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The Universal Computer: The Road from Leibniz to Turing

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Computers are everywhere today -- at work, in the bank, in artist's studios, sometimes even in our pockets -- yet they remain to many of us objects of irreducible mystery. How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essen Computers are everywhere today -- at work, in the bank, in artist's studios, sometimes even in our pockets -- yet they remain to many of us objects of irreducible mystery. How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.


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Computers are everywhere today -- at work, in the bank, in artist's studios, sometimes even in our pockets -- yet they remain to many of us objects of irreducible mystery. How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essen Computers are everywhere today -- at work, in the bank, in artist's studios, sometimes even in our pockets -- yet they remain to many of us objects of irreducible mystery. How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.

30 review for The Universal Computer: The Road from Leibniz to Turing

  1. 4 out of 5

    Andrew Nguyen

    Originally assigned as an optional read in a theory of computation class 5 years ago, I finally got around to reading this (Dr. Lutz, please revise my grade to an A). I'm going to heavily caveat this review because I'm a big fan of both history and computing, a pretty specific niche. Further, a reader probably won't enjoy this book without a little formal training in mathematics. This book is a whirlwind tour of mathematical ideas and people that led to the birth of the digital computer. Startin Originally assigned as an optional read in a theory of computation class 5 years ago, I finally got around to reading this (Dr. Lutz, please revise my grade to an A). I'm going to heavily caveat this review because I'm a big fan of both history and computing, a pretty specific niche. Further, a reader probably won't enjoy this book without a little formal training in mathematics. This book is a whirlwind tour of mathematical ideas and people that led to the birth of the digital computer. Starting with Gottfried Leibniz and his dream of a language to describe abstract ideas and ending with Alan Turing's universal computing machine, Davis does a really nice job in drawing the line from abstract logic to formal mathematical systems to the computers we see today. I really enjoyed the biographical portions of this book. Academic holy wars are part and parcel of any revolutionary idea, and each mathematician has a worthy foe: institutionalized ideas, vengeful colleagues or himself. Unlike in a Michael Lewis biography, these men aren't deified ad nauseam. Rather, Davis lays out their insecurities, horrifying political views and academic failures very plainly. Even the most brilliant mathematicians have failures of foresight or imagination in the realm of their greatest power. These failures really emphasize the difficulty of the journey from abstract thought to physical computer and gives the book a fun story arc. Besides just biographical details, each chapter describes the ideas pioneered by each mathematician. Davis tries to explain these ideas in the most elementary ways possible and this succeeds for the most part. I personally enjoyed the description of diagonalization proofs, and the Turing Machine examples made me nostalgic for computer science curriculum. I followed very closely until the chapter on Godel's completeness theorem. This theorem is so subtle and gets referenced so often, I really wished that section would have given more explicit examples instead of oblique references to Principa Mathematica or Peano's Arithmetic. Overall, I really enjoyed this read. Definitely recommended if you're interested in math, computers and history.

  2. 5 out of 5

    Adam Casto

    An excellent overview of the history of mathematics as it pertains to the development of the concept of the modern computer. It can be a little difficult to follow at times as it chronologically jumps around between references and anecdotes. However with a bit of attention, it works to weave a wonderful picture of how a machine many of us take for granted these days came to be.

  3. 4 out of 5

    Griffin Strain

    I was tasked to read this discussion of the evolution of logical thought and mathematics for my final class in my computer science degree, introduction to computational theory. Overall, I was very impressed with the work and the ability of the author to work the line between presentation of mathematical theory and historical background on the important figures in the creation of computable thought. On several occasions, it is evident that the author has strong opinions on certain facts and makes I was tasked to read this discussion of the evolution of logical thought and mathematics for my final class in my computer science degree, introduction to computational theory. Overall, I was very impressed with the work and the ability of the author to work the line between presentation of mathematical theory and historical background on the important figures in the creation of computable thought. On several occasions, it is evident that the author has strong opinions on certain facts and makes those opinions known, especially with some of the discussion about who should receive the credit for first putting the idea of a computing machines into practice. However, overall, I think the work reads as a fairly comprehensive view at a good number of mathematical ideas that came together to form computational theory. I would definitely recommend this book to anyone interesting in the origin of computing or computational logic.

  4. 4 out of 5

    Aadeshnpn

    Great interesting book and finished it in one go. Had read bit and pieces of all the awesome people mentioned in this book. This book provided details in their life and their contributions for the advancement of mathematics, computation and human knowledge.

