约翰·图基John Tukey

约翰·图基的父母Ralph H 图基和Adah M 图基认识到，弗瑞兹·约翰还只是个孩子时就具有巨大潜力，因此他们安排他在家里而不是在学校接受教育。这是可能的，因为他的父母本身就是受过古典学训练的中学教师。事实上，是约翰的母亲Adah承担了儿子的大部分教学，因为作为一名已婚妇女，她当时在马萨诸塞州被禁止担任全职教师。这种教育对约翰的一生影响很大[17]：-

他们的教育方法是，对约翰的提问通过提供线索和进一步提问来回应，而不是给出直接答案，这是约翰继承并在整个职业生涯中使用的特点。

约翰还受益于新贝德福德一个出色的公共图书馆，该图书馆甚至藏有Journal of the American Chemical Society和Transactions of the American Mathematical Society等期刊。因此，他能够在进入大学之前将教育提升到高水平。他的正规教育始于进入罗德岛州普罗维登斯的布朗大学学习数学和化学。

1936年，布朗大学授予他化学学士学位，次年又授予他化学硕士学位。之后，图基于1937年前往普林斯顿大学，打算攻读化学博士学位。事实上，他在第一年同时学习数学和化学，但令他失望的是，普林斯顿不允许他像在布朗大学那样担任化学实验室助理。在这一年的某个时候，他顺利地从化学转向数学，并于1938年参加了数学的博士资格考试。图基的研究由所罗门·莱夫谢茨指导，他于1939年获得博士学位，学位论文为Denumerability in topology，该论文于1940年以Convergence and uniformity in topology为题出版。在获得博士学位之前，他已经发表了三篇论文，毕业后，他被任命为普林斯顿的讲师。

外部事件在图基的职业生涯方向上发挥了重要作用，主要是因为他加入了火控研究办公室，为战争努力做出贡献。这个名称可能会让现代读者困惑，因为该研究处理的不是燃烧意义上的“火”，而是火炮研究意义上的“火”。这里的工作涉及统计学，图基很快发现这项工作非常合他的心意[17]：-

那里的主要问题是数学问题，涉及弹道学、火炮与炮兵控制、测距、计算移动目标提前量等等。……有迹象表明他可能参与了密码破译。

普林斯顿还有其他统计学家也在为战争出力，特别是塞缪尔·S·威尔克斯和威廉·格梅尔·科克伦，图基很快就开始与这些人交流想法。

1945年第二次世界大战结束时，塞缪尔·S·威尔克斯此时已充分了解图基非凡的统计才能，便给他提供了一个普林斯顿数学系内的统计学职位。然而，一个职位不足以消耗他的精力，同样在1945年，图基加入了AT&T贝尔实验室，他的同事包括沃特·阿曼德·休哈特、理查德·卫斯里·汉明和克劳德·香农。他还花了大量时间在华盛顿处理政府事务。只有像图基这样的工作狂才能在所有这些三项活动中发挥如此重要的作用。

1950年，图基与Elizabeth Louise Rapp结婚，婚后她以古董商为业。他们没有孩子，但Elizabeth的妹妹Phyllis嫁给了Frank Anscombe，他也是一位统计学家，有时与图基合作。Phyllis和Frank有四个孩子，他们经常造访图基家。Thompson写道[21]：-

图基开创了统计学的新时代。他质疑Fisher关于规则不确定性的假设，并让我们洞见现实世界的不规则性。他毕生的工作主要在于发现如何收集和分析数据。在自身学习的过程中，他乐于教我们如何应对这样一个世界：其中不仅有不确定性，而且还有关于不确定性的不确定性。作为一对学术伉俪，约翰和Elizabeth Tukey在智慧与善良方面达到了最高标准。

图基对统计学的第一个重大贡献是引入了估计时间序列谱的现代技术。E J Hannan在评述图基关于这一主题的论文时写道：-

它们展现出一种显著一致的态度，其特征是：对情境复杂性的现实认识，由此对渐近理论的不信任，将标准统计技术用作基准而非（比如说）精确置信区间，对假设的持续质疑，对计算方面的强调，对展示分析方式的强调，这种展示采用主要使用者熟悉的方式，而非数学处理中采用的方式，早期认识到数字设备在通用目的上（相较于模拟设备）的优越品质，以及对新词新语的显著迷恋，其中一些已成为固定用语。当然，还有新方法的引入，其中一些已被证明是重要的。这些包括估计谱的方法、高阶矩谱、复解调、确定经过一个（或多或少）固定线性系统传输后观察到的初始脉冲的幅度和符号的方法，以及对谱估计取对数以辨别回声的傅里叶分析。

