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从“Laplace”的传记谈起
最近,听人提起了拉普拉斯方程,就搜集了这个数学家的传记材料。从中可以看出,拉普拉斯在他的87年的人生历程中,著述颇多。单是多卷本的《天体力学》就足以傲视科学界的群雄们了。即使他没有成为院士,更不用说成为法国科学院院长了,他的成就也足以和比他早辞世100年的牛顿大师媲美。江山代有人才出,各领风骚若干年。那些大师们,看起来是突兀而立的名山。其实也不是高不可攀的。有人选择站在巨人的肩上,取得骄人的成就;也有人乐意“行幽径者得雅趣”,开辟属于自己的道路、领域或者空间,虽然更辛苦、更艰难,也更多开拓者的乐趣和收获。
我觉得选择18岁前后上路(on the road)比较合适,在成年人的入口处开始自己的事业和追求。英文版传记中提到了“Laplace now threw himself into original research, and in the next seventeen years, 1771-1787, he produced much of his original work in astronomy.”
在人生的第二个17年中,Laplace开创了自己的光辉事业,在astronomy中站稳了脚跟;50岁后,Laplace已经成熟,陆续推出了自己的天体力学著作5卷16册……有良好的开端以及过程,修成正果亦在情理之中。
Laplace在180年后的今天仍然以其著作和成就影响着当代学子、激励着他们在自己的学科领域里积极进取。科学大师的作用不仅是在科学中,即使不从事科学研究的,也可以从他们的传记中获得启发。这就是我愿意阅读传记材料的原因之一。
以下是拉普拉斯的中英文传记资料:
http://baike.baidu.com/view/5864.htm
拉普拉斯(Laplace,Pierre-Simon,marquisde),法国著名数学家和天文学家,拉普拉斯是天体力学的主要奠基人,是天体演化学的创立者之一,是分析概率论的创始人,是应用数学的先躯。拉普拉斯用数学方法证明了行星的轨道大小只有周期性变化,这就是著名拉普拉斯的定理。他发表的天文学、数学和物理学的论文有270多篇,专著合计有4006多页。其中最有代表性的专著有《天体力学》、《宇宙体系论》和《概率分析理论》。1796年,他发表《宇宙体系论》。因研究太阳系稳定性的动力学问题被誉为法国的牛顿和天体力学之父。
拉普拉斯生于法国诺曼底的博蒙,父亲是一个农场主,他从青年时期就显示出卓越的数学才能,18岁时离家赴巴黎,决定从事数学工作。于是带着一封推荐信去找当时法国著名学者达朗贝尔,但被后者拒绝接见。拉普拉斯就寄去一篇力学方面的论文给达朗贝尔。这篇论文出色至极,以至达朗贝尔忽然高兴得要当他的教父,并使拉普拉斯被推荐到军事学校教书。此后,他同拉瓦锡在一起工作了一个时期,他们测定了许多物质的比热。1780年,他们两人证明了将一种化合物分解为其组成元素所需的热量就等于这些元素形成该化合物时所放出的热量。这可以看作是热化学的开端,而且,它也是继布拉克关于潜热的研究工作之后向能量守恒定律迈进的又一个里程碑,60年后这个定律终于瓜熟蒂落地诞生了。拉普拉斯的主要注意力集中在天体力学的研究上面,尤其是太阳系天体摄动,以及太阳系的普遍稳定性问题。他把牛顿的万有引力定律应用到整个太阳系,1773年解决了一个当时著名的难题:解释木星轨道为什么在不断地收缩,而同时土星的轨道又在不断地膨胀。拉普拉斯用数学方法证明行星平均运动的不变性,并证明为偏心率和倾角的3次幂。这就是著名的拉普拉斯定理,从此开始了太阳系稳定性问题的研究。同年,他成为法国科学院副院士,1784~1785年,他求得天体对其外任一质点的引力分量可以用一个势函数来表示,这个势函数满足一个偏微分方程,即著名的拉普拉斯方程。1785年他被选为科学院院士。 1786年证明行星轨道的偏心率和倾角总保持很小和恒定,能自动调整,即摄动效应是守恒和周期性的,即不会积累也不会消解。1787年发现月球的加速度同地球轨道的偏心率有关,从理论上解决了太阳系动态中观测到的最后一个反常问题。1796年他的著作《宇宙体系论》问世,书中提出了对后来有重大影响的关于行星起源的星云假说。他长期从事大行星运动理论和月球运动理论方面的研究,在总结前人研究的基础上取得大量重要成果,他的这些成果集中在1799~1825年出版的5卷16册巨著《天体力学》之内。在这部著作中第一次提出天体力学这一名词,是经典天体力学的代表作。这一时期中席卷法国的政治变动,包括拿破仑的兴起和衰落,没有显著地打断他的工作,尽管他是个曾染指政治的人。他的威望以及他将数学应用于军事问题的才能保护了他。他还显示出一种并不值得佩服的在政治态度方面见风使舵的能力。
拉普拉斯在数学上也有许多贡献。1812年发表了重要的《概率分析理论》一书。1799年他还担任过法国经度局局长,并在拿破仑政府中任过6个星期的内政部长。
拉普拉斯的著名杰作《天体力学》,集各家之大成,书中第一次提出了“天体力学”的学科名称,是经典天体力学的代表著作。《宇宙系统论》是拉普拉斯另一部名垂千古的杰作。在这部书中,他独立于康德,提出了第一个科学的太阳系起源理论——星云说。康德的星云说是从哲学角度提出的,而拉普拉斯则从数学、力学角度充实了星云说,因此,人们常常把他们两人的星云说称为“康德-拉普拉斯星云说”。
拉普拉斯在数学和物理学方面也有重要贡献,以他的名字命名的拉普拉斯变换和拉普拉斯方程,在科学技术的各个领域有着广泛的应用。
http://www.maths.tcd.ie/pub/HistMath/People/Laplace/RouseBall/RB_Laplace.html
From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball.
