马哈拉诺比斯Prasanta Chandra Mahalanobis

马哈拉诺比斯 的父母是 Probodh 马哈拉诺比斯 和 Nirodbashini。Probodh 马哈拉诺比斯（1869-1942）曾在他父亲（Gurucharan（1833-1916））的药店工作了一段时间，之后自己创业，成为体育用品经销商。他于1891年与 Nandalal Sarkar 的女儿 Nirodbashini 结婚。这个家庭信奉梵天协会宗教，相对富裕，在孟加拉生活中颇具影响力。Probodh 马哈拉诺比斯 和 Nirodbashini 有两个儿子和四个女儿，最大的孩子是本传记的主人公 马哈拉诺比斯 马哈拉诺比斯。诗人 Rabindranath Tagore 在 马哈拉诺比斯 年幼时对他产生了重要影响。Rabindranath Tagore 的父亲 Devendranath Tagore 曾是 马哈拉诺比斯 的祖父 Gurucharan 的朋友，并在复兴梵天协会宗教方面发挥了重要作用 [26]：-

[马哈拉诺比斯 的] 分析性思维在很小的时候就显现出来，他喜欢与朋友甚至上级争论事情。甚至在很小的时候，他就受到了 Rabindranath Tagore 的影响，后者喜欢年轻的 马哈拉诺比斯，尤其对他将文学热爱与逻辑分析天赋相结合这一点印象深刻。

马哈拉诺比斯 在加尔各答的梵天 查尔斯·弗农·博伊斯 学校就读，于1908年，即他在该校的最后一年，通过了大学入学考试。1908年进入加尔各答管区学院，他的叔叔 Subodh 马哈拉诺比斯 是那里的生理学教授，马哈拉诺比斯 两年后通过了理科中级考试，并于1912年以物理学荣誉学士学位毕业。

1913年夏天，马哈拉诺比斯前往英国，打算在伦敦大学攻读理学学士学位。在伦敦等待课程开始时，他去了剑桥一趟，被国王学院教堂所震撼。偶然间，他错过了回伦敦的火车，便在一个朋友家过夜。在朋友家里，他遇到了一位在国王学院学习的学生，听说马哈拉诺比斯觉得那座教堂如此吸引人，便建议他申请到那里学习。令人惊讶的是，他第二天就接受了面试，并获得了入学名额。他于1913年10月在国王学院注册入学，并于1914年通过了数学荣誉学位考试第一部分。随后，他转入自然科学荣誉学位考试，于1915年在第二部分获得一等通过，并被国王学院授予高级奖学金。在剑桥期间，他与拉马努金成为了朋友。

在自然科学荣誉学位考试中，马哈拉诺比斯专攻物理学，并在卡文迪什实验室设立了一个研究项目。他于1915年7月返回印度，打算在开始研究项目之前短暂度假。然而，一回到印度，他的叔叔、加尔各答管区学院生理学教授Subodh 马哈拉诺比斯就把他介绍给了该学院院长，院长正试图填补物理系的一个临时空缺。此时第一次世界大战正在进行，管区学院的一位资深物理学家正在服兵役。当被问及是否愿意在该学院临时承担物理教学工作以帮忙时，马哈拉诺比斯同意了，但他仍然打算在临时职位结束后返回剑桥开展他的研究项目。然而，他很快就如此投入管区学院的工作，以至于放弃了返回剑桥的想法。

马哈拉诺比斯与统计学的结缘，如同他生活中的许多方面一样，源于一次偶然。就像他因错过火车而最终来到剑桥一样，这一次则是因为要在剑桥等待前往印度的船。船因第一次世界大战而延误，马哈拉诺比斯便在国王学院的图书馆里消磨时光。在那里，他翻阅了几卷Biometrika，被所读内容深深吸引，于是买下了一整套，带回印度[16]：-

他在旅途中开始在船上阅读这些卷册，抵达加尔各答后，又在业余时间继续自学并演算习题。他认识到统计学是一门与测量及其分析相关的新科学，因此具有广泛的应用前景。他试图寻找能够应用自己所学新知识的问题。幸运的是，他在气象学和人类学中发现了一些极其有趣的问题，并开始着手研究。这是他科学生涯的转折点。

