Trivially, for any finite string (in a finite alphabet), there is a finite program (Turing machine, whatever) which outputs that string given empty input. Hence, "the mental activities of conscious, aware living beings" are trivially computable if there exists a finite string which describes them with perfect accuracy.
Furthermore, there obviously are some computable patterns in those activities, so the shortest possible computable program to generate that description will actually be shorter than the length of the description itself.
One could respond that a string describing those mental activities, no matter how accurately, is a different thing from the mental activities themselves. I think that is indeed the correct response, but it has nothing to do with any questions of computability.
(Another response would be to claim that those mental activities cannot be finitely described because they are actually infinite. Few however will want to claim that human minds are infinite.)
Furthermore, there obviously are some computable patterns in those activities, so the shortest possible computable program to generate that description will actually be shorter than the length of the description itself.
One could respond that a string describing those mental activities, no matter how accurately, is a different thing from the mental activities themselves. I think that is indeed the correct response, but it has nothing to do with any questions of computability.
(Another response would be to claim that those mental activities cannot be finitely described because they are actually infinite. Few however will want to claim that human minds are infinite.)