignty (Wriston), 101 U UBS, 127 unemployment rates, xi–xiii, 35, 55, 100, 150, 152 Unenumerated, 73 “unicorns,” 50, 87, 119–23, 171 Union of Soviet Socialist Republics (USSR), 42. See also Soviet Union United Kingdom (UK), 87–89, 104.

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, behavioural economics, Berlin Wall, Big Tech, Bill Duvall, bitcoin, Boeing 747, Charles Babbage, cognitive load, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, data science, David Heinemeier Hansson, David Sedaris, delayed gratification, dematerialisation, diversification, Donald Knuth, Donald Shoup, double helix, Dutch auction, Elon Musk, exponential backoff, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, fulfillment center, Garrett Hardin, Geoffrey Hinton, George Akerlof, global supply chain, Google Chrome, heat death of the universe, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, Johannes Kepler, John Nash: game theory, John von Neumann, Kickstarter, knapsack problem, Lao Tzu, Leonard Kleinrock, level 1 cache, linear programming, martingale, multi-armed bandit, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, power law, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, Sam Altman, scientific management, 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

Tom and his colleagues have used this approach to develop models of human cognition; see Griffiths, Lieder, and Goodman, “Rational Use of Cognitive Resources.” analogy to a human mathematician: In section 9 of Turing, “On Computable Numbers,” Turing justifies the choices made in defining what we now call a Turing machine by comparing them to operations that a person might carry out: a two-dimensional piece of paper becomes a one-dimensional tape, the person’s state of mind becomes the state of the machine, and symbols are written and read as the person or machine moves around on the paper. Computation is what a computer does, and at the time the only “computers” were people.

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“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.

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See also Transmission Control Protocol (TCP) teaching to the test technical investors telegraph telephone temperature temporal locality Tenenbaum, Josh tennis tournaments Texas Hold ’Em text messages “TeX Tuneup of 2012, The” (Knuth) Thanksgiving commerce theft, irrational responses and Things a Computer Scientist Rarely Talks About (Knuth) 37% rule Thoreau, Henry David thrashing threading Three Princes of Serendip, The Threshold Rule throughput Tibshirani, Robert Tikhonov, Andrey time interval of timeboxing time costs time management time-space tradeoffs Tolins, Jackson Tomlinson, Ray town size distributions Toxoplasma gondii traffic tragedy of the commons training scars transit systems Transmission Control Protocol (TCP) ACKs and backchannels and flow control and price of anarchy and traveling salesman problem Treat, Tyler “Treatise on the Probability of the Causes of Events” (Laplace) Tree, Jean Fox Trick, Michael triple handshake triple-or-nothing game trip planning. See also traveling salesman problem Turing, Alan Turing machine turn-taking Tuskegee Syphilis Study Tversky, Amos Twain, Mark twin primes Twitter two-factor models two-machine scheduling UC Berkeley Ulam, Stanislaw “Stan” Ullman, Ellen uncertainty Unilever “Unreasonable Effectiveness of Data, The” (Norvig) “up or out” system Upper Confidence Bound urban planners US Armed Forces US Census US House of Representatives US Public Health Service U-turns vacation email and itinerary of policy on vaccination Vail, Alfred valet stand veil of ignorance verification, gap between search and Vickrey, William Vickrey auction Vita Coco voicemail voice transmission, Internet Voltaire Von Neumann, John Wagenmakers, E.

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

Ada Lovelace, adjacent possible, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, AlphaGo, Andrew Wiles, Bayesian statistics, bioinformatics, bitcoin, Bletchley Park, Build a better mousetrap, Claude Shannon: information theory, computer age, computer vision, Computing Machinery and Intelligence, CRISPR, deep learning, disinformation, double entry bookkeeping, double helix, Douglas Hofstadter, Elon Musk, epigenetics, experimental subject, Fermat's Last Theorem, Gödel, Escher, Bach, Higgs boson, information asymmetry, information retrieval, invention of writing, Isaac Newton, iterative process, John von Neumann, language acquisition, megaproject, 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, Stuart Kauffman, TED Talk, 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

This is very hard to imagine or even to take seriously, and this has inspired some thinkers to conclude that since evolution couldn’t create a computer (or a computer program to run on it), human minds must not be products of natural selection alone, and the aspirations of Artificial Intelligence must be forlorn. The mathematician and physicist Roger Penrose (1989) is the most illustrious example. For the sake of argument let’s concede that evolution by natural selection could not directly evolve a living digital computer (a Turing machine tree or a Turing machine turtle, for example). But there is an indirect way: let natural selection first evolve human minds, and then they can intelligently design Hamlet, La Sagrada Familia, and the computer, among many other wonders. This bootstrapping process seems almost magical at first, even self-contradictory.

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More importantly, he showed that if their instructions included conditional branching (if-then instructions, such as “if you observe 0, replace it with 1 and move left, and if you observe 1 leave it as is and move right, and change to state n.”), then these machines could pursue indefinitely complex paths determined by the instructions, which gave them a remarkable competence: they could do anything computational. In other words, a programmable digital computer is a Universal Turing Machine, capable of mimicking any special-purpose digital computer by following a set of instructions that implement that special-purpose computer in software.13 (You don’t have to rewire your smartphone to get it to do new tasks; just download an app and turn it into a star finder or translator or hand calculator or spell-checker or.…) A huge Design Space of information-processing was made accessible by Turing, and he foresaw that there was a traversable path from Absolute Ignorance to Artificial Intelligence, a long series of lifting steps in that Design Space.

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The short explanation is that Turing himself is one of the twigs on the Tree of Life, and his artifacts, concrete and abstract, are indirectly products of the blind Darwinian processes in the same way spider webs and beaver dams are, so there is no radical discontinuity, no need for a skyhook, to get us from spiders and beaver dams to Turing and Turing machines. Still, there is a large gap to be filled, because Turing’s way of making things was strikingly different from the spider’s way and the beaver’s way, and we need a good evolutionary account of that difference. If competence without comprehension is so wonderfully fecund—capable of designing nightingales, after all—why do we need comprehension—capable of designing odes to nightingales and computers?

Structure and Interpretation of Computer Programs, Second Edition by Harold Abelson, Gerald Jay Sussman, Julie Sussman

Andrew Wiles, conceptual framework, Donald Knuth, Douglas Hofstadter, Eratosthenes, functional programming, Gödel, Escher, Bach, higher-order functions, industrial robot, information retrieval, iterative process, Ivan Sutherland, Johannes Kepler, loose coupling, machine translation, Multics, probability theory / Blaise Pascal / Pierre de Fermat, Richard Stallman, Turing machine, wikimedia commons

Turing (1912-1954), whose 1936 paper laid the foundations for theoretical computer science. In the paper, Turing presented a simple computational model—now known as a Turing machine—and argued that any “effective process” can be formulated as a program for such a machine. (This argument is known as the Church-Turing thesis.) Turing then implemented a universal machine, i.e., a Turing machine that behaves as an evaluator for Turing-machine programs. He used this framework to demonstrate that there are well-posed problems that cannot be computed by Turing machines (see Exercise 4.15), and so by implication cannot be formulated as “effective processes.” Turing went on to make fundamental contributions to practical computer science as well.

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Knuth, Fundamental Algorithms (Volume 1 of The Art of Computer Programming) Jump to: A B C D E F G H I K L M N O P Q R S T U V W Z Index Entry Section A abstract models: 2.1.3 abstract syntax: 4.1.1 abstraction barriers: Chapter 2 abstraction barriers: 2.1.2 accumulator: 2.2.3 accumulator: 3.1.1 acquired: 3.4.2 action: 5.1.1 additive: 2.4.3 additively: Chapter 2 additively: 2.4 address: 5.3.1 address arithmetic: 5.3.1 agenda: 3.3.4 algebraic specification: 2.1.3 aliasing: 3.1.3 and-gate: 3.3.4 applicative-order: 4.2.1 applicative-order evaluation: 1.1.5 arbiter: 3.4.2 arguments: 1.1.1 assembler: 5.2.1 assertions: 4.4.1 assignment operator: 3.1 atomically: 3.4.2 automatic storage allocation: 5.3 average damping: 1.3.3 B B-trees: 2.3.3 backbone: 3.3.3 backquote: 5.5.2 backtracks: 4.3.1 balanced: 2.2.2 barrier synchronization: 3.4.2 base address: 5.3.1 Bertrand’s hypothesis: 3.5.2 bignum: 5.3.1 bindings: 3.2 binds: 1.1.8 binomial coefficients: 1.2.2 block structure: 1.1.8 bound variable: 1.1.8 box-and-pointer notation: 2.2 breakpoint: 5.2.4 broken heart: 5.3.2 bugs: Chapter 1 C cache-coherence: 3.4.1 call-by-name: 3.5.1 call-by-name: 4.2.2 call-by-name thunks: 3.5.1 call-by-need: 3.5.1 call-by-need: 4.2.2 call-by-need thunks: 3.5.1 capturing: 1.1.8 Carmichael numbers: 1.2.6 case analysis: 1.1.6 cell: 3.4.2 chronological backtracking: 4.3.1 Church numerals: 2.1.3 Church-Turing thesis: 4.1.5 clauses: 1.1.6 closed world assumption: 4.4.3 closure: Chapter 2 closure property: 2.2 code generator: 5.5.1 coerce: 2.5.2 coercion: 2.5.2 combinations: 1.1.1 comments: 2.2.3 compacting: 5.3.2 compilation: 5.5 compile-time environment: 5.5.6 composition: 1.3.4 compound data: Chapter 2 compound data object: Chapter 2 compound procedure: 1.1.4 computability: 4.1.5 computational process: Chapter 1 concurrently: 3.4 congruent modulo: 1.2.6 connectors: 3.3.5 consequent expression: 1.1.6 constraint networks: 3.3.5 constructors: 2.1 continuation procedures: 4.3.3 continued fraction: 1.3.3 control structure: 4.4.3 controller: 5.1 conventional interfaces: Chapter 2 conventional interfaces: 2.2.3 current time: 3.3.4 D data: Chapter 1 data: 2.1.3 data abstraction: Chapter 2 data abstraction: 2.1 data paths: 5.1 data-directed: 2.4 data-directed programming: Chapter 2 data-directed programming: 2.4.3 deadlock: 3.4.2 deadlock-recovery: 3.4.2 debug: Chapter 1 deep binding: 4.1.3 deferred operations: 1.2.1 delayed argument: 3.5.4 delayed evaluation: Chapter 3 delayed evaluation: 3.5 delayed object: 3.5.1 dense: 2.5.3 dependency-directed backtracking: 4.3.1 depth-first search: 4.3.1 deque: 3.3.2 derived expressions: 4.1.2 digital signals: 3.3.4 dispatching on type: 2.4.3 displacement number: 5.5.6 dotted-tail notation: 2.2.1 driver loop: 4.1.4 E empty list: 2.2.1 encapsulated: 3.1.1 enclosing environment: 3.2 entry points: 5.1.1 enumerator: 2.2.3 environment: 1.1.2 environment model: Chapter 3 environments: 3.2 Euclid’s Algorithm: 1.2.5 Euclidean ring: 2.5.3 evaluating: 1.1.1 evaluator: Chapter 4 event-driven simulation: 3.3.4 evlis tail recursion: 5.4.1 execution procedure: 4.1.7 explicit-control evaluator: 5.4 expression: 1.1.1 F failure continuation: 4.3.3 FIFO: 3.3.2 filter: 1.3.1 filter: 2.2.3 first-class: 1.3.4 fixed point: 1.3.3 fixed-length: 2.3.4 forcing: 4.2.2 forwarding address: 5.3.2 frame: 4.4.2 frame coordinate map: 2.2.4 frame number: 5.5.6 framed-stack: 5.4.1 frames: 3.2 free: 1.1.8 free list: 5.3.1 front: 3.3.2 full-adder: 3.3.4 function boxes: 3.3.4 functional programming: 3.1.3 functional programming languages: 3.5.5 G garbage: 5.3.2 garbage collection: 5.3 garbage collection: 5.3.2 garbage collector: 3.3.1 garbage-collected: 4.2.2 generic operations: Chapter 2 generic procedures: 2.3.4 generic procedures: 2.4 glitches: Chapter 1 global: 1.2 global: 3.2 global environment: 1.1.2 golden ratio: 1.2.2 grammar: 4.3.2 H half-adder: 3.3.4 half-interval method: 1.3.3 Halting Theorem: 4.1.5 headed list: 3.3.3 hiding principle: 3.1.1 hierarchical: 2.2 hierarchy of types: 2.5.2 higher-order procedures: 1.3 Horner’s rule: 2.2.3 I imperative programming: 3.1.3 indeterminates: 2.5.3 index: 5.3.1 indexing: 4.4.2 instantiated with: 4.4.1 instruction counting: 5.2.4 instruction execution procedure: 5.2.1 instruction sequence: 5.5.1 instruction tracing: 5.2.4 instructions: Chapter 5 instructions: 5.1.1 integerizing factor: 2.5.3 integers: 1.1 integrator: 3.5.3 interning: 5.3.1 interpreter: Chapter 1 interpreter: Chapter 4 invariant quantity: 1.2.4 inverter: 3.3.4 iterative improvement: 1.3.4 iterative process: 1.2.1 K k-term: 1.3.3 key: 2.3.3 L labels: 5.1.1 lazy evaluation: 4.2.1 lexical address: 5.5.6 lexical addressing: 4.1.3 lexical scoping: 1.1.8 linear iterative process: 1.2.1 linear recursive process: 1.2.1 linkage descriptor: 5.5.1 list: 2.2.1 list: 2.2.1 list: 2.2.1 list structure: 2.2.1 list-structured: 2.1.1 list-structured memory: 5.3 local evolution: 1.2 local state variables: 3.1 location: 5.3.1 logic-programming: Chapter 4 logical and: 3.3.4 logical deductions: 4.4.1 logical or: 3.3.4 M machine language: 5.5 macro: 4.1.2 map: 2.2.3 mark-sweep: 5.3.2 memoization: 1.2.2 Memoization: 3.3.3 memoize: 4.2.2 merge: 3.5.5 message passing: 2.1.3 message passing: 2.4.3 message-passing: 3.1.1 metacircular: 4.1 Metalinguistic abstraction: Chapter 4 Miller-Rabin test: 1.2.6 modular: Chapter 3 modulo: 1.2.6 modulo: 1.2.6 modus ponens: 4.4.3 moments in time: 3.4 Monte Carlo integration: 3.1.2 Monte Carlo simulation: 3.1.2 mutable data objects: 3.3 mutators: 3.3 mutex: 3.4.2 mutual exclusion: 3.4.2 N n-fold smoothed function: 1.3.4 native language: 5.5 needed: 5.5.1 networks: Chapter 4 Newton’s method: 1.3.4 nil: 2.2.1 non-computable: 4.1.5 non-strict: 4.2.1 nondeterministic: 3.4.1 nondeterministic choice point: 4.3.1 nondeterministic computing: Chapter 4 nondeterministic computing: 4.3 normal-order: 4.2.1 normal-order evaluation: 1.1.5 normal-order evaluation: Chapter 4 O obarray: 5.3.1 object program: 5.5 objects: Chapter 3 open-code: 5.5.5 operands: 1.1.1 operator: 1.1.1 operator: 4.1.6 or-gate: 3.3.4 order of growth: 1.2.3 ordinary: 2.5.1 output prompt: 4.1.4 P package: 2.4.3 painter: 2.2.4 pair: 2.1.1 pair: 2.1.1 parse: 4.3.2 Pascal’s triangle: 1.2.2 pattern: 4.4.1 pattern matcher: 4.4.2 pattern matching: 4.4.2 pattern variable: 4.4.1 pipelining: 3.4 pointer: 2.2 poly: 2.5.3 power series: 3.5.2 predicate: 1.1.6 predicate: 1.1.6 prefix: 2.3.4 prefix code: 2.3.4 prefix notation: 1.1.1 pretty-printing: 1.1.1 primitive constraints: 3.3.5 probabilistic algorithms: 1.2.6 procedural abstraction: 1.1.8 procedural epistemology: Preface 1e procedure: 1.2.1 procedure definitions: 1.1.4 procedures: Chapter 1 process: 1.2.1 program: Chapter 1 programming languages: Chapter 1 prompt: 4.1.4 pseudo-random: 3.1.2 pseudodivision: 2.5.3 pseudoremainder: 2.5.3 Q quasiquote: 5.5.2 queries: 4.4 query language: 4.4 queue: 3.3.2 quote: 2.3.1 R Ramanujan numbers: 3.5.3 rational functions: 2.5.3 RC circuit: 3.5.3 read-eval-print loop: 1.1.1 reader macro characters: 4.4.4.7 real numbers: 1.1 rear: 3.3.2 recursion equations: Chapter 1 Recursion theory: 4.1.5 recursive: 1.1.3 recursive: 1.1.8 recursive process: 1.2.1 red-black trees: 2.3.3 referentially transparent: 3.1.3 register machine: Chapter 5 register table: 5.2.1 registers: Chapter 5 released: 3.4.2 remainder of: 1.2.6 resolution principle: 4.4 ripple-carry adder: 3.3.4 robust: 2.2.4 RSA algorithm: 1.2.6 rules: 4.4 rules: 4.4.1 S satisfy: 4.4.1 scope: 1.1.8 selectors: 2.1 semaphore: 3.4.2 separator code: 2.3.4 sequence: 2.2.1 sequence accelerator: 3.5.3 sequences: 1.3.1 serializer: 3.4.2 serializers: 3.4.2 series RLC circuit: 3.5.4 shadow: 3.2 shared: 3.3.1 side-effect bugs: 3.1.3 sieve of Eratosthenes: 3.5.2 smoothing: 1.3.4 source language: 5.5 source program: 5.5 sparse: 2.5.3 special forms: 1.1.3 stack: 1.2.1 stack: 5.1.4 state variables: 1.2.1 state variables: 3.1 statements: 5.5.1 stop-and-copy: 5.3.2 stratified design: 2.2.4 stream processing: 1.1.5 streams: Chapter 3 streams: 3.5 streams: 3.5 strict: 4.2.1 subroutine: 5.1.3 substitution: 1.1.5 substitution model: 1.1.5 subtype: 2.5.2 success continuation: 4.3.3 summation of a series: 1.3.1 summer: 3.5.3 supertype: 2.5.2 symbolic expressions: Chapter 2 syntactic sugar: 1.1.3 syntax: 4.1 systematically search: 4.3.1 systems: Chapter 4 T tableau: 3.5.3 tabulation: 1.2.2 tabulation: 3.3.3 tagged architectures: 5.3.1 tail-recursive: 1.2.1 tail-recursive: 5.4.2 target: 5.5.1 thrashing: UTF thunk: 4.2.2 thunks: 4.2.2 time: 3.4 time segments: 3.3.4 tower: 2.5.2 tree accumulation: 1.1.3 tree recursion: 1.2.2 trees: 2.2.2 truth maintenance: 4.3.1 Turing machine: 4.1.5 type field: 5.3.1 type tag: 2.4.2 type tags: 2.4 type-inferencing: 3.5.4 typed pointers: 5.3.1 U unbound: 3.2 unification: 4.4 unification: 4.4.2 unification: 4.4.2 unification algorithm: 4.4 univariate polynomials: 2.5.3 universal machine: 4.1.5 upward-compatible extension: 4.2.2 V value: 1.1.2 value of a variable: 3.2 values: 2.3.1 variable: 1.1.2 variable-length: 2.3.4 vector: 5.3.1 W width: 2.1.4 wires: 3.3.4 wishful thinking: 2.1.1 Z zero crossings: 3.5.3 Jump to: A B C D E F G H I K L M N O P Q R S T U V W Z Next: Colophon, Prev: Figures, Up: Top [Contents] Prev: Term Index, Up: Top [Contents] Colophon On the cover page is Agostino Ramelli’s bookwheel mechanism from 1588.

