William Kaye Estes

William Kaye Estes (born June 17, 1919 in Minneapolis, Minnesota) is an American psychologist.

As an undergraduate, he was a student of Richard M. Elliott at the University of Minnesota. As a graduate student he stayed at the University of Minnesota, and worked under B. F. Skinner. When he later had his doctorate, he joined Skinner on the faculty at Indiana University.

After Estes got out of the U. S. Army at the end of World War II, he established his reputation as one of the originators of mathematical learning theory. When high speed, high capacity computers later came along, Estes' models laid the foundation for modern artificial intelligence and artificial neural network developments. Estes went from Indiana University to Stanford University, to Rockefeller University in New York, and finally to Harvard University. After retiring from Harvard, he returned to Bloomington, Indiana, where he remained active in academics to become professor emeritus at his original academic home department.

One of William Estes's most famous contributions to learning theory was his model of intelligence, in which he postulated that the rate of change in a human's knowledge is equal to the product of their intelligence and the difference between their current level of knowledge and their studiousness. Mathematically, this can be expressed by the differential equation dk/dt+lk=λl, where knowledge k and studiousness λ are expressed as percentages, which has the solution k=λ(1-e^(-lt)), assuming that the human began with no knowledge of the subject. Taking the limit as time approaches infinity, one finds that, given an infinite amount of time, a human's knowledge is equal only to their studiousness; the intelligence l merely affects the rate at which his or her knowledge approaches that limit.