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MugaSofer comments on By Which It May Be Judged - Less Wrong
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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...
</sarcasm>
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.
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.
By my reading, the meaning of that statement is that EY is claiming that elegance is (at least partially) objective.