这种对统计学的兴趣并未改变马哈拉诺比斯的职业道路，他于1922年被任命为管区学院的物理学教授。此后三十年，他继续在该学院教授物理学，但在此期间，他带来了深远的变化，影响了印度统计学的未来发展。然而，在我们详细介绍马哈拉诺比斯创建印度统计研究所之前，让我们注意到他娶了加尔各答城市学院院长的女儿尼尔玛尔库玛丽，她像马哈拉诺比斯一样，是梵社宗教的重要成员。这听起来像是理想的婚姻背景，但实际情况并非如此，因为梵社社群内部存在严重分歧。我们不会详述（更多信息见[1]或[16]或[26]），但只需说马哈拉诺比斯的观点代表了梵社年轻成员，他积极抨击当权派的观点，而尼尔玛尔库玛丽的父亲正是当权派的一员。婚礼于1923年2月27日举行，尽管尼尔玛尔库玛丽的父亲表示反对，拒绝在仪式中担任应有的角色。

在上面的引文中提到了“气象学和人类学中极其有趣的问题”，我们现在应该更仔细地看看这些。1920年，他参加了在纳格浦尔举行的印度科学大会，印度动物调查局局长找到他，问他是否有兴趣查看他收集的关于加尔各答混血种族的数据。马哈拉诺比斯确实感兴趣，他对数据的分析促成了他的第一篇科学论文Anthropological observations on the Anglo-Indians of Calcutta I Analysis of male stature（1922年）。这是一项卓越的工作，为此以及他后来进行的许多其他类似研究，他引入了$D^{2}$统计量，今天被称为“马哈拉诺比斯距离”。MathSciNet列出了144篇论文，其中马哈拉诺比斯距离发挥了重要作用，并在论文标题或评论中被提及。看到这篇论文后，天文台台长问马哈拉诺比斯是否有兴趣研究一些气象学问题。结果是三篇论文：On the seat of activity in the upper air（1923年）；On errors of observation and upper air relationships（1923年）；和Correlation of upper air variables（1923年）。他还在1923年发表了Statistical note on the significant character of local variation in proportion of dextral and sinistral shells in samples of the snail。这些是马哈拉诺比斯发表的200多篇论文中的第一批，涵盖了从农业到加尔各答中产阶级家庭饮茶等广泛主题。

也许马哈拉诺比斯除了他的科学论文之外，最重要的两项贡献是建立了印度统计研究所和创办了Sankhya期刊。我们现在简要地看一下这些。印度统计研究所大约在1920年起步，当时是一个非正式的团体，在管区学院研究统计问题。它很快就获得了统计实验室的名称，并设在马哈拉诺比斯在物理系的房间里。印度统计研究所的正式成立是在1931年12月17日，当时马哈拉诺比斯与管区学院的经济学教授和应用数学教授在实业家Rajendranath Mukherjee爵士的主持下会面，并通过了一项决议，正式成立印度统计研究所。它于1932年4月28日正式“根据1860年第二十一号社团注册法注册为一个非营利性学术团体”。基本上在整个20世纪20年代直到1931年，印度所做的几乎所有统计工作都是由马哈拉诺比斯完成的。然而，在建立印度统计研究所之后，作为所长和秘书，他能够通过新的任命来建设该研究所。例如，1932年12月，马哈拉诺比斯向钱德拉·鲍斯提供了印度统计研究所的一个兼职职位。兼职意味着全年每周六工作，并在夏季和Pujah假期全职工作。马哈拉诺比斯给了他一份要阅读的论文清单，他很快就成为了一位世界级的统计学家。从1935年起，钱德拉·鲍斯在印度统计研究所有了一个全职职位，Samarendra Nath Roy也是如此，他在钱德拉·鲍斯之后几个月被任命为兼职职位。统计培训课程被设立起来，例如亚木普迪‧拉达克利西纳‧劳在1940年开始了为期一年的统计培训课程。亚木普迪‧拉达克利西纳‧劳很快就开始了研究，接着在加尔各答大学攻读统计学学位，并从1943年11月开始被任命为印度统计研究所的技术学徒。他成为了统计学领域的世界领袖之一。

