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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