  5. 5 out of 5

    Steve

    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 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.

  6. 4 out of 5

    Ushan

    This short book consists of mini-biographies of Leibnitz, Boole, Cantor, Hilbert, Frege, Gödel and Turing. Davis is a co-discoverer of the Davis-Putnam algorithm, and he knew personally some of the people he mentions; other than his short reminiscences, there is little in this book that a reader of Neal Stephenson does not already know. There is of course much more to the story; the P=?NP problem was first formulated in Gödel's letter to von Neumann; Davis mentions a biographer of Leibnitz who w This short book consists of mini-biographies of Leibnitz, Boole, Cantor, Hilbert, Frege, Gödel and Turing. Davis is a co-discoverer of the Davis-Putnam algorithm, and he knew personally some of the people he mentions; other than his short reminiscences, there is little in this book that a reader of Neal Stephenson does not already know. There is of course much more to the story; the P=?NP problem was first formulated in Gödel's letter to von Neumann; Davis mentions a biographer of Leibnitz who was executed by the Nazis for anti-Nazi activities, but not the great German logician who starved to death in a Czech prison because he was a Nazi.

  7. 4 out of 5

    Alex

    Since picking up "Logicomix", I realized I have a few other books on the mathematical foundations of computing. While Logicomix disappointed, "Engines of Logic" certainly had to meaty math goods I was looking for. If nothing else, it was a good pointer to topics that warrant further investigation from a variety of other sources. I can't imagine anyone but a computer-dork like me would find this interesting. Kinda like Rush…for books. But if you're into this sort of thing, it's worth picking up.

  8. 4 out of 5

    Peter Mcloughlin

    This book is a fun book to read on the history and development of the idea behind the universal computer. It is not very deep in terms of the Mathematical ideas involved but it gives a flavor of the ideas. It is really good at profiling the colorful characters who developed these ideas and their often dramatic lives. A fun book to read and not very technical despite the title.

  9. 5 out of 5

    Jim Mccormick

    Outstanding review of key personalities behind the development of logic. Interesting summary of the design of the earliest computers. Very reasonable perspective based on first-hand experience of mid-century computer developments. Objective presentation of divergent personal views of many of these great minds.

  10. 5 out of 5

    John Doe

    Its a must read for any person works on computers. There are many people already commented on the contents of this book. Here I want to talk about how and why I picked up this book, or how the hell this book interests me in the first place. So I was learning and reading how to write programs and getting familiar with several programing languages, then what intricate me most is how similar all those so called programing languages are and in a way they all follow certain patterns, like they all hav Its a must read for any person works on computers. There are many people already commented on the contents of this book. Here I want to talk about how and why I picked up this book, or how the hell this book interests me in the first place. So I was learning and reading how to write programs and getting familiar with several programing languages, then what intricate me most is how similar all those so called programing languages are and in a way they all follow certain patterns, like they all have these very basic concepts: class, objects, structures, logic operations and most importantly control flow structure aka the iteration and recursion loop. But how are all these related to programing? What is programing exactly? there are so many sources saying that its kind of a smart way to solve problems. Then how about algorithms? Isn't Algorithm the way to solve problems? Like step by step find answer to a specific problem? well, I guess everyone is right, but I still couldn't understand what the hell are all those things, and most importantly why bother?? I bet lots of people have the same confusion as me. And the key to understand these two basic questions is .....eeemmm... this book. lol I am not joking. Here comes my personal version of understanding. Centuries ago, people who were searching for truth, god's existence, laws of nature,wanted to find a way to deductively/mathematically/logically/systematically unfold *All The Truth*, aka Leibniz's crazy idea... then comes with the continual efforts of great mathematicians, logicians and philosophers, finally we have computable machines, encodings which use math logic operations to abstract lots of information of human knowledge into machine language: 0s and 1s. Boom we have computer that almost fufills Leibniz's dream. Yet, its a litter different from the original hope. That's machine mostly can just operate under defined instructions(leave machine learning and neural network alone). And the biggest advantage of machine is that it can exhaustively do the same thing over and over again, aka loops. Finally I have an idea what the hell is programing and algorithms. That is to build an abstraction such that the problem in our human knowledge could be expressed/understood in a simulated/repetitive/iterative/recursive way such that it could be whole heartily embraced by machines 0s and 1s.. To put it in a rude and unprecise way, when we say we are programing, we are indeed trying to turn things into loops. Nonetheless, according to mathematicians world view, everything is based on addition, the acceleration brought by computers binary operation makes our world looping effortlessly. Ins't it the case???

