The Universal Computer: The Road from Leibniz to Turing
By pcparts. Filed in Books |Tags: Computer, from, Leibniz, Road, Turing, Universal
Product Description
One of the world’s pioneers in the development of computer knowledge offers a mesmerizing history of computers. 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 incredible 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.Amazon.com Review
Computers rely on such things as semiconductors, memory chips, and electricity. But they also rely on a hard-won body of methodical 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 veer,” 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 clarified, Davis reports, that he had turned to mathematics because he had so small money as a student to buy books, and mathematics books provided more value for the money because they took so long to work owing to.) Davis traces the development of this logic, essential to the advent of “thinking machines,” owing to the workshops and studies of such thinkers as Georg Cantor, Kurt Gödel, and Alan Turing, each of whom puzzled out just a small bit more of the workings of the world–and who, in the bargain, made the present possible. –Gregory McNamee
The Universal Computer: The Road from Leibniz to Turing
Friday, May 14th 2010 at 8:37 pm |
In 1972, during the conflict over “who invented the computer” I published a letter in ComputerWorld asking why Turing’s contributions were being ignored. Though, a letter from a long-haired kid working as a programmer in a small university isn’t “knowledge” properly understood, and therefore I was gratified to get belated confirmation from the eminent Martin Davis.
Davis shows that Turing anticipated computation in general with his 1936 paper “On the Choice Problem.” But in addendum, Turing’s work in codebreaking during the war and his postwar work on the Pilot Ace showed a connection between the abstract Turing machine and the computer.
Turing’s work on the Enigma machine was subdue under official secrecy in 1972, but I’d seen the Pilot Ace in a collection of papers on computer architecture edited by Bell and Newell.
It subdue may be open whether Turing invented the computer. But more vital is that a reading of Turing shows that inside computing, there are Two Cultures: “engineering” versus “logic.”
In 1972, when I wrote my letter, the leading computing culture was that of von Neumann. This was the “engineering” culture. In this culture software is subordinated as the “inferior term” of literary theory (using deconstruction, without apology): hardware is “male” and software is “female”.
Von Neumann was unamused by early programmers who not compulsory that the computer itself could transliterate mathematical formulae into code. Von Neumann felt that the computer was too vital for such a trivial task.
The early computers were presented as Serious Iron…”male.” Most managers in 1972 felt that programming was at best a marginal annoyance. But in his work on the Pilot Ace, Turing foresaw the need to take programming seriously.
To make Serious the marginalized serious is the ultimate marginal gesture, which is why American “literary theorists” seem to prefer recreational pursuits; Jacques Derrida questioned an American graduate student to examine technology and she was offended. It is safer and more respectable to be Serious about Jane Austen. Like an Austen heroine, who would reckon of Mr. Napoleon as at best most inconvenient, literary theory seems uninterested in software, yet software provides a rich vein, in my view, of the interaction of the marginal and the Serious.
The late, distinguished computer scientist Edsger Dijkstra in the 1950s in the Netherlands informed his mentors that he wanted to be, not a mathematician or physicist, but a programmer, which dismayed hiss mentors. They probably said “you can’t be serious.”
Like Glenn Gould, Edward Said, and other intellectuals of the pressing postwar, Dijkstra’s negative dialectic seems to have hurt his career somewhat. Glenn Gould refused to perform with about 1960 with the result that many musical professionals regard Gould, today, as an irritant. Edward Said refused to reconcile himself to exile and in some circles is scorned. Dijkstra’s choices resulted, I reckon, in some lack of later recognition: his Turing award was awarded by insiders while his work was of Nobel quality.
Turing’s contributions as a result of his refusal to conform lifestyle-wise obscured his accomplishment.
The “software” part of the Two Cultures of computing is to some extent to blame for its consistent failure, even today, to be heard. This is because the software Eloi refuse to join world intellectual traditions and disempower themselves.
One example occurs when the software guy must step outside the box into the realm of what Marx would call his relations with his own kind, everywhere “all that is levelheaded melts into air.”
Davis finds Hegel incomprehensible. But it’s possible that there are forms of life external to software in which Hegel makes sense.
Hegel identified complete “self self” with oblivion. A software guy’s expression would be “a brain in a vat”, coding using pure logic innocent of the dialectic and subsisting on pizza, provided by an employer (who lays our boy off a year later, showing that there is no getting away from from Hegel’s world of lordship and bondage with all.)
The predominance of hardware culture has brutalized several generations of programmers. The hardware view is the source of the hideous phrase “a simple matter of programming” which encapsulates the irrational subordination of the disfavored term. In consequence, programmers are held to rigid deadlines in which they have no say. In consequence, many software efforts including using the computer to build one’s own needed tools have become termination offenses.
This is a sexual politics. The irrational “business” necessity has become the elimination of any need to be conscious of logic as marginal, and the implication is that we can, if need be, do without the marginal term. But examination of the hardware and its representation either as explicit “firmware” (programming instructions implementing the hardware in read-only memory) or the result of a process in which the hardware guys had to reckon like programmers with all. It is a sexual politics because the irrational demand takes dignity away from the marginal people in the name of a hypostatized rationality in a vat.
In part, I identify with the frustration of the engineering administrator. I have heard the phrase “a line in the sand” more than once in the 1990s everywhere it originated in the senior Bush’s campaign to liberate Kuwait (or something.) The engineering administrator, unaware of what Dijkstra called the cruelty of programming considered as applied logic and math, feels that the intellectual content of programming is nil and therefore appeals for more time constitute slacking off. He needs to set boundaries.
The engineering administrator feels like Yogi Berra: “I want to go back to college and study but I would not study music because I already like music.” Precisely because of logic’s universality (Wittgenstein’s “allumfassende, weltspiegelnde Logik”, all-embracing Logic, which mirrors the world) it becomes for the engineering male a form of driving. We all reckon we know how to guide because of the universal necessity of driving and it is the other bozo who doesn’t know how to guide.
Martin Davis has given programming respectability by linking it to an academic tradition. This is a start.
Rating: 5 / 5
Friday, May 14th 2010 at 10:28 pm |
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 thoughts mean for modern computing.
The Universal Computer is a rather quick read, with the biographical content being particularly brisk, and there are points everywhere 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 thoughts mean for modern computing.
The Universal Computer is a rather quick read, with the biographical content being particularly brisk, and there are points everywhere 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 instigator includes a lengthy notes section explaining the beginnings of the finer points of these matters and references for working owing to the actual mathematics and technology discussed.
Rating: 4 / 5
Saturday, May 15th 2010 at 12:26 am |
A very fun read chalk full of and lively fascinating personal and biographical information on some of the greatest logicians and mathematicians to have ever lived (e.g. Godel, Hilbert, Boole).
If you’re interested in the history of computation theory (computational logic) and even mathematical logic more generally, this book is highly not compulsory. Davis himself was part of that history by making contributions, e.g., to the Entscheidungsproblem (choice problem).
At the same time, he does not skimp on technical details and explanations, though some of the more technical are regularly relegated to lengthy endnotes, and so most of these are easily skipped, if desired, without loss of continuity.
A fun read!
Rating: 4 / 5
Saturday, May 15th 2010 at 12:55 am |
Anyone who wants to know 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 delight in it too!
Rating: 5 / 5
Saturday, May 15th 2010 at 2:29 am |
I thought that this book was an brilliant 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 small dull. I found myself rereading several of the sections to try to better know some of the math involved, but overall, I reckon 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 regularly 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 make. The Universal Computer generally is presented that way, but there are some events that happen more or less simultaneously. This is vital to the overview of the history of the field. I reckon the book could really 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.
Rating: 4 / 5