图基在1962年发表的论文The future of data analysis的引言中，以他思考其主题的方式描述了他的发展：-

长期以来，我一直认为自己是一名统计学家，对从特殊到一般的推断感兴趣。但当我目睹数理统计的演变时，我有理由感到惊奇和怀疑。而当我思考为什么诸如时间序列的谱分析这样的技术被证明如此有用时，就变得清楚了：在许多情况下，它们“处理波动”的方面，不如那些为了有效处理非常广泛的数据（此时波动已不再是问题）这一更简单情形所已经需要的方面重要。总而言之，我开始感到我的核心兴趣在于数据分析……

1965年，在与J W Cooley合著、发表于Mathematics of Computation的一篇论文中，他引入了重要的快速约瑟夫·傅里叶变换算法。对许多人来说，这将是其最为人所知的工作。然而，这只是他做出重大贡献的众多领域中的一小部分。A D Gordon将他在统计学与研究哲学方面的工作总结为包括以下主题：-

……数理统计的用处与局限；拥有对违反其使用假设具有稳健性的统计分析方法的重要性；积累具体分析方法行为经验以便为其使用提供指导的必要性；允许数据影响分析方法选择的可能性之重要性；统计学家需要拒绝“已被证明的真理的守护者”这一角色，并抵制提供一劳永逸的解决方案以及对该主题进行整齐过度统一的尝试；数据分析的迭代性质；计算设施日益增强的能力、可获得性和廉价性的影响；统计学家的培训。

图基的整个职业生涯都在普林斯顿度过。1956年新成立的统计研究小组成立时，他成为其主任。1965年普林斯顿成立统计系时，他是首任系主任，担任该职位四年。在AT&T贝尔实验室，图基参与了电子计算机的开发。自1952年AT&T成立统计与数据分析部以来，他一直在该部担任高级职位。

图基还在方差分析以及从单次实验中对一组参数值进行同时推断的问题上做出了重大贡献。他的许多论文是与他人合写的，其中一位合著者菲德里克·莫斯提勒在[2]中写道：-

约翰喜欢与他人合作，许多人都有幸参与到他天才的工作中。他的成就以多样性和广度著称。他在大规模和小规模问题上、在实践和理论问题上都取得了成功。……他总是乐于回应新问题，并慷慨地奉献自己的时间和想法。

图基的讲课风格很不寻常。McCullagh在17中描述了图基1977年在伦敦帝国理工学院的一次讲课：——

图基缓步走向讲台，他是个身材魁梧的大汉，穿着宽松的裤子和黑色针织衫。这两件衣服也许曾经是一套，但年代久远，已难以分辨。……一份标题清单被仔细而从容地用粉笔写在黑板上。话也随之而来，不多，像超重的包裹，以缓慢而坚定的节奏送出。……写完后，图基转身面对听众和讲台……“评论、疑问、建议？”他问听众……在等待回应时，他爬上讲台，挪动身体，直到盘腿坐着面对听众。……我们听众坐在那里，像动物园里的观众等着那头大熊动一动或说点什么。但大熊似乎也在做同样的事，这种感觉并不舒服。

McCullagh认为：——

……图基喜欢按自己的方式玩游戏，让人们自己去弄明白他已经知道的事情。最重要的是，他喜欢争论中的你来我往，但他也期望自己的观点占上风，而通常也确实如此。

图基因其杰出贡献获得了许多荣誉。这些包括1965年美国统计协会颁发的S S 塞缪尔·S·威尔克斯奖、1973年美国国家科学奖章以及1982年电子与电气工程师学会的荣誉奖章。

他很少有时间花在应用科学专长之外的兴趣上，但他喜欢读科幻小说和推理小说。他的工作把他带入了许多意想不到的领域，如铀浓缩、参与U2间谍飞机的研制，他还于1959年在日内瓦代表美国参加核裁军会议。此外，他还在许多小组中任职，就环境和人口普查等问题提出报告。

