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GGP (Gratuitous Gödel Escher Bach post)
May. 8th, 2004 02:36 amThis is one for you, Richard ![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
reality_calls. Or anybody else, really. I'm reading Gödel, Escher, Bach, and it's lovely, and this is going to sound pretentious, but I've got a question and you guys might be interested. Feel free to ignore.
So Douglas Hofstadter (the author of GEB, yes?), presents this problem, fairly early on in the book (this is my paraphrase):
Assume that for any record player, there exists some sound that can cause it to break, just by shaking it apart at its resonant frequency, or whatever. Now we'll call a record player "perfect" if it can reproduce any sound (or sequence of sounds) correctly. There can be no perfect record player, because if it started to play its own Break-Me Sound, then it would break, and it wouldn't finish the rest of the record (you could get around this by just not reproducing sounds accurately, but then you wouldn't have a very good record player at all, so it clearly wouldn't be Perfect, although perhaps more durable...)
Now Hofstadter has one of the characters suggest a record-player that has a video camera on it, and before it plays a record, it scans it in, analyzes what sounds it would make if played, and then automatically rebuilds itself (like its mechanical parts) such that it wouldn't be broken by that sound. He then suggests that this wouldn't work...
And I'm trying to figure out why. It's clearly got to do with the whole Incompleteness Theorem thing, but it also feels like he's talking about the Halting Problem...
It feels like, if you have an arbitrarily long record that contains sounds that would break players A, B, and C, then to play that record, the pre-analyzing player would have to realize this ahead of time and come up with some shape D that it could take. But then what if the record contained sounds to break player-shapes A through D? On a stupid level, it seems like this is a problem about "so, are there more ways to build a record-player, or are there more sounds that would break players?" But at that point, we go back to our earlier assertation and say "Well, there's at least one sound to break each player". So if there are a finite number of possible record players, then you could have an Ultimately Unplayable Record which contains, one at a time, a sound that would break each one, so no matter which shape the thing picked, it would get b0rked.
On the other hand, it seems like if there were an infinite number of possible record players, but records could only be of a finite length... then you'd be set, because you just pick a shape that doesn't get broken by the given record.
Of course, all of this could be danced around by just having a record player that takes only two shapes, changes between them dynamically, and has a lookahead for potentially Break-Me Sounds (assuming that the shapes would be broken by disjoint sets of sounds). But that's probably missing the point.
Also! My dad's side of the family is in town, because he and Mary are having their "we got married a few months ago" party (*shrugs*), so tonight Natalie and I headed over for that, and we hung around and chatted with the relatives. It's always interesting, particularly, to see my Relative Sid (he's my great-grandmother's brother -- what do you call that?) -- he's well up into his 70s, but he's still really active, riding around on his bike and taking long walks and playing tennis and still learning about psychology and philosophy and whatnot... tremendously cool guy. Among the things discussed tonight were "Don't vote for Nader!" (he's fairly politically charged), The Brights (which I hadn't heard of, but I find fairly interesting...), and what I've been up to in school, which is relative-interesting, just in that a quick google for Herbert Leass turns up interesting computational linguistics stuff, and Herb is Sid's son, and both Herb and Sid think it's cool that I want to get into this sort of thing :)
It's nice to have cool relatives :)
I also spoke with one of Mary's aunts, who's a biology professor at St. Mary's College, and she had all sorts of interesting stuff to say about teaching/learning and academia, as well as biology problems that the bioinformatics people are addressing...
Also, somethingawful is totally bizarre. You sometimes click links that you think are prankful, only to find out that... they're not prankful. There's no punchline. They're actual pr0n sites. Oy.
Wordcount? 781.
reality_calls. Or anybody else, really. I'm reading Gödel, Escher, Bach, and it's lovely, and this is going to sound pretentious, but I've got a question and you guys might be interested. Feel free to ignore.So Douglas Hofstadter (the author of GEB, yes?), presents this problem, fairly early on in the book (this is my paraphrase):
Assume that for any record player, there exists some sound that can cause it to break, just by shaking it apart at its resonant frequency, or whatever. Now we'll call a record player "perfect" if it can reproduce any sound (or sequence of sounds) correctly. There can be no perfect record player, because if it started to play its own Break-Me Sound, then it would break, and it wouldn't finish the rest of the record (you could get around this by just not reproducing sounds accurately, but then you wouldn't have a very good record player at all, so it clearly wouldn't be Perfect, although perhaps more durable...)
Now Hofstadter has one of the characters suggest a record-player that has a video camera on it, and before it plays a record, it scans it in, analyzes what sounds it would make if played, and then automatically rebuilds itself (like its mechanical parts) such that it wouldn't be broken by that sound. He then suggests that this wouldn't work...
And I'm trying to figure out why. It's clearly got to do with the whole Incompleteness Theorem thing, but it also feels like he's talking about the Halting Problem...
It feels like, if you have an arbitrarily long record that contains sounds that would break players A, B, and C, then to play that record, the pre-analyzing player would have to realize this ahead of time and come up with some shape D that it could take. But then what if the record contained sounds to break player-shapes A through D? On a stupid level, it seems like this is a problem about "so, are there more ways to build a record-player, or are there more sounds that would break players?" But at that point, we go back to our earlier assertation and say "Well, there's at least one sound to break each player". So if there are a finite number of possible record players, then you could have an Ultimately Unplayable Record which contains, one at a time, a sound that would break each one, so no matter which shape the thing picked, it would get b0rked.
On the other hand, it seems like if there were an infinite number of possible record players, but records could only be of a finite length... then you'd be set, because you just pick a shape that doesn't get broken by the given record.
Of course, all of this could be danced around by just having a record player that takes only two shapes, changes between them dynamically, and has a lookahead for potentially Break-Me Sounds (assuming that the shapes would be broken by disjoint sets of sounds). But that's probably missing the point.
Also! My dad's side of the family is in town, because he and Mary are having their "we got married a few months ago" party (*shrugs*), so tonight Natalie and I headed over for that, and we hung around and chatted with the relatives. It's always interesting, particularly, to see my Relative Sid (he's my great-grandmother's brother -- what do you call that?) -- he's well up into his 70s, but he's still really active, riding around on his bike and taking long walks and playing tennis and still learning about psychology and philosophy and whatnot... tremendously cool guy. Among the things discussed tonight were "Don't vote for Nader!" (he's fairly politically charged), The Brights (which I hadn't heard of, but I find fairly interesting...), and what I've been up to in school, which is relative-interesting, just in that a quick google for Herbert Leass turns up interesting computational linguistics stuff, and Herb is Sid's son, and both Herb and Sid think it's cool that I want to get into this sort of thing :)
It's nice to have cool relatives :)
I also spoke with one of Mary's aunts, who's a biology professor at St. Mary's College, and she had all sorts of interesting stuff to say about teaching/learning and academia, as well as biology problems that the bioinformatics people are addressing...
Also, somethingawful is totally bizarre. You sometimes click links that you think are prankful, only to find out that... they're not prankful. There's no punchline. They're actual pr0n sites. Oy.
Wordcount? 781.
