Shadows Of The Mind: A Search for the Missing Science of Consciousness [Paperback]

Penrose's argument that conscious thought is not based on computation as we understand it is sound. Whether this can be strictly ascertained from Godel's theorem is still open to question I think.

However his overall conclusion that when we think, we may be using quantum mechanical counterfactuals to take us beyond the limits of computation, is an intriguing possibility.

I would recommend this book strongly to anyone with a reasonably high level of scientific education. Its hard work to read because the questions he asks are so deep and his approach to answering them is so exhaustively rigorous.

Penrose is not an evangelist like Richard Dawkins so his writing style is not as engaging to a popular audience. Nevertheless it is worth ploughing through this book to at least be rewarded in the end with the firm belief that one is definitely not merely a computer controlled robot!

However he is also a grossly mistaken man who has strayed far from his own field - a good Mathematical Physicist he may be but he's no Philosopher or Psychologist.

The main argument of the book centres around Godel's Theorem (or rather Turing's formally equivalent version) to show that mathematical reasoning is non-computational.

This basically begins with the premise 'assume that A is the algorithm which can decide if any given algorithm will terminate' and ends with the contradiction 'if A terminates then A never terminates'.

Penrose concludes that therefore A never terminates and that we must have used a non-algorithmic method for telling this ourselves (since A is the best algorithmic method).

However Penrose has misrepresented Godel, the actual conclusion is the falsity of the premise (that there could ever actually be an algorithm which would tell us if any algorithm terminates).

If Penrose is right and A never terminates then he has violated the initial premise of what A does and invalidated the whole argument.

The whole book then flows from this failure of logical reasoning to a far-out theory of consciousness that is highly implausible and scientifically naive.