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Thank you for the response, I find this very interesting.

So is it true to say that the production of a particular solution to a differential equation is a statement about how a system will behave based on its initial conditions, and that the statement captures within it the principle of action minimization by virtue of the fact that it is a derivation of information from natural laws?

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"Action is minimized" and "F = ma" are the same in the sense that x+5=0 and x+6=1 are the same. In both cases you can go from one to the other with a sequence of deductions. There's no way to tell which one is the "natural law" because you can take either one as a fact and derive the other as a consequence.

Interesting - your response makes sense. Thanks again for the information.

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