特亚林·科普曼斯Tjalling Koopmans

特亚林·科普曼斯被同事们称为Challing。他的父母Sjoerd 科普曼斯和Wijtske van der Zee都是学校教师，对教育极为重视。他的父亲是严格的加尔文主义者，而母亲的宗教观点则较为开明。科普曼斯有两个哥哥，三个男孩都就读于他们父亲Sjoerd 科普曼斯担任校长的学校。事实上，他们的家夹在两栋构成学校的建筑之间。最大的男孩Jan成为荷兰归正会的牧师，而中间的男孩Hendrik成为化学工程师。家庭生活幸福，常有音乐演奏（科普曼斯被教会拉小提琴），也经常接受宗教教育。

科普曼斯十二岁时被送到希尔弗瑟姆的基督教中学，那里离家约15公里。在那里他学习了数学、物理、化学、拉丁语、希腊语和三门现代语言。十四岁时，科普曼斯获得了Wijmbritseradeel的St Geertruidsleen提供的助学金，这笔助学金支持他在基督教中学剩余三年的学习，也支持他在乌得勒支大学的学习，他于1927年入学。在那里他学习数学和理论物理，对科学哲学感兴趣，但也对经济学产生了兴趣。然而，他在乌得勒支读本科期间的最初两篇论文是关于量子力学的。科普曼斯于1932年毕业，获得相当于硕士学位的学历。

在乌得勒支学习之后，科普曼斯于1934年在阿姆斯特丹师从扬·廷贝亨，随后于1935年在奥斯陆师从Ragnar Frisch。他的学位论文Linear regression analysis of economics提交给了莱顿大学，并于1936年获得博士学位。同年十月，他与经济学家Truus Wanningen结婚；他们有三个孩子，两个女儿Anne和Helen，以及一个儿子Henry。科普曼斯于1936年被任命为鹿特丹荷兰经济学院的讲师，在那里他与扬·廷贝亨共事了几年，之后前往日内瓦的国际联盟。在这里，他从事商业周期建模工作，并再次与在那里担任科学顾问的扬·廷贝亨成为同事。1940年5月，德国军队入侵荷兰和法国，到6月中旬他们占领了巴黎。科普曼斯于6月逃离纳粹威胁，带着妻子和六周大的女儿前往美国。塞缪尔·S·威尔克斯在这段困难时期给予了他一切帮助，但找到一份永久工作却很艰难。他先在1940-41年期间在普林斯顿担任研究助理，然后在费城的宾夕法尼亚互惠人寿保险公司工作了一年。此后，科普曼斯在华盛顿的英国商船代表团工作了两年[1]：-

在那个职位上，他关注的是选择航运路线，以最小化将美国各地可获得的所需数量货物运送到英格兰指定目的地的总成本。他表明，通过直接求解一个包含材料在来源地的成本和通过替代路线运输它们的成本的方程组，可以获得所需的结果。他还设计了一个该问题的一般数学模型，从而得出了必要的方程。

1944年，他写了Exchange ratios between cargoes on various routes，但直到1970年才首次发表在[2]中，这是一本为庆祝科普曼斯六十岁生日而出版的28篇论文的合集。在这项1944年的工作中，他开创了被称为“活动分析”的运筹学主题，为此他（与列昂尼德·坎托罗维奇共同）获得了1975年诺贝尔经济学奖。他也被认为是这一时期线性规划的三位发明者之一。Dorfman写道[6]：-

大约在1940年，线性规划是一个时机已到的想法。因此，在1939年至1947年间，它被独立发现了三次，但每次的形式都因那次发现的特殊情况而有所不同。第一次发现是由列昂尼德·坎托罗维奇，一位苏联公民，第二次是由T C 科普曼斯，荷兰人，第三次是由丹齐格，美国人。

丹齐格还在[5]中考察了科普曼斯对线性规划的贡献，他写道：-

线性规划被视为一项革命性的发展，使人类能够陈述一般目标，并通过单纯形法为一大类极其复杂的实际决策问题找到最优策略决策。

科普曼斯于1944年加入芝加哥大学考尔斯经济学研究委员会。他于1946年成为归化美国公民，并在该委员会于1955年成为考尔斯基金会并迁至耶鲁大学后继续与其保持联系。他被任命为耶鲁大学阿尔弗雷德·考尔斯经济学教授，并担任此职直至1980年退休。

