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第1行： − + − {{简述}法国数学家、物理学家、工程师和科学哲学家}}+ − {{More citations needed|date=April 2017}}+ − {{更多引文{日期=2017年4月}} − {{Use dmy dates|date=November 2020}} − {{使用dmy日期|日期=2020年11月}} − − − {{Infobox scientist − − {{Infobox scientist − − {信息盒科学家 − − |name = Henri Poincaré − − |other_names = Jules Henri Poincaré − − 其他名字 = 儒勒·昂利·庞加莱 − − |image = PSM V82 D416 Henri Poincare.png − − |image = PSM V82 D416 Henri Poincare.png − − 82 D416 Henri Poincare.png − − |caption = Henri Poincaré <br />(photograph published in 1913) − − |caption = Henri Poincaré <br />(photograph published in 1913) − − 摄于1913年 − − |birth_date = {{birth date|df=yes|1854|4|29}} − − |birth_date = − − 出生日期 − − |birth_place = [[Nancy, France|Nancy]], [[Meurthe-et-Moselle]], France − − |birth_place = Nancy, Meurthe-et-Moselle, France − − 出生地: 南希，默尔特-摩泽尔省，法国 − − |death_date = {{death date and age|df=yes|1912|7|17|1854|4|29}} − − |death_date = − − 死亡日期 − − |death_place = [[Paris]], France − − |death_place = Paris, France − − 死亡地点: 法国巴黎 − − − − |residence = France − − 居住地: 法国 − − |nationality = [[French people|French]] − − |nationality = French − − | 国籍: 法国 − − |fields = Mathematics and [[physics]] − − |fields = Mathematics and physics − − | fields = 数学和物理 − − |workplaces = {{plainlist| − − |workplaces = {{plainlist| − − 工作场所 = { plainlist | − − *[[Corps des Mines]] − − *[[Caen University]] − − *[[University of Paris|La Sorbonne]] − − *[[Bureau des Longitudes]]}} − − |education = {{plainlist| − − |education = {{plainlist| − − 2009年10月11日 − − *Lycée Nancy (now {{ill|Lycée Henri-Poincaré|fr}}) − − *[[École Polytechnique]] − − *[[École des Mines]] − − *[[University of Paris]] ([[Doctorat|Dr]], 1879)}} − − |thesis_title = Sur les propriétés des fonctions définies par les équations différences − − |thesis_title = Sur les propriétés des fonctions définies par les équations différences − − |thesis_title = Sur les propriétés des fonctions définies par les équations différences − − |thesis_url = https://web.archive.org/web/20160506152142/https://iris.univ-lille1.fr/handle/1908/458 − − |thesis_url = https://web.archive.org/web/20160506152142/https://iris.univ-lille1.fr/handle/1908/458 − − Https://web.archive.org/web/20160506152142/https://iris.univ-lille1.fr/handle/1908/458 − − |thesis_year = 1879 − − |thesis_year = 1879 − − 论文年份 = 1879 − − |doctoral_advisor = [[Charles Hermite]] − − |doctoral_advisor = Charles Hermite − − 博士生导师查尔斯 · 赫米特 − − |academic_advisors = − − |academic_advisors = − − 学术顾问 − − |doctoral_students = {{plainlist| − − |doctoral_students = {{plainlist| − − 博士生 = { plainlist | − − *[[Louis Bachelier]] − − *[[Jean Bosler]] − − *[[Dimitrie Pompeiu]] − − *[[Mihailo Petrović]]}} − − |notable_students = {{plainlist| − − |notable_students = {{plainlist| − − 2012年10月12日 − − *[[Tobias Dantzig]] − − *[[Théophile de Donder]]}} − − |known_for = {{plainlist| − − |known_for = {{plainlist| − − 2009年10月11日 − − *[[Poincaré conjecture]] − *[[庞加莱猜想]] − *[[Three-body problem]] − *[[三体问题]] − *[[Topology]] − *[[拓扑]] − *[[Special relativity]] − *[[狭义相对论]] − *[[Poincaré–Hopf theorem]] − *庞加莱-霍普夫定理 − − *[庞加莱对偶性]] − − *{{nowrap|[[Poincaré–Birkhoff–Witt theorem]]}} − *{{nowrap |[[庞加莱–伯克霍夫–维特定理]]}} − *[[Poincaré inequality]] − *[[庞加莱不等式]] − *[[Hilbert–Poincaré series]] − *[[希尔伯特-庞加莱系列]] − *[[Poincaré series (modular form)|Poincaré series]] − *[[庞加莱系列（模块形式）|庞加莱系列]] − *[[Poincaré metric]] − *[[Poincarémetric]] − *[[Rotation number]] − *[[旋转数]] − *[[Fundamental group]] − *[[基本群]] − *[[Betti number|Coining the term "Betti number"]] − *[[贝蒂编号|创造术语“贝蒂编号”]] − *[[Bifurcation theory]] − *[[分岔理论]] − *[[Chaos theory]] − *混沌理论 − *[[Brouwer fixed-point theorem]] − *[[Brouwer不动点定理]] − *[[Sphere-world]] − *[[球体世界]] − *[[Poincaré–Bendixson theorem]] − *彭加勒-本迪克森定理 − *[[Poincaré–Lindstedt method]] − *[方法] − *[[Poincaré recurrence theorem]] − *庞加莱递推定理 − *[[Kelvin's circulation theorem#Poincaré–Bjerknes circulation theorem|Poincaré–Bjerknes circulation theorem]] − *[[开尔文循环定理#庞加莱–比约克内斯循环定理|庞加莱–比约克内斯循环定理]] − *[[Poincaré group]] − *[[庞加莱集团]] − *[[Poincaré gauge]] − *[[Poincarégauge]] − *[[French historical epistemology]] − *法国历史认识论 − *[[Preintuitionism]]/[[conventionalism]] − *[[前直觉主义]/[[传统主义]] − *[[Predicativism]] − *[[谓词论]] − − }} − − }} − + + − |influences = {{plainlist|+ − + − |influences = {{plainlist|+ − + − 2009年10月11日+ − + − *[[Lazarus Fuchs]]+ − + − *[[Immanuel Kant]]<ref>[http://www.iep.utm.edu/poi-math/#H3 "Poincaré's Philosophy of Mathematics"], entry in the [[Internet Encyclopedia of Philosophy]].</ref>+ − + − *[[伊曼纽尔·康德]]<ref>[http://www.iep.utm.edu/poi-math/#H3 "Poincaré's Philosophy of Mathematics"], entry in the [[Internet Encyclopedia of Philosophy]].</ref>+ − + − *[[Ernst Mach]]<ref>[https://plato.stanford.edu/entries/poincare/ "Henri Poincaré"], entry in the [[Stanford Encyclopedia of Philosophy]].</ref>}}+ − + − |influenced = {{plainlist|+ − + − |influenced = {{plainlist|+ − − 2009年10月11日 − − *[[Louis Rougier]] − − *[[George David Birkhoff]] − − [[Albert Einstein]]<ref>Einstein's letter to Michele Besso, Princeton, 6 March 1952</ref>}} − − Albert Einstein}} − − 阿尔伯特 · 爱因斯坦 − − |awards = {{plainlist| − − |awards = {{plainlist| − − 2012年10月12日 − − *{{nowrap|[[Gold Medal of the Royal Astronomical Society|RAS Gold Medal]] (1900)}} − − *[[Sylvester Medal]] (1901) − − *[[Matteucci Medal]] (1905) − − *[[Bolyai Prize]] (1905) − − *[[Bruce Medal]] (1911)}} − − |signature = Henri Poincaré Signature.svg − − |signature = Henri Poincaré Signature.svg − − 签名: Henri poincaré Signature.svg − − |footnotes = He was an uncle of [[Pierre Boutroux]]. − − |footnotes = He was an uncle of Pierre Boutroux. − − 他是皮埃尔 · 布特鲁克斯的叔叔。 − − }} − − }} − − }} − − − − '''Jules Henri Poincaré''' ({{IPAc-en|UK|ˈ|p|w|æ̃|k|ɑr|eɪ}}<ref>{{OED|Poincaré}}</ref> [US: stress final syllable], {{IPA-fr|ɑ̃ʁi pwɛ̃kaʁe|lang|Fr-Henri Poincaré.ogg}};<ref name="forvo">{{cite web|url=http://www.forvo.com/word/poincar%C3%A9/ |title=Poincaré pronunciation: How to pronounce Poincaré in French |website=forvo.com|accessdate=}}</ref><ref name="pronouncekiwi">{{cite web|url=http://www.pronouncekiwi.com/Henri%20Poincaré |title=How To Pronounce Henri Poincaré |website=pronouncekiwi.com|accessdate=}}</ref> 29 April 1854 – 17 July 1912) was a French [[mathematician]], [[theoretical physicist]], [[engineer]], and [[philosophy of science|philosopher of science]]. He is often described as a [[polymath]], and in mathematics as "The Last Universalist",<ref>{{cite book | first1=J. M. | last1=Ginoux | first2=C. | last2=Gerini | title=Henri Poincaré: A Biography Through the Daily Papers | publisher=World Scientific | date=2013 | isbn=978-981-4556-61-3 | doi=10.1142/8956 }}</ref> since he excelled in all fields of the discipline as it existed during his lifetime. − − Jules Henri Poincaré ( [US: stress final syllable], ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime. − − <font color="#ff8000"> 儒勒·昂利·庞加莱Jules Henri Poincaré</font> 是法国数学家、理论物理学家、工程师和科学哲学家。