Barrow, J.D. 　著

内容

目次

From mystery to history - a mystery within an enigma, illusions ofcertainty, the secret society, non-euclideanism, logics, the Rashomoneffect, the analogy that never breaks down, symbols, thinking aboutthinking; the counter culture - by the pricking of my thumbs, the barebones of history, creation or evolution, the ordinals versus thecardinals, counting without counting, fingers and toes, baser methods,counting with the base "2", the neo-2 system of counting, counting infives, what's so special about 60? the spread of the decimal system,the dance of the seven veils, ritual geometry, the place-value systemand the intervention of zero, conclusions about numbers; with form butvoid - numerology, the very opposite, Hilbert's scheme, Kurt Goedel,more surprises, thinking by numbers, Bourachique mathematique,arithmetic in chaos, logical friction, mathematics off form; themothers of inventionism - mind from matter, shadowlands, trap-doorfunctions, mathematical creation, Marxist mathematics, complexity andsimplicity, maths as psychology, pre-established mental harmony?,self-discovery; intuitionism: the immaculate construction - mathematicsfrom outer space, Ramanujan, intuitionism and three-valued logic, avery peculiar practice, a closer look at Broouwer, 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; Platonic heavens above and within - thegrowth of abstraction, footsteps through Plato's footnotes, thePlatonic world of mathematics, far away and long ago, the presence ofthe past, the unreasonable effectiveness of mathematics, difficultieswith Platonic relationships, seance or science?, revel without a cause,a computer ontological argument, a speculative anthropic interpretationof mathematics, maths and mysticism, supernatural numbers?.