Customer Reviews

The Universal Computer: The Road from Leibniz to Turing

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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.

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.

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.

An entertaining book that will be enjoyed by anyone interested in mathematical logic or computation theory. Davis weaves history, anecdote, and mathematics into an exciting sketch of the major developments in mathematical logic and their role in the development of the computer. He does a commendable job in explaining the mathematics in an accessible fashion, without distorting it by over-simplification. A good book for people new to the field as well as those already familiar with these stories.

This book traces the contributions of mathematical logicians to the development of modern day computers. Its cast of characters begins with Gottfried Leibnitz in the 17th century, continues with George Boole in the 19th century, Gottlob Frege and David Hilbert straddling the 19th and 20th centuries, and ends with Kurt Goedel, Alan Turing and John von Neumann in the 20th century. The author brings these great scientists to life by describing their works in the context of their lives and times. He shows that despite their exceptional intellects, they often had difficult obstacles to overcome, both in their own frailties as well as in their adversaries.

The book's main theme is that although modern computers were born out of the need to do heavy number crunching during WWII, their foundation is in logic, the very logic by which our own brains work. It tells a compelling story of how the quest for understanding of the very foundations of mathematics led to the development of the machines that we have come to depend on so heavily in our daily lives.

There are a few places where the reading becomes a bit difficult as the author outlines the work of Goedel and Turing in the early part of the 20th century. Nevertheless, this book is quite readable overall and very enjoyable (as soon as I finished reading it the first time, I immediately started reading it again). I recommend it to general reader who would like to know more about the theoretical underpinnings of computers.

The only comment I have is that all of the mathematicians covered were from Germany, England and the United States. I was left wondering if there might be contributors from other countries that were overlooked.

I thought that this book was an excellent overview of the development of logical thought and it's relevance to the modern computer. Davis does a superior job of energizing a subject that is admittedly a little dull. I found myself rereading several of the sections to try to better understand some of the math involved, but overall, I think Davis found a nice balance between the complexity of the math and the history of logic. My one serious criticism of the book is that I found the chronology to be tough to follow, and I often found myself referring back to previous chapters to try and get a better sense of when events were happening. It is natural to assume that a book like this is presented in chronological fashion. The Universal Computer generally is presented that way, but there are some events that happen more or less simultaneously. This is important to the overview of the history of the field. I think the book could actually use a graphical timeline with the birth dates of the mathematicians and the significant events (i.e. 1902 - Russell's letter to Frege, etc.) that are involved. Other than that, the book is informative and enjoyable for those interested in the origins of the modern computer.

As a recent college graduate, who earned a B.S. in computer science, I thought this book provided some good background information on the people who worked to discover the underlying principles of automated mathematics implemented in a machine. The book was, for the most part, not terribly difficult to follow and gave more insight on the actual history of the individual people and times than I thought it might. Nevertheless, the individual histories, and time context put the points being made into a better framework. Not a long book, I recommend this to the more intellectual type, rather than an occasional reader.

Anyone who wants to understand computers should read this book. It describes the intellectual pre-histroy of the computer, and blends biographic vignettes in with the technical information. You'll learn alot, and enjoy it too!

John von Neumann, learning from Alan Turing, understood that a computing machine is really a logic machine. G.W. Leibniz, b. 1646, had dreamed of a universal artificial mathematical language. Leibniz invented a machine to do ordinary arithmetic. In 1674 he described a machine that would solve algebraic equations.

The explosion of research in the seventeenth century rested on a technique for solving algebraic exopressions and the discovery of Fermat and Descartes that geometry could be reduced to algebra. Leibniz saw the inverse relation of finding areas and calculating rates of change, (integration and differentiation). Leibniz proposed an algebra of logic. George Boole's family, (moving forward two centuries), recognized his ability. The family was too poor to provide him with a formal education. For fifteen years beginning at age nineteen, he ran and taught in a school he founded and worked as a creative mathematician. In his early work Boole applied algebraic methods. His classic monograph is on logic as a form of mathematics.

Bertrand Russell wrote to Gottlob Frege in 1902 that he agreed. Frege provided a fully developed system of logic. Russell's letter of 1902 stated that in the arithmetic of natural numbers using the logic Frege developed was inconsistent and that reasoning with sets of sets easily lead to contradictions. Cantor discovered infinite sets came in more than one size. Developing his set theory, considering transfinite numbers, Cantor worked in a backwater, Halle.

David Hilbert was at the University of Gottingen, (following Gauss and Riemann). His assistant aws Richard Courant. Hilbert had a profound interest in the foundations of mathematics. In 1900 for an international conference Hilbert made a list of problems fascinating generations of mathematics students. Hilbert's student Weyl and another mathematician, Brouwer, decided the limit processes develped by Cantor and others were shaky. In 1922 Hilbert issued a denunciation. During the 1920's Hilbert worked on the problem of consistency in arithmetic with Ackermann, Bernays, and von Neumann. He began with the Frege-Russell goal of defining purely logical terms. Hilbert's bold idea was proof theory.

Kurt Godel was born in Brno, Czechoslavakia. He attended the Univesity of Vienna. Hans Hahn, a member of the Vienna Circle, was Godel's principal teacher. Godel's paper on undecidability, 1930, looks like a computer program. Alan Turing found a mathematical model for an all-purpose computing machine. He showed computing could encompass more than arithmetical and algebraic functions.

Modern computers are combinations of logic and engineering. Many ideas converged to create the modern computer. The author knows many of the people described in his history and he is a specialist in the fields of logic, mathematics, and computer science. The account is excellent. This general reader found the book can be a positive experience even for neophytes.

Martin Davis, a notable logician who work for (and with) very notable mathematicians and scientists, writes about the relationship amongst math, logic, and computation.

He surveys the lives and achievements of thinkers from Leibniz and Babbage to von Neumann and Turing and discusses what these ideas mean for modern computing.

The Universal Computer is a rather quick read, with the biographical content being particularly brisk, and there are points where some readers may lik...more Martin Davis, a notable logician who work for (and with) very notable mathematicians and scientists, writes about the relationship amongst math, logic, and computation.

He surveys the lives and achievements of thinkers from Leibniz and Babbage to von Neumann and Turing and discusses what these ideas mean for modern computing.

The Universal Computer is a rather quick read, with the biographical content being particularly brisk, and there are points where some readers may like more detail, but this can be viewed as an accomplishment considering the density of the topics covered, including boolean Algebra, set theory and diagonal method, algebraic invariants, Godel's undecidable propositions, and Turing machines. Also, the author includes a lengthy notes section explaining the beginnings of the finer points of these matters and references for working through the actual mathematics and technology discussed.