Structure and interpretation of computer programs by Harold Abelson, Gerald Jay Sussman, Julie Sussman

Andrew Wiles, conceptual framework, Donald Knuth, Douglas Hofstadter, Eratosthenes, Fermat's Last Theorem, functional programming, Gödel, Escher, Bach, higher-order functions, industrial robot, information retrieval, iterative process, Ivan Sutherland, Johannes Kepler, loose coupling, machine translation, Multics, probability theory / Blaise Pascal / Pierre de Fermat, Richard Stallman, Turing machine

Turing (1912-1954), whose 1936 paper laid the foundations for theoretical computer science. In the paper, Turing presented a simple computational model – now known as a Turing machine – and argued that any “effective process” can be formulated as a program for such a machine. (This argument is known as the Church-Turing thesis.) Turing then implemented a universal machine, i.e., a Turing machine that behaves as an evaluator for Turing-machine programs. He used this framework to demonstrate that there are well-posed problems that cannot be computed by Turing machines (see exercise 4.15), and so by implication cannot be formulated as “effective processes.” Turing went on to make fundamental contributions to practical computer science as well.

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Solver tower of types tracing instruction execution register assignment transform-painter transparency, referential transpose a matrix tree B-tree binary, see also binary tree combination viewed as counting leaves of enumerating leaves of fringe of Huffman lazy mapping over red-black represented as pairs reversing at all levels tree accumulation tree->list... tree-map tree-recursive process order of growth trigonometric relations true true true? truncation error truth maintenance try-again Turing machine Turing, Alan M., [2] Turner, David, [2], [3] type field type tag, [2] two-level type(s) cross-type operations dispatching on hierarchy in symbolic algebra hierarchy of lowering, [2] multiple subtype and supertype raising, [2] subtype supertype tower of type-inferencing mechanism type-tag using Scheme data types typed pointer typing input expressions unbound variable unev register unification discovery of algorithm implementation pattern matching vs., [2] unify-match union-set binary-tree representation ordered-list representation unordered-list representation unique (query language) unique-pairs unit square univariate polynomial universal machine explicit-control evaluator as general-purpose computer as University of California at Berkeley University of Edinburgh University of Marseille UNIX, [2] unknown-expression-type unknown-procedure-type unordered-list representation of sets unspecified values define display if without alternative newline set!

Concepts, Techniques, and Models of Computer Programming by Peter Van-Roy, Seif Haridi

computer age, Debian, discrete time, Donald Knuth, Eratosthenes, fault tolerance, functional programming, G4S, general-purpose programming language, George Santayana, John von Neumann, Lao Tzu, Menlo Park, natural language processing, NP-complete, Paul Graham, premature optimization, sorting algorithm, the Cathedral and the Bazaar, Therac-25, Turing complete, Turing machine, type inference

This is as expressive as a Turing machine.1 For example, table 2.1 defines a language at this level. See the introduction to chapter 6 for more on the relationship between the descriptive and programmable levels. There are two fundamentally different ways to view programmable declarativeness: A definitional view, where declarativeness is a property of the component implementation. For example, programs written in the declarative model are guaranteed to be declarative, because of properties of the model. An observational view, where declarativeness is a property of the component in- 1. A Turing machine is a simple formal model of computation, first defined by Alan Turing, that is as powerful as any computer that can be built, as far as is known in the current state of computer science.

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Figure 2.5 shows the three ways that the translation approach has been used for defining programming languages: 2.1 Defining practical programming languages 41 Programming language Translations Kernel language Foundational calculus Abstract machine Aid the programmer in reasoning and understanding Mathematical study of programming Efficient execution on a real machine Figure 2.5: Translation approaches to language semantics. The kernel language approach, used throughout the book, is intended for the programmer. Its concepts correspond directly to programming concepts. The foundational approach is intended for the mathematician. Examples are the Turing machine, the λ calculus (underlying functional programming), first-order logic (underlying logic programming), and the π calculus (to model concurrency). Because these calculi are intended for formal mathematical study, they have as few elements as possible. The abstract machine approach is intended for the implementor.

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A Turing machine is a simple formal model of computation, first defined by Alan Turing, that is as powerful as any computer that can be built, as far as is known in the current state of computer science. That is, any computation that can be programmed on any computer can also be programmed on a Turing machine. 116 Declarative Programming Techniques terface. The observational view follows the principle of abstraction: that to use a component it is enough to know its specification without knowing its implementation. The component just has to behave declaratively, i.e., as if it were independent, stateless, and deterministic, without necessarily being written in a declarative computation model.

2312 by Kim Stanley Robinson

agricultural Revolution, Anthropocene, caloric restriction, caloric restriction, clean tech, double helix, full employment, higher-order functions, hive mind, if you see hoof prints, think horses—not zebras, Jevons paradox, Kim Stanley Robinson, Kuiper Belt, late capitalism, Late Heavy Bombardment, mutually assured destruction, Nelson Mandela, Neolithic agricultural revolution, off-the-grid, offshore financial centre, orbital mechanics / astrodynamics, pattern recognition, phenotype, post scarcity, precariat, quantum entanglement, retrograde motion, rewilding, Skinner box, stem cell, strong AI, synthetic biology, the built environment, the High Line, Tragedy of the Commons, Turing machine, Turing test, Winter of Discontent

Extracts (9) One question for computability: is the problem capable of producing a result If a finite number of steps will produce an answer, it is a problem that can be solved by a Turing machine Is the universe itself the equivalent of a Turing machine? This is not yet clear Turing machines can’t always tell when the result has been obtained. No oracle machine is capable of solving its own halting problem A Turing jump operator assigns to each problem X a successively harder problem, X prime. Setting a Turing machine the problem of making its own Turing jump creates a recursive effect called the Ouroboros All problems solvable by quantum computers are also solvable by classical computers.

Wireless by Charles Stross

air gap, anthropic principle, back-to-the-land, Benoit Mandelbrot, Buckminster Fuller, Cepheid variable, cognitive dissonance, colonial exploitation, cosmic microwave background, Easter island, epigenetics, finite state, Georg Cantor, gravity well, hive mind, hydroponic farming, jitney, Khyber Pass, Late Heavy Bombardment, launch on warning, lifelogging, Magellanic Cloud, mandelbrot fractal, MITM: man-in-the-middle, Neil Armstrong, peak oil, phenotype, Pluto: dwarf planet, security theater, sensible shoes, Turing machine, undersea cable

Okay, you’re a research cell working on some ultimate black problem, and you’re using the Farm because it’s about the most secure environment anyone can imagine, and you’re emulating some kind of minimal universal Turing machine using the chessboard. Say, a 2,5 UTM—two registers, five operations—you can encode the registers positionally in the chessboard’s two dimensions, and use the moves to simulate any other universal Turing machine, or a transform in an eleven-dimensional manifold like AXIOM REFUGE—” Godel’s waving frantically. “She’s coming! She’s coming!” I hear doors clanging in the distance. Shit. “But why are you so afraid of the Nurses?”

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“Or even”—Mandelbrot takes a deep breath—“a brains trust!” “A-ha! AhaHAHAHA! Hic.” Godel covers his mouth, face reddening. “What do you think the rules are?” Cantor repeats, and they’re still staring at me, as if, as if . . . “Why does it matter?” I ask. I’m thinking that it could be anything; a 2,5 universal Turing machine encoded in the moves of the pawns—that would fit—whatever it is, it’s symbolic communication, very abstract, very pared-back, and if they’re doing it in this ultimately firewalled environment and expecting to report directly to the Board, it’s got to be way above my security clearance— “Because you’re acting cagey, lad.

