Pi in the sky : counting, thinking and being
著者
書誌事項
Pi in the sky : counting, thinking and being
（Penguin mathematics）
Penguin, 1993
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注記
Originally published: New York : Oxford University Press, 1992
Includes bibliographical references (p. [298]-310) and index
内容説明・目次
内容説明
We have learnt that there is safety in numbers. Our understanding of the world around us has grown with our appreciation of its habits and repetitions. We live in a world of consequences rather than coincidences. This understanding of the way the world is founded upon our discovery of the power and utility of "number" in unravelling its innermost workings. From the farthest reaches of space to the inner space of elementary particles of matter we have found the world to dance to a mathematical tune. This book takes a philosophical look at mathematics, and 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. It should be of interest to physicists, philosophers of science, and general readers.
目次
- Part 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. Part 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. Part 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. Part 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. Part 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. Part 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?.
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