
The Interesting Number Paradox - chaosmachine
http://en.wikipedia.org/wiki/Interesting_number_paradox
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michael_nielsen
The Wikipedia Paradox: what's the most notable subject that's not notable
enough for Wikipedia?

Now, one could reasonably argue that merely being the answer to this question
would not, by itself, be enough to make a subject notable. However, the act of
arguing this point, if seriously engaged in by enough people, would, in fact,
make the question (and the answer) notable, and thus the answer to the
question would deserve inclusion in Wikipedia.

Inductively, you can use this argument to show every subject is notable enough
for inclusion in Wikipedia. Take that, deletionists!

(Inspired by a lunchtime conversation with a group of physicists and
philosophers.)

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mkyc
Were you among the physicists? :) Notability is not an intrinsic property of
articles: it's like weight, not like mass. Your argument fails at the "if
seriously engaged in by enough people" point, since it's simply false (by
definition) that at time T1 the first uninteresting thing is sufficiently
popular, at T1. It's also false that people will a) notice and b) care enough
to make it sufficiently popular even at time T2.

Same goes for numbers. The fallacy is in confusing intrinsic and extrinsic
properties.

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Dove
Persuasive enough, mathematically. Practically, though, people wouldn't allow
the definition to recurse like that.

Consider a hypothetical person filling in descriptions for all the interesting
numbers. "Smallest prime", "Smallest odd prime", "Smallest square" . . . He
would get to the smallest uninteresting number and write, "Smallest
uninteresting number." Then when he got to the next one, he'd start to write
that, realize he already had one, and ponder for a bit.

The divergence occurs here.

If he was a mathematician, he would shout, "Aha! There are no uninteresting
numbers!" If particularly diligent, he would go on to write "Was the smallest
uninteresting number until that made it interesting" on all the other numbers.

If he was a normal person, he'd criticize the definition. Yes, he does think
the smallest uninteresting number is interesting, but he doesn't think the
next one is. So the technical definition shouldn't be recursive, and that
keeps the initial annotation from being so self-defeating. He'd then go back
and write, "Smallest number which would otherwise be uninteresting" on the
first one, and leave the rest alone.

I side with the normal person. A definition which allows so many numbers with
the same description to be considered "interesting" doesn't actually
correspond with what I think interesting means. I think it is reasonable to
require that the definition of interesting be stable regardless of what order
you evaluate the integers in, so a definition that allows for this sort of
nonsense should be modified until it doesn't.

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spuz
Does the same apply to HN submissions? ;)

~~~
serhei
If it did, you would be forced to classify spam and old Valleywag articles as
"interesting".

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DanielBMarkham
This and the hanging prisoner paradox in the afternoon.

Must be epistemology night on HN :)

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mixmax
The theory also applies to trees, ropes and pipes.

~~~
roundsquare
The set in question needs some ordering (at least for the proof to easily
cross over).

Though, I suppose we can use "number of molecules" and almost always get away
with it.

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mayanks
sounds like a catch 22 kinda situation to me. Or for that matter Heisenberg
uncertainty principle.

