Method of Serial Extrapolation

Abstract

A psychophysical procedure is proposed for measuring a subject's power of discerning “lawfulness,” “regularity,” “invariance” in a stimulus sequence. The task consists of supplying the next term in a given series. The method is tested by applying it to a visual series consisting of lines subdivided in geometric progression. The effect upon accuracy of judgement is investigated by varying the settings of the stimulus, in particular the rate of increase or gradient of the series and the number of segments given prior to extrapolation, and of presenting the next-but-one position in the series, thereby converting the task into one of interpolation. Where possible, quantitative predictions are made concerning these variables on the basis of certain explicit assumptions.

Results show that accuracy decreases, as predicted, as the gradient of the series increases, but does not seem to be affected by adding to the number of terms presented. Interpolation shows a reduction in variable error compared with extrapolation more or less as required by theory. Finally, discrepancies in the findings are discussed with special reference to their bearing on the validity of the method.