他经常被描述为一个博学者，在数学方面被称为“最后的普遍主义者” ，因为他在他有生之年在所有学科领域都表现出色。 − − − − As a mathematician and physicist, he made many original fundamental contributions to [[Pure mathematics|pure]] and [[applied mathematics]], [[mathematical physics]], and [[celestial mechanics]].<ref>{{cite journal|author=Hadamard, Jacques|authorlink=Jacques Hadamard|title=The early scientific work of Henri Poincaré|journal=The Rice Institute Pamphlet|date=July 1922|volume=9|issue=3|pages=111–183|url=http://catalog.hathitrust.org/Record/100592035}}</ref> In his research on the [[three-body problem]], Poincaré became the first person to discover a chaotic [[deterministic system]] which laid the foundations of modern [[chaos theory]]. He is also considered to be one of the founders of the field of [[topology]]. − − As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology. − − 作为一名数学家和物理学家，他对<font color="#ff8000"> 纯粹数学</font>和<font color="#ff8000">应用数学、数学物理学和</font><font color="#ff8000"> 天体力学</font>做出了许多原创性的基础性贡献。在他对<font color="#ff8000"> 三体问题</font>的研究中，庞加莱成为第一个发现<font color="#ff8000"> 混沌确定性模型</font>的人，它奠定了现代<font color="#ff8000"> 混沌理论</font>的基础。他也被认为是<font color="#ff8000"> 拓扑学Topology</font>领域的创始人之一。 − − − − Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the [[Lorentz transformations]] in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to [[Hendrik Lorentz]] in 1905. Thus he obtained perfect invariance of all of [[Maxwell's equations]], an important step in the formulation of the theory of [[special relativity]]. In 1905, Poincaré first proposed [[gravitational wave]]s (''ondes gravifiques'') emanating from a body and propagating at the speed of light as being required by the Lorentz transformations. − − Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations. − − 庞加莱阐明了物理定律在不同变换下的不变性的重要性，并率先提出了<font color="#ff8000"> 洛伦兹变换</font>的现代对称形式。庞加莱发现了剩下的相对论速度变换，并在1905年写给亨德里克 · 洛伦兹的信中记录了它们。因此，他得到了所有<font color="#ff8000">麦克斯韦方程</font>的完美不变性，这是<font color="#ff8000">狭义相对论理论 </font>形成过程中的重要一步。1905年，庞加莱首次提出<font color="#ff8000">引力波(ondes 引力波)</font>，它从物体中发射出来，并按照<font color="#ff8000"> 洛伦兹变换</font>的要求以光速传播。 − − − − The [[Poincaré group]] used in physics and mathematics was named after him. − − The Poincaré group used in physics and mathematics was named after him. − − 用于物理和数学的庞加莱小组就是以他的名字命名的。 − − − − Early in the 20th century he formulated the [[Poincaré conjecture]] that became over time one of the famous [[unsolved problems in mathematics]] until it was solved in 2002–2003 by [[Grigori Perelman]]. − − Early in the 20th century he formulated the Poincaré conjecture that became over time one of the famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman. − − 在20世纪早期，他制定了<font color="#ff8000"> 庞加莱猜想Poincaré conjecture</font>，随着时间的推移，这成为著名的悬而未决的数学问题之一，直到2002年至2003年被<font color="#ff8000">格里戈里·佩雷尔曼Grigori Perelman</font>解决。 − − − − ==Life生平== − − Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, [[Nancy, Meurthe-et-Moselle]], into an influential French family.<ref>Belliver, 1956</ref> His father Léon Poincaré (1828–1892) was a professor of medicine at the [[University of Nancy]].<ref>Sagaret, 1911</ref> His younger sister Aline married the spiritual philosopher [[Émile Boutroux]]. Another notable member of Henri's family was his cousin, [[Raymond Poincaré]], a fellow member of the [[Académie française]], who would serve as President of France from 1913 to 1920.<ref name="IEP">[http://www.utm.edu/research/iep/p/poincare.htm The Internet Encyclopedia of Philosophy] Jules Henri Poincaré article by Mauro Murzi – Retrieved November 2006.</ref> − − Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle, into an influential French family. His father Léon Poincaré (1828–1892) was a professor of medicine at the University of Nancy. His younger sister Aline married the spiritual philosopher Émile Boutroux. Another notable member of Henri's family was his cousin, Raymond Poincaré, a fellow member of the Académie française, who would serve as President of France from 1913 to 1920. − − 1854年4月29日，庞加莱出生在公爵城 Cité Ducale 一个有影响力的法国家庭，家住默尔特-摩泽尔省南希。他的父亲 莱翁·波因加Léon poincaré (1828-1892)是南希大学的医学教授。他的妹妹艾琳嫁给了精神哲学家埃米尔 · 布特鲁克斯。家族中另一个著名的成员是他的表弟，雷蒙·普恩加莱，法兰西学术院的同事，他在1913年到1920年间担任法国总统。 − − − − ===Education教育=== − − [[File:Henri Poincaré maison natale Nancy plaque.jpg|thumb|right|200px| Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy]] − − [[资料图：亨利·彭卡尔娜塔莉·南希斑块.jpg|拇指|右| 200px |南希市格兰德街117号房子亨利·彭加勒出生地的牌匾]] − − Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy − − 位于南希市大街117号的昂利 · 庞加莱出生地的牌匾 − − − − During his childhood he was seriously ill for a time with [[diphtheria]] and received special instruction from his mother, Eugénie Launois (1830–1897). − − During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897). − − 在童年时期，他曾一度患有严重的白喉病，受到他母亲欧热尼 · 劳诺伊斯(Eugénie Launois，1830-1897)的特别照料。 − − − − In 1862, Henri entered the Lycée in [[Nancy, Meurthe-et-Moselle|Nancy]] (now renamed the {{ill|Lycée Henri-Poincaré|fr}} in his honour, along with [[Henri Poincaré University]], also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the [[concours général]], a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best".<ref>O'Connor et al., 2002</ref> However, poor eyesight and a tendency towards absentmindedness may explain these difficulties.<ref>Carl, 1968</ref> He graduated from the Lycée in 1871 with a bachelor's degree in letters and sciences. − − In 1862, Henri entered the Lycée in Nancy (now renamed the in his honour, along with Henri Poincaré University, also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best". However, poor eyesight and a tendency towards absentmindedness may explain these difficulties. He graduated from the Lycée in 1871 with a bachelor's degree in letters and sciences. − − 1862年，亨利进入南希的莱西学院（现与亨利庞加莱大学一起为纪念他而改名，也在南希）。他在莱西大学呆了11年，在这段时间里，他证明了他所学的每一个科目都是尖子生之一。他擅长写作。他的数学老师称他为“数学怪兽”，他在法国所有莱卡顶尖学生的竞赛中获得一等奖。他最差的科目是音乐和体育，被描述为“充其量一般”。然而，视力差和心不在焉的倾向可能解释了这些困难。他于1871年毕业于莱西大学，获得文学和科学学士学位。 − − − − − During the [[Franco-Prussian War]] of 1870, he served alongside his father in the Ambulance Corps. − − During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps. − − 1870年的普法战争，他和父亲一起在救护队服役。 − − − − Poincaré entered the [[École Polytechnique]] as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of [[Charles Hermite]], continuing to excel and publishing his first paper (''Démonstration nouvelle des propriétés de l'indicatrice d'une surface'') in 1874. From November 1875 to June 1878 he studied at the [[École des Mines]], while continuing the study of mathematics in addition to the mining engineering syllabus, and received the degree of ordinary mining engineer in March 1879.