Planets do not precisely follow the Newton's law because it is a first order approximation of general relativity. In what sense do we intend that planets move according to general relativity? The laws of physics are extrapolated by complex sets of experiments and they are considered fundamental the more they allow to describe concisely acceptable ideal approximations of real systems. The subsequent mathematical description, combined with initial conditions, enables to predict time evolution (or time-dependent probabilities in quantum physics). Currently, general relativity is the best model to fit the orbit of planets once external perturbation are estimated and subtracted. Recently the deep learning paradigm is challenging scientific method thanks to its Bayesian capability to account for complicated systems when complexity sets in, based on the exploitation of huge amount of data. Deep learning ignores Newton's and Einstein's laws but it is significantly much more efficient for instance to design the best trajectory to send a spacecraft from the Earth to Mars in the shortest time. I define a criterion based on algorithmic information theory to assess a hierarchy between scientific models to define the fundamental one, and to compare how different methods such as scientific method, deep learning, and non-scientific methods perform in the description of a set of experiments.
Enrico Prati