  11. 5 out of 5

    Kerem

    Probably one of the most fascinating "history" books I've ever read. Starting with Leibniz' far ahead vision, the book goes through the history of "logic" that resulted in today's computers (and whatever will come next of them). The exciting lives of Boole, Frege, Cantor, Hilbert and Gobel, how they reached the major milestones in this history, and their failures and problems are presented almost in a novel fashion (rather than heavy maths). The book's final is a lengthy tribute to Turing, who w Probably one of the most fascinating "history" books I've ever read. Starting with Leibniz' far ahead vision, the book goes through the history of "logic" that resulted in today's computers (and whatever will come next of them). The exciting lives of Boole, Frege, Cantor, Hilbert and Gobel, how they reached the major milestones in this history, and their failures and problems are presented almost in a novel fashion (rather than heavy maths). The book's final is a lengthy tribute to Turing, who was again well ahead of his time, and got frustrated and suffered a lot that he well deserves such a tribute. Truly exciting book with some of the key logic and maths behind, and strongly recommend.

  12. 4 out of 5

    Roberto Paredes

    I really enjoyed this one. It has some math and logic concepts that are easy to digest, along with their historical context. The Universal Computer will show you who are the fathers of modern computing: how their lives where; their science, ideas, and how each one put a piece on the puzzle that was finally solved by Alan Turing.

  13. 4 out of 5

    John Doherty

    Pretty good but I would recommend anyone interested in this subject first read Charles Petzold's book "The Annotated Turing". It goes into much more depth. If I hadn't read the Petzold book first I think I would have been confused by this one.

  14. 4 out of 5

    Samuel

    Intellectual History of Computing

  15. 5 out of 5

    Kevin Gross

    Davis’ book has an interesting enough goal: to draw a line connecting some of the great modern mathematicians and their work in the field of logic, to the development of digital computer. Start with Leibniz’s ideas around symbolic mathematics, trace the path to Turing and von Neumann’s designs. There is a chapter for each of the big brains, including Boole, Frege, Cantor, Hilbert, and Goedel – but oddly omitting von Neumann and his contemporaries as chapter-worthy. Von Neumann (along with Turing Davis’ book has an interesting enough goal: to draw a line connecting some of the great modern mathematicians and their work in the field of logic, to the development of digital computer. Start with Leibniz’s ideas around symbolic mathematics, trace the path to Turing and von Neumann’s designs. There is a chapter for each of the big brains, including Boole, Frege, Cantor, Hilbert, and Goedel – but oddly omitting von Neumann and his contemporaries as chapter-worthy. Von Neumann (along with Turing) is unique in being clearly someone with a foot in both the pure logic science and digital computing worlds. Alas Davis pretty much misses the mark for a number of reasons. Most of the book is given over to discussion of each mathematician’s major contributions. Their description in most cases isn’t very satisfactory: if you are already facile with the theory, you’ll find the discussion familiar, a bit arbitrary in focus, and not bringing much new insight. Kind of like walking into the middle of a conversation on a well-worn topic at the local bar. If you’re not already sheep-dipped in the topic, Davis’ explanations won’t be enough to give you a solid understanding, despite his liberal use of examples. The last few chapters turn to what we recognize as modern computers, surveying the work of Turing and von Neumann, as well as giving a little attention to other players and the controversies around who deserves credit for “inventing” the computer. On that issue, fundamentally a stupid question: you might as well ask, Who invented art? They were invented in steps and pieces, and there was never an “Aha!” moment at which the digital computer popped into conception. Ultimately Davis fails to convince that mathematical logic had much to do with inventing the modern digital computer. If there’s a connection between Cantor’s Continuum Hypothesis or Goedel’s incompleteness work and a digital computer, it isn’t drawn convincingly in this book. Perhaps a better book will make this point.

