Memories of John W. Tukey
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Dear viewer, Here is the url of the Memorial that I prepared for the Notices of the American Mathematical Society http://www.stat.berkeley.edu/~brill/jwt.pdf It will appear in the February issue and has my favorite picture of John.
John Tukey: A Memory from 1968
After completing my first year as an Assistant Professor at Kansas
State University, I presented a contributed paper at the Statistical
Meetings in Pittsburgh, PA, in August 1968. The paper was the last
paper in one of the last sessions in the meetings. The title of the
paper was "A Monte Carlo Study of Fisher's LSD, Tukey's Honest
Significant Difference, and a Corresponding Bayes Procedure." The
paper included results of a simulation study comparing the three
multiple comparisons procedures. The simulation results were provided
on a handout available on a table as people entered the meeting
room.
On entering the session, I was surprised to see John Tukey among the
few individuals in the room. He was sitting in the back of the room.
After the first or second paper, I noticed that he had left the room.
He resumed his former position near the back of the room just as I
began my presentation. Following my presentationm there was time for
a few questions. During the question period, it became obvious that
(1) John had a comment/question and (2) he wanted to be last. When no
other hands were raised, John was recognized, came to the front of the
room, and turned on the overhead projector. On his way to the front
of the room, he commented that he only wanted to emphasize what the
speaker had said. (That statement was most comforting to me at that
moment, but did not completely remove all of my anxiety.) He then
proceeded to show viewgraphs of his analysis of the simulation results
provided on the handout. He apparently had entered the session,
obtained the handout from the table, left the session to complete his
analysis of the frequency tables summarizing the simulation results,
and prepared his viewgraphs before returning to share his findings.
There is a transcript of JWT's expert witness testimony in the 1992 census trial at http://www.stat.ucla.edu/census. It makes very interesting reading, with some nice personal touches. When asked how many honorary degrees did he have, he said, "About five".
The following appears in the book Computer Speech: Recognition, Compression, Synthesis (with introductions to hearing and signal analysis and a glossary of speech and comuter terms) by Manfred R. Schroeder and was contributed by the author. The Bell mathematician with whom I had the most frequent contacts for over 30 years was John W. Tukey, one of the sharpest minds around, who split his time between Bell and the Princeton Statistics Department. Tukey, who seemed to thrive on half a dozen glasses of skim milk for lunch, was the first human parallel processor I have known: during staff meetings he would regularly work out some statistical problem while hardly ever missing a word said during the discussion. He is of course best known for his (re)invention, with IBM's Jim Cooley, of the fast Fourier transform, (FFT) which changed the topography of digital signal processing (never mind that Gauss had the FFT 150 years earlier). Tukey was also a great wordsmith: he coined the terms bit, byte, software and cepstrum, (the Fourier transform of the logarithm of the Fourier transform). But some of his cookier coinages, like quefrency (for cepstral frequency) and saphe (for cepstral phase) didn't catch on. I first heard about the cepstrum from John, which he had invented to distinguish underground nuclear explosions from earth quakes in connection with the US-Soviet test ban negotiations. It became immediately clear to me that the cepstrum was ideally suited for extracting the fundamental frequency (the pitch) from speech signals -- a difficult task for distorted telephone signals. The cepstrum was an ingenious idea and today, 40 years later, it remains the best method for separating long delays (travel times of seismic waves in the earth's mantle or times intervals between the puffs of the human vocal cords) from short-delay and resonance effects (of the human vocal tract).
As my graduate advisor, of course John Tukey was a major influence on my career, teaching me how to think about statistics and problems in general and opening doors for my post-graduate professional employment. But what I remember most are some of the little things. There's no point to it, really, but I remember a touch football game during my first year of graduate school (probably spring, 1968). On offense, I lined up opposite "John". When the ball was snapped, I just stood there. He wasn't going to hit me, and I wasn't going to hit him! During the late 1960's, John was heading a team that was compiling the first statistical citation index. Of course, he didn't just head the team, but did a lion's share of the grunt work. Everywhere he went in those days, he had 10 or 15 side-inches of journals under his arm. He would attend seminars, and spend the whole time copying references out of said journals onto data entry sheets. Of course, he always had the appropriate question or observation at end of the talk. It's not that he wasn't paying attention! Some of us would try to emulate him by sitting in the back of the room doing crossword puzzles, but it was to our detriment. Then there was the program he wrote and handed to me one day. I believe it's true that he never or seldom used a computer in those days, but he had a book-learning acquaintance with FORTRAN. It was so unreadable! FORTRAN ignores arguments that aren't used, so he made each subroutine's argument list into a sentence with commas between the words. Typical John! I remember a when John and Ruben Gabriel were standing at a blackboard working on a problem. As I recall, they had several columns of numbers and needed square roots of them. They took turns writing down the square roots to 3 decimal places. Again, Typical John -- and I was impressed by Professor Gabriel, as well. Finally, John never wasted a minute of time. There were several occasions when he had to drive somewhere and would invite me along to discuss whatever it was that we had to discuss. I remember one time when he said he had to go to his home to get something for his wife who was spending the day at an auction. (I'm embarrassed now to say that) I responded in mock horror, "What. You let her go to an auction alone?" His quiet, terse response, "She's selling." Little did I know then that Elizabeth was an antique dealer and professional appraiser, and John was a feminist, too.
