Absolutely not a good analogy, or rather, only if you think elegance is an objective property, like the number 6. Granted it rather looked like that’s the direction in which EY’s argument was going. Besides, I didn’t react to the statement “certain proofs are elegant...”, but rather to the statement “You could .. say that certain proofs are elegant even if no conscious agent sees them”, whereas in truth You can’t say (in a meaningful way though you can mouth any words you want, I’m not denying that), that a proof is elegant unless you see it. Maybe there’s a way to object it one takes “see” too literally—you can’t say anything meaningful unless you’ve seen it, or a shadow of it, or function or extract, or at least a number output by, say, an “elegance measuring algorithm”, and in the latter case, you would just be parroting the evaluation of the algorithm, so that wouldn’t seem all that meaningful come to think of it—so it would have to be a shadow, function...… that conveys enough of the original so that your mental process might have something to add.
You can know about things without observing them? Excellent! I could do with a map of New York, you see, but I’m much too busy to go there and draw one...
Seriously, though, you may have misunderstood a part of this conversation.
Yes, I recommend looking into the novel new divination techniques “Physics” and “Mathematics”. The former allows one to form a tolerably accurate model of the present based on knowledge of precursor states. The latter allows reasoning about the logical implications of assumed axioms.
Excellent! I could do with a map of New York, you see, but I’m much too busy to go there and draw one...
Which brings us to the third mystic divination art: Google it.
Next time, try opening with that.
Seriously, though, you may have misunderstood a part of this conversation.
Instead consider that disagreement with a particular claim of yours does not, in fact, imply that I support your opponent’s position. In fact, it doesn’t imply that I care about the rest of the conversation at all. The particular claim about what can and cannot be known about a proof without seeing (or actually deriving) said proof is the only part remotely interesting. It is intuitive but likely to be false.
Wait … are you suggesting, say, I could predict the elegance of a proof without observing it, perhaps by my awareness that it was formulated by someone who values elegance, for example.
Well, I can’t argue with that. Of course, it is somewhat irrelevant to this discussion, but … fair enough, I suppose. Quibble accepted.
The amended version: “You can’t know that a proof is elegant until someone sees it. ”
You can’t know that a proof is elegant until someone sees it.
Sorry, that doesn’t capture it either. You can prove all sorts of things about a proof that nobody’s found yet, without actually finding the proof yet. It would not be terribly surprising if elegance was one of those things.
Sorry, that doesn’t capture it either. You can prove all sorts of things about a proof that nobody’s found yet, without actually finding the proof yet. It would not be terribly surprising if elegance was one of those things.
Thanks thomblake, this was what I was getting at. It is likely to be possible to prove some things such as “There exists of proof of X that is below complexity measure Y” while also knowing “X is perceived by the relevant audience to have complexity of at least Z”. That could be the kind of information that allows us to expect that the proof will be perceived as “elegant”.
If I am remembered for anything, it will be for elucidating the words of wiser men.
On a tangential note, is there a word I could have used above instead of “men” that would preserve the flow but is gender-neutral? I couldn’t find one. Ideally one falling syllable.
ETA: The target word should probably end in a nasal or approximate consonant, or else a vowel.
On a tangential note, is there a word I could have used above instead of “men” that would preserve the flow but is gender-neutral? I couldn’t find one. Ideally one falling syllable.
“Minds” is pretty good, and I also like “souls”, but “wiser” seems like the wrong adjective in both cases and the ending fricative is less pleasant. Still, I think I’ll use one of those in the future when formulating such statements. Thanks!
The correct pronoun to use, if you insist, is “those wiser than me” (or “those wiser than I am”). Normally I wouldn’t be correcting you, but someone who puts an “I” in that sentence probably cares about pronouns.
“Than” governing nominative pronouns it’s widely attested, especially in older texts (I think the standard analysis is that there’s an implicit verb after it); it’s just terribly stilted those days.
