## John W. Tukey (1915–2000)

*Foreword by Karen Kafadar*

Shortly after my arrival at Princeton University as a graduate student in the fall of 1975, the chairman told me to see John Tukey “because he has some project for you to work on.” Summoning all my courage, I approached him, introduced myself, and reported the directive I’d received. Tukey broke out into a huge grin and replied, “Wait here.” He disappeared across the hall into his office and reappeared momentarily. “Read this—and then I think you will agree that we have a lot of computing to do.”
It took me the better part of that first year to understand just what I was supposed to do, much less to do it. It wasn’t much different for anyone else. Professors from other departments, even statistics ones, often sat in on his lectures and spent much time trying to understand his ideas, often delivered with profound wisdom.

Professor James Thompson visited Princeton in the fall of 1977; I remember him saying, “I asked Tukey about this problem, and he devoted all of five minutes to it. I figure five minutes of Tukey time is roughly equivalent to about five weeks of Thompson time.”

All of Tukey’s 54 PhD students, and some of his 120 grad students, and many of his colleagues and associates have similar stories about their interactions and conversations with John W. Tukey. The following article presents only a glimpse of the contributions and character of this remarkable member of our profession.

Other more personal accounts of Tukey’s life can be found in The Collected Works of John W. Tukey (biography by Frederick Mosteller), The Practice of Data Analysis: A Festschrift for John W. Tukey (Brillinger, Fernholz, and Morgenthaler 1998), in “A Conversation with John W. Tukey and Elizabeth Tukey,” by Luisa Fernholz and Stephan Morgenthaler in Statistical Science 15 (1), 79–94.

The world has lost a great scientist and contributor to statistics, but, through his writings, teachings, and methods, his ideas will continue to influence the directions of statistical research for years to come.

*The following is adapted from an announcement published here by Princeton University.*

As one of the most influential statisticians of the last 50 years, John Wilder Tukey developed many important tools of modern statistics and introduced concepts that were central to the creation of today’s telecommunications technologies. In addition to his formidable research achievements, Tukey was known for his penchant for coining terms that reflected new ideas and techniques in the sciences and is credited with introducing the computer science terms “bit” (short for binary digit) and “software.”

Tukey, Princeton’s Donner Professor of Science Emeritus, actively applied his mathematical insights to real-world problems in engineering and social sciences, serving as staff researcher and associate executive director for research at Bell Labs, now the research and development arm of Lucent Technologies. For decades, he was an active consultant to such companies as Educational Testing Service and Merck & Co. and contributed to such areas as military operations in World War II, U.S. census-taking strategies, and projecting the election-day results of presidential contests for national television.

“He probably made more original contributions to statistics than anyone else since World War II,” said Frederick Mosteller, retired professor of mathematical statistics at Harvard University. “I believe that the whole country—scientifically, industrially, financially—is better off because of him and bears evidence of his influence,” said retired Princeton Professor John A. Wheeler, who is a major figure in the history of physics and the development of the atomic bomb.

“He had a penetrating understanding of so many areas in the field of statistics and was happy to share those insights with anyone who engaged him in a discussion,” said David Hoaglin, a statistician at the social research firm Abt Associates who co-authored books and papers with Tukey. “It’s hard to find an area that he did not work in or have a significant impact on.”

Among Tukey’s most far-reaching contributions was his development of techniques for “robust analysis,” an approach to statistics that guards against wrong answers in situations where a randomly chosen sample of data happens to poorly represent the rest of the data set. Tukey also pioneered approaches to exploratory data analysis, developing graphing and plotting methods that are fixtures of introductory statistics texts, and authored many publications on time series analysis and other aspects of digital signal processing that have become central to modern engineering and science.

In 1965, with James Cooley, he introduced an analytical tool known as fast Fourier transform, which remains a ubiquitous technique for understanding waveforms in fields from astrophysics to electrical engineering. And in addition to his research achievements, Tukey was known for his passions for folk dancing and collecting murder mystery and science fiction books.

“John was a very lively presence on campus,” said Princeton Professor of Mathematics Robert Gunning, former chairman of the mathematics department and dean of the faculty.

In one commonly told anecdote, Tukey put his extraordinary calculating abilities to work as chairman of the Faculty Committee on Schedule, working out the seemingly intractable complexities of arranging times for classes and exams. “He would lie flat on his back on a table and people would list the scheduling difficulties and he would reel off solutions,” Gunning said. “He did it quickly and quietly in his head.”

Tukey also was instrumental in creating a citation index for statistical literature and was known for carrying publication lists with him and working out the complexities of cross-references in his spare time.

“He did an amazing number of things,” Gunning said. “And he was a good and energetic teacher.”

