Turing machine

The Infinity Machine: Demis Hassabis, DeepMind, and the Quest for Superintelligence

by Sebastian Mallaby;  · 30 Mar 2026  · 607pp  · 161,998 words

. The clue to Hassabis’s meaning lay in the word “classical.” By classical, Hassabis meant not quantum. Sometimes Hassabis also referred to classical computers as “Turing machines,” and to himself as “Turing’s champion.” A classical or Turing computer, first proposed by Alan Turing in 1936, operates on bits of information, which

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formulated it in the late 1980s and 1990s, but absurd given AI’s progress a quarter of a century later. DeepMind’s achievements demonstrated that Turing machines were far more powerful than Penrose had suspected: They could mimic intuition and spatial intelligence; they could chat and model proteins. A large part of

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processed a near infinity of bits, attaining a scale that allowed classical computers to transcend the constraint of binary information. As Turing had foretold, a Turing machine of infinite size could discover infinite patterns, solving the problem of induction and disproving Penrose’s claims about the limits of classical computers. Where Penrose

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found a way of building it!’ “If Manhattan is what humans have achieved with the classical computers in their heads, what does that say about Turing machines? “It says that we don’t know what the limit is. “And that has huge implications. The fullest version of this theory means that we

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brain, and firm on the prevalence of quantum effects within the universe. “Now, of course I acknowledge that there are problems in mathematics that a Turing machine probably can’t solve, like factorizing large numbers,” Hassabis conceded, referring to the challenge of starting with a very big number and finding the two

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large prime numbers that can be multiplied together to produce it. “For a Turing machine to solve a problem, there has to be a pattern that a model can learn. If there’s no pattern, the search becomes intractable. And

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enough examples. And you don’t need quantum mechanics for these patterns to be discovered. “So it’s a very interesting question—what can a Turing machine actually find out? “And that’s what I’d like to find out. “I see myself as kind of like Turing’s champion, pushing

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Turing machines to their limit.” * * * • • • I pondered Hassabis’s ambivalence about power, his indifference to riches, his quasi-spiritual desire for scientific knowledge. How did such a

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, 207, 209 translational systems, 207, 209 Trump, Donald, xxi, 237, 370 Tsai, Joe, 248 Tunyasuvunakool, Kathryn, 429n9 Turing, Alan, 57, 84, 332, 389–94, 409n27 Turing machines, 389–94 280B project, 286 U UniProt database, 267–69 United Arab Emirates, 328 University College London, 45, 50 University of Cambridge Daugman at, 27

The Information State: Politics in the Age of Total Control

by Jacob Siegel  · 24 Mar 2026  · 348pp  · 103,246 words

.” * * * Alan Turing designed a universal computer that could solve any solvable problem. Though it existed only in his mind as an abstract thought experiment, the Turing machine named for the English mathematician became one of the most important and influential computers ever conceived. The abstract machine contained the same parts and followed

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

by George Zarkadakis  · 7 Mar 2016  · 405pp  · 117,219 words

computers and genetics constantly push the envelope of how we manipulate our nature, ideas that were once never questioned suddenly come to the forefront. The Turing machine in the Imitation Game was both female and male. Its future offspring will be a cyborg, machine and human all in one. The delineations that

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do so they borrowed ideas from Alan Turing. Turing’s influence has been tremendous in America, and his ideas for calculating machines (the so-called ‘Turing machines’) provided an excellent theoretical framework for McCulloch and Pitts. In their paper, they demonstrated how neurons could be equivalent to programs run on a

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Turing machine. In doing so, they effectively proposed that neurons might be regarded as information processing machines, and as the base logic units of the brain. This

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kind of information – a concept he termed a ‘Universal Machine’. 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

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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. He

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substitution, von Neumann substituted bits of information (for example, sets of positions on the infinite tape of a Universal Turing Machine, or a ‘program’ as we would call it today) with whole Turing machines, in order to prove his theorem for self-replicating automata. And here’s the deep insight of this substitution: it

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symbol. 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

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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

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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

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result: the statement was either true or false. The first thing that Turing showed was that a Turing machine capable of performing a mathematical computation was equivalent to an algorithm (i.e. a series of logical steps that processed a statement and arrived at

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a little later. But then Turing went on to show something even more earth-shattering: that it was not possible to determine algorithmically whether a Turing machine would ever halt. By ‘halting’, Turing meant that the machine would come to a conclusion and thus end its operation. So imagine a

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Turing machine beginning to work on a problem, say a logical statement. It starts applying a set of instructions to examine if the logical statement is true

