Darkness was upon the face of the deep. And the spirit of God moved upon the face of the vacuum.
And God said, "let there be a coherent state of closed superstrings with initial conditions specified on a spacelike slice of an 11-dimensional lorentzian manifold". (1/?)
Few students know this, but you can perform intertemporal intellectual arbitrage to seem smarter than you really are by reading one chapter ahead of the class.
any serious philosophy of computation should reference realizability toposes. they're the natural setting in which programs live.
turing machines ≅ set theory (arbitrary choices, unæsthetic)
realizability topos ≅ topos (clean, grothendieckian, æsthetic)
When thought about in the right way, this is actually a theorem: the realizability topos for any model of computation that is at least as strong as Kleene’s first partial combinatory algebra must contain a natural numbers object (satisfying recursive Heyting arithmetic).