<ref>F. Verhulst</ref> − − Poincaré entered the École Polytechnique as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper (Démonstration nouvelle des propriétés de l'indicatrice d'une surface) in 1874. From November 1875 to June 1878 he studied at the École des Mines, while continuing the study of mathematics in addition to the mining engineering syllabus, and received the degree of ordinary mining engineer in March 1879. − − 庞加莱于1873年以第一名的预选资格进入<font color="#32CD32">埃科尔综合理工学院École Polytechnique</font>，并于1875年毕业。在那里，他作为查尔斯赫米特的学生学习数学，继续取得优异成绩，并于1874年发表了他的第一篇论文（“表面指示器性能的新示范”）。从1875年11月到1878年6月，他在埃科尔矿山学院学习，同时在采矿工程课程之外继续学习数学，并于1879年3月获得普通采矿工程师学位。 − − − − − − As a graduate of the École des Mines, he joined the [[Corps des Mines]] as an inspector for the [[Vesoul]] region in northeast France. He was on the scene of a mining disaster at [[Magny-lès-Jussey|Magny]] in August 1879 in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way. − − As a graduate of the École des Mines, he joined the Corps des Mines as an inspector for the Vesoul region in northeast France. He was on the scene of a mining disaster at Magny in August 1879 in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way. − − 毕业于埃科尔矿业学院后，他加入了矿业兵团，担任法国东北部维苏尔地区的检查员。1879年8月，他在马格尼矿难现场，18名矿工遇难。他以典型的彻底和人道的方式对事故进行了正式调查。 − − − − At the same time, Poincaré was preparing for his [[Doctorate in Science]] in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of [[differential equations]]. It was named ''Sur les propriétés des fonctions définies par les équations aux différences partielles''. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the [[solar system]]. Poincaré graduated from the [[University of Paris]] in 1879. − − At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les propriétés des fonctions définies par les équations aux différences partielles. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the solar system. Poincaré graduated from the University of Paris in 1879. − − 与此同时，庞加莱在查尔斯·赫米特的指导下，正在准备攻读数学科学博士学位。他的博士论文是关于微分方程的。它被命名为“关于部分差公式定义的函数属性”。庞加莱发明了一种研究这些方程性质的新方法。他不仅面临确定这类方程积分的问题，而且是第一个研究这些方程一般几何性质的人。他意识到，它们可以用来模拟太阳系内多个自由运动物体的行为。庞加莱于1879年毕业于巴黎大学。 − − − − [[Image:Young Poincare.jpg|left|upright|thumb|The young Henri Poincaré]] − [[图片：Young Poincare.jpg|左|直立|拇指|年轻的亨利·庞加莱]] − The young Henri Poincaré − − 年轻的亨利 · 庞加莱 − − − − ===First scientific achievements最初科学成就=== − − After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the [[Caen University|University of Caen]] in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of [[automorphic function]]s. − − After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of automorphic functions. − − 获得学位后，庞加莱开始在诺曼底的卡昂大学（1879年12月）担任数学初级讲师。同时，他发表了第一篇关于一类自守函数处理的重要文章。 − − − There, in [[Caen]], he met his future wife, Louise Poulain d'Andecy and on 20 April 1881, they married. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893). − − There, in Caen, he met his future wife, Louise Poulain d'Andecy and on 20 April 1881, they married. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893). − − 在卡昂，他遇到了他未来的妻子路易丝 · 普兰 · 德安德西，并于1881年4月20日结婚。他们共有四个孩子: 珍妮(生于1887年)、伊冯娜(生于1889年)、亨利埃特(生于1891年)和莱昂(生于1893年)。 − − − − Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the [[University of Paris]]; he accepted the invitation. During the years of 1883 to 1897, he taught mathematical analysis in [[École Polytechnique]]. − − Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris; he accepted the invitation. During the years of 1883 to 1897, he taught mathematical analysis in École Polytechnique. − − 庞加莱立即跻身欧洲最伟大的数学家之列，吸引了许多著名数学家的注意。1881年，庞加莱被邀请到巴黎大学理学院担任教学职务；他接受了邀请。1883年至1897年间，他在<font color="#32CD32">埃科尔综合理工学院École Polytechnique</font>教授<font color="#ff8000"> 数学分析Mathematical analysis</font>。 − − − − In 1881–1882, Poincaré created a new branch of mathematics: [[qualitative theory of differential equations]]. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in [[celestial mechanics]] and [[mathematical physics]]. − − In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics. − − 1881-1882年，庞加莱创立了一个新的数学分支: 微分方程定性理论。他展示了如何不用解方程就可以得到关于一组解的行为的最重要的信息(因为这可能并不总是可能的)。他成功地用这种方法解决了天体力学和数学物理的问题。 − − − − ===Career职业生涯=== − − He never fully abandoned his mining career to mathematics. He worked at the [[Ministry of Public Services]] as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910. − − He never fully abandoned his mining career to mathematics. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910. − − 他从未完全放弃采矿业而投身于数学。1881年至1885年，他在公共服务部担任工程师，负责北方铁路的发展。他最终在1893年成为矿业公司的总工程师，1910年成为监察长。 − − − − Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the [[University of Paris|Sorbonne]]). He was initially appointed as the ''maître de conférences d'analyse'' (associate professor of analysis).<ref>Sageret, 1911</ref> Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability,<ref>{{cite book|first =Laurent|last= Mazliak|chapter= Poincaré’s Odds |title = Poincaré 1912-2012 : Poincaré Seminar 2012|editor1-first= B.|editor1-last= Duplantier |editor2-first= V.|editor2-last= Rivasseau|volume = 67 |series = Progress in Mathematical Physics|publisher = Springer|isbn = 9783034808347|location = Basel|page = 150|url = https://books.google.com/books?id=njNpBQAAQBAJ|date= 14 November 2014}}</ref> and Celestial Mechanics and Astronomy. − − Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the Sorbonne). He was initially appointed as the maître de conférences d'analyse (associate professor of analysis). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy. − − 从1881年开始，他在巴黎大学(索邦大学)教书，直到他的职业生涯结束。他最初被任命为分析师(分析学副教授)。最终，他获得了物理力学和实验力学、数学物理学和概率论、天体力学和天文学的学位。 − − − − In 1887, at the young age of 32, Poincaré was elected to the [[French Academy of Sciences]]. He became its president in 1906, and was elected to the [[Académie française]] on 5 March 1908. − − In 1887, at the young age of 32, Poincaré was elected to the French Academy of Sciences. He became its president in 1906, and was elected to the Académie française on 5 March 1908. − − 1887年，32岁的庞加莱当选为法国科学院院士。他于1906年成为法兰西学术院主席，并于1908年3月5日当选为议员。 − − − − In 1887, he won [[Oscar II of Sweden|Oscar II, King of Sweden]]'s mathematical competition for a resolution of the [[three-body problem]] concerning the free motion of multiple orbiting bodies. (See [[#Three-body problem|three-body problem]] section below.) − − In 1887, he won Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. (See three-body problem section below.) − − 1887年，他以解决有关多个轨道物体自由运动的三体问题，赢得了瑞典国王奥斯卡二世的数学竞赛。