# John Wilder Tukey

### Quick Info

New Bedford, Massachusetts, USA

Princeton, New Jersey, USA

**John Tukey**introduced the Fast Fourier Transform and worked in other areas of Statistics.

### Biography

**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.

### References (show)

- H I Braun (ed.),
*The collected works of John W Tukey Vol. VIII. Multiple comparisons : 1948-1983*(Pacific Grove, CA, 1994). - D R Brillinger (ed.),
*The collected works of John W Tukey Vol. I. Time series : 1949-1964*(Belmont, CA, 1984). - D R Brillinger (ed.),
*The collected works of John W Tukey Vol. II. Time series : 1965-1984*(Belmont, CA, 1984). - W S Cleveland (ed.),
*The collected works of John W Tukey Vol. V. Graphics : 1965-1985*(Pacific Grove, CA, 1988). - W S Cleveland (ed.),
*The collected works of John W Tukey Vol. VI. More mathematical : 1938-1984*(Pacific Grove, CA, 1990). - D R Cox (ed.),
*The collected works of John W Tukey Vol. VII. Factorial & ANOVA : 1949-1962*(Pacific Grove, CA, 1992). - L V Jones (ed.),
*The collected works of John W Tukey Vol. III. Philosophy and principles of data analysis : 1949-1964*(Monterey, CA, 1986). - L V Jones (ed.),
*The collected works of John W Tukey Vol. IV. Philosophy and principles of data analysis : 1965-1986*(Monterey, CA, 1986). - F J Anscombe, Frederick Mosteller and John W Tukey : a conversation,
*Statist. Sci.***3**(1) (1988), 136-144. - Biographical information [on John Wilder Tukey], in
*The practice of data analysis, Princeton, NJ, 1995*(Princeton, NJ, 1997), 5-8. - D R Brillinger, John W Tukey : his life and professional contributions, in
*In memory of John W Tukey, Ann. Statist.***30**(6) (2002), 1535-1575. - D R Brillinger, John Wilder Tukey (1915-2000),
*Notices Amer. Math. Soc.***49**(2) (2002), 193-201. http://www.ams.org/notices/200202/fea-tukey.pdf - Curriculum vitae of John Wilder Tukey, in
*The practice of data analysis, Princeton, NJ, 1995*(Princeton, NJ, 1997), 9-15. - L T Fernholz and S Morgenthaler, A conversation with John W Tukey and Elizabeth Tukey,
*Statist. Sci.***15**(1) (2000), 79-94. - L T Fernholz, A conversation with John W Tukey, in
*The practice of data analysis, Princeton, NJ, 1995*(Princeton, NJ, 1997), 26-45. - K Kafadar, In memoriam: John Wilder Tukey, June 16, 1915-July 26, 2000,
*Technometrics***43**(3) (2001), 251-255. - P McCullagh, John Wilder Tukey,
*Biographical Memoirs of Fellows of the Royal Society***49**(2003), 538-559. - Partial list of John W Tukey's grandstudents, in
*The practice of data analysis, Princeton, NJ, 1995*(Princeton, NJ, 1997), 19-25. - PhD theses directed by John W Tukey - Princeton University, 1940-1990, in
*The practice of data analysis, Princeton, NJ, 1995*(Princeton, NJ, 1997), 16-18. - The publications and writings of John W Tukey, in
*In memory of John W Tukey, Ann. Statist.***30**(6) (2002), 1666-1680. - J R Thompson, The age of Tukey,
*Technometrics***43**(3) (2001), 256-265.

### Additional Resources (show)

Other websites about John Tukey:

### Honours (show)

Honours awarded to John Tukey

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update June 2004

Last Update June 2004