universal Turing machine

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

by M. Mitchell Waldrop  · 14 Apr 2001

, 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

Turing's Cathedral

by George Dyson  · 6 Mar 2012

Neumann (1972), Nicholas Metropolis’s History of Computing in the Twentieth Century (1980), Andrew Hodges’s Alan Turing: The Enigma (1983), Rolf Herken’s The Universal Turing Machine: A Half-Century Survey (1988), and William Aspray’s John von Neumann and the Origins of Modern Computing (1990). Julian Bigelow and his colleagues designed

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or on paper tape. “Being digital should be of more interest than being electronic,” Turing pointed out.6 Von Neumann set out to build a Universal Turing Machine that would operate at electronic speeds. At its core was a 32-by-32-by-40-bit matrix of high-speed random-access memory—the

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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

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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

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).”25 Turing showed that undecidable statements, resistant to the assistance of an external oracle, could still be constructed, and the Entscheidungsproblem would remain unsolved. The Universal Turing Machine of 1936 gets all the attention, but Turing’s O-machines of 1939 may be closer to the way intelligence (real and artificial) works: logical

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self-reproduction is fundamentally a problem of communication, over a noisy channel, from one generation to the next. “Turing!” refers to the powers of the Universal Turing Machine, and “Not Turing!” refers to the limitations of those powers—and how they might be transcended by living and nonliving things. “Pitts-McCulloch!” refers to

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, and migrate from one place to another as an electromagnetic signal, as long as there’s a digital world—a civilization that has discovered the Universal Turing Machine—for it to colonize when it gets there. And that’s why von Neumann and you other Martians got us to build all these computers

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. 179. 10. I. J. Good to Sara Turing, December 9, 1956, AMT; Robin Gandy, “The Confluence of Ideas in 1936,” in Rolf Herken, ed., The Universal Turing Machine: A Half-Century Survey (Oxford: Oxford University Press, 1988), p. 85. 11. Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,” Proceedings of

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, 1937, AMT. 17. Freeman Dyson, interview with author, May 5, 2004, GBD; Martin Davis, “Influences of Mathematical Logic on Computer Science,” in Herken, ed., The Universal Turing Machine, p. 315. 18. Alonzo Church, “Review of A.M. Turing, ‘On Computable Numbers, with an Application to the Entscheidungsproblem,’ ” Journal of Symbolic Logic 2, no

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.1, 8.1, 8.2 and termination of the ECP, 14.1, 18.1, 18.2 on time (vs. sequence), 16.1, 16.2 on Universal Turing Machine, 8.1, 14.1 visits Manchester (1948) on von Neumann, 5.1, 5.2, 7.1, 8.1, 8.2, 14.1, 14.2 on

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.1, 8.2, 14.1 reliability of, 7.1, 7.2, 8.1, 8.2, 11.1, 12.1 speed (and asynchronous arithmetic) of as Universal Turing Machine, 1.1, 8.1 see also ECP; Williams (memory) tubes IBM (International Business Machines), 4.1, 7.1, 7.2, 8.1, 8.2, 10

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.1, 17.2 and nondeterministic machines on “oracle machines” on unorganized machines and von Neumann, 5.1, 13.1, 13.2, 13.3 see also Universal Turing Machine Turing, Ethel Sara Turing, Julius Mathison Turing, Sara, 13.1, 13.2, 13.3 Turing’s cathedral, Google as turtles Ujelang (Marshall Islands) Ulam, Adam

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see also incompleteness United States Atomic Energy Commission, see Atomic Energy Commission (AEC) UNIVAC (Universal Automatic Computer), 5.1, 18.1 Universal Constructor (von Neumann) Universal Turing Machine, prf.1, 1.1, 5.1, 6.1, 11.1, 13.1, 13.2, 13.3, 14.1, 15.1, 15.2, 17.1 and

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, 6.1, 8.1, 10.1, 16.1 superstitions of and theory of self-reproducing automata, 1.1, 15.1, 15.2 and Turing (and Universal Turing Machine), 1.1, 3.1, 5.1, 6.1, 8.1, 13.1, 13.2, 13.3, 13.4, 13.5, 15.1 and Stan Ulam

The Stack: On Software and Sovereignty

by Benjamin H. Bratton  · 19 Feb 2016  · 903pp  · 235,753 words

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

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footprint of the Cloud is measured at the scale of continents, not enterprises. Some see it as an uneven computational troposphere, others as a prototype universal Turing machine, arranged not with tape but with uneven networks of fiber optics, data centers, nested databases, terminals, and browsers.8 The Cloud layer is also a

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by testing its reflection in human cognition, projects like Bell's suggest capture of the totality of autobiographical experience by couching it within a personal universal Turing machine and so (as the research was for Microsoft) to prototype the sorts of data management, visualization, semantic sorting, editing, and indexing interfaces necessary for the

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–40 software espionage, 398n21 subdividing with postal codes, 195 superjurisdictional enforcement, 123, 125 surveillance, 35, 120, 287 universalization, deterritorializing, 31–32 Universal Postal Union, 194 universal Turing machine, 78–79, 82, 110, 262 universal User, 257–258, 264, 274 uProxy, 361 urban design, 160–163, 168–172, 248, 296, 442n14 urban envelopes, 153

From Bacteria to Bach and Back: The Evolution of Minds

by Daniel C. Dennett  · 7 Feb 2017  · 573pp  · 157,767 words

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

Human Compatible: Artificial Intelligence and the Problem of Control

by Stuart Russell  · 7 Oct 2019  · 416pp  · 112,268 words

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

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–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

