For better or for worse, one of the greatest minds of mankind has to borrow a great musician's glamor and celebrity in order to catch more eyeballs. Why isn't Mozart "Euler of music"? :-)
Happy Birthday, Mr. "Oiler". :-)
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The Countless Achievements of a Math Master
By David Brown
Washington Post Staff Writer
Monday, April 9, 2007; A06
You should approach Joyce's "Ulysses" as the illiterate
Baptist preacher approaches the Old Testament: with faith.
-- William Faulkner
Let's approach Leonhard Euler and his work the same way. It will make things a whole lot easier.
If one is not a mathematician (and except for a few of you out there, who is?), it's going to be impossible to actually understand why Euler was such a great man. Other people will have to tell us, and we should probably believe them.
In 1988, the journal Mathematical Intelligencer asked its readers to list the most beautiful equations in mathematics. Of the top five, Euler, who was born in Basel, Switzerland, 300 years ago next Sunday, discovered three of them, including No. 1:
ei(pi) + 1 = 0.
(The other two were from Euclid, who worked in the 4th and 3rd centuries B.C.)
In 2004, Physics World put the same question to its readers. Of the top 20 equations, Euler had two. The one listed above, known as "Euler's equation," was second only to James Clerk Maxwell's equations describing electromagnetism, which were counted as one entry.
Some have called Euler the "Mozart of Mathematics," not only because of his genius but because of his prodigious output.
Before his death at 76, he had written more than 800 papers and books on pure and applied mathematics. In 1775, he composed about one paper a week, ranging in length from 10 to 50 pages. (Twenty papers is considered a good lifetime output for modern mathematicians.) His collected works fill 25,000 pages in 79 volumes, including five of correspondence to the leading thinkers of his day.
Amazingly, that's not all of it.
More letters and a dozen notebooks will be published over the next decade. If the past is a guide, they are likely to contain work that in some sense is original even today.
Three centuries after his birth, Euler is far from a household name (unless you live in Switzerland, where his face used to be on the 10-franc note). He didn't jump out of the bathtub and run naked through the streets, like Archimedes. His head didn't get hit by an apple, like Newton's. He didn't figure out, before age 10, how to add every number from 1 to 100 in less than a minute, like Gauss.
Nevertheless, he's right there with them.
"The four greatest mathematical scientists of all time are Archimedes, Isaac Newton, Leonhard Euler and Carl Friedrich Gauss," said Ronald S. Calinger, a historian of mathematics at Catholic University. He is nearly done with the first book-length biography of Euler written in English.
William Dunham, a professor of mathematics at Muhlenberg College in Pennsylvania, added that Euler is "an amazingly seminal figure in physics, as well. He wrote about optics, classical mechanics, fluid mechanics and astronomy -- in those days it was all sort of one big subject."
Euler (pronounced "oiler") was the first child of a pastor and his wife. His father had a talent for mathematics and instructed Leonhard, who enrolled in the University of Basel at age 13.
There, he studied under Johann Bernoulli, one of Europe's eminent mathematicians, and met Bernoulli's sons, Nicholas and Daniel, who were to become famous scientists themselves. Daniel was to be Euler's best friend.
The younger Bernoullis went to St. Petersburg to join the Russian Academy of Sciences. Soon after arriving, they persuaded Catherine I, Peter the Great's widow, to invite Euler, too. He arrived in 1727, at age 20.
Euler spent about 30 years in Russia in two long stints, interrupted by about 25 years in Berlin, to which he was called by Frederick the Great of Prussia. He never returned to Switzerland, possibly because he was offended that his Dutch-born wife would not qualify for citizenship.
Now, Switzerland is honoring him as both a native son and an example of the achievements of the Swiss diaspora. It is issuing a stamp with his image on it. Consulates around the world are holding lectures and other events marking the tercentenary of his birth.
"He is at the very top," said Daniela Stoffel, head of cultural affairs at the Swiss Embassy here.
