The Universal Computer: The Road from Leibniz to Turing (Hardcover)

~ (Author) "SITUATED SOUTHEAST OF the German city of Hanover, the ore-rich veins of the Harz mountain region had been mined since the middle of the tenth..." (more)
Key Phrases: halting set, unary string, transfinite ordinal numbers, Alan Turing, Continuum Hypothesis, World War (more...)

Editorial Reviews

Amazon.com Review

Computers rely on such things as semiconductors, memory chips, and electricity. But they also rely on a hard-won body of scientific knowledge that has enabled the now-ubiquitous devices to perform complex calculations, multitask, and even play a game of solitaire.

Martin Davis, a fluent interpreter of mathematics and philosophy, locates the source of this knowledge in the work of the remarkable German thinker G. W. Leibniz, who, among other accomplishments, was a distinguished jurist, mining engineer, and diplomat but found time to invent a contraption called the "Leibniz wheel," a sort of calculator that could carry out the four basic operations of arithmetic. Leibniz subsequently developed a method of calculation called the calculus raciocinator, an innovation his successor George Boole extended by, in Davis's words, "turning logic into algebra." (Boole emerges as a deeply sympathetic character in Davis's pages, rather than as the dry-as-dust figure of other histories. He explained, Davis reports, that he had turned to mathematics because he had so little money as a student to buy books, and mathematics books provided more value for the money because they took so long to work through.) Davis traces the development of this logic, essential to the advent of "thinking machines," through the workshops and studies of such thinkers as Georg Cantor, Kurt Gödel, and Alan Turing, each of whom puzzled out just a little bit more of the workings of the world--and who, in the bargain, made the present possible. --Gregory McNamee

From Publishers Weekly

This thoroughly enjoyable mix of biographical portraits and theoretical mathematics reveals how a sequence of logicians posed the conceptual questions and contributed the crucial insights resulting in the development of computers long before the technology was available to build even the simplest machines. An intriguing portrait of the great 17th-century mathematician G.W. Leibniz, a pivotal figure in the history of the search for human knowledge, launches this account by New York University professor emeritus Davis (Computability and Unsolvability). Steeped in Aristotelian ideas of perfection but trained in modern engineering, Leibniz conceived the idea of a universal system for determining truth. His contributions to this system are as diverse as the ingenious Leibniz Wheel (an early calculating machine) and the notation used today for calculus. His ideasDin particular, his recognition of the deep connection between systems of notation and actual physical devices for performing computationDinspired mathematicians and logicians, including George Boole, Gottlob Frege, Georg Cantor, David Hilbert and Kurt G del, until Alan Turing used them to develop the powerful mathematical tools that underlie modern computers as well as some of the earliest computer prototypes. After Leibniz, people thought about the problem of building computational systems; after Turing, people got busy building the machines. Davis has told the fascinating story in between. Full of well-honed anecdotes and telling detail, the book reads like a masterful lecture. Presenting key mathematical ideas in moderate depth, it also offers a solid introduction to the field of computer science that will captivate motivated readers. Agent, Alex Hoyt.
Copyright 2000 Reed Business Information, Inc.

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Product Details

• Hardcover: 256 pages
• Publisher: W. W. Norton & Company (October 2000)
• Language: English
• ISBN-10: 0393047857
• ISBN-13: 978-0393047851
• Product Dimensions: 9.2 x 6.8 x 1 inches
• Shipping Weight: 1.2 pounds
• Average Customer Review: 4.7 out of 5 stars  See all reviews (10 customer reviews)
• Amazon.com Sales Rank: #376,339 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

63 of 66 people found the following review helpful:

5.0 out of 5 stars magnificent; will become a classic, October 29, 2000

By A Customer

This is one of the best popular books on computer science or mathematics in years. Most authors in this area (e.g., Berlinski) have no special expertise in the subject matter or its history; that doesn't guarantee a bad book, but makes it hard to write a good one. Davis is a refreshing exception:

* He is a brilliant researcher, who made fundamental contributions to areas such as computability (the Davis-Putnam- Robinson theorem, related to Hilbert's 10th problem) and algorithms (the Davis-Putnam algorithm for solving satisfiability problems).

* He is a master expositor (his 1958 book "Computability and Unsolvability" was one of the very first textbooks in its area, yet it is still widely read today despite the many other books written on this subject over the past 42 years).

* He has spent the last twenty years studying the history of logic and computation.

Davis's book is all one would hope for given his qualifications. It is insightful and engaging, and full of fascinating information that is hard to find elsewhere. I cannot imagine a better book on this subject.

13 of 13 people found the following review helpful:

5.0 out of 5 stars What a compelling book!, January 24, 2001

By	Josh Fisher (Miami, FL) - See all my reviews

This popular treatment of the development of computing turned out to be a book that I simply couldn't put down. Martin Davis interlaces the lives of the people who laid the groundwork for computing (and what interesting lives they led!) with a very understandable treatment of the technical side of the underpinnings of computing. I've heartily recommended this to my friends--technical minded and not--as book I think they really want to read.

11 of 11 people found the following review helpful:

5.0 out of 5 stars The best popular history of the computer as logic engine, March 18, 2003

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

While most of us consider computers to be some special silicon in a white box, they are in fact machines that execute rules in applied logic. For this reason, the history of computing has two tracks. The first is the hardware track, which generally starts with Charles Babbage and progresses through the recent advances in integrated circuits. One chapter of the book traces the historical development of computer hardware, starting with the Jacquard loom and moving up to the modern personal computer. The second is the history of logic that can be mechanically applied, which is the primary focus of this book.
Once again, the mathematics largely predates the applications. It is amazing how mathematicians develop mathematical structures that initially have no applications and then after some time, something appears that requires that form of mathematics. To me, it is nothing sort of amazing that Alan Turing invented an abstract universal computer long before any of the physical counterparts existed. No one has ever been able to substantially improve on his Turing machines and it is widely believed that they cannot be improved. This theme permeates the book and Davis does a very good job in presenting all of the advances in a historical context.
The contributions of Leibniz, Boole, Frege, Cantor, Hilbert, Godel and Turing are all described in detail, and it is clear how one person's work was built using that done by their predecessors. Other people noted include Bertrand Russell, Leopold Kronecker, and Albert Einstein.
This is the best popular history of the development of the computer viewed as a logic engine. I strongly recommend it as a book for courses in the history of mathematics and computing.