That’d be a much harder question to answer; my talent is specialized toward figuring out the shape of the right theorem to be proved, not the actual proof which is where most modern math concentrates its prestige. (This is an objectively verifiable form of mathematical talent; it means that sometimes Marcello would prove something and I would look at it and say, “That doesn’t look right” and at least half the time there’d be a mistake.) I feel insecure about not being an expert in the tools by which most modern mathematicians measure basic competence; I can also apparently make “well, if that’s your problem, try transforming it this way” suggestions to someone doing graduate mathematical research at Yale that are accepted as brilliant. I confidently depose that, even taking unusual talents into account, I am not in the literal top tier of mathematical potential—if I can explain basic Bayes better than anyone or was first to state the Lob problem or invented TDT, those outputs drew on at least some non-mathematical high-percentile sections of my brain (explanatory ability in the first case, or what’s somewhat vaguely referred to as “philosophical” talent in the other two). I’m also reasonably confident that, given a hundred modern mathematicians, an average of zero will pick the right problem to solve.
I think I’m comfortable at this point with saying that I’m in the top 99+% of writers—I’ve been picking up “real” books and trying to read them and finding that they seem visibly badly-written to me now that I’ve written HPMOR. Though I’m still not in the literal top tier; there are basic things in writing that I still don’t do too well, despite being outstanding in others, and my new level of skill is just enough to start noticing that Neil Gaiman and Terry Pratchett are doing things way the hell above me.
“What did you mean when you said 99%” should not be a hard question to answer. “Which alternative is correct” may be hard, but did you have in mind “one alternative is correct but I don’t know which”?
figuring out the shape of the right theorem to be proved, not the actual proof which is where most modern math concentrates its prestige.
Many geniuses have a bad reputation for checking all the details and writing them down. Kontsevich and Thurston are good examples. People complain about this but the status hierarchy isn’t much affected by those complaints. Low-status mathematicians don’t often get away with Thurston’s attitude, but nor do they accumulate status by being more conscientious.
That’d be a much harder question to answer; my talent is specialized toward figuring out the shape of the right theorem to be proved, not the actual proof which is where most modern math concentrates its prestige.
Being able to give some actual proofs is a prerequisite of prestige. But it’s not clear to me that it’s right to say that mathematics concentrates its prestige there. See, for example, Fields Medalist Timothy Gower’s article The Two Cultures of Mathematics (pdf):
The “two cultures” I wish to discuss will be familiar to all professional mathematicians. Loosely speaking, I mean the distinction between mathematicians who regard their central aim as being to solve problems, and those who are more concerned with building and understanding theories.
...
Let me now briefly mention an asymmetry similar to the one pointed out so forcefully by C. P. Snow. It is that the subjects that appeal to theory-builders are, at the moment, much more fashionable than the ones that appeal to problem-solvers.
I suspect the distinction Eliezer is making is more akin to the controversial “theoretical vs. experimental” one proposed by Jaffe and Quinn than the traditional “theory-builder vs. problem-solver” one discussed by Gowers.
It’s been years since I read the Jaffe–Quinn article. But, as I recall, it was more about the methods used to answer questions, and about how rigorous human-verifiable proofs might give way to heuristic/probabilistic and computer-aided proofs. Eliezer, on the other hand, seemed to be saying that mathematicians concentrate prestige on answering questions (by whatever means the community considers to be adequate), as opposed to “figuring out the shape of the right theorem to be proved”.
Jaffe and Quinn mainly advocate that labor should be divided between people who make conjectures (“theoreticians”) and people who prove them (“experimentalists”). I don’t think there is much of anything about probabilistic or computer-aided proofs.
You are right. Looking at the Jaffe–Quinn paper again, it is closer to the distinction that Eliezer was making. (However, I note that the mathematical “theoreticians” in that article are generally high-prestige, and the “rigorous mathematicians” have to fight the perception that they are just filling in details to results already announced.)
My mischaracterization of Jaffe and Quinn’s thesis happened because (1) Thurston replied to their article, and he discusses computer-aided proofs in his reply; and (2) even more embarrassingly, I conflated the Jaffe–Quinn article with the Scientific American article The Death of Proof, by John Horgan.
And I don’t know what people see in American Gods—I’ve read over one hundred books I think were better. And I mean that literally; if I spent a day doing it, I could actually go through my bookshelves and write down a list of one hundred and one books I liked more. I couldn’t do that for most of Terry Pratchett’s novels.
Oddly, I don’t like Gaiman much at all on his own, and I don’t like large doses of Pratchett either, but I loved Good Omens—they balanced each other’s weaknesses.
Oh wow, I have the exact opposite reaction; I love both Gaiman and Pratchett separately, but dislike Good Omens—they undercut each other’s strengths.
