Andrei Vitalyevich Kolesnikov, Svetlana Nikolaevna Sirenko and Georgy Gennadjevich Malinetsky

Keywords: Time, chaos, nonlinearity, foundations of mathematics, number, set theory, cellular automata, computational modelling

Abstract: The concept of time differs significantly in philosophy and the humanities, on the one hand, and mathematics and physics, on the other. Mathematics and physics traditionally focus on reproducible periodic processes for the purpose of predicting their results. Philosophy and the humanities mostly consider time as a historical irreproducible flow of unique events that create history and the unique development scenario. An important scientific issue is to converge of both concepts, which is possible due to the modern views on the deterministic chaos theory. The concepts “dynamic set”, “true”, or “temporal” number should be used to adequately describe historical time. The characteristics of deterministic chaos processes with temporal numbers can be showed on an example of computational models of continuous cellular automata whose rules of transition between states include nonlinearity

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