JOURNAL OF MATHEMATICAL PSYCHOLOGY 16, 68-90 (1977) Processing Power and Delay-Limits on Human Performance* GEORGE R. KISS Department of Psychology, University of Warwick, Coventry, England AND JOHN E. SAVAGE Program in Computer Science and the Division of Engineering, Brown University, Providence, Rhode Island 02912 A computational approach to cognition is developed that has both broad scope and precision. The theory is based on a few simple assumptions and draws its conclusions from an analysis of limits on computational activity. These limits are a delay limit and a processing power limit. The theory explains published findings on memory span, measure- ment of spatial numerosity (and subitization), total-time effects, and the behavior of RT curves for the Sternberg item recognition experiment. For at least 30 years computational models for cognition have been objects of serious investigation (McCulloch and Pitts, 1943). W e continue in this spirit by developing a quantitative theory for cognition that has just a few simple assumptions and yet explains many different empirical findings in the area of human performance (Fitts and Posner, 1967). For example, it treats two of the three topics discussed by Miller (1956), namely, memory span and subitization, but also speaks to the nature of performance curves in the Sternberg item recognition experiment (Sternberg, 1966) and to total-time effects in learning. Our theory contains many familiar ideas, including an assumed limit on the “processing capacity” (which we call “processing power”) of a central processing component of a hypothetical mental computer (Craik and Lockhart, 1972; Norman and Bobrow, 1975). It also recognizes a distanction between static and dynamic memory and assumes that dynamic memory has to be refreshed and that “work” has to be done to refresh it as well as to enter items into static memory. We make the notion of work precise and show that a limit on the capacity of dynamic (or short term) memory is implied by the need to refresh and the assumed limit on processing power (the time rate at which the central * The Research reported in this paper was supported in part by the National Science Foundation under Grant DCR72-03612-AOl; by a grant from the Foxboro Company; and by the Medical Research Council (U.K.). Author J. E. Savage was also supported in part by a John Simon Guggenheim Fellowship. 68 Copyright 0 1977 by Academic I’ress, Inc. All rights of reproduction in any form reserved. ISSN 0022-2496