Godel, Escher, Bach的笔记(10)

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  • 皮波迪先生

    皮波迪先生 (择善固执,止于至善)

    Primes vs. composites P64 Rules for typographical operations reading and recognizing any of a finite set of symbols; writing down any symbol belong to that set; copying any of those symbols from one place to another; erasing any of these symbols; checking to see whether one symbol is the same as another; keeping and using a list of previously generated theorems. P64 Definition of formal system...

    2017-12-31 11:45

  • 皮波迪先生

    皮波迪先生 (择善固执,止于至善)

    Two-part invention P45 「 以上无穷推理的过程相当于把人看作了没有意识和逻辑从而无法跳出这个无穷级的规则系统而在其外对其进行审视。而这便等同于不承认先验知识的存在性,也不认可其合理性。」 Chapter 2 Meaning and form in mathematics P47 If --p---q- turns out to be a theorem, then so will --p----q--. the statement establishes a causal connection between the theoremhood of two strings, but without ass...

    2017-12-22 09:02

  • 皮波迪先生

    皮波迪先生 (择善固执,止于至善)

    abolition 废除, 废止 ad infinitum 无限地;永久地;无止境地 afford vt. 给予,提供;买得起 alight 1. vi. 下来;飞落2. adj. 烧着的;点亮着的 all along 自始至终,一直 allegory n. 寓言 allegro 1. n. 急速的乐章;快板2. adj. 快速的 allusion n. 暗示;提及 anticipate 预料 apologist 辩护士,辩解者 apparent adj. 显然的;表面上的 arrest 1. vt. 吸引;逮捕;阻止2. n. 逮捕;监禁 assent 1. vi. 赞成;同意2. n. ...

    2017-12-02 12:03

  • 皮波迪先生

    皮波迪先生 (择善固执,止于至善)

    Formal systems P33 Requirement of Formality: The major point, which almost doesn't need stating, is that you must not do anything which is outside the rules. We might call this restriction the “Requirement of Formality”. Even jumping out of the system to think about the meaning. Theorems, axioms, rules P35 Such strings, producible by the rules, are called theorems. I gave you a theorem for fr...

    2017-12-01 23:06

  • 皮波迪先生

    皮波迪先生 (择善固执,止于至善)

    P3 Frederick The Great, King of Prussia, came to power in 1740. ... The celebrated mathematician Leonhard Euler spent twenty-five years there Potsdam where Fredrick’s courts located. Many other mathematicians and scientists came, as well as philosophers - including Voltaire and La Mettrie, who wrote some of their most influential works while there. But music was Frederick’s real love. He was ...

    2017-10-29 12:50

  • PEAR

    PEAR (起床干活嘞!)

    Hofstadter's Law: It always takes longer than you expect, even when you taken into account Hofstadter's Law. Recursive enumeration is a process in which new things emerge from old things by fixed rules. There seem to be many surprises in such processes - for example the unpredictability of the Q-sequence. It might seem that recursively defined sequences of that type posses some sort of inherent...

    2013-05-22 07:17

  • PEAR

    PEAR (起床干活嘞!)

    The drive to eliminate paradoxes at any cost, especially when it requires the creation of highly artificial formalisms, puts too much stress on bland consistency, and too little on the quirky and bizarre, which make life and mathematics interesting. It is of course important to try to maintain consistency, but when this effort forces you into a stupendously ugly theory, you know something is wrong...

    2013-05-10 06:29

  • 小新

    小新 (be more)

    The initials of this inscription are RICERCAR - an Italian word, meaning 'to seek'. And certainly there is a great deal to seek in the Musical Offering. Happy seeking, fellow readers http://m.youtube.com/#/watch?v=KYouXtuk0T8&desktop;_uri=%2Fwatch%3Fv%3DKYouXtuk0T8

    2013-03-01 05:34

  • 肯特沟技校

    肯特沟技校

    严重怀疑这货是写连载小说出生的。。。每次写到最精彩的地方总是跳闸。。。

    2013-01-09 22:05

  • Tina_小添

    Tina_小添 (我想我也是个少女( ̄▽ ̄))

    Meaning and Form in Mathematics Isomorphism The string --p---q----- is a theorm because 2 plus 3 equals 5. Incredible! I have not thought about it when I was into its rules. When you confront a formal system you know nothing of, and if you hope to discover some hidden meaning in it, your problem is how to assign interpretations to its symbols in a meaningful way that a true statements corre...

    2011-07-23 20:46

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Godel, Escher, Bach

>Godel, Escher, Bach