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The Universal Computer: The Road from Leibniz to Turing, Turing Centenary Edition

Martin Davis
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
[Reviewed by
Richard Wilders
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The Turing Centenary Edition is a mildly edited republication of the original, brought out as part of the celebration of the 100th anniversary of Alan Turing’s birth. I read and enjoyed the first edition. Upon reading the second I was again impressed. The book remains fresh and compelling.

The review of the first edition did not mention the final chapter on “Computers, Brains, and Minds.” The author presents a very nice summary of the issues regarding the question of computer intelligence. This is an issue which was first raised by Turing himself when he proposed his famous Turing Test. The question relates to the limitations of formal systems — how much can we learn/prove using a system which manipulates strings according to a rigid set of rules? Gödel’s Incompleteness Theorem and the Turing Halting Problem seem to point to a permanent human advantage, but that’s mainly because we are willing to give up and jump outside any system which seems to block our path. The also includes a nice discussion of Deep Blue and Watson — the famous Chess and Jeopardy playing computers. Davis argues that neither passes the Turing Test because of the restricted domain they were designed to deal with. While I agree with his assessment, they are both amazing demonstrations of what is now possible.

As did the previous reviewer, I recommend this book very highly. It is suitable for a high school or college library.

Richard Wilders ( is Professor of Mathematics and Marie and Bernice Gantzert Professor in the Liberal Arts and Sciences at North Central College. His chief interests are in the history and philosophy of mathematics and science.

Leibniz’s Dream 
Boole Turns Logic into Algebra 
Frege: From Breakthrough to Despair 
Cantor: Detour through Infinity
Hilbert to the Rescue
Gödel Upsets the Applecart
Turing Conceives of the All-Purpose Computer 
Making the First Universal Computers
Beyond Leibniz’s Dream