Pi in the Sky: Counting, Thinking, and Being

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Whether one studies the farthest reaches of outer space or the inner space of elementary particles of matter, our understanding of the physical world is built on mathematics. But what exactly is mathematics? A game played on pieces of paper? A human invention? An austere religion? Part of the mind of God? And equally important, why do we believe it can reveal to us the nature of the universe?
John D. Barrow explores these tantalizing questions in Pi in the Sky, a lively and ...
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Oxford 1992 Hard Cover First Edition New in New jacket 8vo-over 7?"-9?" tall. FIRST PRINTING of the First Edition. A thoughtful study of the origins, meaning, and mysteries of ... mathematics, from primitive counting to complex computing, the propensities of the human mind for numerical work, number mysticism, Euclid's geometry and its impact upon philosophy, much more. Hardcover with dust jacket, contains further reading list, indexed, 317pp. A very nice copy, the jacket neatly encased in an acid-free archival plastic protector. Rare. Read more Show Less

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Overview


Whether one studies the farthest reaches of outer space or the inner space of elementary particles of matter, our understanding of the physical world is built on mathematics. But what exactly is mathematics? A game played on pieces of paper? A human invention? An austere religion? Part of the mind of God? And equally important, why do we believe it can reveal to us the nature of the universe?
John D. Barrow explores these tantalizing questions in Pi in the Sky, a lively and illuminating study of the origins and nature of mathematics. His tour takes us from primitive counting to the latest scientific ideas about the physical world, from the notched animal bones of the hunter-gatherers to the visions of Galileo and Descartes, and from the intricate mathematical systems of Egypt, Sumeria, and other early civilizations, to the work of such modern giants as Einstein, Kurt Godel, Alfred Tarski, and Bertrand Russell. We meet Pythagoras and his mystical "cult of numbers" as well as an eighteenth-century Swiss mathematician who proved to his colleagues--through an algebraic formula--the existence of God. Barrow examines ancient Chinese counting rods colored black and red for negative and positive numbers; the Botocoudo Indians of Brazil, who indicate any number over four by pointing to the hairs on their head; and the dethroning of Euclidian geometry in the nineteenth century with the rise of Darwin and cultural relativism. And in an eye-opening last chapter, Barrow discusses how the traditional picture of the universe as a vast mechanism is currently being replaced by a new paradigm--one that sees the universe, in essence, as a cosmic computer program.
Bristling with riddles and paradoxes, and quoting everyone from Lao-Tse and Robert Pirsig, to Charles Darwin and G.K. Chesterton, to Roger Bacon, Baron de Montesquieu, and Umberto Eco, Pi in the Sky is a profound--and profoundly edifying--journey into the world of mathematics. It illuminates the way that numbers shape how we see the world and how we see ourselves.

Our understanding of the physical world is built on mathematics, but what exactly is mathematics? Barrow explores this tantalizing question in this lively and illuminating study of the origins and nature of math. Along the way we meet Pythagoras and his "cult of numbers, " Galileo and Descartes, Einstein and Bertrand Russell. Line drawings.

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Editorial Reviews

Publishers Weekly - Publisher's Weekly
A history of--and reflection upon--the role of mathematics in the human enterprise. Oct.
Bryce Christensen
Mathematics has rarely found such a gifted and provocative exponent! From Pythagoras to Godel, Barrow plumbs the human fascination with numbers. No dry treatise, this investigation draws the reader into a world of jealously guarded mysteries, of feverish ambitions, and of irrational fears. Himself a mathematician and astronomer, Barrow ponders the strange power of formulas in modern science. This power has fired some theorists with the hope of developing one ultimate theory of the universe. Such hope, Barrow shows, must finally meet frustration, for there are paradoxical limits inherent in all formal systems of logic, including mathematics. The discovery of these limits has sent intellectual shock waves felt far beyond the lecture hall. Rich in philosophical insights and literary allusions, this remarkable study will stimulate and challenge serious readers.
Booknews
Famous cosmologist and prolific author John Barrow explores the origin and nature of mathematics and explains the important implications of the numerous unanswered questions in our search for a theory of everything. He weaves together a history of math that illuminates its far-reaching capabilities and its intrinsic limitations, its proven and unproven theories, and its pervasive impact on the way people think and live. Annotation c. Book News, Inc., Portland, OR booknews.com
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Product Details

  • ISBN-13: 9780198539568
  • Publisher: Oxford University Press, USA
  • Publication date: 10/1/1992
  • Edition number: 1
  • Pages: 336
  • Product dimensions: 6.13 (w) x 9.25 (h) x 1.09 (d)

Meet the Author

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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Table of Contents

1 From mystery to history 1
A mystery within an enigma 1
Illusions of certainty 2
The secret society 6
Non-euclideanism 8
Logics - To Be or Not To Be 15
The Rashomon effect 19
The analogy that never breaks down? 21
Tinkling symbols 23
Thinking about thinking 24
2 The Counter Culture 26
By the pricking of my thumbs 26
The bare bones of history 28
Creation or evolution 33
The ordinals versus the cardinals 36
Counting without counting 41
Fingers and toes 45
Baser methods 49
Counting with base 2 51
The neo-2 system of counting 56
Counting in fives 60
What's so special about sixty? 64
The spread of the decimal system 68
The dance of the seven veils 72
Ritual geometry 73
The place-value system and the invention of zero 81
A final accounting 101
3 With form but void 106
Numerology 106
The very opposite 108
Hilbert's scheme 112
Kurt Godel 117
More surprises 124
Thinking by numbers 127
Bourbachique mathematique 129
Arithmetic in chaos 134
Science friction 137
Mathematicians off form 140
4 The mothers of inventionism 147
Mind from matter 147
Shadowlands 149
Trap-door functions 150
Mathematical creation 154
Marxist mathematics 156
Complexity and simplicity 159
Maths as psychology 165
Pre-established mental harmony? 171
Self-discovery 176
5 Intuitionism: the immaculate construction 178
Mathematicians from outer space 178
Ramanujan 181
Intuitionism and three-valued logic 185
A very peculiar practice 188
A closer look at Brouwer 192
What is 'intuition'? 196
The tragedy of Cantor and Kronecker 198
Cantor and infinity 205
The comedy of Hilbert and Brouwer 216
The Four-Colour Conjecture 227
Transhuman mathematics 234
New-age mathematics 236
Paradigms 243
Computability, compressibility, and utility 245
6 Platonic heavens above and within 249
The growth of abstraction 249
Footsteps through Plato's footnotes 251
The platonic world of mathematics 258
Far away and long ago 265
The presence of the past 268
The unreasonable effectiveness of mathematics 270
Difficulties with platonic relationships 272
Seance or science? 273
Revel without a cause 276
A computer ontological argument 280
A speculative anthropic interpretation of mathematics 284
Maths and mysticism 292
Supernatural numbers? 294
Further reading 298
Index 311
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