As one would expect, Euler was good at all kinds of things. His first language was German. He wrote principally in Latin, with many papers in French (the language of the Prussian court) and a few in German. He spoke Russian. A few letters to London's Royal Society in English survive. As a young man, he studied Greek and Hebrew.
Euler contributed to essentially every field of mathematics -- calculus, geometry, number theory and the vast realm of applied mathematics. "He was a universalist when that was still possible," said Dunham, who has just edited a book, "The Genius of Euler," published by the Mathematical Association of America.
Nevertheless, Euler's greatest achievements may lie in what became mathematical analysis, which includes calculus and differential equations.
Although Newton and Gottfried Leibniz discovered calculus, Euler systematized it, made hundreds of discoveries and invented differential equations, which he successfully applied to mechanics and astronomy, transforming them from geometry-based disciplines to fully calculus-based ones. He almost single-handedly invented the calculus of variations, which among other things allowed the Apollo moon shot to hit its mark.
Euler also recognized the importance of the number e, which he named (although not after himself, as some believe). It is an irrational number approximately equal to 2.7183, the base of natural logarithms and essential to the calculation of such things as compound interest. Like pi, it is also a value that pops up in all sorts of unexpected places -- one of the universe's favored numbers.
Euler's achievements were all the more remarkable because he lived a life that was both relatively normal and quite difficult.
He married twice and fathered 13 children. Only five of them survived into adolescence. He played the clavier and composed a small corpus of music based on mathematical equations. (A concert of it will be presented in St. Petersburg in May as part of an Euler festival.) He was a masterful chess player. He liked to go to the Berlin zoo with his children and watch the bear cubs.
In his early 30s, Euler lost most of the sight in his right eye. He developed a cataract in the other and was legally blind for the last dozen years of his life. As his sight failed, he took to writing on a huge slate on a round table, dictating his papers to a Swiss secretary.
He worked incessantly even after his eyesight failed, and was, it appears, a happy man. On the day he died in St. Petersburg, Sept. 18, 1783, his slate reportedly contained a calculation of the height to which a hot-air balloon could rise. News of the first balloon ascent, in Paris the previous June, had recently arrived.
Says Dunham: "You could hardly argue that he wasted a day of his life."
- posted on 04/10/2007
哈哈,James Clerk Maxwell's equations describing electromagnetism 是我大学二年级的恶梦,那个电磁学的物理老师,讲了一口我听不懂的安徽方言不说,还不时地从讲台上掉下来,我至今不知道我是如何把电磁学考了个B的, 那可是我生命中的一个奇迹:)
In 2004, Physics World put the same question to its readers. Of the top 20 equations, Euler had two. The one listed above, known as "Euler's equation," was second only to James Clerk Maxwell's equations describing electromagnetism, which were counted as one entry.
- Re: Mozart of Mathematicsposted on 04/10/2007
我的量子力学老师又漂亮又幽默,所以不费吹灰之力就学得很好了:)
固体物理老师是个麻子,现在想着固体物理就想起了天花:)
- posted on 04/10/2007
Ha, I guess that's because you were in the audience. Typically an instructor gets distracted and displays sheepish behavior when there is a pretty girl in his class. :-)
Maxwell eqs are difficult to work with for the beginners, but they are also a beauty to behold once you are able to derive from a set of mere 4 eqs some truly amazing results (such as the exisitence of the eletromagnetic wave and electromagnetic radiations, and calculating the speed of light.)