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, Big Tech, British Empire, business process, Californian Ideology, Charles Babbage, 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, Hacker News, haute couture, hype cycle, 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, synthetic biology, tech worker, the Cathedral and the Bazaar, theory of mind, Therac-25, Turing machine, wikimedia commons, women in the workforce

Correctness is guaranteed by the correct application of rules.13 The systematic, deterministic workings of these rules may remind you of the orderly on-and-off workings of logic gates. The Ashtadhyayi is, of course, an algorithm, a machine that consumes phonemes and morphemes and produces words and sentences. Panini’s machine—which is sometimes compared to the Turing machine—is also the first known instance of the application of algorithmic thinking to a domain outside of logic and mathematics. The influence of the Ashtadhyayi was and remains immense. In the Sanskrit ecumene, later grammarians suggested some additions and modifications, and other grammars were written before and after Panini’s intervention, but all have been overshadowed by this one “tersest and yet most complete grammar of any language.”14 The West discovered the Ashtadhyayi during the great flowering of Orientalist research and translation in the eighteenth and nineteenth centuries.

…

“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. New York: Oxford University Press, 2001. ______. The Power of Tantra: Religion, Sexuality and the Politics of South Asian Studies. London: IB Tauris, 2009.

The Ethical Algorithm: The Science of Socially Aware Algorithm Design by Michael Kearns, Aaron Roth

23andMe, affirmative action, algorithmic bias, algorithmic trading, Alignment Problem, Alvin Roth, backpropagation, Bayesian statistics, bitcoin, cloud computing, computer vision, crowdsourcing, data science, deep learning, DeepMind, Dr. Strangelove, Edward Snowden, Elon Musk, fake news, Filter Bubble, general-purpose programming language, Geoffrey Hinton, Google Chrome, ImageNet competition, Lyft, medical residency, Nash equilibrium, Netflix Prize, p-value, Pareto efficiency, performance metric, personalized medicine, pre–internet, profit motive, quantitative trading / quantitative finance, RAND corporation, recommendation engine, replication crisis, ride hailing / ride sharing, Robert Bork, Ronald Coase, self-driving car, short selling, sorting algorithm, sparse data, speech recognition, statistical model, Stephen Hawking, superintelligent machines, TED Talk, telemarketer, Turing machine, two-sided market, Vilfredo Pareto

We deliberately say “computation” and not “computers,” because for the purposes of this book (and perhaps even generally), the most important thing to know about theoretical computer science is that it views computation as a ubiquitous phenomenon, not one that is limited to technological artifacts. The scientific justification for this view originates with the staggeringly influential work of Alan Turing (the first theoretical computer scientist) in the 1930s, who demonstrated the universality of computational principles with his mathematical model now known as the Turing machine. Many trained in theoretical computer science, ourselves included, view the field and its tools not simply as another scientific discipline but as a way of seeing and understanding the world around us—perhaps much as those trained in theoretical physics in an earlier era saw their own field. So a theoretical computer scientist sees computation taking place everywhere—certainly in computers, but also in nature (in genetics, evolution, quantum mechanics, and neuroscience), in society (in markets and other systems of collective behavior), and beyond.

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See also gender data and bias sexual orientation data, 25–26, 51–52, 86–89 Shapley, Lloyd, 129–30 The Shining (King), 118, 120 Shmatikov, Vitaly, 25 Simmons, Joe, 157–58 simple algorithms, 174 simulated game play, 134–35 single nucleotide polymorphisms (SNPs), 30–31 singularity, 180 Smith, Adam, 36 smoking, 27–28, 34–36, 39, 51–54 Snowden, Edward, 47–48 social awareness, 16–17, 131 social welfare, 97, 113, 115 societal norms and values, 12, 15–18, 20–21, 86, 134, 169–70 socioeconomic groups, 57 software engineers, 48–49 sorting algorithms, 4–5 spurious correlations, 150, 159 stable equilibriums, 99–100, 128 stable matchings, 128–30 standoffs, 98 statistics and adaptive data analysis, 159 and aggregate data, 22–23, 30–31 and algorithmic violations of fairness and privacy, 96 Bayesian, 38–39, 173 and the Bonferroni correction, 149 criminal sentencing, 14–15 and differential privacy, 40, 44–45, 47–52, 167 and fairness issues, 193–94 flawed statistical reasoning, 140–41 and interpretability of model outputs, 171–72 and investing scams, 138–41 and medical research, 34 and online shopping algorithms, 117 and p-hacking, 144–45, 153–55, 157–59, 161, 164, 169–70 statistical modeling, 90 statistical parity, 69–74, 84 and US Census data, 195 and “word embedding” models, 57–58, 63–64 stock investing, 81, 137–41 strategy, 97–102 Strava, 50–51 subgroup protections, 88–89 subjectivity, 86, 172 subpoenas, 41, 45–46, 48 “superfood” research, 143–44 superintelligent AI, 179–81, 185, 187 supervised machine learning, 63–64, 69–70, 183 supply and demand, 94–97 Supreme Court nomination hearings, 24 survey responses, 40–45 Sweeney, Latanya, 23 synthetic images, 132–35 target populations, 172–73 TD-Gammon program, 132 technological advances, 100–101, 103 TED Talks, 141–42 telemarketing calls, 38 temporal difference, 132 Tesauro, Gerry, 132 test preparation courses, 74–75 theoretical computer science, 11–13, 36 threshold rule, 75 Title VII, 15 tobacco research, 34–36 torturing data, 156–59 traffic and navigation problems, 19–20, 101–11, 113–15, 179 training data, 61–62 transparency, 125–26, 170–71 trust, 45–47, 170–71, 194–95 “truthfulness” in game theory, 114 “tunable” parameters, 37–39, 125–26, 171 Turing, Alan, 11–12, 180 Turing Award, 133 Turing machine, 11 23andMe, 54–55 2020 Census, 49, 195 Twitter Predictor Game, 52–53 two-route navigation problem, 107 two-sided markets, 127 2001: A Space Odyssey (film), 184 typing, 118 underspecified problems, 183 unintended consequences, 6–8, 16–17, 184–85, 188 unique data points, 26–27 unsupervised learning, 63–64 upstream effects, 194 US Census Bureau, 49 US Constitution, 49 US Equal Employment Opportunity Commission, 86–87 user identifiers, 24 user modeling, 121 user ratings, 118–21 US military deployments, 50–51 US State Department, 15 validation sets, 162–63 value alignment problems, 184 values.

Prime Obsession:: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire

Albert Einstein, Andrew Wiles, Bletchley Park, Charles Babbage, Colonization of Mars, Eratosthenes, Ernest Rutherford, four colour theorem, Georg Cantor, Henri Poincaré, Isaac Newton, John Conway, John von Neumann, Paul Erdős, Richard Feynman, Turing machine, Turing test

Andrew has also computed the CLIMBING THE CRITICAL LINE 261 first 100 zeros to 1,000 decimal places each.93 The first zero (I mean, of course, its imaginary part) begins 14.13472514173469379045725198356247027078425711569924 31756855674601499634298092567649490103931715610127 79202971548797436766142691469882254582505363239447 13778041338123720597054962195586586020055556672583 601077370020541098266150754278051744259130625448… V. There are stories behind Table 16-1. That A.M. Turing, for example, is the very same Alan Turing who worked in mathematical logic, developing the idea of the Turing Test (a way of deciding whether a computer or its program is intelligent), and of the Turing machine (a very general, theoretical type of computer, a thought experiment used to tackle certain problems in mathematical logic). There is a Turing Prize for achievement in computer science, awarded annually since 1966 by the Association for Computing Machinery, equivalent to a Fields Medal94 in mathematics, or to a Nobel Prize in other sciences.

…

Hilbert’s “metamathematics” program tried to encompass both logic and mathematics in a more waterproof symbolism. This inspired the work of Kurt Gödel and Alan Turing. Gödel proved important theorems by attaching numbers to Hilbert-type symbols; Turing coded both instructions and data as arbitrary numbers in his “Turing machine” concept. Picking up on this idea, John von Neumann developed the stored-program concept on which all modern software is based, that code and data can be represented in the same way in a computer’s memory…. EPILOGUE 138. In a letter to his brother dated June 26, 1854, he mentioned a recurrence of mein altes Übel—“my old malady”—brought on by a spell of bad weather. 139.

…

., 373 Steiner, Jakob, 119 Step functions, 124, 297-302 Stern, Moritz, 27 Stevens, Wallace, 198 Stieltjes integral, 160 Stieltjes, Thomas, 154, 160, 161, 376 Stirling, James, 123 Strachey, Lytton, 370, 380 Summation sign (Σ), 78 “Sweet Betsy from Pike” (tune), 394, 395 Sylvester, James Joseph, 154, 225 T “Taiye,” 82-83; pl. 8 Teichmüller, Oswald, 255-256, 383 Teichmüller Theory, 383 Telegraph, electric, 120 Tenenbaum, Gérald, 389 Theory of Numbers (Hardy and Wright), 302 Theory of performances, 52 Theory of the Riemann Zeta-function, The (Titchmarsh), 217, 384 Thread, The (Davis), 122 Three-body problem, 314 Time reversal symmetry, 316 Titchmarsh, Edward Charles, 217, 258, 262, 394 Tocqueville, Alexis de, 118 Topology, 18, 121, 209, 374 Trace formula, 321, 388 Transcendental numbers, 174, 185, 354 Trigonometry, 18 Trinity College, Cambridge, 193, 223224, 225-226, 229, 287, 379, 380 Trinity Hall, Cambridge, 380 Truman, Harry S., 166 Turán, Paul, 238, 239, 378 Turing, Alan, 258, 261-262, 357, 377, 391; pl. 5 Turing machine, 261, 391 Turing Prize, 261 Turing Test, 261 Twiddle principle, 46 Twiddle sign, 45, 368 U Uncle Petros and Goldbach’s Conjecture (Doxiadis), 90 Universal Computer, The (Davis), 187 Universities, academies distinguished from, 30 University of Bordeaux, 158-159 University of Breslau, 93, 94 University of Bristol, England, 390 University of Cambridge, 259 University of Copenhagen, 228 INDEX 421 University of Leipzig, 270 University of Louvain, 161 University of Manchester, 259 University of Marburg, 270 University of Minnesota, 322, 357 University of Wales, Cardiff, 391 University of Washington in Seattle, 352 Upper bound, 235-236 Wilhelm I, German Kaiser, 160 William IV, King of England and Hanover, 26 Wolfram, Stephen, 389 Wright, Sir Edward, 302 V Z Vallée Poussin, Charles de la, x, 153, 155-156, 161, 189, 223, 232, 237, 352, 356, 376; pl. 3 Value plane, 219-221, 335 Victoria, Queen of England, 26 Vienna Academy, 153 “Villikens and his Dinah” (song), 395 Vis viva equation, 313, 315 Volterra, Vito, 92 Vorhauer, Ulrike, 350, 390 z plane, 379 Zeno, 88 Zeros, 85 in conjugate pairs, 190-191 density of, 396 dividing by, 35 of a function, 139, 154, 160, 169, 190-192, 206, 211-212, 385 gradient, 110 mathematical legitimacy, 89 non-trivial, 77, 190-192, 198-199, 217, 221-222, 232, 289-290, 295 number of, 258 order of a, 385 of a polynomial, 173 power, 65, 66 spacing in critical strip, 217-218, 232, 290 trivial, 148, 169, 206 Zeta function, 135 Basel problem and, 63-65 on complex plane, 183, 213-216 critical line, 221-222 critical strip, 216 decomposition, 358 domain, 142-145, 205-206 expression, 77, 79, 137 graph, 142-144 Mertens’s function and, 250-251 Möbius function and, 250-251 W w plane, 379 Wagon, Stan, 389 Wallace, William, 92 Wave functions, 318 Weber, Heinrich, 29, 119, 257, 366 Weber, Wilhelm, 27, 120, 127, 374 Wedeniwski, Sebastian, 258, 259 Weierstrass, Karl, 135, 164 Weil, André, 270, 325, 385, 395; pl. 6 Weil Conjectures, 270, 355 Wendland, 22, 94 Weyl, Hermann, 170, 255, 385 Whitehead, Alfred North, 225 Whitemore, Hugh, 262 Wigner, Eugene, 282, 387 Wild Numbers, The (Schogt), 161 Wiles, Andrew, 90, 161, 245, 271, 354355 Y Yorke, James, 387 422 sieve of Eratosthenes and, 102-104, 138 values of, 79-81, 146-147, 263 visualization, 216-218 zeros of, 154, 160, 169, 190-192, 206, 211-212, 217-218, 221-222, 232-233, 234, 259-261, 287-288, 295, 395 INDEX ζ(s), 77.

