Someone - I forget who - made the observation that either: (a) we're alone in the Universe; or (b) we're not; and that (c) either is staggering.https://twitter.com/hrheingold/status/1171920444435288064 …
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I enjoy dichotomies like this, where either outcome is, upon consideration, really rather remarkable. Feels like something from nothing. #LawOfTheExcludedMiddleFTW
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As with many excluded middles though it's a surprisingly dodgy binary. What does "alone" mean in a relativistic universe?
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Make it "in our backward lightcone", and it's just as remarkable a dichotomy, and a lot more precise. Another approach would be to use a natural spacetime foliation to define "alone", but I like the simplicity of the backward lightcone...
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Littlewood, who is really a more amazing mathematician than most people think, proved one theorem this way: "Assume the Riemann Hypothesis is true... then the theorem follows. Assume the Riemann Hypothesis is false... then the theorem follows."
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Such theorems are always dangerously close to vacuous! E.g.: Thm: There is a constant C, such that if all the nontrivial zeros of zeta up to height C are on the critical line, then RH is true! So just verify RH numerically up to height C, and collect $1m! What's the proof?...
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Another one I like is to imagine the world a million years from now: either humanity survives, or it doesn't. In either case, something astounding must have happened
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A profound example is what
@DavidDeutschOxf calls 'the momentous dichotomy' — either something is forbidden by the laws of physics, or it is possible given the right knowledge.Thanks. Twitter will use this to make your timeline better. UndoUndo
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