July wrote:
哈哈,James Clerk Maxwell's equations describing electromagnetism 是我大学二年级的恶梦,那个电磁学的物理老师,讲了一口我听不懂的安徽方言不说,还不时地从讲台上掉下来,我至今不知道我是如何把电磁学考了个B的, 那可是我生命中的一个奇迹:)
In 2004, Physics World put the same question to its readers. Of the top 20 equations, Euler had two. The one listed above, known as "Euler's equation," was second only to James Clerk Maxwell's equations describing electromagnetism, which were counted as one entry. - posted on 04/11/2007
萊昂哈德·歐拉
维基百科,自由的百科全书
莱昂哈德·欧拉莱昂哈德·欧拉(Leonhard Euler,又譯為尤拉,1707年4月15日-1783年9月18日)是瑞士数学家和物理学家。他被称为历史上最伟大的两位数学家之一(另一位是卡尔·弗里德里克·高斯)。欧拉是第一个使用“函数”一词来描述包含各种参数的表达式的人,例如:y = F(x)(函数的定义由莱布尼兹在1694年给出)。他是把微积分应用于物理学的先驱者之一。
欧拉出生于瑞士,在那里受教育。欧拉是一位数学神童。他作为数学教授,先后任教于圣彼得堡和柏林,尔后再返圣彼得堡。欧拉是史上發表論文數第二多的数学家,全集共计75卷,他的紀錄一直到了二十世紀才被保羅·艾狄胥打破。他發表的論文達856篇(另一說865篇),著作有32部(另一說31部)。產量之多。無人能及,欧拉实际上支配了18世纪什至现在的数学,对于当时新发明的微积分,他推导出了很多结果。在1735年至1771年歐拉的雙眼先後失明(據說因雙眼直接觀察太陽),尽管最後七年,欧拉的双目完全失明,,他还是以惊人的速度产出了生平一半的著作。
很多數學的分技,也是由歐拉所創或因而有大大的進展
歐拉年輕時曾研讀神學,他一生虔诚、篤信上帝並不能容許任何詆毀上帝的言論在他面前發表。在广泛流传有一个传说。传说中说到,欧拉在叶卡捷琳娜二世的宫廷里,挑战當時造訪宮廷的無神論者德尼·狄德罗:“先生,,所以上帝存在,这是回答!”不懂數學的德尼完全不知怎麼應對,只好投降。
歐拉的離世也很特別:據說當時正是下午茶時間,正在逗孫兒玩的時候,被一塊蛋糕卡在喉頭窒息而死。另有一說是,當時他突然病發,說了一聲「我死」之後便辭世。
小行星欧拉2002是为了纪念欧拉而命名的。
欧拉和丹尼尔·伯努利一起,建立了弹性体的力矩定律:作用在弹性细长杆上的力矩正比于物质的弹性和通过质心轴和垂直于两者的截面的惯性动量。
他还直接从牛顿运动定律出发,建立了流体力学里的欧拉方程。这些方程组在形式上等价于粘度为0的纳维-斯托克斯方程。人们对这些方程的主要兴趣在于它们能被用来研究冲击波。
他对微分方程理论作出了重要贡献。他还是欧拉近似法的创始人,这些计算法被用于计算力学中。此中最有名的被称为欧拉方法。
在数论里他引入了欧拉函数。自然数n的欧拉函数φ(n)被定义为小于n并且与n互质的自然数。例如,φ(8) = 4,因为有四个自然数1,3,5和7与8互质。
在计算机领域中广泛使用的RSA公钥密码算法也正是以欧拉函数为基础的。
在分析领域,是欧拉综合了莱布尼兹的微分与牛顿的流数。
他在1735年由于解决了长期悬而未决的贝塞尔问题而获得名声:
其中ζ(s)是黎曼函数。
欧拉将虚数的幂定义为如下公式
这就是欧拉公式,它成为指数函数的中心。在初等分析中,从本质上来说,要么是指数函数的变种,要么是多项式,两者必居其一。被理查德·费曼称为“最卓越的数学公式”的则是欧拉公式的一个简单推论(通常被称为欧拉恒等式):
在1735年,他定义了微分方程中有用的欧拉-马歇罗尼常数:
他是欧拉-马歇罗尼公式的发现者之一,这一公式在计算难于计算的积分、求和与级数的时候极为有效。
在1739年,欧拉写下了《音乐新理论的尝试(Tentamen novae theoriae musicae)》,书中试图把数学和音乐结合起来。一位传记作家写道:这是一部"为精通数学的音乐家和精通音乐的数学家而写的"著作。
在经济学方面,欧拉证明,如果产品的每个要素正好用于支付它自身的边际产量,在规模报酬不变的情形下,总收入和产出将完全耗尽。
在几何学和代数拓扑学方面,欧拉公式给出了单联通多面体的边、顶点和面之间存在的关系:
其中,F为给定多面体的面数之和,E为边数之和,V为顶点数之和。这个定理也可用于平面图。对非平面图,欧拉公式可以推广为:如果一个图可以被嵌入一个流形M,则:
其中χ为此流形的欧拉特征值,在流形的连续变形下是不变量。单联通流形,例如球面或平面,的欧拉特征值是2。对任意的平面图,欧拉公式可以推广为: F - E + V - C = 1 ,其中C为图中连通分支数。
在1736年,欧拉解决了柯尼斯堡七桥问题,并且发表了论文《关于位置几何问题的解法(Solutio problematis ad geometriam situs pertinentis)》,对一笔画问题进行了阐述,是最早运用图论和拓扑学的典范。
- posted on 04/11/2007
List of topics named after Leonhard Euler
From Wikipedia, the free encyclopedia
