法国数学家物理学家——拉普拉斯

强国之心

写在前面的话/编者 拉普拉斯与力学大家达朗贝尔，著名化学家拉瓦锡是基本同时代的人。他奠定了概率论的基础，特别是拉普拉斯变换，是电学信号变换的基础。高中数学会有概率论基础入门，大学二年级会有概率论和数理统计，是工科学生的必修课程之一，也是研究生入学考试必考科目之一。了解一下拉普拉斯，知道这个人名，当再出现老师干讲的时候，或许理解内容有一点帮助。知道鸡下蛋固然重要，知道哪个鸡下的蛋怎么下的，也许很有帮助。 PIERRE-SIMON, MARQUIS DE LAPLACE皮艾尔西蒙拉普拉斯爵士 Physicists 物理学家Pierre-Simon, marquis de Laplace皮艾尔西蒙拉普拉斯爵士 French scientist and mathematiciann法国科学家与数学家。 Pierre-Simon, marquis de Laplace, (born March 23, 1749, Beaumount-en-Auge, Normandy, France—died March 5, 1827, Paris), French mathematician, astronomer, and physicist who was best known for his investigations into the stability of the solar system. 皮埃尔-西蒙，拉普拉斯侯爵，(1749年3月23日生于法国诺曼底的博芒特-恩-奥吉，1827年3月5日死于巴黎)，法国数学家、天文学家和物理学家，以其对太阳系稳定性的研究而闻名 Pierre-Simon, marquis de LaplaceQUICK FACTS小资料Laplace, Pierre-Simon, marquis de BORN出生March 23, 1749 Beaumont-en-Auge, FranceDIED 逝世March 5, 1827 (aged 77)Paris, France 法国巴黎NOTABLE WORKS著作“Analytic Theory of Probability” 概率分析理论“Celestial Mechanics” 天体力学“The System of the World” 世界体系 SUBJECTS OF STUDY 研究领域Solar System 太阳系Laplace’s equation 拉普拉斯方程Laplace transform 拉普拉斯变换Laplace operator 拉普拉斯算子 Laplace successfully accounted for all the observed deviations of the planets from their theoretical orbits by applying Sir Isaac Newton’s theory of gravitation to the solar system, and he developed a conceptual view of evolutionary change in the structure of the solar system. He also demonstrated the usefulness of probability for interpreting scientific data. 拉普拉斯通过将艾萨克·牛顿爵士的引力理论应用于太阳系，成功地解释了所有观察到的行星偏离理论轨道的情况，他发展了太阳系结构进化变化的概念观点。他还证明了概率对于解释科学数据的有用性。 Hubble Space Telescope 哈勃太空望远镜READ MORE ON THIS TOPIC 本主题上了解更多astronomy: Laplace 天文学: 拉普拉斯 Since every planet is attracted not only by the Sun but also (much more weakly) by all the other planets,.. 因为每一个星球不仅仅被太阳吸引，而且也被其他行星吸引(尽管要弱的多)。 Laplace was the son of a peasant farmer. Little is known of his early life except that he quickly showed his mathematical ability at the military academy at Beaumont. In 1766 Laplace entered the University of Caen, but he left for Paris the next year, apparently without taking a degree. He arrived with a letter of recommendation to the mathematician Jean d’Alembert, who helped him secure a professorship at the École Militaire, where he taught from 1769 to 1776. 拉普拉斯是一个农民的儿子。人们对他早年生活知之甚少，只知道他很快在博蒙特军事学院展示了他的数学能力。1766年，拉普拉斯进入卡昂大学，但第二年他去了巴黎，显然没有获得学位。他带着给数学家让·达朗贝尔的推荐信来了，后者帮助他获得了军事学院的教授职位，他从1769年到1776年在那里任教。 In 1773 he began his major lifework—applying Newtonian gravitation to the entire solar system—by taking up a particularly troublesome problem: why Jupiter’s orbit appeared to be continuously shrinking while Saturn’s continually expanded. The mutual gravitational interactions within the solar system were so complex that mathematical solution seemed impossible; indeed, Newton had concluded that divine intervention was periodically required to preserve the system in equilibrium. Laplace announced the invariability of planetary mean motions (average angular velocity). This discovery in 1773, the first and most important step in establishing the stability of the solar system, was the most important advance in physical astronomy since Newton. It won him associate membership in the French Academy of Sciences the same year. 1773年，他开始了他的主要人生工作——将牛顿引力应用于整个太阳系——通过解决一个特别麻烦的问题:为什么木星的轨道似乎在不断缩小，而土星的轨道却在不断扩大。太阳系内部的相互引力相互作用是如此复杂，以至于数学解决方案似乎是不可能的；事实上，牛顿已经得出结论，为了保持系统的平衡，神的干预是周期性需要的。拉普拉斯宣布了行星平均运动(平均角速度)的不变性。1773年的这一发现是建立太阳系稳定性的第一步，也是最重要的一步，是自牛顿以来物理天文学最重要的进步。同年，他获得了法国科学院的准会员资格。 Applying quantitative methods to a comparison of living and nonliving systems, Laplace and the chemist Antoine-Laurent Lavoisier in 1780, with the aid of an ice calorimeter that they had invented, showed respiration to be a form of combustion. Returning to his astronomical investigations with an examination of the entire subject of planetary perturbations—mutual gravitational effects—Laplace in 1786 proved that the eccentricities and inclinations of planetary orbits to each other will always remain small, constant, and self-correcting. The effects of perturbations were therefore conservative and periodic, not cumulative and disruptive. 1780年，拉普拉斯和化学家安托万·洛朗·拉瓦锡在他们发明的冰量热计的帮助下，将定量方法应用于生物和非生物系统的比较，表明呼吸是燃烧的一种形式。1786年，拉普拉斯回到他的天文学研究中，考察了行星扰动的整个主题——相互引力效应，证明了行星轨道之间的偏心率和倾角将始终保持较小、恒定和自校正。因此，扰动的影响是保守的和周期性的，而不是累积的和破坏性。 