Editing AndrewSchoonmaker
Andrew is currently out in the world (whoa, scary), one of the many ex-Mudders at LaserFiche. He used to be a JointMajor at HarveyMuddCollege. He has many interests in matters small and technical, to badly mangle a quote from a FilkSong of GilbertAndSullivan by ZachWalters (IamTheVeryModelOfaHarveyMuddProfessional, to be exact). Current status: * EmailAddress: [mailto:aps@cs.hmc.edu aps@cs.hmc.edu] * (Fast +0) I am numbered among the former members of CrackSuite, PearIntoPeachesSuite, FunBallSuite (I believe I'm still a FunBallPeople, for very small values of ...) and AngbandAndPuritySuite. I don't maintain anything. (except this wiki node, occasionally ;-) I sleep ApproximatelyWheneverIFeelLikeIt (it's kinda sorta not at all like a RotatedSchedule). Current interests include: * SamuraiWarriors * FinalFantasyX2 * TitanTheMonsterSlugathonFantasyWargame (well, darn it, I'd *like* to play...) * AngBand * MOD files, and assorted variants. My current goal is to get enough digital music on my computer that I can stuff it all into a playlist and still not have to hear axelf.mod more often than I want to. (Andrew is sometimes also known as NeonElephant) (Andrew is appararently also known as RealAndrew on another Wiki (which may or may not exist anymore (and is also found several times in the story itself (isn't LISP grand? ;-)))) Misc. anagrams of name, divided by type: * '''Descriptive''' * He's a C-rank Dew moron * Am Neon, Sword Hacker * '''Bizarre''' * A neon red wok's charm FunFact: Apparently, mu X.mu Y.(X -> X) is equivalent to mu X.mu Y.(X -> (mu Z.Y)) in the, ah, limit, even when you use weak unfolding. Ask him about the cat and dog / dog and cat joke -- BenZeckel (warning: it's tasteless) * 4'33" is a song. * Every song has a remix, which is also a song. * 4'33" is not the remix of any song. * Different songs have different remixes. * If a song collection contains 4'33" and also the remix of every song in the collection, then the collection contains every song. ''Not sure if I follow: why can't 4'33" be its own remix, since the point is that it's different every time? (though the logic is cute :-)'' If it's different, then it's not the same song. Its remix may sound just like it, but... (4'33" was selected for a reason, though it's not the only song that would fit there) ''I think you need to define remix then, because loosely I'd say a remix is a song that carries the basic concept of the original song, though may sound nothing like it. And I think saying "if it sounds different, it's a different song" doesn't work if you're calling 4'33" a song...'' ''Note that the fifth statement is in fact a separate hypothesis, and doesn't follow from the first four. Maybe I've just been too much of a math major for too long... Things like this show some of the inherent drawbacks of using words that already possess colloquial meanings as teriminology. That said, I like the idea of a musical arithmetic. -- AlexWilkins'' ''In fact, the fifth statement follows from the first four if and only if every song is an nth remix of 4'33" for some n. This is possible only when the songs are countably infinite, although that condition is not sufficient. If there are uncountably many songs, the fifth statement is false, and if there are finitely many songs, the first four are inconsistent. -- AriNieh'' * I'm confused. How does the fifth statement follow from the first four? ** Like I said, it follows if every song is an nth remix of 4'33" for some n. The converse holds because otherwise, one could consider the collection consisting of 4'33" and all its remixes, which would not be every song. * Why are the first four inconsistent if there are countably many songs? ** They aren't. Ari said they are inconsistant if there are ''finitely'' many songs. * I agree that the fifth statement is false if there are uncountably many songs, but I don't understand the other two statements. -- CurtisVinson ** If you look on the collection of songs and remixes as a directed graph, with each song a vertex and each remixing an edge, then it becomes more obvious. The second axiom says that each vertex has out-degree at least one, the fourth says that each vertex has in-degree at most one (counting all edges from the same vertex as one edge), and the third says that the vertex 4'33" has in-degree 0. Thus, if there are only finitely many vertices in the graph, the total in-degree of the graph is less than the total out-degree, and so the four axioms are inconsistent. -- AlexWilkins ''As Alex (sort of) notes, I'm not defining remix here; any meaning you attach to it not implied by the statements may not be true. The fifth statement isn't a hypothesis, it's an axiom. Only the current adaptation is (as far as I know) due to me. I'm surprised they aren't more recognizable. --AndrewSchoonmaker'' ''Well, not everyone has taken a class in logic (not that I blame them) -- AlexWilkins'' ''Yeah, true. They should've all read GEB, though (more or less by definition) ;-> --AndrewSchoonmaker'' ''How about this problem: If there exists a song that is not a remix of any song, then it is not within the collection, violating your fifth statement. What would be the effects of a song being its own remix? (Doesn't make any sense in the real definition of the word, but an interesting possibility.) -- BenjAzose'' The statements are axioms, and not theora; since a song (other than 4'33") that is not the remix of any song would violate the fifth, it cannot exist. For similar reasons, a song cannot be its own remix in this system. (It doesn't make much sense in the real world, but it's neat to think about anyway, IMO -- if you want to get especially fallacious, there's also the Brouwer Fixed-Point Theorem :-) ''THWAAACK! Bad pundit! --ArielBarton'' Excuse me? Are you giving me credit for a pun I didn't make? *Music-based number theory axioms? What did you expect me to think? **Given some of the other responses, I'd have to go with "Huh?" **Ohhhhh. Right. A flat min[eo]r. Hope you weren't expecting any *useful* information... ---- CategoryHomePage (have these tags been turned into HistoricArtifact""s yet?)
Summary:
This change is a minor edit.
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