（参见下面的<font color="#ff8000"> 三体问题Three-body problem</font>部分。） − − − − [[File:Poincaré gravestone.jpg|upright|thumb|The Poincaré family grave at the [[Cimetière du Montparnasse]]]] − − The Poincaré family grave at the [[Cimetière du Montparnasse]] − − 庞加莱家族在[蒙帕纳斯公墓]]的坟墓 − − In 1893, Poincaré joined the French [[Bureau des Longitudes]], which engaged him in the [[Clock synchronization|synchronisation of time]] around the world. In 1897 Poincaré backed an unsuccessful proposal for the [[Decimal degrees|decimalisation of circular measure]], and hence time and [[longitude]].<ref>see Galison 2003</ref> It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See [[#Work on relativity|work on relativity]] section below.) − − In 1893, Poincaré joined the French Bureau des Longitudes, which engaged him in the synchronisation of time around the world. In 1897 Poincaré backed an unsuccessful proposal for the decimalisation of circular measure, and hence time and longitude. It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See work on relativity section below.) − − 1893年，他加入了<font color="#ff8000">法国经度局French Bureau des Longitudes </font>,使他参与了世界各地时间的同步工作。1897年，庞加莱支持了一个不成功的建议，即循环尺度的十进制化，从而得到时间和经度。正是这篇文章促使他考虑建立国际时区的问题，以及相对运动的物体之间的时间同步问题。（参见下面相对论部分的工作。） − − − − In 1899, and again more successfully in 1904, he intervened in the trials of [[Alfred Dreyfus]]. He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by colleagues. − − In 1899, and again more successfully in 1904, he intervened in the trials of Alfred Dreyfus. He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by colleagues. − − 1899年，更成功的是1904年，他介入了对阿尔弗雷德 · 德雷福斯的审判。他抨击了一些针对德雷福斯的虚假科学证据，德雷福斯是法国军队中一名被同事指控犯有叛国罪的犹太军官。 − − − − Poincaré was the President of the [[Société astronomique de France|Société Astronomique de France (SAF)]], the French astronomical society, from 1901 to 1903.<ref name=BSAF1911>[http://gallica.bnf.fr/ark:/12148/bpt6k9626551q/f616.item ''Bulletin de la Société astronomique de France'', 1911, vol. 25, pp. 581–586]</ref> − − Poincaré was the President of the Société Astronomique de France (SAF), the French astronomical society, from 1901 to 1903. − − 从1901年到1903年，庞加莱是法国天文学会（SAF）的主席。 − − − ====Students学生==== − − Poincaré had two notable doctoral students at the University of Paris, [[Louis Bachelier]] (1900) and [[Dimitrie Pompeiu]] (1905).<ref>[http://www.genealogy.ams.org/id.php?id=34227 Mathematics Genealogy Project] {{Webarchive|url=https://web.archive.org/web/20071005011853/http://www.genealogy.ams.org/id.php?id=34227 |date=5 October 2007 }} North Dakota State University. Retrieved April 2008.</ref> − − Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905). − − 庞加莱在巴黎大学有两个著名的博士生，路易斯 · 巴切利耶(1900年)和迪米特里 · 庞佩尤(1905年)。 − − − − === Death 死亡=== − − − − In 1912, Poincaré underwent surgery for a [[prostate]] problem and subsequently died from an [[embolism]] on 17 July 1912, in Paris. He was 58 years of age. He is buried in the Poincaré family vault in the [[Cimetière du Montparnasse|Cemetery of Montparnasse]], Paris. − − In 1912, Poincaré underwent surgery for a prostate problem and subsequently died from an embolism on 17 July 1912, in Paris. He was 58 years of age. He is buried in the Poincaré family vault in the Cemetery of Montparnasse, Paris. − − 1912年，庞加莱因前列腺问题接受手术，随后于1912年7月17日在巴黎死于栓塞。时年58岁。他被安葬在巴黎蒙帕纳斯公墓的庞加莱家族墓穴中。 − − − − A former French Minister of Education, [[Claude Allègre]], proposed in 2004 that Poincaré be reburied in the [[Panthéon, Paris|Panthéon]] in Paris, which is reserved for French citizens only of the highest honour.<ref>[https://web.archive.org/web/20041127160356/http://www.lexpress.fr/idees/tribunes/dossier/allegre/dossier.asp?ida=430274 Lorentz, Poincaré et Einstein]</ref> − − A former French Minister of Education, Claude Allègre, proposed in 2004 that Poincaré be reburied in the Panthéon in Paris, which is reserved for French citizens only of the highest honour. − − 法国前教育部长克劳德·阿雷格里（Claude Allègre）在2004年提议将庞加莱重新安葬在巴黎的潘太翁教堂（Panthéon），那里只为最高荣誉的法国公民保留。 − − − − ==Work工作== − − − − ===Summary综述=== − − Poincaré made many contributions to different fields of pure and applied mathematics such as: [[celestial mechanics]], [[fluid mechanics]], [[optics]], electricity, [[telegraphy]], [[capillarity]], [[Elasticity (physics)|elasticity]], [[thermodynamics]], [[potential theory]], [[Quantum mechanics|quantum theory]], [[theory of relativity]] and [[physical cosmology]]. − − Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology. − − 庞加莱在纯数学和应用数学的不同领域做出了很多贡献，例如: 天体力学、流体力学、光学、电学、电报学、毛细现象、弹性力学、热力学、势论、量子理论、相对论和物理宇宙学。 − − − − He was also a populariser of mathematics and physics and wrote several books for the lay public. − − He was also a populariser of mathematics and physics and wrote several books for the lay public. − − 他还是数学和物理的普及者，并为普通大众写了几本书。 − − − − Among the specific topics he contributed to are the following: − − Among the specific topics he contributed to are the following: − − 他提出的具体主题包括: − − *[[algebraic topology]] − *[[代数拓扑]] − *[[several complex variables|the theory of analytic functions of several complex variables]] − *多复变量|多复变量解析函数理论 − *[[abelian variety|the theory of abelian functions]] − *[abelian变体|交换函数理论]] − *[[algebraic geometry]] − *[[代数几何]] − *the [[Poincaré conjecture]], proven in 2003 by [[Grigori Perelman]]. − *[[庞加莱猜想]]，2003年由[[格里高里佩雷尔曼]]证明。 − *[[Poincaré recurrence theorem]] − *[[庞加莱递推定理]] − *[[hyperbolic geometry]] − *[[双曲几何]] − *[[number theory]] − *[[数论]] − *the [[three-body problem]] − *[[三体问题]] − *[[diophantine equation|the theory of diophantine equations]] − *丢番图方程|丢番图方程理论 − *[[electromagnetism]] − *[[电磁学]] − *[[Special relativity|the special theory of relativity]] − *狭义相对论 − *the [[fundamental group]] − *[[基本群]] − *In the field of [[differential equations]] Poincaré has given many results that are critical for the qualitative theory of differential equations, for example the [[Poincaré homology sphere|Poincaré sphere]] and the [[Poincaré map]]. − *在[[微分方程]]领域，庞加莱给出了许多对微分方程定性理论至关重要的结果，例如[[庞加莱同调球|庞加莱球]]和[[庞加莱映射]]。 − *Poincaré on "everybody's belief" in the [[q:Henri Poincaré|''Normal Law of Errors'']] (see [[normal distribution]] for an account of that "law") − *庞加莱关于“每个人的信仰”的[[q:Henri Poincaré‘正态误差定律’]]（参见[[正态分布]]中关于“法则”的解释） − *Published an influential paper providing a novel mathematical argument in support of [[quantum mechanics]].<ref name=McCormmach>{{Citation | last = McCormmach | first = Russell | title = Henri Poincaré and the Quantum Theory | journal = Isis | volume = 58 | issue = 1 | pages = 37–55 | date =Spring 1967 | doi =10.1086/350182| s2cid = 120934561 }}</ref><ref name=Irons>{{Citation | last = Irons | first = F. E. | title = Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms | journal = American Journal of Physics | volume = 69 | issue = 8 | pages = 879–884 | date = August 2001 | doi =10.1119/1.1356056 |bibcode = 2001AmJPh..69..879I }}</ref> − *发表了一篇有影响力的论文，提供了一个新的数学论证来支持[[量子力学]]。