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

Shadows of the Mind is undoubtedly a less populist book than its predecessor "The Emperor's New Mind". It is also significantly more technical in places than the predecessor. Its purpose is to extend the Godel based arguments used in ENM in several directions. Firstly to attempt to address various criticisms of the central argument of the previous book and then to develop some new ones. Also there is a discussion of the application to Robotics. An example of this sort of discussion is whether any capability of a Robot to learn would undo any of the Robot restrictions deduced in his basic argument. After all learning (human or robotic) will imply going beyond previous restrictions and being aware of new facts.

So there is a subtle argument needed to continue to show that despite this, humans will come out on top. If you are interested in this kind of subtlety after reading ENM then this is the book for you.

In effect Penrose is right at the heart of the Mind-Machine debate in this book. I give an overview of this debate as follows:

We need to find a scientific theory of the Mind. So we can examine what kind of cognitive or thinking device it might be, recognising that it also thinks about Mathematics. For that we need a model of cognition sufficiently general: the Turing Machine model is available and generally considered to be that model - there are no obvious rivals. So one can focus on whether the Turing Machine model could really be a model for the Human Mathematical Mind. If the answer is "yes" we would conclude also: Robots could have Minds.

Penrose draws the conclusion about mathematical reasoning that:

G: "Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth".

This statement isn't quite the statement that the Mind is not a Turing Machine (algorithm here), and some critics have attempted to expose the gaps. In this book Penrose discusses several lines of argument to close the gap. A possible rebuttal might be: "could mathematicians just be using unsound algorithms" - the faulty machine argument. This is very close to questions in the foundations of mathematics itself - after all is this suggesting that mathematics itself is fundamentally unsound? If so where is that unsoundness? So Penrose comes round to the conclusion step by step and through 100 odd pages, that the statement G above implies that indeed the Mind is not a Turing Machine.

This latter conclusion however introduces another problem: if the Mind is not a Turing Machine / algorithm then what sort of (scientific) model exists for it? At the end of the book Penrose examines a generalisation of the Turing Machine model (called Oracle Machines and also due to Alan Turing) and determines that a statement similar to G also applies to that model class as well. Thus the story is left incomplete and I would be tempted to say that somewhere a model M exists of which we can deduce:

"Human mathematicians are using M to ascertain mathematical truth"

However Shadows of the Mind ends without a discovery of that model M. So maybe the answer lies in studying Quantum properties, or in other aspects of these obscure machine models? If you want to be able to study this question further Shadows needs to be studied (and "studied" is the word)!

Shadows of the mind is a terrific book from a brilliant author.

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!

The purpose of this book is to explore the connection between what is known in the areas of mathematics and physics to the way in which human brains function. Quite apart from this, the book is an excellent commentary on some on the more significant developments in physics and mathematics during the last hundred years. It is written so as to be readable by the non-scientist but those without a scientifc background could find some parts heavy going.