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Notes
In this article we use the terms “mathematical model” and “computational model” as synonyma. We are quite aware of the fact that many scholars distinguish between these concepts but we believe that this distinction is a rather superfluous one. After all, algorithms like, e.g., artificial neural networks are basically mathematical procedures and nothing else (cf. e.g. Klüver and Klüver 2011).
Another example is the name of a well-established journal, namely the “Journal of Mathematical Sociology”, which we have also used for publication purposes. The name suggests the deplorable truth that a “mathematical” sociology is something else than the sociology most social scientists are used to. Not long ago, by the way, we ourselves received an answer from a reviewer of an established German sociological journal that “one knows that a mathematical sociology is impossible”.
In the Greek mythology Procrustes was a robber who put travelers on a bed and made them fit it: If the travelers were not large enough for the bed Procrustes stretched them until their legs were long enough; if the travelers were too long their legs would be cut off. The Greek hero Theseus killed Procrustes the same way.
It always was a bit unfair to the great Dutch physicist Hendrik Lorentz that the most spectacular consequences of the special theory of relativity, namely the space-time contractions and the time paradoxes, were considered by the public as a consequence from Einstein’s equation. In fact they are a consequence from the Lorentz transformations, which Einstein used for his theory.
In contrast to the logical structure of, e.g. physical theories the theory of Piaget could be called an algorithmic one in the sense that the basic processes like assimilation should be modeled by according algorithms and not by equations. We successfully constructed such an algorithmic model of Piaget’s theory via a new neural network (cf. Klüver and Klüver 2011; for the description of this network cf. the contribution of C. Klüver to this issue).
We omit of course options for academic disciplines like law, medicine, or economics where the motivation for according choices are the orientations to the respective professions.
We have been academic teachers for many years in “soft sciences” like education science and communication science as well as in “hard sciences” like computer science and parts of business administration. The main difference between the students in “soft” and “hard” sciences was always the readiness to deal with mathematical models and theories.
For example, the popularity of the theoretical approach of Rational Choice in the community of constructors of mathematical social models has a lot to do with the fact that this approach can be very well modeled by using game theory as mathematical basis. Yet even one of the earliest and most famous partisans of this approach, namely Robert Axelrod (1997), admitted rather melancholy that it is empirically not very valid.
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Klüver, C., Klüver, J. Introduction: social-cognitive complexity, computational models and theoretical frames. Comput Math Organ Theory 18, 145–152 (2012). https://doi.org/10.1007/s10588-012-9115-0
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DOI: https://doi.org/10.1007/s10588-012-9115-0