Power and Progress: Our Thousand-Year Struggle Over Technology and Prosperity by Daron Acemoglu, Simon Johnson

"Friedman doctrine" OR "shareholder theory", "World Economic Forum" Davos, 4chan, agricultural Revolution, AI winter, Airbnb, airline deregulation, algorithmic bias, algorithmic management, Alignment Problem, AlphaGo, An Inconvenient Truth, artificial general intelligence, augmented reality, basic income, Bellingcat, Bernie Sanders, Big Tech, Bletchley Park, blue-collar work, British Empire, carbon footprint, carbon tax, carried interest, centre right, Charles Babbage, ChatGPT, Clayton Christensen, clean water, cloud computing, collapse of Lehman Brothers, collective bargaining, computer age, Computer Lib, Computing Machinery and Intelligence, conceptual framework, contact tracing, Corn Laws, Cornelius Vanderbilt, coronavirus, corporate social responsibility, correlation does not imply causation, cotton gin, COVID-19, creative destruction, declining real wages, deep learning, DeepMind, deindustrialization, Demis Hassabis, Deng Xiaoping, deskilling, discovery of the americas, disinformation, Donald Trump, Douglas Engelbart, Douglas Engelbart, Edward Snowden, Elon Musk, en.wikipedia.org, energy transition, Erik Brynjolfsson, European colonialism, everywhere but in the productivity statistics, factory automation, facts on the ground, fake news, Filter Bubble, financial innovation, Ford Model T, Ford paid five dollars a day, fulfillment center, full employment, future of work, gender pay gap, general purpose technology, Geoffrey Hinton, global supply chain, Gordon Gekko, GPT-3, Grace Hopper, Hacker Ethic, Ida Tarbell, illegal immigration, income inequality, indoor plumbing, industrial robot, interchangeable parts, invisible hand, Isaac Newton, Jacques de Vaucanson, James Watt: steam engine, Jaron Lanier, Jeff Bezos, job automation, Johannes Kepler, John Markoff, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, Joseph-Marie Jacquard, Kenneth Arrow, Kevin Roose, Kickstarter, knowledge economy, labor-force participation, land reform, land tenure, Les Trente Glorieuses, low skilled workers, low-wage service sector, M-Pesa, manufacturing employment, Marc Andreessen, Mark Zuckerberg, megacity, mobile money, Mother of all demos, move fast and break things, natural language processing, Neolithic agricultural revolution, Norbert Wiener, NSO Group, offshore financial centre, OpenAI, PageRank, Panopticon Jeremy Bentham, paperclip maximiser, pattern recognition, Paul Graham, Peter Thiel, Productivity paradox, profit maximization, profit motive, QAnon, Ralph Nader, Ray Kurzweil, recommendation engine, ride hailing / ride sharing, Robert Bork, Robert Gordon, Robert Solow, robotic process automation, Ronald Reagan, scientific management, Second Machine Age, self-driving car, seminal paper, shareholder value, Sheryl Sandberg, Shoshana Zuboff, Silicon Valley, social intelligence, Social Responsibility of Business Is to Increase Its Profits, social web, South Sea Bubble, speech recognition, spice trade, statistical model, stem cell, Steve Jobs, Steve Wozniak, strikebreaker, subscription business, Suez canal 1869, Suez crisis 1956, supply-chain management, surveillance capitalism, tacit knowledge, tech billionaire, technoutopianism, Ted Nelson, TED Talk, The Future of Employment, The Rise and Fall of American Growth, The Structural Transformation of the Public Sphere, The Wealth of Nations by Adam Smith, theory of mind, Thomas Malthus, too big to fail, total factor productivity, trade route, transatlantic slave trade, trickle-down economics, Turing machine, Turing test, Twitter Arab Spring, Two Sigma, Tyler Cowen, Tyler Cowen: Great Stagnation, union organizing, universal basic income, Unsafe at Any Speed, Upton Sinclair, upwardly mobile, W. E. B. Du Bois, War on Poverty, WikiLeaks, wikimedia commons, working poor, working-age population

He imagined an abstract computer, now called a Turing machine, that can carry out computations according to the inputs specified on a possibly infinite tape—for example, instructions to implement basic mathematical operations. He then defined a function to be computable if such a machine could compute its values. A machine is said to be a universal Turing machine if it can compute any number that can be calculated by any Turing machine. Notably, if the human mind is in essence a very sophisticated computer and the tasks that it performs are within the class of computable functions, then a universal Turing machine could replicate all human capabilities.

Thinking Machines: The Inside Story of Artificial Intelligence and Our Race to Build the Future by Luke Dormehl

"World Economic Forum" Davos, Ada Lovelace, agricultural Revolution, AI winter, Albert Einstein, Alexey Pajitnov wrote Tetris, algorithmic management, algorithmic trading, AlphaGo, Amazon Mechanical Turk, Apple II, artificial general intelligence, Automated Insights, autonomous vehicles, backpropagation, Bletchley Park, book scanning, borderless world, call centre, cellular automata, Charles Babbage, Claude Shannon: information theory, cloud computing, computer vision, Computing Machinery and Intelligence, correlation does not imply causation, crowdsourcing, deep learning, DeepMind, driverless car, drone strike, Elon Musk, Flash crash, Ford Model T, friendly AI, game design, Geoffrey Hinton, global village, Google X / Alphabet X, Hans Moravec, hive mind, industrial robot, information retrieval, Internet of things, iterative process, Jaron Lanier, John Markoff, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kickstarter, Kodak vs Instagram, Law of Accelerating Returns, life extension, Loebner Prize, machine translation, Marc Andreessen, Mark Zuckerberg, Menlo Park, Mustafa Suleyman, natural language processing, Nick Bostrom, Norbert Wiener, out of africa, PageRank, paperclip maximiser, pattern recognition, radical life extension, Ray Kurzweil, recommendation engine, remote working, RFID, scientific management, self-driving car, Silicon Valley, Skype, smart cities, Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia, social intelligence, speech recognition, Stephen Hawking, Steve Jobs, Steve Wozniak, Steven Pinker, strong AI, superintelligent machines, tech billionaire, technological singularity, The Coming Technological Singularity, The Future of Employment, Tim Cook: Apple, Tony Fadell, too big to fail, traumatic brain injury, Turing machine, Turing test, Vernor Vinge, warehouse robotics, Watson beat the top human players on Jeopardy!

It has been likened to a steam engine. But that was before we knew as much about the way it works as we know now. It really is a gas engine: like the engine of an automobile, a motor boat, or a flying machine. One of Turing’s most significant concepts related to something called the Universal Turing Machine. Instead of computers being single-purpose machines used for just one function, he explained how they could be made to perform a variety of tasks by reading step-by-step instructions from a tape. By doing so, Turing wrote that the computer ‘could in fact be made to work as a model of any other machine’.

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(TV show) 135–9, 162, 189–90, 225, 254 Jobs, Steve 6–7, 32, 35, 108, 113, 181, 193, 231 Jochem, Todd 55–6 judges 153–4 Kasparov, Garry 137, 138–9, 177 Katz, Lawrence 159–60 Keck, George Fred 81–2 Keynes, John Maynard 139–40 Kjellberg, Felix (PewDiePie) 151 ‘knowledge engineers’ 29, 37 Knowledge Narrator 110–11 Kodak 238 Kolibree 67 Koza, John 188–9 Ktesibios of Alexandria 71–2 Kubrick, Stanley 2, 228 Kurzweil, Ray 213–14, 231–3 Landauer, Thomas 201–2 Lanier, Jaron 156, 157 Laorden, Carlos 100, 101 learning 37–9, 41–4, 52–3, 55 Deep 11–2, 56–63, 96–7, 164, 225 and email filters 88 machine 3, 71, 84–6, 88, 100, 112, 154, 158, 197, 215, 233, 237, 239 reinforcement 83, 232 and smart homes 84, 85 supervised 57 unsupervised 57–8 legal profession 145, 188, 192 LegalZoom 145 LG 132 Lickel, Charles 136–7 ‘life logging’ software 200 Linden, David J. 213–14 Loebner, Hugh 102–3, 105 Loebner Prize 102–5 Lohn, Jason 182, 183–5, 186 long-term potentiation 39–40 love 122–4 Lovelace, Ada 185, 189 Lovelace Test 185–6 Lucas, George 110–11 M2M communication 70–71 ‘M’ (AI assistant) 153 Machine Intelligence from Cortical Networks (MICrONS) project 214–15 machine learners 38 machine learning 3, 71, 84–6, 88, 100, 112, 154, 158, 197, 215, 233, 237, 239 Machine Translator 8–9, 11 ‘machine-aided recognition’ 19–20 Manhattan Project 14, 229 MARK 1 (computer) 43–4 Mattersight Corporation 127 McCarthy, John 18, 19, 20, 27, 42, 54, 253 McCulloch, Warren 40–2, 43, 60, 142–3 Mechanical Turk jobs 152–7 medicine 11, 30, 87–8, 92–5, 187–8, 192, 247, 254 memory 13, 14, 16, 38–9, 42, 49 ‘micro-worlds’ 25 Microsoft 62–3, 106–7, 111–12, 114, 118, 129 mind mapping the 210–14, 217, 218 ‘mind clones’ 203 uploads 221 mindfiles 201–2, 207, 212 Minsky, Marvin 18, 21, 24, 32, 42, 44–6, 49, 105, 205–7, 253–4 MIT 19–20, 27, 96–7, 129, 194–5 Mitsuku (chatterbot) 103–6, 108 Modernising Medicine 11 Momentum Machines, Inc. 141 Moore’s Law 209, 220, 231 Moravec’s paradox 26–7 mortgage applications 237–8 MTurk platform 153, 154, 155 music 168, 172–7, 179 Musk, Elon 149–50, 223–4 MYCIN (expert system) 30–1 nanobots 213–14 nanosensors 92 Nara Logics 118 NASA 6, 182, 184–5 natural selection 182–3 navigational aids 90–1, 126, 127, 128, 241 Nazis 15, 17, 227 Negobot 99–102 Nest Labs 67, 96, 254 Netflix 156, 198 NETtalk 51, 52–3, 60 neural networks 11–12, 38–9, 41, 42–3, 97, 118, 164–6, 168, 201, 208–9, 211, 214–15, 218, 220, 224–5, 233, 237–8, 249, 254, 256–7 neurons 40, 41–2, 46, 49–50, 207, 209–13, 216 neuroscience 40–2, 211, 212, 214, 215 New York World’s Fair 1964 5–11 Newell, Alan 19, 226 Newman, Judith 128–9 Nuance Communications 109 offices, smart 90 OpenWorm 210 ‘Optical Scanning and Information Retrieval’ 7–8, 10 paedophile detection 99–102 Page, Larry 6–7, 34, 220 ‘paperclip maximiser’ scenario 235 Papert, Seymour 27, 44, 45–6, 49 Paro (therapeutic robot) 130–1 patents 188–9 Perceiving and Recognising Automation (PARA) 43 perceptrons 43–6 personality capture 200–4 pharmaceuticals 187–8 Pitts, Walter 40–2, 43, 60 politics 119–2 Pomerlau, Dean 54, 55–6, 90 prediction 87, 198–9 Profound Hypothermia and Circulatory Arrest 219–20 punch-cards 8 Qualcomm 93 radio-frequency identification device (RFID) 65–6 Ramón y Cajal, Santiago 39–40 Rapidly Adapting Lateral Position Handler (RALPH) 55 ‘recommender system’ 198 refuse collection 142 ‘relational agents’ 130 remote working 238–9 reverse engineering 208, 216, 217 rights for AIs 248–51 risks of AI 223–40 accountability issues 240–4, 246–8 ethics 244–8 rights for AIs 248–51 technological unemployment 139–50, 163, 225, 255 robots 62, 74–7, 89–90, 130–1, 141, 149, 162, 217, 225, 227, 246–7, 255–6 Asimov’s three ethical rules of 244–8 robotic limbs 211–12 Roomba robot vacuum cleaner 75–7, 234, 236 Rosenblatt, Frank 42–6, 61, 220 rules 36–7, 79–80 Rumelhart, David 48, 50–1, 63 Russell, Bertrand 41 Rutter, Brad 138, 139 SAINT program 20 sampling (music) 155, 157 ‘Scheherazade’ (Ai storyteller) 169–70 scikit-learn 239 Scripps Health 92 Sculley, John 110–11 search engines 109–10 Searle, John 24–5 Second Life (video game) 194 Second World War 12–13, 14–15, 17, 72, 227 Sejnowski, Terry 48, 51–3 self-awareness 77, 246–7 self-driving 53–6, 90, 143, 149–50 Semantic Information Retrieval (SIR) 20–2 sensors 75–6, 80, 84–6, 93 SHAKEY robot 23–4, 27–8, 90 Shamir, Lior 172–7, 179, 180 Shannon, Claude 13, 16–18, 28, 253 shipping systems 198 Simon, Herbert 10, 19, 24, 226 Sinclair Oil Corporation 6 Singularity, the 228–3, 251, 256 Siri (AI assistant) 108–11, 113–14, 116, 118–19, 125–30, 132, 225–6, 231, 241, 256 SITU 69, 93 Skynet 231 smart devices 3, 66–7, 69–71, 73–7, 80–8, 92–7, 230–1, 254 and AI assistants 116 and feedback 73–4 problems with 94–7 ubiquitous 92–4 and unemployment 141–2 smartwatches 66, 93, 199 Sony 199–200 Sorto, Erik 211, 212 Space Invaders (video game) 37 spectrometers 93 speech recognition 59, 62, 109, 111, 114, 120 SRI International 28, 89–90, 112–13 StarCraft II (video game) 186–7 story generation 169–70 strategy 36 STUDENT program 20 synapses 209 Synthetic Interview 202–3 Tamagotchis 123–5 Tay (chatbot) 106–7 Taylorism 95–6 Teknowledge 32, 33 Terminator franchise 231, 235 Tetris (video game) 28 Theme Park (video game) 29 thermostats 73, 79, 80 ‘three wise men’ puzzle 246–7 Tojan Room, Cambridge University 69–70 ‘tortoises’ (robots) 74–7 toys 123–5 traffic congestion 90–1 transhumanists 205 transistors 16–17 Transits – Into an abyss (musical composition) 168 translation 8–9, 11, 62–3, 155, 225 Turing, Alan 3, 13–17, 28, 35, 102, 105–6, 227, 232 Turing Test 15, 101–7, 229, 232 tutors, remote 160–1 TV, smart 80, 82 Twitter 153–4 ‘ubiquitous computing’ 91–4 unemployment, technological 139–50, 163, 225, 255 universal micropayment system 156 Universal Turing Machine 15–16 Ursache, Marius 193–7, 203–4, 207 vacuum cleaners, robotic 75–7, 234, 236 video games 28–9, 35–7, 151–2, 186–7, 194, 197 Vinge, Vernor 229–30 virtual assistants 107–32, 225–6, 240–1 characteristics 126–8 falling in love with 122–4 political 119–22 proactive 116–18 therapeutic 128–31 voices 124–126, 127–8 Viv Labs 132 Vladeck, David 242–4 ‘vloggers’ 151–2 von Neumann, John 13–14, 17, 100, 229 Voxta (AI assistant) 119–20 waiter drones 141 ‘Walking Cities’ 89–90 Walter, William Grey 74–7 Warwick, Kevin 65–6 Watson (Blue J) 138–9, 162, 189–92 Waze 90–91, 126 weapons 14, 17, 72, 224–5, 234–5, 247, 255–6 ‘wetware’ 208 Wevorce 145 Wiener, Norbert 72–3, 227 Winston, Patrick 49–50 Wofram Alpha tool 108–9 Wozniak, Steve 35, 114 X.ai 116–17 Xbox 360, Kinect device 114 XCoffee 70 XCON (expert system) 31 Xiaoice 129, 130 YouTube 151 Yudkowsky, Eliezer 237–8 Zuckerberg, Mark 7, 107–8, 230–1, 254–5 Acknowledgments WRITING A BOOK is always a bit of a solitary process.