In mathematics and physics, there are a large number of topics named in honour of Leonhard Euler. Many of these topics involve a function, formula or identity, often ambiguously called Euler's formula, Euler's function, or Euler's identity. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. Physicists and mathematicians sometimes jest that, in an effort to avoid naming everything after Euler, discoveries or theorems are named after the "first person after Euler to discover it".
Topics including "Euler":
AMS Euler typeface
Euler angles defining a rotation in space.
Euler approximation
Euler-Bernoulli beam equation, concerning the elasticity of structural beams.
Euler brick
Euler-Cauchy equation, a second-order linear differential equation
Euler characteristic in algebraic topology and topological graph theory, and the corresponding Euler's formula χ(S2) = F − E + V = 2.
Euler's conjecture
Euler derivative (as opposed to Lagrangian derivative)
Euler diagram
Euler's disk
Euler-Lagrange equation (in regard to minimization problems)
Euler's equation usually refers to Euler's equations, Euler's formula, or Euler's identity
Euler's equations, concerning the rotations of a rigid body.
Euler equations in fluid dynamics.
Euler's formula eix = cosx + isinx in complex analysis.
Euler's formula for planar graphs: v − e + f = 2
The Euler function, a modular form that is a prototypical q-series.
Eulerian graph
Euler's identity eiπ + 1 = 0.
Euler's identity may also refer to the pentagonal number theorem.
Euler's idoneal numbers
The Euler integrals of the first and second kind, namely the beta function and the gamma function.
Euler's line
Euler-Maclaurin formula
Euler-Mascheroni constant or Euler's constant γ ≈ 0.577216
Euler Medal, a prize for research in combinatorics
Euler's method
Euler's number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant.
Euler numbers are an integer sequence.
Euler number, the cavitation number in fluid dynamics.
Eulerian path or Euler cycle, a path through a graph that takes each edge once.
Euler polynomials
Euler product
Euler programming language
Euler pseudoprime
Euler-Rodrigues parameters
Euler's rule
Euler spline
Euler squares, usually called Graeco-Latin squares.
Euler system, a collection of cohomology classes.
Euler's three-body problem
Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer.
Euler-Tricomi equation
2002 Euler (an asteroid)
Theorems:
Euclid-Euler Theorem
Euler's rotation theorem
Euler's homogeneous function theorem, a theorem about homogeneous polynomials.
Euler-Fermat theorem, that aφ(m) = 1(mod m) whenever a is coprime to m, and φ is the totient function.
Euler's summation formula, a theorem about integrals.
Euler's theorem in geometry, relating the circumcircle and incircle of a triangle.
