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Sensation strength: Another point of view

Murray deserves much praise for his wide-ranging analysis of the nineteenth-century antecedents of contemporary issues in psychophysics; we owe him a debt of gratitude for helping us better understand the important work done by the pioneers in our field. Of the many interesting topics he has raised I have selected just two for comment Delboeuf's classic study of judged greyness, and the status of the problem of measuring sensation strength. Murray notes that Delboeuf compared the results of his version of the psychophysical law with the obtained data and took comfort from the good agreement. In an extended footnote Murray shows that Delboeuf had little grounds for pleasure with these data since it can readily be shown that they are compatible both with Fechner's version of a logarithmic law and with a power law (for which Plateau was the contemporary advocate). The point I wish to make about Murray's analysis is that it is not really necessary to undertake the calculations made by Delboeuf or by Murray to show that the data are consistent with either a logarithmic or a power law, and that this dual consistency can be understood in terms of the uncertainty about what it is that the subject is actually doing. The important feature of all 13 sets of values for/,, J2, and/3is that they define geometric progressions. Were it not for the fact that Delboeuf was concerned to distinguish his own model from that of Fechner, he could have tested the adequacy of a simple logarithmic law by using the ratio /2// i as a multiplier for 72 to obtain a predicted value for 73. (In fact, such "predictions" are in excellent agreement with Delboeuf's data, perhaps better than the fit to his own model.) It only remains to argue that the three corresponding sensations define equal intervals on a scale of sensation strength to allow the conclusion that there is a logarithmic relation between sensation and degree of greyness. The critical question, of course, is whether one can indeed assume equal intervals on a sensation scale under the instruction to make 72 appear "intermediate" between 7, and 73. As Murray notes, a number of writers have drawn attention to the fact that there need be no simple or universal relation between what the subject is told to do and what he in fact does. Assuming that the subject in Table 1 of the target article adjusts 73 so that S3IS2 = S2/Slt that is, creates a geometric progression of sensations, his results can be said to conform with a power law. (It should be noted that this line of argument is rather different from that proposed by Murray in Note 3 where he shows that a power law fits Delboeuf's data even if it is assumed that the sensations in question define equal intervals; that is the familiar demonstration that, with a low exponent, a power relation is difficult to distinguish from one that is logarithmic.)