- xw, have you ever read the GEB?
http://www.edge.org/3rd_culture/vhd05/vhd05_index.html
I had heard of the book Gödel, Escher, Bach from some enthusiastic students at Calgary, but not seen it, when I visited the Tarski's in summer 1979 in Berkeley. Noticing the Hofstadter book in Alfred's bookcase I asked him what he thought of it and he exclaimed: "awful, of course it's awful". When I asked whether he had read it he said "of course not". But when I asked him to let me borrow it he got annoyed; the publishers had sent it to him, it belonged to him, and I could not borrow it, of course not.
I must add that I had been working with Tarski, that we were old friends and that it is not too far fetched to call Tarski and Gödel the two pillars of modern mathematical logic. They were of the same generation and had come to America during the late thirties from Poland and from Austria respectively. But they were temperamentally totally different personalities. Tarski was an empire builder.
Anyway, I went straight to Cody's and bought the Hofstadter book, fervently hoping that I would find it wonderful and could teach Alfred a lesson about his prejudices. Well, Alfred had been right after all. When I returned to Calgary at the end of the summer I found a copy of the Hofstadter book waiting for me with a note from the Canadian Journal of Philosophy asking me to review it. I actually had fun doing that review, I was younger then and instead of getting upset I enjoyed making it into a twin enterprise of a parody and a minimal no-nonsense account of Gödel's proof.
What does get me down nowadays is to find the same kind of rash misconceptions still proliferating in the public arena. The popular writers don't consult the experts, or don't listen to them, and the experts don't encourage the public to ask and listen.
- xw
虻叔，我今天休假，咖啡转一圈。看到老爱与老戈的合影，读到你细
细的文字。虻叔的英文好，来历也很棒，容我时间好好学习。
明天再多叙！
rain, rain, go away, come here another day
rain, rain, go away, all the kids want to play.
..... - 椹収鍏�我不很喜欢GEB这本书，而且对“打通”，“边缘”等等企图不怎么乐观。虽然，这种努力本身，可以提供了解几个学科的新鲜角度。
的确，同时精通音乐数学美术的人很少，能发现它的破绽的人很少，所以它很有市场。
不过就BACH那部份，我个人感觉陈词滥调多了些。
也许是我没看懂。
- dkjld什么心性，读得进什么书 品流也
看一个人，看他读什么书便知一二
看深一步，只需听他开口便知虚实
- 浠よ儭鍐�
神。搞得这么复杂，是要相亲还是要搞soulmate ? :)
- gadfly
Brutally true! :) So with the music he listens to, people he befriends or defriends with. :)
- adagio
这部砖头般沉重的书放在我的案上两年了，一直没时间钻进去，只看过一些讲Godel的篇章。也许该多翻翻了。阿姗也曾提到这书，你和她都是学理科又通音乐的，对这本书可能会交流得深入些。
- gadfly
Ain't being kids fun? I am going all the way back to Aesop's fables for fiction writing 101. :)
- liaokangAnything new from the Golden Braid?
- xw说了今天回，果然讨论的热烈。可惜此书我只闻大名，参加不了讨论
。本来准备一读，听说有砖头一样的厚。。。平时工作家庭忙，只能
注意一些萝卜青菜一类的小事，还有很多小人物的事情，当然也会有
几支拉摩或巴赫为儿童写的小曲。
昨天去买菜，碰到一位比较纯净的非裔姑娘，我直觉是海地人。然后
我就问她，您是来自非洲呢，还是来自南美?
她说：我来自海地。
我说：我就猜你来自海地，Vous parlez francais?
她说：�
- xw
Expect to read your fiction 100, seriouly.
&&&&&
细读了你的LINK，原来是误会了。LINK中谈到了群论和FORMAL语言，
，这两个是我在数学中的至爱。至于那么多哲学，就不懂了。。。
希尔伯特我不懂，不懂就是不懂。数学是需要门阶的，我不是学的数
学，也不希望这里不是学数学的人瞎附和。我有一极好友，数学攻得
深，他跟我说四维空间和十一维空间比较和谐，我听了笑笑。
然后我问，连续投中十个蓝球�
- qls
？？？老虻也不说明一下，就这样顺水推舟了？XW粗心啊。
- gadflyHere's my good old friend fourteen's response copied from CND forum:
Interesting read, and it is such a heart-breaking reminder of the german-austrian brilliance that had been destroyed by history (Nazis+ U.S). Isn't she brilliant?
