Let’s put aside the distiction between initial conditions and rules, I think it is just a distraction at this point.
In general I would even expect a complete simulation of the univers to be non-computable. Ie I expect that the univers contains an infinite amount of information.
If we bound the problem to some finite part of time and space then I expect, just as an intuition, that a complete simulation would require a lot of information. Ie, the minimal turing machine / python code that consistently outputs the same result as the simulation for each input is very long.
I do not have a good number to give that translates this intuition of “very long”.
Let’s say that simulating the earth during the last 10 days would take multiple millions of terrabits of data?
Of course the problem is underspecified. We also need to specify what the legal inputs are.
Let’s put aside the distiction between initial conditions and rules, I think it is just a distraction at this point.
In general I would even expect a complete simulation of the univers to be non-computable. Ie I expect that the univers contains an infinite amount of information. If we bound the problem to some finite part of time and space then I expect, just as an intuition, that a complete simulation would require a lot of information. Ie, the minimal turing machine / python code that consistently outputs the same result as the simulation for each input is very long.
I do not have a good number to give that translates this intuition of “very long”. Let’s say that simulating the earth during the last 10 days would take multiple millions of terrabits of data? Of course the problem is underspecified. We also need to specify what the legal inputs are.
Anyway, do you agree with this intuition?
I think that simulating a specific slice of spacetime is more kolmogorov-complex that simulating the entire universe.