In Appreciation of John Tukey John Tukey was more than a renowned statistician, he was a creative phenomenon! Although I did not know him well, I was privileged to be exposed to many of his insights. I frequently observed John sitting in the rear of a presentation, either working furiously on his own material or appearing to be asleep, and then telling the speaker what he did wrong and also how he might be able do it right the next time. In my experience, he was the only person capable of absorbing deep complexities while being fully occupied. It is well known that John coined the key computer terms "bit" and "software," yet not as well known that he also coined the term "side-foot" to measure size of computer output. When I was at the NACA (predecessor of NASA) High Speed Flight Station in 1956, I used the brand-new Power Spectral Density Analysis of Harry Press and John Tukey. Neither this analytic technique nor his Fast Fourier Transform to make implementation easier would have been feasible without the computer to perform its many calculations. My next contact with him was as a graduate student at Stanford during a 1958 or 1959 seminar at which he wisely stated, "We need to sit loosely in the saddle of the data." That was a very early, and might have been his first, utterance on Data Analysis. The computer also made Data Analysis and its popular descendant Data Mining possible. John portrayed statistics as a potentially heavy user of computing in "The Inevitable Collision between Statistics and Computation" at the 1963 IBM Scientific Computing Symposium. This was two years before Arthur Samuel of IBM inspired me to envision the interface of computer science and statistics as composed of not only the statistical use of computer science, but also the computer science use of statistics and the use of both by other disciplines to solve significant problems. In a special session organized by Nancy Mann and me for the 1968 Annual Meeting of the American Statistical Association, he then spoke on "Computer Science and Statistics: A View of the Bridge." John was Keynote Speaker at the 6th Symposium on the Interface of Computer Science and Statistics in 1972 and again at the 14th Symposium in 1982, outlining graphics and other computer needs of statistics in "Another Look at the Future." Karen Kafadar is currently organizing a session for Interface '01 to recognize his many and varied contributions to the interface of computer science and statistics.
A Remembrance of John Tukey I first met John Tukey in the late 1970's, many years before I even thought of running for local office. I had heard of his international reputation, his professional accomplishments and of his outstanding academic achievements, in short I knew he was a "very famous" mathematician with a specialty in statistics. We were introduced at a neighborhood meeting, called to mobilize forces of residents in the Cherry Hill Road/Arreton Road/Route 206 area who were concerned about the magnitude of a proposed development in the area and the traffic it would generate. We were also interested in the various alignments being put forth by the DOT for Route S-92. The first order of business was to get some traffic counts. In order to save money, the group initially suggested having a volunteer from the neighborhood take an informal count on several days at different times of the day. Since it was summer I volunteered to oversee my young teenage son to sit on Route 206 and Arreton Road and count cars. Imagine my surprise when Professor John Tukey, the Donner Professor of Science at Princeton University, and one of the most influential statisticians came over and offered to do the job. A man who could command hundreds of dollars an hour for statistical consulting and analysis, had agreed to sit in a lawn chair and count cars as they passed by. John Tukey with all his fame, volunteered his expertise, and without calculators, computers or any fancy technology, sat on a chair at the designated spot on Route 206 and with a pad of paper and a pencil counted the cars and trucks as they traveled past. I smile as I think of that image. How lucky we were to have John as a member of this citizen group! He along with Elizabeth were active in raising money and raising consciousness about environmental sensitivity, quality of life, and historic preservation. We were blessed to have the Tukeys in our town, because they both cared about the place called "Princeton" and they donated their professional expertise and personal commitment to our community.