During 1784–85 Laplace worked on the subject of attraction between spheroids; in this work the potential function of later physics can be recognized for the first time. Laplace explored the problem of the attraction of any spheroid upon a particle situated outside or upon its surface. Through his discovery that the attractive force of a mass upon a particle, regardless of direction, can be obtained directly by differentiating a single function, Laplace laid the mathematical foundation for the scientific study of heat, magnetism, and electricity. 在1784-1785年间，拉普拉斯致力于研究球体之间的吸引力；在这项工作中，可以第一次认识到后来物理学的潜在功能。拉普拉斯研究了任何球体对位于其表面之外的粒子的吸引力问题。拉普拉斯发现，无论方向如何，质量对粒子的吸引力都可以通过微分单个函数直接获得，从而为热、磁和电的科学研究奠定了数学基础。 Laplace removed the last apparent anomaly from the theoretical deion of the solar system in 1787 with the announcement that lunar acceleration depends on the eccentricity of the Earth’s orbit. Although the mean motion of the Moon around the Earth depends mainly on the gravitational attraction between them, it is slightly diminished by the pull of the Sun on the Moon. This solar action depends, however, on changes in the eccentricity of the Earth’s orbit resulting from perturbations by the other planets. As a result, the Moon’s mean motion is accelerated as long as the Earth’s orbit tends to become more circular; but, when the reverse occurs, this motion is retarded. The inequality is therefore not truly cumulative, Laplace concluded, but is of a period running into millions of years. The last threat of instability thus disappeared from the theoretical deion of the solar system. 拉普拉斯在1787年宣布月球加速度取决于地球轨道的偏心率，从而消除了太阳系理论描述中最后一个明显的异常。虽然月球绕地球的平均运动主要取决于它们之间的引力，但由于太阳对月球的引力，它略有减弱。然而，这种太阳活动取决于其他行星扰动引起的地球轨道偏心率的变化。因此，只要地球的轨道趋向于变得更圆，月球的平均运动就会加速；但是，当相反的情况发生时，这个运动就被延迟了。拉普拉斯总结道，因此这种不平等并不是真正累积的，而是一个持续数百万年的时期。最后一个不稳定的威胁就这样从太阳系的理论描述中消失了。 In 1796 Laplace published Exposition du système du monde (The System of the World), a semipopular treatment of his work in celestial mechanics and a model of French prose. The book included his “nebular hypothesis”—attributing the origin of the solar system to cooling and contracting of a gaseous nebula—which strongly influenced future thought on planetary origin. His Traité de mécanique céleste (Celestial Mechanics), appearing in five volumes between 1798 and 1827, summarized the results obtained by his mathematical development and application of the law of gravitation. He offered a complete mechanical interpretation of the solar system by devising methods for calculating the motions of the planets and their satellites and their perturbations, including the resolution of tidal problems. The book made him a celebrity. 1796年，拉普拉斯发表了《世界体系的阐述》，这是对他在天体力学方面的工作的半大众化处理，也是法国散文的典范。这本书包括他的“星云假说”——将太阳系的起源归因于气体星云的冷却和收缩——这极大地影响了未来对行星起源的思考。他在1798年至1827年间出版的五卷本《天体力学》总结了他的数学发展和万有引力定律应用所取得的成果。他通过设计计算行星及其卫星运动及其扰动的方法，包括潮汐问题的解决，对太阳系进行了完整的机械解释。这本书使他成为名人。 In 1814 Laplace published a popular work for the general reader, Essai philosophique sur les probabilités (A Philosophical Essay on Probability). This work was the introduction to the second edition of his comprehensive and important Théorie analytique des probabilités (Analytic Theory of Probability), first published in 1812, in which he described many of the tools he invented for mathematically predicting the probabilities that particular events will occur in nature. He applied his theory not only to the ordinary problems of chance but also to the inquiry into the causes of phenomena, vital statistics, and future events, while emphasizing its importance for physics and astronomy. The book is notable also for including a special case of what became known as the central limit theorem. Laplace proved that the distribution of errors in large data samples from astronomical observations can be approximated by a Gaussian or normal distribution. 1814年，拉普拉斯出版了一部面向普通读者的通俗作品《概率哲学随笔》。这项工作是对他的全面和重要的概率分析(概率分析理论)第二版的介绍，第一次出版于1812年，其中他描述了他发明的许多工具，用于数学预测特定事件在自然界发生的概率。他不仅将自己的理论应用于普通的偶然性问题，还应用于对现象、生命统计和未来事件的原因的探究，同时强调了其对物理学和天文学的重要性。这本书值得注意的地方还包括一个被称为中心极限定理的特例。拉普拉斯证明了来自天文观测的大数据样本中误差的分布可以用高斯或正态分布来近似。 Probably because he did not hold strong political views and was not a member of the aristocracy, he escaped imprisonment and execution during the French Revolution. Laplace was president of the Board of Longitude, aided in the organization of the metric system, helped found the scientific Society of Arcueil, and was created a marquis. He served for six weeks as minister of the interior under Napoleon, who famously reminisced that Laplace “carried the spirit of the infinitesimal into administration.” 可能是因为他没有强烈的政治观点，也不是贵族成员，所以在法国大革命期间逃脱了监禁和处决。拉普拉斯是经度委员会的主席，协助组织公制，帮助建立了阿尔库伊尔科学协会，并被封为侯爵。他在拿破仑手下担任了六个星期的内政部长，拿破仑有一句著名的回忆:拉普拉斯“将无穷小的精神带入行政管理。”