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Sure, but you'd think we would shift our focus to using models explicitly tailored with that aim in mind. Using something that explicitly approximates a desired
by tw1010 9y ago
Sure, but you'd think we would shift our focus to using models explicitly tailored with that aim in mind. Using something that explicitly approximates a desired, precise, foundation. Perhaps parameterized by model accuracy. I would think taking inspiration from approximation algorithms would be a much more appropriate lens with which to model physics.
- auntienomen 9y agoIn the case of Navier-Stokes, this was done in 1934 by Jean Leray, who showed that the so-called 'weak' solutions always exist. (A weak solution is not a function, but a more general object called a distribution which can be fuzzed out on very short distance scales.) It's a very reasonable idea, and useful enough for computations, but it lacks the essential tension that makes Navier-Stokes a mathematical Everest.
- btilly 9y agoThe mental model of a bunch of hard little atoms flying around, colliding, rebounding, etc is actually NOT the desired, precise, foundation for understanding how gases behave. The better foundation is quantum mechanics. An example of a macroscopically visible difference between these foundations are the van der Waals forces.