Nine Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's Computers by John MacCormick, Chris Bishop

Ada Lovelace, AltaVista, Charles Babbage, Claude Shannon: information theory, Computing Machinery and Intelligence, fault tolerance, information retrieval, Menlo Park, PageRank, pattern recognition, Richard Feynman, Silicon Valley, Simon Singh, sorting algorithm, speech recognition, Stephen Hawking, Steve Jobs, Steve Wozniak, traveling salesman, Turing machine, Turing test, Vannevar Bush

But to assist his argument, Turing describes a particular type of machine (for Turing, a “machine” is what we would call a “computer” today) that can also do calculations. Part of the paper is devoted to demonstrating that certain calculations cannot be performed by these machines—this is the proof of undecidability, which we have discussed in detail already. But another part of the same paper makes a detailed and compelling argument that Turing's “machine” (read: computer) can perform any calculation done by a “computer” (read: human). You may be beginning to appreciate why it is difficult to overstate the seminal nature of Turing's “On computable numbers.” paper. It not only defines and solves some of the most fundamental problems in computer science, but also strikes out into the heart of a philosophical minefield, making a persuasive case that human thought processes could be emulated by computers (which, remember, had not been invented yet!).

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threshold; soft title: of this book; of a web page to-do list to-do list trick Tom Sawyer training. See also learning training data transaction: abort; atomic; in a database; on the internet; rollback travel agent Traveling Salesman Problem trick, definition of TroubleMaker.exe Turing, Alan Turing machine Turing test TV Twain, Mark twenty questions, game of twenty-questions trick two-dimensional parity. See parity two-phase commit U.S. Civil War Ullman, Jeffrey D. uncomputable. See also undecidable undecidable. See also uncomputable undefined unicycle universe unlabeled Vazirani, Umesh verification Verisign video video game virtual table virtual table trick Waters, Alice web.

Purely Functional Data Structures by Chris Okasaki

Donald Knuth, Ford Model T, functional programming, higher-order functions, reversible computing, Turing machine, type inference

It has since been used in many situations, including real-time queues [HM81], realtime deques [Hoo82, GT86, Sar86, CG93], catenable deques [BT95], and the order maintenance problem [DS87]. Deques Hood [Hoo82] first modified the real-time queues of [HM81] to obtain real-time deques based on global rebuilding. Several other researchers later duplicated this work [GT86, Sar86, CG93]. These implementations are all similar to techniques used to simulate multihead Turing machines [Sto70, FMR72, LS81]. Hoogerwoord [Hoo92] proposed amortized deques based on batched rebuilding, but, as always with batched rebuilding, his implementation is not efficient when used persistently. The real-time deques in Figure 8.4 first appeared in [Oka95c]. Coroutines and Lazy Evaluation Streams (and other lazy data structures) have frequently been used to implement a form of coroutining between the producer of a stream and the consumer of a stream.

…

Computer response time and user performance. In Conference on Human Factors in Computing Systems, pages 5862, December 1983. (p. 83) Richard S. Bird and Philip Wadler. Introduction to Functional Programming. Prentice Hall International, 1988. (p. 29) Tyng-Ruey Chuang and Benjamin Goldberg. Real-time deques, multihead Turing machines, and purely functional programming. In Conference on Functional Programming Languages and Computer Architecture, pages 289-298, June 1993. (pp. 109,113) Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to algorithms. MIT Press, 1990. (p. 27) Richard H. Connelly and F.

The Best of Best New SF by Gardner R. Dozois

back-to-the-land, Buckminster Fuller, Burning Man, call centre, Columbine, congestion charging, dark matter, Doomsday Book, double helix, Extropian, flag carrier, Future Shock, gravity well, hydroponic farming, Kim Stanley Robinson, language acquisition, lateral thinking, Mason jar, military-industrial complex, offshore financial centre, out of africa, pattern recognition, phenotype, pneumatic tube, Silicon Valley, slashdot, Stephen Hawking, telepresence, three-masted sailing ship, Turing machine, Turing test, Winter of Discontent, Y2K, zero-sum game

Think of a row of Wang Tiles as being like the data tape of a Turing Machine.” Paolo had the library grant him knowledge of the term; it was the original conceptual form of a generalized computing device, an imaginary machine which moved back and forth along a limitless one-dimensional data tape, reading and writing symbols according to a given set of rules. “With the right set of tiles, to force the right pattern, the next row of the tiling will look like the data tape after the Turing Machine has performed one step of its computation. And the row after that will be the data tape after two steps, and so on. For any given Turing Machine, there’s a set of Wang Tiles which can imitate it.”

…

You’ve found a pattern? Don’t tell me: our set of twenty thousand polysaccharide Wang Tiles just happens to form the Turing Machine for calculating pi.” “No. What they form is a universal Turing Machine. They can calculate anything at all – depending on the data they start with. Every daughter fragment is like a program being fed to a chemical computer. Growth executes the program.” “Ah.” Paolo’s curiosity was roused – but he was having some trouble picturing where the hypothetical Turing Machine put its read/write head. “Are you telling me only one tile changes between any two rows, where the ‘machine’ leaves its mark on the ‘data tape’ . . . ?”

…

“Are you telling me only one tile changes between any two rows, where the ‘machine’ leaves its mark on the ‘data tape’ . . . ?” The mosaics he’d seen were a riot of complexity, with no two rows remotely the same. Karpal said, “No, no. Wang’s original example worked exactly like a standard Turing Machine, to simplify the argument . . . but the carpets are more like an arbitrary number of different computers with overlapping data, all working in parallel. This is biology, not a designed machine – it’s as messy and wild as, say . . . a mammalian genome. In fact, there are mathematical similarities with gene regulation: I’ve identified Kauffman networks at every level, from the tiling rules up; the whole system’s poised on the hyperadaptive edge between frozen and chaotic behavior.”

A Discipline of Programming by E. Dijkstra

finite state, Turing machine, Y Combinator

This shows quite clearly why I regard general recursion as an order of magnitude more complicated than just repetition, and it therefore hurts me to see the semantics of the repetitive construct "while B do S" defined as that of the call "whiledo(B, S)" of the recursive procedure (described in ALGOL 60 syntax): procedure whiledo (condition, statement); begin if condition then begin statement; whiledo (condition, statement) end end Although correct, it hurts me, for I don't like to crack an egg with a sledgehammer, no matter how effective the sledgehammer is for doing so. For the generation of theoretical computing scientists that became involved in the subject during the sixties, the above recursive definition is often not only "the natural one", but even "the true one". In view of the fact that we cannot even define what a Turing machine is supposed to do without appeal- ing to the notion of repetition, some redressing of the balance seemed indi- ca ted. For the absence of a bibliography I offer neither explanation nor apology. Acknowledgements. The following people have had a direct influence on this book, either by their willingness to discuss its intended contents or by com- menting on (parts of) the finished manuscript: C.

…

In other words, we accept an HSLM that is only able to simulate properly a subset of the computations that are guaranteed to terminate prop- erly when executed by the UM. Note 4. The notion of the liberal pre-condition is introduced here in recognition of the fact that the HSLM is so bounded. This is in sharp contrast to the very similar notion of "partial correctness", which has been introduced in connection with unbounded machines (such as Turing machines) because of the undecidability of the Halting Problem. (End of note 4.) One may raise the question -but I shall not answer it- of what the UM will do when started at an initial state for which we don't know whether it satisfies wp(S, T) or not. I take the position (from a philosophical point of view probably very shaky) that as long as we have not proved that the initial state satisfies wp(S, T), the UM may do as it likes, in the sense that we have no right to complain.

The Ages of Globalization by Jeffrey D. Sachs

Admiral Zheng, AlphaGo, Big Tech, biodiversity loss, British Empire, Cape to Cairo, circular economy, classic study, colonial rule, Columbian Exchange, Commentariolus, coronavirus, cotton gin, COVID-19, cuban missile crisis, decarbonisation, DeepMind, demographic transition, Deng Xiaoping, domestication of the camel, Donald Trump, en.wikipedia.org, endogenous growth, European colonialism, general purpose technology, global supply chain, Great Leap Forward, greed is good, income per capita, invention of agriculture, invention of gunpowder, invention of movable type, invention of the steam engine, invisible hand, Isaac Newton, James Watt: steam engine, job automation, John von Neumann, joint-stock company, lockdown, Louis Pasteur, low skilled workers, mass immigration, Nikolai Kondratiev, ocean acidification, out of africa, packet switching, Pax Mongolica, precision agriculture, profit maximization, profit motive, purchasing power parity, rewilding, South China Sea, spinning jenny, Suez canal 1869, systems thinking, The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, The Wealth of Nations by Adam Smith, trade route, transatlantic slave trade, Turing machine, Turing test, urban planning, warehouse robotics, Watson beat the top human players on Jeopardy!, wikimedia commons, zoonotic diseases

Smartphones are only a decade old, but they have already upended how we live. How did this revolution come about? The roots of the digital revolution can be traced to a remarkable paper by British genius Alan Turing, writing in 1936. Turing envisioned a new conceptual device, a universal computing machine—a Turing machine, as it became known—that could read an endless tape of 0s and 1s in order to calculate anything that could be calculated. Turing had conceptualized a general-purpose programmable computer before one had been invented. His ideas would fundamentally shape the digital revolution to come. Turing also made legendary contributions to the Allied war effort by showing how to use mathematical cryptography and an early electronic device to decipher the Nazi military secret code.

…

.), 170 social democracy, 202 social-democratic ethos, 201–3 social institutions, 19–20 societies: Eurasia with horse-based, 62–63, 65; Greek, 76–79; hierarchical structure of, 39; horse-based, 59; human, 38–40 soil nutrients, 19 Song Dynasty, 88–91, 89, 104 Soviet Union, 30, 161–62, 207 Spain, 97, 108–11, 110 state law, 71 steam engine, 4; global trading of, 137; in Industrial Age, 16–17, 131–34, 132; Watt patenting, 17 steel, 139 steppes: of Asia, 53; climate zones of, 53; Eurasian, 24, 54; horse domestication in, 59; migration from, 64 subsidiarity doctrine, 196, 203–4 sugar, 119–20 sugar plantations, 120 Summa Theologica (Aquinas), 78 Sun Yat-Sen, 147 sustainable agriculture, 13 sustainable development, 31, 183–85, 196–200; economic growth from, 187; governance of, 200; public goods for, 204–5; religious leaders on, 211–12; U.N. goals of, 198, 201–2 Sustainable Development Goals (SDG), 178, 198, 202 syphilis, 102 tabula rasa (blank-slate learning), 176 Taiping Rebellion, 147 tea infusion, 152 technologies, 1–2, 11, 18, 70; digital, 181; digital revolution and, 166; economic development from, 21; environmental impact of, 188–90; Eurasian advances in, 49; of farm villages, 45; geography and, 18; of Han Empire, 82; horses distributing, 64; inequalities and changes in, 30; information, 4–5; innovative designs for, 138–41; institutions and, 17; intelligent, 141; lucky latitudes innovations in, 50–51; military, 29–30; naval, 96; North America cut off from, 51–52; Old World, 21; for poverty reduction, 177; upheavals from, 130; U.S. advances in, 160; wireless, 181 tellurocracy (land power), 72 temperate zones: advantages to, 22–25; empires, 51; of Eurasia, 48; slavery in, 119 territorial competition, 28 tertiary sectors, 14–16 textile industry, 134; of Britain, 121; of India, 149; robots in, 186 thalassocracy (sea power), 72–73 theileria parva (equine piroplasmosis), 55 Thirty Years’ War, 156–57 Thucydides, 75 Timurid Empire, 83, 93, 93–94 tin mines, 61 tobacco, 119–20 Tokugawa Shogunate, 150 trade, 67 Trajan (emperor), 79 transistors, 171, 172 transnational cooperation, 205 transoceanic empires, 4 transportation vehicle, 54 transport systems, 203 Treaty of Tordesillas (1494), 109–10 Treaty of Versailles, 157 Treaty of Zaragoza (1529), 109–10 triangular trade, 119 tropical vector-borne diseases, 49, 117 tropical zones, 22–23 trucks, self-driving, 186 trypanosomiasis disease, 50 tsetse flies, 56, 152 Turing, Alan, 170, 173 Turing machine, 170 Turkish tribes, 88 Turse, Nick, 162 U.K. See United Kingdom Umayyad Empire, 87, 87 U.N. See United Nations UN Framework Convention on Climate Change (UNFCCC), 204 United Kingdom (U.K.), 144 United Nations (U.N.), 167; as anti-fascist alliance, 207; global center of gravity and, 209–10; reformation of, 207–10; Security Council, 210; sustainable development goals of, 198, 201–2; U.S. supporting, 208–10 United States (U.S.): birth of, 130–31; Britain’s economic dominance with, 154; China’s rising power and, 193; Civil War of, 161; Declaration of Independence of, 131; decolonization supported by, 166–67; Department of Defense, 171; dominant economy of, 159; economic development of, 154, 154; farmer’s food in, 15; GDP of, 154; geopolitical leadership of, 162; global hegemony of, 159–62, 168; global output of, 181; infrastructure development of, 161; lucky latitudes in, 49; military bases of, 162, 163; primary sector employment in, 16; R&D spending of, 182, 182; regime change operations of, 162; Soviet Union challenges to, 161–62; technology advances of, 160; UK comparisons with, 144; unlimited resources of, 121; U.N. supported by, 208–10; War of Independence of, 123; world output of, 155 Universal Declaration of Human Rights, 207 universal health care, 199–200 Upper Pleistocene, 37–40 Urban II (pope), 88 urbanization, 7; population and, 130; rates of, 8, 9; transformation to, 14–16 U.S.

