Church-Turing Thesis

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Slightly more in detail, the (physical) says vaguely that what is computable in the mathematical sense of computation is precisely what is “effectively” computable (physically computable).

In interpreting this one has to be careful which concept of computation is used, there are two different main types: Indeed, there are physical processes (described by the wave equation) which are not type-I computable (Pour-El et al.

He seems to be arguing that since Turing machines cannot represent real numbers, they cannot compute this algorithm.

On the other hand, it can be easily computed with pen and paper, and he gives an example of a ruler-and-compass algorithm for evaluating it.

Equivalently, it holds that a function is recursive if and only if it is computable.

While this thesis is not a precise mathematical statement, and therefore cannot be proved, it is almost universally held to be true.These traditional algorithms are known also as classical or sequential.In the original thesis, effectively computable meant computable by an effective classical algorithm.All links about things talked in this talk just seem to lead to other texts and such by this author.Might not be a good sign but maybe it's just a very hard to grasp realm.the Church-Turing thesis is not a theorem and cannot be proven true or false This is not quite correct: It cannot be proven true.But it could be proven false with a counterexample.New species of algorithms have been and are being introduced.We argue that the generalization of the original thesis, where effectively computable means computable by an effective algorithm of any species, cannot possibly be true.The speaker would simply have to point to a concrete algorithm that can be performed by a person with pencil and paper but not by a Turing machine (or vice versa).I haven't had the time to watch the video, but from the comments here it appears that the speaker did not provide such an example.


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