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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*