刘易斯·弗赖伊·理查森Lewis Fry Richardson

刘易斯·弗赖伊·理查森出生于一个贵格会家庭。他的母亲是Catherine 理查森，出身于谷物商家庭，父亲是David Richardson，出身于制革匠家庭，他自己也曾进入家族企业。弗洛伦斯·南丁格尔·大卫和Catherine Richardson育有七个孩子，理查森是这个大家庭中最小的。他就读于纽卡斯尔预备学校，在那里他最喜欢的科目是欧几里得的学习。1894年，他进入约克的Bootham学校，这是一所成立于1823年的贵格会学校，最初是为“富有的贵格会教徒的儿子们”而设。他在Bootham学校接受的教育对他很重要，一方面，他被学校的一位气象学专家J Edmund Clark老师引向了科学，另一方面，他从父母那里学到的贵格会高尚道德与和平主义的信仰得到了加强。尽管在这所学校培养了对科学的热爱，他离开时却认为：-

……科学应当从属于道德。

有趣的是，这种信念在他生活方式和他投入大量精力的研究课题中得到了充分体现。他于1898年离开⟦N1⟧学校，在纽卡斯尔度过了两年，就读于达勒姆理学院。在那里，他学习了数学、物理、化学、植物学和动物学。他的教育在剑桥大学国王学院完成，于1903年以自然科学荣誉学位考试一等成绩毕业。

理查森担任过大量职位。他曾在国家物理实验室（1903-04，1907-09）和气象局（1913-16）工作，并在阿伯里斯特威斯大学学院（1905-06）和曼彻斯特技术学院（1912-13）担任大学职位。此外，他还是国家泥炭工业公司的化学家（1906-07），并负责Sunbeam Lamp公司的物理和化学实验室（1909-12）。他于1909年与Dorothy Garnett结婚，尽管他们没有自己的孩子，但他们收养了两个儿子和一个女儿。

1914年第一次世界大战爆发时，理查森正在气象局工作，担任Eskdalemuir天文台的负责人。根据他的贵格会信仰，他宣布自己为依良心拒服兵役者，因此不能被征召入伍。然而，作为依良心拒服兵役者意味着他再也不能获得大学职位。然而，作为依良心拒服兵役者并不意味着理查森没有参与战争。相反，他做了出色的战时工作，从1916年到1919年在附属于法国第16步兵师的公谊会救护队服役。

在公谊会救护队的工作结束后，他回到了气象局的职位。然而，1920年气象局成为空军部的一部分，这意味着理查森将成为军队的一部分。他的和平主义信仰绝不允许他在这一变化后继续留在气象局，因此他辞职了。从1920年到1929年，理查森担任威斯敏斯特培训学院的物理系主任，然后从1929年到1940年，他担任苏格兰佩斯利技术学院和艺术学校的校长。他于1940年59岁时退休，以便专注于研究。

正是理查森首先将数学，特别是有限差分法，应用于预测天气，见于Weather Prediction by Numerical Process（1922年）。他最初发展有限差分法是为了求解微分方程，这些方程源于他在国家泥炭工业公司关于泥炭中水流的工作。在发展了这些能够获得高精度解的方法后，自然的一步是将同样的方法应用于解决他在气象局工作中遇到的大气动力学问题。在这部重要论著中，他使用了威廉·皮耶克尼斯发表在Dynamical meteorology and hydrography中的数据，并用自己的话说，构建了：-

……一种天气预测方案，它类似于制作航海天文历的过程，因为它建立在微分方程的基础上，而不是建立在现象整体的部分重现上。

从气象站进行观测将提供定义初始条件的数据，然后可以用这些初始条件求解方程，并做出天气预测。这是一项非凡的工作，但从某种意义上说，它超前于时代，因为在计算机时代之前，必要的手工计算所需的时间如此之长，以至于即使有许多人致力于求解方程，找到解的时间也远远太晚，无法用于预测天气。他自己计算过，需要6万人参与计算，才能在天气实际到来之前预测明天的天气。尽管如此，理查森的工作为当今的天气预报奠定了基础。

除了1922年的书之外，理查森还发表了约30篇关于天气数学的论文，在这些论文中，他对微积分和扩散理论，特别是大气中的涡流扩散做出了贡献。以他命名的“理查森数”是一个涉及温度和风速梯度的基本量。他的成就得到了认可，于1926年当选为皇家学会会士。

理查森对数学的另一应用是在他对战争原因的研究中，他在几部重要著作中发表了他的分析结果：Generalized Foreign Politics（1939年）、Arms and Insecurity（1949年）和Statistics of Deadly Quarrels（1950年）。理查森再次对数学做出了新颖的应用。以前人们假设战争是一种理性的国家政策，是为了国家利益而使用的。然而，理查森对战争原因的建模方式完全不同，给出了微分方程组，这些方程支配着国家之间的相互作用，这种相互作用由态度和情绪等因素引起。这些量几乎与个别领导人无关，但他声称，它们是主要因素。整个群体的心理才是相关的，这是一种潜在因素，当个体的态度被平均时就会显现出来。正如他写道：-