John Tukey's parents, Ralph H Tukey and Adah M Tukey, recognised that John had great potential while he was still only a child, so they arranged for him to be educated at home rather than in school. This was possible since his parents were themselves secondary school teachers who were trained in classics. In fact it was John's mother Adah who undertook most of the teaching of her son since, as a married woman, she was prohibited from working as a full-time teacher in Massachusetts at that time. It was an education which greatly influenced John throughout his life [17]:-

Their educational method was to respond to John's queries by providing clues and asking further questions rather than giving a direct answer, a characteristic that John inherited and used throughout his career.

John also had the benefit of an excellent public library in New Bedford which even possessed journals such as the Journal of the American Chemical Society and the Transactions of the American Mathematical Society. He was able therefore to take his education to a high level before entering university. His formal education began only when he entered Brown University in Providence, Rhode Island, to study mathematics and chemistry.

After Brown University awarded him a Bachelor's Degree in chemistry in 1936 and a Master's Degree in chemistry in the following year, Tukey went to Princeton University in 1937 intending to study for his doctorate in chemistry. In fact he studied both mathematics and chemistry in his first year but was disappointed to find that Princeton did not allow him to act as a chemistry laboratory assistant as he had done at Brown. At some time during this year he made a smooth transition from chemistry to mathematics and took the PhD qualifying examinations in mathematics in 1938. Tukey's research was supervised by Lefschetz and he received his doctorate in 1939 for a dissertation Denumerability in topology which was published in 1940 as Convergence and uniformity in topology . He had already had three papers published before his doctorate was awarded and, after graduating, he was appointed as an instructor at Princeton.

External events were to play a major role in the direction of Tukey's career mainly as a result of him joining the Fire Control Research office to contribute towards the war effort. This title may confuse the modern reader for the research was not dealing with 'fire' as in burning, but rather 'fire' as in artillery studies. The work here involved statistics and Tukey quickly found the work very much to his liking [17]:-

The principal problems there were mathematical, involving ballistics, gun and artillery control, range finding, calculating leads for moving targets and so on. ... there are suggestion he may have been involved in code breaking.

There were other statisticians in Princeton, also contributing towards the war effort, in particular Wilks and Cochran, and Tukey soon began exchanging ideas with these men.

When World War II ended in 1945 Wilks, by this time well aware of Tukey's remarkable statistical talent, offered him a post in statistics within the mathematics department at Princeton. However one post was not enough to absorb his energy and, also in 1945, Tukey joined the AT&T Bell Laboratories where his colleagues included Shewhart, Hamming and Shannon. He also spent a major amount of time in Washington on government business. Only a workaholic like Tukey could have played such a major role in all three of these activities.

In 1950 Tukey married Elizabeth Louise Rapp who, after their marriage, made a career as an antiques dealer. They had no children but Elizabeth's sister Phyllis was married to Frank Anscombe who was also a statistician who sometimes collaborated with Tukey. Phyllis and Frank had four children who were frequent visitors to the Tukey house. Thompson writes [21]:-

John Tukey ushered in a new era of statistics. He questioned the Fisherian assumptions of regular uncertainty and gave us insights into the irregularity of the real world. His life's work consisted largely of discovering how to collect and analyse data. As he learned, he gladly taught us ways of coping with a world in which there was not only uncertainty but uncertainty about uncertainty. As an academic couple, John and Elizabeth Tukey achieved the highest standards for wisdom and kindness.

Tukey's first major contribution to statistics was his introduction of modern techniques for the estimation of spectra of time series. E J Hannan, reviewing Tukey's papers on this topic writes:-

They show a remarkable uniformity of attitude characterised by a realistic recognition of the complexity of the situation, a consequent distrust of asymptotic theory, the use of standard statistical techniques as providing benchmarks rather than (say) precise confidence intervals, continual questioning of assumptions, emphasis on computational aspects, emphasis on ways of presenting the analysis, this presentation in ways familiar to the main users rather than in ways adopted in mathematical treatments, the early recognition of the superior qualities of digital devices for general purposes (as compared to analog devices) and a conspicuous fascination with new words and phrases, some of which have become established. There is, of course, also the introduction of new methods, some of which have proved to be important. These include methods for estimating spectra, spectra of higher moments, complex demodulation, methods for determining the magnitude and sign of initial impulses observed after transmission through a (more or less) fixed linear system and the Fourier analysis of the logarithm of a spectral estimate to discern echoes.