Emergence by Steven Johnson

A Pattern Language, agricultural Revolution, AOL-Time Warner, Brewster Kahle, British Empire, Claude Shannon: information theory, complexity theory, Danny Hillis, Douglas Hofstadter, edge city, epigenetics, game design, garden city movement, Gödel, Escher, Bach, hive mind, Howard Rheingold, hypertext link, invisible hand, Jane Jacobs, Kevin Kelly, late capitalism, Lewis Mumford, Marshall McLuhan, mass immigration, Menlo Park, mirror neurons, Mitch Kapor, Murano, Venice glass, Naomi Klein, new economy, New Urbanism, Norbert Wiener, PalmPilot, pattern recognition, pez dispenser, phenotype, Potemkin village, power law, price mechanism, profit motive, Ray Kurzweil, SimCity, slashdot, social intelligence, Socratic dialogue, stakhanovite, Steven Pinker, The Death and Life of Great American Cities, The Wealth of Nations by Adam Smith, theory of mind, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, trickle-down economics, Turing machine, Turing test, urban planning, urban renewal, Vannevar Bush

Turing’s war research had focused on detecting patterns lurking within the apparent chaos of code, but in his Manchester years, his mind gravitated toward a mirror image of the original code-breaking problem: how complex patterns could come into being by following simple rules. How does a seed know how to build a flower? Turing’s paper on morphogenesis—literally, “the beginning of shape”—turned out to be one of his seminal works, ranking up their with his more publicized papers and speculations: his work on Gödel’s undecidability problem, the Turing Machine, the Turing Test—not to mention his contributions to the physical design of the modern digital computer. But the morphogenesis paper was only the beginning of a shape—a brilliant mind sensing the outlines of a new problem, but not fully grasping all its intricacies. If Turing had been granted another few decades to explore the powers of self-assembly—not to mention access to the number-crunching horsepower of non-vacuum-tube computers—it’s not hard to imagine his mind greatly enhancing our subsequent understanding of emergent behavior.

…

., 14–15 Shannon, Claude, 44–47, 53, 62–65, 241n Shapiro, Andrew, 159–60 Shelley, Mary Wollstonecraft, 125 shopping malls, 90, 92 sidewalk culture, 51, 91–97, 99, 146, 147, 148, 230–31 silk weavers, 101, 102, 104–7, 124 SimCity, 66, 87–89, 98, 186, 205, 208, 229 Sims, The, 186–89, 209–10, 229 simulations, computer: of aggregation, 16–17, 23, 59–63, 163–69 of ants, 59–63, 65 of cities, 66, 87–89, 98, 186, 229–30 of evolution, 56–63, 182–89, 193, 209–10 of genetics, 57–59, 182–86 models for, 9, 16–17, 23, 59–63 of self-organization, 59–63, 76, 163–69 60 Minutes, 144 Slashdot, 152–62, 205, 212, 223, 260n Slate, 118, 128 sleep cycles, 140 slime mold (Dictyostelium discoideum), 11–17, 18, 20–21, 23, 43, 52, 63–64, 67, 163–69, 179, 180, 220, 235n, 236n, 246n slums, 41, 49–50, 137 Smarties experiment, 196–97, 200, 261n–62n Smith, Adam, 18, 156 Societas Mercatorum, 101 society: ant colonies compared with, 97–98, 248n emergence in, 22–23, 36–40, 49–50, 92–100 hierarchical, 14–15, 98 organization of, 9, 27, 33–41, 92–94, 97–100, 109, 204, 252n–54n patterns in, 18, 36–40, 41, 49–50, 52, 91, 95, 137, 185 Society of Mind theory, 65 software: emergent, 17, 21, 22, 121–26, 170–74, 186, 189, 204–8, 221–22, 223 gaming, 163–89 learning, 53–63, 65 for online communities, 148–62 Open Source, 222 pattern-recognition, 18, 21, 54, 56, 123–24, 126–29 personalized, 159–60, 207–8, 211, 212–13 see also programs, computer SoHo (New York City), 50 Solenopsis invicta, 75 Sopranos, The, 219 spam, 153, 156, 161, 215–16 speech encryption, 44–45 spokescouncils, 226 StarLogo, 76, 163–69, 179, 205, 219, 247n, 260n statistical analysis, 46–47, 76–77, 78 storytelling, 188–89 suburbia, 94–95, 230, 259n Sun Microsystems, 224 surf engines, 122–23 synapses, 134 system events, 145 systems: adaptive, 18, 19–20, 119, 128, 137, 139–40 bottom-up, 17, 18, 22, 53–57, 66–67, 83, 97–98, 115, 116, 133, 148, 164, 166, 207, 221–23, 231 climax stage of, 147–48, 152, 154 command, 15, 77, 83–84 complex, 18, 29, 78, 139–40, 246n decentralized, 17, 22, 31–32, 39–40, 66, 76–79, 86, 117, 118–21, 163–89, 204–5, 217–18, 222, 233–34, 236n–37n, 263n dynamic, 20, 248n–49n emergent, see emergence interactive, 22, 79, 81, 120, 123, 126, 158–59, 231 open-ended, 57–58, 180–89, 208 polycentric, 90–91, 159, 223 representational, 157–59 rule-governed, 19, 180–81, 226 self-organizing, see self-organization self-regulating, 138, 140–41, 143, 146–47, 148, 149, 151, 154, 159 simple, 46, 47, 78 top-down, 14–15, 18, 30–31, 33, 98, 132, 136, 145, 148–49, 153, 208, 223, 225 “Take It to the Streets” (Berman), 95 Tap, Type, Write, 174–75, 177 Taylor, Chuck, 59–63, 65 TCG, 224 technology: innovation in, 108–9, 111–12, 113, 116, 254n slave, 125–26 see also computers Teilhard de Chardin, Pierre, 115–16, 120 telephones, 47, 229 television, 95, 130–36, 137, 143–46, 158, 159, 160–61, 210–13, 217, 218 Terminator, 127 termites, 22, 73, 82 “theory of other minds,” 195–226 thermostats, 137–38, 150, 258n thinking: associative, 206 bottom-up, 66–67 decentralized, 17 group, 160 serial, 127 see also intelligence Thomas, Lewis, 9 Thompson, D’Arcy, 236n, 259n threaded discussion boards, 149–50 TiVo, 211–13, 214, 218 Tocqueville, Alexis de, 35 toys, 165–66, 178–80, 181 Tracker program, 59–63, 65 trade, 101–2, 104–7, 109, 110 traffic patterns, 97, 166, 204, 230–31, 232 traveling salesman problem, 227–29 tumors, brain, 119 Turing, Alan, 14, 18, 42–45, 49, 53, 54, 62–65, 67, 206, 236n, 242n, 254n–56n, 263n Turing Machine, 42, 45 Turing Test, 42, 206 Turner, Ted, 135–36 “turtles,” 166, 167–68, 260n undecidability problem, 42 Unreal, 208–9 urbanization, 99, 108, 109–13, 116, 146–48, 253n–54n urban planning, 49–50, 51, 89, 92, 109, 146–47, 230–31 Usenet, 162 user ratings, 121–26, 129, 156–62, 214–15, 221–22 varicella-zoster virus, 103, 104 VCRs, 212 ventral premotor area, 198 video games, see games, computer Virtual Community, The (Rheingold), 148 visual cortex, 201 Vocoder, 44 Washington Post, 131 Weaver, Warren, 46–49, 50, 51, 64–66 Well, 147–52, 153 West Village (New York City), 50, 93 Wheatley, Bill, 136 Wheeler, William Morton, 242n White, Leslie, 253n White, Lynn, Jr., 112 Wide Area Information Server (WAIS), 122 Wiener, Norbert, 53, 57, 64–65, 125–26, 139, 140, 143, 151–52, 162, 169, 238n, 251n, 259n–60n Wilson, Edward O., 52, 60, 75 Wittgenstein, Ludwig, 41 Wooten, Jim, 130–36, 137, 144–45 Wordsworth, William, 27, 39, 92, 98 working class, 37, 41, 52, 91, 95, 240n, 259n World Wide Web, see Internet Wright, Robert, 114, 115–17, 118 Wright, Will, 66, 87, 88, 186–89, 209–10, 229–30 Yahoo, 114, 117 Zelda: Ocarina of Time, 176, 177 Zimmerman, Eric, 178–80, 182, 186, 189 SCRIBNER 1230 Avenue of the Americas New York, NY 10020 www.SimonandSchuster.com Copyright © 2001 by Steven Johnson All rights reserved, including the right of reproduction in whole or in part in any form.

The Future of the Brain: Essays by the World's Leading Neuroscientists by Gary Marcus, Jeremy Freeman

23andMe, Albert Einstein, backpropagation, bioinformatics, bitcoin, brain emulation, cloud computing, complexity theory, computer age, computer vision, conceptual framework, correlation does not imply causation, crowdsourcing, dark matter, data acquisition, data science, deep learning, Drosophila, epigenetics, Geoffrey Hinton, global pandemic, Google Glasses, ITER tokamak, iterative process, language acquisition, linked data, mouse model, optical character recognition, pattern recognition, personalized medicine, phenotype, race to the bottom, Richard Feynman, Ronald Reagan, semantic web, speech recognition, stem cell, Steven Pinker, supply-chain management, synthetic biology, tacit knowledge, traumatic brain injury, Turing machine, twin studies, web application

And unlike worms and flies with their high degree of stereotypy, in which genetically determined neural circuits mediate innate behaviors, mammalian neocortical circuits are shaped by the experiences of their ancestors, in the form of genetic specialization within cortical regions, as well as by personal experiences in the form of synaptic learning, and exploit more general-purpose, flexible population coding principles that are highly sensitive to context. In that sense, the cortical column may be the closest that nature has come to evolving a universal Turing machine, a machine whose settings are adapted by a combination of genomic and learned (synaptic) mechanisms to the particular statistics of its input, be it visual, olfactory, linguistic, or otherwise. Of Men and Mice A deep understanding of the cortex necessitates querying the relevant microvariables, in particular spiking neurons, by recording the occurrences and timing of action potentials.

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., 5 transcranial magnetic stimulation (TMS), 228 transcriptome, 48 transducer, 246, 250 transistor, 82, 84, 85f, 86–88, 135, 177, 181, 183, 210, 221, 245, 250 traumatic brain injury, 194, 266 trilevel hypothesis: brain, 84–85 Tsuchiya, Nao, 168, 169 tuberculosis, 171 tuberous sclerosis, 241 tumors, 266 Turing machine, 26 23andMe, 198 Twitter, 103 two-photon imaging: mouse cortex, 107 two-photon microscopy, 32 two-photon tomography, 34 ulcerative colitis, 234 ultrasonic frequencies, 246 ultrasonic waves, 249 ultrasound, 250 Universidad Politécnica de Madrid, 116 University College London, 122, 177 University of California–San Diego, 177 University of Edinburgh, 115 University of Oslo, 115, 116 US BRAIN Initiative, 113, 124 US Human Connectome Project, 113 Vallortigara, Giorgio, 207 Vandenbroucke, Annelinde, 166 Van Essen, David, 12 variable binding: brain, 213–14; language, 212 Venter, Craig, 256 Vesalius, Andreas, 3, 4f vestibular system, 22 virtual brains: building, 97–99 virtual reality: whole brain neuroimaging and, 17–24 vision: restoration, 227, 230 Vision (Marr), 181 visual processing: stimuli, 163 visual responses: brute-force data collection, 105 visual-spatial extinction, 163–64 visual system: primates, 104–5 visual thalamus, 264 Vogt, Karl, 91 Vogt, Marthe, 4 von Economo, Constantin, 4 von Neumann, John, 208, 212–13 V2 neurons: hypothesis, 105–6 Waddington, Conrad, 189 Watson, James, 7, 46 Waxholm Space, 115 Werbos, Paul, 41 White, John, 12 whole-brain neuroimaging, 20–21, 17–24 whole-brain neuroscience: behavior as brain output, 121–22; building the brain, 118–19; ethics, 123; global collaboration, 123–24; global effort to understand brain, 124; modeling brain disorders and diseases, 122; unifying brain models, 120–21; validity of model, 119–20 whole-brain simulation: creating to understand, 111–13; neuroinformatics for computing, 113–15; next generation brain atlases, 115–17; ongoing debate, 267–68; predictive neuroscience, 117–18.

The Chip: How Two Americans Invented the Microchip and Launched a Revolution by T. R. Reid

Albert Einstein, Bob Noyce, Claude Shannon: information theory, computer age, cotton gin, discovery of penicillin, double helix, Ernest Rutherford, Fairchild Semiconductor, full employment, George Gilder, Guggenheim Bilbao, hiring and firing, industrial robot, Internet Archive, Isaac Newton, John von Neumann, Menlo Park, New Journalism, Norbert Wiener, oil shock, PalmPilot, Parkinson's law, popular electronics, Richard Feynman, Ronald Reagan, seminal paper, Silicon Valley, Turing machine, William Shockley: the traitorous eight

While pondering Hilbert’s problem, Turing hit upon an extraordinary new idea: that a machine could be designed, or programmed, to perform any mathematical computation a human could carry out as long as there was a clear set of instructions for this machine to follow. This ideal computer, with universal application as long as it was programmed correctly, came to be called the Turing Machine, and the concept served as a key inspiration for computer pioneers in Europe and the United States—among them von Neumann, whom Turing met during a stay at Princeton in the mid-thirties. During the war, Turing joined the team of mathematicians who gave the Allies an invaluable step up by cracking the Germans’ Enigma military code.

