book 29: godel esher bach
几年前，我们在136聊天， monika 是奥地利人，我们说到奥地利的数学家，monika 说，只有一个有名的 Godel. 最出名的是 godel incompleteness theorem.
然后她说有一本特别有意思的书 ，godel escher bach, 这本书完美的把数学，绘画和音乐联系在了一起，因为他们的大共同点，无穷….
后来，我去johns hopkins 教夏令营，一个学生讲 godel incompleteness therom.我是完全不知道他在讲什么。于是借了这本书翻了一下， 放弃了…
然后时间切到去年，我在波士顿，和eshcer 的展览擦肩而过，然后这两年因为都是断断续续画一下画，加上今年开始练一些巴赫的无伴奏组曲，于是就下定决心读一下这本书。 不出所料的非常难读。 就是读不下去。我看MIT 公开课那个老师说，i read this book for 7 years and still can’t comprehend it all. 我就想那我就至少读一遍吧。 这本书里有好多知识，音乐，绘画，数论就不说了， 还有好多生物，人工智能，国际象棋的知识。
我觉得作者把 godel, bach , escher 放在一起就是因为他们三个在各自的领域都是和无穷infinity这个概念走的最近的。 escher 的画我们去看就是infinite loops 出不来， 或者是黑的白的你怎么看都是一幅画 。 bach 的卡农只要不停永远是两个声部的互相追逐也是停不下来的。 一般的重奏，都会有一个拉主旋律，一个是伴奏。bach 的赋格fugue两个声部拿出来都可以单打独斗当主旋律，但是合在一起又好听！ godel 的incompleteness theorem 也是表达不能停的自我矛盾.
本来有一天不想跑步，看到 阿兰.图灵是个非常厉害的长跑者还自学了小提琴，我就还是跑了0.3mile, every step counts!
MIT open lecture notes:
Five main ideas:
2.Recursion: Fibonacci, piscal triangle, fratoral
3.Paradox: zeno, birthday paradox, veridical,falsidical, barbar
4.Infinity: the different degree of infinity
5.Formal System: MU system
a gifted mathematician doesn’t usually think up and try out all sours of the false pathway to the desired theorem as a less gifted people might do.rather he just “smells” the promising paths and take them immediately.
Fermat 24 keys fugue the margin is too narrow to contain it .
a single neuron can respond to firing or not firing
earth warons have isomorphic brains
is Godel’s incompleteness theorem self mapped onto?
the ratio of 2 squares never equal to 2(sqrt 2 is irrational )
there’s no infallible method for telling true from the false statement of number theory.
mathematics problems can be solved only by doing mathematics.
Ramanujan’s mathematical personality was his friendship with the integers.
all mathematician think, at the bottom in the same kind of way, and Ramanujuan was no exception.
intelligence involves learning, creativity, emotional response, a sense of beauty, a sense of self then there is a long road ahead.
zerl algebra (mediationting on)
musical meaning is spread around the interpreters’ role being to assemble it gradually
alan turing was a strong long-distance runner, as a student at Cambridge. he brought himself a second-hand violin and taught himself to play. thought not very musical, he delivered a great deal of enjoyment from it.
how do you choose a good internal representation of a problem?
what kinds of action reduce the “distance” between you and your goal in the space you have chosen.
you want to find a metric in which the distance between you and your goal is very small.
no, great music will not come out of such an easy formalism
what do we think “almost” happened or “could have” happened, even though is unambiguously did not?
“almost” lies in the mind, not the external facts.
often mathematician physicists use c as constant, p as a parameter, v as a variable.
the strict art of canons, note-perfect imitation is occasionally foregone for sake of elegance or beauty
prophase, anaphase, telophase musical crab cannon
harmonious “ideal -chords” are often widely seperated
categorical statements such as right or wrong, beautiful or ugly, typical of rationalistic thinking of tonal aesthetic
music and painting, have traditionally expressed idea or emotions through a vocabulary of “symbol” (visual image chords, rhythm)
vortex of self is responsible for tangleleness
on a high chunked level qualities such as will, intuition, creativity and consciousness can emerge.
there is extraordinary complex fugue there is beauty and extreme depth of emotion, even exultation in the many levelness of work comes through.