Thanks—“folk” technically fits the requirements, but totally changes the feel. I’m not sure you can say “folk” and still sound solemn. And I’m not a fan of the hard ending consonant. You’re definitely casting a wider net than I was though, and I now imagine there’s something to be found.
What’s wrong with “people” (plural) or “person” (sing.)?
Nothing in denotative expression but a lot in terms of poetic flow and syllable count. Substituting “people” into that context just wouldn’t have sounded pretty. In fact it would make the attempt at eloquent elucidation seem contrived and forced—leaving it worse off than if the meaning had just been conveyed unadorned and without an attempt to appear quotable and deep.
I was actually surprised by TheOtherDave’s response. My poetic module returned null and I was somehow fairly certain that there just wasn’t a word that would fit the requirements.
Doesn’t change my view that you can’t “meaningfully” say what you have no grounds for knowing. In my view of the world, which it that it isn’t ruled by dream logic, and the past is fixed, whether we can know certain things about it or not, Abraham Lincoln either did or did not masturbate on his 15th birthday. But no one can “meaningfully” (in the sense in which I’ve used the word) say that he did or didn’t.
Anyway, going back a bit, there are problems with “elegance”, like a lack of agreement on what it means, unless you say “elegance as defined by …” (assuming you can come up with a coherent definition)” Then you could say there is a set of all elegant mathematical proofs whether anyone has ever thought them or not. (Maybe not really, because Gödel, I believe shows that no matter how hard we try, we will never have a “well defined” (let along the one and only correct) specification of the set of all mathematical proofs).
Abraham Lincoln either did or did not masturbate on his 15th birthday. But no one can “meaningfully” (in the sense in which I’ve used the word) say that he did or didn’t.
OK, that’s not the local definition of “meaningful”. That explains the confusion.
there are problems with “elegance”, like a lack of agreement on what it means, unless you say “elegance as defined by …”
Well, yeah. But we can look at proofs and sort ’em into “elegant” and “inelegant”, I guess, so presumably the are criteria buried somewhere in our circuitry. Doubtless inordinately complex ones.
Conceivably someone could have observed Lincoln’s activities (or lack thereof) at the relevant time and written down their observations. Such a record might still exist, but not be known to historians, let alone the general public; and yet anyone who had read it would be able to meaningfully say.
It’s conceivable the way it’s conceivable that the English upper class are giant lizards in disguise. If you’ve read much 19c history and sources, you should know that nobody said anything about anybody masturbating or not, and Lincoln at that time probably lived a mile from his nearest neighbour.
Lincoln is an interesting example because if you read enough biographies of him, it becomes funny just how much mileage people can get out of the most trivial and dubious piece of evidence about his early life.
Anyway, the past is full of things that either happened or didn’t—at least I don’t believe they’re like Schrodinger’s cat, but which we’ll never know if they did or not.
It’s conceivable the way it’s conceivable that the English upper class are giant lizards in disguise.
Yup. That’s generally considered a form of conceivable, at least around here.
(You might want to try lurking around, reading sequences and interesting comments, at least until you absorb the local jargon, assumptions, and so on. Learning from experience probably works, but it has a high cost in karma, or even regular reputation if you’re lucky.)
Yeah. Karma is good. I’ve never put a bumper sticker on my car but if I did it would probably say either
My Karma Ran Over My Dogma
or
Question Bumper-sticker Slogans
I have a mental block for reading the instruction manual, and a strong prejudice towards experimentalism, so while over time I’m sure to soak up a lot of the threads, you’ll probably see me going on my bumptious way.
P.S. As an online book dealer, I’ve spent most of the last 11 years working alone and losing my social skills. While I’m sure to make mistakes, it’s exhilarating to be talking on a forum where the responses are above the level of “poopy-head”.
Um, no. That’s like saying that there isn’t really six apples until you count them.