…

The work involved reading pages and pages of sheer gobbledygook, looking for repetitive patterns of letters that would reveal, under ingenious mathematical manipulation, the inner workings of the German cipher machines. To carry out the calculations, the codebreakers developed simple mathematical machines of their own—real-life variations on the abstract Turing Machine. After the war, Turing worked on the first generation of British computers. At the age of forty-one, shortly after being tried and convicted for homosexual conduct (“Accused Had Powerful Brain,” a London tabloid reported), he died from eating an apple tainted with cyanide he was using for an experiment.

Schild's Ladder by Greg Egan

framing effect, gravity well, invisible hand, Turing machine

That's very nearly what Sophus is claiming lies behind the border: an enormous quantum computer that could perform any operation that falls under the general description of quantum physics--and in fact is in a superposition of states in which it's doing all of them." Mariama's eyes widened, but then she protested, "Sophus never puts it like that." "No, of course not," Yann agreed. "He's much too careful to use overheated language like that. 'The universe is a Deutsch-Bennett-Turing machine's is not a statement that goes down well with most physicists, since it has no empirically falsifiable content." He smiled mischievously. "It does remind me of something, though. If you ever want a good laugh, you should try some of the pre-Qusp anti-AI propaganda. I once read a glorious tract which asserted that as soon as there was intelligence without bodies, its 'unstoppable lust for processing power' would drive it to convert the whole Earth, and then the whole universe, into a perfectly efficient Planck-scale computer.

…

It doesn't mean that there is a quantum computer underlying anything." "No," Tchicaya agreed. "But qubit network theory doesn't claim that. It just says that when you get to a low enough level, you have nothing left to lose by treating the system as if it were software. It's like all the proofs in applied algorithmic theory that are based on imagining Turing machines. No one complains that the real universe is conspicuously devoid of paper tape." "Old habits die hard," she confessed. "I'm still in mourning for the Sarumpaet rules, and they were disproved before I was born. They're what I was brought up on, they're what I've thought of all my life as the template for a physical theory.

Einstein's Unfinished Revolution: The Search for What Lies Beyond the Quantum by Lee Smolin

adjacent possible, Albert Einstein, Brownian motion, Claude Shannon: information theory, cosmic microwave background, cosmological constant, Ernest Rutherford, Isaac Newton, Jane Jacobs, Jaron Lanier, John von Neumann, Murray Gell-Mann, mutually assured destruction, quantum entanglement, Richard Feynman, Richard Florida, Schrödinger's Cat, Stephen Hawking, Stuart Kauffman, the scientific method, Turing machine

That talk, and other early anticipations of the idea, seemed to make little impression until David Deutsch, originally a specialist in quantum gravity who held a position at Oxford, proposed in 1989 an approach to quantum computation in the context of a paper on the foundations of mathematics and logic.2 In his paper, Deutsch introduced the idea of a universal quantum computer, analogous to a Turing machine. A few years later Peter Shore, a computer scientist working for an IBM research laboratory, proved that a quantum computer could factor large numbers much faster than a regular computer. At that point people began to take notice, because one application of being able to factor large numbers is that many of the codes now in common use could be broken.

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See also quantum states of atoms, 49–51, 60–61, 77–78, 146–47 classical, 30 contrary, 38–43, 45, 123, 298 correlated, 51, 145–47, 146n, 149 definition, 15, 304 of electrons, 78 superposing, 32–33 stationary states, 77, 87, 92 stochastic quantum mechanics, 223 Stoppard, Tom, 15 string theory, 189, 234n, 278, 304 subjective probabilities, 162, 163n, 170, 172, 174, 193, 208 subjectivity, entropy and, 191n subsystem principle, 26, 27 superdeterminism, 220–22 superposition, 4–5 of atoms, 6–7, 50, 139–40, 146, 152, 156–57 of electrons, 152 entanglement and, 195 general relativity and, 138 gravity and, 140 measurement and, 64 of molecules, 6 of objects, 139 of particles, 4–5 of photons, 50 pilot wave theory and, 214 quantum, 6 quantum mechanics and, 37, 138–39 quantum states and, 32–33 of quantum systems, 37, 137–38 reality and, 147 Schrödinger’s cat, 49–53 of states, 32–33, 196–97 wave function and, 139–40, 213 superposition principle, 33, 137–39 symmetry, 104n, 255n, 263, 263–64 ’t Hooft, Gerard, 221–22 technology, entanglement, 48 temperature, 29, 30 temporal relationalism, 237, 253, 265 thermodynamics, 120, 159, 177, 191n, 214, 303 time capsules, 203 causality and, 204, 236 as emergent, 237 events and, 266 gravity and, 137, 140 as illusion, 202–4 irreversibility of, 236, 236n laws of, 265 laws of nature and, 265 moments and, 201–3 momentum and, 262 nature and, 265 quantum mechanics and, 63, 137 quantum state and, 31 retrocausality, 216–17, 217 topological field theories, 193–94 transactional interpretation, 216–17 truth, xx, xxvi, 276–77 Tumulka, Roderich, 107 Turing machine, 185 twistor theory, 136 tyranny, 178 uncertainty principle, 18–22, 32, 58, 61, 90, 92–93, 117, 145, 304 Unger, Roberto Mangabeira, 265 unification, 216, 229 unification of forces, xvii unitary law, 31 universal quantum computer, 185 universe as causal set, 260 chosen aspect of, 221 expansion of, 4 information and, 189 living mirror of, 245 nadic, 242–43, 243 observation and, 166–67, 231 parallel, 145, 148, 247 physics in early, 175–76 pilot wave theory and, 121 quantum mechanics and, 28, 159n, 231 quantum states and, 193, 197, 231 quantum theory and, 27–28 relational model of, 242 theory of, 27 wave function and, 231 Valentini, Antony, 120, 121, 210 variety, 244, 247 velocity, 20–21, 21, 23, 81, 262n, 304 views, causal theory of, 269–71 Vigier, Jean-Pierre, 114 von Neumann, John, 93–94, 104–5, 110 water, xv wave function, 31n, 32, 99n, 176 atomic systems and, 141, 213 beables and, 224 definition of, 304 information and, 193, 249n particles and, 99–100, 109, 118–20, 209, 210 phases of, 214n pilot wave theory and, 125–26, 210 probabilities and, 124, 128, 151, 165 Rule 1 and, 116, 118 spacetime and, 140 spontaneous collapses and, 143 squaring, 99–100, 100, 151 superposition and, 139–40, 213 theory of relativity and, 142 universe and, 231 wave-function collapse, 35–36, 129–30, 139, 186 definition, 298 drawbacks of, 214–15 ghost branches and, 213 lessons from, 213–16 measurement problem and, 213 Rule 2 and, 215 wavelength, xxviii, 22 wave mechanics, 304 wave-particle duality, 86, 97–98 de Broglie, L., and, 83–84, 103 decoherence and, 156 definition of, 304 double slit experiment and, 98, 199–200, 210–11 Einstein and, 83–84 electrons and, 98–99 light and, 84 measurement problem and, 223 pilot wave theory and, 142, 208–10, 222 realism and, 89 Schrödinger and, 83–84 waves in electric field, 40 electrons as, 79–80, 82, 83 frequency of, 22, 61 height of, 34 light as, 68, 68, 72, 80 matter as, 5, 23, 84 particles and, 21–24, 34, 60, 66, 79–80, 81, 83–84, 99–100, 213 photons as, 69 sum of, 124 wave theory, 67 Weinberg, Steven, 179 Weyl, Hermann, 82–83 Wheeler, John Archibald, xxvii, 37, 145, 187–88 Wheeler-DeWitt equation, 203 Wigner, Eugene, 195–96 Wigner’s friend, 196n Witten, Edward, 136 Wittgenstein, Ludwig, 72n World War I, 12 wormholes, 240, 240n X-rays, 79–80 Young, Thomas, 67–68 ABCDEFGHIJKLMNOPQRSTUVWXYZ ABOUT THE AUTHOR Lee Smolin has made influential contributions to the search for a unification of physics.

Nervous States: Democracy and the Decline of Reason by William Davies

active measures, Affordable Care Act / Obamacare, Amazon Web Services, Anthropocene, bank run, banking crisis, basic income, Black Lives Matter, Brexit referendum, business cycle, Cambridge Analytica, Capital in the Twenty-First Century by Thomas Piketty, citizen journalism, Climategate, Climatic Research Unit, Colonization of Mars, continuation of politics by other means, creative destruction, credit crunch, data science, decarbonisation, deep learning, DeepMind, deindustrialization, digital divide, discovery of penicillin, Dominic Cummings, Donald Trump, drone strike, Elon Musk, failed state, fake news, Filter Bubble, first-past-the-post, Frank Gehry, gig economy, government statistician, housing crisis, income inequality, Isaac Newton, Jeff Bezos, Jeremy Corbyn, Johannes Kepler, Joseph Schumpeter, knowledge economy, loss aversion, low skilled workers, Mahatma Gandhi, Mark Zuckerberg, mass immigration, meta-analysis, Mont Pelerin Society, mutually assured destruction, Northern Rock, obamacare, Occupy movement, opioid epidemic / opioid crisis, Paris climate accords, pattern recognition, Peace of Westphalia, Peter Thiel, Philip Mirowski, planetary scale, post-industrial society, post-truth, quantitative easing, RAND corporation, Ray Kurzweil, Richard Florida, road to serfdom, Robert Mercer, Ronald Reagan, sentiment analysis, Silicon Valley, Silicon Valley billionaire, Silicon Valley startup, smart cities, Social Justice Warrior, statistical model, Steve Bannon, Steve Jobs, tacit knowledge, the scientific method, Turing machine, Uber for X, universal basic income, University of East Anglia, Valery Gerasimov, W. E. B. Du Bois, We are the 99%, WikiLeaks, women in the workforce, zero-sum game

In the years immediately before the Second World War, various mathematicians, philosophers, and psychologists mused on whether human thought and communication could be modeled as mathematical formulae. The British mathematician (and subsequently celebrated code breaker) Alan Turing’s 1937 paper, “On Computable Numbers,” imagined a “Turing Machine” which could be programmed to perform basic instructions in response to different symbols that it was fed in a random order. While the Turing Machine was never built, this vision signaled the leap from the abstract mathematics of computation to its technological construction. Humans would be required to program such machines, but the machines could then perform various acts of calculation on their own.

We Are Data: Algorithms and the Making of Our Digital Selves by John Cheney-Lippold

algorithmic bias, bioinformatics, business logic, Cass Sunstein, centre right, computer vision, critical race theory, dark matter, data science, digital capitalism, drone strike, Edward Snowden, Evgeny Morozov, Filter Bubble, Google Chrome, Google Earth, Hans Moravec, Ian Bogost, informal economy, iterative process, James Bridle, Jaron Lanier, Julian Assange, Kevin Kelly, late capitalism, Laura Poitras, lifelogging, Lyft, machine readable, machine translation, Mark Zuckerberg, Marshall McLuhan, mass incarceration, Mercator projection, meta-analysis, Nick Bostrom, Norbert Wiener, offshore financial centre, pattern recognition, price discrimination, RAND corporation, Ray Kurzweil, Richard Thaler, ride hailing / ride sharing, Rosa Parks, Silicon Valley, Silicon Valley startup, Skype, Snapchat, software studies, statistical model, Steven Levy, technological singularity, technoutopianism, the scientific method, Thomas Bayes, Toyota Production System, Turing machine, uber lyft, web application, WikiLeaks, Zimmermann PGP

Users of OkCupid and Facebook are not just profiles but mediated social actors whose relations are made, according to traces of data, in a “just-in-time,” on-the-fly algorithmic interpretation.93 “Just-in-time” means there’s another space and yet another politically productive gap in the progression of subject making. To make a claim about something or to have any position from which to act (or not) requires a pause, like cultural theorist Stuart Hall’s arbitrary closure, from chapter 1, or the Turing Machine’s staccatoed, sequential processing. For Hall, this closure constructs a theoretical stasis that is present at every imagined moment, a hypothetical suspension to life and discourse that lets us, briefly, make a temporal claim about who we are. In algorithmic processing, there’s an empirical stasis that accompanies this suspension.

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., 205 Thoreau, Henry David, 211 Thrift, Nigel, 105, 112, 180 Tinder, 133 Tor, 168, 238–40, 242, 301n98 Totaro, Paolo, 112 TrackMeNot, 230–32 Trafficthief. See National Security Agency (NSA) transcoding, 10, 12, 18–19, 33–34, 47, 53–55, 71, 78, 97, 104, 107, 115, 159, 172, 180, 252 Tribe, Laurence, 224 Truth, Sojourner, 166 Tufekci, Zeynep, 146 Turing, Alan, 64; Turing Machine, 185 Turner, Graeme, xi Turrow, Joseph, xii, 73 Twitter, 31, 47, 58, 80–81, 82–83, 87, 107, 246, 282n124. See also “Cuban Twitter” Uber, 133 United Nations, 176 United States v. Microsoft, 20 University of California, Berkeley, 137 U.S. Agency for International Development (USAID), 130–31, 262 U.S.

The Art of Computer Programming by Donald Ervin Knuth

Abraham Wald, Brownian motion, Charles Babbage, complexity theory, correlation coefficient, Donald Knuth, Eratosthenes, G4S, Georg Cantor, information retrieval, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Menlo Park, NP-complete, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, sorting algorithm, Turing machine, Y2K

The results cited in the text therefore give an estimated running time of O(n log m log log m) on Turing machines, or O(n log m) on machines with random access to words of bounded size, or O(n) on pointer machines. 15. The best upper bound known is O(n(lognJ log log n), due to M. J. Fischer and L. J. Stockmeyer [J. Comp. and Syst. Sci. 9 A974), 317-331]; their construction works on multitape Turing machines, and is O(n log n) on pointer machines. The best lower bound known is of order nlogn/loglogn, due to M. S. Paterson, M. J. Fischer, and A. R. Meyer [SIAM/AMS Proceedings 7 A974), 97-111]; this applies to multitape Turing machines but not to pointer machines. 16.