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or not. And keeps going, and going … without end. The Turing machine is stuck in an eternal ‘hmmm’ moment. It cannot give an answer. It cannot tell whether the statement is true or not. It does not

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as the coup de grâce for all of those who hoped that logic was grounded on sound foundations. And he then went further. By inventing Turing machines he sparked the computer revolution that would follow. Computers are algorithms, and Turing showed how to build the mechanical ‘algorithm of algorithms’, or the ‘Universal

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a very valid one, and has to be dealt with. Let’s analyse it a little more. Turing was also aware of the limitations of Turing machines compared with human intelligence, and was not too happy either. In his 1938 PhD thesis at Princeton,21 he introduced the concept of ‘oracles’ in

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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

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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

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require ‘reasoning’. The machine oracle can be like a simple on/off switch. The randomness of the oracle takes care of the determinism of classical Turing machines. No given set of inputs will produce the same set of outputs. The oracle’s answer ‘yes’ or ‘no’ could happen by chance alone. A

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choose to call that chance happening ‘free will’. Bailed out by paradox There is also another way of viewing Turing’s oracle machine concept. Classical Turing machines are simple calculators. In today’s terms we can regard them as offline batch computing processes: a stand-alone computer performing a computational process on

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external database, or stop its process and let another machine take over. Online computing is a model of Turing’s oracle machines connecting to classical Turing machines. The Internet, where billions of computers interconnect and query one another in a continuous, dynamic and non-deterministic fashion, is a realisation of Turing’s

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’s insight. If we abstract Dahaene’s ‘signatures of consciousness’, and rephrase them in computational terms, our brain is a massive network of densely interconnected Turing machines. Each of these tiny machines (our individual neurons) processes a set of inputs (electrochemical excitations entering their axons) either by amplifying or reducing the strength

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by Frege’s predicate logic, laid the foundations of modern computer languages. However, it was Alan Turing who linked logic and computational machines forevermore: the ‘Turing machine’ is in effect an Analytical Engine that processes a strip of tape with logical symbols written on it. Processing is executed according to a table

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of rules – the ‘program’.13 The only difference between the Turing machine and what Babbage and Lovelace had in mind is that the Turing machine is comparatively indiscriminate about the symbols it processes. The symbols can include numbers, theorems, or any other logical construct. That

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curious happened in the human brain that AI research could not reproduce in a computer. Perhaps general intelligence and self-awareness were functions that no Turing machine could possibly emulate. It was an exasperating and tormenting thought that led to many getting cold feet about the future of AI. Not surprisingly, by

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’ in his play R.U.R. 1921: Ludwig Wittgenstein publishes Tractatus Logico-philosopicus. 1931: Kurt Gödel publishes The Incompleteness Theorem. 1937: Alan Turing invents the ‘Turing machine’. 1938: Claude Shannon demonstrates that symbolic logic can be implemented using electronic relays. 1941: Konrad Zuse constructs Z3, the first Turing-complete computer. 1942: Alan

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, 25 Tower of the Winds, Athens 30–1 Transcendence (2014 film) 270 Turing, Alan 48–9, 93, 147, 181, 183, 203, 230–1, 234–5 Turing machines 177, 179, 180, 209–15, 229 Turing Test 48–9, 52, 54, 71, 72, 130, 122, 263, 312–13 Tutuola, Amos 19 Twitter 250 Uber

Ways of Being: Beyond Human Intelligence

by James Bridle  · 6 Apr 2022  · 502pp  · 132,062 words

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

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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

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, 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

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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

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a maze of dead-ends and bad answers. For this reason, the travelling salesman problem is a classic example of a problem that a Universal Turing Machine – the a-machine – cannot reliably solve. It’s computationally undecidable. And what did we say about undecidability? It must be time for the o-machine

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do so would advance the current state of computation exponentially. Nonetheless, they would at heart still be the same kind of computers: the same old Turing machines with a very different architecture. What if – rather than asset-stripping other organisms for their useful components, treating them as so many spare parts for

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machine becomes less and less visible as the machine itself becomes more and more abstract. The highest level of abstraction is the completely abstract (automatic) Turing machine. But Oracle machines, among them the water integrators, are attempts to bring this abstraction back down to earth: to recombine the awesome power of mechanical

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, 185 aspens 77 astrobiology 87 atomic bomb 224–5 Augustin, Regynald 156 Australopithecus 88 Author of the Acacia Seeds, The 169–71 automatic machine see Turing machine Autonomous Trap 26–7, 26, 204 autonomous vehicles 23–6, 65, 275 avocados 108 Babbage, Charles 30 baboons 32, 52–55, 64, 74 bacteria 17

