David R. Brillinger
David R. Brillinger is professor of statistics at the University of California, Berkeley. He obtained his Ph.D. under John Tukey's supervision in 1961, and he edited the Time Series volumes of The Collected Works of John W. Tukey. His e-mail address is bri17@astat.berke7ey.edu.
David R. Brillinger是加州大学伯克利分校的统计学教授。他于1961年在John Tukey指导下获得了博士学位，他编辑了《John W. Tukey 作品集》（Tukey，1977，J. W. Tukey's Collected Works）中时间序列的部分。他的电子邮件地址是bri17@astat.berke7ey.edu。
I believe that the whole country，scientifically, industrially, financially，is better off because of him and bears evidence of his influence.
-John A. Wheeler, Princeton emeritus professor of physics
我相信，整个国家在科学、工业和财政上都因他而变得更好，这证明了他的影响力。
-John A. Wheeler，普林斯顿荣休物理学教授
We have watched at least four Presidents of the United States listen to him and heed his counsel.
-William O. Baker, retired chairman of the board, Bell Labs
我们看到至少有四位美国总统听取了他的意见和建议。
-William O. Baker，贝尔实验室董事会退休主席
John Wilder Tukey (JWT): chemist, topologist, advisor, information scientist, researcher, statistician, educator, data analyst, executive, died of a heart attack on July 26,2000 , in New Brunswick, New Jersey. The death followed a short illness. He was eighty-five years old.
John Wilder Tukey（JWT）：化学家、拓扑学家、顾问、信息科学家、研究员、统计学家、教育家、数据分析师、执行官，于2000年7月26日在新泽西州新不伦瑞克因心脏病发作去世。他是在一场短暂的疾病之后去世的。他85岁了。
John Tukey's whole life was one of public service, and as the preceding quotes make clear, he had profound influence. He was a member of the President's Scientific Advisory Committee for each of Presidents Eisenhower, Kennedy, and Johnson. He was special in many ways. He merged the scientific, governmental, technological, and industrial worlds more seamlessly than, perhaps, anyone else in the 1900s. His scientific knowledge, creativity, experience, calculating skills, and energy were prodigious. He was renowned for creating statistical concepts and words.
John Tukey的一生是为公共服务的，正如前面的引语所表明的，他有深远的影响。他是艾森豪威尔、肯尼迪和约翰逊总统的总统科学咨询委员会成员。他在许多方面都很特别。他比20世纪的任何人都更无缝地融合了科学、政府、技术和工业世界。他的科学知识、创造力、经验、计算技巧和精力惊人。他以创造统计概念和单词而闻名。
JWT's graduate work was in mathematics, but driven by World War II, he left that field to go on to revolutionize the world of the analysis of data. At the end of the war he began a joint industrial-academic career at Bell Telephone Laboratories and at Princeton University. Science and the analysis of data were ubiquitous. This split career continued until he retired in 1985. Even after retirement his technical and scientific work continued at a very high level.
JWT研究生时做的是数学，但受第二次世界大战的推动，他离开了这个领域，继续改革数据分析的世界。战争结束时，他在贝尔实验室和普林斯顿大学开始了工业和学术的联合职业生涯。科学和数据分析无处不在。这种分裂的职业生涯一直持续到他1985年退休。即使退休后，他的技术和科学工作仍保持在非常高的水平。
In memorializing John Tukey's life, one has to review his contributions to both science and society. It is further interesting to follow his evolution from mathematician to statistician. The sections of this article are: Narrative of the Professional Life, The Scientific Legacy, Concluding Remarks, and Epilogue. Sidebars list his Ph.D. students and his books.
在纪念约翰·图基的一生时，我们必须回顾他对科学和社会的贡献。跟踪他从数学家到统计学家的演变更有趣。这篇文章的章节分别是：职业生涯、科学遗产和结束语。侧边栏列出了他的博士生名单和出版物清单。
John Tukey was born in New Bedford, Massachusetts on June 16,1915 . After being schooled precollege at home, he earned bachelor's and master's degrees in chemistry. For a Ph.D. he went to Princeton, where he quickly switched to mathematics.
约翰·图基于1915年6月16日出生于马萨诸塞州的新贝德福德。在家里接受大学预科教育后，他获得了化学学士和硕士学位。为了获得博士学位，他去了普林斯顿，在那里他很快转向了数学。
Graduate School. He arrived at Princeton in September 1937. One has the strong impression that John and his friends had a wonderful time during their graduate studies. The Graduate College and Fine Hall, where the mathematics department was located, were very special places. Meals in the Graduate College were taken in academic gowns, and eating groups formed. In the first year JWT was drafted into the "Fuhrocracy" whose members included L. Spitzer, F. Smithies, R. P. Boas, G. W. King, M. Kanner, H. Wallman, and A. Stone. In later years his group included G. W. Brown, Richard Feynman, and O. Morgenstern. His other friends included N. Steenrod, B. MacMillan, and Bill Baker.
研究生院。 他于1937年9月到达普林斯顿。人们对John和他的朋友们在研究生学习期间度过的一段美好时光有着深刻的印象。研究生院和数学系所在的费恩厅（Fine Hall）是非常特别的地方。研究生院的饭菜都穿着学位服, （疑问，应该是比喻研究生院学术氛围浓厚） 吃饭小组也成立了。第一年，JWT被征召到“ Fuhrocracy”，其成员包括L. Spitzer，F.Smithies，R.P.Boas，G.W.King，M.Kanner，H. Wallman和A. Stone。在后来的几年中，他的小组包括G. W. Brown，Richard Feynman（理查德·费曼）和O. Morgenstern。他的其他朋友包括N. Steenrod，B. Macmillan和Bill Baker。
Fine Hall, besides housing the mathematics faculty, was renowned for its library and for tea time in the lounge. The Princeton mathematics faculty at that time included: C. Eisenhart, S. Lefschetz, S. S. Wilks, and A. W. Tucker. The members of the Institute for Advanced Studies (IAS), such as John von Neumann, were also housed in Fine Hall then.
费恩厅除了有数学系外，还以图书馆和休息室的茶点时间而闻名。当时普林斯顿的数学系的教员有：C. Eisenhart, S. Lefschetz, S. S. Wilks, and A. W. Tucker。当时高等研究院（IAS，Institute for Advanced Studies）的成员，如John von Neumann（冯·诺依曼），也住在费恩厅。
JWT attended many (all?) mathematics lectures. Of those by Marston Morse on symbolic dynamics, he said that Steenrod and he did their best to keep "Morse honest". Keeping people honest remained a key part of his scientific life. Of a course A. W. Tucker gave in 1938, Tucker once said that every time he gave a definition of a combinatorial manifold, JWT would come up with a counterexample. Tucker further remarked, "It ended in a draw."
JWT参加了许多（全部？）数学讲座。在Marston Morse关于符号动力学（symbolic dynamics）的讲座中，他说Steenrod和他尽了最大努力让Morse“诚实”。让人们诚实仍然是他科学生活的关键部分。JWT参加了A. W. Tucker 1938年的一个课，Tucker说，他每给出一个组合流形（combinatorial manifold）的定义，JWT都会想出一个反例。Tucker进一步评论道，“它以平局告终。”
At the party celebrating the completion of their graduate studies, JWT and Robert Eddy became famous for serving milk rather than the traditional beer. In a story whose authenticity was not denied by JWT, John von Neumann is reputed to have remarked, "There is this very bright graduate student, and the remarkable thing is that he does it all on milk."
在庆祝研究生毕业的派对上，Tukey和Robert Eddy因供应牛奶而不是传统啤酒而出名。在一个Tukey没有否认真实性的故事中，John von Neumann据说说过，“有一个非常聪明的研究生，了不起的是他全靠牛奶做到了。”【疑问：不太理解全靠牛奶啥意思，不喝酒也能做出成就的玩笑？】
While living in the Graduate College, John came to know the physicist Richard Feynman, and he appears in various of the books by and about Feynman. One special story relates to keeping time. Feynman knew that he could keep track of time while reading, but not while speaking. He presented this as a challenge. Rising to it, JWT showed that he could speak and keep track of time simultaneously. Of this Feynman remarks: "Tukey and I discovered that what goes on in different people's heads when they think they're doing the same thing-something as simple as counting-is different for different people." This may also be the source of JWT's remark, "People are different."
