Kenneth H. Norwich

On the theory of Weber fractions

The Weber fraction is treated as part of an information theoretical view of perception. In this theory of sensory perception, subjective magnitude is related to the information transmissible from stimulus to perceiver. The derived psychophysical law can be approximated as a power or logarithmic law, depending on conditions. The mathematical expression for the Weber fraction is obtained as a derivative of the psychophysical law. One of many interesting relationships derived here is that the product of the Stevens exponent with log10 stimulus range, for many sensory modalities, is equal to the maximum information transmitted per stimulus (in bits, measured in a test of categorical judgments) multiplied by 0.6. This number is a derived constant and is not measured from the data.

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

AbstractThe 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 anentropy 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 expressionn

On the information received by sensory receptors

log _2 sqrt {{{tau _2 } mathord{left/ {vphantom {{tau _2 } {tau _1 }}} right. kern-nulldelimiterspace} {tau _1 }}}

To perceive is to doubt: The relativity of perception

n, 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.

On the fundamental nature of perception

During the process of perceiving a steady taste stimulus, information is received, or (information) entropy is reduced. A single equation, the entropy equation, relates three fundamental variables—magnitude estimate, stimulus intensity, and stimulus duration. From this single equation, we can derive, in principle, all psychophysical relations for a steady taste stimulus, involving these three variables only. A number of examples are given. The Stevens exponent for taste is derived theoretically for certain experimental conditions, using statistical mechanics. Weber’s constant is derived in terms of the information transmitted per taste stimulus. The concept of a “surface of perception” is introduced.

Power functions in physiology and pharmacology

It is hypothesized that a sensory neuron, a neuron issuing from a sensory receptor, encodes the rate at which entropy or uncertainty is removed at the receptor level. This hypothesis is tested for the case of the entropy associated with the magnitude of a signal (stimulus) applied at the sensory receptor. A simple mathematical model of the process is presented and a number of well-known stimulus-response relationships are seen to emerge. For example, the adaptation of a receptor may be seen to occur as a consequence of reduced uncertainty regarding stimulus intensity. A general equation relating stimulus and response is developed, and this equation will simplify, depending upon the ratio of signal power to noise power, to either a logarithmic or a power law.

The dispersion of indicator in the cardio-pulmonary system

Simple reaction time is the minimum time required to respond to a signal such as a steady light or tone. Such a reaction time is taken to be the time required for transmission of a fixed quantity of information. delta H, from stimulus to subject. That is, information summation replaces energy summation. This information is calculated from consideration of the quantum nature of the stimulus. The theoretically derived equation for reaction time is fitted to experimental data. Piérons empirical law for reaction time is obtained as an approximation from a proposed informational equation. The exponent in Piérons law is found to be the same as the exponent in the power law of sensation. Threshold appears to be the smallest stimulus capable of transmitting the quantity of information delta H.

Unification of psychophysical phenomena : The complete form of Fechner's law

The uncertainty or entropy theory of perception is founded on the premise that for perception to occur, there must first of all be uncertainty. That is, perception or awareness is relative to the expectation of the perceiver. This view of perception leads to a seeming-paradox. How can there be uncertainty unless the alternatives have previously been perceived? But, by the premise of the theory, how can the alternatives have been perceived unless there was prior uncertainty? It is shown that this paradox may result physiologically in the concurrence of sensory and motor (or active) events during the process of perceiving. It is shown, further, that a close analogy exists between systems of formal logic and systems which perceive through uncertainty. This, in turn, suggests a basis for a calculus of perception.