Tukey described his development in the way he thought about his subject in the introduction to his paper The future of data analysis published in 1962:-

For a long time I have thought that I was a statistician, interested in inferences from the particular to the general. But as I have watched mathematical statistics evolve, I have had cause to wonder and to doubt. And when I have pondered about why such techniques as the spectrum analysis of time series have proved so useful, it has become clear that their 'dealing with fluctuations' aspects are, in many circumstances, of lesser importance than the aspects that would already have been required to deal effectively with the simpler case of very extensive data where fluctuations would no longer be a problem. All in all, I have come to feel that my central interest is in data analysis ...

In 1965, in a paper with J W Cooley published in the Mathematics of Computation, he introduced the important fast Fourier transform algorithm. For many people this will be the work for which is best known. However, it is only a small part of a large number of areas with he made significant contributions. His work on the philosophy of statistics and of research is summarised by A D Gordon to include the following topics:-

... the usefulness and limitation of mathematical statistics; the importance of having methods of statistical analysis that are robust to violations of the assumptions underlying their use; the need to amass experience of the behaviour of specific methods of analysis in order to provide guidance on their use; the importance of allowing the possibility of data's influencing the choice of method by which they are analysed; the need for statisticians to reject the role of 'guardian of proven truth', and to resist attempts to provide once-for-all solutions and tidy over-unifications of the subject; the iterative nature of data analysis; implications of the increasing power, availability and cheapness of computing facilities; the training of statisticians.

Tukey spent his whole career at Princeton. He became director of the newly founded Statistics Research Group when it was set up in 1956. He was the first Head of the Department of Statistics which was set up at Princeton in 1965, holding the position for four years. At the AT&T Bell Laboratories, Tukey was involved in the development of electronic computers. He held a senior position in the Department of Statistics and Data Analysis from the time it was set up at AT&T in 1952.

Tukey also made substantial contributions to the analysis of variance and the problem of making simultaneous inferences about a set of parameter values from a single experiment. Many of his papers are written with others and one of his co-authors, F Mosteller writes in [2]:-

John loves to work with others, and many have had the pleasure in participating in his genius. Variety and breadth mark his accomplishments. He works successfully on both large- and small- scale problems and on both practical and theoretical problems. ... He is always eager to respond to new questions, and he gives generously of his time and ideas.

Tukey's lecturing style was unusual. McCullagh in [17] describes a lecture Tukey gave at Imperial College, London, in 1977:-

Tukey ambled to the podium, a great bear of a man dressed in baggy pants and a black knitted shirt. These might once have been a matching pair but the vintage was such that it was heard to tell. ... Carefully and deliberately a list of headings was chalked on the blackboard. The words came too, not many, like overweight parcels, delivered at a slow unfaltering pace. ... When it was complete, Tukey turned to face the audience and the podium ... "Comments, queries, suggestions?" he asked the audience ... As he waited for a response, he clambered onto the podium and manoeuvred until he was sitting cross-legged facing the audience. ... We in the audience sat like spectators at the zoo waiting for the great bear to move or say something. But the great bear appeared to be doing the same thing, and the feeling was not comfortable.

McCullagh suggests that:-

... Tukey liked to play games his way to get people to figure out for themselves the things that he already knew. More than anything else, he liked the give and take of an argument, but he also expected his views to prevail, and they usually did.

Tukey was awarded many honours for his outstanding contributions. These include the S S Wilks award of the American Statistical Association in 1965, the US National Medal of Science in 1973 and the Medal of Honour from the Institute of Electronic and Electrical Engineers in 1982.

He had little time for interests outside applying his scientific expertise, but he enjoyed reading science fiction and mystery novels. His work took him into many unexpected areas such as uranium enrichment, working on the development of the U2 spy plane, and he represented the United States at the nuclear disarmament conference in Geneva in 1959. In addition he served on many panels reporting on issues such as the environment and the census.