在研究生院生活时，Tukey认识了物理学家Richard Feynman（理查德·费曼），他出现在Feynman的各种著作中。一个特别的故事与计时有关。Feynman知道他可以在阅读时记录时间，但不能在说话时记录时间。他把这作为一个挑战。Tukey意识到这一点，证明他可以同时说话和记录时间。关于Feynman的评论：“Tukey和我发现，当不同的人认为他们在做同样的事情——像计数这样简单的事情——时，他们的头脑中发生的事情是不同的。”这也可能是Tukey的评论“人是不同的”的来源。
In 1939 Feynman and Tukey, together with Bryant Tuckerman and Arthur Stone, were members of the Flexagon Committee. This group formed directly following the discovery of certain origamilike objects by Stone. Flexagons are folded from strips of paper and reveal different faces as they are flexed. A theory of flexagons was worked out by Tukey and Feynman, the theory being a hybrid of topology and network theory. Feynman created a diagram that showed all the possible paths through a hexaflexagon. The Feynman-Tukey theory was never published, but parts were later rediscovered.
1939年，Feynman和Tukey与Bryant Tuckerman和Arthur Stone组成了Flexagon（译者注：一种用纸折出的多边形）小组。这个小组是由Stone有了某些折纸上的发现后直接成立的。Flexagons是从纸条上折叠起来的，当它们弯曲时，会显示出不同的面孔。Tukey和Feynman提出了一个flexagons理论，该理论是拓扑和网络理论的混合体。Feynman创造了一个图表，显示了通过六边形的所有可能路径。Feynman-Tukey理论从未发表过，但后来部分被重新发现。
World War II. In 1941 Tukey was appointed assistant professor of mathematics at Princeton. That year he listed his interests in American Men of Science as point set topology and analysis. With America's entry into World War II, things changed dramatically. John joined the Fire Control Research Office at 20 Nassau Street, Princeton. This organization was concerned with armored vehicle fire control, ballistic behavior of rocket powder, gunfire control, and the accuracy of anti-aircraft stereoscopic height and bomber range finders.
第二次世界大战。 1941年，Tukey被任命为普林斯顿大学的数学助理教授。这一年，他在《美国科学人》(American Men of Science)中列出他的兴趣是点集拓扑学和分析。随着美国加入第二次世界大战，事情发生了巨大的变化。Tukey加入了位于普林斯顿纳索(Nassau）街20号的火控研究室（Fire Control Research Office）。这个组织关注的是装甲车的火力控制、火箭火药的弹道行为、火力控制以及防空立体高度和轰炸机测距仪的准确性。
While working there, JWT had countless interactions with Charles P. Winsor (1895-1951), a Harvard engineer with a Ph.D. in physiology. He was referred to as an "engineer-turned-physiologist-turned statistician." To quote John: "It was Charlie and the experience of working on the analysis of real data that converted me to statistics." JWT encountered many others at 20 Nassau Street who went on to renowned careers in statistics. It is hard to know just what the research consisted of, but one finds the following "example" in the Mosteller and Tukey regression book:
在那里工作期间，Tukey与哈佛大学的工程师、生理学博士Charles P. Winsor（1895-1951）有过无数次交流。他被称为“工程师转为生理学家，又转为统计学家”。引用Tukey的话：“是Charles和对真实数据进行分析的经历让我转向了统计学。”Tukey在纳索街20号遇到了许多其他人，他们后来在统计学领域获得了著名的职业生涯。很难确切知道这项研究包括什么，但你可以在Mosteller和Tukey所写的回归方面的书中找到以下“例子”：
During World War II, in investigating aiming errors made during bomber flights over Europe, one of the research organizations developed a regression equation with several carriers (explanatories). Among its nine or so carriers were altitude, type of aircraft, speed of the bombing group, size of group, and the amount of fighter opposition. On physical grounds, one might expect higher altitudes and higher speeds to produce larger aiming errors. It would not be surprising if different aircraft differed in performance. What the effect of size of group might be can be argued either way. But few people will believe that additional fighter opposition would help a pilot and bombardier do a better job. Nevertheless, amount of fighter opposition appeared as a strong term in the regression equation-the more opposition, the smaller the aiming error. The effect is generally regarded as a proxy phenomenon, arising because the equation had no variable for amount of cloud cover. If clouds obscured the target, the fighters usually did not come up and the aiming errors were ordinarily very large.
第二次世界大战期间，在调查轰炸机在欧洲上空飞行时的瞄准误差时，一个研究机构用几个变量（解释性）开发了一个回归方程。在它的九个左右的变量中，有高度、飞机类型、轰炸群的速度、机群的规模和战斗机的对抗数。从物理角度来看，人们可能会期望更高的高度和更高的速度会产生更大的瞄准误差。不同的飞机在性能上有所不同，也不足为奇。机群规模的影响可能是什么也可以争论。但是很少有人会相信额外的战斗机对抗会帮助飞行员和投弹手做得更好。然而，在回归方程中，战斗机的对抗数作为一个强项出现——对抗越多，瞄准误差越小。这种效应通常被认为是一种代理现象，因为方程中没有关于云层的变量。如果云层遮蔽了目标，战斗机通常不会上来，瞄准误差通常非常大。
Bell Telephone Laboratories and Princeton. In early 1945 "Mr. Tukey" began his long association with Bell Labs, Murray Hill, perhaps the foremost industrial research organization the world has known. He never left. He was full time at the Labs for a very brief period, taking leave from Princeton, but quickly switched to half time at Princeton and half time at the Labs. At the Labs he was in succession member of technical staff, subdepartment head of statistics research, associate executive director communication principles research, and associate executive director information sciences.
贝尔电话实验室和普林斯顿。 1945年初，“ Tukey先生”开始了他与贝尔实验室的长期联系，这也许是世界上最重要的工业研究组织。他从没离开过。他从普林斯顿休假后，在实验室全职工作了很短的一段时间，但很快就转到了普林斯顿的一半时间和实验室的一半时间。在实验室，他先后是技术人员、统计研究部门负责人、传播原理研究副执行董事和信息科学副执行董事。
In his parallel career at Princeton, John rose through the ranks to become full professor of mathematics, a position he held 1950-1966. He was first chair of the new statistics department 1966-1970, and professor of statistics from 1966 until his retirement in 1985.
在普林斯顿的平行生涯中，Tukey一路晋升，1950年成为数学系正教授，他担任这个职位直到1966年。1966年至1970年，他是新统计系的第一任主任，1966年至1985年退休，他一直是统计系教授。
At the Labs JWT was involved in a myriad of projects. One such project was the Nike missile system, in whose research and development the Bell System played a very substantial role. B. D. Holdbrook and JWT did the aerodynamics, the trajectory, and the warhead design. A collaboration with Ralph Blackman led to two highly influential papers that introduced the engineering and scientific worlds to the computational practice of spectrum analysis. The Labs supported much of his more academic research, as he has acknowledged.
在实验室，Tukey参与了无数项目。其中一个项目是Nike导弹系统，贝尔实验室在该系统的研发中发挥了非常重要的作用。B. D. Holdbrook和Tukey负责空气动力学、弹道和弹头设计。Tukey与Ralph Blackman的合作导致了有两篇高度影响力的论文，这些论文将工程和科学世界引入了频谱分析的计算实践。正如他所承认的那样，实验室支持了他更多的学术研究。
In 1956, Tukey set up the Statistical Techniques Research Group (STRG) at Princeton. The first computer on the Princeton campus was very possibly the IBM 650 at STRG's Gauss House on Nassau Street. Calculation and computers were ever present in JWT's life. The Fire Control Office had one of the first IBM multiplying punches and used it creatively. The classic work by Burks, Goldstine, and von Neumann (1946) states in the preface: "The authors also wish to express their thanks to Dr. John Tukey, of Princeton, for many valuable discussions and suggestions." Of just what JWT did Arthur Burks writes:
1956年，Tukey在普林斯顿组建了统计技术研究组（STRG）。普林斯顿校园的第一台计算机很可能是STRG位于纳索街高斯大厦的IBM650。计算和计算机一直存在于Tukey的生活中。火控研究室拥有首批IBM倍增冲头之一，并创造性地使用了它。Burks, Goldstine, and von Neumann（1946，*[Preliminary discussion of the logical design of an electronic computer instrument](https://deepblue.lib.umich.edu/bitstream/handle/2027.42/3972/bab6286.0001.001.pdf?sequence=5*）的经典著作在序言中写道：“作者还希望感谢普林斯顿的John Tukey博士，感谢他提出了许多有价值的讨论和建议。”Arthur Burks描述了Tukey的帮助：
John Tukey designed the electronic adding circuit we actually used in the IAS Computer. In this circuit, each binary adder fed its carry output directly into the next stage without delay. ... And this was the circuit actually used because it was reliable and much simpler than the alternative.
