Randomness and determinism in the interplay between the continuum and the discrete

Abstract

This paper provides a conceptual analysis of the role of the mathematical continuumversusthe discrete in the understanding of randomness as a notion with a physical meaning or origin. The presentation is ‘informal’ as we will not write formulas; however, we will refer to non-obvious technical results from various scientific domains, and we will also propose a conceptual framework for understanding randomness (and predictability), which we believe is, essentially, original. As a matter of fact, unpredictability and randomness may be conveniently identified in various physico-mathematical contexts. This will allow us to explore these concepts in continuousversusdiscrete frameworks, with particular emphasis on the relationships and differences between classical approaches and quantum theories in Physics.