<ref name=McCormmach>{{Citation | last = McCormmach | first = Russell | title = Henri Poincaré and the Quantum Theory | journal = Isis | volume = 58 | issue = 1 | pages = 37–55 | date =Spring 1967 | doi =10.1086/350182| s2cid = 120934561 }}</ref><ref name=Irons>{{Citation | last = Irons | first = F. E. | title = Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms | journal = American Journal of Physics | volume = 69 | issue = 8 | pages = 879–884 | date = August 2001 | doi =10.1119/1.1356056 |bibcode = 2001AmJPh..69..879I }}</ref> − − − ===Three-body problem三体问题=== − − The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since [[Isaac Newton|Newton's]] time. This was known originally as the three-body problem and later the [[n-body problem|''n''-body problem]], where ''n'' is any number of more than two orbiting bodies. The ''n''-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, [[Oscar II of Sweden|Oscar II, King of Sweden]], advised by [[Gösta Mittag-Leffler]], established a prize for anyone who could find the solution to the problem. The announcement was quite specific: − − The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since Newton's time. This was known originally as the three-body problem and later the n-body problem, where n is any number of more than two orbiting bodies. The n-body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, Oscar II, King of Sweden, advised by Gösta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific: − − 自从牛顿时代以来，数学家们就一直没有解决太阳系中两个以上轨道天体运动的一般解的问题。这个问题最初被称为<font color="#ff8000"> 三体问题</font>，后来又被称为 <font color="#ff8000"> n 体问题</font>，其中 n 是任意数量的两个以上的轨道天体。在19世纪末，n 体解被认为是非常重要和具有挑战性的。事实上，在1887年，为了庆祝他的60岁生日，瑞典国王奥斯卡二世在哥斯塔·米塔-列夫勒的建议下，设立了一个奖项，奖励任何能够找到解决此问题的方法的人。声明非常具体: − − − − <blockquote>Given a system of arbitrarily many mass points that attract each according to [[Newton's law of universal gravitation|Newton's law]], under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series [[uniform convergence|converges uniformly]].</blockquote> − − <blockquote>Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.</blockquote> − − <blockquote>给定一个由任意多个质点组成的系统，这些质点根据牛顿定律相互吸引，在假设没有两个质点相撞的情况下，找出每个质点的坐标在一个已知的时间函数的变量中的一个级数的表示，对该变量的所有值都是一致收敛的。</blockquote > − − − − In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished [[Karl Weierstrass]], said, ''"This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics."'' (The first version of his contribution even contained a serious error; for details see the article by Diacu<ref name=diacu>{{Citation − − In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics." (The first version of his contribution even contained a serious error; for details see the article by Diacu and the book by Barrow-Green). The version finally printed contained many important ideas which led to the theory of chaos. The problem as stated originally was finally solved by Karl F. Sundman for n = 3 in 1912 and was generalised to the case of n > 3 bodies by Qiudong Wang in the 1990s. − − 如果这个问题无法解决，那么对经典力学的任何其他重要贡献都将被认为能够获奖。虽然庞加莱没有解决最初的问题，但最终还是把奖颁给了他。其中一位评委，著名的卡尔·魏尔斯特拉斯说：“这项工作确实不能被视为提供了所提出问题的完整解决方案，但它的出版将开创天体力学史上的一个新纪元。”详细内容见格林的一篇文章。最终印刷的版本包含了许多导致混沌理论的重要思想。最初所述的问题最终由Karl F.Sundman在1912年解决了n = 3的情况，并在1990年代将其推广到王秋东的n > 3体的案例中。 − − − − − | issue=3|s2cid= 119728316 }}</ref> and the book by [[June Barrow-Green|Barrow-Green]]<ref>{{Cite book|title=Poincaré and the three body problem|title-link= Poincaré and the Three-Body Problem |last=Barrow-Green|first=June|publisher=[[American Mathematical Society]]|year=1997|isbn=978-0821803677|location=Providence, RI|series=History of Mathematics|volume=11|pages=|oclc=34357985}}</ref>). The version finally printed<ref>{{Cite book|title=The three-body problem and the equations of dynamics: Poincaré's foundational work on dynamical systems theory|last=Poincaré|first=J. Henri|publisher=Springer International Publishing|others=Popp, Bruce D. (Translator)|year=2017|isbn=9783319528984|location=Cham, Switzerland|pages=|oclc=987302273}}</ref> contained many important ideas which led to the [[chaos theory|theory of chaos]]. The problem as stated originally was finally solved by [[Karl F. Sundman]] for ''n'' = 3 in 1912 and was generalised to the case of ''n'' > 3 bodies by [[Qiudong Wang]] in the 1990s. − − − − [[Marie Curie and Poincaré talk at the 1911 Solvay Conference]] − − [[玛丽 · 居里和庞加莱在1911年索尔维会议大会上的演讲]] − − ===Work on relativity相对论部分的工作=== − − [[Image:Curie and Poincare 1911 Solvay.jpg|thumb|right|[[Marie Curie]] and Poincaré talk at the 1911 [[Solvay Conference]]]] − [[图片：居里和庞加莱1911苏威.jpg|拇指|右|[[玛丽居里]]和1911年的庞加莱谈话[[索尔维会议]]] − {{main|Lorentz ether theory|History of special relativity}} − − {{main{洛伦兹以太理论{狭义相对论史}} − − Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math> − − 在经度局建立国际时区的工作使庞加莱考虑如何使地球上静止的时钟（相对于绝对空间（或“<font color="#ff8000">以太Luminiferous aether</font>”）以不同的速度移动）进行同步。与此同时，荷兰理论家亨德里克·洛伦兹正在将麦克斯韦理论发展成带电粒子（“电子”或“离子”）运动及其与辐射相互作用的理论。1895年，洛伦兹引入了一个辅助量（没有物理解释），叫做“本地时间”<math>t^\prime = t-v x/c^2 \,</math> − − − ==== Local time本地时间==== − − and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment). − 并且引入了长度收缩假说来解释光学和电学实验相对于<font color="#ff8000"> 以太</font>探测运动的失败(见 迈克尔逊·莫利Michelson-Morley 实验)。 − − Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "[[luminiferous aether]]"), could be synchronised. At the same time Dutch theorist [[Hendrik Lorentz]] was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math><ref>{{Citation|title=A broader view of relativity: general implications of Lorentz and Poincaré invariance|volume=10|first1=Jong-Ping|last1=Hsu|first2=Leonardo|last2=Hsu|publisher=World Scientific|year=2006|isbn=978-981-256-651-5|page=37 − − Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, " − − 庞加莱一直是洛伦兹理论的解释者（有时是友好的批评家）。作为一个哲学家，庞加莱对“更深层的意义”很感兴趣。因此，他解释了洛伦兹的理论，并由此提出了许多与<font color="#ff8000"> 狭义相对论</font>相关的见解。在《时间的度量》(1898)中，庞加莱说 − − |url=https://books.google.com/books?id=amLqckyrvUwC}}, [https://books.google.com/books?id=amLqckyrvUwC&pg=PA37 Section A5a, p 37]</ref> − − A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form. − − “稍加反思就足以理解，所有这些肯定本身都没有意义。只有在约定成立的情况下，才能成立。”他还认为，科学家必须将光速的恒定性作为一个假设，以使物理理论具有最简单的形式。 − − Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame. − − 基于这些假设，他在1900年对洛伦兹关于本地时间的“奇妙发明”进行了讨论，并指出，当移动的时钟通过交换假定在移动帧中以相同速度在两个方向上传播的光信号来同步时，就出现了这种情况。 − − and introduced the hypothesis of [[length contraction]] to explain the failure of optical and electrical experiments to detect motion relative to the aether (see [[Michelson–Morley experiment]]).<ref>{{Citation − − | last=Lorentz|first= Hendrik A. | authorlink=Hendrik Lorentz| year=1895 | title=Versuch einer theorie der electrischen und optischen erscheinungen in bewegten Kõrpern | place =Leiden| publisher=E.J. Brill| title-link=s:de:Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern }}</ref> − − Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In [[s:The Measure of Time|The Measure of Time]] (1898), Poincaré said, " − − 庞加莱一直是洛伦兹理论的解释者（有时是友好的批评家）。