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AlanCrowe comments on Tell it to someone who doesn't care - Less Wrong
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Embed the particles in a viscous medium. Add partilce decay after 70 years and particle creation at random locations. That should give you the possibility of stable distributions of average density over a lower level of continual flux.
Particle creation should probably have a tendency to occur near other particles.
(slightly) viscous medium makes sense though, maybe.
I'm not sure the model should have stable equilibriums. ie, I'm not sure the way people actually behave is such that a model with stable equilibriums would actually accurately reflect reality. In real life, attitudes change over time, no? So do we really want to select/reject models based on whether or not there are stable equilibria? We should probably expect states that are stable...ish. That is, chunks of the system that are slow to change.