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text: '[summary:Every [-effectively_computable] [-3jy] is [Turing_machine Turing-computable].]\n\nThe **Church-Turing thesis** (often abbreviated **CT thesis**) states:\n> Every effectively computable function is Turing-computable\n\nThat is, for every function which can be computed by physical means %%note:So no [ hypercomputers]%% there exists a [ Turing machine] which computes exactly that.\n\nThe Church-Turing thesis is not a definite mathematical statement, but an inductive statement which affirms that every sensible model of computation we can come up with is equivalent or at least [reduction reducible] to the model proposed by Turing. Thus, we cannot prove it in a mathematical sense, but we can [ gather evidence for it].\n\nFor example, this model was proven to coincide with Church's lambda calculus, another universal model of computation, and the equivalence between Church's lambda calculus and Turing's automatic machines is often taken as [4j7 evidence] that they correctly capture our intuition of "effectively computable".\n\nThere are many [ consequences] of the CT thesis for computer science in general, artificial intelligence, [11w epistemology], and other fields of knowledge.',
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