Professor John, is now gone,
Phyllis L. Marchand
Mayor, Township of Princeton NJ (9/8/00)
I first met John Tukey in 1986. I was working with Walt Federer on a Fulbright Postdoctoral Fellowship at Cornell University and accompanied him to an army conference on design of experiments in California. It was a humbling experience to be sitting next to John during some of the talks. He was editing papers, reading his mail and reading the newspaper, seemingly not listening to the speaker, yet able to give an insightful critique at the conclusion of each talk. His ability to do all of these things at once was awe-inspiring. I accepted John's subsequent invitation to work with him with alacrity. Our association as both colleagues and friends continued until his recent death. One of the most heart-warming things about John was that he didn't make you feel inadequate when you couldn't keep up with his line of reasoning. He would just give you three or four of his papers to read and then expect you to understand his viewpoint and discuss the pertinent issues the next morning. What a way to get the best out of people by having them strive to live up to those expectations! John's eye for detail was amazing. When we were preparing some of the material for our book (which was published last year), it was most disconcerting to have him glance at the data and question one value out of several thousand points. Of course, he was correct and I had missed identifying this anomaly. Elizabeth Tukey was a worthy partner for John and those close to him knew how well they worked together as a team. She enabled him to give so much of his time and energy to the statistical profession, government consultancies and industrial and research corporations to the benefit of the whole community. Elizabeth once told me that John felt that his students were his children and they were taking his teachings (with his unique way of looking at things) throughout the world. What a legacy to leave behind! I was extremely fortunate to be able to visit with John just before he took ill in July. We had several days together in which we discussed many aspects of the analysis of two-way tables and their extensions. He was so generous in his ideas that I shall never be short of leads to follow. Although not in top physical condition, he was in good spirits and positive about the future. He wanted to know when I would be getting back to him, but without applying undue pressure. When I phoned him from Australia (usually first thing in the morning New Jersey time), he was always pleased to hear from me and find out how things were going. I consider myself privileged to have had the opportunity to work closely with John Tukey. My commitment is to live up to his confidence in me as an applied statistician. He is sadly missed.
Remembrance I was fortunate to be in the Statistics Department at Princeton in the early eighties when I first met John Tukey. He was a person that you only need to contact briefly in order to feel a tremendous impact. I was also fortunate to be able to audit John's lectures of Stat 411, Data Analysis. There I discovered that the "over-utopian" world of the textbooks was something we should beware of, that the random sample is indeed a "batch of values" which "fail to be utopian" most of the time. I soon understood why the jackknife can be seen as "a meat-grinder with some reusable pieces of meat." His way of looking at uncertainty made me reflect on my statistical training and has enlarged, deepened, and changed my approach to statistics and consequently my own work. John's warm human dimension complemented his profound intellect. He had a subtle sense of humor, when I was pregnant with my second child and I was attending his Stat 411 lectures he commented to me that, "I'm glad to see that you are training your baby to be good in Data Analysis." His sense of humor, his deep insight, were crucial components of his individuality. His devoted wife Elizabeth captured this perfectly when she said that "[John] is a New Englander through and through" and his individuality" is one of the things that John has in spades." (1) John's passion for his work is legendary. Elizabeth mentioned that her father had asked her "whether while he was waiting for [her] at the altar, he would whip out a yellow pad and not waste time." Until the last days of his life John had statistical discussions with me and other statisticians in Princeton, as well as with several other statisticians around the world with whom he was doing research. John enjoyed very much working with others and many of us had the privilege to participate in his genius. John was extremely generous with his ideas as witnessed by the long list of his Ph.D. students (more than 50) that he referred to as "his children" as well as "his grandchildren" (his students' students). My family enjoyed getting together with John and Elizabeth. My children were privileged to be able to participate in discussions with John on a wide range of topics: from poison ivy and poison oak, to the different kinds of berries in New England, to quantum computing. Clearly, in every topic John was an expert. Among the many influential positions held by John was that of vice-president of the American Philosophical Society from 1974 to 1977. His deep philosophical interests were always present in his scientific work. As he said, "We live in a paradoxical world, where the only true safety, true though limited, comes from admitting both our uncertainty and the incompleteness with which we are able to meet it." (2) John Tukey's scientific contributions will stay with us in our minds, his kindness and humanity will stay with us in our hearts. References
