A counterargument (albeit from the physics side) is the fine structure constant (~1/137). The dimensionless gravitational fine structure constant is even smaller (~10^-45). This is arguably exquisitely beautiful; the existence of a macroscopic universe requires its smallness.
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Replying to @fisherastro
immensely beautiful indeed .. but for the sake of definiteness i was thinking of sticking closer to the numbers that have every right to just live in the "idea world" but finding themselves nevertheless being immensely applicable
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Replying to @InertialObservr
I like your question - very thought provoking. If anything, the importance of "large" numbers in other domains like physics makes these "big three" order unity constants in pure math seem even more peculiar.
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Replying to @fisherastro
have you heard Paul Dirac's talk on dimensionless numbers? it's wonderfulhttps://www.youtube.com/watch?v=kgXYvaSfFdE …
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Replying to @InertialObservr
I've known about the idea for many years, but this is the first time I've heard it explained in Dirac's own voice! Very cool! His big number theory, like the Dirac sea, is misguided at a superficial level, yet on a deeper level is insightful and hugely influential.
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exactly .. that's how i like to take in things like this .. is that the bigger ideas that we can take away from his thinking, even though some of the details we know are off
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