The human brain isn't Turing-complete.
Turing completeness implies infinite recursion, which the brain obviously can't do.
Turing completeness implies infinite recursion, which the brain obviously can't do.
But also, the claim lacks evidence: We’ve never seen a human being yet whose program didn’t eventually halt.
That doesn’t mean the hardware isn’t capable of running a program that never halts, just that we haven’t found such a program yet.
Indeed if you consider human mindware as a whole, given that when humans reproduce they create new copies of the mind running in new bits of hardware... maybe Human minds are infinitely recursive after all?
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.
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.