Retrieved from "http://en.wikipedia.org/wiki/List_of_topics_named_after_Leonhard_Euler"
- posted on 04/11/2007
今天,这条线让我没完没了地想起了我曾是一个物理系的学生,读过许多物理书,热爱过爱恩斯坦和量子力学,因为搞不懂麦克斯韦方程组,绝望的要自杀:)
-----------------------------------
詹姆斯·克拉克·麦克斯韦(James Clerk Maxwell,又譯馬克斯威爾、馬克斯威,1831年6月13日—1879年11月5日),英国物理学家。经典电动力学的创始人,统计物理学的奠基人之一。
麦克斯韦1831年6月13日生于英国的爱丁堡,1847年~1850年在爱丁堡大学学习。1850年~1854年进入剑桥三一学院攻读数学。1856年~1860年担任阿伯丁郡的马里查尔学院教授。1860年~1865年在伦敦皇家学院执教,并从事气体运动理论的研究。1860年成为英国皇家学会会员。1871年任剑桥大学教授,创建并领导了英国第一个专门的物理实验室卡文迪许实验室。
麦克斯韦的主要贡献是建立了麦克斯韦方程组,创立了经典电动力学,并且预言了电磁波的存在,提出了光的电磁说。
麦克斯韦方程组是麦克斯韦在19世纪建立的描述电磁场的基本方程组。他含有四个方程,不仅分别描述了电场和磁场的行为,也描述了它们之间的关系。麦克斯韦的四个方程分别表达了:电荷是如何产生电场的(高斯定理);验证了磁单极子的不存在(高斯磁场定律);电流和变化的电场是怎样产生磁场的(安培定律),以及变化的磁场是如何产生电场(法拉第电磁感应定律)。
- posted on 04/11/2007
我喜欢麦克斯韦。他有一张理想的科学家的面孔,智慧的眼睛,络腮胡子下的敏感的嘴唇,庄严的表情里有一种宿命的色彩。他是英年早逝,48岁就死于癌症。可他却是物理学的一座丰碑。 他是一个虔诚的基督教徒。而最让我着迷的是他的诗人气质,他热爱诗歌,还出版过诗集,自弹自唱过他自己的诗:
Gin a body meet a body
Flyin' through the air.
Gin a body hit a body,
Will it fly? And where?
在他无数的科学发现里,我最喜欢的是麦克斯韦妖的假想。1871年他为了说明违反热力学第二定律的可能性而设想:麦克斯韦妖是在物理学中,假想的能探测并控制单个分子运动的“类人妖”。他意识到自然界存在着与熵增加相拮抗的能量控制机制,但他无法清晰地说明这种机制,只能称之为一种“妖”。 这就是第二类永动机的理论。其实,因为忽略了对分子运行状态进行判断所需能量以及其他消耗的能量,这个模型是不可能成立的。
- Re: Mozart of Mathematicsposted on 04/11/2007
数学和音乐的关系是紧密相关的。音乐用数字来表示。这是人类两种最抽象,最复杂,最简明,最高贵的语言。
在1739年,欧拉写下了《音乐新理论的尝试(Tentamen novae theoriae musicae)》,书中试图把数学和音乐结合起来。一位传记作家写道:这是一部"为精通数学的音乐家和精通音乐的数学家而写的"著作。 - Re: Mozart of Mathematicsposted on 04/11/2007
谢谢七月提供的信息。有人说,上帝是个数学家,你信不信?:-)
也有人说过,不是心灵的诗人,不可能成为数学家。
数学与音乐的形式表达之间的关系,肯定有人研究过。不过我看两者有个很大的不同,数学是天然的语言,而音乐是人造的语言。在我看来,最好的数学应能呈现对天地精神、宇宙造化的深刻领悟和把握,而最好的音乐应能刻划人的内心感情世界中最深层的东西。 - Re: Mozart of Mathematicsposted on 04/11/2007
Mozart of Mathematics,这个标题不好。
莫扎特是很可爱的,但这欧拉麦克斯韦之类的,还有巴赫。都是大山
啊,大石头山!
山上的每棵树都抱不过来。我个人觉得。
女孩子一钻进去就成压寨夫人啦:)
倒是小泉小溪小花小草的,能符合人的尺寸,显得更可爱。
故而我喜欢青年达尔文,还有晚年达尔文。
咖啡里抬个小杠。
- posted on 04/11/2007
中年的达尔文为什麽不好?他的life很sad,孩子是先天病。
莫扎特浑然天成,这点和欧拉很像。莫扎特就不是山吗?凡没人能跨越的都是山。只是,莫扎特这座山上特别云蒸霞蔚,草木葱茏,上山的路满是欢笑。其他的山比较陡峭险峻而已:)
我也抬杠:)阿基米德说,他一抬杠就能举起世界 :)我也得试试 :)
xw wrote:
Mozart of Mathematics,这个标题不好。
莫扎特是很可爱的,但这欧拉麦克斯韦之类的,还有巴赫。都是大山
啊,大石头山!