Pierre Simon Laplace was born at Beaumont-en-Auge in
Secure of a competency,
During the years 1784-1787 he produced some memoirs of exceptional power. Prominent among these is one read in 1784, and reprinted in the third volume of the Méchanique céleste, in which he completely determined the attraction of a spheroid on a particle outside it. This is memorable for the introduction into analysis of spherical harmonics or
This paper is also remarkable for the development of the idea of the potential, which was appropriated from Lagrange, who had used it in his memoirs of 1773, 1777 and 1780.
and on this result his subsequent work on attractions was based. The quantity V has been termed the concentration of V, and its value at any point indicates the excess of the value of V there over its mean value in the neighbourhood of the point.
This memoir was followed by another on planetary inequalities, which was presented in three sections in 1784, 1785, and 1786. This deals mainly with the explanation of the ``great inequality'' of Jupiter and Saturn. Laplace shewed by general considerations that the mutual action of two planets could never largely affect the eccentricities and inclinations of their orbits; and that the peculiarities of the Jovian system were due to the near approach to commensurability of the mean motions of Jupiter and Saturn: further developments of these theorems on planetary motion were given in his two memoirs of 1788 and 1789. It was on these data that Delambre computed his astronomical tables.
The year 1787 was rendered memorable by
Laplace now set himself the task to write a work which should ``offer a complete solution of the great mechanical problem presented by the solar system, and bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables.'' The result is embodied in the Exposition du système du monde and the Méchanique céleste.
The former was published in 1796, and gives a general explanation of the phenomena, but omits all details. It contains a summary of the history of astronomy: this summary procured for its author the honour of admission to the forty of the
The nebular hypothesis was here enunciated. According to this hypothesis the solar system has been evolved from a globular mass of incandescent gas rotating around an axis through its centre of mass. As it cooled this mass contracted and successive rings broke off from its outer edge. These rings in their turn cooled, and finally condensed into the planets, while the sun represents the central core which is still left. On this view we should expect that the more distant planets would be older than those nearer the sun. The subject is one of great difficulty, and though it seems certain that the solar system has a common origin, there are various features which appear almost inexplicable on the nebular hypothesis as enunciated by
Another theory which avoids many of the difficulties raised by
Probably the best modern opinion inclines to the view that nebular condensation, meteoric condensation, tidal friction, and possibly other causes as yet unsuggested, have all played their part in the evolution of the system.
The idea of the nebular hypothesis had been outlined by Kant in 1755, and he had also suggested meteoric aggregations and tidal friction as causes affecting the formation of the solar system: it is probable that
According to the rule published by Titius of Wittemberg in 1766-but generally known as Bode's Law, from the fact that attention was called to it by Johann Elert Bode in 1778 - the distances of the planets from the sun are nearly in the ratio of the numbers 0 + 4, 3 + 4, 6 + 4, 12+4, etc., the (n+2)th term being ( 3) + 4. It would be an interesting fact if this could be deduced from the nebular, meteoric, or any other hypotheses, but so far as I am aware only one writer has made any serious attempt to do so, and his conclusion seems to be that the law is not sufficiently exact to be more than a convenient means of remembering the general result.
The matter of the Méchanique céleste is excellent, but it is by no means easy reading. Biot, who assisted Laplace in revising it for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, ``Il est aisé à voir.'' The Méchanique céleste is not only the translation of the Principia into the language of the differential calculus, but it completes parts of which
In 1812
This treatise includes an exposition of the method of least squares, a remarkable testimony to
In 1819
Amongst the minor discoveries of Laplace in pure mathematics I may mention his discussion (simultaneously with Vandermonde) of the general theory of determinants in 1772; his proof that every equations of an even degree must have at least one real quadratic factor; his reduction of the solution of linear differential equations to definite integrals; and his solution of the linear partial differential equation of the second order. He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that the solution of an equation in finite differences of the first degree and the second order might be always obtained in the form of a continued fraction. Besides these original discoveries he determined, in his theory of probabilities, the values of a number of the more common definite integrals; and in the same book gave the general proof of the theorem enunciated by Lagrange for the development of any implicit function in a series by means of differential coefficients.
In theoretical physics the theory of capillary attraction is due to Laplace, who accepted the idea propounded by Hauksbee in the Philosophical Transactions for 1709, that the phenomenon was due to a force of attraction which was insensible at sensible distances. The part which deals with the action of a solid on a liquid and the mutual action of two liquids was not worked out thoroughly, but ultimately was completed by Gauss: Neumann later filled in a few details. In 1862 Lord Kelvin (Sir William Thomson) shewed that, if we assume the molecular constitution of matter, the laws of capillary attraction can be deduced from the Newtonian law of gravitation.
Laplace in 1816 was the first to point out explicitly why
Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almost phenomenal As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing.
It would have been well for
Although
That Laplace was vain and selfish is not denied by his warmest admirers; his conduct to the benefactors of his youth and his political friends was ungrateful and contemptible; while his appropriation of the results of those who were comparatively unknown seems to be well established and is absolutely indefensible - of those whom he thus treated three subsequently rose to distinction (Legendre and Fourier in France and Young in England) and never forgot the injustice of which they had been the victims. On the other side it may be said that on some questions he shewed independence of character, and he never concealed his views on religion, philosophy, or science, however distasteful they might be to the authorities in power; it should be also added that towards the close of his life, and especially to the work of his pupils, Laplace was both generous and appreciative, and in one case suppressed a paper of his own in order that a pupil might have the sole credit of the investigation.
This page is included in a collection of mathematical biographies taken from A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908).
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