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Ideas & Trends

The Math Was Complex, the Intentions, Strikingly Simple

By GEORGE JOHNSON

Published: August 27, 2006

LONG before John Forbes Nash, the schizophrenic Nobel laureate fictionalized onscreen in “A Beautiful Mind,” mathematics has been infused with the legend of the mad genius cut off from the physical world and dwelling in a separate realm of numbers. In ancient times, there was Pythagoras, guru of a cult of geometers, and Archimedes, so distracted by an equation he was scratching in the sand that he was slain by a Roman soldier. Pascal and Newton in the 17th century, Gödel in the 20th — each reinforced the image of the mathematician as ascetic, forgoing a regular life to pursue truths too rarefied for the rest of us to understand.

Agence France-Press/Getty Images, top; Granger Collection

CALCULATIONS Newton feuded with Leibniz over the discovery of calculus, but Grigory Perelman, top, claimed to put himself above such banalities.

Last week, a reclusive Russian topologist named Grigory Perelman seemed to be playing to type, or stereotype, when he refused to accept the highest honor in mathematics, the Fields Medal, for work pointing toward the solution of Poincaré’s conjecture, a longstanding hypothesis involving the deep structure of three-dimensional objects. He left open the possibility that he would also spurn a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass.

Unlike Brando turning down an Academy Award or Sartre a Nobel Prize, Dr. Perelman didn’t appear to be making a political statement or trying to draw more attention to himself. It was not so much a medal that he was rejecting but the idea that in the search for nature’s secrets the discoverer is more important than the discovery.

“I do not think anything that I say can be of the slightest public interest,” he told a London newspaper, The Telegraph, instantly making himself more interesting. “I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”

Mathematics is supposed to be a Wikipedia-like undertaking, with thousands of self-effacing scriveners quietly laboring over a great self-correcting text. But in any endeavor — literature, art, science, theology — a celebrity system develops and egos get in the way. Newton and Leibniz, not quite content with the thrill of discovering calculus, fought over who found it first.

As the pickings grow sparser and modern proofs sprawl in size and complexity, it becomes that much harder, and more artificial, to separate out a single discoverer. But that is what society with its accolades and heroes demands. The geometry of the universe almost guarantees that a movie treatment heralding Dr. Perelman is already in the works: “Good Will Hunting” set in St. Petersburg, where he lives, unemployed, with his mother, or a Russian rendition of “Proof.”

To hear him tell it, he is above such trivialities. What matters are the ideas, not the brains in which they alight. Posted without fear of thievery on the Internet beginning in 2002, his proof, consisting of three dense papers, gives glimpses of a world of pure thought that few will ever know.

Who needs prizes when you are free to wander across a plane so lofty that a soda straw and a teacup blur into the same topological abstraction, and there is nothing that a million dollars can buy? Until his death in 1996, the Hungarian number theorist Paul Erdos was content to live out of a suitcase, traveling from the home of one colleague to another, seeking theorems so sparse and true that they came, he said, “straight from The Book,” a platonic text where he envisioned all mathematics was prewritten.

Down here in the sublunar realm, things are messier. Truths that can be grasped in a caffeinated flash become rarer all the time. If Poincaré’s conjecture belonged to that category it would have been proved long ago, probably by Henri Poincaré.

It has taken nearly four years for Dr. Perelman’s colleagues to unpack the implications of his 68-page exposition, which is so oblique that it doesn’t actually mention the conjecture. The Clay Institute Web site carries links to three papers by others — 992 pages in total — either explicating the proof or trying to absorb it as a detail of their own.

Those intent on parceling out credit may have as hard a time with the intellectual forensics: Who got what from whom? Dr. Perelman’s papers are almost as studded with names as with numbers. “The Hamilton-Tian conjecture,” “Kähler manifolds,” “the Bishop-Gromov relative volume comparison theorem,” “the Gaussian logarithmic Sobolev inequality, due to L. Gross” — all have left their fingerprints on The Book. Spread among everyone who contributed, the Clay Prize might not go very far.