John Tukey设计了我们在IAS计算机中实际使用的电子添加电路。在此电路中，每个二进制加法器将其携带输出直接输入下一阶段。...这是实际使用的电路，因为它比替代方案可靠且简单得多。
Retirement. JWT retired from both the Labs and Princeton in 1985 at age seventy. At the retirement event W. O. Baker, retired chair of the board, remarked:
退休。 1985年，70岁的Tukey从实验室和普林斯顿退休。在退休活动中，董事会退休主席W. O. Baker说：
John has had an incisive role in each major frontier of telecommunications science and technology: uses of transistors and solid state; digital coding and computers; ...; evolution of software and operations support systems; earth satellite and other microwave techniques; electronic switching; laserbased photonics; topology of integrated circuits; ....
约翰在电信科学和技术的每个主要领域都敏锐地作用：晶体管和固态的使用； 数字编码和计算机； ...; 软件和操作支持系统的演变； 地球卫星和其他微波技术； 电子开关； 基于激光的光子学； 综合电路的拓扑； ...
At Princeton JWT became Emeritus Donner Professor of Science and Senior Research Statistician. He further worked as a consultant at places including: Xerox PARC, Bellcore, Merck, the Health Effects Institute, and the Educational Testing Service (ETS).
在普林斯顿，Tukey成为Donner荣誉科学教授和高级统计学研究员。他还在包括施乐PARC（Xerox PARC）、贝尔科勒（Bellcore）、默克（Merck）、健康影响研究所（Health Effects Institute）和美国教育考试服务中心（ETS, Educational Testing Service）在内的地方担任顾问。
Through the Bell Labs, Princeton, and Washington connections Tukey's skills became well known to many, and there were countless calls on his time. Throughout the years, he chaired or was a member of countless national panels, particularly ones concerned with protecting the environment. Here I mention some of his most notable activities.
通过与贝尔实验室、普林斯顿和华盛顿的联系，Tukey 的技能为许多人所熟知，他的时间被无数多的电话占用。 多年来，他担任了无数国家小组的主席或成员，特别是那些与环境保护有关的小组。这里我要提到他的一些最值得注意的活动
The Kinsey Report. In 1950, following a request, the American Statistical Association assembled a committee to review the statistical problems in Alfred C. Kinsey's work on sex research, work described in his controversial 1948 book, Sexual Behavior in the Human Male. The members of the committee were W. G. Cochran, F. Mosteller, and JWT. They were concerned particularly with the sampling methods and the absence of controlled randomness.
金赛(Kinsey)报告。 1950年，应要求，美国统计协会组建了一个委员会，审查 Alfred C. Kinsey性研究工作中的统计问题，他在1948年颇具争议的著作《人类男性的性行为》([Sexual Behavior in the Human Male])中描述了这一工作。委员会成员包括W. G. Cochran、F. Mosteller和Tukey。他们特别关注抽样方法和受控随机性的缺失。
Things did not go well in the committee's interaction with Kinsey. For example, following a dinner at the Kinsey home, Kinsey's wife, Clara, said, "I never fed a group of men that I would have so liked to have poisoned. ... Tukey was the worst." This and other anecdotes may be found in the J.H. Jones biography Alfred C. Kinsey.
委员会与金赛的互动并不顺利。例如，在金赛家中的一次晚餐后，金赛的妻子Clara说，“我从来没有喂过一群我非常想毒死的人。……Tukey是最糟糕的。”这件事和其他轶事可以在J.H. Jones为金赛写的传记中找到。
The U-2 Airplane. The "Cold War" was in full flight in the middle 1950s. One concern was the existence of a "bomber gap" that might enable the USSR to launch a surprise attack. Spurred by such concerns, President Eisenhower created the Killian Committee in 1954. Its Project 3 concerned technical intelligence collection. It was chaired by E. H. Land of Polaroid camera fame and included the astronomer J. G. Baker, the chemist J. W. Kennedy, the engineer A. Latham Jr., the Nobel laureate physicist E. M. Purcell, and JWT. Project 3 recommended the adoption of "a vigorous program for the extensive use ... of the most advanced knowledge in science and technology." The end proposal was to create a high-flying spy plane, and the development of the U-2 followed very quickly. Photos obtained by overflights of the USSR refuted the claims of a bomber gap, but at the same time they gave evidence of efforts to build long-range missiles. I heard it said that it was JWT who suggested the use of titanium in the construction of the bodies of such airplanes.
U-2飞机。 20世纪50年代中期，“冷战”全面爆发。一个担忧是“轰炸机缺口”的存在，这可能使苏联能够发动突然袭击。在这种担忧的刺激下，艾森豪威尔总统于1954年创建了Killian委员会。该委员会的项目3涉及技术情报收集。该委员会由宝丽来相机之乡的E. H. Land，包括天文学家 J. G. Baker、化学家J. W. Kennedy、工程师A. Latham Jr.、诺贝尔物理学奖得主E. M. Purcell和JWT。项目3建议采用“一个可以广泛使用强有力的计划…科学和技术中最先进的知识。”最终的提议是制造一架高空间谍飞机，U-2间谍飞机的发展也很快。通过飞越苏联获得的照片驳斥了轰炸机缺口的说法，但同时它们提供了（苏联）制造远程导弹的证据。我听说是JWT建议在这种飞机的机身构造中使用钛。
$\begin{array}{ll}\text { John W. Tukey的博士生名单 } \ \text { Fredrick Mosteller (1946) } & \text { Charles Lewis (1970) } \ \text { John Walsh (1947) } & \text { Stanislaus D'Souza (1971) } \ \text { Donald Fraser (1948) } & \text { Jon Knudsen (1971) } \ \text { Melvin Peisakoff (1950) } & \text { James Schlesselmen (1971) } \ \text { Leo Goodman (1950) } & \text { David Hoaglin (1971) } \ \text { Bernard Sherman (1950) } & \text { Alan Gross (1973) } \ \text { Ray Murphy (1951) } & \text { Anita Nowlin (1973) } \ \text { Paul Meier (1951) } & \text { Edward Binkowski (1974) } \ \text { Alan James (1953) } & \text { Steven Finch (1974) } \ \text { David Wallace (1953) } & \text { Lincoln Polissar (1974) } \ \text { Marvin Minsky (1954) } & \text { Paul Velleman (1976) } \ \text { Richard Link (1954) } & \text { Tony Quon (1976) } \ \text { Ralph Wormleighton (1955) } & \text { Susan Arthur (1979) } \ \text { Arthur Dempster (1956) } & \text { Michael Schwarzchild (1979) } \ \text { Thomas E. Kurtz (1956) } & \text { Karen Kafadar (1979) } \ \text { N. Roy Goodman (1957) } & \text { Roberta Guarino (1981) } \ \text { Bradley Bucher (1957) } & \text { Katherine Krystinik (1981) } \ \text { James Templeton (1957) } & \text { Paul Horn (1981) } \ \text { Harvey Arnold (1958) } & \text { Stephan Morgenthaler (1983) } \ \text { David Brillinger (1961) } & \text { Fanny O'Brien (1984) } \ \text { Donald Burdick (1961) } & \text { Dhammika Amaratunga (1984) } \ \text { John Hartigan (1962) } & \text { Clifford Hurvich (1985) } \ \text { Peter Nemenyi (1963) } & \text { George Easton (1985) } \ \text { Thomas Wonnacott (1963) } & \text { Ha Nguyen (1986) } \ \text { James Thompson (1965) } & \text { David Brown (1987) } \ \text { Morton Brown (1965) } & \text { Katherine Hansen (1988) } \ \text { W. Morven Gentleman (1966) Eugene Johnson (1988) } \ \text { James Filliben (1969) } & \end{array}$
In 1957 Eisenhower formed the President's Scientific Advisory Panel partly in response to the effective way that the scientists had dealt with the bomber gap.
