阿道夫·凯特勒Adolphe Quetelet

阿道夫·凯特勒的母亲是Anne-Françoise Vandervelde，父亲是François-Augustin-Jacques-Henri 凯特勒。凯特勒的父亲出生在皮卡第的Ham，但曾在英国生活过一段时间，成为英国公民，在那里他成为一位苏格兰贵族的秘书。在这个职位上，他与雇主一起在欧洲大陆旅行，特别是在意大利度过了一段时间。1787年，大约31岁时，他定居在根特，并受雇于该市。他于1803年去世，当时凯特勒只有七岁，因此在根特就读中学后，他感到必须找一份工作来养家。他在中学时就表现出是一位非常有才华的数学家，所以尽管他被文学所吸引，还是在1813年成为Audenaerde一所学校的数学教师。他在那里任教，直到1815年2月被任命为根特学院的数学讲师。

当德兰比凯特勒大两岁，但两人在中学学习时成为了朋友。两人都对数学、文学和音乐感兴趣。当德兰随后去了巴黎学习，曾为拿破仑作战，但在拿破仑于滑铁卢战败后返回比利时。他随后与在根特学院任教的凯特勒重续友谊。这两位朋友为一部歌剧创作了剧本，在成功演出后，又写了更多的戏剧。然而，凯特勒在根特学院的时光并非全都花在文学追求上，因为他受到了Garnier的影响，Garnier是天文和高等数学教授。正是Garnier阻止了凯特勒对艺术日益增长的兴趣，并使他热衷于在数学方面进行更深入的研究。

荷兰国王兼卢森堡大公（当时包括比利时）威廉一世于1817年在根特创办了一所国立大学；该大学于当年10月开学。凯特勒于1819年在根特获得他的第一个博士学位，学位论文是关于conic sections理论的。获得该博士学位后，他被任命为布鲁塞尔雅典学院初等数学讲席。1820年2月，他当选为比利时皇家科学院院士，并在随后的几年里极大地振兴了该科学院。1823年12月，他前往巴黎，在巴黎天文台学习天文学。他从弗朗索瓦·阿拉戈和亚历克西·布瓦尔那里学习天文学，并在约瑟夫·傅里叶和皮埃尔·西蒙·拉普拉斯指导下学习theory of probability。他还结识了西莫恩·德尼·泊松、冯·洪堡和奥古斯丁·菲涅耳。回到布鲁塞尔后，他成为雅典学院高等数学教授。他在1824-25学年首次讲授概率论课程。他还开始在布鲁塞尔的博物馆就几何、概率、物理和天文学等主题进行公开讲座。他还开始讲授科学史课程。这些讲座于1828年以Instructions populaires sur le calcul des probabilitésⓉ（《概率计算通俗教程》）为标题出版。我们现在从这些讲座中给出四段引文：-

1. The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of centre towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation。
2. It seems to me that the theory of probabilities ought to serve as the basis for the study of all the sciences, and particularly of the sciences of observation。
3. Since absolute certainty is impossible, and we can speak only of the probability of the fulfilment of a scientific expectation, a study of this theory should be a part of very man's education。
4. Chance, that mysterious, much abused word, should be considered only a veil for our ignorance; it is a phantom which exercises the most absolute empire over the common mind, accustomed to consider events only as isolated, but which is reduced to naught before the philosopher, whose eye embraces a long series of events and whose penetration is not led astray by variations, which disappear when he gives himself sufficient perspective to seize the laws of nature。

1825年，凯特勒与法国医生M·库尔泰的女儿结婚；他们有一个儿子欧内斯特和一个女儿。欧内斯特成为一位有成就的天文学家，并最终接替父亲担任布鲁塞尔天文台台长。凯特勒热爱音乐，是一位不错的音乐家；然而他的妻子是一位出色的音乐家。在每周六和周日的晚宴之后，他们会在家里用音乐款待客人。

凯特勒曾由国家出资派往巴黎，以便获得实用天文学方面的经验。长期以来，他一直敦促建立一座比利时天文台，但该项目进展相当缓慢。1827年，在国王的指示下，凯特勒受命为天文台选择仪器。他与当德兰一起前往伦敦，并从那里访问了英格兰、苏格兰和爱尔兰的大学、天文台和学术团体，寻求建议。1829年，这次由妻子陪同，他又访问了荷兰和德国的天文学家，并熟悉了所有德国天文台。接着，他于1830年访问了意大利和西西里，以进一步了解天文台和学会的运作方式。1832年，他成为新落成的天文台的台长。