A purist would say that no one person deserves to stake a claim on a theorem. That seemed to be what Dr. Perelman, who has said he disapproves of politics in mathematics, was implying.

“If anybody is interested in my way of solving the problem, it’s all there — let them go and read about it,” he told The Telegraph. “I have published all my calculations. This is what I can offer the public.”

He sounded a little like J. D. Salinger, hiding away in his New Hampshire hermitage, fending off a pesky reporter: “Read the book again. It’s all there.”

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沟通啊沟通

到了Barbarosa,等两个人过来。9:30PM,刚下越洋飞机就过来的两人。真是水深火热。

飞机晚点,他们迟到,现在我只好一人坐在所谓阿拉伯风情的沙发椅上,先来几杯冰啤酒把自己降降温。

过来一个看上去立刻就可以参加选美的男Waiter。

对Waiter说,“半升,Erdinger白啤。”

Waiter回答,“Erdinger,白啤,你要0.3升的?”

“半升的。”

“我们有0.3升和0.5升,半升是?”他瞪大眼睛。

“0.5升。”我也瞪大眼睛。

我们大眼瞪大眼瞪了有半秒也就是约等于0.5秒,然后他说,“哦,0.5升。”

Erdinger的白啤,很冰,味道也不错。

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片断

片断。今儿个没打算要论述什么或者哭着喊着要探究点人生真谛。人生真谛就那么多,每天都探究,岂不是很快就没有什么可探究得了?那岂不是人生的悲剧,人类的苦痛,世界的尽头,文明的终结,思想和肉体的冲突,人类社会的大规则和个体突变自我寻找的结局????

这些废话确实很容易一套一套地写。

今天这个,就叫闲扯。把脑子里乌七抹黑地一堆,全给倒出来,就清爽了,这世界就一片清爽了,就亮堂了,就晶晶亮透心凉了。

每天过道里过,就踢一脚沙包。不过,沙包是死的,人是活的。

天气似乎有些凉爽了。夜里,坐在户外,吹吹风,也算是人生的一个小享受。露台上应该弄个大椅子,可以躺着,再弄个小架子,可以搁啤酒,再弄个搁脚的架子,就齐了。

和Sam在新天地吃了个饭。奇了怪了,最近两周,只要是在新天地附近吃饭,就一定是这个Simply Thai。而且每一次都不是我订的座。这个问题如果要仔细研究研究,说不定挺有意思。是互相影响,还是我的朋友们和我的口味比较接近,还是新天地周围其实只有这么一家的餐馆适合我们这种口味的?

八卦新闻看起来还是很好玩儿的。大小人等在那儿闹得这个热闹,自愿的或是不自愿的,爽的或是不爽的。

有一个不解的问题,为什么这么有娱乐精神的中国人民,就没见有多少好玩儿的电影、剧本、小说,写将出来?是大伙儿只顾了看了?还是大伙儿只顾了演了?还是大伙儿一边演着一边打着哈欠连演都演得三心二意何况写了?

连哼哼都有气无力的了。

昨晚没什么事儿,拿出Quentin Taratino的Pulp Fiction又研究了研究,顺带网上搜了搜,搜出他最早还在一个录像店打工时候合Bob Avery合写的Pulp Fiction的剧本。从头到尾仔细看了看。看他的手稿,就一个感觉,奇思妙想,穿插来去,就像在看个空中特技表演队似的,经常想,靠,这要不行了吧,要撞上了吧,忽然来一个出乎意料却又是情理之中的一个转折,极漂亮极惊险地就过去了。

他的剧本里的世界,就是Quentin Taratino的世界。精彩,紧凑,不过就是他的世界。Guy Richie的也有些影子。疯狂的石头,前面到还罢了,不少人说是抄袭,我倒觉得抄得还不错。不过最后的10分钟,那些结尾,就太愚蠢,太形式化,太自己把自己当回事儿地又要娱乐又要艺术还要点人生,就像是个耍把戏的,手里3球已经累得满头大汗,边上已经看得让人心惊肉跳担心他要掉下来,他好,还非要再加两球,然后还非要摆一特酷的Pose收场。

