Thank you for the interesting piece. You write « In our example, it seems likely that “simulate the entire universe” is simpler than “simulate Earth” or “simulate part of Earth” because the initial conditions of the universe are simpler than the initial conditions of Earth. » but since the laws of physics are reversible we can get from the initial conditions for a neighborhood of Earth to the initial conditions of the universe. We must take a cutoff (a smooth bump function in space time around the Earth in a time slice. This determines a single initial universe condition, and the set of admissilbe bump functions would determine a set of initial conditions for the universe. While conversely the universe determines the Earth later. Thus the Kolmogorov complexity of the initial conditions for the universe are more Kolmogorov-complex than those of Earth—as the overhead for simulating the universe up to any given future state of Earth is negligible, any small universal TM’s code will do, plus the spacetime region to evolve to, by the physical version of Church-Turing thesis.
Thank you for the interesting piece. You write « In our example, it seems likely that “simulate the entire universe” is simpler than “simulate Earth” or “simulate part of Earth” because the initial conditions of the universe are simpler than the initial conditions of Earth. » but since the laws of physics are reversible we can get from the initial conditions for a neighborhood of Earth to the initial conditions of the universe. We must take a cutoff (a smooth bump function in space time around the Earth in a time slice. This determines a single initial universe condition, and the set of admissilbe bump functions would determine a set of initial conditions for the universe. While conversely the universe determines the Earth later. Thus the Kolmogorov complexity of the initial conditions for the universe are more Kolmogorov-complex than those of Earth—as the overhead for simulating the universe up to any given future state of Earth is negligible, any small universal TM’s code will do, plus the spacetime region to evolve to, by the physical version of Church-Turing thesis.