从这时起，凯特勒 就住在天文台，在那里他研究统计、地球物理和气象数据，研究流星雨，并建立了比较和评估数据的方法。1825年至1835年间，他撰写了关于社会统计的论文。在这一时期写成的 Recherches sur le Penchant au Crime aux Différens Âges Ⓣ（《对不同年龄犯罪倾向的研究》）中，他写道：-

在我看来，就人类整体而言，所涉及的事情属于物理事实的范畴：个体数量越多，个人意志的影响就越被抹去，而被一系列一般事实所取代，这些一般事实取决于社会赖以存在和维持自身的一般原因。这些就是我们试图把握的原因，而当我们确实知道它们时，我们就能够确定它们在社会事务中的结果，正如我们在物理科学中从原因确定结果一样。

1835年，他出版了 Sur l'homme et le developpement de ses facultés, essai d'une physique sociale Ⓣ（《论人及其能力的发展：社会物理学尝试》），从而赢得了世界性的声誉。这部著作的意义在[1]中有所讨论：-

凯特勒 1835年的著作开启了统计学的新时代。它提出了一种新的统计技术，或者更确切地说，是第一种统计技术。材料经过深思熟虑的加工，按照某些预先确立的原则加以安排，并使之可以比较。书中没有很多统计数字，但所报告的每一个数字都有意义。对于每一个数字，凯特勒 都试图找出决定性的影响、其自然原因以及人为造成的扰动。这部著作把平均人描述为一种静态现象和动态现象。

受 皮埃尔·西蒙·拉普拉斯 和 约瑟夫·傅里叶 的影响，凯特勒 是第一个把正态曲线用于误差定律之外的人。在 Sur l'homme et le developpement de ses facultés, essai d'une physique sociale Ⓣ（《论人及其能力的发展：社会物理学尝试》）中，他提出了他的平均人概念，即平均人是人类某一性状的测量值据以按正态曲线分组的中心值。他对犯罪数字一致性的研究，激发了对自由意志与社会决定论的广泛讨论。你可以读到 Sur l'homme 的一段摘录，其中是他从1826年至1831年间法国刑事法庭收集的统计资料中得出的结论。

更多细节见凯特勒在THIS LINK上关于犯罪的摘录。

他为政府收集并分析了关于犯罪、死亡率等的统计资料，并设计了人口普查方法的改进。他的工作引起了19世纪社会科学家的极大争议。下面引自1848年一份出版物的文字表明，凯特勒 非常清楚自己在测量什么：-

这一概率可以被视为在城市中给出了25至30岁比利时人表面婚姻倾向的度量。我说表面倾向是有意为之，以避免与真实倾向混淆，后者可能完全不同。一个人可能一生都有真实的结婚倾向却从未结婚；相反，另一个人可能被偶然情况所驱使，在几乎没有结婚倾向的情况下结了婚。这一区分至关重要。

Royal Belgium Academy于1769年在布鲁塞尔成立，最初是一个纯文学科学院，但在1816年在荷兰的威廉一世的赞助下改组为皇家科学与文学科学院。凯特勒于1820年当选为比利时科学院成员，并在使其成为一个活跃有力的组织方面发挥了重要作用。他于1832年至1833年担任院长，随后成为科学院秘书，这一职务他一直担任到四十年后去世。他不仅对学会的科学方面感兴趣，还在艺术方面发挥了重要作用。在担任院长期间，他试图引入一个新的美术类别，但未能成功。他最终在1832年成功了。Hankins在[4]中写道：-

失败后，他满足于协助组织艺术与文学圈，并曾一度担任其院长。作为科学院秘书，他总是迅速而勤勉地履行职责。

凯特勒于1853年组织了第一次国际统计会议[4]：-

……凯特勒被选为主席，在开幕致辞中，他详细阐述了官方统计出版物在计划、目的和术语方面国际统一的好处。大会取得了决定性成功，随后又举行了其他会议。大会对统计学的理论和实践产生了巨大影响。

1855年夏天，凯特勒遭受了一次疾病打击，一次中等严重程度的中风。他的身体恢复良好，但精神上再也不如从前敏锐，记忆力也变得很差。尽管此后他仍写文章，但写作质量很差，必须经过大幅修改才能让人理解。

至于他的性格，[4]中给出的描述当然是指1855年他生病之前的那段时间：-

他谦逊而慷慨，对自己的信念坚定不移，又尊重他人的意见，总是沉着而体贴，学识广博，谈吐迷人，无论走到哪里都能赢得并保持友谊。他为人极有分寸，同时又热情洋溢……他智力兴趣广泛，同时又具有惊人的工作能力……总是生气勃勃、和蔼可亲，喜欢诙谐和欢笑。

