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Contrapositive 34
You've probably already heard of Rule 34 of the Internet:
[Pause to digest that for a second if you haven't thought about contrapositives before.]
Hence, Rule 34 is equivalent to its contrapositive:
Note that Rule 34 is not equivalent to its converse, which states "If there is porn of it on the Internet, it exists". That one's probably false. Links NSFW, obviously. This means that we can't, for instance, construct existence proofs by writing pornography featuring the thing whose existence we wish to prove ("'Come here, you sexy thing,' said the set whose cardinality was greater than that of the integers but less than that of the real numbers"). Bummer. However, Contrapositive 34 does have some interesting consequences:
Will Strinz suggested that you could build an accurate database of all things by searching for Internet pornography ("mining pornspace", as he called it). Unfortunately this doesn't quite work, since the converse of Rule 34 is false; you could, however, build an accurate database of things that might exist. If your search engine were powerful enough, you could try building a database of things that are believed with high confidence not to exist - generate search queries somehow (taking sets of dictionary words and adding "porn" would be a good starting point), and anything that returns no hits probably doesn't exist.
You might have a hard time explaining your multi-petabyte porn collection to your grant committee, though.
¹ *snigger*
If it exists, there is porn of it on the Internet. No exceptions.Now, as any mathematician can tell you, the statement "if X then Y" is equivalent to its contrapositive, "if not-Y then not-X". For instance, "if Socrates is human, then he is mortal" is equivalent to "if Socrates is not mortal, then he is not human".
[Pause to digest that for a second if you haven't thought about contrapositives before.]
Hence, Rule 34 is equivalent to its contrapositive:
If there is no porn of it on the Internet, it doesn't exist. No exceptions.At DrMathochist's suggestion, I'm going to refer to this equivalent statement as Contrapositive 34, though we could just think of it as a re-statement of Rule 34: it's true if and only if the original Rule 34 is true.
Note that Rule 34 is not equivalent to its converse, which states "If there is porn of it on the Internet, it exists". That one's probably false. Links NSFW, obviously. This means that we can't, for instance, construct existence proofs by writing pornography featuring the thing whose existence we wish to prove ("'Come here, you sexy thing,' said the set whose cardinality was greater than that of the integers but less than that of the real numbers"). Bummer. However, Contrapositive 34 does have some interesting consequences:
- While the amount of pornography on the Internet is mindbogglingly large, it's still finite; hence, there are only finitely many things in existence.
- Since all Internet pornography, when you get right down to it¹, consists of finite strings of bits, the set of all possible Internet pornography is countable. Hence, there are only countably many possible things.
Will Strinz suggested that you could build an accurate database of all things by searching for Internet pornography ("mining pornspace", as he called it). Unfortunately this doesn't quite work, since the converse of Rule 34 is false; you could, however, build an accurate database of things that might exist. If your search engine were powerful enough, you could try building a database of things that are believed with high confidence not to exist - generate search queries somehow (taking sets of dictionary words and adding "porn" would be a good starting point), and anything that returns no hits probably doesn't exist.
You might have a hard time explaining your multi-petabyte porn collection to your grant committee, though.
¹ *snigger*
Two points
2) Rule 34 is usually phrased so that "exists" means something different to the way you're using it. Spongebob cartoons exist, so there is spongebob porn, for instance.
But I like the way you twist logic, so it's all good :->
Re: Two points
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I've always had a little problem with this - largely because I think I was introduced to it badly by the statement 'All Ravens are black' => 'All not-Ravens are not-black', which strikes me as being false, as it implies that blackbirds (a black not-raven) cannot exist.
I understand that this is a fun post, and all a bit tongue-in-cheek, but isn't a true counter-positive to Rule 34 as stated:
"If it does not exist, there is not porn of it on the Internet"
Which could be construed as also false, depending on your definition of 'exists'.
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If all ravens are black, then anything which is not black can't be a raven. And if anything that isn't black can't be a raven, all ravens must be black.
The contrapositive (i.e., literally, the "opposite-way-of-putting-it") is "all-not-blacks are not-ravens", which is true.
As blackbirds (and, oh, black cats) show, the converse is false.
"If it does not exist, there is not porn of it on the Internet" is the converse of Contrapositive 34---and means roughly the same as the converse of Rule 34; it's obviously wrong.
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"All true Scotsmen eat salt with their porridge"
goes to:
"All people who do not eat salt with their porridge are not true Scotsmen." (True if we accept the above)
not:
"All people who are not true Scotsmen, do not eat salt with their porridge." (Not necessarily true).
Ah! That actually makes sense!
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"If you can imagine it, there is porn of it [on the Internet]"
In which case would both the converse and counter-positive be true?
Converse: "If you cannot imagine it, there is no porn of it." [True if 'you' means 'humanity' as a whole']
Counter-Positive: "If there is not porn of it, you cannot imagine it."
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Are you seriously suggesting that I'd make a joke about logic which was incorrect?
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[Sorry - a bad attempt at counter-positive humour.]
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[And while we're at it, the word is contrapositive.]
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Also I am unhappy about your probabilistic interpretation. For "high confidence" you need a probabilistic measure and for a measure you need your functor "is porn of [ ] on the internet" (or, on the restricted domain of the internet, "is porn of") to have certain topological properties[1]. But we know that internet porn can defy all topology as well as all logic.
[1] I am not sure about compactness, though I would like to see a fixed point of the "is internet porn of" operator. That's a fairly abstract "like", though---I'm not sure how truly arousing it could be. Maybe I have the wrong proclivities to be aroused by fixed points.
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did you see
(Anonymous) 2011-06-21 08:05 pm (UTC)(link)I put it on hype a while back, not sure if you caught it..
Re: did you see