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GGP (Gratuitous Gödel Escher Bach post)
This 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.
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Does that make sense? I'm half-dead, so I've no way of knowing.
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Yowza. You just graduated :) Congratulations! :) :) *dances, hugs* The extent to which we should convene over the summer is very large...
... But since the Perfect Player could play any sequence of sounds, that implies infinite length...
Well, arbitrary length, at least -- that seems important, because it means that while you can always have a record Longer Than The One You've Got, there are only a finite number of sounds on a given record, which means that it could only break a finite number of players. It becomes an issue of whether there are an infinite number of possible player-shapes...
... but you'll be driving back to Florida pretty soon, yes? Like on Monday? ...
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as i was reading that (through one eye, b/c i tend to keep one eye closed when i'm tired and the light hurts) it seemed a diagonalization argument would suffice... although i'm not sure because it really comes down to 'what does broken mean'... for instance, if a record player can 'fix' itself is it really broken? (if i break my arm it will heal... but i don't consider by body broken until it does... just part of it... but that may be just me)
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The second one wouldn't work because physical things have resonant frequencies, and sound waves ain't nothin' but changes in air pressure. I could have a "destroy anything" machine (well, "destroy anything in the atmosphere), if I could have some way of knowing their resonant frequencies (or the frequencies of each of the component parts) and then making arbitrary-amplitude sound waves. Granted, it might have to be a very powerful sound...
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This is why the metaphor breaks down: Alex is right in that sound that we hear is just changes in air pressure. Usually people describe sound with the amplitude and a frequency of a pressure wave in the air. To reproduce any sound then we need to reproduce any frequency coupled with any amplitude. A number of things strike me at this point. First, are amplitudes bounded? If they aren't, does this mean the player must need infinite power? Second, won't the thing shake itself apart at a certain amplitude? Thirdly, I just pulled piece of bran muffin out of my long, unkempt hair.
In any case, this talk about perfect things is upsetting my stomach.
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my hair has been long and unkepmt but never have i pulled food from it
*bows*
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