I have recently finished a lecture of “The Emperor's new mind” by Roger Penrose. The book deals with the consciousness from the point of view of mathematician and physicist turned philosopher.
It starts by examining an idea of artificial intelligence. Is it possible to build a computer that will be intelligent? What are the criteria for deciding if such mechanism is truly intelligent? Penrose is doubting that a real SI can be constructed. The reason for this is that a computer works according to the rules of classical physics, hence is only able to follow an algorithm. The brain, on the other hand, allow as to jump to the conclusion, without following an algorithm. There are mathematical theorems whose truthfulness cannot be decided upon by following strict rules invoked by a well defined algorithm. Yet mathematicians are able to achieve this. How is it possible? What could be a source of indeterminism driving non-algorithmic operation? Penrose want's to convince a reader that the source may be hidden in quantum effects that are happening in our brain.
The rest of the book serves as a detailed explanation of this, highly controversial, position. It is interesting, yet challenging journey. Penrose starts it from a discussion of Turing machine, as a theoretical model of a classical computer, the Godel theorem then goes to fractals, classical mechanics, quantum mechanics, theory of relativity and finally quantum gravity.
As I said the book was a real challenge to me. I am a wet lab biologist. I learned basic physics and math, that is needed in my work, but the complexity of the topic was mind-boggling. That being said I feel that Penrose was doing generally a good job in explaining the inherently complicated physics and mathematics needed to follow his argument. I would certainly need to re-read “The Emperor's new mind” to get a better understanding of the subject but I am quite happy that I did work my way through it. It was not easy, but I think it was well worth it. Even if I still suck at quantum physics, or all physics for that matter, at least I got a good refresh from my days as a freshman at the university. At worst, Penrose ideas can serve as a pot of tasty ideas for some good science-fiction story. If I am not mistaken, some similar concepts can be find in Mars trilogy by Kim Stanley Robinson. On the other hand Vernor Vinge would probably argue with the premise of Penrose's book as it kills his Singularity idea.
I will finish by saying that I believe it is necessary to crawl out from one's professional niche once in a while and give a try to some idea from other parts of science. Even when one is getting a serious headache trying to figure out lambda calculus and multidimensional space.