## Pi in the Sky: Counting, Thinking, and BeingWhether 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 upon that strange symbolic language we call mathematics. But what exactly is mathematics? And why does it work? Is it just an elaborate computer game? Or merely a human invention inspired by our practical needs? Or is it something larger than life? An immaterial 'pi in the sky' reality all of its own? Part of the mind of God? And how do the answers to these questions affect our quest to arrive at an understanding of the Universe? John D. Barrow explores these tantalizing questions in this book, a lively and illuminating study of the origins, the meaning, and the mystery of mathematics. He takes us from primitive counting to computability, from the counting rituals of the ancients to logics that govern universes other than our own, from Egyptian hieroglyphics to logical friction, from number mysticism to Marxist mathematics. We learn of the origins of counting the world over, the propensities of the human mind for the numerical when in pursuit of the ineffable, and how the dethronement of Euclid's geometry ushered in a new world of philosophical relativism in which traditional truths were dissolved. We meet a host of peculiar individuals who have thought some of the deepest and strangest thoughts that human minds have ever thought. And in a extraordinary final chapter, the Platonic picture of mathematics is developed in a startling new way that challenges us to consider how the mathematics of the future may turn out to be radically different from that of the present, and how it impinges upon our efforts to create an artificialintelligence. Full of the off-beat and the unexpected and quoting everyone from Lao-Tse to Robert Pirsig, to Charles Darwin and Stephen Leacock, Kurt Godel and Umberto Eco, 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. |

### Contents

From mystery to history | 1 |

Sextus Empiricus Against the Logicians in Sextus Empiricus transl R G Bury | 4 |

The Counter Culture | 26 |

Copyright | |

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### Common terms and phrases

2-counting abstract algorithm ancient arithmetic aspects axiomatic axiomatic system axioms Babylonians believe Bourbaki Brouwer Cantor century collection complexity constructed continuum hypothesis counting system created cultures decimal deduction discover discovery early entities Euclidean geometry evolution example exist experience extraterrestrials fact finger counting finite number formal system formalist Gödel Gödel's theorem Henri Poincaré Hilbert human mind INDIA Indo-European languages infinite infinity interesting intuition intuitionism intuitionist invented knowledge Kronecker Kurt Gödel language larger numbers laws of Nature logical mathem mathematical concepts mathematical truths mathematicians meaning natural numbers non-Euclidean geometry notion number symbols number words objects origin Pallava particular philosophy of mathematics physical world physicists Platonic possess possible prime number problem proof prove Pythagoras quantities reality reasoning regarded result rules scientists seems sense sequence set theory simple statements structure tallying theory things thinking traditional true undecidable Universe whilst zero