Pi in the sky : counting, thinking, and being

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. 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. Cover......Page 1 Title......Page 2 Copyright......Page 3 Epigraph......Page 4 Dedication......Page 5 Preface......Page 8 CONTENTS......Page 11 A MYSTERY WITHIN AN ENIGMA......Page 13 ILLUSIONS OF CERTAiNTY......Page 14 THE SECRET SOCIETY......Page 18 NON- EUCLIDEANLSM......Page 20 LOGICS TO BE OR NOT TO BE......Page 27 TIlE RASHOMON EFFECT......Page 31 THE ANALOGY THAT NEVER BREAKS DOWN?......Page 33 TINKLING SYMBOLS......Page 35 THINKING ABOUT THINKING......Page 36 BY THE PRICKING OF MY THUMBS......Page 38 THE BARE BONES OF HISTORY......Page 40 CREATION OR EVOLUTION......Page 45 THE ORDINALS VERSUS THE CARDINALS......Page 48 COUNTING WITHOUT COUNTING......Page 53 FINGERS AND TOES......Page 57 BASER METHODS......Page 61 COUNTING WITH BASE 2......Page 63 THE NEO-2 SYSTEM OF COUNTING......Page 68 COUNTING IN FIVES......Page 72 WHAT'S SO SPECIAL ABOUT SIXTY?......Page 76 THE SPREAD OF THE DECIMAL SYSTEM......Page 80 THE DANCE OF THE SEVEN VEILS......Page 84 RITUAL GEOMETRY......Page 85 TIlE PLACE-VALUE SYSTEM AND THE INVENTION OF ZERO......Page 93 A FINAL ACCOUNTING......Page 113 NUMEROLOGY......Page 118 THE VERY OPPOSITE......Page 120 HILBERT'S SCHEME......Page 124 KURT GÖDEL......Page 129 MORE SURPRISES......Page 136 THINKING BY NUMBERS......Page 139 BOURBACHIQUE MATUEMATIQUE......Page 141 ARITHMETIC IN CHAOS......Page 146 SCiENCE FRICTION......Page 149 MATHEMATICIANS OFF FORM......Page 152 MIND FROM MATTER......Page 159 TRAP DOOR FUNCTIONS......Page 162 MATHEMATICAL CREATION......Page 166 MARXIST MATHEMATICS......Page 168 COMPLEXITY ANIJ SIMPLICITY......Page 171 MATHS AS PSYCHOLOGY......Page 177 PRE-ESTABLISHED MENTAL HARMONY?......Page 183 SELF-DISCOVERY......Page 188 MATHEMATICS FROM OUTER SPACE......Page 190 RAMANUJAN......Page 193 INTUITIONISM AND THREE-VALUED LOGIC......Page 197 A VERY PECULIAR PRACTICE......Page 200 A CLOSER LOOK AT BROUWER......Page 204 WHAT IS 'INTUITION'?......Page 208 THE TRAGEDY OF CANTOR AND KRONECKER......Page 210 CANTOR AND INFINITY......Page 217 THE COMEDY OF HILBERT AND BROUWER......Page 228 TIlE FOUR-COLOUR CONJECTURE......Page 239 TRANSHUMAN MATHEMATICS......Page 246 NEW-AGE MATHEMATICS......Page 248 PARADIGMS......Page 255 COMPUTABILITY, COMPRESSIBILITY, AND UTILITY......Page 257 THE GROWTH OF ABSTRACTiON......Page 261 FOOTSTEPS THROUGH PLATO'S FOOTNOTES......Page 263 THE PLATONIC WORLD OF MATHEMATICS......Page 270 FAR AWAY AND LONG AGO......Page 277 THE PRESENCE OF THE PAST......Page 280 THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS......Page 282 DIFFICULTIES WITH PLATONIC RELATIONSHIPS......Page 284 SEANCE OR SCIENCE?......Page 285 REVEL WITHOUT A CAUSE......Page 288 A COMPUTER ONTOLOGICAL ARGUMENT......Page 292 A SPECULATIVE ANTHROPIC INTERPRETATION OP MATHEMATICS......Page 296 MATHS AND MYSTICISM......Page 304 SUPERNATURAL NUMBERS?......Page 306 FURTHER READING......Page 310 INDEX......Page 323 Back Cover......Page 330 "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. Book jacket."--Jacket A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention except in rather esoterically refined circles: that at the root of the success of twentieth-century science there lies a deeply 'religious' belief-a belief in an unseen and perfect transcendental world that controls us in an unexplained way, yet upon which we seem to exert no influence whatsoever.