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tortoise (robot) 179, 180–81, 212 Trolley Problem 276–7 Trump, Donald 136 Turia, Tariana 267 Turing, Alan 29–31, 176–8, 186, 211, 215 Turing machine 176–8, 193, 195, 200, 223 Turing Test 29–31 turnips 118 Tuva 149 Twitter 136, 156 U-Machine 186, 190, 202, 211 Uexküll, Jakob

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

by Michal Zalewski  · 4 Apr 2005  · 412pp  · 104,864 words

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

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of confusion among the laity.) The device is also equipped with an internal register that can hold a finite number of equally internal states. A Turing machine starts at a certain position on the tape, in a given state, and then reads a character from a cell on the tape. Every automaton

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internal state to S1, and will not move the reading head. Figure 2-5 shows an example of a Turing machine positioned at cell C with internal state S. Figure 2-5. Sample Turing machine execution stages Let’s walk through this. As you can see in Figure 2-5, the machine uses an

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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

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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

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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. This über-machine is neither particularly

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abstract nor complex. Its existence is guaranteed because a specific Turing machine can be devised to perform any finite algorithm (according to

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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

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, 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. It is a construct that begs to be implemented

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prerequisite for an infinitely long input tape cannot be satisfied in the real world. Nevertheless, we can provide plenty of it, making such a hardware Turing machine quite usable for most of our everyday problems. Enter the universal computer. Real computers, of course, go far beyond the sequential access single-bit memory

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Simplicity Coming up with such an unimpressive set of instructions is, of course, not going to make the device fast or easy to program. Universal Turing Machines can do just about everything (in many cases, by virtue of their simplicity), but they are painfully slow and difficult to program, to a degree

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tasks in a number of cycles. In such a multicycle design, the processor goes through a number of internal stages, much like the add-one Turing machine example. It runs the data through simple circuits in the right order, thus implementing a more complex functionality step by step, which relies on more

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of systems work on a problem together. World domination at hand? Not so fast. * * * [33] In complexity theory, polynomial problems can be solved by a Turing machine in time that is polynomially proportional to input length (number or size of variables for which the answer must be found). This means that the

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Keystroke Timing Attacks Over SSH Con-nections,” CS588 Research Project, School of Engineering and Applied Science, University of Virginia (2001). [52] Yurii Rogozhin, “A Universal Turing Machine with 22 States and 2 Symbols,” Romanian Journal of Information Science and Technology 1 no. 3 (1998). [53] Milena Milenkovic, Aleksandar Milenkovic, Jeffrey Kulick, “Demystifying

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Identification for origin identification, Using Topology Data for Origin Identification in IP headers, The Destination Address in passive fingerprinting, Initial Time to Live (IP Layer) Turing machines, Turing and Instruction Set Complexity, Holy Grail: The Programmable Computer, Split the Task, Execution Stages, The Lesser Memory, Do More at Once: Pipelining, Implications: Subtle

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Transfer Protocol Primer Universal Serial Bus (USB), Sometimes, a Modem Is Just a Modem Universal Serial Bus devices, activity LEDs for, Food for Thought Universal Turing Machines (UTMs), Functionality, at Last unpredictability, reproducible, Exploiting System Diagnostics URG (urgent) pointers, Other TCP Header Parameters, Window Size (TCP Layer) in passive fingerprinting, Window Size

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Protocol (UDP), User Datagram Protocol, Lost in Translation address translation with, Lost in Translation headers in, User Datagram Protocol User-Agent program, Camouflage UTMs (Universal Turing Machines), Functionality, at Last V V.22bis standard, From Your Email to Loud Noises . . . Back and Forth V.32 standard, From Your Email to Loud Noises

The Information: A History, a Theory, a Flood

by James Gleick  · 1 Mar 2011  · 855pp  · 178,507 words

his machine. He listed the very few items his machine must possess: tape, symbols, and states. Each of these required definition. Tape is to the Turing machine what paper is to a typewriter. But where a typewriter uses two dimensions of its paper, the machine uses only one—thus, a tape, a

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any digital computer—encoded in symbols and solved algorithmically—the universal machine can solve it as well. Now the microscope is turned onto itself. The Turing machine sets about examining every number to see whether it corresponds to a computable algorithm. Some will prove computable. Some might prove uncomputable. And there is

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Gödel’s. Turing went further than Gödel by defining the general concept of a formal system. Any mechanical procedure for generating formulas is essentially a Turing machine. Any formal system, therefore, must have undecidable propositions. Mathematics is not decidable. Incompleteness follows from uncomputability. Once again, the paradoxes come to life when numbers

