Abstract
Recent work has shown that the power function, a ubiquitous characteristic of learning, memory, and sensation, can emerge from the arithmetic averaging of exponential curves. In the present study, the forgetting process was simulated via computer to determine whether power curves can result from the averaging of other types of component curves. Each of several simulations contained 100 memory traces that were made to decay at different rates. The resulting component curves were then arithmetically averaged to produce an aggregate curve for each simulation. The simulations varied with respect to the forms of the component curves: exponential, range-limited linear, range-limited logarithmic, or power. The goodness of the aggregate curve’s fit to a power function relative to other functions increased as the amount of intercomponent slope variability increased, irrespective of componentcurve type. Thus, the power law’s ubiquity may reflect the pervasiveness of slope variability across component functions. Moreover, power-curve emergence may constitute a methodological artifact, an explanatory construct, or both, depending on the locus of the effect. John Wixted, and Steven Sloman, for their helpful comments on the manuscript.
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Anderson, J. R. (1982). Acquisition of cognitive skill.Psychological Review,89, 369–406.
Anderson, J. R. (1993).Rules of the mind. Hillsdale, NJ: Erlbaum.
Anderson, J. R., &Schooler, L. J. (1991). Reflections of the environment in memory.Psychological Science,2, 396–408.
Anderson, R. B., &Tweney, R. D. (1997). Artifactual power curves in forgetting.Memory & Cognition,25, 724–730.
Anderson, R. B., Tweney, R. D., Rivardo, M., &Duncan, S. (1997). Need probability affects retention: A direct demonstration.Memory & Cognition,25, 867–872.
Estes, W. K. (1956). The problem of inference from curves based on group data.Psychological Bulletin,53, 134–140.
Heathcote, A., Brown, S., &Mewhort, D. J. K. (2000). The power law repealed: The case for an exponential law of practice.Psychonomic Bulletin & Review,7, 185–207.
Hintzman, D. L. (1986). “Schema abstraction” in a multiple-trace memory model.Psychological Review,93, 411–428.
Hintzman, D. L. (1988). Judgments of frequency and recognition memory in a multiple-trace memory model.Psychological Review,95, 528–551.
Logan, G. D. (1988). Toward an instance theory of automatization.Psychological Review,95, 492–527.
Myung I. J., Kim, C., &Pitt, M. A. (2000). Toward an explanation of the power law artifact: Insights from response surface analysis.Memory & Cognition,28, 832–840.
Neves, D. M., &Anderson, J. R. (1981). Knowledge compilation: Mechanisms for the automatization of cognitive skills. In J. R. Anderson (Ed.),Cognitive skills and their acquisition (pp. 57–84). Hillsdale, NJ: Erlbaum.
Newell, A., &Rosenbloom, P. S. (1981). Mechanisms of skill acquisition and the law of practice. In J. R. Anderson (Ed.),Cognitive skills and their acquisition (pp. 1–55). Hillsdale, NJ: Erlbaum.
Rubin, D. C. (1982). On the retention function for autobiographical memory.Journal of Verbal Learning & Verbal Behavior,21, 21–38.
Rubin, D. C., &Wenzel, A. E. (1996). One hundred years of forgetting: A quantitative description of retention.Psychological Review,103, 734–760.
Stevens, S. S. (1971). Neural events and the psychophysical law.Science,170, 1043–1050.
Wickelgren, W. A. (1972). Trace-resistance and the decay of long-term memory.Journal of Mathematical Psychology,9, 418–455.
Wickens, T. D. (1998). On the form of the retention function: Comment on Rubin and Wenzel (1996): A qualitative description of retention.Psychological Review,105, 379–386.
Wixted, J. T., &Ebbesen, E. B. (1991). On the form of forgetting.Psychological Science,2, 409–415.
Wixted, J. T., &Ebbesen, E. B. (1997). Genuine power curves in forgetting: A quantitative analysis of individual subject forgetting functions.Memory & Cognition,25, 731–739.
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Anderson, R.B. The power law as an emergent property. Memory & Cognition 29, 1061–1068 (2001). https://doi.org/10.3758/BF03195767
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DOI: https://doi.org/10.3758/BF03195767