I tend to describe it as: “They have a similar worldview, but Gaiman is dark, whereas Pratchett is light. When you put them together the result is a rather bland gray.”
I also tried American Gods for a while and found that its charm was mostly lost on me—maybe I didn’t get far enough in. Good Omens, on the other hand...
Understand, I always knew that Good Omens was a great book and that I wasn’t yet writing that well; it’s only now that I’m staring at a Neil Gaiman short story, thinking, “I can tell that he’s doing something outstandingly right here that I’m not doing, but it’s hard to say exactly what...”
American Gods is pretty evenly written; if it didn’t grab you in the first fifty pages or so it was probably never going to. (I say this as someone who fell in love with it and considers it among my favorite of his work.)
Personally, I disliked that trope even before I’d seen it enough times for it to seem cliche, but I count American Gods among my favorites of Gaiman’s work in spite of it.
Perhaps. It was far from being my introduction to that trope, but I found it worth reading for something other than the originality of that particular idea. Still, different people like different things in their art.
Gaiman frequently doesn’t grab me, though I think “A Study in Emerald” is brilliant.
I wish American Gods had been written by someone who understood and liked America better. Why was the computer god a marketing monster rather than a programmer? Or a computer? And I know it’s not fair to blame a writer for not writing a different book, but I’d like to see a version of the idea with the guts to engage with actual American religions.
I’ve read over one hundred books I think were better. And I mean that literally; if I spent a day doing it, I could actually go through my bookshelves and write down a list of one hundred and one books I liked more.
I’ve read many, many books I liked more than many books which I would consider “better” in a general sense. From the context of the discussion, I’d think “were better” was the meaning you meant. Alternatively, maybe you don’t experience such a discrepancy between what you like and what you believe is “good writing”?
A book can be well written and still be bad because of other flaws. Nathaniel Hawthorne’s The Scarlet Letter was very well written in a technical sense, but the story itself was boring as hell and Hawthorne’s skill couldn’t save it.
I think I’m comfortable at this point with saying that I’m in the top 99+% of writers—I’ve been picking up “real” books and trying to read them and finding that they seem visibly badly-written to me now that I’ve written HPMOR. Though I’m still not in the literal top tier; there are basic things in writing that I still don’t do too well, despite being outstanding in others, and my new level of skill is just enough to start noticing that Neil Gaiman and Terry Pratchett are doing things way the hell above me.
What of Pratchett’s work are you judging by? Middle-Pratchett is top tier, but I’m much less impressed with recent-Pratchett (going back at least a few years before the Alzheimer’s diagnosis.)
I get the feeling that a lot of the top experts at writing aren’t necessarily experts on writing, because they can and do lose their touch without noticing that something is wrong.
Is the 99+% for math also compared to mathematicians?
That’d be a much harder question to answer; my talent is specialized toward figuring out the shape of the right theorem to be proved, not the actual proof which is where most modern math concentrates its prestige. (This is an objectively verifiable form of mathematical talent; it means that sometimes Marcello would prove something and I would look at it and say, “That doesn’t look right” and at least half the time there’d be a mistake.) I feel insecure about not being an expert in the tools by which most modern mathematicians measure basic competence; I can also apparently make “well, if that’s your problem, try transforming it this way” suggestions to someone doing graduate mathematical research at Yale that are accepted as brilliant. I confidently depose that, even taking unusual talents into account, I am not in the literal top tier of mathematical potential—if I can explain basic Bayes better than anyone or was first to state the Lob problem or invented TDT, those outputs drew on at least some non-mathematical high-percentile sections of my brain (explanatory ability in the first case, or what’s somewhat vaguely referred to as “philosophical” talent in the other two). I’m also reasonably confident that, given a hundred modern mathematicians, an average of zero will pick the right problem to solve.
I think I’m comfortable at this point with saying that I’m in the top 99+% of writers—I’ve been picking up “real” books and trying to read them and finding that they seem visibly badly-written to me now that I’ve written HPMOR. Though I’m still not in the literal top tier; there are basic things in writing that I still don’t do too well, despite being outstanding in others, and my new level of skill is just enough to start noticing that Neil Gaiman and Terry Pratchett are doing things way the hell above me.
“What did you mean when you said 99%” should not be a hard question to answer. “Which alternative is correct” may be hard, but did you have in mind “one alternative is correct but I don’t know which”?
Have you written anything about the process of figuring out the shape of the theorem to be proved, and/or identifying the plausibility of a theorem?
Many geniuses have a bad reputation for checking all the details and writing them down. Kontsevich and Thurston are good examples. People complain about this but the status hierarchy isn’t much affected by those complaints. Low-status mathematicians don’t often get away with Thurston’s attitude, but nor do they accumulate status by being more conscientious.