1948年，研究所从印度政府获得一笔巨额拨款，得以建立研究与培训学校，并任命教授、助理教授及其他学术职级。在马哈拉诺比斯的领导下，研究所蓬勃发展。1950年，他们在加尔各答B T路203号购买了约4英亩土地。随即在该地块上开始建设，主楼于1951年由罗纳德·费希尔揭幕。研究与培训学校随后迁入此楼。1959年，印度政府通过了《印度统计研究所法案》（1959年第57号法案）——以下是简短摘录：-

一项宣布名为印度统计研究所、目前注册办事处位于加尔各答的机构为国家重要机构，并规定相关事项的法案。……研究所可举行此类考试，并授予统计学、数学、定量经济学、计算机科学以及研究所不时确定的其他与统计学相关学科的学位和文凭。

马哈拉诺比斯的另一项重大成就是在1933年创办了统计学杂志Sankhya，作为印度统计研究所的出版物。我们引用马哈拉诺比斯在第一卷第一部分的社论：-

我们这些积极参与创办这份期刊的人之所以这样做，是因为我们对统计学的兴趣，以及我们相信一份致力于统计学的期刊在印度将是有用的。……《Sankhya》的精神和视野将是普世的，但其形式和内容在某种程度上必然是区域性的。我们将关注印度的特殊需求，但不会以任何方式限制期刊的范围。我们自然会更加密切地关注与印度有关的数据的收集和分析，但我们将努力把所有印度问题与世界问题联系起来研究。研究期刊服务于区分已知与未知的那片狭窄边缘地带，而未来发展的路线并不总是能够清晰地看到。因此，我们将邀请各种类型的论文，仅根据观察的准确性和逻辑推理来评价它们。我们将发表精心收集的统计材料，不论其主题如何，即使它们尚未经过任何分析处理。我们将特别关注统计学数学理论的发展，并收录在其他地方发表的重要论文的摘要和阐述。我们将努力通过联系印度不同地区的工作者，并提供交流思想的媒介，来帮助合作路线的统计研究。印度统计出版物的书目、有助于减少计算劳动的数值表、书评以及对当前主题的笔记和评论，是我们试图使《Sankhya》对印度统计工作者有用的几种方式。我们知道我们的资源有限，因此将寻求其他国家的指导与帮助，我们将欢迎并感激地接收来自国外的论文。现代统计方法的研究在我国尚处于起步阶段，我们并不期望能够立即取得成果。如果我们能够通过微薄的努力为未来的工作奠定基础，我们就心满意足了。

马哈拉诺比斯因其对统计学发展和印度生活的杰出贡献而获得了许多荣誉。例如，他获得了牛津大学的拉斐尔·韦尔登奖章和奖金（1944年）、Sir Deviprasad Sarvadhikari金质奖章（1957年）、Czech Academy of Sciences的金质奖章（1964年）以及亚洲学会的Durgaprasad Khaitan金质奖章（1968年）。他于1950年担任印度科学大会主席，并于1957年担任国际统计学会主席。他当选为许多学会和科学院的会士，例如：伦敦皇家学会（1945年）、美国计量经济学会（1951年）、巴基斯坦统计协会（1952年）、英国皇家统计学会（1954年）、USSR Academy of Sciences（1958年）和美国统计协会（1961年）。他获得了加尔各答大学（1957年）、索菲亚大学（1961年）和德里大学（1964年）的荣誉学位。1959年，他当选为剑桥大学国王学院荣誉会士。1968年，印度政府授予他莲花赐勋章：-

