The magical number seven: Making a “bit” of “sense”

Abstract

The maximum number of categories distinguishable in making an absolute judgment was estimated by Miller to be “seven plus or minus two,” corresponding to about 3 bits of information transmitted per stimulus. Later work extended this range to include at least 2 to 4 bits of information, which reached 16 categories. In contrast, the number of distinguishable differences between two stimuli is in the order of 100. Why is this so? It is shown here that an answer to these questions can be obtained by constructing an entropy function, Hs, which is a measure of the uncertainty of a subject (or a sensory receptor) as it perceives the magnitude of an applied stimulus. Using this function, it is demonstrated that the ubiquitous 3 bits of information per stimulus can be approximated from the expression(Formula presented.), where τ1 and τ2 are known time constants. The same entropy function can be used to derive various other psychophysical laws, such as the Weber-Fechner law, Stevens’ law, and the Bunsen-Roscoe law. © 1981, Psychonomic Society, Inc.. All rights reserved.