Being able to give some actual proofs is a prerequisite of prestige. But it’s not clear to me that it’s right to say that mathematics concentrates its prestige there. See, for example, Fields Medalist Timothy Gower’s article The Two Cultures of Mathematics (pdf):
I suspect the distinction Eliezer is making is more akin to the controversial “theoretical vs. experimental” one proposed by Jaffe and Quinn than the traditional “theory-builder vs. problem-solver” one discussed by Gowers.
It’s been years since I read the Jaffe–Quinn article. But, as I recall, it was more about the methods used to answer questions, and about how rigorous human-verifiable proofs might give way to heuristic/probabilistic and computer-aided proofs. Eliezer, on the other hand, seemed to be saying that mathematicians concentrate prestige on answering questions (by whatever means the community considers to be adequate), as opposed to “figuring out the shape of the right theorem to be proved”.
Jaffe and Quinn mainly advocate that labor should be divided between people who make conjectures (“theoreticians”) and people who prove them (“experimentalists”). I don’t think there is much of anything about probabilistic or computer-aided proofs.
You are right. Looking at the Jaffe–Quinn paper again, it is closer to the distinction that Eliezer was making. (However, I note that the mathematical “theoreticians” in that article are generally high-prestige, and the “rigorous mathematicians” have to fight the perception that they are just filling in details to results already announced.)
My mischaracterization of Jaffe and Quinn’s thesis happened because (1) Thurston replied to their article, and he discusses computer-aided proofs in his reply; and (2) even more embarrassingly, I conflated the Jaffe–Quinn article with the Scientific American article The Death of Proof, by John Horgan.
I once got this feeling reading Stephen R. Donaldson’s The Runes of the Earth—that this was a level of writing that was way beyond what I could see myself reaching. Oddly, I didn’t get this feeling when reading Terry Pratchett, even though I still think that Terry Pratchett is probably a better writer than, say, Shakespeare.
And I don’t know what people see in American Gods—I’ve read over one hundred books I think were better. And I mean that literally; if I spent a day doing it, I could actually go through my bookshelves and write down a list of one hundred and one books I liked more. I couldn’t do that for most of Terry Pratchett’s novels.
Oddly, I don’t like Gaiman much at all on his own, and I don’t like large doses of Pratchett either, but I loved Good Omens—they balanced each other’s weaknesses.
Not at all like this
Oh wow, I have the exact opposite reaction; I love both Gaiman and Pratchett separately, but dislike Good Omens—they undercut each other’s strengths.
I tend to describe it as: “They have a similar worldview, but Gaiman is dark, whereas Pratchett is light. When you put them together the result is a rather bland gray.”
I also tried American Gods for a while and found that its charm was mostly lost on me—maybe I didn’t get far enough in. Good Omens, on the other hand...
Understand, I always knew that Good Omens was a great book and that I wasn’t yet writing that well; it’s only now that I’m staring at a Neil Gaiman short story, thinking, “I can tell that he’s doing something outstandingly right here that I’m not doing, but it’s hard to say exactly what...”
American Gods is pretty evenly written; if it didn’t grab you in the first fifty pages or so it was probably never going to. (I say this as someone who fell in love with it and considers it among my favorite of his work.)
I blame the SeinfeldIsUnfunny effect. I’ve seen GodsNeedPrayerBadly done so many other times that it seemed like a cliche.
Personally, I disliked that trope even before I’d seen it enough times for it to seem cliche, but I count American Gods among my favorites of Gaiman’s work in spite of it.
Perhaps. It was far from being my introduction to that trope, but I found it worth reading for something other than the originality of that particular idea. Still, different people like different things in their art.
Gaiman frequently doesn’t grab me, though I think “A Study in Emerald” is brilliant.
I wish American Gods had been written by someone who understood and liked America better. Why was the computer god a marketing monster rather than a programmer? Or a computer? And I know it’s not fair to blame a writer for not writing a different book, but I’d like to see a version of the idea with the guts to engage with actual American religions.
I’ve read many, many books I liked more than many books which I would consider “better” in a general sense. From the context of the discussion, I’d think “were better” was the meaning you meant. Alternatively, maybe you don’t experience such a discrepancy between what you like and what you believe is “good writing”?
A book can be well written and still be bad because of other flaws. Nathaniel Hawthorne’s The Scarlet Letter was very well written in a technical sense, but the story itself was boring as hell and Hawthorne’s skill couldn’t save it.
What of Pratchett’s work are you judging by? Middle-Pratchett is top tier, but I’m much less impressed with recent-Pratchett (going back at least a few years before the Alzheimer’s diagnosis.)
I get the feeling that a lot of the top experts at writing aren’t necessarily experts on writing, because they can and do lose their touch without noticing that something is wrong.