Absolutely not a good analogy, or rather, only if you think elegance is an objective property, like the number 6. Granted it rather looked like that’s the direction in which EY’s argument was going. Besides, I didn’t react to the statement “certain proofs are elegant...”, but rather to the statement “You could .. say that certain proofs are elegant even if no conscious agent sees them”, whereas in truth You can’t say (in a meaningful way though you can mouth any words you want, I’m not denying that), that a proof is elegant unless you see it. Maybe there’s a way to object it one takes “see” too literally—you can’t say anything meaningful unless you’ve seen it, or a shadow of it, or function or extract, or at least a number output by, say, an “elegance measuring algorithm”, and in the latter case, you would just be parroting the evaluation of the algorithm, so that wouldn’t seem all that meaningful come to think of it—so it would have to be a shadow, function...… that conveys enough of the original so that your mental process might have something to add.
No, you cant know that a proof is elegant until you see it. Quite different.
I’d be surprised if this is actually true. There are features of a proofs that can be themselves proven without actually identifying the proof itself.
You can know about things without observing them? Excellent! I could do with a map of New York, you see, but I’m much too busy to go there and draw one...
Seriously, though, you may have misunderstood a part of this conversation.
Yes, I recommend looking into the novel new divination techniques “Physics” and “Mathematics”. The former allows one to form a tolerably accurate model of the present based on knowledge of precursor states. The latter allows reasoning about the logical implications of assumed axioms.
Which brings us to the third mystic divination art: Google it.
Next time, try opening with that.
Instead consider that disagreement with a particular claim of yours does not, in fact, imply that I support your opponent’s position. In fact, it doesn’t imply that I care about the rest of the conversation at all. The particular claim about what can and cannot be known about a proof without seeing (or actually deriving) said proof is the only part remotely interesting. It is intuitive but likely to be false.
Wait … are you suggesting, say, I could predict the elegance of a proof without observing it, perhaps by my awareness that it was formulated by someone who values elegance, for example.
Well, I can’t argue with that. Of course, it is somewhat irrelevant to this discussion, but … fair enough, I suppose. Quibble accepted.
The amended version: “You can’t know that a proof is elegant until someone sees it. ”
Sorry, that doesn’t capture it either. You can prove all sorts of things about a proof that nobody’s found yet, without actually finding the proof yet. It would not be terribly surprising if elegance was one of those things.
Oh. OK.
You’re absolutely right. I hadn’t thought of that. Point, I guess.
Thanks thomblake, this was what I was getting at. It is likely to be possible to prove some things such as “There exists of proof of X that is below complexity measure Y” while also knowing “X is perceived by the relevant audience to have complexity of at least Z”. That could be the kind of information that allows us to expect that the proof will be perceived as “elegant”.
If I am remembered for anything, it will be for elucidating the words of wiser men.
On a tangential note, is there a word I could have used above instead of “men” that would preserve the flow but is gender-neutral? I couldn’t find one. Ideally one falling syllable.
ETA: The target word should probably end in a nasal or approximate consonant, or else a vowel.
‘Minds’? ‘Tongues’?
“Minds” is pretty good, and I also like “souls”, but “wiser” seems like the wrong adjective in both cases and the ending fricative is less pleasant. Still, I think I’ll use one of those in the future when formulating such statements. Thanks!
Were I writing it, I would likely go with “it will be for elucidating the words of those wiser than I.”
But if you insist on the structure, perhaps “folk”?
The correct pronoun to use, if you insist, is “those wiser than me” (or “those wiser than I am”). Normally I wouldn’t be correcting you, but someone who puts an “I” in that sentence probably cares about pronouns.
“Than” governing nominative pronouns it’s widely attested, especially in older texts (I think the standard analysis is that there’s an implicit verb after it); it’s just terribly stilted those days.
Thank you.
You are absolutely correct… and yet, I would probably keep “I” there.
Or “ones”.
Thanks—“folk” technically fits the requirements, but totally changes the feel. I’m not sure you can say “folk” and still sound solemn. And I’m not a fan of the hard ending consonant. You’re definitely casting a wider net than I was though, and I now imagine there’s something to be found.