这些方程仅仅描述了如果人们不停下来思考会做什么。

他关于这个主题的第一篇论文The mathematical psychology of war写于1919年，当时私下印刷。直到1935年才广泛发表。事实上，在此之前理查森已回到大学学习，并于1929年作为伦敦大学学院的外部学生获得了心理学学士学位。

他建立了支配国家军备建设的方程，考虑了军备竞赛的费用、国家之间的不满、国家的野心等因素。他为方程中的各种参数选择不同的值，然后试图研究在什么情况下局势是稳定的，在什么情况下是不稳定的。显然，在所有这些工作中，他对其在促进防止战争方面的价值没有错误的幻想，但他显然受到对战争的强烈仇恨的驱使。与一些认为战争是国家正常行为的一部分的人不同，他明确地将战争视为人类正在遭受的一种苦难。

1940年从佩斯利技术学院退休后，理查森开始了另一项与战争有关的重要工作。他收集了自拿破仑战争结束以来发生的所有“致命争吵”的数据。他为这类争吵制定了一个量级尺度，定义为被杀者人数的对数。然后，他分析了与这类“致命争吵”相关的大量因素，寻找它们之间的关系。战争的频率与其量级之间有关系吗？频率与双方共同语言之间有关系吗？频率与共同宗教之间有关系吗？频率与共同边界之间有关系吗？

他寻找能降低战争频率的因素。国家之间的体育赛事会降低战争频率吗？双方强大的军事力量会降低战争的机会吗？对第三国的共同仇恨会降低两国之间战争的机会吗？试图理解战争是一种引人入胜的方法，然而理查森调查的所有因素似乎都没有统计学意义。防止两国之间战争最有希望的因素似乎是它们之间强大的国际贸易。Rapoport在[6]中写道：-

……从这一巨著分析中，几乎没有任何关于战争“原因”的新知识出现，除非人们将既定观念的否定结果视为新知识。特别是，与普遍观点相反，无论是武装力量还是集体安全措施，都没有成为显著的防止战争的影响因素。

Gold在[5]中关于理查森的性格写道：-

对理查森的研究是他心智机器几乎但不完全自行运转倾向的必然结果。因此，他是个糟糕的倾听者，被自己的思绪分心；也是个糟糕的司机，看到的是自己的梦想而不是交通。同样的倾向解释了为什么他有时举止唐突，这在他的性格中否则无法解释。在法国的汽车车队中，他赢得了所有人的喜爱，并以简朴的方式执行最卑微的任务，展现了服务的尊严；那种善良和服务的性格在威斯敏斯特和佩斯利一直保持。

Lewis Fry Richardson was born into a Quaker family. His mother was Catherine Fry who came from a family of corn merchants, and his father was David Richardson who came from a family of tanners, and he had gone himself into the family business. David and Catherine Richardson had seven children, and Lewis was the youngest of this large family. He attended Newcastle Preparatory School where his favourite subject was the study of Euclid. Then in 1894 he entered Bootham school in York which was a Quaker school established in 1823, originally intended it to be for 'the sons of wealthy Quakers'. The education he received at Bootham school was important for him for, on the one hand he was directed towards science by J Edmund Clark, a master at the school who was an expert in meteorology, while on the other hand the Quaker beliefs in high morals and pacifism which he had been taught by his parents were reinforced. Despite gaining a love for science at this school he left believing that:-

... science ought to be subordinate to morals.

It is interesting to see just how much this belief was reflected in the way he led his life and in the research topics in which he devoted so much effort. He left Bootham school in 1898 to spend two years in Newcastle attending the Durham College of Science. There he studied mathematics, physics, chemistry, botany and zoology. His education was completed at King's College, Cambridge, graduating with a First Class degree in the Natural Science Tripos in 1903.

Richardson held a large number of posts. He worked in the National Physical Laboratory (1903-04, 1907-09) and the Meteorological Office (1913-16), and he held university posts at University College Aberystwyth (1905-06) and Manchester College of Technology (1912-13). In addition he was a chemist with National Peat Industries (1906-07) and in charge of the physical and chemical laboratory of the Sunbeam Lamp Company (1909-12). He married Dorothy Garnett in 1909 and although they had no children of their own, they adopted two sons and a daughter.

When World War I broke out in 1914 Richardson was working for he Meteorological Office as superintendent of the Eskdalemuir Observatory. In line with his Quaker beliefs he declared himself a conscientious objector so he could not be drafted into the military. However, being a conscientious objector meant that he was never again eligible for university posts. Being a conscientious objector, however, did not mean that Richardson was not involved in the War. On the contrary he did outstanding war work serving from 1916 to 1919 in the Friend's Ambulance Unit which was attached to the 16th French Infantry Division.

