Manifesto of Transparent Mathematical Modeling: From Ecology to General Science

Abstract

AbstractMathematical black box models, which hide the structure and behavior of the subsystems, currently dominate science. Errors and paradoxes, such as the biodiversity paradox and the limiting similarity hypothesis, often arise from subjective interpretations of these hidden mechanisms. To address these problems, we have developed transparent mathematical models of the white box type. Here we justify the hypothesis that transparent mathematical models of the white box type can be built by means of logical deterministic cellular automata whose rules are based on the general theory of the corresponding domain. Using white box models, we were able to directly identify the mechanisms of interspecific competition, test the principle of competitive exclusion and the hypothesis of limiting similarity, resolve the paradox of biodiversity, and formulate for the first time the general principle of competitive coexistence. As a basis for reproducing and further developing the method, we present two transparent mathematical models of an ecosystem with one and two competing species. C++ code for our models provided. Cellular automata thinking can be traced back from ancient cellular board games in the histories of all civilizations. The transparent mathematical modeling opens a rational approach to ensuring the safety, reliability, and trustworthiness of automatic decisions. A shift to transparency in the mathematical modeling paradigm has the potential to revolutionize scientific research and to advance knowledge and technology in a wide variety of domains.