Another good, non-technical exposition is in Rudy Rucker's Infinity and the Mind
He also claims to disprove Penrose's speculations, but I didn't follow the argument. (something to do with Goedel numbers being bigger than people can name...)
I just finished reading the reviews and it sounds like a must read for me. Rucker seems to have an interesting view of the implication of Gödel's Platonism. The main difference with Penrose that stands out in those reviews -and what I've scanned thus far on the web - is that Rucker believes a Robot can be conscious as well, rocks are conscious, etc.
That sounds a bit similar to Grandpierre's view, so I'm also pinging betty boop for comments