It seems that the good old Viennese school is unhappy about the “cheesy” American rendition of its most brilliant intellectual accomplishment, so much so she
- gadfly
I never knew this side of xw. :)
比老爱身边站的那位强多了, so true, so true! A living body speaks more thuths than any theorem, however ground-breaking it is.
- gadfly
Guilty as charged. But I didn't want to draw attention away from the talking points to the personal. Sincerity could lead to bullshit. :)
- sckNever heard of drawing attention away from one thing to another. You either draw attention away from st or draw attention to st. Good command of up-to-date vocabulary, poor grasp of grammar and syntax.
- gadfly
I never cared to write perfect English, I never knew one and would doubt there is one. However, how much do you want to bet on this one?
This could be your first time, but now you know.
- 鐪嬪ソ鎴�音乐，
数学，
还有视觉艺术之间的关系不是不同学科或不同艺术种类之间的关系，
他们之间的相通之处来源于创作或研究过程中的相似性，
如果没有做过数学研究，
即使学数学的人，
也不见得能体验到这点，
而即使是研究数学的人，
如果对艺术缺少了解和感悟，
自然也无法体验。
我没有读过GEB，
对这类面向社会大众的读物向来没有太多兴趣，
不过马慧元没有太多人同时精通音乐，数学和美术的说法并不确切，
应该说中�
- xw
崇高的地位？不敢苟同。
看到杨振宁博士最近很喜欢把巴赫的乐谱，什么离骚天问，还有杜诗
之类的拿来作报告，胡扯一气，怕是受这本书影响的。
欣赏这一段：
- benbenXW，还记得你以前问过我为什么老把数学和音乐放在一起提吗？
我说我也不知道为什么，因为都不懂。现在你可以再问一遍了，
看好戏他们可能知道:)
- 闃垮
见到我的名字。
正巧上两个礼拜开始读这本书的下半部。上半部是五年前读的，读起来很艰难，努力啃了两三个月就放下了，但非常非常有启发。这次读了一些下半部，也感到异常惊喜，令人爱不释手。每章每节和整体结构中到处都闪着作者天分的光芒，而且文字沉稳，逻辑清晰，弛张有度，又幽默又专业，有很强的纵横透视力。建议读英文版，慢慢读。上半部的习题也要尽量去做。
关于 Bach 的篇章，只是用来阐述作者的观点�
- SusanHey 阿姗, are you going to Music school this fall?
I am going to take classes from community college next semester. I can only take 1 class per semester so I need 3 years to get an associate degree and 5 more year to get the BA. Then it will be about the right time for me to have a mid-life crisis and I will go get my master. :-)
- benben再次同意你。
虽然我本应是”面向社会大众的读物“的读者。但我也不读：)
往往是真内行不屑写大众读物，或者也写不来，不会深入浅出。
都是些学了点生僻术语，不常用词的人出来蒙外行的。
或者是某一种内行喜欢当众玩一些小圈子里自娱自乐的东西。
>
- benben对女人来说， mid-life crisis 几岁的时候发生？男人呢，是四十？五十?
是一次性的还是多发性的？
Then it will be about the right time for me to have a mid-life crisis and I will go get my master. :-)
- 闃垮
I missed the application deadline for international students (this is the time when I wish I had a green card, after 15 years living in the US). So I am going to apply for the winter term which starts January. I think I have a mid-life crisis everyday for the last 15 years. I was so jazzed up for music school and for marriage and all that, then I read this book which seemed to have solved
- gadfly
The book is not really 面向社会大众的读物, unless you want to belittle 阿姗. :)
90% of the population don't care, don't know any of the three, for good or bad.
- 闃垮This GEB book is a very interesting case. I have heard over a dozen very intelligent people telling me about this book. But then I have never met anyone who has actually finished the book except a friend's brother. This brother is also a very interesting case--he has dyslexia (reading disability) and can only read one word at a time, but he spends all his time reading.
On amazon.com there ar
- xwI agree with what 阿姗 had said. Since I am not familiar with any
a single one of them, I should quit from this reading game.
Glad 阿姗 and Gadfly can have very serious discussion...
- gadfly
Looking for polymorphism is a very highbrow game of fun. Specialists tend to think this dilettante, but the fun goes on.:)
- benben我觉得有必要DEFINE一下“社会大众”，直觉“看好戏”和你所指的不是一拨人。现在觉得他说的应该不包括我。
我没怎么看这篇，直觉是一种“小圈子里自娱自乐的东西”，就听XW的吧,
I should quit from this reading game.
