Real numbers are not real. The argument is simple, real numbers cannot reflect reality (i.e. not real) because they assume to have infinite precision. Infinite precision is an impossibility in nature because it assumes that an infinite amount of information is contained in a single real number. Therefore, we must assume that reality uses numbers with finite precision. A real number is only significant after a certain number right of the decimal point.

in most numerical simulations infinite precision is not an immediate concern. That’s because finite precision numbers have always been used to approximate infinite precision real numbers. Computationally, the only time you really need extremely high precision numbers is in cryptography. However, a majority of numerical simulation code requires just 64-bit floating point numbers.

The question that however needs to be asked is, how does this relate to existing analytic theories of reality? Newton’s laws and Maxwell equations, both classical physics theories, are analytic tools (i.e. calculus) that assume infinite precision numbers (i.e. real numbers). What are the consequences if we assume finite precision numbers? This idea is explored in a recent paper by Nicolas Gisin (Experimental and theoretical physicist at the University of Geneva). In his paper “Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?” he emphasizes:

Mathematical real numbers are physical random numbers.