让我们简要提及科普曼斯的一些论文。在Identification problems in economic model construction（1949）中，他使用矩阵方法研究线性经济模型中的结构方程。他与O Reiersol合写的论文The identification of structural characteristics（1950）涉及从观测变量的假设精确概率分布推断生成该分布的理论结构的问题。与M Beckmann合写的Assignment problems and the location of economic activities（1957）考察不可分割资源的配置。Three Essays on the State of Economic Science（1957）[9]：-

……以活动分析的方式对竞争性配置机制的福利性质作了精湛的导论。

与A F Bausch合写的Selected topics in economics involving mathematical reasoning（1959）概述了一门关于经济理论数学方面的讲座课程。Dorfman写道：-

重点主要在于凸集理论，特别是凸多面体理论，在经济资源有效配置相关问题上的应用，如下列提纲所示：竞争均衡的存在性与最优性；国际贸易中的均衡；跨期均衡与资本理论；冯·诺伊曼的线性增长模型；线性活动分析及其一些应用；宏观经济动力学；计量经济学。

他发表了Stationary ordinal utility and impatience（1960年），并在Stationary utility and time perspective（1964年）中进一步延续了这项工作。与R E 约翰·威廉森合写的论文On the existence of a subinvariant measure（1964年）是一篇关于测度论的有趣工作，给出了类似于紧集阿尔弗雷德·哈尔测度的构造。他的文章On the concept of optimal economic growth（1965年）是对他在经济资源跨期最优配置方面主要贡献的最佳导论之一。最后，科普曼斯自己对Objectives, constraints, and outcomes in optimal growth models（1967年）的总结如下：-

本文综述了关于最优总量经济增长模型的大部分近期研究成果，并评论了所遇到的困难以及进一步研究的理想方向。

Matthews在[9]中写到了科普曼斯的性格和兴趣：-

科普曼斯被朋友们认为是一位谦逊的学者，致力于为狭窄而明确的问题提供精确答案，同时也是一位有造诣的业余音乐家和国际象棋爱好者。

他最大的荣誉是于1975年获得诺贝尔经济学奖。他还被选为国家科学院（美国）和美国艺术与科学院的成员。他曾担任美国经济学会和计量经济学会的主席。

科普曼斯住在康涅狄格州哈姆登，在遭受一系列脑中风后于耶鲁-纽黑文医院去世。

Tjalling Charles Koopmans was known as Challing to his colleagues. His parents, Sjoerd Koopmans and Wijtske van der Zee, were both school teachers who held education in the highest regard. His father was a strict Calvinist but his mother was more liberal in her religious views. Tjalling had two older brothers and all three boys attended the school of which their father, Sjoerd Koopmans, was the headmaster. In fact their home was sandwiched between two buildings which formed the school. The oldest boy, Jan, became a minister of the Dutch Reformed Church, while the middle boy, Hendrik, became a chemical engineer. Home life was happy with much music making (Tjalling was taught to play the violin) and frequent religious instruction.

When he was twelve years old, Tjalling was sent to the Christian High School at Hilversum which was about 15 km from his home. There he learnt mathematics, physics, chemistry, Latin, Greek, and three modern languages. At age fourteen Tjalling was awarded a stipend by the St Geertruidsleen of Wijmbritseradeel which supported him during his remaining three years at the Christian High School and it also supported him at the University of Utrecht, which he entered in 1927. There he studied mathematics and theoretical physics, was interested in the philosophy of science, but he also became interested in economics. However his first two publications, while still an undergraduate at Utrecht, were on quantum mechanics. Koopmans graduated with the equivalent of a Master's degree in 1932.

After his studies at Utrecht, Koopmans studied under Jan Tinbergen in Amsterdam during 1934 and then under Ragnar Frisch in Oslo in 1935. His doctoral thesis Linear regression analysis of economics was presented to the University of Leiden and he was awarded his doctorate in 1936. In October of the same year he married Truus Wanningen who was an economist; they had three children, two daughters Anne and Helen, and a son Henry. Koopmans was appointed as a lecturer at the Netherlands School of Economics, Rotterdam, in 1936 where he spent a couple of years as a colleague of Tinbergen before moving to the League of Nations in Geneva. Here he worked on business cycle modelling and again was a colleague of Tinbergen who worked there as a scientific advisor. In May 1940 German troops invaded the Netherlands and France and by the middle of June they occupied Paris. Koopmans fled from the Nazi threat in June, going to the United States with his wife and six week old daughter. Samuel Wilks gave him every assistance during this difficult period but finding a permanent job was hard. He was first a research assistant at Princeton during 1940-41 then was employed by the Penn Mutual Life Insurance Company in Philadelphia for a year. Following this Koopmans worked for two years for the British Merchant Shipping Mission in Washington [1]:-

