The Empirical Laws of Sensation and Perception

In this chapter, we set down the weighty ballast of philosophy and information theory, and examine the somewhat lighter matter of the empirical rules of sensation and perception. By empirical laws we mean (Webster’s dictionary) laws “making use of, or based on, experience, trial and error, or experiment, rather than theory or systematized knowledge.” For somewhat more than one hundred years, beginning (probably) with the work of Weber, empirical laws of sensation have been formulated. These algebraic rules, based essentially on laboratory observations, relating only occasionally to each other, and not derived theoretically from laws in other sciences, have dominated the scientific literature. Each empirical law stands as a universe unto itself: it is neither derived from any simpler principle, nor does it lead to the generation of other laws. Each law has absolute dominion over its own territory. Such is the state of scientific polytheism that we now describe. The reason for introducing these laws early in the book is that they provide, so to speak, grist for the mill. We shall endeavor, as the informational theory of sensation is developed, to provide theoretical derivations for all of these empirical laws. It is probably better to introduce them earlier and in a group, rather than later as they are invoked. Some of the empirical laws carry the names of their originator; some, such as “the exponential decay” of this or that quantity are just rules of thumb. We are not concerned with all of these rules, but only a subset of them. In particular, we shall be interested in those empirical laws that govern the relationship between three fundamental variables: I, the steady intensity of a stimulus; t, the time since onset of the stimulus, or, occasionally, the duration of this stimulus; and F, the perceptual variable related to the stimulus. F, you will recall, was defined in Chapter 2. As mentioned in the Introduction to Chapter 1, all stimuli with which we shall be concerned here are steady, or constant stimuli, given in the form of a step function (Figure 1.1). While stimuli that vary with time are of very definite interest, for example those that may vary sinusoidally, their formal treatment is more difficult within this informational or entropic theory, and such progress as has been made with these stimuli will not be reported here. Neither do we grapple with the effects of multiple stimuli that are applied concurrently. So we shall not deal, for example, with the sweetness of a solution of two types of sugar, or with the effect of a masking sound on a pure tone. With these restrictions in mind, let us examine eight types of experiment performed by physiologists, psychologists and physicists that give rise to well-known empirical equations of sensation. In each case in which the perceptual variable, F, occurs, recall from Chapter 2 that it can be interpreted both psychophysically, as a subjective magnitude (e.g. brightness), and physiologically, as a rate of impulse propagation in a neuron. In Chapter 13, we shall begin to distinguish mathematically between these two interpretations.