1957年，艾森豪威尔组成了总统科学顾问小组（President's Scientific Advisory Panel），部分原因是为了顺应科学家们处理“轰炸机缺口”的有效方式。
Nuclear Disarmament. In 1959 JWT spent a month in Geneva, Switzerland, as a U.S. delegate to Technical Working Group 2 of the Conference on the Discontinuance of Nuclear Weapon Tests. His expertise, in part, concerned the time series problem of distinguishing earthquakes from nuclear explosions. John's wife, Elizabeth, said once that JWT was the one who suggested that tests might be able to be masked to a degree. This possibility very much startled the Russians.
核裁军。 1959年，JWT作为美国代表在瑞士日内瓦呆了一个月，参加了停止核武器试验会议第二技术工作组。他的专业知识部分涉及区分地震和核爆炸的时间序列问题。JWT的妻子 Elizabeth曾经说过，是JWT提出试验可能能够在一定程度上被掩盖的。这种可能性让俄罗斯人非常吃惊。
（译者注，技术工作组的会议主要目的在于研究一旦各方签订停止核爆炸试验的协定后要用什么方法来侦察可能的违约行为的问题。因此对地下核试验的监测问题十分重要，JWT的工作意在从地震波中鉴别出核试验信号，但当时并不能做到这一点，同时计算上的困难导致了快速傅里叶变换（FFT，fast Fourier transform）的发明。）
JWT has spoken about the difficulties of that period, describing it as a "time of stress ... like a utilities rate case." In 1967 he wrote:
JWT谈到了那个时期的困难，称之为“压力时期”...就像公用事业费率的案例一样。”1967年，他写道：
... resembles my experiences with Geneva ... where the political conference set up technical working groups in the hope that the scientists would settle some of the questions that the politicians could not. ... The politicians' attempt to evade responsibility failed, as was inevitable.
...类似于我在日内瓦的经历…在日内瓦，政治会议设立了技术工作组，希望科学家能解决政治家们无法解决的一些问题…政治家逃避责任的企图失败了，这是不可避免的。
Psephology-Election Forecasting. In 1960 RCA/NBC hired a statistical consulting firm to develop a procedure for projecting election results on the basis of partial counts. They involved John Mauchly and JWT amongst others. John Tukey became renowned that year for preventing an early call of victory for Richard Nixon.
选举学-选举预测。 1960年，RCA/NBC聘请了一家统计咨询公司，开发一种基于部分计数预测选举结果的程序。他们包括John Mauchly和JWT等人。JWT因阻止1960年理查德·尼克松（即1972年访华的尼克松总统，他在1968年才胜选美国总统）提前宣布胜选而闻名。
Starting with the 1962 congressional election, John assembled a statistical team to develop required methodology and to analyze the results as they flowed in. In the development of methods, the uncertainty was just as important as the point estimates. It turned out that the problem of projecting turnout was more difficult than that of projecting candidate percentage. The procedures developed might be described as an early example of empirical Bayes, or "borrowing strength", to use JWT's term.
从1962年国会选举开始，John组建了一个统计团队，开发所需的方法论，并在结果流入时对其进行分析。在方法的开发中，不确定性和点估计一样重要。事实证明，预测投票率的问题比预测候选人百分比的问题更困难。开发的程序可以被描述为经验贝叶斯的早期例子，或者用Tukey的术语“借力”。
NBC stopped involving John in 1980. One reason was that exit polls, where people are interviewed after they leave a polling station, had gotten refined. One can speculate on what might have happened had JWT been involved with one of the networks in making the Florida projections in the fall of 2000.
全国广播公司在1980年停止了雇佣John。一个原因是，出口民调方法已经得到了完善。出口民调是指人们离开投票站后接受采访。人们可以推测，如果JWT在2000年秋季参与了其中一个电视网对佛罗里达州的预测，会发生什么。（译者注：2000年时，乔治·华克·布什和阿尔·戈尔在2000年美国总统选举的投票结果未有明显差距，并在多处重新展开计票工作，其中佛罗里达州成为最关键的地区。见佛罗里达州选举重新计票事件。）
Education. JWT was very interested in the effectiveness of education. From 1965 on he was a consultant to ETS in Princeton. He had a long involvement with the National Assessment of Educational Progress (NAEP), which is a long-term program of assessing what the inhabitants of the U.S. can do as measured by their performance on exercises at various ages. JWT, Lee Cronbach, Ralph Tyler, Bob Abelson, and Lyle Jones met often in the late 1960s to guide its formation. JWT brought robust procedures, novel ways to measure change, uncertainty estimation, and careful interpretation of the results into the work.
教育。 Tukey对教育的有效性非常感兴趣。从1965年开始，他是普林斯顿ETS的顾问。他长期参与国家教育进步评估（NAEP，National Assessment of Educational Progress），这是一个评估美国居民能力的长期项目，通过他们在不同年龄阶段的练习成绩来衡量。Tukey、Lee Cronbach、Ralph Tyler、 Bob Abelson和Lyle Jones在20世纪60年代末经常会面，指导其形成。Tukey将稳健的程序、衡量变化的新方法、不确定性估计和对结果的仔细解释引入了这项工作。
Information Retrieval. Starting in the mid-1960s, John Tukey sought to bring order to the literature of statistics and probability by constructing indexes of the papers of those fields. He had done extensive work for Mathematical Reviews and prepared bibliographies before, e.g., for time series, and perhaps this is what spurred him on. In particular he constructed a citation index. Regarding that effort, it is impressive to see the roll call of eminent statisticians that JWT recruited to compile the papers and the reference lists. The citation index that was constructed then was one of the earliest outside of the legal profession. JWT constructed other indices as well. These were taken over later by the American Mathematical Society and are part of MathSciNet.
信息检索。 从20世纪60年代中期开始，John Tukey试图通过构建统计和概率领域的论文索引来给这些文献带来秩序。他为《数学评论》（Mathematical Reviews）做了大量工作，以前还准备了参考书目，例如时间序列，也许这就是激励他的原因。特别是，他构建了一个引文索引。关于这一努力，看到JWT招募杰出统计学家来汇编论文和参考文献列表令人印象深刻。当时构建的引文索引是法律界以外最早的索引之一。JWT还构建了其他索引。这些后来被美国数学学会接管，是MathSciNet的一部分。
After retirement JWT consulted at Xerox PARC. His name, with a variety of co-inventors from that company, appears on quite a number of patents, some of the key words of which are: information access, ordering document clusters, identifying drop words, generating thematic summaries, automatic document summarization, phase query formation.
退休后，JWT在Xerox Parc做咨询。他的名字，以及该公司的各种共同发明人，出现在相当多的专利上，其中一些关键词是：信息访问、排序文档集群、识别下拉词、生成主题摘要、自动文档摘要、阶段查询形成。
Census Adjustment. JWT advised the Census Bureau for many years. In 1980 the Census Bureau's step of adjusting the raw values to obtain "improved" estimates became a political issue. Probably to the great surprise of the Bureau, it found itself tangled up in the adversarial setup of the U.S. legal and political systems. This happened because congressional apportionment and the allocation of funds are both based on census counts. The Constitution states, regarding the House of Representatives, "The actual Enumeration shall be made ... in such Manner as they shall by Law direct." This leaves lots of room for argument.
人口普查调整。 JWT多年来一直为人口普查局提供咨询。1980年，人口普查局调整原始值以获得“改进”估计的步骤成为一个政治问题。可能令人口普查局非常惊讶的是，它发现自己陷入了美国法律和政治制度的对抗性设置中。这是因为国会的分配和资金分配都是基于人口普查。宪法规定，关于众议院，“应以法律规定的方式进行实际计数...”这留下了很多争论的空间。
JWT felt that adjustment should be made because errors would be smaller and their direction unpredictable. Regarding the idea that the errors would be smaller, he was perhaps spurred by the success of the borrowing strength procedure in election forecasting.
JWT认为应该作出调整，因为误差会较小，而且方向不可预测。关于误差会较小的想法，他可能是受到选举预测中借力程序成功的刺激。
Teaching. JWT's teaching style was on the oblique side. Indeed, sometimes people wondered if he was being deliberately obscure. It has been suggested that his home schooling background led to some of the difficulties. My personal impression was that he wanted the people with whom he interacted to figure things out on their own, to the degree possible.