After his work with the Friend's Ambulance Unit had ended, he returned to his position in the Meteorological Office. However in 1920 the Meteorological Office became part of the Air Ministry which would have meant that Richardson would have become part of the military. There was no way that his pacifist beliefs would allow him to continue in the Meteorological Office after this change, so he resigned. From 1920 to 1929 Richardson was head of the Physics Department at Westminster Training College, then from 1929 to 1940, he was Principal of Paisley College of Technology and School of Art in Scotland. He retired in 1940 at the age of 59 so that he could concentrate on his research.

It was Richardson who was the first to apply mathematics, in particular the method of finite differences, to predicting the weather in Weather Prediction by Numerical Process (1922). He first developed his method of finite differences in order to solve differential equations which arose in his work for the National Peat Industries concerning the flow of water in peat. Having developed these methods by which he was able to obtain highly accurate solutions, it was a natural step to apply the same methods to solve the problems of the dynamics of the atmosphere which he encountered in his work for the Meteorological Office. In this important treatise he used data from work by Vilhelm Bjerknes published in Dynamical meteorology and hydrography and constructed, in his own words:-

... a scheme of weather prediction which resembles the process by which the Nautical Almanac is produced in so far as it is founded upon the differential equations and not upon the partial recurrence of phenomena in their ensemble.

Making observations from weather stations would provide data which defined the initial conditions, then the equations could be solved with these initial conditions and a prediction of the weather could be made. It was a remarkable piece of work but in a sense it was ahead of its time since the time taken for the necessary hand calculations in a pre-computer age took so long that, even with many people working to solve the equations, the solution would be found far too late to be useful to predict the weather. He calculated himself that it would need 60,000 people involved in the calculations in order to have the prediction of tomorrow's weather before the weather actually arrived. Despite this, Richardson's work laid the foundations for present day weather forecasting.

In addition to his 1922 book, Richardson published about 30 papers on the mathematics of the weather and in these he made contributions to the calculus and to the theory of diffusion, in particular eddy-diffusion in the atmosphere. The 'Richardson number', a fundamental quantity involving gradients of temperature and wind velocity is named after him. His achievements were recognised by election to the Royal Society in 1926.

Another application of mathematics by Richardson was in his study of the causes of war and he published the results of his analysis in a number of major books: Generalized Foreign Politics (1939), Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950). Again Richardson made novel applications of mathematics. Previously it had been assumed that war was a rational national policy, to be used in the interests of a nation. However the way that Richardson modelled the causes of war was quite different, giving systems of differential equations which governed the interactions between countries caused by such things as attitudes and moods. Here were quantities which were little to do with individual leaders yet, he claimed, were major factors. Psychology of a whole population was what was relevant, an underlying factor which emerged when attitudes of individuals were averaged. As he wrote:-

The equations are merely a description of what people would do if they did not stop and think.

His first paper on this topic The mathematical psychology of war was written in 1919 and privately printed at that time. It was not widely published until 1935. In fact before this Richardson had returned to university study and obtained a B.Sc. in psychology as an external University College, London, student in 1929.

He set up equations governing arms build-up by nations, taking into account factors such as the expense of an arms race, grievances between states, ambitions of states, etc. Choosing different values for the various parameters in the equation he then tried to investigate when situations were stable and when they were unstable. It is clear that in all this work he had no false illusions regarding its value for contributing to the prevention of wars, yet he was clearly motivated by his strong hatred of war. Unlike some who believe that war is part of the normal behaviour of nations, he clearly treated war as an affliction from which the human race was suffering.

After he retired from Paisley College of Technology in 1940 Richardson began another major piece of work related to wars. He gathered data on all "deadly quarrels" that had taken place since the end of the Napoleonic Wars. He developed a magnitude scale for such quarrels defined to be the logarithm of the number who were killed. He then analysed a large number of factors associated with such "deadly quarrels" looking for relations between them. Is there a relation between the frequency or wars and their magnitude? Is there a relation between frequency and a common language for the two sides? Is there a relation between frequency and a common religion? Is there one between frequency and common frontiers?

He looked for factors which would reduce the frequency of wars. Do sporting fixtures between nations reduce the frequency of war? Does strong military force on each side reduce the chance of war? Does a common hatred of a third country reduce the chance of war between two countries? It is a fascinating approach to try to understand war, yet none of the factors Richardson investigated seemed statistically significant. The most promising factor to prevent war between two countries appeared to be strong international trade between them. Rapoport writes in [6]:-

... hardly anything in the way of new knowledge as to the "causes" of wars has emerged from this monumental analysis, unless one views as new the refutation of established notions by negative results. In particular, neither armed might nor collective security measures (contrary to widespread opinion) emerge as significant war-preventing influences.

Gold writes in about Richardson's character in [5]:-

Research for Richardson was the inevitable consequence of the tendency of his mental machine to run almost, but not quite, by itself. So he was a bad listener, distracted by his thoughts, and a bad driver, seeing his dream instead of the traffic. The same tendency explains why he sometimes appeared abrupt in manner, otherwise inexplicable in one of his character. In the motor convoy in France he evoked the affection of all and demonstrated the dignity of service by the simplicity with which he performed the most menial tasks; that character of kindness and service was maintained at Westminster and Paisley.