“If you have money in the bank you always have a sense of assurance,” said Wheeler. “John Tukey was a special kind of money in the bank because you could take up a difficult question with him and get a new point of view and sound advice. The country will be poorer for his loss.”

Tukey was born in New Bedford, Massachusetts on June 16, 1915. He earned bachelor’s and master’s degrees in chemistry from Brown University in 1936 and 1937 before coming to Princeton for graduate work in mathematics. He earned his PhD in just two years. After spending wartime years in the government’s Fire Control Research Office in Princeton, Tukey rose to the rank of full professor by 1950 at age 35.

Building on a foundation laid by statistician Samuel S. Wilks, Tukey helped found a department of statistics, which split from the mathematics department in 1966, and chaired the department until 1970. The department later became today’s Committee for Statistical Studies.

Among many awards and honors, Tukey received the National Medal of Science in 1973 and an honorary doctorate from Princeton in 1998, and was a member of the National Academy of Sciences and the Royal Society of England.

## Many Happy Returns

##### The Washington Post*, November 5, 2000, reprinted with permission from the author, David Alan Grier*

When asked for a prediction on the coming election, I suggest that Bush will win the popular vote, Gore will take the electoral college and that we will not know the results until the sun rises on the morning of November 8. When pressed for my reasons, I give only one. This will be the first election since the second world war without the presence of John Tukey, the man who destroyed the suspense of election night.

Tukey, a professor of statistics at Princeton University, was a self proclaimed psephologist (se-fo’-lo-gist), an expert on the mathematical prediction of election. Every fall, he would sit down to plan how to predict the outcome of the season’s election, be the election presidential, midterm Congressional or the off year election of a local mayor. The country got its first taste of the power of mathematical election prediction in 1952, when CBS television used the first commercial computer, the Univac I, to predict the vote in the Eisenhower-Stevenson election.

By early evening, the computer model predicted a landslide for Eisenhower. The production staff, used to late drama of election nights resisted using the numbers. One producer recalled thinking that they “just couldn’t be right.” Only four years before, in 1948 Harry Truman had gone without knowing the results of the election that would return him to the White House. He learned that he had retained the presidency only when the state of Ohio announced its vote at 8:30 am the following day. But the 1952 numbers proved to be accurate and with them began the decline of election night.

The election of 1952 and its rematch in 1956 were easy tests for psephology, for in both the leading candidate was popular war hero and even those who did not have electronic computers predicted a easy win by General Eisenhower. The real test for the mathematical crystal ball came in 1960, when Kennedy went against Nixon.

In 1960, Tukey joined NBC as a consulting psephologist, though he liked to pronounce the word as if the initial “p” was not silent, calling it (pee’-se-fo’-lo-gist). He had been trained as a classical mathematician at Brown University but had learned during the war as a consultant for the Office of Research and Development. He liked statistics and applied mathematics because you get “to play in everyone’s backyard.”

To the study of elections, he brought the lessons he had learned during the war, lessons that had taught him how to use mathematics to remove variability. During the war, the mathematicians of the OSRD had used mathematics to remove the variability in manufacturing, the variability in supply and even the variability of combat. Under the guidance of mathematically prepared plans, the pilots of D-Day bombed the French coast in a pattern that created the greatest amount of damage while exposing the pilots to the least amount of risk.

In elections, variability comes from the swing districts, the areas where the Republicans and Democrats are in balance and the election is determined by the swing voters who actually listen to the issues. The remainder of the districts are dominated by one party or the other and their outcome can be estimated in advance. The problem of predicting the outcome of the election becomes the problem of identifying the swing districts and determining, as early as possible, how they vote.

Tukey attacked the election problem as if it were an operations problem from the war. The trick to remove variability was to use what you knew to predict what you did not. Once you knew how soccer moms in New York would vote, then you would have some idea of how they would vote in Texas and California. Once you knew how they would vote in Indiana, you would have more information that would allow you to predict the California vote more accurately. As you received more information, you would get an ever more accurate prediction of what you did not know.

Over the years, Tukey built a mathematical model that was increasingly efficient. As he refined his equations, he was able to predict the results ever earlier in the day. By 1980, he claimed that he could accurately predict the vote “by 9:30 eastern time.” By then, election evenings had all the excitement of a delivery schedule. Every hour would bring a new round of polls closed, a new round of commercials and a new round of predictions that had long been known to network producers.

But now we are living in a post-Tukey age. He departed this earth just before the nominating conventions last July. Unless election night is filled with a round of creative advertisements, such as those aired during the Superbowl, I anticipate that we will have a boring night of election coverage. Yet, I cherish a small hope that the psephologists will be wrong this year, that their equations will fail and that we will see just a bit more drama when they report the votes.

Related Links“John Wilder Tukey“, School of Mathematics and Statistics, University of St. Andrews, Scotland