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Pi in the sky : counting, thinking, and being

Author: John D Barrow
Publisher: Oxford : Clarendon Press ; New York : Oxford University Press, 1992.
Edition/Format:   Print book : EnglishView all editions and formats
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  Read more...
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Additional Physical Format: Online version:
Barrow, John D., 1952-
Pi in the sky.
Oxford : Clarendon Press ; New York : Oxford University Press, 1992
Document Type: Book
All Authors / Contributors: John D Barrow
ISBN: 0198539568 9780198539568
OCLC Number: 26097247
Description: ix, 317 pages : illustrations ; 24 cm
Contents: 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?
Other Titles: Pi in the sky :
Responsibility: John D. Barrow.
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A philosophical look at mathematics, this book asks whether it is just a human invention, a discovery, part of the mind of God, or a game played on paper with any rules we like.  Read more...
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