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