Remarks in memory of John Wilder Tukey When I was about eight, my uncle took me to Candlestick Park in San Francisco to watch the Giants play baseball with the St. Louis Cardinals. The Cards won 3 to 1. Curt Flood, who at great personal sacrifice later liberated players from their servitude to owners in a Supreme Court case, hit a homer. In those days, Willie Mays, the greatest player of all time, patrolled center field for the Giants, catching fly balls with glove at waist level, basket catches they were called. My uncle and I had to laugh as Mays grabbed one after another. As was his way, Uncle John said something short and to the point: what a man. Willie was so gifted that he was bored to merely catch the ball, rather he challenged himself to catch it in a difficult way, yet still make it appear routine. Mays played in a league of his own. I am reminded, because in utterly different fields of human endeavor, so was John Wilder Tukey -- in a league of his own. Doing the extraordinary, while acting ordinary, with self-assurance yes, but empty of normal human vanity and petty pretensions. John did not need to stay at posh hotels, a Travel Lodge near Palo Alto was quite sufficient. His wardrobe was modest; one set of black polo shirts served 40 years. He was likewise economical with words, not given to chatter. But his professional talks and writings showed immense power to communicate, with grace and wit. One of John's defining credos was: "people are different." That was his succinct way of accepting and respecting everyone, from all walks of life. John Tukey dutifully gave of himself for a lifetime: On a personal level, he was steadfast on behalf of relatives and his extended family at Princeton, Bell Labs, Brown, ETS, Merck, Xerox, and many places beyond. His extensive public service began at Princeton during World War II. He continued to support national defence for decades. Under Presidents Kennedy, Johnson, and Nixon, John contributed importantly to trail-blazing consideration of air quality and chemical pollution issues. During the Carter years, he chaired a National Academy of Sciences investigation of ozone layer depletion. Later he contributed to an assessment of acid rain. He advised the Education Department for 20+ years, and the Census Bureau on how to adjust statistically for those missed by the Census. He studied how the less advantaged in society tended to receive harsher legal penalties. Sometimes this work was unpaid; I expect he saw it simply as his obligation to apply his talents. Yet John's most profound contribution was methodological, building upon the foundations of statistics by creatively developing new methods for interpreting data, encouraging flexibility and expert judgment under uncertainty. In so doing, he has opened doors of possibility for break-throughs by others. Through his teachings and regard for colleagues, he was clearly conscious of a special onus to pass a torch to posterity. He regarded the time span for a seismic shift in data analysis to be ninety years. Ironically, for someone credited with coining the words software and bit, my uncle never made much use of computers; he applied his mind to more fundamental things. He also spent a good deal of time reading sci fi and adventure stories. Some were no doubt good yarns, others a far cry from literature. My interpretation was that John's mind was so powerfully restless that he constantly needed to use it somehow, even in repose. John very much liked to observe birds and loved the oceans and their living resources. His few wants were a house near the sea, a convertible, a small catamaran, classical music recordings, ping pong, used paperbacks, mince or apple pie, cider, skim milk. Whenever I would visit my uncle, he would ask with gentle interest what I was working on. I expect this was his standard question of everyone. His mind was ever fresh, ever striving to think outside the box, from different perspectives. John went away from us as he lived: not seeking for himself, but quietly. When I learned, my reaction was anger, because his mind was 85 years young, and I was frustrated that his future contributions will not happen. But this was fleeting. John wanted to go away while in possession of his faculties, to die with his working boots on. His passing was by definition always going to be premature. Henceforth is a time for appreciation of someone not so broadly famous as Einstein or Willie Mays, but who qualifies as a hero. Computing, the environment, national defence and arms reduction, sociology, medicine, education, space physics: he touched all. His titanic, protean genius, scientific leadership in service to society, coupled with personal modesty and gentle consideration for others, has inspired awe and love from many. For me, it has been a profound blessing and privilege to have by some quirk of fate direct acquaintance with greatness. For that one can only pay homage and give thanks.
