On 9/12/2011 8:06 AM Jason Resch said the following:


What about of dumb water molecules, can they not form a wave?
Complex things can result from very simple rules, when you have a
huge number of those simple things interacting with each other.

I will use this example to continue my thoughts about

Simulation Hypothesis and Simulation Technology

I will change the original question as follows. Can we simulate a wave starting from water molecules? I will consider it not in principle, but rather in the objective reality given to us in sensation. (This what I have learned in the USSR: Vladimir Il'ich Lenin: "Matter is the objective reality given to us in sensation")

If we imagine brute-force simulation, then the answer is definite no. Even if we consider a level of molecular simulation when the water molecules are considered classically with a given force field, then it is definitely out of reach, also for foreseeable future. The Moore law just does not help.

In what sense then do we usually say "Yes, we can do it"? Presumably this means that we do not have to simulate each molecule to simulate a wave. The laws of continuum mechanics actually suffice. If we consider this numerically, then there is nice way to come to continuum mechanics through coarse-graining. One can think for example of dissipative particle dynamics (DPD, some equivalent of molecular dynamics) where we simulate not water molecules but rather bigger pseudo-particles. Funny enough DPD is pretty similar to smooth particle hydrodynamics (SPH), an alternative method to discretize the Navier-Stokes equations. In this sense a pseudo-particle is some equivalent of a cell in finite elements/finite volumes. In a way, molecular dynamics is also could be considered as a course-graining scheme. First we use quantum chemistry to evaluate the force field and then we use it at the next level.

In this sense, an interesting question is how simulation hypothesis is supposed to work. As brute-force simulation? Or along the second way?


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