Waubonsee Community College

Pi in the sky, counting, thinking, and being, John D. Barrow

eng

Includes bibliographical references (p. [298]-310) and index

illustrations

index present

non fiction

Pi in the sky

bibliography

26097247

John D. Barrow

counting, thinking, and being

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 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 artificial intelligence. 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

1. From mystery to history. A mystery within an enigma. Illusions of certainty. The secret society. Non-euclideanism. Logics -- To Be or Not To Be. The Rashomon effect. The analogy that never breaks down? Tinkling symbols. Thinking about thinking -- 2. The Counter Culture. By the pricking of my thumbs. The bare bones of history. Creation or evolution. The ordinals versus the cardinals. Counting without counting. Fingers and toes. Baser methods. Counting with base 2. The neo-2 system of counting. Counting in fives. What's so special about sixty? The spread of the decimal system. The dance of the seven veils. Ritual geometry. The place-value system and the invention of zero. A final accounting -- 3. With form but void. Numerology. The very opposite. Hilbert's scheme. Kurt Godel. More surprises. Thinking by numbers. Bourbachique mathematique. Arithmetic in chaos. Science friction. Mathematicians off form -- 4. The mothers of inventionism. Mind from matter. Shadowlands. Trap-door functions. Mathematical creation. Marxist mathematics. Complexity and simplicity. Maths as psychology. Pre-established mental harmony? Self-discovery -- 5. Intuitionism: the immaculate construction. Mathematicians from outer space. Ramanujan. Intuitionism and three-valued logic. A very peculiar practice. A closer look at Brouwer. What is 'intuition'? The tragedy of Cantor and Kronecker. Cantor and infinity. The comedy of Hilbert and Brouwer. The Four-Colour Conjecture. Transhuman mathematics. New-age mathematics. Paradigms. Computability, compressibility, and utility -- 6. Platonic heavens above and within. The growth of abstraction. Footsteps through Plato's footnotes. The platonic world of mathematics. Far away and long ago. The presence of the past. The unreasonable effectiveness of mathematics. Difficulties with platonic relationships. Seance or science? Revel without a cause. A computer ontological argument. A speculative anthropic interpretation of mathematics. Maths and mysticism. Supernatural numbers?