弗朗西斯·高尔顿Francis Galton

弗朗西斯·高尔顿是一位探险家和人类学家，以其对人类智力的开创性研究而闻名。他将晚年献给了优生学，即通过选择性生育来改善人类物种的体质和心智构成。

高尔顿 的父母都来自重要的贵格会家庭，他们可能是他关于遗传天才思想的绝佳例证。他的母亲弗朗西丝·安妮·维奥莱塔·达尔文是医生伊拉斯谟·达尔文的女儿，伊拉斯谟·达尔文是 Zoonomia 或 Laws of Organic Life 的作者，在书中他阐述了他的进化思想。查尔斯·高尔顿·达尔文 也是伊拉斯谟·达尔文的孙子。高尔顿 的父亲 皮埃尔·萨米埃尔·特尔提乌斯·高尔顿 是一位银行家，来自一个包含许多富有的银行家和枪匠的家庭。高尔顿 是他父母七个孩子中最小的，有三个哥哥和三个姐姐。

高尔顿在1836年进入伯明翰的爱德华国王学校之前，曾在伯明翰地区上过几所小学校。他在这所学校待了两年，但并不喜欢那里对古典文学和宗教的侧重。由于父母决定让他从事医学职业，他在伯明翰跟随几位不同的医生当了大约一年的学徒。此后，他前往伦敦，在国王学院学习医学一年。然后，在1840年，他快速游历了欧洲大陆，访问了吉森、维也纳、康斯坦察、君士坦丁堡、士麦那的塞翁和雅典。正是在这个阶段，用他自己的话说（见[6]）：-

……一种对旅行的热情攫住了我，仿佛我是一只候鸟。

回到英格兰后，高尔顿于1840年秋进入剑桥大学三一学院学习医学。他很快将学习转向数学，跟随威廉·霍普金斯学习，这是剑桥最好的数学导师，但他在第三年生病，无法完成学位。此时他的许多问题源于他父亲病重，这无疑是他未能完成数学荣誉学位考试的一个主要因素。他当时的打算是重返医学职业，事实上他回到伦敦，重新开始医学学习。然而，在他父亲于1844年去世后，他发现自己因[6]而富裕：-

……一笔足够的财富，使我无需依赖医学职业。

由于经济上有了保障，不再需要考虑职业问题，高尔顿决定追随自己对旅行的热情，与朋友一起沿尼罗河而上前往喀土穆。当时人们对尼罗河兴趣浓厚，对其源头有大量猜测。事实上，尼罗河是两条河，白尼罗河和青尼罗河，它们在喀土穆汇合，一起流向大海。（事实上，直到1858年才发现尼罗河的源头是维多利亚湖。）高尔顿还访问了圣地和叙利亚，然后决定献身于运动，从1845年到1850年，他这样做了五年。

认定运动不适合自己后，高尔顿开始筹划更为宏大的旅行。在决定前往非洲西南部之前，他咨询了皇家地理学会。弗洛伦斯·南丁格尔·大卫利文斯通曾于1849年向皇家地理学会的一次会议提交报告，讲述发现位于今博茨瓦纳西北部的恩加米湖。该湖位于无水的卡拉哈里沙漠以北，其存在已为欧洲人所知，但利文斯通是第一个亲眼见到它的欧洲人。高尔顿的目标是从西南方找到通往该湖的通道，带着这一计划，他的探险队在今纳米比亚的沃尔维斯湾登陆。沃尔维斯湾以东是被称为达马拉兰的地区，欧洲人于1791年首次到访。事实上，从沃尔维斯湾到恩加米湖约550英里，尽管两次尝试抵达该湖，高尔顿的队伍两次都未能成功。然而，这是一次非常有价值的探险，他们对该地区了解甚多，而此前欧洲人对这里的探索很少。当高尔顿回到英格兰后，他在Tropical South Africa（1953）中发表了自己的旅行记述。由于他的探险，他于1853年当选为皇家地理学会会士，三年后，他又当选为皇家学会会士。

