29 December 2007

Unparadoxes

I just discovered Scott Aaronson's blog, Shtetl-optimized. You should discover it as well.

I am currently being amused by the comments to his post soliciting unparadoxes, which are what they sound like -- results that superficially resemble well-known paradoxes, but are actually not paradoxes at all. For example, "The Banach-Tarski Unparadox: If you cut an orange into five pieces using a standard knife, then put them back together, the result will have exactly the same volume as the original orange." This seems to me to be a new class of mathematical jokes; only someone who had heard of the Banach-Tarski paradox would appreciate why one would ever expect it to be possible to cut an orange up in any other way!

Take a look through the comments to Aaronson's post, which give about a hundred more examples; I won't try to come up with any of my own.

1 comment:

complexzeta said...

Not exactly an unparadox, but a lot of people at my undergrad liked this proof:

Theorem: There are infinitely many composite numbers.

Proof: Assume there are only finitely many. Then multiply them together and don't add one. (Technically you also need that there are at least two composites, but that's a minor point.)