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@Prahar I understand your point, but I think I would be more convinced if you could give me an example of when such an answer has been found previously in physics. I can't think of any other example where the mathematical basis for a constant or the reason for the proportion between two quantities of the same dimension has been found.
@Prahar but asking "Why?" does not seem to be a sensible question in physics. Physicists rather try to find how nature works. Feynman states this in the very same book earlier, "while I am describing to you how Nature works, you won't understand why Nature works that way . But you see, nobody understands that. I can't explain why Nature behaves in this peculiar way." and also in this clip: youtube.com/watch?v=MO0r930Sn_8.
@Prahar I don't really see how that question makes sense, as it just seems like asking why something happens, which in physics should just be because that's how nature is. It would be like asking why gravity isn't stronger or weaker or why there are a certain number of fundamental interactions and not more or less.
well, if dimensionless numbers are different then why are we not trying to find a mathematical formula for the ratio of an electron's rest mass to a proton's rest mass, that clearly just seems like the way nature is so how is the fine structure constant different?
