The smallest uninteresting number

[munin]

http://www.johndcook.com/blog/2012/12/31/fuzzy-logic/

[Sniffnoy]

This isn't a paradox. It's simply a proof that all natural numbers are interesting, if we accept the premises. We shouldn't accept the premises, because there really is a real paradox lurking around the corner, but this isn't it.

The paradox occurs when we replace "natural number" by "ordinal". Then the same line of reasoning demonstrates that all ordinals must be interesting. But surely there can only be countably many interesting ordinals! (Because "interesting" is really code for "definable".) Which shows what the real problem in the premises were -- we failed to distinguish between definable in some particular theory and definability in the meta-theory.

See: http://en.wikipedia.org/wiki/Berry_paradox

[nathell]

Theorem: All natural numbers are boring.

Proof (by contradiction): Assume the set of non-boring natural numbers is nonempty, so it must have a smallest element. Call it x. So what? yawn

QED

[JoeAltmaier]

2013 is sort of interesting - first year with non-duplicate digits since 1987

[dexen → JoeAltmaier]

While interesting, that is property of decimal notation rather than the integer number itself. In hexadecimal notation, 2013 is the first (since 2007 -> 0x7d7) with duplicate digits ;-)

    1987 -> 0x7c3
    1988 -> 0x7c4
    1989 -> 0x7c5
    ...
    2007 -> 0x7d7
    2008 -> 0x7d8
    2009 -> 0x7d9
    2010 -> 0x7da
    2011 -> 0x7db
    2012 -> 0x7dc
    2013 -> 0x7dd

[cowpewter]

Perhaps this is the point of the original article, but couldn't one say that the actual "smallest uninteresting number" is actually the second smallest uninteresting number? The first smallest uninteresting number is only interesting by virtue of being otherwise uninteresting, but once we have a second number that is only interesting by virtue of being uninteresting, it's no longer a novelty to be uninteresting. So it's legitimately uninteresting.

[praxulus → cowpewter]

So it's the first legitimately uninteresting number, that's pretty interesting if you ask me.

[javajosh]

Uh, the smallest uninteresting number is clearly 14.

[DanBC → javajosh]

"14 is the smallest even number n with no solutions to φ(m) = n."

(http://www2.stetson.edu/~efriedma/numbers.html)

[javajosh → DanBC]

When you have to go to those kind of lengths to describe the interestingness of a number, you confirm that it's not interesting!

[furyofantares → javajosh]

The fact that someone is willing to go to those lengths indicates a level of interest on their part

[asimjalis → DanBC]

According to this table 391 is the smallest uninteresting number.

[vacri → asimjalis]

Some of those are a bit of a reach. "57 is 111 in base 7"? 111 in base 10 isn't interesting because it's a sequence of the same digit. "22 is the number of partitions of 8" is an interesting thing about 8, not 22, I would argue, since it's not a property inherent to 22.

Mind you, 22 is a sequence of the same digit, so I guess that counts as interesting for some reason...

[solox3 → asimjalis]

Aha! It's a Smith number! http://en.wikipedia.org/wiki/391_(number)#390s

[Avshalom → javajosh]

interesting... tell me more

[lubos]

relevant: http://www.njohnston.ca/2009/06/11630-is-the-first-uninteres...