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3 of 4 people found the following review helpful
4.0 out of 5 stars About Non-computability, 25 Sept. 2010
This review is from: The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Popular Science) (Paperback)
My copy of this book is now 21 years old, but I thought it appropriate to write a short historical review. When I first read this book I was interested to read in a semi-technical way about many of the Physics and Computation ideas of Roger Penrose. I am sure that many are still interested in the book for that reason. Since then Penrose has written other books, but this provides an introduction to his ideas which is half way between popular science and textbook. What has happened in the years that have followed is that this work has undoubtedly stimulated many researchers and others.

The other aspect of the book was his specific arguments about AI: which have ired many critics. Indeed his later book (Shadows of the Mind) contained a revised argument and dealt with about 20 criticisms of the AI argument from this book. Nevertheless this was not enough and more criticisms appeared which he later discussed in other works. So there is quite a trail to follow here for those who wish to take these topics seriously.

I would now suggest that he was really trying to make the case for the importance of non-Turing-Computability in this book. That it is important in scientific arguments from Cognition Theory and AI to Quantum Physics. Non-Turing computability is a very subtle topic to discuss (it was the subject of Turing's logic Ph.D) especially in a philosophically broad way. Many of the topics like Fractals and Penrose Tiling which found their way into this book, and do not immediately seem relevant to the arguments, are there to emphasise and display some non-computable mathematical entities. Oversimplifications of Penrose's arguments usually miss the significance of non-computability in them.

Having said all this I think that were this book to be written now, then some sections could be reworded. As a specific detail I think that in discussing the historical evolution of "algorithm" the definition of that term changes in the book without being noticed. It took me a few readings to notice this.

So if you want to delve into the debate about non-computability in physics and AI this is a book to read, but be aware that it is only the beginning of a longer story. The physics/cosmology discussions are a good introduction to his approach to those topics too.
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