其结果必然是灰头土脸,几个球全砸脑门子上。

写着写着怎么又成这个了?最近老是好为人师,估计是。而且估计一时半会儿还改不了。

一会儿我要嘴里咬一布条,闭嘴,反省去了。

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传说中将要发布的视频管理规定 – 我真想说,吾不言

这两天接了不少媒体打来的电话,估计大伙儿猜也能猜得到,就是传说中广电总局要发的这个规定,要监管互联网上的内容。

这些敏感一些的问题,我也不得不向很多先烈们学习,把我的原话在这儿写出来,免得将来如果哪一个报纸杂志登出来什么,说是我说的,如果是我从来没说过的,不免就有些百口莫辩的感觉。当然,先强调一下,绝大多数的兄弟们还是比较能忠实原话的。烦的是象China Daily前两月这种土豆网融资一亿美元的报道(我融一亿美元干啥?真要象keso建议说我干脆投身房地产业难道?),更烦的是像这不知道算媒体还是不算媒体的飞猪的商业评论,立刻就把China Daily新闻拿来作为泡沫和自吹自擂典型的典型来引用。最最烦的是,这个商业评论下面的这个对话:

“土豆融资1亿美元,看了那英文报道,可能是那记者搞错了!
虽然视频分享服务及模式在北美获得认可,但是,对于在本土监管政策和手段不清的条件下,其发展之路还是要摸索,尝试。

StanCHU 发表于 2006年08月08日 11:38

核实过的,记者没搞错,toodou的人这么说的。

由 flypig 发表于 2006年08月08日 11:41

 
 
看得我气不打一处来,就忍不住留了个言,屁,谁都没跟我们核实过。愿意说泡沫,大伙儿都乐呵呵地说着,没事儿,都自娱自乐。不过,就算非要找个角度,没事儿,客观就好,别自己写着写着就造出来了。
 
不做臆断地核实一下难道真的很困难吗?Thomas Friedman写一篇评论,还能发两回草稿来核实是否与事实相符。尚进那儿忽悠一个Web 2.0也能发稿之前发来草稿核对一下数字和事实是否有出入。至于这么困难吗。
 
回头说广电总局这个传说中的规定,我这么说的:
 
1。对规定什么意见?答:规定还没正式出来呢,我还没看到,您说我能发表什么意见呢?

2。广电总局发是不是对互联网视频有管辖权?答:我不知道。你得自己问问。我哪儿知道这事谁定,是国务院还是人民代表大会,还是信产部和广电总局商量商量就可以自己定了。

3。对于传说中的只有上市公司才有资质怎么看?假如,如果,传说中的规定确实要发布,假如,如果,广电总局确实有管辖权,假如,如果,资质认证是上市公司才有的,那我就很不解了。这个上市公司,上的是美国的纳斯达克,啥时候纳斯达克评估公司能不能上市的标准也作为广电总局的资质认证标准了?美国的FCC都没有听说拿上市与否作为评估资质的标准,难道广电为了要和世界接轨,直接就把纳斯达克的规章当作自己的政策了?

4。你觉得这个规定能执行下去吗?答:规定还没正式出来呢,我还没看到,您说我哪儿知道它能不能执行下去。反正,合理的,自然就能执行,不合理的或者根本没法执行的,它不用我说,也谁都知道没法执行。

5。对土豆有影响吗?没啥影响。该干嘛就干嘛。我们的计划都排到明年了。
 
6。你做土豆之前,考虑过政策风险吗?当然考虑过。不过,这些属于可预期的范围之内的风险。我相信,各个部门的监管水平和政策制定的水平,总体来说,一定是日益提高,日趋合理的。对于中国,我有信心。尤其,我是中国人。不对中国有信心,对美国有信心有啥用?
 
兄弟我不容易吧?呵呵。
 
 

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土豆窝的这个巨大外部涂鸦

哈哈,土豆窝的阁楼上,周末刷出了这个巨大的涂鸦。

高架路上,正好可以看到土豆的这一大幅图。堵车的时候,正好可以娱乐娱乐。

今天the New York Times上,说到Poincare Conjecture,数学的七大难题之一,终于有解的时候,Poincare在100年前说过的一句话:"Thought is only a flash in the middle of a long night, but the flash that means everything."

