SOCIAL SCIENCE RESEARCH COUNCIL
VOLUME 11 • NUMBER 4 . DECEMBER 1957 230 PARK AVENUE NEW YORK 17, N. Y.
APPLICATIONS OF MATHEMATICS IN SOCIAL PSYCHOLOGICAL RESEARCH by George A. Miller·
THE amount of formal symbolism that finds its way into social science journals has increased dramatically in recent years. I base my judgment of the increase on personal impressions--certainly the amount of mathematics that I encounter in the psychological literature has increased in both quantity and quality since the days of my graduate study. And I think I see a similar trend in the neighboring fields of economics, sociology, anthropology, and political science. One reason the Committee on Mathematical Training of Social Scientists has been so very effective is that it has filled a need created by this recent growth of interest in the more rigorous forms of argument. The time seems to have come, however, to turn the training function over to the colleges and universities where it properly belongs. We certainly should not encourage students to postpone their mathematical education in the expectation that they can fill it in later by spending two months in a postdoctoral institute sponsored by the Council-such a situation would defeat most of the purposes the committee and the Council hoped to promote. But even though the training function should become secondary, the mathematical fashion is still with us. Presumably, any new functions that the Council might undertake in this direction would be oriented • The author is Associate Professor of Psychology at Harvard University, and a former member of the Council's Committee on Mathematical Training of Social Scientists. He conducted a workshop on the construction and use of mathematical models in the field of communication and language, as a part of the program of the Summer Institute on Applications of Mathematics in Social Science Research, held at Stanford University, June 24-August 17, 1957, under the sponsorship of the committee. Mr. Miller presented this report informally at the annual meeting of the board of directors of the Council, September 1957.
more toward the substantive content of the social sciences involved, and less toward teaching the general concepts and methods of mathematics that are more or less neutral with respect to content. Insofar as Bertrand Russell's claim that a mathematician is a man who never knows what he is talking about is true, it is possible for him to talk to all varieties of social scientists simultaneously. But that happy stage is passing, and specialization with respect to content is becoming increasingly necessary. Learning theorists, game theorists, communication theorists, economic theorists, linear programming theorists, and the many other theorists who have been learning their mathematical fundamentals together in recent years can still compare problems as a matter of coffee conversation, but when the coffee is finished they go back to work in relative isolation. If the Council is to contribute to this newer phase of the development of mathematical theories in the various social sciences, it may have to face these facts of specialization with a consequent proliferation of its committees.
"TEACHING MODELS" AND "WORKING MODELS" The shift of emphasis from training to substantive content also has some implications for the kind of mathematical models we should be interested in. For example, a number of the mathematical models that have been proposed do not really contribute much to our understanding of social science problems in any substantive way, even though they are useful for teaching mathematical concepts in a social science setting. I think any person with competence in some given area of 41