## 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 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. |

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### Contents

From mystery to history l | 1 |

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

The Counter Culture | 26 |

Copyright | |

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