Disclaimer: I haven't read the book (but am now planning to) and may be completely off mark with my comments, but here's what I make of all this. Sure, there a

Disclaimer: I haven't read the book (but am now planning to) and may be completely off mark with my comments, but here's what I make of all this. Sure, there are certain things that are not computable. This is a theoretical limitation on any computational system. Is Penrose saying that there's something special about consciousness or high-level thought that puts them into the class of things that are not computable? But the computability of something is a mathematical concept, and surely we'd have to define consciousness and intelligence in a mathematical way to be able to put them in such a class. In light of this and the fact that we're only really beginning to have a theoretical understanding of what brains do, it seems to me very dubious to make the bold claim that intelligence/consciousness come about via non-algorithmic processes. Perhaps I don't understand what he means by non-algorithmic processes outside the abstract computation theoretic setting, and in the context of neural computation (in fact, "non-algorithmic" and "computation" seem to contradict each other right off the bat). Not only that, but our brains compute as well. We get input, and we produce output in the form of neuronal firing and motor activity, the latter being what amounts to behavior, and the former being (according to materialists) responsible for intelligence and consciousness. So the brain does compute outputs! But according to Penrose, it seems, such outputs are not computable! Or if they are, they are not enough to account for intelligence/consciousness. So what gives? Again, I might have failed to appreciate his and your points completely, but you've certainly piqued my curiosity and I will check out some more of Penrose's work.