"....The most fruitful areas for the growth of the sciences were those which had been neglected as a no-man's land between the various established fields.
.....It is these boundary regions of science which offer the richest opportunities to the qualified investigator. ........
a proper exploration of these blank spaces on the map of science could only be made by a team of scientists, each a specialist in his own field but each possessing a thoroughly sound and trained acquintance with the fields of his neighbors; all in the habit of working together, of knowing one another's intellectual customs, and of recognizing the significance of a colleague's new suggestion before it has taken on a full formal expression.
.............We had dreamed for years of an institution of independent scientists, working together in one of these backwoods of science, not as subordinates of some great executiove officer, but joined by the desire , indeed by the spiritual necessity, to understand the region as a whole, and to lend one another the strength of that understanding."
Norbert Wiener (1948, 1962) in his
own introduction to Cybernetics.
For a long time I have thought I was a statistician, interested in
inferences from the particular to the general. But as I have watched mathematical statistics evolve, I have had cause to wonder and to doubt. .......
To the extent that pieces of mathematical statistics fail to contribute, or
are not intended to contribute, even by a long and tortuous chain, to the
practice of data analysis, they must be judged as pieces of pure mathematics,
and criticized according to its purest standards.
Individual parts of mathematical statistics must look for their justification toward either data analysis or pure mathematics. Work which obeys neither ......, to be doomed to sink out of sight. And we must be careful that, in its sinking, it does not take with it work of continuing value.
John W Tukey (1962), in
The Future of Data Analysis.
Statisticians should strive to be first-rate scientists, not second-rate mathematicians.
G.E.P. Box (1968), The Future of Statistics.
Clearly, I have been much influenced by Thomas Kuhn's ideas on the structure of scientific revolutions. In statistics as well as other fields of applied mathematics, one can usually distinguish three phases .... In Phase One, there is a vague awareness of an area of open problems, one develops ad hoc solutions to poorly posed questions, and one gropes for the proper concepts. In Phase Two, the "right" concepts are found, and a viable and convincing theoretical treatments is put together. In Phase Three, the theory begins to have a life of its own, its consequences are developed further and further, and its boundaries of validity are explored by ....; in short, it is squeezed dry.
Peter J. Huber (1975), in
Applications vs. Abstraction: The Selling out of Mathematical Statistics?
Proceedings of the Conference on Directions for Mathematical Statistics (Advances of Applied Probability, 1975, Vol.7, No.3, pp.84-89).
So for the future I recommend that we work on interesting problems, avoid
dogmatism, contribute to general mathematical theory or concrete practical applications according to our abilitities and interests and, most important, formulate for ourselves a canon of humanistic (scientific? JL) values that will inspire and justify our work on a higher level than that of the well-trained and useful technician .......I am not sure whether someone with a statistical problem would be well-advised even today to consult a statistician. So I would add ....that if you are consulted about a practical problem and aren't sure that you can supply the correct answer, at least try to follow the Hippocratic Oath and do no harm.
Herbert Robbins In
Wither Mathematical Statistics?,
Proceedings of the Conference on Directions for Mathematical Statistics (Advances in Applied Probability, Vol. 7, Sep. 1975, pp. 116-121).
John W. Tukey:"...It's better to have an approximate solution to the right problem than to have an exact solution to the wrong one. ......the use of techniques is not confined to the instances that are covered by theory. If you had to have theory to cover evey application, very few techniques would ever get used. ........that statistics needs to be broad, not narrow."
in
Frederick Mosteller and John W. Tukey: A Conversation.
Moderated by F.J. Anscombe. Statistical Science, 1986, Vol.3, No.1, 136-144.
There's another trait on the side which I want to talk about; that trait is ambiguity. It took me a while to discover its importance. Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance. But most great scientists are well aware of why their theories are true and they are also well aware of some slight misfits which don't quite fit and they don't forget it. ........When you find apparent flaws you've got to be sensitive and keep track of those things, and keep an eye out for how they can be explained or how the theory can be changed to fit them. Those are often the great contributions. Great contributions are rarely done by adding another decimal place. It comes down to an emotional commitment. Most great scientists are completely committed to their problem. Those who don't become committed seldom produce outstanding, first-class work.
Richard Hamming "You and Your Research", March 1986. Bellcore Colloquium.
"Mathematicians only slowly realized that an intellectual revolution was taking place through the new inductive uses of mathematics. Even now, people often think statistics can be reduced to deduction--that once you have learnt the theory you understand statistics. Gosset and Fisher believed otherwise. They believed that understanding of inductive reasoning is acquired through learning to deal with real data inductively, knowing that practical action will be taken on the basis of your conclusions. Knowing the theory is not the answer, but (though) it can (may) help you find the answer to statistical problems."
Joan Fisher Box (1987) in Guinness, Gosset, Fisher, and Small Samples. Statistical Science, Vol.2, No.1, p.45.
Fisher believed that the primary task of the practicing statistcian is to get inside the mind of a research scientist facing a set of challenging questions. Only then should he or she turn to mathematical idealizations that represent aspects of a question under study and lead directly to answering carefully formulated and situation-specific questions involving uncertainties. It was largely because so much statistical research came to be dominated by exclusively mathematical techniques, with scarcely any reference to backgrounds in science, ....... A basic thesis .....is that the logic of applied statistics is a logic of scientific practice, with mathematics in a supporting role.
Arthur P. Dempster in Logicist Statistics II: Inference. Springer, 2007.
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