Glad 阿姗 and Gadfly can have very serious discussion...
- benbenANOTHER THOUGHT, GADFLY可不可以请你不太SERIOUSLY地讲几句音乐和数学，如果有任何关系的话？我只是好奇，太麻烦就算了：)
- gadfly
I know neither music nor math. For people like Pythagoras, music is sounding numerical relations, math is dumb music. :)
I don't how good Bach was at math. But he could be doing the sounding math without realizing it was math, just like all of us speak prose our whole life whithout realizing it is prose. :)
- 闃垮
Yes, I agree that this book is all about some serious fun. The author's attitude is more like "Hey, look what I've found here! Isn't it cool?" and hoping someone will share the fun in this mind game. Nothing else needs to be taken seriously. Specialists should relax and not get too worked up if others are having some fun. I am not an expert of anything except for certain planets but then
- 濂藉都说是大智若愚
算术题：
笨＋笨＝笨笨＝如何“若愚”＝多大“智”？
- 闃垮今天收到个网友的信，还没看，放在这里先。谁来看看？
I have two links which you may have interests in=)
Math and the Musical Offering [illustration of how math relates to canons]
@ http://www.ams.org/featurecolumn/archive/canons.html
The Canons and Fugues of J. S. Bach [beauty of contrapuntal music, by Timothy A. Smith]
@ http://jan.ucc.nau.edu/%7Etas3/bachindex.html
- 鐪嬪ソ鎴�
我说的是在西方文化中，
不要把杨阵宁这个世界上第一恶心之人提出来，
他出了歌颂湖南农民暴动这种杀人放火行为还对社会有什么了解？
不过只要你和西方知识分子交谈，
数学的地位是显然的，
尤其是法国德国人。
- 鐪嬪ソ鎴�
其实不见得内行不屑写，
更多的可能是怕误解。
要写大众读物，
就必须牺牲很多精确的语言才能描述的东西，
这样描述出来的东西不可能是非常准确的，
如果被有些人按照自己的企图解释之后，
可能会被人用来做些自己不愿意看到的事情，
所以还是不写为好。
从某种意义上来说，
这里好像有个“说不准原理”，
如果用专业语言，
可以表述得很准确，
却无法表述得大众可以看懂，
如果用了大众的语言，
却�
- 鐪嬪ソ鎴�这里的大众读物不是指大众喜不喜欢，
而是指大众只要有兴趣而且能坚持就可以看懂，
区别大众读物和专业读物只要看看此书能不能作为教科书即可，
GEB这样的书要做数学，
或音乐，
或美术的教科书注定是要误人子弟的，
所以这是一本在这个意义下的大众读物。
- 鐪嬪ソ鎴�下面连接的这位哈佛教授既是数学家也是作曲家，
如果有兴趣了解数学和音乐之间的关系，
应该和这样的人作朋友，
从随意的言谈中会了解比读书能得到的更多的东西。
Noam D. Elkies
- SusanI kind of lost my way also lately... Feeling doing something real crazy. Perhaps one shouldn't overanalyze why she wants certain things. Maybe we should act like a kid: I want it, so I am going to get it one way or another.
One thing I need to warn myself: when I am at a thredshold or a crossroad or a tipping point or whatever, I would suddenly fall into some sort of addiction, something that I
- 闃垮I perfectly understand your sudden addiction to things. I do similar things and our psychology is probably similar too--we are afraid of the things we say we want because we are afraid of finding out that we are wrong (we fail to achieve, we don't really want it, we are not good at it, etc.). Whenever I get close to starting a project in one area, I suddenly will work on another area (like watch
- 椹収鍏�Intersting discussions. Probably I'll find it out to read.
