I believe that we should start mathematics education with programming, then go to generator systems for numbers and operators over them, then how to form lattices and operators on patterns in the lattice, and do approximately continuous math and physics only at the very end.
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Replying to @Plinz
I wish I'd read https://mitpress.mit.edu/books/structure-and-interpretation-classical-mechanics … before I did it the 'standard' way.
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Replying to @StrayTaoist
Apart from the fact that math teaching is universally bad in most schools: once we form the belief that continuous spaces describe the foundational plane of reality, it takes often more than a lifetime to fix.
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Replying to @Plinz @StrayTaoist
Do we know that it isn't ? Could you elaborate ?
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Replying to @darkgreyarea @StrayTaoist
You can construct every observable and mathematics itself using computational principles (i.e. via a trivially simple automaton), but if you introduce real infinities (including continuity), you have to already presuppose hypercomputation, and your axiomatic systems become filthy
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Replying to @Plinz @StrayTaoist
The very essence of the problem is the assumption that a space consists of infinitely many sizeless points. That idea goes back to Greeks, leads to Zeno paradoxes. Aristotle had a (finite) treatment to avoid those but it was reversed by Cantor and his colleagues. Hmm, no good.
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Aristotle is also underrated as a psychologist! What a guy!
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