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Accelerated Turing Machines
 Minds and Machines
, 2002
"... Abstract. Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of π contains n consecutive 7s, for any n; solve the Turingmachine halti ..."
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Abstract. Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of π contains n consecutive 7s, for any n; solve the Turingmachine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary to a recent paper by Bringsjord, Bello and Ferrucci, however, the concept of an accelerating Turing machine cannot be used to shove up Searle’s Chinese room argument.
Even Turing Machines Can Compute Uncomputable Functions
 Unconventional Models of Computation
, 1998
"... Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability. 2 1. Introduction Neither Turing nor Post ..."
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Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability. 2 1. Introduction Neither Turing nor Post, in their descriptions of the devices we now call Turing machines, made much mention of time (Turing 1936, Post 1936). 1 They listed the primitive operations that their devices perform  read a square of the tape, write a single symbol on a square of the tape (first deleting any symbol already present), move one square to the right, and so forth  but they made no mention of the duration of each primitive operation. The crucial concept is that of whether or not the machine halts after a finite number of operations. Temporal considerations are not relevant to the functioning of the devices as described, nor  so we are clearly supposed to believe  to the soundness of the proofs that Turi...
The Narrational Case against Church's Thesis
 Journal of Philosophy
, 1998
"... this paper presented at the 1993 Eastern APA meetings in Atlanta  comments which I incorporate in my response to Mendelson's response. I'm grateful to Michael McMenamin for providing, in his unpublished "Deciding Uncountable Sets and Church's Thesis," an excellent objecti ..."
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this paper presented at the 1993 Eastern APA meetings in Atlanta  comments which I incorporate in my response to Mendelson's response. I'm grateful to Michael McMenamin for providing, in his unpublished "Deciding Uncountable Sets and Church's Thesis," an excellent objection to my attack on Church's Thesis (which I rebut below).
FROM DESCARTES TO TURING: THE COMPUTATIONAL CONTENT OF SUPERVENIENCE
"... Mathematics can provide precise formulations of relatively vague concepts and problems from the real world, and bring out underlying structure common to diverse scientific areas. Sometimes very natural mathematical concepts lie neglected and not widely understood for many years, before their fundame ..."
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Mathematics can provide precise formulations of relatively vague concepts and problems from the real world, and bring out underlying structure common to diverse scientific areas. Sometimes very natural mathematical concepts lie neglected and not widely understood for many years, before their fundamental relevance is recognised and their explanatory power is fully exploited. The notion of definability in a structure is such a concept, and Turing’s [77] 1939 model of interactive computation provides a fruitful context in which to exercise the usefulness of definability as a powerful and widely applicable source of understanding. In this article we set out to relate this simple idea to one of the oldest and apparently least scientifically approachable of problems — that of realistically modelling how mental properties supervene on physical ones.
Universality in Two Dimensions
, 2012
"... ! daehl jilr d`ad jxcd zivgn z`xwl—mixd ogehe xwer,epzinre epxag,oepx`l Turing, in his immortal 1936 paper, observed that “[human] computing is normally done by writing... symbols on [twodimensional] paper”, but noted that use of a second dimension “is always avoidable ” and that “the twodimension ..."
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! daehl jilr d`ad jxcd zivgn z`xwl—mixd ogehe xwer,epzinre epxag,oepx`l Turing, in his immortal 1936 paper, observed that “[human] computing is normally done by writing... symbols on [twodimensional] paper”, but noted that use of a second dimension “is always avoidable ” and that “the twodimensional character of paper is no essential of computation”. We propose to exploit the naturalness of twodimensional representations of data by promoting twodimensional models of computation. In particular, programs for a twodimensional Turing machine can be recorded most naturally on its own twodimensional inputoutput grid, in such a transparent fashion that schoolchildren would have no difficulty comprehending their behavior. This twodimensional rendering allows, furthermore, for a most perspicacious rendering of Turing’s universal machine. 1
1.1 A Brief History of Quantum Physics.............. 4 1.1.1 Particles and Waves................... 4
, 2000
"... ..."
Post’s Machine.
"... In 1936 Turing gave his answer to the question ”What is a computable number? ” by constructing his now wellknown Turing machines as formalisations of the actions of a human computor. Less wellknown is the almost synchronously published result by Emil Leon Post, in which a quasiidentical mechanism ..."
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In 1936 Turing gave his answer to the question ”What is a computable number? ” by constructing his now wellknown Turing machines as formalisations of the actions of a human computor. Less wellknown is the almost synchronously published result by Emil Leon Post, in which a quasiidentical mechanism was developed for similar purposes. In 1979 these Post ”toy ” machines were described in a little booklet, called ”Post’s machine ” by the Russian mathematician Uspensky. The purpose of this text was to advance abstract concepts as algorithm and programming for school children. In discussing this booklet in relation to the historical text it is based on, the author wants to show how this kind of ideas cannot only help to teach school children some of the basics of computer science, but furthermore contribute to a training in formal thinking. 1