Inferring representation type from the fractal dimension of biological communication waveforms
Digital representation is based on an arbitrary relation between physical signal structure and assigned meanings; analog representation uses a proportionality between changes in meaning and changes in the physical structure of the signal that represents the meaning. For recursive information, the physical structure of the analog signal will also be recursive. Since a digital signal will be physically arbitrary for both recursive and non-recursive information, a measure of physical recursion can provide an index for analog/ digital differences. A simple model for this relation is examined by computational experiment for spectral density, and by analytic expression for Kolmogorov complexity. It is examined by empirical measure of fractal dimension for samples of a capella music, poetry, and prose, in a comparison of rap vs. reggae music, and for cetacean vocalizations. Generalizations of this analysis for other communication systems are discussed.