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I could sell them to H. M. Government for quite a substantial sum, but am rather doubtful about the morality of such things.”♦ Indeed, a Turing machine could make ciphers. But His Majesty’s Government turned out to have a different problem. As war loomed, the task of reading messages intercepted from

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the same. They have a single answer. 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

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, 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

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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,

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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

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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

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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

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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

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distinguish between numbers like Alice and Bob’s A and B. He could write a program to make a Turing machine print out “010101 …” a million times, and he could write down the length of that program—quite short. But given a million random digits—no

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make the IBM mainframe print out those million digits, he would have to put the whole million digits into the punched cards. To make the Turing machine do it, he would still need the million digits for input. Here is another number (in decimal this time): C: 3.1415926535897932384626433832795028841971693993751… This looks random

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as a string of any length—we ask, what is the length of the shortest program that will generate it? Using the language of a Turing machine, that question can have a definite answer, measured in bits. Chaitin’s algorithmic definition of randomness also provides an algorithmic definition of information: the size

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is solved by using computer language. It does not matter which computer language, because they are all equivalent, reducible to the language of a universal Turing machine. The Kolmogorov complexity of an object is the size, in bits, of the shortest algorithm needed to generate it. This is also the amount of

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about English, but that’s much too vague,”♦ Chaitin says. “I pick a computer-programming language instead.” Naturally he picks the language of a universal Turing machine. And then what does it mean, how do you name an integer? Well, you name an integer by giving a way to calculate it. A

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NEXT PRIME NUMBER, AND REPEAT A MILLION TIMES generates a number that is interesting: the sum of the first million primes. It would take a Turing machine a long time to compute that particular number, but a finite time nonetheless. The number is computable. But if the most concise algorithm for n

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number that we can prove cannot be named in fewer than n syllables.” (We are not really talking about syllables any more, of course, but Turing-machine states.)♦ It is another recursive, self-looping twist. This was Chaitin’s version of Gödel’s incompleteness. Complexity, defined in terms of program size, is

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of recalculating these positions. The amount of work it takes to compute something had been mostly disregarded—set aside—in all the theorizing based on Turing machines, which work, after all, so ploddingly. Bennett brought it back. There is no logical depth in the parts of a message that are sheer randomness

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+ 123 = 93 + 103 ♦ More precisely, it looked like this: “The finite binary sequence S with the first proof that S cannot be described by a Turing machine with n states or less” is a (log2 n+cF)–state description of S. 13 | INFORMATION IS PHYSICAL (It from Bit) The more energy, the

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be expended, but no one is counting. Stranger still, Bennett tried investigating the thermodynamics of the least thermodynamic computer of all—the nonexistent, abstract, idealized Turing machine. Turing himself never worried about his thought experiment consuming any energy or radiating any heat as it goes about its business of marching up and

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down imaginary paper tapes. Yet in the early 1980s Bennett was talking about using Turing-machine tapes for fuel, their caloric content to be measured in bits. Still a thought experiment, of course, meant to focus on a very real question

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, California, and Argonne National Laboratory in Illinois, and then joined IBM Research in 1972. IBM did not manufacture Turing machines, of course. But at some point it dawned on Bennett that a special-purpose Turing machine had already been found in nature: namely RNA polymerase. He had learned about polymerase directly from Watson; it

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(in Bennett’s view, anyway).♦ The younger man pursued Landauer’s principle by analyzing every kind of computer he could imagine, real and abstract, from Turing machines and messenger RNA to “ballistic” computers, carrying signals via something like billiard balls. He confirmed that a great deal of computation can be done with

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all. In every case, Bennett found, heat dissipation occurs only when information is erased. Erasure is the irreversible logical operation. When the head on a Turing machine erases one square of the tape, or when an electronic computer clears a capacitor, a bit is lost, and then heat must be dissipated. In

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the moment, might still be to simulate the probabilistic Nature by a computer C which itself is probabilistic.” A quantum computer would not be a Turing machine, he said. It would be something altogether new. “Feynman’s insight,” says Bennett, “was that a quantum system is, in a sense, computing its own

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in Peter Galison, Image and Logic: A Material Culture of Microphysics (Chicago: University of Chicago Press, 1997), 703. ♦ “WHEN THE READING HEAD MOVES”: “A Universal Turing Machine with Two Internal States,” in Claude Elwood Shannon, Collected Papers, ed. N. J. A. Sloane and Aaron D. Wyner (New York: IEEE Press, 1993), 733

