I was reviewing some math in preparation for my tutoring tomorrow, when I came across a curious question involving a trumpet shape that is infinitely long but has a finite area. The book, in typical annoying math book fashion writes “We have a paradox: it takes an infinite amount of paint to paint the region but only a finite amount to fill the horn obtained by rotating the region (How can you resolve this paradox?)”.
I resolved this paradox by flipping the book the bird and looking on the internet. There I found this interesting article about the universe and how it may be shaped like one of these strange trumpets, which would mean that our universe is infinitely long but has finite volume. Who ever said math wasn’t practical?
I did find a tentative resolution to the paradox
here
but even that was hedging its bets with a “One possible explanation of the
paradox” statement. Basically, there is no good ‘resolution’ to the
paradox. That’s why it’s a paradox. Evil math book! My personal take on
this is that it is a place where the mathematical system we have going is
being pushed to the breaking point, a la Godel, and disolving into
nonesense. That’s pretty much my take on all paradoxes.
posted at 13:47 on Tue, 30 Nov, 2004 |
path: /work
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