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

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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 http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html

`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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