In that position he was concerned with the selection of shipping routes that would minimize the total cost of transporting required quantities of goods, available at various locations in America, to specified destinations in England. He showed that the desired result is obtainable by the straightforward solution of a system of equations involving the costs of the materials at their sources and the costs of shipping them by alternative routes. He also devised a general mathematical model of the problem that led to the necessary equations.

In 1944 he wrote Exchange ratios between cargoes on various routes but it was only published for the first time in 1970 in [2] which is a collection of 28 of Koopmans' papers published to celebrate his sixtieth birthday. In this 1944 work he initiated the topic of operational research called 'activity analysis' for which he received (jointly with Kantorovich) the Nobel Prize in Economics for 1975. He is also considered as one of the three inventors of linear programming during this period. Dorfman writes [6]:-

Around 1940, linear programming was an idea whose time had come. Accordingly, it was discovered three times, independently, between 1939 and 1947, but each time in a somewhat different form dictated by the special circumstances of that discovery. The first discovery was by L V Kantorovich, a Soviet citizen, the second was by T C Koopmans, Dutch, and the third by G B Dantzig, American.

Dantzig also examines Koopmans' contributions to linear programming in [5] where he writes:-

Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity.

Koopmans joined the Cowles Commission for Research in Economics at the University of Chicago in 1944. He became a naturalized U.S. citizen in 1946, continuing his association with the Cowles Commission when it became the Cowles Foundation and moved to Yale University in 1955. He was appointed as Alfred Cowles Professor of Economics at Yale and held this post until he retired in 1980.

Let us briefly mention some of Koopmans' papers. In Identification problems in economic model construction (1949) he used matrix methods to study structural equations within a linear economic model. His paper The identification of structural characteristics (1950), written jointly with O Reiersol, is concerned with the problem of drawing inferences from the hypothetically exact probability distribution of observed variables to the theoretical structure which generates the distribution. Assignment problems and the location of economic activities (1957), written jointly with M Beckmann, examines the allocation of indivisible resources. Three Essays on the State of Economic Science (1957) [9]:-

... is a masterful introduction to the welfare properties of competitive allocation mechanisms in terms of activity analysis.

Selected topics in economics involving mathematical reasoning (1959), written jointly with A F Bausch, summarizes a course of lectures on mathematical aspects of economic theory. Dorfman writes:-

The emphasis lies heavily on applications of the theory of convex sets, and in particular of convex polyhedra, to problems relating to efficient allocation of economic resources, as the following outline indicates: Existence and optimality of competitive equilibrium; equilibrium in international trade; equilibrium over time and capital theory; von Neumann's linear growth model; linear activity analysis and some applications; macroeconomic dynamics; econometrics.

He published Stationary ordinal utility and impatience (1960) and a further continuation of this work in Stationary utility and time perspective (1964). The paper On the existence of a subinvariant measure (1964), written with R E Williamson, is an interesting work on measure theory which gives a construction analogous to that of the Haar measure for compact sets. His article On the concept of optimal economic growth (1965) is one of the best introductions to his major contributions to the optimal allocation of economic resources over time. Finally Koopmans own summary of Objectives, constraints, and outcomes in optimal growth models (1967) is as follows:-

This paper surveys the results of mostly recent research on optimal aggregate economic growth models, and comments on the difficulties encountered and on desirable directions of further research.

Matthews writes of Koopmans character and interests in [9]:-

Koopmans was known to friends as a modest scholar, one committed to precise answers for narrow, well-defined questions, and as an accomplished amateur musician and chess enthusiast.

His greatest honour was receiving the Nobel Prize for Economics in 1975. He was also honoured by election to the National Academy of Sciences (United States) and the American Academy of Arts and Sciences. He was president of the American Economics Association and also of the Econometric Society.

Koopmans, who lived in Hamden, Connecticut, died at Yale-New Haven Hospital after suffering a series of cerebral strokes.