1853年8月1日，高尔顿与路易莎·简·巴特勒结婚，她是彼得伯勒教长的女儿，后者此前曾任哈罗公学校长。他写了另一本有趣的书，旨在向探险者提供建议，即The art of travel，但尽管他继续在欧洲大量旅行，由于他的健康从未从非洲经历中恢复，他没有再进行进一步的探险。

也许正是1859年达尔文的Origin of the species的出版，标志着高尔顿兴趣方向的转变。高尔顿是达尔文的表亲，所以他成为最早被这本书转变的人之一也许是自然的。他确信，各个领域的卓越几乎完全归因于遗传因素，这与当时基本上认为每个人生来能力平等的思想完全相悖。在阅读了高尔顿的书Hereditary Genius（1869年）之后，达尔文写信给他说[7]：-

从某种意义上说，你使一个对手转变了，因为我一直坚持认为，除了傻瓜之外，人在智力上差别不大，只是在热情和勤奋上有所不同。

高尔顿反对那些声称智力或性格由环境因素决定的人，并将“天才”定义为：-

……一种异常高且同时与生俱来的能力。

他探究种族差异，这在今天几乎不可接受，并且是最早采用问卷和调查方法的人之一，他用这些方法研究不同人群的心理意象。

尽管数学薄弱，尽管学习了两年数学荣誉学位课程，他的思想强烈影响了统计学的发展，特别是他证明了正态分布的正态混合本身是正态的。他的另一个主要发现是回归。这是他对回归及其与二元正态分布联系的表述。他的工作引导他研究优生学[3]：-

高尔顿可以说是优生学研究的创始人。他对科学的主要贡献在于他的人类学探究，尤其是对遗传规律的研究，其工作的显著特点是应用统计学方法。1869年，在《遗传天才》一书中，他力图证明天才是由祖先决定的，随后他又就这一主题的各个方面写了许多其他书籍和论文。

让我们更详细地考察一下高尔顿对统计学的贡献。大约在1875年，他用香豌豆种子做实验。他使用了七个不同直径的各100粒种子，并绘制了原始种子直径与下一代种子直径的二维图。他注意到，大种子的后代的中位直径小于其亲本的中位直径，而小种子的后代的中位直径大于其亲本的中位直径。高尔顿意识到后代倾向于回归到平均大小。当然，在这个阶段他还不明白他的发现适用于任何二维图，反而认为这是他所实验的情况所特有的。起初他把这种现象称为“返祖”，但后来改名为“回归”。

1884-85年举办了国际健康展览会，与此相关，高尔顿建立了一个实验室来测量人类统计数据。他收集了大量人的身高、体重和力量等数据，并自己设计了用于测量的仪器。该实验室在国际健康展览会闭幕后继续存在，它是卡尔·皮尔逊在伦敦大学学院运行的生物统计实验室的前身。

高尔顿现在在他已经形成的关于回归的思想上取得了进一步的进展。他绘制了父母身高和其成年子女身高的双向图。他能够以这样的方式绘制这些图，使得回归系数成为回归线的斜率。1888年，他还检查了同一个人两个不同器官的大小，并应用他一直在开发的方法来研究大小之间的关联程度。他定义了一个相关指数，作为衡量两者相关程度的度量。然而，当有两个以上相关的度量时，他未能理解所涉及数学的复杂性。

1889年，高尔顿出版了Natural inheritance，其中总结了他所做的关于相关和回归的工作。他很好地阐述了他所引入的概念以及他所发现的技术。卡尔·皮尔逊读了Natural inheritance，这对他的思想产生了深远的影响：-

正是高尔顿首先把我从只有因果范畴下的自然现象才能应用可靠数学的偏见中解放出来。在这里，第一次出现了一种可能性——我不会说是一种确定性——即在生命形式领域，尤其是在人类行为领域，获得与人们所认为的物理知识同样有效的知识。

