Psychophysical Law PDF

The Psychophysical Law Recently invented procedures have shown that whenever the stimulus increases, the intensity of the sensation grows in accordance with a common basic principle. Two conflicting laws The issue concerns the form of the psychophysical law, the equation that tells ho...

The Psychophysical Law Recently invented procedures have shown that whenever the stimulus increases, the intensity of the sensation grows in accordance with a common basic principle. Two conflicting laws The issue concerns the form of the psychophysical law, the equation that tells how the strength of the external stimulus determines your impression of subjective intensity. The two contending laws are known as the logarithmic law and the power law. The two conflicting laws made their first appearance in connection with a friendly game of chance. More than two centuries ago a paradox in a gambling game led to one of the first conjectures about the law that governs the subjective value of stimuli. If we regard money as a stimulus· and the subjective value attached to its ownership as a response, then the problem becomes a stimulus response relation. Two laws of utility Gabriel Cramer puzzled said, that the subjective value of money, what economists now call utility, grows less rapidly than the numerical amount of money, the number of pennies or dollars. We know about Cramer's conjecture only because Daniel Bernoulli, mentioned the idea in a footnote attached to his famous paper of 1738 in which he proposed his own solution to the paradox. Bernoulli's hypothesis, which he reached quite independently, resembled Cramer's in one important respect. Both men concluded that the subjective value of each penny becomes less as the number of pennies increases. In the jargon of the economist, money exhibits a decreasing marginal utility. But Bernoulli chose a logarithmic function to represent the decreasing marginal utility, whereas Cramer had chosen a power function with an ex- ponent of one-half, which is the square root. In Fig. 1 we see a graph of the power function that Cramer used to explain the growth of utility (ordinate) as a function of gains in wealth (abscissa). Both curves are similar in one important respect. They are both concave downward in a manner consistent with the principle that has appeared so obvious to nearly everyone, namely, that the value of one added dollar seems less when you have a thousand than when you have only two or three. Nevertheless, there are important differences between the two functions, even though both are concave downward. The exponent is 0.5, which means that the function expresses a simple square-root function. In other words, the subjective value grows as the square root of the number of dollars, so that it takes a fourfold inCrease in dollars to double the subjective value. It was supposed to express the relation between subjective value in utiles and number of dollars. Bernoulli derived his logarithmic function by first making a simple assumption. The added utility, he said, grows smaller as the number of dollars grows larger-a simple inverse relation. Cramer's power function derives from an assumption that is just as simple and perhaps even more plausible. This alternative assumption states that the added utility grows smaller as the total utility grows larger. Again a simple inverse relation, but this time it is between the added utility and the total utility, not between the added utility and the total number of dollars. Fechner's jnd scale Fechner proposed to measure sensation by way of indirect experiments a kind of assault from the rear. Instead of asking a person to make a direct estimation of the relative magnitudes of his sensations, Fechner conducted scores of discrimination tests in which he measured the JND. (just noticeable difference ) Fechner's law is a logarithmic function. When the stimulus increases geometrically (for example, by doubling at each step), the sensation, according to Fechner, increases arithmetically (in steps of constant size). Metathetic versus prothetic The prototypes of the two kinds of perceptual continua are exemplified by loudness and pitch. Loudness is an aspect of sound that has what can best be described as degrees of magnitude or quantity. Pitch does not. Pitch varies from high to low;· it has a kind of position, 3nd in a sense it is a qualitative continuum. Loudness may be called a prothetic continuum, and pitch a metathetic one. The criteria that define those two classes of continua reside wholly in how they behave in psychophysical experiments, but the names themselves were suggested to me by the nature of the physiological processes that appear to underlie some of the sensory continua. The psychophysical power law Equal stimulus ratios produce equal subjective ratios. The general rule is this: on all continua governed by the power law, a constant percentage change in the stimulus produces a constant percentage change in the sensed effect. Why a power function? If nature has favored the power function over competing alternatives, some compelling reason must lie behind the choice. But in thinking about the power law we need to remind ourselves that the power function is a common form throughout all of physics. In fact, most of the laws of physics are power functions. Each scale is made to satisfy what is called the ratio requirement, which means simply that measured ratios are independent of the scale units. By making the perceived aspects of stimuli depend on power functions of the stimulus dimensions, nature has contrived an operating mechanism that is compatible with the need for reasonable stability among perceptual relations.