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If the mathematics is not a priori, one must explain why it is the case particles follow particular mathematical laws instead of moving about randomly without any particular logic to them. How do these elementary particles know what to do and have always known?

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particles follow particular mathematical laws

We don’t know that they do. We assume they do, but our laws are not their laws.

You’re like the person who sees a birdwatcher recording their observations and asking “why do birds exist?” You’re asking the wrong question to the wrong person and demanding satisfaction.

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