高尔顿在他的实验室收集的数据中包括指纹印。他能够证明指纹图案随着人年龄的增长保持不变，并且他根据将指纹图案分为弓型、箕型和斗型，设计了可用作个人唯一标识的指纹特征。关于这个主题，他出版了Finger prints（1893年）、Blurred finger prints（1893年）和Finger print directory（1895年）。他的识别系统成为爱德华·R·亨利爵士分类的基础，亨利后来成为伦敦大都会警察局局长。高尔顿-亨利指纹分类系统于1900年6月发表，并于1901年开始在苏格兰场用于犯罪记录的身份识别。它很快在世界各地的刑事调查中得到应用。

除了作为人类智力的不知疲倦的研究者外，高尔顿还在气象学、人体测量学和体质人类学领域做出了重要贡献。他于1863年出版了Meteorographica, or methods of mapping the weather。他创造了反气旋这个术语，并指出了它在天气预报中的重要性。连同对气象学的其他重要贡献，这使他成为气象局管理委员会的成员。

高尔顿因其贡献获得了许多荣誉，其中最引人注目的也许是他在1909年被封为爵士[4]：-

当首相提出将他的名字呈交国王授予爵士爵位时，他已年届89岁。他一如既往地谦逊，接受了……

他还在1876年获得了皇家学会的皇家奖章，1902年获得了同一学会的达尔文奖章，1910年获得了它的科普利奖章。1901年，他获得了人类学研究所颁发的赫胥黎奖章，1908年获得了林奈学会颁发的达尔文-华莱士奖章。

他在英国科学界发挥了重要作用。除了上述贡献外，他还在1863年至1867年间担任英国协会的秘书长，并四次担任分会主席。他还曾在皇家学会的邱园委员会任职。随着年龄增长，他的健康状况开始限制他所能做出的贡献[4]：-

他第一次痛苦的考验是耳聋，这使他无法参加科学聚会，而那里曾是他熟悉的身影。……一段时间后，他失去了行走能力，不得不将每日散步换成浴椅，但他从未发出过一声抱怨。他深爱新鲜空气，不在乎如何获得它，常常坐在敞开的阳台上，而大多数他这个年纪的人都会蜷缩在炉火旁。

An explorer and anthropologist, Francis Galton is known for his pioneering studies of human intelligence. He devoted the latter part of his life to eugenics, i.e. improving the physical and mental makeup of the human species by selected parenthood.

Galton's parents, both from important Quaker families, might have served as excellent examples of his ideas on hereditary genius. His mother, Frances Anne Violetta Darwin, was the daughter of the physician Erasmus Darwin, the author of Zoonomia or the Laws of Organic Life, in which he set out his ideas of evolution. Charles Darwin was also a grandson of Erasmus Darwin. Galton's father, Samuel Tertius Galton, was a banker from a family which contained many rich bankers and gunsmiths. Francis was youngest of his parents seven children having three older brothers and three older sisters.

Francis attended a number of small schools in the Birmingham area before entering King Edward's School in Birmingham in 1836. He spent two years at this school but did not find the emphasis on classics and religion to his liking. Since his parents had decided that he should follow a medical career, he was an apprentice to several different medical men in Birmingham for around a year. Following this he went to London where he studied medicine at King's College for one year. Then, in 1840, he made a quick tour of the Continent visiting Giessen, Vienna, Constanza, Constantinople, Smyrna, and Athens. It was at this stage that, in his own words, (see [6]):-

... a passion for travel seized me as if I had been a migratory bird.

On his return to England Galton entered Trinity College, Cambridge, to study medicine in the autumn of 1840. He quickly changed his studies to mathematics, studying with Hopkins, the best Cambridge mathematics tutor, but he became ill during his third year and was unable to complete his degree. Much of his problems at this time came from the fact that his father was seriously ill, and that was undoubtedly a major factor in his failing to be able to complete the Mathematical Tripos. His intention at this time was to return to a medical career, and indeed he went back to London where he took up his medical studies again. However, after his father died in 1844, he found himself well off with [6]:-

... a sufficient fortune to make me independent of the medical profession.

