The Universal Computer: The Road from Leibniz to TuringComputers 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. |
Contents
Boole Turns Logic into Algebra | 21 |
Frege From Breakthrough to Despair | 41 |
Cantor Detour through Infinity | 59 |
Hilbert to the Rescue | 83 |
Gödel Upsets the Applecart | 107 |
Turing Conceives of the AllPurpose Computer | 139 |
Making the First Universal Computers | 177 |
Beyond Leibnizs Dream | 199 |
| 239 | |
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Common terms and phrases
Alan Turing algebra algorithm arithmetic axioms Begriffsschrift bers Bletchley Park Boole's Brouwer calculation called Cantor's transfinite cardinal number century chapter chess code number concepts conclusion consistency consistency proof Continuum Hypothesis David Hilbert decimal developed diagonal method digits dissertation EDVAC engineers ENIAC Entscheidungsproblem equation example express first-order logic foundations of mathematics Frege Frege's logic Georg Cantor George Boole German halting set Hilbert Hilbert's program ideas inference infinite sets input John von Neumann Königsberg Kronecker Kurt Gödel language later lectures Leibniz Leibniz's dream letter logician math mathematicians metamathematics natural numbers notation one-one matching operations ordinary package paper philosopher premises Princeton problem proof proposed provable in PM proved question quintuples real numbers reasoning represented Russell's sentence set of natural set of real student tape theorem theory things thought tion translation true tube Turing machine Turing's unary string universal machine unsolvable Weyl write written wrote