山上的每棵树都抱不过来。我个人觉得。
女孩子一钻进去就成压寨夫人啦:)
倒是小泉小溪小花小草的,能符合人的尺寸,显得更可爱。
故而我喜欢青年达尔文,还有晚年达尔文。
咖啡里抬个小杠。
- Re: Mozart of Mathematicsposted on 04/12/2007
xw wrote:
故而我喜欢青年达尔文,还有晚年达尔文。
上回xw说不喜欢中年达尔文时就想问来着,为什么呢?我可不是跟着July MM 起哄抬杠哈,就是想知道:) - posted on 04/12/2007
七月 MM,这么快就喜欢上一个人了啊?
麦克斯韦是第一任卡文迪许教授(剑桥物理系一把手)。在他任内,他从不允许女学生进卡文迪许实验室。只有在他每年夏天回苏格兰度假的那几个月时间里,那些可怜的想学物理的女生才可以进实验室,她们必须赶在麦克斯韦回来之前把所有的课上完,所有的实验做完。poor them!
听了这个故事你还喜欢他吗?:-)
July wrote:
我喜欢麦克斯韦。他有一张理想的科学家的面孔,智慧的眼睛,络腮胡子下的敏感的嘴唇,庄严的表情里有一种宿命的色彩。他是英年早逝,48岁就死于癌症。可他却是物理学的一座丰碑。 他是一个虔诚的基督教徒。而最让我着迷的是他的诗人气质,他热爱诗歌,还出版过诗集,自弹自唱过他自己的诗:
Gin a body meet a body
Flyin' through the air.
Gin a body hit a body,
Will it fly? And where?
在他无数的科学发现里,我最喜欢的是麦克斯韦妖的假想。1871年他为了说明违反热力学第二定律的可能性而设想:麦克斯韦妖是在物理学中,假想的能探测并控制单个分子运动的“类人妖”。他意识到自然界存在着与熵增加相拮抗的能量控制机制,但他无法清晰地说明这种机制,只能称之为一种“妖”。 这就是第二类永动机的理论。其实,因为忽略了对分子运行状态进行判断所需能量以及其他消耗的能量,这个模型是不可能成立的。
- posted on 04/12/2007
不喜欢了:)
guanzhong wrote:
七月 MM,这么快就喜欢上一个人了啊?
麦克斯韦是第一任卡文迪许教授(剑桥物理系一把手)。在他任内,他从不允许女学生进卡文迪许实验室。只有在他每年夏天回苏格兰度假的那几个月时间里,那些可怜的想学物理的女生才可以进实验室,她们必须赶在麦克斯韦回来之前把所有的课上完,所有的实验做完。poor them!
听了这个故事你还喜欢他吗?:-)
July wrote:
我喜欢麦克斯韦。他有一张理想的科学家的面孔,智慧的眼睛,络腮胡子下的敏感的嘴唇,庄严的表情里有一种宿命的色彩。他是英年早逝,48岁就死于癌症。可他却是物理学的一座丰碑。 他是一个虔诚的基督教徒。而最让我着迷的是他的诗人气质,他热爱诗歌,还出版过诗集,自弹自唱过他自己的诗:
Gin a body meet a body
Flyin' through the air.
Gin a body hit a body,
Will it fly? And where?