I come at nearly the end of the very long list of students that appear in the Festschrift (Brillinger Fernholz, Morganthaler 1998). Like all of John Tukey's students, I benefited enormously from the experience, both personally and professionally. The professional benefits are more visible: his name on my dissertation opened up many more doors for me and brought me into contact with the outstanding contributors of our field that I am quite sure I would have never been so fortunate to have met had I not had the benefit of my association with him. My first encounter with John Tukey occurred during the spring of my senior year in college; he, Geoff Watson, Peter Bloomfield, and Don MacNeil were all visiting Stanford, and someone introduced them to me. Tukey did not say anything but he smiled and was wearing his trademark black T-shirt whose pocket held the usual Bic 4-color pens. Later that fall, during my first year at Princeton, Geoff Watson (as chairman) said to me, "Tukey said he might have something for you to do in connection with your assistantship here, so you should talk to him." I timidly approached Dr. Tukey following a 411 class (the famous "undergraduate" course attended by even full professors), introduced myself, and reported Watson's directive. He broke into a big grin and said, "Wait here." He returned in a flash with a 35-page "draft" and said, "Read this, and then I think you'll see that we have a lot of computing to do." Note the use of the word "we" -- not "*you* have a lot of computing to do" -- but "we". In fact, John Tukey chose his words very carefully. Many people thought that he "made up" words -- but those of us who wrote theses for him saw him cross out our use of "Tukey" words, like "hinge", and replace them with conventional words, like "interquartile range", if that was the intended meaning of our sentence. When he "made up" a word, he did it because he had a *very* precise definition in mind. The personal benefits included learning about *being* a statistician. He told me about the doctor at Sloan Kettering, with whom he met, off and on, for nearly 8 months before he ever came so close as to mentioning something as simple as a t-test (moral: learn to talk *their* language). As a graduate student, I once asked him how many decimal points he wanted me to copy down from a table of numbers I'd computed, and he responded, "How many do you believe?" (It was such a sensible reply that I felt silly having asked the question.) He was an inherent adjustor -- hence his position with respect to the decennial census. At the Detroit JSM (1982?), he countered the position of "do not adjust because there are so many ways to do it and none of them will ever be right" by arguing, "As statisticians, we constantly face up to the fact that our answers are never `right' -- they always have uncertainty -- but that doesn't stop us from trying to get a little closer to the truth." Paul Tukey and others mentioned how generous he was with ideas: he just threw them out, and let others work on them. Many of them have taken people 20 or 30 years to work out why they perform so well. Consistent with that characteristic, he never used his own name for his ideas, procedures, or methods. They were always the "Duckworth test", or the "Bruceton test", or "Winsorization", or "decigalt" ("for Francis Galton, who started so many things")..... The other characteristic of his personality that always impressed me was his constant encouragement to his students. At one of my meetings with him during my disseration years, I started out by apologizing for how little I'd accomplished in the last three weeks. At the end of the meeting, he came back to that first sentence and said, "And, Karen, if I am surprised by anything, it is not by how *little* you have accomplished, but by how *much*." He always knew just the right thing to say to make his students feel better. Throughout his life, everyone in my family always addressed him formally. People asked me why, after 20 years, I still called him "Dr. Tukey". Partly habit, but mostly because I am the daughter of a product of the French educational system: my father, born only one month later, always referred to him, in both his presence and his absence, as "Professor Tukey." It was our way of showing our enormous respect for the great man that he was. Luisa told me last week that his instructions for the Festschrift were "to include a list of my children and my grandchildren." It touched me deeply to know that he thought of us as his "children" -- because, to me, he was in fact so much more than an "academic father." He and his beloved wife came to mean a great deal to me, and I will miss them both very much.
Today it seems obvious that the digital computer is as important to a statistical practitioner as the optical telescope is to an astronomer. Considered from this viewpoint, John W. Tukey has played the role for our field that Galileo Galilei played during the first half of the 17th Century. The first time I saw him, John Tukey was sitting at the head table during the 125th anniversary, American Statistical Association, banquet. This banquet was part of the first meeting that I attended after receiving my Ph.D. degree. As is no doubt common, buyer's remorse was beginning to set in. In an after-dinner speech he predicted much of what has since then actually happened to our field and this was enough to dispel any doubts on my part concerning career choice. Five years later it was my privilege to introduce John, who had agreed to serve as that year's Computer Science and Statistics, Interface Conference, keynote speaker. A few months before the conference I happened to stay in London and have access to the British Museum. To have something interesting to say by way of introduction, it seemed appropriate to search for any correspondence between the pioneers of the two fields of computer science and statistics, Charles Babbage and Francis Galton. As far as I could tell, only one letter survives and, unfortunately, it had nothing at all to do with either field. That times have changed so that it is hard today to think of one field without thinking of the other is, in my opinion, the accomplishment of one person.
