When physicists (and mathematicians) say a system is simple they usually mean that it exhibits features such as the following:
– High degree of symmetry: laws that govern the system are invariant under various transformations
– Reducibility: complex entities can be understood as being composed of building blocks governed by a smaller set of rules instead of being irreducible, ”ontologically basic”
– Differentiability: the way the system evolves can be modeled using differential equations and other tools of analysis
– Low order of approximation: the behavior of the system can be approximated by power series with a small number of terms; higher-order terms converge quickly
– Small number of free parameters: the laws of the system do not require a large number of ad-hoc parameters with arbitrary values
For a completely rigorous definition of simplicity, we can introduce the Kolmogorov complexity of an object, defined as the length of the shortest computer program (in some agreed-on encoding) that produces the object as output when run.
– High degree of symmetry: laws that govern the system are invariant under various transformations
– Reducibility: complex entities can be understood as being composed of building blocks governed by a smaller set of rules instead of being irreducible, ”ontologically basic”
– Differentiability: the way the system evolves can be modeled using differential equations and other tools of analysis
– Low order of approximation: the behavior of the system can be approximated by power series with a small number of terms; higher-order terms converge quickly
– Small number of free parameters: the laws of the system do not require a large number of ad-hoc parameters with arbitrary values