Overview

"We have learnt that there is safety in numbers. Our understanding of the world around us has grown with our appreciation of its habits and repetitions. We live in a world of consequences rather than coincidences. This understanding of the way the of the world is founded upon our discovery of the power and utility of ""number"" in unravelling its innermost workings. From the farthest reaches of space to the inner space of elementary particles of matter we have found the world to dance to a mathematical tune. This book takes a philosophical look at mathematics, and asks whether it is just a human invention, a discovery, part of the mind of God, or a game played on paper with any rules we like. It should be of interest to physicists, philosophers of science, and general readers."

Full Product Details

Author:   John D. Barrow
Publisher:   Oxford University Press
Imprint:   Clarendon Press
Dimensions:   Width: 15.00cm , Height: 2.70cm , Length: 23.00cm
Weight:   0.558kg
ISBN:  

9780198539568

ISBN 10:   0198539568
Pages:   329
Publication Date:   01 October 1992
Audience:   College/higher education ,  Professional and scholarly ,  General/trade ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

"From mystery to history - a mystery within an enigma, illusions of certainty, the secret society, non-euclideanism, logics, the Rashomon effect, the analogy that never breaks down, symbols, thinking about thinking; the counter culture - by the pricking of my thumbs, the bare bones of history, creation or evolution, the ordinals versus the cardinals, counting without counting, fingers and toes, baser methods, counting with the base ""2"", the neo-2 system of counting, counting in fives, what's so special about 60? the spread of the decimal system, the dance of the seven veils, ritual geometry, the place-value system and the intervention of zero, conclusions about numbers; with form but void - numerology, the very opposite, Hilbert's scheme, Kurt Goedel, more surprises, thinking by numbers, Bourachique mathematique, arithmetic in chaos, logical friction, mathematics off form; the mothers of inventionism - mind from matter, shadowlands, trap-door functions, mathematical creation, Marxist mathematics, complexity and simplicity, maths as psychology, pre-established mental harmony?, self-discovery; intuitionism: the immaculate construction - mathematics from outer space, Ramanujan, intuitionism and three-valued logic, a very peculiar practice, a closer look at Broouwer, what is ""intuition""?, the tragedy of Cantor and Kronecker, Cantor and infinity, the comedy of Hilbert and Brouwer, the four colour conjecture, transhuman mathematics, new-age mathematics, paradigms, computability, compressibility and utility; Platonic heavens above and within - the growth of abstraction, footsteps through Plato's footnotes, the Platonic world of mathematics, far away and long ago, the presence of the past, the unreasonable effectiveness of mathematics, difficulties with Platonic relationships, seance or science?, revel without a cause, a computer ontological argument, a speculative anthropic interpretation of mathematics, maths and mysticism, supernatural numbers?."

Reviews

The Sussex astronomer (Theories of Everything, 1991, etc.) has done it again - i.e., wrought a brilliant summation of ideas about mathematics that shows a depth of scholarship and an analysis that will leave the reader more than a little shaken. For example, Barrow traces the origins of counting and number systems in the Old and New Worlds (very much in parallel with John McLeish, reviewed below). His somewhat startling conclusion is that number systems do not arise like language, common to all human societies, but probably spread from one place to another. And thank God for the Indus culture, for without it - and without the Arabs who later spread the word about the decimal-place system and the zero - we might be stuck with Roman numerals. But Barrow's real point here is philosophical: Is mathematics a discovery or an invention; the ultimate description of reality or a form of abstract beauty in the eyes of the mathematician-logician beholder? Here, he points to the developments in the late-19th and early-20th centuries of the formalists like David Hilbert and the latter-day French descendants who called themselves the Bourbaki, eschewing all representations or models. Along came Godel to pull the rug out from under, declaring the incompleteness of math and the undecidability of statements in axiomatic arithmetical systems. Barrow contrasts the formalists with constructivist-empiricists and today's ultimate hackers to conclude that there remains a residue of Platonic religious mysticism in our feelings about mathematics. All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics 'is'...why it works nor where it works; if it fails or how it fails. Heady stuff this, caviar for the connoisseur - but not for the innumerate. (Kirkus Reviews)

Author Information

"About the Author: John D. Barrow is Professor in the Astronomy Centre of the University of Sussex. His is the author of several highly acclaimed volumes on the philosophy of science, including most recently Theories of Everything, which Publishers Weekly hailed as ""a mind-boggling intellectual adventure."""

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