作为一个哲学家，庞加莱对“更深层的意义”很感兴趣。因此，他解释了洛伦兹的理论，并由此提出了许多与<font color="#ff8000"> 狭义相对论</font>相关的见解。在《时间的度量》(1898)中，庞加莱说 − − A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a [[postulate]] to give physical theories the simplest form.<ref>{{Citation − − “稍加反思就足以理解，所有这些肯定本身都没有意义。只有在约定成立的情况下，才能成立。”他还认为，科学家必须将光速的恒定性作为一个假设，以使物理理论具有最简单的形式。 − − | last=Poincaré|first= Henri | year=1898 | title=The Measure of Time | journal=Revue de Métaphysique et de Morale | volume =6 | pages =1–13| title-link=s:The Measure of Time }}</ref> − − Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.<ref name=action>{{Citation − − 基于这些假设，他在1900年对洛伦兹关于本地时间的“奇妙发明”进行了讨论，并指出，当移动的时钟通过交换假定在移动帧中以相同速度在两个方向上传播的光信号来同步时，就出现了这种情况。 − − In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval <math>x^2+y^2-z^2=-1</math>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions. In addition, Poincaré's other models of hyperbolic geometry (Poincaré disk model, Poincaré half-plane model) as well as the Beltrami–Klein model can be related to the relativistic velocity space (see Gyrovector space). − 1881年，庞加莱用<font color="#ff8000"> 双曲面模型Hyperboloid model</font>描述了<font color="#ff8000"> 双曲几何学Hyperbolic geometry</font>，提出了洛伦兹区间<math>x^2+y^2-z^2=-1</math>上不变的变换，使其在数学上等价于2+1维的<font color="#ff8000"> 洛伦兹变换</font>。此外，庞加莱的其他双曲几何模型(<font color="#ff8000"> 庞加莱圆盘模型，庞加莱半平面模型</font>)以及<font color="#ff8000"> 贝尔特拉米-克莱因Beltrami–Klein模型</font>都可以与相对论速度空间（见<font color="#ff8000"> 陀螺矢量空间</font>）相关。+ − caré|first= Henri | year=1900 | title=La théorie de Lorentz et le principe de réaction | journal=Archives Néerlandaises des Sciences Exactes et Naturelles | volume =5 | pages =252–278| title-link=s:fr:La théorie de Lorentz et le principe de réaction }}. See also the [http://www.physicsinsights.org/poincare-1900.pdf English translation]</ref> + − In 1892 Poincaré developed a mathematical theory of light including polarization. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the Poincaré sphere. It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions.+ + + − 1892年庞加莱发展了包括偏振在内的光的数学理论。他关于偏振器和延迟器作用于代表极化状态的球体的观点称为<font color="#ff8000"> 庞加莱球</font>。证明了<font color="#ff8000"> 庞加莱球</font>具有一个基本的洛伦兹对称性，可以作为<font color="#ff8000"> 洛伦兹变换</font>和速度加法的几何表示。+ + + + + + − + + + + + + + − {{Further|History of Lorentz transformations#Poincare|History of Lorentz transformations#Poincare3|label1=History of Lorentz transformations - Poincaré (1881)|label2=History of Lorentz transformations - Poincaré (1905)}}+ − {{更进一步|洛伦兹变换的历史#庞加莱|洛伦兹变换的历史#庞加莱3 | label1=洛伦兹变换的历史-庞加莱（1881）| label2=洛伦兹变换的历史-庞加莱（1905）}}+ + − He discussed the "principle of relative motion" in two papers in 1900+ − 他在1900年的两篇论文中讨论了“相对运动原理”+ + + + + + − + + + + + + + + + + + + + − 并在1904年将其命名为<font color="#ff8000"> 相对性原理Principle of relativity</font>，根据这一理论，没有任何物理实验能够区分匀速运动状态和静止状态。+ + + + + + − In 1881 Poincaré described [[hyperbolic geometry]] in terms of the [[hyperboloid model]], formulating transformations leaving invariant the [[Lorentz interval]] <math>x^2+y^2-z^2=-1</math>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions.<ref>{{Cite journal|author=Poincaré, H.|year=1881|title=Sur les applications de la géométrie non-euclidienne à la théorie des formes quadratiques|journal=Association Française Pour l'Avancement des Sciences|volume=10|pages=132–138|url=http://henripoincarepapers.univ-nantes.fr/chp/hp-pdf/hp1881af.pdf}}{{Dead link|date=June 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{Cite journal|author=Reynolds, W. F.|year=1993|title=Hyperbolic geometry on a hyperboloid|journal=The American Mathematical Monthly|volume=100|issue=5|pages=442–455|jstor=2324297|doi=10.1080/00029890.1993.11990430}}</ref> In addition, Poincaré's other models of hyperbolic geometry ([[Poincaré disk model]], [[Poincaré half-plane model]]) as well as the [[Beltrami–Klein model]] can be related to the relativistic velocity space (see [[Gyrovector space]]).+ + + + − In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.+ + + + − 1905年庞加莱写信给洛伦兹，谈到他1904年的论文，庞加莱称之为“极其重要的论文”在这封信中，他指出了洛伦兹在对麦克斯韦方程组中的一个电荷占据空间进行变换时所犯的一个错误，并对洛伦兹给出的<font color="#ff8000"> 时间膨胀因子Time dilation factor</font>提出了质疑。+ + + + + + + + − + − 在写给洛伦兹的第二封信中，庞加莱给出了他自己的理由，为什么洛伦兹的<font color="#ff8000"> 时间膨胀因子</font>终究是正确的ーー把洛伦兹变换变成一个群是必要的ーー他还给出了现在所知的<font color="#ff8000">相对论速度加法定律Relativistic velocity-addition law</font>。+ + + + − In 1892 Poincaré developed a mathematical theory of light including [[polarization (waves)|polarization]]. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the [[Poincaré sphere (optics)|Poincaré sphere]].<ref>{{Cite book|author=Poincaré, H. |year=1892|title=Théorie mathématique de la lumière II|location=Paris|publisher=Georges Carré|chapter-url=https://archive.org/details/thoriemathma00poin|chapter=Chapitre XII: Polarisation rotatoire}}</ref> It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions.<ref>{{Cite journal|author=Tudor, T.|year=2018|title=Lorentz Transformation, Poincaré Vectors and Poincaré Sphere in Various Branches of Physics|journal=Symmetry|volume=10|issue=3|pages=52|doi=10.3390/sym10030052|doi-access=free}}</ref>+ + + − Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that he wrote:+ + − 后来，庞加莱在1905年6月5日于巴黎举行的科学院会议上发表了一篇论文，论述了这些问题。在出版的版本中，他写道:+ + + − He discussed the "principle of relative motion" in two papers in 1900<ref name=action /><ref>{{Citation − <blockquote>The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:+ + − 洛伦兹建立的基本观点是，电磁场的方程不会因某种形式的变换（我称之为洛伦兹）而改变：+ − | author=Poincaré, H. | year=1900 | title= Les relations entre la physique expérimentale et la physique mathématique | journal=Revue Générale des Sciences Pures et Appliquées | volume =11 | pages =1163–1175 | url=http://gallica.bnf.fr/ark:/12148/bpt6k17075r/f1167.table}}. Reprinted in "Science and Hypothesis", Ch. 9–10.</ref>+ − <math>x^\prime = k\ell\left(x + \varepsilon t\right)\!,\;t^\prime = k\ell\left(t + \varepsilon x\right)\!,\;y^\prime = \ell y,\;z^\prime = \ell z,\;k = 1/\sqrt{1-\varepsilon^2}.</math></blockquote>+ − X ^ prime = k ell left (x + varepsilon t right) ! ; t ^ prime = k ell left (t + varepsilon x right) ! ; y ^ prime = ell y; z ^ prime = ell z; k = 1/sqrt {1-varepsilon ^ 2} </math > </blockquote > + − and named it the [[principle of relativity]] in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest.<ref name=louis>{{Citation|author=Poincaré, Henri|year=1913|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=The Foundations of Science (The Value of Science)|pages=297–320|publisher=Science Press|place=New York|postscript=; article translated from 1904 original}} available in [https://books.google.com/books/about/The_Foundations_of_Science.html?id=mBvNabP35zoC&pg=PA297 online chapter from 1913 book]</ref> − 并于1904年将其命名为[[相对论]]，根据这一原理，任何物理实验都无法区分均匀运动状态和静止状态。