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

by Ananyo Bhattacharya  · 6 Oct 2021  · 476pp  · 121,460 words

may compute anything a Turing machine can – assuming the human in question does not die of boredom first – but nothing that the machine cannot. The universal Turing machine is now considered an abstract prototype of a general-purpose ‘stored program’ computer – one that can, like any laptop or smart phone today, execute an

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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

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write-up, entitled ‘Man Viewed as a Machine’, is barely less sensational than the sci-fi story. ‘Are we, as rational beings, basically different from universal Turing machines?’ he asks. ‘The usual answer is that whatever else machines can do, it still takes a man to build the machine. Who would dare to

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transmission cells (representing ‘1’).19 Adding a control unit that can read from and write in tape cells, von Neumann is able to reproduce a universal Turing machine in two dimensions. He then designs a constructing arm which snakes out to any cell on the grid, stimulates it into the desired state then

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Conway had smuggled a trick question into Gardner’s column to tantalize his readers. The glider was the first piece he needed to build a Universal Turing machine within Life. Like von Neumann’s immensely more complicated cellular automaton, Conway wanted to prove that Life would have the power to compute anything. The

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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

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, 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. Jack 121–2, 307n37 Copenhagen 58, 76 Copenhagen

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Trinity test 91–2 Turing’s influence 121–2, 301n22 unification of quantum mechanics 30, 36, 37–9, 43–9 unique gift 12–13 on universal Turing machine 120 at University of Budapest 11–13 at University of Berlin 12, 39–41 view of the Cold War 208–9 vision of future technical

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, Stanisław 27, 70, 71–2, 77, 85, 85, 98, 100, 104, 132, 133–4, 136, 234, 241, 272, 279, 282 uncertainty principle 33, 69, 294n11 Universal Turing machine 119–20, 121, 229–30, 235, 241, 243, 306–7n35, 307n37 universal wave function, the 58 University of California in Berkeley 78 uranium, instability 77

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

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

any 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 fact

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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. He

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one, and becomes famous forevermore. Using logical 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

Complexity: A Guided Tour

by Melanie Mitchell  · 31 Mar 2009  · 524pp  · 120,182 words

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

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part of memory. It is notable that the first programmable computers were developed only ten years or so after Turing proved the existence of a universal Turing machine. Turing’s Solution to the Entscheidungsproblem Recall the question of the Entscheidungsproblem: Is there always a definite procedure that can decide whether or not a

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statement is true? It was the existence of a universal Turing machine that enabled Turing to prove that the answer is “no.” He realized that the input I to a Turing machine M could be the code

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then run M on the code for a second Turing machine M’. M would simply count the 1s in M’’s code. Of course, the Universal Turing Machine U could have the code for M in the “program” part of its tape, have the code for M’ in the “input” part of its

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of the Nazis. After the war, Turing participated in the development of one of the first programmable electronic computers (stemming from the idea of his universal Turing machine), at Manchester University. His interests returned to questions about how the brain and body “compute,” and he studied neurology and physiology, did influential work on

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they can compute. The physicist Stephen Wolfram, for example, has proposed that systems are complex if their computational abilities are equivalent to those of a universal Turing machine. However, as Charles Bennett and others have argued, the ability to perform universal computation doesn’t mean that a system by itself is complex; rather

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, we should measure the complexity of the behavior of the system coupled with its inputs. For example, a universal Turing machine alone isn’t complex, but together with a machine code and input that produces a sophisticated computation, it creates complex behavior. Statistical Complexity Physicists Jim

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of any initial pattern placed on the cellular automaton lattice. 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

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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

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it is hard to prove that a particular cellular automaton, Turing machine, or any other device is universal. Turing’s proof that there exists a universal Turing machine was a triumph, as was von Neumann’s proof that his self-replicating automaton was also a universal computer. Since then several researchers have proved

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of idea model, 211 meaning of information in, 171 simulation of in Game of Life, 150 in solution to the Entscheidungsproblem, 65–68 universal (see universal Turing machine) Turing statement, 66 two-body problem, 21 two-person game, 214 Ulam, Stanislaw, xi, 28, 149 uncertainty principle, 20 uncomputability, 60, 158 of the Halting

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, 38 universal computation in cellular automata, 149–150, 156 in defining complexity, 102, 156 definition of, 149 in nature, 157–158 See also universal Turing machine universal computer. See universal Turing machine universal principles (of complex systems), 95, 292–295 examples of proposals for, 294–295 skepticism about, 293–295, 299 universal properties of chaotic systems

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, 34–38 universal Turing machine, 64–65, as blueprint for programmable computers, 65, 69 cellular automata equivalent to, 149–150, 156 in defining complexity, 102, 156 Varela, Francisco, 298 variable

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

by Peter Lunenfeld  · 31 Mar 2011  · 239pp  · 56,531 words

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

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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

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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

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States Cuban Missile Crisis and, xi September 11, 2001 and, 99–101, 130 television’s dominance and, 2, 180n2 Universal Resource Locator (URL), 168–169 Universal Turing Machine, 18–19 University of Pennsylvania, 148 University of Utah, 160 UNIX, 170–171 “Untitled (After Walker Evans)” (Levine), 41 Uploading, xiii–xiv, 180nn1,2 activity

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

by Sinclair McKay  · 24 May 2010  · 351pp  · 107,966 words

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

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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

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– Turing wanted to return to the question that had been haunting him since the 1930s, that of constructing a thinking machine – an electronic brain. A Universal Turing Machine. A machine of such complexity that it could not only speedily handle any kind of mathematical calculation, but also store a memory of the process

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