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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 Turing-machine halting problem; and decide the predicate calculus. Are accelerating(More)
A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine-a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the(More)
A survey of the ÿeld of hypercomputation, including discussion of four a priori objections to the possibility of hypercomputation. An exegesis of Turing's pre-and postwar writings on the mind is given, and Turing's views on the scope of machines are discussed. 1. What is hypercomputation? Hypercomputation is the computation of functions or numbers that(More)
It's really good to see Alan Turing finally getting his due in the popular media. He's been a large figure in the mathematical foundations of modern computing from the 1930s (along with John von Neumann and Emil Post, to name just a couple) for quite a long time. Despite this, and despite the fact that Tur-ing's work is often glossed in elementary computing(More)