On the diversity and similarity of mathematical models in science

Abstract

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different areas of science. In the present article the use of models in statistics is taken as a basis, but links are given to several other areas. Two particular such links are described in some detail here: First the link connected to the chemometrical Partial Least Squares algorithm, a link that now has been generalized to the more sophisticated envelope model. Secondly, statistics, as is well known, relies heavily on making decisions, and it may also in certain cases be connected to a process of taking measurements. A mathematical model for these two activities, connected to the mind of an observer, is introduced. This model is taken further, and shown to be important in a new proposal for a foundation of quantum theory. Quantum mechanics, as seen from this point of view, is described in some detail. The discussion here is close to the discussion in a recent book and in recently published articles by the author.