You also need a specification of the initial state, which dramatically increases the size of the program! Because the formalism only requires turing machines (or any equivalent computation formalism), there is no distinction between the representation of the “rules” and the rest of the necessary data. So even if the rules of physics themselves are very simple (like in the game of life), the program that simulates the world is very big. It probably requires something like “position of every atom at step t
The initial conditions can be simple. Do you expect that the real universe requires very specific boundary conditions?
In the game of life it is necessary to set up specific initial configurations for something interesting to happen, but the configurations can be computed with a program much smaller than the number of cells to set (e.g., repetitive patterns). It is not necessary to explicitly lay out the values of all the cells.
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.
The initial conditions can be simple. Do you expect that the real universe requires very specific boundary conditions?
In the game of life it is necessary to set up specific initial configurations for something interesting to happen, but the configurations can be computed with a program much smaller than the number of cells to set (e.g., repetitive patterns). It is not necessary to explicitly lay out the values of all the cells.
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.