For me, Berrypick6′s suggestion of “minds” has the denotative formality that you desire. Can’t comment on the phonetics.
“Heads”? ”...the words of those wiser than me”?
What’s wrong with “people” (plural) or “person” (sing.)?
Nothing in denotative expression but a lot in terms of poetic flow and syllable count. Substituting “people” into that context just wouldn’t have sounded pretty. In fact it would make the attempt at eloquent elucidation seem contrived and forced—leaving it worse off than if the meaning had just been conveyed unadorned and without an attempt to appear quotable and deep.
I was actually surprised by TheOtherDave’s response. My poetic module returned null and I was somehow fairly certain that there just wasn’t a word that would fit the requirements.
Yes. With “people” it sounds less like an epitaph and more like a commercial slogan to me. My favourite suggestion so far is MixedNuts’.
If you say it but don’t know it, well that’s why I said “can’t meaningfully...”.
A hypothesis is true or false before it is tested.
Doesn’t change my view that you can’t “meaningfully” say what you have no grounds for knowing. In my view of the world, which it that it isn’t ruled by dream logic, and the past is fixed, whether we can know certain things about it or not, Abraham Lincoln either did or did not masturbate on his 15th birthday. But no one can “meaningfully” (in the sense in which I’ve used the word) say that he did or didn’t.
Anyway, going back a bit, there are problems with “elegance”, like a lack of agreement on what it means, unless you say “elegance as defined by …” (assuming you can come up with a coherent definition)” Then you could say there is a set of all elegant mathematical proofs whether anyone has ever thought them or not. (Maybe not really, because Gödel, I believe shows that no matter how hard we try, we will never have a “well defined” (let along the one and only correct) specification of the set of all mathematical proofs).
OK, that’s not the local definition of “meaningful”. That explains the confusion.
Well, yeah. But we can look at proofs and sort ’em into “elegant” and “inelegant”, I guess, so presumably the are criteria buried somewhere in our circuitry. Doubtless inordinately complex ones.
Conceivably someone could have observed Lincoln’s activities (or lack thereof) at the relevant time and written down their observations. Such a record might still exist, but not be known to historians, let alone the general public; and yet anyone who had read it would be able to meaningfully say.
It’s conceivable the way it’s conceivable that the English upper class are giant lizards in disguise. If you’ve read much 19c history and sources, you should know that nobody said anything about anybody masturbating or not, and Lincoln at that time probably lived a mile from his nearest neighbour.
Lincoln is an interesting example because if you read enough biographies of him, it becomes funny just how much mileage people can get out of the most trivial and dubious piece of evidence about his early life.
Anyway, the past is full of things that either happened or didn’t—at least I don’t believe they’re like Schrodinger’s cat, but which we’ll never know if they did or not.
Yup. That’s generally considered a form of conceivable, at least around here.
(You might want to try lurking around, reading sequences and interesting comments, at least until you absorb the local jargon, assumptions, and so on. Learning from experience probably works, but it has a high cost in karma, or even regular reputation if you’re lucky.)
Yeah. Karma is good. I’ve never put a bumper sticker on my car but if I did it would probably say either
My Karma Ran Over My Dogma
or
Question Bumper-sticker Slogans
I have a mental block for reading the instruction manual, and a strong prejudice towards experimentalism, so while over time I’m sure to soak up a lot of the threads, you’ll probably see me going on my bumptious way.
Thanks
P.S. As an online book dealer, I’ve spent most of the last 11 years working alone and losing my social skills. While I’m sure to make mistakes, it’s exhilarating to be talking on a forum where the responses are above the level of “poopy-head”.
By my reading, the meaning of that statement is that EY is claiming that elegance is (at least partially) objective.
Didn’t I cover that? (“Granted it rather looked like that’s the direction in which EY’s argument was going”)? Did you really read what I wrote?
But I think a statement like “you could say 2 x 3 = 6” would sound funny.