[mikeash]

Alternately: if there are no interesting numbers, that fact is itself interesting. But that fact can be encoded as a number (see Gödel), and the number must be interesting if the fact is interesting. Thus there is at least one interesting number.

[galonk]

The fact being interesting doesn't mean its encoding is interesting. I might find a movie interesting but looking at the raw bytes of the MP4 file much less so ;)

[mikeash]

Does such a thing actually exist outside of the encoding used to represent it?

Uh oh, I think we may have run into... PHILOSOPHY!

http://xkcd.com/903/