为了结束这篇关于凯特勒的简述，让我们引用在他葬礼上的一段讲话：-

作为科学人，他受人钦佩；在政治事务中，他受人尊重；在私人生活中，他受人爱戴。

作为脚注，让我们提一下，国际上使用的肥胖衡量标准是Body Mass Index或Quetelet Index。这就是

QI =（体重，千克）/（身高，米）$^{2}$。

如果QI > 30，那么此人即被正式认定为肥胖。

要计算你的凯特勒指数，请点击THIS LINK。

Adolphe Quetelet's mother was Anne-Françoise Vandervelde and his father was François-Augustin-Jacques-Henri Quetelet. Adolphe's father had been born in Ham in Picardy but lived for a time in Britain, becoming a British citizen, where he became the secretary of a Scottish nobleman. In this capacity he travelled with his employer on the Continent, particularly spending time in Italy. In 1787, at age about 31, he settled in Ghent and he was employed by the city. He died in 1803 when Adolphe was only seven years old so after attending the Lyceum in Ghent, he felt he had to take a job to support his family. He had shown himself to be a very talented mathematician at the Lyceum, so despite being attracted by literature, he became a mathematics teacher at a school in Audenaerde in 1813. He taught there until he was appointed as an instructor in mathematics at the College of Ghent in February 1815.

Germinal Dandelin was two years older than Quetelet but the two became friends while they studied at the Lyceum. Both were interested in mathematics, literature and music. Dandelin had then gone to Paris to study, had fought for Napoleon but returned to Belgium after Napoleon's defeat at Waterloo. He then renewed his friendship with Quetelet who was teaching at the College of Ghent. The two friends composed a libretto for an opera and after it was successfully performed, wrote to further dramas. Quetelet's time at the College of Ghent was not all spent on literary pursuits, however, for he came under the influence of Garnier, the professor of astronomy and higher mathematics. It was Garnier who halted Quetelet's growing involvement in the arts, and made him become enthusiastic to undertake deeper studies in mathematics.

William I, king of The Netherlands and grand duke of Luxembourg (which included Belgium at that time), founded a state university in Ghent in 1817; the university opened in October of that year. Quetelet received his first doctorate in 1819 from Ghent for a dissertation on the theory of conic sections. After receiving this doctorate he was appointed to the chair of elementary mathematics at the Athenaeum in Brussels. In February 1820 he was elected to the Royal Belgium Academy of Science and greatly invigorated the Academy over the following years. In December 1823, he went to Paris to study astronomy at the Observatory there. He learnt astronomy from Arago and Bouvard and the theory of probability under Joseph Fourier and Pierre Laplace. He also met Poisson, von Humboldt and Fresnel. Returning to Brussels, he became professor of higher mathematics at the Athenaeum. He gave his first course on probability in the academic year 1824-25. He also began to give public lectures at the Museum in Brussels on topics such as geometry, probability, physics, and astronomy. He also began to give courses on the history of science. These lectures were published in 1828 under the title Instructions populaires sur le calcul des probabilités Ⓣ. We now give four quotes from these lectures:-

1. The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of centre towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.
2. It seems to me that the theory of probabilities ought to serve as the basis for the study of all the sciences, and particularly of the sciences of observation.
3. Since absolute certainty is impossible, and we can speak only of the probability of the fulfilment of a scientific expectation, a study of this theory should be a part of very man's education.
4. Chance, that mysterious, much abused word, should be considered only a veil for our ignorance; it is a phantom which exercises the most absolute empire over the common mind, accustomed to consider events only as isolated, but which is reduced to naught before the philosopher, whose eye embraces a long series of events and whose penetration is not led astray by variations, which disappear when he gives himself sufficient perspective to seize the laws of nature.

In 1825 Quetelet married the daughter of the French physician M Curtet; they had one son, Ernest, and one daughter. Ernest became an accomplished astronomer, and eventually took over his father's role as Director of the Brussels Observatory. Quetelet loved music and was a reasonable musician; his wife, however, was an excellent musician. They would entertain guests at their home with music after their regular Saturday and Sunday dinner parties.

Quetelet had been sent to Paris at the expense of the state in order that he could gain experience in practical astronomy. For a long time he had been pressing for a Belgium observatory to be set up, but the project progressed rather slowly. In 1827, on the direction of the King, Quetelet was given the task of choosing instruments for the observatory. Together with Dandelin, he went to London and from there visited universities, observatories and learned societies in England, Scotland, and Ireland seeking advice. Again in 1829, this time accompanied by his wife, he visited astronomers in Holland and Germany, and became familiar with all German observatories. Next he visited Italy and Sicily in 1830 to learn more of the workings of observatories and societies. In 1832 he became director of the newly opened Observatory.