教学。 JWT的教学风格偏向于隐晦。事实上，有时人们会怀疑他是否在故意隐晦。有人认为，他的家庭教育背景导致了一些困难。我的个人印象是，他希望与他打交道的人在可能的范围内自己把事情弄清楚。
The courses he presented at Princeton were state of the art, indeed introducing the art in many cases. The topics included: Monte Carlo, fractional replication, time series,.... Major investigators, such as Cuthbert Daniel, came along to class.
他在普林斯顿教授的课程是最先进的（state of the art，即SOTA），在许多情况下确实是引入了艺术。主题包括：蒙特卡洛、分数复制、时间序列...主要的研究人员，如Cuthbert Daniel，都来上课了。
John's interactions with students often took place at the house on Arreton Road, particularly on Saturdays. In particular he believed that gardening was a social activity.
John与学生的互动经常发生在阿雷顿（Arreton）路的房子里，尤其是在星期六。特别是他认为园艺是一项社交活动。
John was always very busy. In one period of his life, to deal with obligations in Washington and elsewhere, he scheduled four classes each week. Then he picked the three times that were the most convenient for the week at hand. Another method was to schedule classes for, say, 2:00-4:00 p.m. Tuesday/Thursday instead of the usual 2:00-3:15 p.m., and to skip a class sometimes and at other times to run it for two hours.
John总是很忙。在他一生中的一段时间里，为了处理在华盛顿和其他地方的义务，他每周安排四节课。然后他选择了手头一周最方便的三个时间。另一种方法是安排周二/周四下午2:00-4:00的课程，而不是通常的下午2:00-3:15，有时跳过一节课，有时则上两个小时的课。
JWT's contributions to mathematics proper were pre-World War II. They evidenced the mathematical ability that stood him in such good stead in his statistical and scientific work.
JWT对数学的贡献是在第二次世界大战前。它们证明了他的数学能力，这使他在统计和科学工作中受益匪浅。
His thesis, "On denumerability in topology", was submitted in 1939, nominally under the supervision of Lefschetz. Part of it later appeared in 1942 in the Annals of Mathematics Studies series under the title Convergence and Uniformity in Topology. Chapter 3 was never published because of overlap with work of M. M. Day.
他的论文 "论拓扑学中的可数性（On denumerability in topology） "于1939年提交，名义上是由Lefschetz指导的。其部分内容后来于1942年出现在《数学研究年鉴》（Annals of Mathematics Studies series）系列中，标题为《拓扑学中的收敛性和均匀性》（译者注：John W. Tukey，1942，Convergence and Uniformity in Topology）。第三章因为与M.M.Day的工作重叠而没有发表。
The principal part of the thesis was a formulation of uniformity in topology. JWT was seeking to extend convergence techniques to general spaces. The structures have three distinct, but equivalent, definitions via: Weil's pseudometrics, Bourbaki's entourages, and Tukey's families of covers. Appearing in the thesis is the so-called TeichmüllerTukey Lemma: "Every nonempty collection of finite character has a maximal set with respect to inclusion." This lemma is equivalent to the Axiom of Choice. Also in his book JWT christens Zorn's Lemma.
论文的主要部分是对拓扑学中一致性（uniformity）的表述。JWT试图将收敛技术扩展到一般空间(译者注：即一致空间（uniform space））。这些结构有三个不同但等价的定义:Weil的伪度量(pseudometrics），Bourbaki的随从（entourages），以及Tukey的覆盖族。论文中出现了所谓的Teichmüller-Tukey定理："每个非空的finite character在集合包含关系这个偏序下都有一个极大元"。这个定理等价于选择公理。在他的书中，JWT还对Zorn的引理进行了命名。
Tukey's approach was used extensively by J. R. Isbell and N. R. Howse in their books. Howse recently wrote me:
Tukey的方法被J. R. Isbell和N. R. Howse在他们的书中广泛使用。Howse最近写信给我。
... But Tukey's contribution in this area went beyond showing us how we should think about uniform spaces. His insight was almost prophetic. He sensed that the most interesting uniform spaces were the ones that were fully normal... Tukey predicted that the fully normal uniform spaces would play a major role in mathematics, and indeed they have.
...但是Tukey在这一领域的贡献不仅仅是向我们展示了我们应该如何考虑一致空间。他的见识几乎是预言。他感觉到，最有趣的一致空间是完全正常（fully normal）的空间。...Tukey预测，完全正常的一致空间将在数学中起主要作用，而且实际上它们具有。
D. H. Fremlin wrote:
D. H. Fremlin写道：
Of course Tukey's ideas on partial orders did have great influence on me. This was really through J. R. Isbell. Steve Todorovic took the same ideas much further ... I still believe that Tukey's notion of cofinal equivalence gives fundamental insight into some important questions in set-theoretic analysis.
当然，Tukey关于偏序的观点确实对我影响很大。这真的是通过 J. R. Isbell完成的。Steve Todorovic对相同的想法进行了更深入的研究...我仍然相信Tukey的共尾等价（cofinal equivalence）概念为集合论分析中的一些重要问题提供了基本的见解。
There are papers with R. P. Boas and with A. Stone as well as solo-authored articles. The one with Stone, titled "Generalized sandwich theorems", showed that the volumes of any
Tukey有与R. P. Boas和A. Stone合作的论文，也有单人写作的文章。TukeyStone的一篇题为“广义三明治定理”（译者注：A. H. Stone, J. W. Tukey，1942，Generalized sandwich theorems）的文章表明，$\mathbf{R}^{n}$中任何$n$个可测集的测度可以同时被一个$（n-1）$维超平面二分，平面可以被视为无限半径的超平面。火腿三明治定理定理（Ham sandwich theorem）是$n=3$的情况。
Statistics is a science, not a branch of mathematics, but uses mathematical models as an essential tool.
-JWT
统计学是一门科学，不是数学的一个分支，但使用数学模型作为基本工具。
-JWT
The Mosteller-Tukey bombing example mentioned above gives an indication of the difficulties of interpretation of results that statisticians deal with regularly in the world of experiments and data. JWT's statistical contributions reflect his struggles with that often messy world. Some highlights follow.
上面提到的Mosteller-Tukey关于调查轰炸机瞄准误差的例子表明了统计学家在实验和数据世界中经常处理的结果解释的困难。JWT的统计贡献反映了他与这个经常混乱的世界的斗争。下面是一些亮点。
Robustness. Robustness refers to the property of a procedure remaining effective even in the absence of usual assumptions such as normality and no incorrect data values. In simplest terms the idea is to improve upon the use of the simple arithmetic average in estimating the center of a distribution. As a simple case one can ask: Is it ever better to use the sample median than the sample mean, and if so, when?
稳健性（Robustness)。 鲁棒性是指即使在没有通常假设（如正态性和没有不正确的数据值）的情况下，程序仍保持有效的性质。简单地说，这个想法是在使用简单的算术平均值来估计分布中心的基础上改进。作为一个简单的例子，我们可以问：使用样本中位数比使用样本均值更好吗？如果是的话，是什么时候？
Tukey had gotten interested in the problem of robustness in the last stages of his work at 20 Nassau Street. He remarked that C. P. Winsor taught him to beware of extreme deviates. The two learned, for example, that if you add
Tukey在纳索街20号工作的最后阶段对稳健性问题产生了兴趣。他说，C.P. Winsor教他要小心极端偏差。例如，两人了解到，如果你把高斯的$0.1%$加上基本高斯的三倍，那么平均偏差比经典的标准偏差作为衡量尺度的方式更好。
An important part of JWT's contribution was developing particular forms of problem distributions, those displaying the difficulties that occurred in practice. The ones employed included the mixture of Gaussians, the slash, and the
JWT贡献的一个重要部分是开发了特定形式的问题分布，那些显示了在实践中发生的困难。所采用的包括高斯混合模型、斜线（slash）和$g-h$。
For the smoothing case he recommended running medians. This tool has proved exceedingly useful in image processing.
对于平滑的情况，他建议使用中位数。该工具已被证明在图像处理中非常有用。
Time Series. During World War II, JWT had become acquainted with Norbert Wiener's seminal work, later published in book form.
