PI in the Sky Counting, Thinking, and Being

by Barrow, John D.

• ISBN13: 9780316082594
• ISBN10: 0316082597
• Edition: Reprint
• Format: Paperback
• Copyright: 1993-10-20
• Publisher: Back Bay Books

Summary

John D. Barrow's Pi in the Sky is a profound -- and profoundly different -- exploration of the world of mathematics: where it comes from, what it is, and where it's going to take us if we follow it to the limit in our search for the ultimate meaning of the universe. Barrow begins by investigating whether math is a purely human invention inspired by our practical needs. Or is it something inherent in nature waiting to be discovered?In answering these questions, Barrow provides a bridge between the usually irreconcilable worlds of mathematics and theology. Along the way, he treats us to a history of counting all over the world, from Egyptian hieroglyphics to logical friction, from number mysticism to Marxist mathematics. And he introduces us to a host of peculiar individuals who have thought some of the deepest and strangest thoughts that human minds have ever thought, from Lao-Tse to Robert Pirsig, Charles Darwin, and Umberto Eco. Barrow thus provides the historical framework and the intellectual tools necessary to an understanding of some of today's weightiest mathematical concepts.

Author Biography

John D. Barrow is Professor of Astronomy at the Astronomy Centre of the University of Sussex, in England. His many acclaimed books include The Left Hand of Creation, The Anthropic Cosmological Principle, The World within the World, and, most recently, Theories of Everything: The Quest for Ultimate Explanation.

Table of Contents

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