<ref name=louis>{{Citation|author=Poincaré, Henri|year=1913|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=The Foundations of Science (The Value of Science)|pages=297–320|publisher=Science Press|place=New York|postscript=; article translated from 1904 original}} available in [https://books.google.com/books/about/The_Foundations_of_Science.html?id=mBvNabP35zoC&pg=PA297 online chapter from 1913 book]</ref> − In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.<ref name="univ-nantes">+ + − 1905年，庞加莱写信给洛伦兹，谈到洛伦兹1904年的论文，这篇论文被庞加莱称为“最重要的论文”。在这封信中，他指出了洛伦兹在将其变换应用于麦克斯韦方程组（电荷占据空间）时犯下的一个错误，并对洛伦兹给出的时间膨胀因子提出了质疑。<ref name="univ-nantes">+ − and showed that the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is invariant. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <math>ct\sqrt{-1}</math> as a fourth imaginary coordinate, and he used an early form of four-vectors. Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit. So it was Hermann Minkowski who worked out the consequences of this notion in 1907. − 并证明了任意函数<math>\ell\left(\varepsilon\right)</math>对于所有<math>\varepsilon</math>必须是统一的（Lorentz通过一个不同的参数设置<math>\ell = 1</math>），以使变换形成一个组。在1906年发表的论文的放大版中，庞加莱指出组合<math>x^2+ y^2+ z^2- c^2t^2</math>是不变的。他通过引入<math>ct\sqrt{-1}</math>作为第四个虚坐标，指出Lorentz变换仅仅是四维空间中绕原点的旋转，他使用了四个向量的早期形式。庞加莱在1907年表示对他的新力学的四维重新表述不感兴趣，因为在他看来，将物理学翻译成四维几何的语言需要付出太多的努力才能获得有限的益处。1907年，由赫尔曼·明科夫斯基（Hermann Minkowski）得出了这个概念的后果。+ + + + + + + + + + − {{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.3, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=255–257 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz3.html}}</ref>+ + + − In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.<ref name="univ-nantes2">{{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.4, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=257–258 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz4.html}}</ref> − 在给洛伦兹的第二封信中，庞加莱给出了他自己的理由，为什么洛伦兹的时间膨胀因子确实是正确的，毕竟要使洛伦兹变换形成一个群，他还给出了现在所知的<font color="#ff8000">相对论速度加法定律</font>。<ref name="univ-nantes2">{{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.4, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=257–258 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz4.html}}</ref>+ + − Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that he wrote:<ref name="1905 paper">[http://www.academie-sciences.fr/pdf/dossiers/Poincare/Poincare_pdf/Poincare_CR1905.pdf] (PDF) Membres de l'Académie des sciences depuis sa création : Henri Poincare. Sur la dynamique de l' electron. Note de H. Poincaré. C.R. T.140 (1905) 1504–1508.</ref> − 庞加莱后来在1905年6月5日巴黎科学院会议上发表了一篇论文，其中讨论了这些问题。在出版的版本中，他这样写道：<ref name="1905 paper">[http://www.academie-sciences.fr/pdf/dossiers/Poincare/Poincare_pdf/Poincare_CR1905.pdf] (PDF) Membres de l'Académie des sciences depuis sa création : Henri Poincare. Sur la dynamique de l' electron. Note de H. Poincaré. C.R. T.140 (1905) 1504–1508.</ref>+ − Like others before, Poincaré (1900) discovered a relation between mass and electromagnetic energy. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems:+ + +
无编辑摘要
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{{short description|French mathematician, physicist, engineer, and philosopher of science}}
{{#seo:
|keywords=亨利·庞加莱 Henri Poincaré，复杂性理论，复杂性经济学，自主经济学
|description=庞加莱猜想，三体问题，拓扑学，狭义相对论
|residence = France
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}}
== 基本信息 ==
[[File:亨利·庞加莱 Henri Poincaré.jpg|230px|left]]
{| class="wikitable" width="50%"
|-
! 类别 !! 信息
|-
| 姓名 || 布莱恩·阿瑟 W. Brian Arthur
|-
| 出生日期 || 1945年7月31日
|-
| 出生地 || Belfast, Northern Ireland 北爱尔兰贝尔法斯特
|-
|居住地 || Northern California 北加利福尼亚
|-
| 所在机构 || 斯坦福大学、圣达菲研究所、帕罗奥多研究中心系统科学实验室
|-
| 主要研究方向 || 复杂性理论、[[复杂经济学]]和[[自主经济学]]等领域
|-
| 主要贡献 || 埃尔法罗尔酒吧问题 [[El Farol Bar problem]]、收益递增理论 [[Increasing returns]]等
| last=Diacu|first= Florin | year=1996 | title=The solution of the ''n''-body Problem | journal=The Mathematical Intelligencer | volume =18 | pages =66–70 | doi=10.1007/BF03024313
|}
<br>
== 个人介绍 ==
布莱恩·阿瑟 W. Brian Arthur是著名经济学家，圣塔菲研究所外聘教授，帕罗奥多研究中心系统科学实验室访问研究员。阿瑟在上世纪八十年代，受诺贝尔经济学奖得主肯尼斯·阿罗的邀请，来到刚刚建立的圣塔菲研究所。在圣塔菲研究所，阿瑟将复杂系统理论与经济学研究结合在一起，逐渐形成了“[[复杂经济学]]”的构想，创立了对经济学和复杂系统的跨学科研究新模式。
作为圣塔菲研究所最早一批研究复杂性的学者，阿瑟是复杂性科学领域的奠基人之一，由于其突出成绩，于2008年荣获复杂性科学领域首届拉格朗日奖。阿瑟提出了关于经济学中[[收益递增]]的概念，尤其放大经济中的小型随机事件的影响，这项工作也成为了理解高新技术经济的基础。凭借[[收益递增]]理论，阿瑟于1990年获得熊彼特奖。
== 教育经历 ==
* 1973年，获得加州大学伯克利分校运筹学博士学位，博士辅修专业：金融
* 1973年，获得加州大学伯克利分校经济学硕士学位
* 1969年，获得密歇根大学数学硕士学位
* 1967年，获得英国兰卡斯特大学运筹学硕士学位
* 1966年，获得贝尔法斯特皇后大学电气工程学士学位
====Principle of relativity and Lorentz transformations相对论原理与洛伦兹变换====
== 任职经历 ==
* 1994年至今 圣达菲研究所花旗银行教授
* 1998-2000年 普华永道研究员
* 1983-1996年 斯坦福大学经济学和人口研究所院长和弗吉尼亚·莫里森教授
* 1988年至今 圣达菲研究所科学委员会成员，1987年起；董事会成员，1994年起；外聘教授，1998-1994年；1988-1989年和1995年指导SFI的第一个研究项目(经济学)
* 1977-1982年 系统和决策科学组研究学者；奥地利拉克森堡国际应用系统分析研究所学者
* 1974-1977年 纽约人口理事会助理
== 学术背景 ==
=== 研究方向 ===
1、复杂性理论
2、技术如何演变
3、复杂经济学
4、自主经济学
=== 合作学者 ===
* [https://scholar.google.com/citations?user=CiwEc6gAAAAJ&hl=en Blake LeBaron]
* [https://scholar.google.com/citations?user=91RtF7oAAAAJ&hl=en Wolfgang Polak]
* [https://scholar.google.com/citations?user=O5SjWqAAAAAJ&hl=en Andrzej Ruszczyński]
and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest.
=== 代表性文章 ===
# "Complexity Economics: A Different Framework for Economic Thought," in The Economy and Complexity, Oxford U Press, 2014.
# "All Systems will be Gamed: Exploitive Behavior in Policy Systems," in The Economy and Complexity, Oxford U Press, 2014.
# "Do Markets Lead Always to Best Outcomes? A Comment on Neil Kay's paper," Research Policy, 2013.
# "The Second Economy," McKinsey Quarterly, Oct-Nov 2011.
# "The Structure of Invention," Research Policy, 36,2, March 2007.
# "The Evolution of Technology in a Simple Computer Model," with W. Polak, Complexity, 11, 5, May 2006.
# "Agent-Based Modeling and Out-Of-Equilibrium Economics," Handbook of Computational Economics, Vol. 2, K. Judd and L. Tesfatsion, eds, Elsevier/North-Holland, 2006.
# "Cognition: the Black Box of Economics," in The Complexity Vision and the Teaching of Economics, D. Colander, ed., 2000, Edward Elgar Publishers.
# "Time Series Properties of an Artificial Stock Market," with B. LeBaron and R. Palmer, Journal of Economic Dynamics and Control, 23, 1487-1516, 1999.
# "Complexity and the Economy," Science, 2 April 1999, 284, 107-109. Reprinted in The Complexity Vision and the Teaching of Economics, D. Colander, ed., Edward Elgar Publishers, 2000.
# "Asset Pricing Under Endogenous Expectations in an Artificial Stock Market," with J.H. Holland, B. LeBaron, R. Palmer, and P. Tayler, SFI Paper 96-12-093, Economic Notes. Reprinted in The Economy as an Evolving Complex System II. Edited (with S. Durlauf and D. Lane), Addison-Wesley, 1997.