时间序列。 在第二次世界大战期间，JWT已经熟悉了Norbert Wiener的开创性工作，后来以书的形式出版。
JWT has told the story of how he got interested in the spectral analysis of time series. Just after the war, a Bell Laboratories engineer working on tracking radars was heading to a conference and wished to show a slide of an estimated power spectrum. He met with Tukey and Richard Hamming. Those two knew the Fourier relation between the autocovariance function and the spectrum and took the Fourier transform of the sample autocovariance function. The estimate was seen to ripple. This led Hamming to make the suggestion that the engineer's estimate would look better were it smoothed, for example via the weights
JWT讲述了他是如何对时间序列的频谱分析产生兴趣的。战后不久，贝尔实验室一位研究跟踪雷达的工程师正前往一个会议，希望展示一张估计功率频谱的幻灯片。他会见了Tukey和Richard Hamming。这两个人知道自协方差函数和频谱之间的傅里叶关系，并对样本自协方差函数进行傅里叶变换。估计被认为是波动的。这促使Hamming提出建议，如果平滑，工程师的估计会看起来更好，例如通过权重$0.25,0.50,0.25$。结果是惊人的成功，并导致了JWT在时间序列分析领域的重大参与。
Tukey often argued the advantages in favor of the power spectrum over the autocorrelation. Such an argument is needed because the two are mathematically equivalent. He claimed that the analyst could learn more from a spectral analysis, particularly in discovering unexpected phenomena.
Tukey经常论证功率谱而不是自相关函数的优势。这样的论证是需要的，因为两者在数学上是等价的。但他声称，分析者可以从频谱分析中学到更多东西，特别是在发现意外现象方面。
Bogert, Healey, and Tukey introduced cepstral analysis as a way to address the problem of distinguishing an earthquake from an explosion [1]. This was based on the observation that a signal laid on top of itself with a delay leads to a rippling spectrum. The delay may be estimated as the frequency of the ripple and from that the depth of the seismic event. A lot of colorful language, like "saphe cracking", "quefrency", and "alanysis" was also introduced in that paper. Of the language Dick Hamming remarked to John that "from now on you will be known as J. W. Cutie." The cepstrum was quite unlike any time series quantity that had been proposed previously.
Bogert、Healey和Tukey引入倒频谱分析作为解决区分地震和爆炸问题的一种方法（译者注：Bogert, Healy和Tukey, 1963, The quefrency analysis of time series for echoes : cepstrum, pseudo-autocovariance, cross-cepstrum and saphe cracking.）。这是基于这样一个观察，即一个信号叠加在其自身之上并具有延迟，会导致频谱波动。可以将延迟估计为波纹的频率，并根据该频率估计地震事件的深度。该论文还介绍了许多丰富多彩的语言，如“saphe cracking”、“quefrency”和“alanysis”。关于这种语言，Dick Hamming对John说：“从现在开始，你将被称为J. W. Cutie。”倒频谱与之前提出的任何时间序列量都完全不同。
Nearly all of the time series papers may be found in Volumes I and II of the Collected Works.
几乎所有时间序列的论文都可以在《John W. Tukey作品集》的第I和II卷中找到。
Data Analysis. JWT had a philosophy for studying experimental results from early on. He called it data analysis. One of his descriptions was the following:
数据分析。 JWT很早就有一个研究实验结果的哲学。他称之为数据分析。他的一个描述是这样的
... data analysis which I take to include, among other things: procedures for analyzing data, techniques for interpreting the results of such procedures, ways of planning the gathering of data to make its analysis easier, more precise or more accurate, and all the machinery and results of (mathematical) statistics which apply to analyzing data.
...数据分析，我认为其中包括：分析数据的程序，解释这些程序结果的技术，计划收集数据以使其分析更容易、更精确或更准确的方法，以及适用于分析数据的（数学）统计的所有机制和结果。
His 1962 paper on the subject changed the paradigm and language of statistics. His 1977 book made the techniques available to a very broad audience. JWT recognized two types of data analysis: exploratory data analysis (EDA) and confirmatory data analysis (CDA). In the former the data are sacred while in the latter the model is sacred. In EDA the principal aim is to see what the data are "saying". It is used to look for unexpected patterns in data. In CDA one is trying to disconfirm a previously identified indication, hopefully doing this on fresh data. It is used to decide whether data confirm hypotheses the study was designed to test.
他1962年关于这一主题的论文(译者注：The Future of Data Analysis)改变了统计学的范式和语言。他1977年的书(译者注：Exploratory Data Analysis）使这些技术面向非常广泛的受众。JWT认识到两种类型的数据分析：探索性数据分析（EDA,exploratory data analysis）和验证性数据分析（CDA，confirmatory data analysis）。在前者中，数据是神圣的，而在后者中，模型是神圣的。在EDA中，主要目的是看看数据在“说”什么。它被用来寻找数据中意想不到的模式。在CDA中，人们试图推翻以前确定的迹象，希望在新数据上这样做。它被用来决定数据是否证实了这项研究旨在测试的假设。
Some parts of EDA are ugly, but the real world is ugly, particularly when errors and other aberrant material enters a data set.
EDA的某些部分是丑陋的，但现实世界也是丑陋的，尤其是当错误和其他异常材料进入数据集时。
Statistical Graphics.
统计图
The best single device for suggesting, and at times answering, questions beyond those originally posed is the graphical display.
JWT
除了最初提出的问题之外，最好的建议和回答问题的方式的是图形显示。
-JWT
E. Tufte has remarked of Tukey's work on graphics that "he made the field respectable." In particular one can mention JWT's paper at the Vancouver International Congress of Mathematicians.
E. Tufte评论了Tukey在图形方面的工作，“他让这个领域变得受人尊敬。”特别是，人们可以提到JWT在温哥华国际数学家大会上的论文。
Statistical graphics are a critical part of EDA. Tukey's boxplots and stem-and-leaf diagrams now appear throughout scientific presentations and high-school texts. A field that he popularized is dynamic graphics. Following Tukey's direction a display program, PRIM-9, was developed at SLAC (Stanford Linear Accelerator Center) for looking at multidimensional data. It was based on point cloud rotation and associated dynamic operations. Nowadays point cloud rotation is basic to statistical packages. One difficulty was which direction to rotate to. JWT proposed the procedure of projection pursuit to handle this. It seeks 1 and 2 dimensional projections of multivariate data, looking for data points that concentrate near intermediatedimensional manifolds.
统计图形是EDA的重要组成部分。Tukey的箱线图和茎叶图现在出现在科学演讲和高中文本中。他推广的一个领域是动态图形。根据Tukey的指导，斯坦福线性加速器中心（SLAC，Stanford Linear Accelerator Center）开发了一个显示程序PRIM-9，用于查看多维数据。它基于点云旋转和相关的动态操作。如今点云旋转是统计包的基础。一个困难是旋转到哪个方向。JWT提出了投影追踪程序来处理这个问题。它寻求多元数据的1维和2维投影，寻找集中在中间维流形附近的数据点。
JWT's last book, written together with Basford, was titled The Graphical Analysis of Multivariate Data. It contained novel graphical procedures and his current views on the problem of multiple comparisons.
JWT的最后一本书，与Basford合著的《多元数据的图形分析》（译者注：Tukey，Basford，1998，Graphical Analysis of Multiresponse Data），书中包含了新颖的图形化方法和他目前对多重比较问题的看法。
Analysis of Variance (ANOVA). ANOVA and regression are the workhorses of statistics, and JWT made many important contributions to each of them. An assumption of additivity is basic, and JWT was concerned with how to examine that assumption in practice. He remarked, "I carried the problem about how to do something about removable non-additivity 'in my pocket' for at least two years before the right idea dawned." The idea was to work with a bilinear expansion in the additive parts. The resulting paper was titled "One degree of freedom for additivity".
方差分析（ANOVA，Analysis of Variance ）。 方差分析和回归分析是统计学的重中之重，JWT对其中的每一项都做出了许多重要贡献。可加性假设是基本的，JWT关心的是如何在实践中检验这一假设。他说：“关于如何移除非可加性做些什么，我把这个问题‘放在口袋里’至少两年了，直到有了正确的想法。”这个想法是在可加性部分进行双线性展开。由此产生的论文题为《可加性的一个自由度》（疑问：原文错误，论文题目是应为Non-Additivity，非可加性，如何处理？。Tukey,1949,one Degree of Freedom for Non-Additivity)。
Another novel idea of his was dyadic ANOVA, an analysis of variance for vectors. To develop a multivariate analysis of variance he worked with the inner product of the data vector with an abstract-valued vector of the same length.