From this time on, Quetelet lived at the Observatory where he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. Between 1825 and 1835 he wrote papers on social statistics. In Recherches sur le Penchant au Crime aux Différens Âges Ⓣ written during this period, he wrote:-

It seems to me that that which relates to the human species, considered en masse, is of the order of physical facts: the greater the number of individuals, the more the influence of the individual will is effaced, being replaced by the series of general facts that depend on the general causes according to which society exists and maintains itself. These are the causes we seek to grasp, and when we do know them, we shall be able to ascertain their effects in social matters, just as we ascertain effects from causes in the physical sciences.

He gained world-wide fame in 1835 when he published Sur l'homme et le developpement de ses facultés, essai d'une physique sociale Ⓣ. The significance of this work is discussed in [1]:-

With Quetelet's work of 1835 a new era in statistics began. It presented a new technique of statistics, or, rather, the first technique at all. The material was thoughtfully elaborated, arranged according to certain pre-established principles, and made comparable. There were not very many statistical figures in the book, but each figure reported made sense. For every number, Quetelet tried to find the determining influences, its natural causes, and the perturbations caused by man. The work gave a description of the average man as both a static and dynamic phenomenon.

Influenced by Laplace and Fourier, Quetelet was the first to use the normal curve other than as an error law. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale Ⓣ he presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. His studies of the numerical consistency of crimes stimulated wide discussion of free will versus social determinism. You can read an extract from Sur l'homme on the conclusions he drew from statistics gathered from the French criminal courts between 1826 and 1831.

More details are given in the extract of Quetelet on crime at THIS LINK.

For his government he collected and analysed statistics on crime, mortality etc. and devised improvements in census taking. His work produced great controversy among social scientists of the 19th century. The following quotation from a 1848 publication shows that Quetelet understood quite well what he was measuring:-

This probability may be considered as giving, in cities, the measure of the apparent tendency to marriage of a Belgian aged 25 to 30. I say apparent tendency intentionally, to avoid confusion with the real tendency, which may be quite different. One man may have, throughout his life, a real tendency to marry without ever marrying; another, on the contrary, carried along by fortuitous circumstances, may marry without having the least propensity to marriage. The distinction is essential.

The Royal Belgium Academy was founded in Brussels in 1769 as a purely literary academy but in 1816 it was reorganised into the Académie royale des sciences et belles-lettres under the patronage of William I of The Netherlands. Quetelet was elected to the Belgium Academy in 1820 and played a large role in making it an active vigorous organisation. He was director from 1832 to 1833, then became secretary of the Academy, a role he continued to hold until his death forty years later. Not only was he interested in the scientific side of the society, but he also played a large role in the arts side. While president, he tried to introduce a new class of Beaux-Arts but failed. He eventually succeeded in 1832. Hankins writes in [4]:-

Having failed he contented himself with assisting in the organisation of the Cercle artistique et littéraire, of which he was for some time the president. As secretary of the Academy he was always prompt and painstaking in fulfilling his duties.

Quetelet organised the first international statistics conference in 1853 [4]:-

... Quetelet was chosen president, and in his opening address he dwelt upon the advantages of international uniformity in plans, purposes and terminology of the official statistical publications. The Congress was a decided success and other sessions followed. The influence of the Congress on both the theory and practice of statistics was immense.

In the summer of 1855 Quetelet was struck by an illness, a stroke of moderate severity. He made a good physical recovery but mentally he was never as sharp again and his memory became poor. Although he wrote articles after this his writing was poor and had to be corrected very substantially before it was understandable.

As to his character, the description given in [4] relates, of course, to the time before his illness of 1855:-

Modest and generous, convinced but respectful of other' opinions, always calm and considerate, a man of broad learning and an attractive conversationalist, he won and kept friends wherever he went. A man of excellent tact, as well as tremendous enthusiasm ... A man of wide intellectual interests, and at the same time endowed with a prodigious capacity for labour ... always animated and genial, found of wit and laughter.

To finish this sketch of Quetelet let us quote from a speech given at his funeral:-

As a man of science he was admired; in political affairs he was respected; in private life he was beloved.

As a footnote let us mention that the internationally used measure of obesity is the Body Mass Index or Quetelet Index. This is

QI = (weight in kilograms)/(height in metres)$^{2}$.

If QI > 30 then a person is officially obese.

To calculate your Quetelet index click THIS LINK.