Our friend Will Brown points to this article from Chris Chatham:
Chris argues that the metaphor that “our brains are computers” has been valuable. But, like most metaphors, it is eventually checked by reality. He points out how vastly different our brains are from digital computers. Why it’s almost as if one evolved biologically, and the other were artificial!
I suspect that the brain/computer comparison is more than a metaphor. The brain is a strange organic system far different from what any human computer scientist would design. That said, I suspect that it can be emulated by a sufficiently powerful Turing Machine.
Informally the Church–Turing thesis states that if an algorithm (a procedure that terminates) exists then there is an equivalent Turing Machine (equivalently: recursion|recursively-definable function or lambda calculus|λ-definable function) for that algorithm. One conclusion to be drawn is that, IF a computer can effectively calculate an algorithm THEN so can an equivalent Turing Machine.
So even if the brain is not a Turing machine, it could be emulated by a sufficiently powerful Turing machine. In theory.