No longer needing to think in terms of a career since he was financially secure, Galton decided to follow his passion for travel and made a trip with friends up the Nile to Khartoum. There was much interest in the Nile at this time with a great deal of speculation as to its source. In fact the Nile is two rivers, the White Nile and the Blue Nile, which join at Khartoum and flow together to the sea. (In fact the source of the Nile was not discovered to be Lake Victoria until 1858.) Galton also visited the Holy Land and Syria before deciding that he would devote himself to sport, which he did for five years from 1845 at 1850.

Deciding that sport did not suit him, Galton began to plan more ambitious travels. He consulted the Royal Geographical Society before deciding on a trip to south west Africa. David Livingstone had sent a report to a meeting of the Royal Geographical Society on finding Ngami Lake in 1849 which is located in the north west of present day Botswana. The existence of the lake, to the north of the waterless Kalahari Desert, was already known to Europeans but Livingstone was the first European to see it. Galton aimed to find a passage to the lake from the south west, and with this plan in mind his expedition landed in Walvis Bay (in present day Namibia). East of Walvis Bay was the region known as Damaraland, which had been first visited by Europeans in 1791. In fact Walvis Bay to Ngami Lake is around 550 miles and, despite two attempts to reach the lake, Galton's party failed in both attempts. It was a very worthwhile expedition, however, and they learnt much of this region which had been little explored by Europeans. When Galton returned to England he published an account of his journeys in Tropical South Africa (1953). He was elected a fellow of the Royal Geographical Society in 1853 as a result of his explorations and, three years later, he was elected a fellow of the Royal Society.

On 1 August 1853 Galton married Louisa Jane Butler, the daughter of the dean of Peterborough who had previously been headmaster of Harrow School. He wrote another interesting book aimed at giving advice to explorers The art of travel but, although he continued to travel a great deal in Europe, he made no further explorations as a result of his health which never recovered from his African experience.

Perhaps it was the publication of Charles Darwin's Origin of the species in 1859 which marked a change in direction of Galton's interests. Galton was the cousin of Charles Darwin, so perhaps it was natural that he should be one of the first to be converted by the book. He became convinced that pre-eminence in various fields was due almost entirely to hereditary factors, something which was completely at odds with thinking at the time which basically believed that everyone was born with equal abilities. After reading Galton's book Hereditary Genius (1869) Charles Darwin wrote to him saying [7]:-

You have made a convert of an opponent in one sense for I have always maintained that, excepting fools, men did not differ much in intellect, only in zeal and hard work.

Galton opposed those who claimed intelligence or character were determined by environmental factors and defined "genius" as:-

... an ability that was exceptionally high and at the same time inborn.

He inquired into racial differences, something almost unacceptable today, and was one of the first to employ questionnaire and survey methods, which he used to investigate mental imagery in different groups of people.

Although weak in mathematics, despite studying the Mathematical Tripos for two years, his ideas strongly influenced the development of statistics particularly his proof that a normal mixture of normal distributions is itself normal. Another of his major findings was reversion. This was his formulation of regression and its link to the bivariate normal distribution. His work led him to the study of eugenics [3]:-

Galton may be described as the founder of the study of eugenics. His principal contributions to science consisted in his anthropological inquiries, especially into the laws of heredity, where the distinguishing feature of his work was the application of statistical methods. In 1869, in 'Hereditary Genius', he endeavoured to prove that genius is mainly a matter of ancestry, and he followed that up with many other books and papers on various aspects of the subject.

