[jameshart]

This is a silly objection, trivially because obviously no finite physical system - brain or computer or whatever - can be constructed with the storage equivalent of an infinitely long tape. But if you allow for the fact that humans can do things like write things down and share information with other humans and build computers to store information, our information processing capacity is not limited to the set of states we can hold inside the atoms inside our head.

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?