Edward Frenkel on Jungian Archetypes in Mathematics
Or maybe it's the other way around? Jung apparently recognised natural numbers as an archetype. He didn't go so far as to recognise Universal Properties as another, but maybe that was just because of a lack of suitable language.
See Philip Wadler - Propositions as Types, Another Excellent Talk on HoTT by Steve Awodey and the other links in the video description.
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This stuff is all very important if you're God and you're trying to lay down Universal laws of physics so that the Universe is comprehensible to its inhabitants. See Supernovae evidence for foundational change to cosmological models.
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Anton Petrov on gravitational structures that are hundreds of millions of light-years in size. How do we know this? By making assumptions about observable effects of nuclear physics.
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