在他无数的科学发现里,我最喜欢的是麦克斯韦妖的假想。1871年他为了说明违反热力学第二定律的可能性而设想:麦克斯韦妖是在物理学中,假想的能探测并控制单个分子运动的“类人妖”。他意识到自然界存在着与熵增加相拮抗的能量控制机制,但他无法清晰地说明这种机制,只能称之为一种“妖”。 这就是第二类永动机的理论。其实,因为忽略了对分子运行状态进行判断所需能量以及其他消耗的能量,这个模型是不可能成立的。
- Re: Mozart of Mathematicsposted on 04/12/2007
看来咱们对家里有女初长成的父母的心情都有了进一步的理解。:-P
玩笑,别见怪。:-) - posted on 04/12/2007
July wrote:达尔文青年与晚年都很真。中年嘛,病是病得不轻,近亲结婚是最大
中年的达尔文为什麽不好?他的life很sad,孩子是先天病。
的关系,还有南美热雨林的昆虫病毒,还有晕船的神经。
莫扎特浑然天成,这点和欧拉很像。莫扎特就不是山吗?凡没人能跨越的都是山。只是,莫扎特这座山上特别云蒸霞蔚,草木葱茏,上山的路满是欢笑。其他的山比较陡峭险峻而已:)
跨不跨山是一回事。就象我们讨论大乘佛经,就显得不够人情。
也许真理本身即不够人情的。独乐乐,与人乐乐,孰乐?我只好认情
理了。
但莫扎特和欧拉显然不是一类的。还有巴赫。
我也抬杠:)阿基米德说,他一抬杠就能举起世界 :)我也得试试 :)
阿基米德泡澡生机,尤利卡!可亲。
阿基米德画圈圈,被罗马士兵砍了头。可敬。
阿基米德聚镜燃敌帆,也有智慧。
叙拉古阿基米德啊,自己的头都丢了,还要扛地球。地球本来就飘在
太空,不用扛的。另外,既使,支点在哪里?
真是用自己的手提自己的头发,一跳,
这回倒真可爱了!
- Re: Mozart of Mathematicsposted on 04/12/2007
嘻嘻,可怜天下父母心, 都死了一百多年了,喜欢个死人怕什麽?还是当心邻家的男孩子吧:)
guanzhong wrote:
看来咱们对家里有女初长成的父母的心情都有了进一步的理解。:-P
玩笑,别见怪。:-) - posted on 04/12/2007
浮生 wrote:
xw wrote:上回xw说不喜欢中年达尔文时就想问来着,为什么呢?我可不是跟着July MM 起哄抬杠哈,就是想知道:)
故而我喜欢青年达尔文,还有晚年达尔文。
青年达尔文是很茫然,很痴迷,很虔诚,也很可爱。
一张白纸,绘事后素。这里有一张名画:
剑桥的生物地质教授喜欢(他学神学),爱玛喜欢,费兹罗伊喜欢,甚
至大独裁者罗萨斯都喜欢。可惜他老爸不喜欢!
晚年达尔文达到了清明之境,认识到中年的不足,开拓了英美人类学
,人道情怀,并放弃了刺杀小昆虫之举。恐怕也认识到了孟德尔。
这一张照片:
就象你不喜欢社会达尔文,我也曾一直想把达尔文与社会达尔文分开
,看来是分不开的。
中年达尔文不写诗了,说读都读不来。
- posted on 04/13/2007
社会达尔文是拉大旗作虎皮,与老达无关。不能要求老达来负责。
社会达尔文一向是讨人嫌的,真正的社会达尔文的实践者一般是只做不说,说得响的理论家, 如西洋的斯宾塞,中国的严复,考其生平行止,并不怎么社会达尔文。响P不臭,臭P不响是也。
社会达尔文也并非一无是处,物竞天择,适者生存,强者发达,强调任何个体和集体都要适应环境,自我更新,否则就可能被淘汰,这个思想对一个多世纪以前的中国,变法图强,还是有正面意义。
当然,走到极端,那就变成丛林法则,弱肉强食,Might is right这一套了。
窃以为,把“物竞天择,适者生存,强者发达”的思想,与对弱势个体及群体的保护结合起来,不失为一种理性中庸的社会哲学。
xw wrote:
就象你不喜欢社会达尔文,我也曾一直想把达尔文与社会达尔文分开
,看来是分不开的。
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