Structural Information Theory Based on Electronic Configurations

Abstract

The topic of this paper is how different forms of acoustical information may be measured. The specific problem addressed is how information is transferred from a three-dimensional source of longitudinal waves to a one-dimensional vibrating membrane. In previous papers [Barrett, TIT J. Life Sciences 1, 129–135 (1971); Acustica (1973), in press], the author has demonstrated through the derivation of different forms of informational “quanta” that the modulating envelopes for the wave packets representing these quanta are functional solutions to the Weber equation (the Helmholtz equation in parabolic cylinder coordinates). The geometrical structure described by the Weber equation suggests a resonance effect existing between an “angular momentum” involving an “azimuthal quantum number” and one involving a “magnetic quantum number” in analogy with structural chemistry formulations [Barrett, Acustica (1973), in press]. In the present paper the geometrical formulation is carried further. A sound source is commonly spherical; therefore, solutions are found for the wave equation in spherical coordinates, giving a precise meaning to the “azimuthal” and “magnetic quantum number” analogy. These informational wave packets must then be translated into a one-dimensional representation because of the nature of the receiver (the tympanic membrane). The difference between descriptions of electromagnetic and acoustical forms of energy is presented as consisting in the number of variables remaining constant in the acoustical formulation (as compared with the electromagnetic) but not in the basic geometrical formulations, which are primary.