……表彰他对科学的贡献和对国家的服务。

为了结束这篇马哈拉诺比斯的传记，我们引用亚木普迪‧拉达克利西纳‧劳的文章[23]的第一段：-

这位教授，在印度被称为 马哈拉诺比斯，于1972年6月28日在加尔各答进行腹部手术三周后去世。去世之日距他79岁生日仅一天，当时他仍活跃于研究工作，作为名誉秘书和主任照管印度统计研究所，并作为名誉统计顾问协助政府。始于二十年代初的统计学的‘马哈拉诺比斯 时代’已经结束。的确，它将作为印度统计学的黄金时期而被永远铭记，其标志是新技术的深入发展及其为人类福祉的应用。

Prasanta Chandra Mahalanobis's parents were Probodh Chandra and Nirodbashini. Probodh Chandra (1869-1942) worked for a while in his father's (Gurucharan (1833-1916)) chemist's shop before starting up his own business as a dealer in sports goods. He married Nirodbashini, the daughter of Nandalal Sarkar, in 1891. The family were of the Brahmo Samaj religion, relatively wealthy and influential in Bengali life. Probodh Chandra and Nirodbashini had two sons and four daughters, the eldest child being Prasanta Chandra the subject of this biography. The poet Rabindranath Tagore was a significant influence on Mahalanobis when he was a young boy. Rabindranath Tagore's father, Devendranath Tagore, had been a friend of Mahalanobis's grandfather Gurucharan and had played a major role in reviving the Brahmo Samaj religion [26]:-

[Mahalanobis's] analytical turn of mind manifested itself at a very early age and he was given to arguing things out with his friends and even with his superiors. Even at a very early age he came under the influence of Rabindranath Tagore who took a liking to young Mahalanobis, being particularly impressed by the combination in him of a love of literature with a flair for logical analysis.

Mahalanobis attended the Brahmo Boys School in Calcutta, passing the matriculation examination in 1908, his final year at the school. Entering Presidency College, Calcutta in 1908, where his uncle Subodh Chandra Mahalanobis was professor of physiology, Mahalanobis passed the Intermediate Examination in science two years later and graduated with a B.Sc. with honours in physics in 1912.

In the summer of 1913 Mahalanobis went to England where his intention was to study for a B.Sc. at the University of London. While in London, waiting for courses to start, he made a trip to Cambridge where he was stunned by the chapel of King's College. By chance he missed the train back to London and stayed the night with a friend. In the friend's house he met a student who was studying at King's College and, hearing that Mahalanobis found the chapel so attractive, suggested he apply to study there. Remarkably, he was interviewed the next day and offered a place. He matriculated at King's College in October 1913 and passed Part I of the mathematical tripos in 1914. He then transferred to the natural sciences tripos, obtained a first class pass in Part II in 1915, and was awarded a Senior Scholarship by King's College. During his time in Cambridge, he became friendly with Srinivasa Ramanujan.

In the natural sciences tripos, Mahalanobis had specialised in physics and he set up a research project at the Cavendish Laboratory. He returned to India in July 1915 to take a short holiday before beginning his research project. However, once back in India his uncle, Subodh Chandra Mahalanobis the professor of physiology at Presidency College Calcutta, introduced him to the Principal of the College who was trying to fill a temporary vacancy in the physics department. By this time World War I was in progress and a senior physicist at Presidency College was on war service. Asked if he would take on a temporary teaching role in physics at the College to help out, Mahalanobis agreed but he was still intent on returning to Cambridge to undertake his research project once the temporary position ended. However, he soon became so involved with his work in Presidency College that he gave up the idea of returning to Cambridge.

Now Mahalanobis's involvement in statistics came about, as many aspects of his life did, through a chance happening. Like the way he ended up in Cambridge by missing a train, this time it was having to wait in Cambridge for the boat journey to India. The boat was delayed due to World War I, and Mahalanobis put off time in the library of King's College. There he looked at some volumes of Biometrika and, being fascinated by what he read, bought a complete set of volumes and took them back to India with him [16]:-

He started reading the volumes on the boat during the journey, and continued to study and work out exercises on his own during spare time after arrival in Calcutta. He saw that statistics was a new science connected with measurements and their analysis, and as such capable of wide application. He tried to look for problems where he could apply the new knowledge he was acquiring. Fortunately, he found some extremely interesting problems in meteorology and anthropology, and started working on them. This was the turning point in his scientific career.

