osmie: (Default)
I posted a long time ago (and don't want to bother looking up the link right now and am grateful to [livejournal.com profile] koppermoon for looking up the link for me) about my frustration with narratives which are created to explain a statistical inevitability. I remember citing the examples of bisexuals in straight relationships, and of mathematicians who appear most productive in their youth.

Well, here's another such narrative debunked: women and men are equally good at chess; women just play it less often.

In particular, the ratings of female chess masters & grandmasters in Germany are almost exactly what you'd expect from comparing a larger group with a smaller one. Of the 120,000 ranked German chess players, just 7000 are women -- but if you picked 7000 chess players at random, instead of by gender, you'd get a rating distribution which is 96% identical. In fact you'd expect the highest rating to be somewhat lower than Judit Polgar's, but even that matches the narrative that she's the best female chess player in history.
osmie: (Default)
I posted a long time ago (and don't want to bother looking up the link right now and am grateful to [livejournal.com profile] koppermoon for looking up the link for me) about my frustration with narratives which are created to explain a statistical inevitability. I remember citing the examples of bisexuals in straight relationships, and of mathematicians who appear most productive in their youth.

Well, here's another such narrative debunked: women and men are equally good at chess; women just play it less often.

In particular, the ratings of female chess masters & grandmasters in Germany are almost exactly what you'd expect from comparing a larger group with a smaller one. Of the 120,000 ranked German chess players, just 7000 are women -- but if you picked 7000 chess players at random, instead of by gender, you'd get a rating distribution which is 96% identical. In fact you'd expect the highest rating to be somewhat lower than Judit Polgar's, but even that matches the narrative that she's the best female chess player in history.
osmie: (Default)
A couple of months ago, [livejournal.com profile] fimmtiu and I were talking about mathematicians. Why was it, we speculated, that so many mathematicians are (or are perceived to be) over the hill by age 30?

And suddenly the answer -- or at least an answer -- occurred to me. "You know, that's always bugged me," I said, which was a stark lie, because I'd never thought of it until an instant beforehand, but which was also quite true, because what has always bugged me is when people make up additional causes for something that's already perfectly naturally explained by sheer statistics.

For example, evolution vs. intelligent design. )

For another example: bisexuality. )

So to return to mathematicians: Let Pm% be the chance of experiencing some genuine mathematical insight, of a level of brilliance that even some mathematicians will never achieve, in any given year that you're practising mathematics. Of necessity this will be quite low. Now let P0% be the chance of experiencing the same insight in a year that you don't practise mathematics. I believe it's safe to assume that P0 is significantly less than Pm.

Now let Q0% be the chance that any given mathematician will quit practising mathematics in any given year, if she has never experienced such an insight -- and let Qm% be the equivalent chance for a mathematician who has experienced at least one. This time, I believe it's safe to assume that Q0 is rather greater than Qm. (For simplicity, I'm going to assume that the odds of returning to mathematics is uniformly 0% among people who experience no insight that year, and 100% among people who do, but again the important part is only that the latter probability exceeds the former.)

So take an initial population of 20-year-old mathematicians. In year one, Q0 of them will quit, and Pm of them will experience an insight. In year two, Q0(1-Q0-Pm)+QmPm of them will quit; Pm(1-Q0) will experience an insight; and Q0P0 former mathematicians will return to the fold. The formulae get more complex as you iterate, but the upshot is that if all mathematicians stayed mathematicians for life, then flashes of insight would still occur just once in a lifetime, but when viewed over the entire population of mathematicians, they'd be evenly distributed throughout that lifetime. However, mathematicians who reach the age of 25 without an insight are much more likely to quit mathematics (and lose their chance to experience an insight at age 50) than those who've already had one. Over enough iterations, the average age of each insight will tend to skew quite low.

Once again, there's no need to invent bizarre explanations about loss of mathematical creativity when raw statistics already predict the same outcome.

I'm honestly surprised that more mathematicians haven't figured this out.


1Yes, I know there are people who would really prefer to pretend that sexual reproduction doesn't exist either, but I believe that deep in their hearts they know it's real.
2One word: broccoli.
osmie: (Default)
A couple of months ago, [livejournal.com profile] fimmtiu and I were talking about mathematicians. Why was it, we speculated, that so many mathematicians are (or are perceived to be) over the hill by age 30?

And suddenly the answer -- or at least an answer -- occurred to me. "You know, that's always bugged me," I said, which was a stark lie, because I'd never thought of it until an instant beforehand, but which was also quite true, because what has always bugged me is when people make up additional causes for something that's already perfectly naturally explained by sheer statistics.

For example, evolution vs. intelligent design. )

For another example: bisexuality. )

So to return to mathematicians: Let Pm% be the chance of experiencing some genuine mathematical insight, of a level of brilliance that even some mathematicians will never achieve, in any given year that you're practising mathematics. Of necessity this will be quite low. Now let P0% be the chance of experiencing the same insight in a year that you don't practise mathematics. I believe it's safe to assume that P0 is significantly less than Pm.

Now let Q0% be the chance that any given mathematician will quit practising mathematics in any given year, if she has never experienced such an insight -- and let Qm% be the equivalent chance for a mathematician who has experienced at least one. This time, I believe it's safe to assume that Q0 is rather greater than Qm. (For simplicity, I'm going to assume that the odds of returning to mathematics is uniformly 0% among people who experience no insight that year, and 100% among people who do, but again the important part is only that the latter probability exceeds the former.)

So take an initial population of 20-year-old mathematicians. In year one, Q0 of them will quit, and Pm of them will experience an insight. In year two, Q0(1-Q0-Pm)+QmPm of them will quit; Pm(1-Q0) will experience an insight; and Q0P0 former mathematicians will return to the fold. The formulae get more complex as you iterate, but the upshot is that if all mathematicians stayed mathematicians for life, then flashes of insight would still occur just once in a lifetime, but when viewed over the entire population of mathematicians, they'd be evenly distributed throughout that lifetime. However, mathematicians who reach the age of 25 without an insight are much more likely to quit mathematics (and lose their chance to experience an insight at age 50) than those who've already had one. Over enough iterations, the average age of each insight will tend to skew quite low.

Once again, there's no need to invent bizarre explanations about loss of mathematical creativity when raw statistics already predict the same outcome.

I'm honestly surprised that more mathematicians haven't figured this out.


1Yes, I know there are people who would really prefer to pretend that sexual reproduction doesn't exist either, but I believe that deep in their hearts they know it's real.
2One word: broccoli.

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