他的另一个新想法是二元方差分析，一种向量方差分析。 为了开发多元方差分析，他研究了数据向量与相同长度的抽象值向量的内积。
Multiple Comparisons. In many statistical situations there is a concern to control the error rate of statements being made. Difficulties arise if one gives in to temptations associated with the application of a number of tests to the same data set, as in asking several questions at the same time, or in carrying out several analyses of the same data set.
多重比较。 在许多统计问题中，需要控制所作陈述的错误率。如果一个人屈服于对同一数据集应用大量测试的诱惑，比如同时提出几个问题，或者对同一个数据集进行几次分析，就会出现困难。
This is another problem that JWT acknowledged working on for a number of years before developing a solution. He actually commented once on how few papers he had written during that period. His solution was developed in a famous 1953 unpublished manuscript, "The problem of multiple comparisons". It now appears in the Collected Works.
这是JWT承认在开发解决方案之前工作了多年的另一个问题。他实际上曾经评论过他在那段时间写的论文有多少。他的解决方案是在1953年一篇著名的未发表手稿《多重比较问题》（The problem of multiple comparisons）中开发的。它现在出现在《John W. Tukey作品集》中。
The Tukey technique is often seen under the rubric of the "honestly significantly difference" (HSD) test, another term that is JWT's. In later years JWT moved on to using the false discovery rate (FDR) of Benjamini and Hochsted when many things were being compared.
Tukey技术经常出现在“诚实显著差异”（HSD，honestly significantly difference）测试的标题下，这是JWT的另一个术语。在后来的几年里，当许多事情被比较时，JWT开始使用Benjamini和Hochsted的错误发现率（FDR，false discovery rate）。
John W. Tukey的出版物清单
- J. W. Tukey's Collected Works
- Volumes I-II, Time Series, 1984-1985, edited by D. R. Brillinger
- Volumes III-IV, Philosophy and Principles of Data Analysis, 1984-1986, edited by L. V. Jones
- Volume V, Graphics, 1988, edited by W. S. Cleveland
- Volume VI, More Mathematical, 1990, edited by C. M. Mallows
- Volume VII, Factorial and ANOVA, 1992, edited by D. R. Cox
- Volume VIII, Multiple Comparisons, 1994, edited by H. I. Braun
- J. W. Tukey's Index to Statistics and Probability
- Volume 1, The Citation Index, 1973
- Volumes 2-3, Permuted Titles, 1975, with I. C. Ross
- Volumes 4, Locations and Authors, 1973, with I. C. Ross
- These indexes appeared as Volumes 2-5 of the Information Access Series; Volume 1 of that series is Statistics CumIndex, 1973, with J. L. Dolby.
- Other Books of J. W. Tukey
- Convergence and Uniformity in Topology, 1940
- Data Analysis and Regression, 1977, with F. Mosteller
- Exploratory Data Analysis, 1977
- Graphical Analysis of Multiresponse Data, 1998, with K. E. Basford
- The Management of Weather Resources, Volume 2, The Role of Statistics, 1978, with D. R. Brillinger and L. V. Jones
- The Measurement of Power Spectra from the Point of View of Communications Engineering, 1959, with R. B. Blackman
- Robust Estimates of Location, 1972, with D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, and W. H. Rogers
- Statistical Problems of the Kinsey Report on Sexual Behavior in the Human Male, 1954, with W. G. Cochran and F. Mosteller
- Books Edited by J. W. Tukey
- Configural Polysampling: A Route to Practical Robustness, 1991, with Stephan Morgenthaler
- Exploring Data Tables, Trends, and Shapes, 1985, with David C. Hoaglin and Frederick Mosteller
- Fundamentals of Exploratory Analysis of Variance, 1991, with David C. Hoaglin and Frederick Mosteller
- Understanding Robust and Exploratory Data Analysis, 1983, with David C. Hoaglin and Frederick Mosteller
The Jackknife. This is a tool that Tukey proposed and used for CDA over many years. In naive terms it provides an indication of the uncertainty of an estimate by judiciously combining estimates based on subsets of the full data set.
刀切法（Jackknife）。 这是Tukey多年来提出并用于CDA的工具。用简单的术语来说，它通过明智地组合基于完整数据集子集的估计来指示估计的不确定性。
He called the procedure the jackknife because
他称该程序为刀切法，因为
The procedure ... shares two characteristics with a Boy Scout Jackknife: (1) wide applicability to very many different problems, and (2) inferiority to special tools for those problems for which special tools have been designed and built.
该程序…与童子军折刀有两个特点：（1）广泛适用于许多不同的问题，以及（2）对于那些已经设计和制造了专用工具的问题，该程序不如专用工具。
It provides uncertainty analyses when exact estimates are unavailable.
当无法获得准确估计时，它提供不确定性分析。
Other Contributions. JWT successfully pushed for applications of statistical methods to a wide variety of fields. To mention a few: economics, aeronautics, geophysics, oceanography, meteorology, space science, and astrophysics.
其他贡献。 JWT成功地推动了统计方法在广泛领域的应用。仅举几例：经济学、航空学、地球物理学、海洋学、气象学、空间科学和天体物理学。
Brief mention may also be made of JWT's novel contributions to: mathematical statistics, quality assurance, theory of games, and medical statistics. There is much that remains unpublished, including various Princeton course notes, working papers, and technical reports. It is a shame that work ended on his Collected Works, which brought various unpublished items into public view.
还可以简要提及智威汤逊在数理统计、质保、博弈论和医学统计方面的新贡献。还有许多未发表的内容，包括普林斯顿的各种课程笔记、工作论文和技术报告。遗憾的是 【疑问：遗憾？应该是庆幸吧】，他的作品集的工作结束了，这使得各种未发表的项目进入了公众的视野。
Head/hand Methods. The arithmetic skills of Feynman and von Neumann are legendary, and Tukey had these too. In particular he developed a variety of quick methods for carrying out statistical analyses in real time. These were basic to his consulting work. He spoke of "using pen, paper, and slide rule." There are a variety of his numerical short cuts presented in the EDA book.
心算/手算方法。 Feynman和von Neumann的算术技巧是传奇，Tukey也有这些技能。特别是，他开发了各种实时进行统计分析的快速方法。这些是他咨询工作的基础。他谈到“使用笔、纸和计算尺”。EDA的书中提供了他的各种数字捷径。
JWT was a member of the Supervising Scientific Committee of the highly influential handbook of mathematical functions edited by Abramowitz and Stegun. The story was the suggestions were all generated spontaneously during a single lunch meeting.
JWT 是 Abramowitz 和 Stegun 主编的极具影响力的数学函数手册的科学监督委员会成员。 故事是这些建议都是在一次午餐会议上自发产生的。
Monte Carlo/Simulation. JWT made contributions to the techniques of Monte Carlo. In 1956 Trotter and Tukey introduced the technique of conditional Monte Carlo wherein one estimates an integral of a weighted function by simple Monte Carlo, instead of the integral of the function itself. This is a means of variance reduction. In it one imbeds the sample space in a larger one.
蒙特卡洛/模拟。 JWT对蒙特卡洛技术做出了贡献。1956年，Trotter 和 Tukey 引入了条件蒙特卡罗技术，其中人们通过简单的蒙特卡罗估计加权函数的积分，而不是函数本身的积分。 这是一种减少方差的方法。其中一个将样本空间嵌入到一个更大的空间中。
He also introduced polysampling where in a single set of samples is able to produce estimates of means and standard errors under two, three, ... different distributions at the same time by combining the sample with two, three, ... sets of weights.
他还引入了多重抽样，其中同一组样本同时在两个、三个……不同的分布下产生均值和标准误差的估计值，再通过他们的加权组合得到均值和标准误差的估计值。(译者注:可参考Tukey,1987,Configural Polysampling）
Fourier Analysis. JWT had picked up on the Gibbs phenomenon and the practical need for convergence factors early on. He also wrote concerning the difficulties of interpretation such as those caused by aliasing.
