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.
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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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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have you heard Paul Dirac's talk on dimensionless numbers? it's wonderfulhttps://www.youtube.com/watch?v=kgXYvaSfFdE …
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