I don't think that particles are best understood as discrete objects, in the same way as gliders in Game of Life are not discrete objects, but stable emergent patterns. Likewise, I don't think that there is anything continuous in this universe.
"I would like to replace fluid dynamics with statistical particle interactions."—"Why do you want to replace simple models with complicated ones?"
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But it's NOT like molecular interactions are more complicated than fluid dynamics. And it turns out that in order to make fluid dynamics tractable, you need to break them down into something else. The elegance of a specification does not equal the complexity of the explanation.
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