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Mathematical Proof,” in Information, Randomness & Incompleteness, 4. ♦ “FROM THE EARLIEST DAYS OF INFORMATION THEORY”: Charles H. Bennett, “Logical Depth and Physical Complexity,” in The Universal Turing Machine: A Half-Century Survey, ed. Rolf Herken (Oxford: Oxford University Press, 1988), 209–10. 13. INFORMATION IS PHYSICAL ♦ “THE MORE ENERGY, THE FASTER THE BITS

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Fe Institute, 1985. ———. “Demons, Engines, and the Second Law.” Scientific American 257, no. 5 (1987): 108–16. ———. “Logical Depth and Physical Complexity.” In The Universal Turing Machine: A Half-Century Survey, edited by Rolf Herken. Oxford: Oxford University Press, 1988. ———. “How to Define Complexity in Physics, and Why.” In Complexity, Entropy, and

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J. John Von Neumann and Norbert Wiener. Cambridge, Mass.: MIT Press, 1980. ———. The Cybernetics Group. Cambridge, Mass.: MIT Press, 1991. Herken, Rolf, ed. The Universal Turing Machine: A Half-Century Survey. Vienna: Springer-Verlag, 1995. Hey, Anthony J. G., ed. Feynman and Computation. Boulder, Colo.: Westview Press, 2002. Hobbes, Thomas. Leviathan, or

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of number’s randomness, 12.1, 12.2 to reconstruct phylogeny scientific method as, 12.1, 12.2 Shor’s factoring, 13.1, 13.2 Turing machine, 7.1, 7.2 Alice in Wonderland (Carroll) Allen, William alphabet(s) as code evolution of, 2.1, 2.2, 3.1 evolution of telegraph

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, 4.2 in evolution of complex structures human computers, 4.1, 4.2, 4.3 thermodynamics of, 13.1, 13.2, 13.3, 13.4 Turing machine for, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6 see also calculators; computers computer(s) analog and digital, 8.1, 8

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, 12.1, 12.2 decision problem and, 7.1, 7.2 proof of, 6.1, 6.2, 6.3 significance of, 6.1, 6.2 Turing machine and indexes, 15.1, 15.2, epl.1, epl.2, epl.3 inductive reasoning Infinities, The (Banville) “Information Is Inevitably Physical” (Landauer) “Information Is Physical

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, 7.3, 7.4, 7.5, 7.6 purposeful behavior of self-replicating, 8.1, 8.2 standardization of manufacturing see also calculators; computer(s); Turing machine(s) Mackay, Charles macrostates, 9.1, 9.2 “Magical Number Seven, Plus or Minus Two, The” (Miller) magnetism, 1.1, 1.2, 5.1, 5

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, 12.1, 12.2 programming to generate random numbers, 12.1, 12.2 Lovelace’s operations for Analytical Engine as, 4.1, 4.2 of Turing machine states, 7.1, 7.2, 7.3, 8.1, 12.1, 12.2 proteins, 10.1, 10.2, 10.3, 10.4, 10.5, 10

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procedures in algorithmic proof of randomness, 12.1, 12.2 in Lovelace’s operations for Analytical Engine paradoxes based on, 6.1, 6.2 in Turing machine operations, 7.1, 7.2 in use of alphabetical ordering systems redundancy control of, for communication, 7.1, 7.2 in English language, 1.1

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, 7.8, 7.9, 7.10, 7.11, 7.12, 7.13, 8.1, 8.2, 8.3 on thinking machines, 8.1, 8.2 Turing machine analysis by Wiener and, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 9.1, 9.2 work with Differential Analyzer, 6

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of information, 6.1, 6.2, 6.3 for perfect language redundancy of communication determined by, 1.1, 1.2 in structure of language for Turing machine see also alphabet(s); code; symbolic logic; writing Szilárd, Leó, 9.1, 9.2, 9.3, 9.4, 13.1 “Table Alphabeticall, A” (Cawdrey), 3

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.1, 7.2, 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3, 8.4, 8.5, 9.1, 14.1 Turing machine(s) capabilities as code generator proof of incompleteness theorem by, 7.1, 7.2, 7.3, 7.4, 12.1 significance of, in computer science

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

by Byron Reese  · 23 Apr 2018  · 294pp  · 96,661 words

machines. Enter Alan Turing. 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

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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. Almost all

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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

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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

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. 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

I Am a Strange Loop

by Douglas R. Hofstadter  · 21 Feb 2011  · 626pp  · 181,434 words

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

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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. 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

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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

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… 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

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to be equivalent to provability in PM; and unprovability perversely entailing each other tu (second-person singular pronoun) addressed to married couple Turing, Alan Mathison Turing machines turkey as “which”, not “who” TV camera: bolted to TV; on long leash; meltdown of; on short leash; universally worn on nose TV screen as

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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

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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

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