〈 Berger | Dillon 〉

No, statement about finite beer but infinite surface confuses math reality (infinite) with physical reality (bounded). Physical reality has lower constraints on fundamental particle scale. Mathematicians should stop make these confusing statements, they sound funny.

Of course I don't think that this could have a physical reality, just like Banach-Tarski--I'm not a mathematical realist. However, these are "mathematical beer mugs" for which the statement is simply accurate. So, I disagree with your philosophical stance on this.

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 .

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?