Pi in the sky : counting, thinking, and being
Pi in the sky : counting, thinking, and being
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天上的圆周率：计数、思考和存在
DOI：
10.2307/3620225
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
J. Barrow
中科院分区：
文献类型：
--
作者：
J. Barrow
第一部分从神秘到历史：谜中之谜，确定性的幻想，秘密社会，非欧几里得主义逻辑--是或不是罗生门效应，永不崩溃的类比？叮当作响的符号思考思考。第二部分反主流文化：用我的拇指戳一下历史的基本原理，创造或进化，序数与红衣主教，不计算手指和脚趾，更低级的方法，用二进制计数，新二进制计数系统，以五为单位，六十有什么特别之处？十进制系统的传播，七层面纱的舞蹈，几何仪式，位置价值系统和零的发明，最终的会计。第三部分有形而无：数字命理学，与希尔伯特的方案恰恰相反，库尔特·哥德尔更令人惊讶的是，用数字思考，布尔巴契式数学，混沌中的算术，科学摩擦，数学家脱离形式。第四部分发明主义的根源：心灵脱离物质、阴影地带、陷阱门功能、数学创造、马克思主义数学、复杂性与简单性、数学作为心理学预设的心理和谐？自我发现第五部分直觉主义：完美无瑕的建筑来自外太空的数学家拉马努金直觉主义和三值逻辑一种非常奇特的实践仔细看看布劳威尔什么是“直觉”？康托和克罗内克的悲剧康托和无穷大希尔伯特和布劳威尔的喜剧四色猜想超人类数学新时代数学范式可计算性，可压缩性和实用性。第六部分柏拉图的天堂之上和之内：增长的抽象的脚步通过柏拉图的脚注柏拉图的数学世界遥远和很久以前的存在过去的不合理的有效性数学困难与柏拉图的关系降神会或科学？毫无理由地陶醉于计算机本体论的争论，对数学数学和神秘主义的投机性人择解释，超自然的数字？。
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?.