I met John Tukey a few weeks after I started working at Bell Labs in the math research department. I was working for Dick Hamming and the department had just purchased an analog computer. Hamming gave me a 5 min. lecture on how to program that computer. In those days, documentation and user manuals did not exist. The next morning, I was introduced to John Tukey, who handed me his problem and told me he would be back in the afternoon to see how things were going. I thought I understood both his problem and the computer so, I made a stab at programming that computer and by noon, I had some data ready for Tukey. Well, Tukey came by, looked at the numbers and said, "This won't do. There cannot be any negative numbers in the results". Did I know Tukey was a genius? Of course not. So, I countered with, "Why not??". Tukey said, "SIT!", so....I sat. Then, Tukey explained what the problem was all about, what he was expecting to find, and he explained all this in a simple and straightforward way. OK, so I agreed the numbers could not be negative. Then, I told Tukey about my 5 min (honest- that was the total amount of time) Hamming lecture on how to program the analog computer, and that I had to think about what I had done wrong. Tukey responded with, "Tell me everything that you remember from Hamming's explanation". I did that. Tukey pursed his lips for a few seconds, then, he looked at what I had done, told me what was wrong, told me how to correct it, gave me a little smile, and left. I followed his suggestions and ran the program again, and got the results Tukey expected. After that, he always had a smile for me when he saw me.
Bea Chambers
(8/8/00)
John Tukey and ``Software'' While John Tukey apparently invented the term software, his most striking relationship with the computer was that he didn't use it. This might be expected to have put a damper on my technical interactions with him. In fact, though, he was far from unsympathetic to the potential benefits of computing for data analysis. He just viewed them from his own unique perspective, as he did most everything. While he never contributed specific designs or requirements for any of the Bell Labs statistical software work, his ideas were influential in a deeper way. The correspondent to the S-news mailing list who suggested, shortly after Tukey's death, that he had some influence on the S language was entirely correct, although the nature of the influence may not be immediately obvious. Tukey wrote on several occasions about the ``collision'' between computing and data analysis. When statistics researchers at Bell Labs were first trying to design a statistical computing system, he responded to one of our meetings with a typically lively memo on the subject. I quoted from this in the Neyman lecture paper. When he came to write Exploratory Data Analysis a decade later, though, the algorithms he outlined used fundamentally pencil and paper as their hardware. There have been attempts to build software around these same techniques, but that strikes me as focusing on the trees, not the forest, of John Tukey's influence on computing. The essence of what we took from him in thinking about S, for example, can be summarized in another of his famous one-liners, which goes roughly like this: Better to have an approximate answer to the right question than a precise answer to the wrong question.To me, this means that the data and the real goals of the analysis should suggest what questions need posing. A convenient or conventional summary is often not good enough. In this sense, I would say that enabling users to ask the ``right'' question (and to get a usable answer) is the most central design principle behind S, and behind nearly all the other research here on statistical software, before and since. There are dozens of technological choices we made over the years that could be related directly to that principle. We didn't cite John Tukey very often, perhaps, but I think all of us were conscious that his enquiring, challenging spirit was there, pushing us to do something better.
A Few Recollections John Tukey was in some respects very much a New Englander; for example, his quiet, measured conversation, and a tendency to avoid personal comments. In his quiet way, though, he could be kind and considerate: It was striking in the funeral service that so many of those who knew him remarked on his kindness. In our occasional interactions over many years, I saw signs of all those traits. My wife and I had both known John, in completely separate contexts, for a number of years before our marriage. Shortly after, Bea had a chance to meet him at Bell Labs and tell him about our new status. The entire conversation in response was a typical John Tukey pause, a quiet smile, and "That's nice." From most people, this would be a perfunctory, if not trivial, comment. We've always felt, though, that John meant exactly what he said, as he usually did. Maybe he even thought we might have some of the marriage of true minds that he shared with Elizabeth. One of his typical little courtesies led to my most uncomfortable memory of him, through no fault of either of us. John Tukey and I were separately involved in a conference in New York City (if memory serves, an ACM meeting around 1970). In those palmy days of Bell System monopoly, executives had a company limousine at their disposal. John invited me to ride from Murray Hill to the meeting with him. Unfortunately, the limousine was long, softly sprung, and prone to pitch and yaw; worse, I was feeling under the weather that day. So the ride to New York was extremely uncomfortable. And, as so often, John was off on one of those challenging intellectual conversations vividly remembered by people who traveled or commuted with him. These were hard enough to keep up with, even when one's mind was not mainly occupied on not being violently ill. I can't remember the topics of discussion, naturally, but do remember thinking afterwards that he must have considered me rather hopeless in conversation. Not totally hopeless, apparently, for in the years after I remember many exciting exchanges in person or in writing, on the occasions when his research and mine intersected. Many people were much more closely involved with John Tukey in their work, but I still treasure the memory of our interactions. I have been fortunate to know some outstanding people, but so far only one I would call a genius. It was a privilege.
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