傅立叶分析。 JWT很早就发现了Gibbs现象和收敛因素的实际需求。他还写了一些关于解释困难的文章，例如由混叠（aliasing）引起的困难。
In lectures at Princeton in 1963 he showed that if one wished the discrete Fourier transform of a sequence of
1963年在普林斯顿的讲座中，他展示了如果希望对一个由$N$个数组成的序列进行离散傅里叶变换，那么当$N=G H$时，经验傅里叶变换的计算只需要$（H+2+G）G H$次乘法。他进一步指出，对于$N=4^{k}$，则需要不到$N+N\log_{2}N$次。由此产生的Cooley-Tukey论文已成为引文经典（译者注：Cooley,Tukey,1965,An algorithm for the machine calculation of complex Fourier series）。当快速傅里叶变换(FFT，fast Fourier transform)普及时，信号处理非常迅速地从模拟型(analog)转向数字型（digital）。
There is one sad aspect to the FFT story. On numerous occasions JWT made remarks of the type, "Gordon Sande ... had purely independently found an algorithm to reach the same effect." He clearly felt bad about Sande's not receiving some share of the credit.
快速傅里叶变换的故事有一个悲伤的方面。JWT在许多场合发表了类似的言论，“Gordon Sande ... 纯粹是独立地找到了一种算法来达到同样的效果。”他显然对桑德没有得到部分荣誉感到难过。
Another side of Tukey's FFT work was his and his collaborators' finding novel applications of the algorithm(s).
Tukey 的FFT工作的另一方面是他和他的合作者发现了算法的新应用。
Throughout his career JWT served in various capacities as an officer in professional societies: AMS Council, vice-president ASA (American Statistical Association), vice-president SIAM (Society for Industrial and Applied Mathematics), president Institute of Mathematical Statistics. He received many prominent honors: member National Academy, recipient National Medal of Science, foreign member Royal Society of London, and some seven honorary doctorates. He received his first from Case Institute of Technology in 1962. The citation of the award from the University of Waterloo in 1999 included the words: "He has pioneered developments in fields that intersect with every development in mathematics facilities."
在他的职业生涯中，JWT以各种身份在专业协会担任职务： 美国统计协会（AMS，American Statistical Association）理事会、副主席，工业和应用数学学会（SIAM ，Society for Industrial and Applied Mathematics)副主席，数理统计学会（IMS，Institute of Mathematical Statistics）会长。他获得了许多杰出的荣誉：美国国家科学院院士、美国国家科学奖章获得者、英国皇家学会外籍会员和大约七个荣誉博士学位。1962年，他第一次从凯斯理工学院获得学位。滑铁卢大学1999年对该奖项的引用包括这样一句话：“他引领了与数学的每一次发展相交叉的领域的发展。”
John Tukey was famous for creating new words and new uses for old ones. He said that he did this to avoid confusions.
John Tukey以创造新词和旧词的新用法而闻名。他说他这样做是为了避免混淆。
He is said to have introduced the terms: "bit", "linear programming", "ANOVA", "Colonel Blotto", and was first into print with "software". Of these efforts L. Hogben and M. Cartwright wrote, "The introduction by Tukey of bits for binary digits has nothing but irresponsible vulgarity to commend it." Tukey's word "polykay" was described as "linguistic miscegenation" by Kendall and Stuart because of its combining a Greek prefix with a Latin suffix. JWT did it again later with "polyspectrum".
据说他引入了“比特（bit）”、“线性规划（linear programming）”、“方差分析（ANOVA，Analysis of Variance ）”、“上校博弈（Colonel Blotto）”等术语，并首次使用“软件(software)”的当代意义。在这些努力中，L. Hogben和M. Cartwright写道：“Tukey为二进制数字引入的比特，除了不负责任的粗俗之外，没有什么值得称赞的。”图基的单词“Polykay”被Kendall和Stuart描述为“语言混杂”，因为它结合了希腊前缀和拉丁后缀。JWT后来用“多谱（polyspectrum）”再次做到了这一点。
His own name led to some amusing confusions. In 1980 NASA sponsored a symposium on using robotics to explore space using self-replicating systems. (Feynman and JWT were among the attendees.) Coming out of the discussion was "Tukey's ratio"-the fraction of total necessary resources that must be supplied by some external agency. It was also referred to in that report as the "Turkey Ratio".
他自己的名字引起了一些有趣的困惑。1980年，美国国家航空航天局主办了一次利用机器人技术利用自我复制系统探索太空的研讨会。（Feynman和JWT是与会者之一。）讨论的结果是“Tukey比率（Tukey Ratio）”——必须由外部机构提供的总必要资源的一部分。该报告还称之为“土耳其比率（Turkey Ratio）”。
Many of the Tukey papers, as well as a number of previously unpublished works, may be found in The Collected Works of John W. Tukey published by Wadsworth, Belmont. These volumes were Bill Cleveland's wonderful prescient idea. There are JWT's and editors' forewords discussing various of the individual papers.
许多Tukey的论文，以及一些以前未发表的作品，可以在贝尔蒙特沃兹沃思出版的《The Collected Works of John W. Tukey》中找到。这些书是Bill Cleveland的绝妙先见之明。有JWT和编辑的前言在讨论各种不同的论文。
There are a partially complete curriculum vitae, a list of coauthors, and a bibliography of his works in [2]. Papers are still appearing. JWT has more than 105 coauthors, the most joint works being with Fred Mosteller. There is a Bell Labs website containing a variety of materials related to John, including personal reminiscences [4]. There is an oral history with JWT and others mentioning him [5].
在[Brillinger,Fernholz, and Morgenthaler, 1997, The Practice of Data Analysis ]中有Tukey有一份部分完整的简历，一份合著者的名单，以及他著作的参考书目。论文仍在出现。JWT有超过105名合著者，合作最多的是Fred Mosteller。还有一个贝尔实验室网站，包含与约翰有关的各种材料，包括个人回忆。有一个与JWT和其他人提到他的口述历史。（译者注：网站链接已失效）
John Tukey was a giant of a scientist and public servant. He was an academic who liked to argue and expected to win. But at the same time he was the most generous, patient, caring soul.
John Tukey是一位伟大的科学家和公务员。他是一个喜欢争论并期望获胜的学者。但同时，他也是最慷慨、最有耐心、最关心他人的人。
When my elder son died after a twenty-year struggle with a brain tumor and JWT heard of his death, he telephoned. He was weeping away.
当我的大儿子在与脑肿瘤的二十年斗争中去世，JWT听说他的死亡时，他打电话给他。他在哭泣。
JWT dealt with his own personal grief when his wife Elizabeth died; he wrote some very special words:
当他的妻子Elizabeth去世时，JWT处理了自己的悲伤。他写了一些非常特别的话：
One is so much less than two.
一个小于两个。
This material derives from a much longer document, rough drafts of which various people commented on. In particular I wish to thank: Bruce Bolt, A. W. Burks, Bill Cleveland, D. H. Fremlin, J. Heyse, N. R. Howse, Lyle Jones, Ernest Michael, Ray Waller, Eugene Garfield, David Gauld, Karen Kafadar, Luisa Fernholz, Mike Godfrey, Garry Tee, Leo Goodman, Ram Gnanadesikan, Stephan Morgenthaler, Manny Parzen, Bill Williams, and the editor, among others. I apologize for not referring more specifically to JWT's collaborators on occasion. JWT himself was totally generous in acknowledging them.
该材料源自一份更长的文件，草稿中有许多人发表了评论。 我要特别感谢：Bruce Bolt、A.W. Burks、Bill Cleveland、D. H. Fremlin、J. Heyse、N. R. Howse、Lyle Jones、Ernest Michael、Ray Waller、Eugene Garfield、David Gauld、Karen Kafadar、Luisa Fernholz、Mike Godfrey， Garry Tee、Leo Goodman、Ram Gnanadesikan、Stephan Morgenthaler、Manny Parzen、Bill Williams 和编辑等。我很抱歉有时没有更具体地提到JWT的合作者。JWT本人非常慷慨地承认了他们。
[1] B. P. BOGert, M. J. R. Healey, and J. W. TuKey, The quefrency alanysis of time series for echoes: cepstrum, pseudo-autocovariance, cross-cepstrum and saphecracking, Proceedings of the Symposium on Time Series Analysis, M. Rosenblatt, ed., Wiley, New York, 1963, pages 209-243.
[2] D. R. Brillinger, L. T. Fernholz, and S. Morgenthaler, eds., The Practice of Data Analysis, Princeton University Press, 1997.
[3] J. W. Cooley and J. W. TuKEY, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 (1965) 297-301.
[4] Memories of John W. Tukey website, http://cm.be11-1abs.com/cm/ms/departments/sia/tukey/.
[5] The Princeton Mathematics Community in the 1930s: An oral history project, http://www.princeton.edu/mudd/math