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A generalized spectral test, based on discrete Fourier transforms, can be used to test how well a sequence measures up to Definition Ql [see A. Compagner, Physical Rev. E52 A995), 5634-5645]. Still another interesting approach to a definition of randomness has been taken by Per Martin-L6f [Information and Control 9 A966), 602-619]. Given a finite 6-ary sequence Xi, ..., Xn, let l(Xi,... ,Xn) be the length of the shortest Turing machine program that generates this sequence. (Alternatively, we could use other classes of effective algorithms, such as those discussed in Section 1.1.) Then l(Xi,... ,Xn) is a measure of the "patternlessness" of 170 RANDOM NUMBERS 3.5 the sequence, and we may equate this idea with randomness. The sequences of length N that maximize l(Xi,...

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., E2) where the product continues until reaching a factor with lg... lgn < 1. Schonhage and Strassen showed how to improve this theoretical upper bound to O(n log n log log n) in their paper, by using integer numbers u to carry out fast Fourier transforms on integers, modulo numbers of the form 2e + 1. This upper bound applies to Turing machines, namely to computers with bounded memory and a finite number of arbitrarily long tapes. If we allow ourselves a more powerful computer, with random access to any number of words of bounded size, Schonhage has pointed out that the upper bound drops to O(nlogn). For we can choose k = I and m = 6k, and we have time to build a complete multiplication table of all possible products xy for 0 < x,y < 2^mj/12\ (The number of such products is 2fc or 2fc+1, and we can compute each table entry by addition from one of its predecessors in O(k) steps, hence O(k2k) = 0{n) steps will suffice for the calculation.)

This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking by John Brockman

23andMe, adjacent possible, Albert Einstein, Alfred Russel Wallace, Anthropocene, banking crisis, Barry Marshall: ulcers, behavioural economics, Benoit Mandelbrot, Berlin Wall, biofilm, Black Swan, Bletchley Park, butterfly effect, Cass Sunstein, cloud computing, cognitive load, congestion charging, correlation does not imply causation, Daniel Kahneman / Amos Tversky, dark matter, data acquisition, David Brooks, delayed gratification, Emanuel Derman, epigenetics, Evgeny Morozov, Exxon Valdez, Flash crash, Flynn Effect, Garrett Hardin, Higgs boson, hive mind, impulse control, information retrieval, information security, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jaron Lanier, Johannes Kepler, John von Neumann, Kevin Kelly, Large Hadron Collider, lifelogging, machine translation, mandelbrot fractal, market design, Mars Rover, Marshall McLuhan, microbiome, Murray Gell-Mann, Nicholas Carr, Nick Bostrom, ocean acidification, open economy, Pierre-Simon Laplace, place-making, placebo effect, power law, pre–internet, QWERTY keyboard, random walk, randomized controlled trial, rent control, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, Satyajit Das, Schrödinger's Cat, scientific management, security theater, selection bias, Silicon Valley, Stanford marshmallow experiment, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, Stuart Kauffman, sugar pill, synthetic biology, the scientific method, Thorstein Veblen, Turing complete, Turing machine, twin studies, Vilfredo Pareto, Walter Mischel, Whole Earth Catalog, WikiLeaks, zero-sum game

Developing concepts that carve nature at its joints is the first crucial step toward understanding, not only in the Game of Life but in science and in ordinary life as well. At a more advanced level, we discover that the Game of Life is Turing complete. That is, it’s possible to build a pattern that acts like a Universal Turing Machine (a computer that can simulate any other computer). Thus, any computable function could be implemented in the Game of Life—including perhaps a function that describes a universe like the one we inhabit. It’s also possible to build a universal constructor in the Game of Life, a pattern that can build many types of complex objects, including copies of itself.

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., 135–36 Turing, Alan, 146–47 Tversky, Amos, 121, 280 Twain, Mark, 111 typewriter keyboards, 285–86 ulcers, 240 umwelt, 143–45 uncertainty, 28, 53–54, 65, 69, 72, 273, 340 and fear of the unknown, 55–57 unpredictableness, 103–4 risk literacy and, 259–61 statistical thinking and, 260 theater and, 262 see also certainty; probability unconscious, 146 rational, 146–49 understanding, 358 unintended effects of actions, 124–26, 372 uniqueness and specialness: Copernican Principle and, 11–12 in dual view of ourselves, 32 of Earth and humans, 3–5 mediocrity principle and, 6–8, 11, 12 Universal Turing Machine, 276 universe, 294, 301 causes and purposes in, 9–10 Copernican Principle and, 11–12 expansion of, 1, 11 life in, 3–5, 13–14, 292 mediocrity principle and, 6–8, 11, 12 truth and, 222 unknown, fear of, 55–57 Uranus, 361 “Use of Knowledge in Society, The” (Hayek), 258 utility, 347 truth vs., 135–36 vaccinations, 268, 279, 394 autism and, 56, 331 vanilla, 142 Veblen, Thorstein, 228 Veeck, Bill, 360 Veeck effect, 360–62 Venter, J.

Enigma by Robert Harris

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

But the fourth—the fourth—will be solved purely electronically, using a relay rack and valves, linked to the bombe by this fat cable form, that looks like a -' Kramer cupped his hands into a circle '—well, that looks like a cobra, I guess. Using valves in sequence—that's a revolution. Never been done before. Your people say it should make the calculations a hundred times, maybe a thousand times, as fast.' Jericho said, almost to himself: 'A Turing machine.' 'A what?' 'An electronic computer.' 'Well, whatever you want to call it. It works in theory, that's the good news. And from what they're saying, this may be just the start. It seems they're planning some kind of super-bombe, all electronic, called Colossus.' Jericho had a sudden vision of Alan Turing, one winter afternoon, sitting cross-legged in his Cambridge study while the lamps came on outside, describing his dream of a universal calculating machine.

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Two Englands, he thought. One England—this one—familiar, safe, obvious. But now another, secret England, secluded in the grounds of stately houses -Beaumanor, Gayhurst, Woburn, Adstock, Bletchley—an England of aerial farms and direction finders, clattering bombes and, soon, the glowing green and orange valves of Turing machines ('it should make the calculations a hundred times, maybe a thousand times as fast'}. A new age beginning to be born in the parklands of the old. What was it that Hardy had written in his Apology? 'Real mathematics has no effect on war. No one has yet discovered any warlike purpose to be served by the theory of numbers.'

How Not to Network a Nation: The Uneasy History of the Soviet Internet (Information Policy) by Benjamin Peters

Albert Einstein, American ideology, Andrei Shleifer, Anthropocene, Benoit Mandelbrot, bitcoin, Brownian motion, Charles Babbage, Claude Shannon: information theory, cloud computing, cognitive dissonance, commons-based peer production, computer age, conceptual framework, continuation of politics by other means, crony capitalism, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Graeber, disinformation, Dissolution of the Soviet Union, Donald Davies, double helix, Drosophila, Francis Fukuyama: the end of history, From Mathematics to the Technologies of Life and Death, Gabriella Coleman, hive mind, index card, informal economy, information asymmetry, invisible hand, Jacquard loom, John von Neumann, Kevin Kelly, knowledge economy, knowledge worker, Lewis Mumford, linear programming, mandelbrot fractal, Marshall McLuhan, means of production, megaproject, Menlo Park, Mikhail Gorbachev, military-industrial complex, mutually assured destruction, Network effects, Norbert Wiener, packet switching, Pareto efficiency, pattern recognition, Paul Erdős, Peter Thiel, Philip Mirowski, power law, RAND corporation, rent-seeking, road to serfdom, Ronald Coase, scientific mainstream, scientific management, Steve Jobs, Stewart Brand, stochastic process, surveillance capitalism, systems thinking, technoutopianism, the Cathedral and the Bazaar, the strength of weak ties, The Structural Transformation of the Public Sphere, transaction costs, Turing machine, work culture , Yochai Benkler

Researchers and historians of science remember his 1943 paper, coauthored with the enigmatic polymath Walter Pitts, “A Logical Calculus of the Ideas Immanent in Nervous Activity,” which proposed models for neural networks in the brain that later became influential in the theory of automata, computation, and cybernetics. Their argument holds that the mind is, given certain reductions, equivalent to a Turing machine. In other words, with sufficient abstraction, it is possible to imagine the neural network in a mind as a logical circuit that is capable of carrying out any computable problem. In McCulloch’s words, he sought “a theory in terms so general that the creations of God and men almost exemplify it.”10 That “almost” packs much into its experimental epistemology.

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The Soviet translation and adoption of cybernetics share with the other case studies glossed here an underlying fascination with the relationship of the mind to the machine, especially as seen in the biology and neurology of the British and Chilean cyberneticists. The mind-machine analog is a politically charged two-way street. Not only does cybernetics prompt us to think about how a logic machine (computer circuits or any other Turing machine) may function like a mind (a neural network), but it also raises McCulloch’s potent possibility that subsequent neuroscience has soundly rejected: the mind (neural network) might function like a logic machine (computer circuits). This reverse comparison (that a mind is like a machine) proves particularly enduring in later discussions of the design and development of national networks.

Journey to the Edge of Reason: The Life of Kurt Gödel by Stephen Budiansky

Abraham Wald, Albert Einstein, anti-communist, business cycle, Douglas Hofstadter, fear of failure, Fellow of the Royal Society, four colour theorem, Georg Cantor, Gregor Mendel, Gödel, Escher, Bach, John von Neumann, laissez-faire capitalism, P = NP, P vs NP, Paul Erdős, rent control, scientific worldview, the scientific method, Thorstein Veblen, Turing machine, urban planning

He ended by saying, “As for any claims I might make perhaps the best I can say is that I would have proved Gödel’s Theorem in 1921—had I been Gödel.”45 Still, Post was able to contribute an important extension of Gödel’s theorem which, along with a near simultaneous paper by Alan Turing, provided a rigorous definition of a formal system as a series of basic, mechanical computational steps—the conceptual model for a computer that would come to be known as the Turing Machine, and which would lay the foundation of modern computer science. Gödel and Turing never met, but each recognized the great significance of the other’s work for the newly emerging field of computing. Gödel in turn credited Post’s and Turing’s “precise and unquestionably adequate definition of the general concept of a formal system” for establishing the complete generality of his proof in “every consistent formal system containing a certain amount of finitary number theory.”46 Post and Turing independently had come up with the idea of a conceptual machine that could perform any calculation by employing a program with just a few primitive binary operations: marking a square on a strip of paper, erasing the mark, moving one square to the left or right, and reading whether the current square is marked or not.

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., 203, 224, 229 Steed, Wickham, 32 Stevenson, Adlai, 247 Stonborough, Margaret “Gretl,” 36, 99 Straus, Ernst, 217–18, 247 Strauss, Johann, the Younger, 32 Strauss, Lewis, 238, 238, 239, 247–48 strophanthin, 178 Students for a Democratic Society, 272 Sudeten Germans, 42, 52–53, 228, 229 synchronicity, 244 syntactical completeness, 115–16 syntax of language, 93–94, 100–101 Systemzeit, 184, 202 Szilard, Leo, 27 Taft, Robert, 244 Tandler, Julius, 84 Tarski, Alfred, 65, 162–63, 163, 176, 177, 268 Taussky, Olga, 68, 103 background and career, 68–69, 76, 186 Café Herrenhof circle and, 65 friendship with KG, 69, 102, 106, 145 Fürtwangler and, 70 KG’s job prospects and, 187, 190 KG’s meeting with Zermelo and, 135 University of Vienna described by, 68 tautology, 112, 121 textile industry, 25, 28, 29, 39–40, 40, 43, 56, 58, 77, 104, 162 This Side of Paradise (Fitzgerald), 154 time, concept of, 225–27 time travel, 226 Time-Life Books, 269 topology, 92 Tractatus Logico-Philosophicus (Wittgenstein), 96, 98, 101 Tristan und Isolde (Wagner), 255 Trotsky, Leon, 95 Truman, Harry S., 246, 247 Tucker, Marcia, 288 Tugendhat, Greta, 58 Turing, Alan, 116, 136 Turing Machine, 136 types, theory of, 110 Ulam, Stanislaw, 133, 248 Uncertainty Principle, 278 undecidable propositions, 123, 130, 136, 162, 241, 245, 258, 267, 279. See also Incompleteness Theorem United Nations, 244 University of Chicago, 93 University of Iowa, 141–42, 150 University of London, 186 University of Vienna, 23, 63 (map), 67 courses of study at, 67–68 denazification at, 260–61 Neuropsychiatry Clinic, 168, 172, 179 persecution of Jews and liberals at, 81–85, 83, 161–62, 181–84, 196–97, 202, 203–4 reputation, 26, 66–67 right-wing student riots, 83–84, 83, 86, 195 science and philosophy at, 37, 84–85 Unknown Quantity, The (Broch), 77–78 “Unreliability of Logical Principles, The” (Brouwer), 113 Urania, 66 Uryshon, Pavel, 92 “Usefulness of Useless Knowledge, The” (Flexner), 149 van der Rohe, Mies, 58 Vanneman, Joseph R., 225 Vaterländische Front, 143 Veblen, Elizabeth (Mrs.

Information: A Very Short Introduction by Luciano Floridi

agricultural Revolution, Albert Einstein, bioinformatics, Bletchley Park, carbon footprint, Claude Shannon: information theory, Computing Machinery and Intelligence, conceptual framework, digital divide, disinformation, double helix, Douglas Engelbart, Douglas Engelbart, George Akerlof, Gordon Gekko, Gregor Mendel, industrial robot, information asymmetry, intangible asset, Internet of things, invention of writing, John Nash: game theory, John von Neumann, Laplace demon, machine translation, moral hazard, Nash equilibrium, Nelson Mandela, Norbert Wiener, Pareto efficiency, phenotype, Pierre-Simon Laplace, prisoner's dilemma, RAND corporation, RFID, Thomas Bayes, Turing machine, Vilfredo Pareto