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simulation

I heard a really interesting debate on mindscape about whether simulations should be considered theoretical or experimental; Sean argued that they were the former, because the idea of an experiment is to get input from the real world: "I think that the answer is that the experiment tells you something about what nature does, not something about what your theory predicts." The simulation is a computational model of some aspects of nature - you start with a theory about how the system works, you write a computer program to execute it, and you observe the results, so the sim is just carrying out the theory. but as the theory gains fidelity, accounting for an increasing number of real-world phenomena, it approaches the behavior of nature; therefore sampling its dynamics tells you as much about reality as does sampling nature, and it begins to look like an experiment.

Let's say we have some objective measure of how good the theory/simulation is — how closely it approximates reality*. The best possible theory might be defined as Laplace's Demon, whereby the positions and momenta of every particle in the universe are accounted for. Practically speaking, this causes difficulty in that there is a

and, theoretically, there is an

I think the space complexity of such a theory is infinite because if the simulation is actually a perfect representation of the universe, then it would simulate the machine performing the simulation. This machine would then have to be simulating a universe, which includes a machine simulating a universe, which includes a machine simulating a universe, which includes a machine simulating a universe, which includes a machine simulating a universe, which incl

*How could the "closeness to reality" of a simulation even be measured? Thinking deterministically, if you knew the initial conditions of the universe to infinite precision and accuracy, then starting at t=0 would play the same sequence of events that has led to the present configuration of things, so the simulated universe's history would match exactly the history of the real universe. However, it's also plausible to imagine that there is true randomness baked into reality; then full knowledge of the wave function of the universe, yielding the true probability distribution for all random variables, is the best we can do. In that case, the best possible simulation is a probabilistic one, and even with infinitely accurate initial conditions the history of the simulated universe will diverge rapidly from the history of reality; in fact, every run of the simulation would with overwhelming likelihood produce a vastly different state after 14 billion years of dynamics. Yet there is still something ultimately "true" about the theory of this simulation.

With real machines and real time scales, I don't think we will have to worry about approaching this theoretical limit. Instead, the problems science faces now are short- and medium-term projections. In 4 or 5 billion years, we will have the pleasure of assessing the accuracy achieved by our model of our collision with Andromeda; before that, we will want a high fidelity model of Earth's atmosphere so we can design a control system for it.

I'm not making an evaluation of the moral worthiness of different scientific disciplines based on the issues of today. I think that many of the developments in techniques for simulation of the cosmos will be directly applicable to simulations of the climate, and vice versa.