# "Beyond Rational Expectations: Indeterminacy in Economic and Financial Markets" in Frontiers of the New Institutional Economics, J.N. Drobak and J.V. Nye (eds.), Academic Press, 1997.
== 荣誉成就 ==
* 2009年获得兰开斯特大学荣誉科学博士学位
* 2008年获得首届复杂性科学拉格朗日奖
* 2000年获得爱尔兰国立大学荣誉经济科学博士学位
* 1990年获得熊彼特经济学奖
* 1987年被授予古根海姆奖学金
== 联系方式 ==
* 地址：Systems Sciences Lab, PARC 3333 Coyote Hill Rd, Palo Alto,CA 94304 USA
* 电子邮箱：mprandoni@gmail.com
* 办公电话：+1 505 989 1014
== 其他信息 ==
* [http://tuvalu.santafe.edu/~wbarthur/Bio_Info/Resume_Web.pdf PDF版简历，更新到2015年]
* [https://en.wikipedia.org/wiki/W._Brian_Arthur 维基百科介绍]
* [http://www.santafe.edu/arthur 布莱恩·阿瑟的个人主页]
== 与集智的关系==
[[File: 布莱恩·阿瑟.jpg |400px|thumb|布莱恩·阿瑟在集智俱乐部的演讲]]
[https://swarma.org/?p=17050 阿瑟受集智俱乐部邀请于2019年9月20日在上海举办《科技把经济带往何方》的主题讲座 | AI&Society系列活动第18期]
== 相关报道 ==
=== 视频内容 ===
[https://www.youtube.com/watch?v=P8IzaECeQOk W. Brian Arthur spoke to the Stanford Complexity Group on Dec. 3, 2015 布莱恩·阿瑟在2015年12月3日斯坦福复杂性小组发表的讲话]
=== 文章报道 ===
[https://www.strategy-business.com/article/16402?gko=d4710 An Interview with W. Brian Arthur 关于布莱恩·阿瑟访谈]
In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.
[https://www.fastcompany.com/3064681/most-important-economic-theory-in-technology-brian-arthur A Short History Of The Most Important Economic Theory In Tech 技术领域最重要的经济理论简史]
== 最新事件 ==
* [https://a16z.com/2018/05/16/network-effects-positive-feedbacks-increasing-returns-complexity-silicon-valley-history-innovation/ 阿瑟与马克·安德森在博客上讨论网络效应、硅谷和人工智能等问题]
* [https://www.mckinsey.com/business-functions/mckinsey-analytics/our-insights/Where-is-technology-taking-the-economy 在麦肯锡季刊上发布一篇新文章：《技术将经济带向何处？》]
* [https://www.mckinsey.com/business-functions/mckinsey-analytics/our-insights/Where-is-technology-taking-the-economy 在Fast公司发布一篇文章：《技术中最重要理论的简史》]
== 相关推荐 ==
=== 书籍推荐 ===
====[https://www.amazon.com/Complexity-Economy-W-Brian-Arthur/dp/0199334293 《复杂经济学》--《Complexity and the Economy》]====
[[File: 复杂经济学.jpeg|200px|thumb|right|复杂经济学]]
1999年，阿瑟在《科学》杂志上发表的重要论文引入了复杂性和经济的概念。自阿瑟第一次提出这一概念以来的15年里，他一直在探索经济进化的复杂性，使用创新和不寻常的理论技术，提炼他早期的观点，并提出新的方法来概念化经济理论的基础。这本书里的文章都是这种恰当探索的结果。这本书是一个丰富的思想来源，所有的结构都在彻底创新的框架内，呈现出一个大师级散文作家的清晰，强烈推荐。--K. V. Veupillai, CHOICE Magazine
“阿瑟的书表明，有许多新的方法和技术可以用来改变我们对经济的看法，并提出政策和法律建议。”-- Andrew Sheng
● 经典的、强调“均衡”的经济学理论建构的是一个充满了确定性的理想世界，在这个世界里，每个人只要按照标准的演绎推理和标准的均衡分析，就能找到最好的决策。而复杂经济学则向我们描绘了一个充满不确定的世界。在这个世界里，有大量的创新在不断涌现，我们每个人都要对这个世界充满开放的心态，接受这个世界的变动和改变，适应这些变化，调整自己的行为。
● 复杂经济学是相对传统经济学提出的全新概念。它从最根本处挑战传统经济学：传统经济学认为人是自私与理性的，而且认为“均衡”是经济常态。与之相对，复杂经济学认为人是非理性的，而且“非均衡”才是经济常态，“均衡”反倒是经济的特例。在颠覆最根本的前提假设下，复杂经济学从宏观上论述何为之“复杂”——多元互动，持续变化的。在此基础上提出了与传统经济学“边际效益递减”规律相反的“收益递增”的正反馈现象。
[[File: 技术的本质.jpg |150px|thumb|right|技术的本质]]
====[https://www.amazon.com/Nature-Technology-What-How-Evolves/dp/1416544062 《技术的本质》--《The Nature of Technology: What It Is and How It Evolves》]====
这本书解释了变革性新技术是如何产生的，以及创新是如何工作的。传统思维将技术的发明归因于“跳出框架思考”，或者模糊地归因于天才或创造力，但阿瑟指出，这种解释是不充分的。发明是解决问题——满足需求——将现有的部分组合在一起，并解决和重新解决一路上出现的问题。
● 本书是打开"技术黑箱"的钥匙，它用平实的语言将技术本质的思想娓娓道来。
● 构建了关于技术的理论体系，阐明了技术的本质及其进化机制。
● 技术思想领域的开创性作品。
[[File:经济中的收益递增和路径依赖.jpg |150px|thumb|right|经济中的收益递增和路径依赖]]
====[https://www.amazon.com/dp/0472064967/ref=cm_sw_su_dp 《经济中的收益递增和路径依赖》--《Increasing Returns and Path Dependence in the Economy》]====
这是阿瑟在1982年至1992年间撰写的关于收益递增的论文集。大部分文章探讨了在不断增加的回报下的市场动态，特别是正反馈在锁定单一主导产品、技术或公司中的作用。并且介绍或讨论了许多对技术经济至关重要的概念:锁定、路径依赖、网络外部性、小历史事件的作用、正反馈、竞争技术和赢家通吃等。
=== 集智课程推荐 ===
====[https://www.zaojiu.com/lives/5d761b97ddc8f60001c52210 科技把经济带往何方]====
2019年9月20日莱恩·阿瑟（W. Brian Arthur）在集智俱乐部进行的以《科技把经济带往何方》为主题的演讲视频，讨论了对下列问题的看法：
* 人工智能等技术变革，会如何影响经济系统的分配规则
* 数字经济（虚拟经济）与实体经济的关系是怎样的
* 数字经济的变革，如何影响经济系统的发展，进而改变社会结构
* 技术变革带对经济的影响，是在持久深入还是日渐平缓
* 如何在技术创新在带来社会福利的同时，消减随之而来的隐私、分配等社会问题
* 当工作机会被新技术挤占，人类如何找到生活的意义
<br>
=== 文章推荐 ===
====[https://swarma.org/?p=16621 布莱恩·阿瑟：数字经济是增长新引擎，还是潘多拉魔盒？]====
本文译自著名经济学家布莱恩·阿瑟2011年发表的经典文章The second economy，阿瑟在文中发表了对数字经济的一系列论述和预言。
-----
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'''本词条内容源自公开资料，遵守 CC3.0协议。'''
[[Category:复杂经济学]]
[[Category:人物]]
ered a relation between mass and electromagnetic energy. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems:
像其他人一样，庞加莱(1900)发现了质量和电磁能量之间的关系。在研究作用力/反作用力原理和洛伦兹理论之间的冲突时，他试图确定当电磁场包括在内时，重心是否仍以均匀速度运动。<font color="#32CD32">能量携带质量和用有争议的乙太解决方案来弥补上述问题的可能性the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems</font>
像其他人一样，庞加莱(1900)发现了质量和电磁能量之间的关系。在研究作用力/反作用力原理和洛伦兹理论之间的冲突时，他试图确定当电磁场包括在内时，重心是否仍以均匀速度运动。<font color="#32CD32">能量携带质量和用有争议的乙太解决方案来弥补上述问题的可能性the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems</font>