Jack copeland gave an interesting lecture on the church-turing thesis today the ct thesis is apparently much misunderstood historically, it's the claim that any algorithm can be computed by a turing machine.
The extra-strong church-turing thesis (which, recall, neither church nor turing ever asserted) entails the impossibility of all such machines but such a strong assertion is entirely unwarranted no-one has ever proved hypercomputation impossible.
The church-turing thesis essentially states that a function is algorithmically computable if and only if it is computable by a turing machine as indicated by tony mason’s response, computability was an ambigious term in the past and in establishing the church-turing thesis, a bit of clarity was restored with regards to what we acknowledge as a computable function. When the church-turing thesis is expressed in terms of the replacement concept proposed by turing, it is appropriate to refer to the thesis also as ‘turing’s thesis’, and as ‘church’s thesis’ when expressed in terms of one or another of the formal replacements proposed by church. Alonso church, at princeton, devised the lambda calculus which formalises algorithms as functionsmore later in the course neither knew of the other’s work in progressboth published in 1936 the demonstrated equivalence of their formalisms strengthened both their claims to validity, expressed as the church-turing thesis. The church-turing thesis (formerly commonly known simply as church's thesis) says that any real-world computation can be translated into an equivalent computation involving a turing machine in church's original formulation (church 1935, 1936), the thesis says that real-world calculation can be done using the lambda calculus , which is equivalent to using general recursive functions.
Notice that the turing-church thesis does not entail thesis m the truth of the turing-church thesis is consistent with the falsity of thesis m (in both its wide and narrow forms. In computability theory, the church–turing thesis (also known as computability thesis, the turing–church thesis, the church–turing conjecture, church's thesis, church's conjecture, and turing's thesis) is a hypothesis about the nature of computable functions.