套用一下, "The graffitti is only a glance in the middle of a big traffic jam, but the glance that means everything."

So are many other things that might be evanescent , but that single burst of life is already worth everything.

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怎么活着

一年前,Web 2.0这个词刚刚开始成为互联网的时尚名词。一夜之间,恨不得是个人都号称自己是个新兴的Web 2.0网站,Web 2.0公司。长尾理论,引爆流行,等等等等。记得去年7月份某次和个投身VC的哥们聊天,他一开口就是,“靠,这个月我已经收到至少10份商业计划书,说自己是Web 2.0的模式。媒体上到处说你们是Web 2.0的样板,你说到底这玩意儿是怎么回事?”

我说,“靠,你问我,我问谁?”

写了一年多的blog,似乎在我自己的blog上,提到Web 2.0这个词的,只有两篇blog。一年多前了,去年6月的第一篇说,在开始做土豆的时候,我听都没听说过Web 2.0这个词。第二篇,是去年12月,在读了Ozzie的memo后,和几个哥们聊完天,有感而发,就Web Service写了个“Web 2.0 我们从哪儿来,我们要到哪儿去。”

到了今天,忽然间满世界都在纷纷火火地说,一批小网站要死掉了,风险投资开始看衰Web 2.0了,Web 2.0的寒冬已经来了。忽然之间,Web 2.0就成了过街老鼠,是个公司就要跟Web 2.0撇清关系。已经很久没有哪个VC来找我说,Gary,说说这Web 2.0到底是怎么回事。

我很喜欢这样。因为我不用再多说一次,“不知道,别问我。”

其实我大约是知道的,只不过,我既不做VC,也不写商业评论,更不用纵览上下五千年有一个历史发展的大局观。喝酒聊天时候可以,哪天想改行写历史评论时候可以。一年前该想的都想过了。现在?现在想这些东西是浪费时间。

所有事情,我只关心,我们是不是在一个恰当的时机做一件符合逻辑的事情,按照一个理性的节奏。

一个网站或者公司,无论它是多大的规模,就算大到了微软、Intel、Google,也只是大趋势中的一个小分子。今天,谁都知道互联网的趋势是多媒体,视频,人与人之间的分享。能够看清楚这个的,100个人当中大概就有50个人,实在是太平常不过了,在满街走的都是极聪明人的高科技和VC业,更加是尽人皆知的道理。

如何创造出一种模式可以从中获取一个公司赖以生存发展的空间?知道的人立时少去了一大截。冒险的成分也陡然间增加了许多。

如何一个团队在一起实现这些模式,日以继夜,毫不放弃地实现下去?能够做到这些事情的人,更少得多了。机遇和运气成分更多。就算是极少数能够坚持到底的当中,真正能够实现想法的,也就是那么寥寥几个罢了。

不过这些都属于废话。反正,泡沫也罢,不泡沫也罢,1.0也罢,2.0也罢,今天的这些网站,一大批的都要死掉,一大批也许很滋润也许不很滋润地继续活着,一些能够在眼下就蓬勃发展,而一些也许要坚持几年后才能等到真正发展的那一天。

作为这个大趋势里的一个小分子,关心这个大的比例有什么意义?没有任何意义。每天做需要做的事,做好它。有可以学习借鉴的新东西,如果合适,就用上。有需要自己发明自己创造的,就赌一把,自己上。坚持到底。

很多事情需要担忧,如果一个个担忧过来,那就什么都别干了。周围的很多事情都很可笑,如果一个个笑过来,也就什么都别干,只顾了笑了。周围也是一堆的听了看着都觉得脑子发胀的疯话,如果真有人想要去一个个扭转过来,他得先把自己气死个几千回。

就这么两手插裤兜里,低头看着路,心里想着要去的地方,爱理不理地往前晃悠着。这么多年都这么活着,挺好。


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