Toward Quantifying Semiotic Agencies: Habits Arising

Mathematics and Semiotics do not at first seem like a natural couple. Mathematics finds most of its applications describing explicit, mechanical situations, whereas the emphasis in Semiotics is usually toward that which remains at least partially obscure. Nonetheless, probability theory routinely treats circumstances that are either acausal or the results of agencies that remain unknown. Between the domains of the explicitly mechanical and the indescribably stochastic lies the realm of the tacit and the semiotic—what Karl Popper has described as 'a world of propensities.' Popper suggested that some form of Bayesian statistics is appropriate to treat this middle ground, and recent advances in the application of information theory to the description of development in ecosystems appear to satisfy some of Popper’s desiderata. For example, the informationtheoretic measure, 'ascendency', calculated upon a network of ecosystem exchanges, appears to quantify the consequences of constraints that remain hidden or only partially visible to an observer. It can be viewed as a prototype of 'quantitative semiotics.' Furthermore, the dynamics consisting of changes in hidden ecosystem constraints do not seem to accord well with the conventional scientific metaphysic, but rather they point towards a new set of postulates, aptly described as an 'ecological metaphysic'. 1 MATHEMATICS AND THE OBSCURE Semiotics deals with that which is not explicit about the operation of a system -Michael Polyani's realm of the tacit. As such, semiotics does not seem to be a particularly fertile discipline for the mathematician or engineer. For example, Stanley Salthe, who writes elsewhere in SEED, once proclaimed to the author, “If one can put a number on it, it is probably too simplistic to warrant serious discussion!” If, then, the normal objects of semiotic discourse challenge one’s abilities at description, what place could the field possibly hold for mathematical discourse and quantification?