  Are minds subject to laws of physics? Are the laws of physics computable? Are
conscious thought processes computable? Currently there is little agreement as
to what are the right answers to these questions. Penrose goes one step further
and asserts that: {\it a radical new theory is indeed needed, and I am
suggesting, moreover, that this theory, when it is found, will be of an
essentially non-computational character.} The aim of this paper is three fold:
1) to examine the incompatibility between the hypothesis of strong determinism
and computability, 2) to give new examples of uncomputable physical laws, and
3) to discuss the relevance of G\"odel's Incompleteness Theorem in refuting the
claim that an algorithmic theory---like strong AI---can provide an adequate
theory of mind. Finally, we question the adequacy of the theory of computation
to discuss physical laws and thought processes.