This interest in statistics did not change the career path of Mahalanobis who was appointed as Professor of Physics at Presidency College in 1922. He continued to teach physics at the College for the next thirty years but during this time he brought about profound changes which influenced the future development of statistics in India. However, before we give some details of the setting up of the Indian Statistical Institute by Mahalanobis, let us note that he married Nirmalkumari, the daughter of the Principal of City College, Calcutta, and, like Mahalanobis, an important member of the Brahmo Samaj religion. This sounds like the ideal backgrounds for a marriage but this was not quite the case since there were serious arguments within the Brahmo Samaj community. We will not go into details (see [1] or [16] or [26] for more information) but suffice it to say that Mahalanobis's views were representative of the younger members of the Brahmo Samaj and he was prominent in attacking the views of the establishment, of which Nirmalkumari's father was a part. The wedding took place on 27 February 1923 although Nirmalkumari's father showed his disapproval but refusing to take his proper role in the ceremony.

In the quote above 'extremely interesting problems in meteorology and anthropology' are mentioned and we should now look at these more closely. In 1920 he attended the Indian Science Congress in Nagpur and was approached by the Director of the Zoological Survey of India asking if he would be interested in looking at data he had collected concerning mixed race people in Calcutta. Mahalanobis was indeed interested, and his analysis of the data led to his first scientific paper Anthropological observations on the Anglo-Indians of Calcutta I Analysis of male stature (1922). This is a remarkable piece of work and for this, and many other similar investigations he carried out later, he introduced the $D^{2}$ statistic, known today as the 'Mahalanobis distance'. MathSciNet lists 144 papers in which the Mahalanobis distance plays a significant role and is mentioned in the title or review of the paper. As a result of seeing this paper, the Director General of Observatories asked Mahalanobis if he would be interested in examining some meteorology problems. The result was three papers: On the seat of activity in the upper air (1923); On errors of observation and upper air relationships (1923); and Correlation of upper air variables (1923). He also published Statistical note on the significant character of local variation in proportion of dextral and sinistral shells in samples of the snail in 1923. These were the first of over 200 papers which Mahalanobis published covering a vast range of topics from agriculture to drinking tea among middle class Indian families in Calcutta.

Perhaps the two most important contributions by Mahalanobis, other than his scientific papers, were setting up the Indian Statistical Institute and the founding of the journal Sankhya. We now look briefly at these. The Indian Statistical Institute began life in around 1920 as an unofficial group working on statistical problems in Presidency College. It soon acquired the name of the Statistical Laboratory and was located in Mahalanobis's room in the Physics Department. The official setting up of the Indian Statistical Institute was on 17 December 1931 when Mahalanobis, together with the Professor of Economics and the Professor of Applied Mathematics at Presidency College met under the chairmanship of the industrialist Sir Rajendranath Mukherjee and passed a resolution formally setting up the Indian Statistical Institute. It was formally "registered on 28 April 1932 as a non-profit distributing learned society under the Societies Registration Act XXI of 1860". Basically through the 1920s and up to 1931 almost all statistical work done in India was by Mahalanobis. However, after setting up the Indian Statistical Institute, as Director and Secretary he could build up the Institute with new appointments. For example, in December 1932 Mahalanobis offered R C Bose a part-time post at the Indian Statistical Institute. Part-time meant working on Saturdays throughout the year and full-time during the summer and Pujah vacations. Mahalanobis gave him a list of papers to read and he soon became a world-class statistician. From 1935 Bose had a full-time position at the Indian Statistical Institute as did Samarendra Nath Roy who had been appointed to a part-time post a few months after Bose. Training courses in statistics were set up, for example C R Rao began the one-year training course in statistics in 1940. Rao was soon undertaking research, went on the take a statistics degree at Calcutta University, and was appointed as a Technical Apprentice at the Indian Statistical Institute beginning in November 1943. He became one of world leaders in statistics.