  16. 4 out of 5

    Damian O

    I wouldn't have said this until reading the other reviews, and agreeing. I've never read it in one go ( or rather never found myself able to ). It sometimes spends a long time explaining some relatively trivial concept, and a short time will skim through another idea in a couple of chapters. All in all, this serves as a good reference manual for anyone interested in computer science, information theory and to some degree cognitive science. I think the ' Subjects-in-sequence ' approach is an attemp I wouldn't have said this until reading the other reviews, and agreeing. I've never read it in one go ( or rather never found myself able to ). It sometimes spends a long time explaining some relatively trivial concept, and a short time will skim through another idea in a couple of chapters. All in all, this serves as a good reference manual for anyone interested in computer science, information theory and to some degree cognitive science. I think the ' Subjects-in-sequence ' approach is an attempt to lighten the admittedly weighty subject matter and make it easier to follow. I think by writing about them chronologically, it is supposed to read and feel like a traditional story. It fails because I don' think that's how the author normally would write, or certainly not how they think. What it does do is make it easy to take any one chapter on it's own and enjoy it without tracking back. I like that some time was spent on the individual logicians/mathematicians personalities ad private lives. I enjoyed reading about people 'shy to the point of weakness', about Newton's pride, plagiarism and peerlessness. I think that he inclusion of anecdotes about private lives achieves the purpose of making it accessible much more effectively than anything else.

  17. 4 out of 5

    Jim Andrews

    This is an important book concerning the history of mathematics, logic, and computer science. It shows how very important threads in the history of mathematics dating from the work of Leibniz to that of Boole, Frege, Cantor, Hilbert, and Godel led to Turing's formulation of the contemporary computer. The book situates the computer in the history of mathematics so that we see the development of the computer in relation to the historical 'crisis of foundations'. While the book is astute as a histo This is an important book concerning the history of mathematics, logic, and computer science. It shows how very important threads in the history of mathematics dating from the work of Leibniz to that of Boole, Frege, Cantor, Hilbert, and Godel led to Turing's formulation of the contemporary computer. The book situates the computer in the history of mathematics so that we see the development of the computer in relation to the historical 'crisis of foundations'. While the book is astute as a history of ideas, it is also fascinating in its biographical sketches of these paragons of logic. We learn, for instance, that Leibniz had a day job. Writing the family history of the Hanovers. His boss became King of England. But wouldn't take Leibniz to England. Finish up that history, Gottfried. Yeesh. Cantor was in and out of sanitoria. Godel starved himself to death out of fear someone was poisoning his food. And Turing probably committed suicide with a poisoned apple. It's a fascinating story along so many dimensions. I consider it a classic. Already.

  18. 5 out of 5

    Dennis O'Brien

    This is an amazing book describing the history of computational logic and the mathematicians who made major contributions to the field that eventually led to the computer. Each chapter focuses on a single contributor, looking at his life and times as well as the radical breakthroughs made. Though the story stretches almost four hundred years, there is a feeling of continuity in the development of logic and it is really exciting to watch the culmination in the intellectual powerhouse of Alan Turi This is an amazing book describing the history of computational logic and the mathematicians who made major contributions to the field that eventually led to the computer. Each chapter focuses on a single contributor, looking at his life and times as well as the radical breakthroughs made. Though the story stretches almost four hundred years, there is a feeling of continuity in the development of logic and it is really exciting to watch the culmination in the intellectual powerhouse of Alan Turing. The book does not assume you are a mathematician or computer scientist, but it does require an attentive read to follow the theory. There were many pages I had to read several times to follow but it was well worth it. There are some popular science books that vaguely gloss over the theory - this is not one of them.

  19. 5 out of 5

    Paul Berg

    After reading "Cryptonomicon" and currently on "Quicksilver" by Neal Stephenson this book at the San Juan College library caught my eye. Martin Davis (who's PHD predates my birth by 8 years) follows the development of the ideas from Leibniz to Turing that lead to the universal computer. I credit Stephenson for sparking an interest in line of thought that is inherent in Crypto' and "The Baroque Cycle". What I found interesting, so far, is that Newton does not have a chapter in this book and is on After reading "Cryptonomicon" and currently on "Quicksilver" by Neal Stephenson this book at the San Juan College library caught my eye. Martin Davis (who's PHD predates my birth by 8 years) follows the development of the ideas from Leibniz to Turing that lead to the universal computer. I credit Stephenson for sparking an interest in line of thought that is inherent in Crypto' and "The Baroque Cycle". What I found interesting, so far, is that Newton does not have a chapter in this book and is only mentioned in passing to the controversy over the Calculus. Davis traces a path from Leibniz through Boole, Frege, Cantor, Hilbert, Godel, to Turing with plenty of notes and a nice bibliography in a concise package.

