Gabriel's horn is a solid of revolution that has a finite volume but an infinite surface area.pic.twitter.com/p9xYUpvJ2B
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Not philosophical. On the contrary, the math beer mugs are philosophical. At Planck scale the surface disintegrates to quantum foam.
I don't understand your statement about the Planck scale and surface area. Physics at the Planck scale is not well understood at all. In either case I don't see how that helps or hurts your assertion. The argument is much simpler than that. Nature has a cutoff, maths doesn't .
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I agree, this is what I wrote also. Math is infinite.
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I think we're in violent agreement
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Exactly. So how, in modeling a physical phenomenon with math, do we know we have crossed a boundary into absurd abstraction with no physical meaning or sensible counterpart in the universe? Do we stay mindful such boundaries exist, or do we presume bad minutia doesn't propagate?
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That's why we need experiment. In QFT we prevent this via the process of renormalizatoin.
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