Testing message diffusion in harmonic logistic curves

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Abstract
The growth of a population of knowers of a message was studied to test a human interactance hypothesis. The conditions investigated involvedpeople interacting in time, with the population pairing off randomly (i.e., determined by many, small, different influences) and transferring an attribute (i.e., an all-or-none act) at either a steady rate or a waning rate, subsequent to the originating stimulus. The mathematical expressions for these pre-conditions were the differential equations for the linear logistic for steady acting and the harmonic logistic for waning acting. Variant forms of these curves were developed. Two exploratory experiments, or pretests, comprised launching a coffee slogan in a town and imitating a badge wearer in a boys' camp. Since the activity rate waned harmonically in both cases, the harmonic logistic fit best in both the town and the camp as expected by the hypothesis.