In 1948 the Institute received a major grant from the Indian government allowing them to set up a Research and Training School and appoint professors, assistant professors and other academic grades. Under Mahalanobis's leadership the Institute flourished. In 1950 they purchased about 4 acres of land at 203, B T Road, Calcutta. Immediately building began on the site and the Main Building was inaugurated by R A Fisher in 1951. The Research and Training School was subsequently moved to this building. In 1959, the Indian government passed the India Statistical Institute Act (the 57th Act of 1959) - here is a short extract:-

An Act to declare the institution known as the Indian Statistical Institute having at present its registered office in Calcutta to be an institution of national importance and to provide for certain matters connected therewith. ... the Institute may hold such examinations and grant such degrees and diplomas in statistics, mathematics, quantitative economics, computer science and such other subject related to statistics as may be determined by the Institute from time to time.

The other major achievement of Mahalanobis was the founding of the statistics journal Sankhya in 1933 as a publication of the Indian Statistical Institute. We quote from Mahalanobis's editorial in the first part of the first volume:-

Those of us who are actively engaged in starting this journal are doing so because of our interest in statistics and our belief that a journal devoted to statistics will be useful in India. ... The spirit and outlook of 'Sankhya' will be universal, but its form and content must necessarily be, to some extent, regional. We shall keep the special needs of India in view without, however, restricting the scope of the journal in any way. We shall naturally devote closer attention to the collection and analysis of data relating to India, but we shall try to study all Indian questions in relation to world problems. A research journal serves that narrow borderland which separates the known from the unknown, and it is not always possible to see clearly the lines of future developments. We shall, therefore, invite papers of all kinds appraising them only on the basis of observational accuracy and logical reasoning. We shall publish carefully collected statistical materials irrespective of the subject even if they have not received any analytic treatment. We shall pay special attention to developments of the mathematical theory of statistics, and include abstracts and expositions of important papers published elsewhere. We shall try to help statistical researches on co-operative lines by bringing workers in different parts of India in contact, and by providing a medium for exchange of ideas. Bibliographies of Indian statistical publications, numerical tables tending to reduce the labour of computation, book reviews, and notes and comments on current topics are some of the ways in which we shall try to make 'Sankhya' useful to statistical workers in India. Knowing that our resources are small we shall seek guidance and help from other countries, and we shall welcome and thankfully receive papers from abroad. The study of modern statistical methods in its infancy in our country, and we do not expect to be able to achieve immediate results. We shall be satisfied if we can help by our humble efforts to lay the foundations for future work.

Mahalanobis received many honours for his remarkable contributions to the development of statistics and to life in India. For example he was awarded the Weldon Medal and prize from Oxford University (1944), the Sir Deviprasad Sarvadhikari Gold Medal (1957), the Gold Medal from the Czech Academy of Sciences (1964), and the Durgaprasad Khaitan Gold Medal from the Asiatic Society (1968). He was President of the Indian Science Congress in 1950 and President of the International Statistical Institute in 1957. He was elected a fellow of many societies and academies such as: the Royal Society of London (1945), the Econometric Society, United States (1951), the Pakistan Statistical Association (1952), the Royal Statistical Society, U.K. (1954), the USSR Academy of Sciences (1958), and the American Statistical Association (1961). He received honorary degrees from the University of Calcutta (1957), Sofia University (1961) and the University of Delhi (1964). In 1959 he was elected an Honorary Fellow of King's College, Cambridge. In 1968 the Government of India awarded him the Padma Vibhushan:-

... for his contribution to science and services to the country.

To end this biography of Mahalanobis, we quote the first paragraph of C R Rao's article [23]:-

The Professor, as Prasanta Chandra Mahalanobis was known in India, passed away on 28 June 1972, three weeks after an abdominal operation in Calcutta. The death occurred one day before his 79th birthday, when he was still active doing his research work, looking after the Indian Statistical Institute as Honorary Secretary and Director and helping the Government as Honorary Statistical Adviser. The 'Mahalanobis Era' in statistics which started in the early twenties has ended. Indeed it will be remembered for all time to come as the golden period of statistics in India, marked by intensive development of a new technology and its applications for the welfare of mankind.