[mannykannot]

While I agree that comparing a human brain or mind to a Turing machine is not helpful, the objection you make here is less significant than it first appears.

There is a subtle difference between unbounded recursion, which a Turing machine is taken to be capable of, and the actual ability to achieve infinite recursion. In no application of a Turing machine, either as an actual physical device or as a hypothetical one in a logical argument, is it ever required to perform infinite recursion, which would just be one way of not halting.

For all practical and theoretical purposes, what matters is that the machine being considered does not exhaust its ability to recurse while performing the computations being considered. Consequently, the standard practice, of saying that computers and certain other devices are Turing-equivalent, with the usually-implicit caveat of being so up to the limit of their recursive ability, is both reasonable and useful.

[otabdeveloper4]

> For all practical and theoretical purposes, what matters is that the machine being considered does not exhaust its ability to recurse while performing the computations being considered.

You're right, and thanks for the more strict definition.

Regardless, the 'recursion limit' of the human brain is really low. (Say, seven things at once or thereabout; not going to links proofs but it's a non-controversial statement.)

Certainly not enough to implement any sort of computing machine. Human brains are notoriously bad at arithmetic and state machines.