- xw
数学我不知道，但伽罗华肯定地位不高。至于音乐与美术，读读十九
世纪上半叶以前的音乐家艺术家传记，恐怕没你说的那么高。
莫扎特死无葬身之地，贝多芬也曾被别人朝脸上吐吐沫的。。。
我也知道一些贵族们研究数学，爱好音乐美术什么的，那是另外一回
事。再说，门德尔松的父辈是坚决反对其行音乐的，而他父辈都是很
有名的“门德尔松”的。
我觉得这两个有共同的地方是在：他们都是由人类�
- 鍏崄涓�瀛�我觉着数学和音乐的共同点是“简单美”。数学揭示最本质也是最简单的真理。音乐宣泄最深层也是最简单的感情。
- 闃垮再提一点。音乐和数学是抽象的，不需要任何经验甚至文字就可以自通，所以会有年纪很小的音乐天才、数学天才。相比之下，它领域比如文学、政治、科学、美术，都或多或少需要一些人生经验，多了很多“人”的因素。我猜想这也是为什么音乐和数学比较接近简单的真理，而其它学科更加人文些。
- 鐪嬪ソ鎴�
一种艺术的地位高低和艺术家是否受尊重不见得是一回事情，
举个例子好了，
中国以前对唐诗宋词向来推崇备至，
书法绘画的地位也绝对是崇高的，
不过大家都不让自己的子女以此为业，
看看红楼梦中贾政对贾宝玉的管教就知道了。
伽罗华地位不高不是因为数学不受尊重，
而是因为他的数学走得太超前，
即使当时一流的数学家也不懂，
这是他在当时地位不高的原因。
不过你要是看看现代数学甚至物理中他的影响，
- 椹収鍏�I always dislike the books trying to unify science and art..I checked out GEB not because of Bach, but of Godel, since in a class I was taking, there were theorems related to him. But I didn't finish this book. I believe A Shan is right, it could be a distinguished one. I'll reread it. :)
- 闃垮是的是的，当小人书看就好了，只是比较难读的好玩的书而已，不用太认真。当成学术报告或科普文学看可能就不行了。
其实我也不知道自己在讲什么。正巧前两天跟男朋友聊起这个，可能有些言重了。
- gadflyOK, I read his preface for the 20th Anniv edition and I'm hooked again. I immediately ordered a copy from Amazon.
In the preface, he clearly says that the book is not really about any three of them. It is about the strange loop, the self-reference phenomenon he believes exhibited in the works of the three and he further believes that this self-referential loop is the key to understand the emerg
- 闃垮I read the Chinese baby version (it was a translation of the first chapter I thought) in middle school without knowing it was from a much greater work. The baby version had enormous influence on my thinking over the years. Maybe that's why I think this book and I have a special "connection". It is so sad about Le Xiucheng....
It would be fun to share the reading with Gadfly. I am on page 34
- 椹収鍏�前些日子心血来潮突然想看看这书，图书馆里的COPY被人占着，我索性在网上买了本旧的平装，八块多。
随便看看，很喜欢。不知道以前为什么看不进去。
作为标题的三个人，两个跟我是老朋友。除了巴赫，还有哥德尔。我选过的课至少两门跟这家伙直接相关。如果说得玄一点，不确定性原理，图灵机这样的概念，是可以当成哲学来说的。巴赫老人家的音乐在某种意义上也可以当作神秘主义符号来说。
我翻看这本书，又惊又喜。简直是专门给
- liaokang才两个月，就有这么大变化，好啊！
- 涓冩牸我常常把巴赫的灵感，想成一种荒诞的规则，一颗怪异的种子。在羽管键琴的机械敲打中，种子当当当地长成盘旋的绿藤。
不过，我现在意识到，我们这个世界是可以被不同的定义和推演所描述的，拟定一个方向，所有的“数”都乖乖地沿它长下去。这个主意可以在我不开心的时候带来一个好梦。
很好的意像，马慧元你写个“数学上的豌豆姑娘”的小说吧～
- 椹収鍏�你这话还真说对了，有的朋友就说我跟豌豆公主似的那么敏感脆弱。
将来我要写个小说，题献给象我一样脆弱和没出息的人。：)
- adagiono no no, should be another fairy tale - Jack and the Beanstalk, call it Pony and the Beanstalk. Your beans grow into the sky and by following the stalk you will find castles and gaints that you never see in the earth - a topic that would interest Sieg I am sure. :)
- 娴敓来这咖啡店潜水有个把礼拜了，发现这儿的东东很提神儿。正好撞上这贴子，想浮出来喘口气儿，顺便给大家问声好，向店主道声谢。
好多年前读过GEB的中文儿童版，当初看懂了啥，一点儿也记不得了－也许啥也没看懂。可当时就是激动，这激动的感觉一直记到现在。后来就买了原版的，也在书架上接了好一阵儿灰了。前些日子翻出来，刚看了个开头儿，就又激动上了。这书不容易看，但也不着急，慢慢儿来。好书我是又着急看不过来，一书在�
- 闃垮
我一直觉得这本书是专门给我写的。:) 好书就是有这本事。支持小马MM！支持浮生潜水员！