[mlyle]

Came here to write this, was glad to see it's already here.

All the limits that exist for computing machines almost certainly exist for us too; we don't need to solve the halting problem; we don't solve large NP-hard problems; etc.

Of course, if one believes there's something mystical about brains -- whether a soul or access to quantum computing -- perhaps one would disagree.

[soist]

The brain is not a computer. Computation is an abstraction of thinking but it does not coincide with it.

[aSanchezStern]

This is a particular philosophical conjecture, not a proven scientific fact. We don't understand enough about the human brain to prove whether it is fundamentally different from a very complex computer.

[roywiggins]

My intuition is that we probably should assume they're different until proven otherwise, but also that brains are probably not Turing oracles either.

[roywiggins]

I think this is quite possible, but it doesn't imply that the strong Church-Turing thesis isn't true: brains could still be Turing equivalent to computers, in that neither would be able to solve the halting problem for the other (at least insofar as humans have a "halting problem", which maybe we don't, but you could formulate other things like predicting behavior, which in standard computation is also Turing complete usually)

Since humans don't seem to be particularly good at solving the halting problem even for very small TMs, it doesn't seem that likely to me that we are categorically stronger at it than computers, whether our cognition is truly "computation" or not.