  20. 4 out of 5

    Blair

    I think the mathematical history behind the development of the computer is interesting, but not having much mathematical background makes is hard to find books on it that I can understand, but I found this book to be pleasantly accessible. It is structured chronologically, and follows the key players whose mathematical ideas allowed for the development of modern computers. I liked that it included bibliographic information and interesting anecdotes about the people as well. My only complaint is I think the mathematical history behind the development of the computer is interesting, but not having much mathematical background makes is hard to find books on it that I can understand, but I found this book to be pleasantly accessible. It is structured chronologically, and follows the key players whose mathematical ideas allowed for the development of modern computers. I liked that it included bibliographic information and interesting anecdotes about the people as well. My only complaint is that sometimes it was hard for me to see where certain parts of the book were going, and it was only later on in the book that the relevance of something previously talked about came to light, so it would have been nice to have more guidance from the beginning, to help the reader along.

  21. 5 out of 5

    Guy Ferguson

    only partially read - a library book. The book followed the development of teh computer, from very non-hardware origins - e.g. philosophers and logisticians work that led the way to its development. Of those I read, they were well written and helped me understand where computers came from. And also helped me to see them as more than a tool we use to print and brows. Incompleteness and halting states are phrases I hear often and this book helped understand them. If you are not tech minded, or don' only partially read - a library book. The book followed the development of teh computer, from very non-hardware origins - e.g. philosophers and logisticians work that led the way to its development. Of those I read, they were well written and helped me understand where computers came from. And also helped me to see them as more than a tool we use to print and brows. Incompleteness and halting states are phrases I hear often and this book helped understand them. If you are not tech minded, or don't have a background in logics or philosophy, then this book may be hard to follow.

  22. 4 out of 5

    Mike

    A fascinating exposition of the factors leading to the development of the universal computer and its partial embodiments in today's computers. Martin Davis writes with a charm and directness that I cannot help but find engaging; he doesn't "talk down" to his readers, and the copious notes at the end of the book are, if anything, even more interesting than the main content itself. His focus on the role of Alan Turing is especially gratifying. [My thanks to Graham Birtwistle for lending me his copy A fascinating exposition of the factors leading to the development of the universal computer and its partial embodiments in today's computers. Martin Davis writes with a charm and directness that I cannot help but find engaging; he doesn't "talk down" to his readers, and the copious notes at the end of the book are, if anything, even more interesting than the main content itself. His focus on the role of Alan Turing is especially gratifying. [My thanks to Graham Birtwistle for lending me his copy of this excellent book.]

  23. 5 out of 5

    Javier Cano

    The history not of computing, but the history of the general purpose computer. The storytelling is from the perspective of the minds that provided the ideas and principles behind such an amazing device, instead of a historical point of view. The author talk about the motivations of these seven characters which lead them to conceive such amazing ideas that converged in a general purpuse computer. The author also discusses philosophical issues and the consequences of these ideas.

  24. 5 out of 5

    Thore Husfeldt

    A solid, lucid, focussed, well-structured, and highly readable exposition of the logical foundations of computation. From Leibniz’s dream of a rational and computable universe, via the logical formalisms of Boole and Frege and Hilbert’s program to heartbreak and catastrophe in the form of Gödel’s results. Until, like a mechanical Phoenix, the Turing machine rises from the ashes and transforms the world. This book is a model of popular scientific writing.

  25. 5 out of 5

    Dragos

    Choosing to rate this book is an undecidable problem. In this case it's a good thing that I'm only human. To hyperbolize the spirit of the book: 'the author writes about all logicians who didn't write about themselves'

  26. 4 out of 5

    Vasco

    Very interesting, a must-read for any computer scientist. If you like logic and computers, this is the book for you. It goes into the deepest math of computers, from the mathematicians of the XVII century to today, it talks about how computers rose from mathematical theorems.

  27. 4 out of 5

    zedoul

    I high recommend this book to understand theoretical basis of modern computer, especially for programmers. There are number of books about those subject, Gödel, Escher, and Bach / The Code / Logicomix for example, but this book is much easier to understand without any detours.

  28. 5 out of 5

    Sarah

    This book traces the developments and the lives of the people who made them, that advanced logic theory until it was fit for digital computers. Excellently written and easy to read, I was equally intrigued by the theory and by the diverse characters who created it.

  29. 5 out of 5

    Douglas Summers-Stay

    Another book I read as research for my book. His discussion of Leibniz was good from a computing perspective, as opposed to the language perspective that Umberto Eco had in his book.

  30. 5 out of 5

    Daniel

    Good story, but Martin's writing is often cumbersome.

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