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It is usual to identify initial conditions of classical dynamical systemswith mathematical real numbers. However, almost all real numbers contain aninfinite amount of information. I argue that a finite volume of space can'tcontain more than a finite amount of information, hence that the mathematicalreal numbers are not physically relevant. Moreover, a better terminology forthe so-called real numbers is ``random numbers'', as their series of bits aretruly random. I propose an alternative classical mechanics, which isempirically equivalent to classical mechanics, but uses only finite-informationnumbers. This alternative classical mechanics is non-deterministic, despite theuse of deterministic equations, in a way similar to quantum theory.Interestingly, both alternative classical mechanics and quantum theories can besupplemented by additional variables in such a way that the supplemented theoryis deterministic. Most physicists straightforwardly supplement classical theorywith real numbers to which they attribute physical existence, while mostphysicists reject Bohmian mechanics as supplemented quantum theory, arguingthat Bohmian positions have no physical reality.

Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?