Let us examine Galton's contribution to statistics in a little more detail. In around 1875 he was experimenting with sweet-pea seeds. He used 100 seeds of each of seven different diameters and constructed a two-way plot of diameters of the original seeds against the diameters of the seeds of the next generation. He noticed that the median diameter of the offspring of the large seeds were less than that of their parents while the median diameter of the offspring of the small seeds were greater than that of their parents. Galton realised that the off-spring tended to revert towards the mean size. Certainly he did not understand at this stage that his findings would apply to any two-way plot, thinking rather than it was peculiar to the situation with which he was experimenting. At first he called the phenomena 'reversion', but later changed the name to 'regression'.

In 1884-85 the International Health Exhibition was held and in connection with this Galton set up a laboratory to measure human statistics. He collected data such as height, weight, and strength of a large number of people devising himself the apparatus used to make the measurements. This laboratory continued in existence after the International Health Exhibition closed and it was the forerunner of the Biometric Laboratory run by Karl Pearson at University College, London.

Galton now made further progress with the ideas he had already formed concerning regression. He made two-way plots of heights of parents and the heights of their adult children. He was able to draw the plots in such a way that the coefficient of regression became the slope of the regression line. In 1888 he also examined the size of two different organs from the same person and applied the methods he had been developing to study the degree of association of the sizes. He defined an index of correlation as a measure of the degree to which the two were related. However, when there are more than two measures which were correlated, he failed to understand the complexity of the mathematics involved.

In 1889 Galton published Natural inheritance in which presented as summary of the work he had done on correlation and regression. He gave a good account of the concepts which he had introduced as well as the techniques which he had discovered. Karl Pearson read Natural inheritance and it had a profound influence on his thinking:-

It was Galton who first freed me from the prejudice that sound mathematics could only be applied to natural phenomena under the category of causation. Here for the first time was a possibility - I will not say a certainty - of reaching knowledge as valid as physical knowledge was thought to be, in the field of living forms and above all in the field of human conduct.

Among the data which Galton collected in his laboratory were impressions of fingers. He was able to show that the fingerprint pattern remained constant as the person grew older, and he devised characteristics of the fingerprints which could be used as unique identifiers of the person based on grouping the patterns into arches, loops, and whorls. On the topic he published Finger prints (1893), Blurred finger prints (1893), and Finger print directory (1895). His identification system became the basis for the classification of Sir Edward R Henry, who later became chief commissioner of the London metropolitan police. The Galton-Henry system of fingerprint classification was published in June 1900, and began to be used at Scotland Yard in 1901 as an identifier on criminal records. It was soon used throughout the world in criminal investigations.

As well as being an indefatigable investigator of human intelligence, Galton made important contributions to the fields of meteorology, anthropometry, and physical anthropology. He published Meteorographica, or methods of mapping the weather in 1863. He created the term anticyclone and pointed out its importance in weather forecasting. Along with other important contributions made to meteorology, this led to him serving on the governing committee of the Meteorological Office.

Galton received many honours for his contributions, perhaps the most notable being that he was knighted in 1909 [4]:-

He was in his 89th year when the Prime Minister offered to submit his name to the King for a knighthood. With his usual modesty he accepted ...

He also received the Royal Medal from the Royal Society in 1876, the Darwin Medal of the same Society in 1902, and its Copley Medal in 1910. He was awarded the Huxley Medal from the Anthropological Institute in 1901 and the Darwin-Wallace Medal from the Linnean Society in 1908.

He played a major role in British science. In addition to the contributions mentioned above he was general secretary of the British Association from 1863 to 1867 and was sectional president on four occasions. He also served on the Kew committee of the Royal Society. His health began to limit the contributions he could make as he grew older [4]:-

His first sore trial was his deafness, which cut him off from scientific gatherings where at one time he was a familiar figure. ... After a time he lost the power of walking and had to exchange his daily constitutional for a bath chair, but no murmur of complaint escaped him. He dearly loved the fresh air and cared not how he got it, often sitting in his open balcony when most persons of his age would have crouched over the fire.