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There is no such thing as masculine probability theory or feminine decision theory. In their pure form, the maths probably aren't even human. But the human practice of rationality—the arts associated with, for example, motivating yourself, or compensating factors applied to overcome your own biases—these things can in principle differ from gender to gender, or from person to person.
My attention was first drawn to this possibility of individual differences in optimization (in general) by thinking about rationality and gender (in particular). I've written rather more fiction than I've ever finished and published, including a story in which the main character, who happens to be the most rational person around, happens to be female. I experienced no particular difficulty in writing a female character who happened to be a rationalist. But she was not an obtrusive, explicit rationalist. She was not Jeffreyssai.
And it occurred to me that I could not imagine how to write Jeffreyssai as a woman; his way of teaching is paternal, not maternal. Even more, it occurred to me that in my writing there are women who are highly rational (on their way to other goals) but not women who are rationalists (as their primary, explicit role in the story).
A parenthetical, at this point, upon my own gender politics (lest anyone misinterpret me here). Of much of what passes for gender politics in present times, I have very little patience, as you might guess. But as recently as the 1970s this still passed for educational material, which makes me a bit more sympathetic.
So this about my gender politics: Unlike the case with, say, race, I don't think that an optimal outcome consists of gender distinctions being obliterated. If the day comes when no one notices or cares whether someone is black or white, any more than they notice eye color, I would only applaud. But obliterating the difference between male and female does not seem to me desirable, and I am glad that it is impossible using present-day technology; the fact that humanity has (at least) two sexes is part of what keeps life interesting.
But it seems to me that, as an inheritance from the dark ages, the concept of "normal" is tilted more toward male than female. Men are not constantly made aware that they are men in the same way that women are made constantly aware that they are women. (Though there are contexts where explicit masculinity is suddenly a focus.) It's not fun for women if female is defined as abnormal, as special. And so some feminists direct their efforts into trying to collapse gender distinctions, the way you would try to collapse racial distinctions. Just have everyone be normal, part of the same group. But I don't think that's realistic for our species—sex is real, it's not just gender—and in any case I prefer to live in a culture with (at least) two genders.
So—rather than obliterate the difference between genders into a common normality—I think that men should become more aware of themselves as men, so that being female isn't any more special or unusual or abnormal or worthy-of-remark than being male. Until a man sees his own argumentativeness as a distinctively male trait, he'll see women as abnormally passive (departures from the norm) rather than thinking "I am a male and therefore argumentative" (in the same way that women now identify various parts of themselves as feminine).
And yes, this does involve all sorts of dangers. Other cultures already have stronger male gender identities, and that's not always a good thing for the women in those cultures, if that culture already has an imbalance of power. But I'm not sure that the safe-seeming path of trying to obliterate as many distinctions as possible, is really available; men and women are different. Moreover, I like being a man free to express those forms of masculinity that I think are worthwhile, and I want to live in a world in which women are free to express whatever forms of feminity they think are worthwhile.
I'm saying all this, because I look over my accumulated essays and see that I am a distinctively male rationalist. Meanwhile, in another thread, a number of my fellow rationalists did go to some length to disidentify themselves as "female rationalists". I am sympathetic; from having been a child prodigy, I know how annoying it is to be celebrated as "having done so much while so young" rather than just "having done neat stuff in its own right regardless of age". I doubt that being singled out as an "amazing female rationalist" is any less annoying. But still: I built my art out of myself, and it became tied into every part of myself, and it happens to be a fact that I'm male. And if a woman were to pursue her art far enough, and tie it into every part of herself, she would, I think, find that her art came to resemble herself more and more, tied into her own motives and preferences; so that her art was, among other things, female.
It's hard to pin down this sort of thing exactly, because my own brain knows only half the story. My understanding of what it means to be female is too much shallower than my understanding of what it means to be male, it doesn't ring as true. I will try, though, to give an example of what I mean, if you will excuse me another excursion...
The single author I know who strikes me as most feminine is Jacqueline Carey. When I read her book Kushiel's Avatar, it gave me a feeling of being overwhelmingly outmatched as an author. I want to write characters with that kind of incredible depth and I can't. She is too far above me as an author. I write stories with female characters, and I wish I could write female characters who were as female as Carey's female characters, and so long as I'm dreaming, I also want to sprout wings and fly.
Let me give you an example, drawn from Kushiel's Avatar. This book—as have so many other books—involves, among its other plot points, saving the world. A shallow understanding of sex and gender, built mostly around abstract evolutionary psychology—such as I myself possess—would suggest that "taking great risks to save your tribe" is likely to be a more male sort of motivation—the status payoff from success would represent a greater fitness benefit to a man, and in the ancestral environment, it is the men who defend their tribe, etcetera. But in fact, reading SF and fantasy books by female authors, I have not noticed any particularly lower incidence of world-saving behavior by female protagonists.
If you told me to write a strongly feminine character, then I, with my shallow understanding, might try to have her risk everything to save her husband. The protagonist of Kushiel's Avatar, Phèdre nó Delaunay, does realize that the world is in danger and it needs to be saved. But she is also, in the same process, trying to rescue a kidnapped young boy. Her own child? That's how I would have written the story, but no; she is trying to rescue someone else's child. The child of her own archenemy, in fact, but no less innocent for all that. When I look at it after the fact, I can see how this reveals a deeper feminity, not the stereotype but a step beyond and behind the stereotype, something that rings true. Phèdre loves her husband—and this is shown not by how she puts aside saving the world to save him, but by how much it hurts her to put him in harm's way to save the world. Her feminity is shown, not by how protective she is toward her own child, but toward someone else's child.
I do dare say that I have developed my art of rationality as thoroughly as Carey has developed her thesis on love. And so my art taps into parts of me that are male. I cultivate the desire to become stronger; I accept and acknowledge within myself the desire to outdo others; I have learned to take pride in my identity as someone who faces down impossible challenges. While my own brain only knows half the story, it does seem to me that this is noticeably more a theme of shĹnen anime than shĹjo anime. Watch Hikaru no Go for an idea of what I mean.
And this is the reason why I can't write Jeffreyssai as a woman—I would not be able to really understand her motivations; I don't understand what taps female drives on that deep a level. I can regurgitate stereotypes, but reading Jacqueline Carey has made me aware that my grasp is shallow; it would not ring true.
What would the corresponding female rationalist be like? I don't know. I can't say. Some woman has to pursue her art as far as I've pursued mine, far enough that the art she learned from others fails her, so that she must remake her shattered art in her own image and in the image of her own task. And then tell the rest of us about it.
I sometimes think of myself as being like the protagonist in a classic SF labyrinth story, wandering further and further into some alien artifact, trying to call into a radio my description of the bizarre things I'm seeing, so that I can be followed. But what I'm finding is not just the Way, the thing that lies at the center of the labyrinth; it is also my Way, the path that I would take to come closer to the center, from whatever place I started out.
(Perhaps a woman would phrase the above, not as "Bayes's Theorem is the high pure abstract thing that is not male or female", but rather, "Bayes's Theorem is something we can all agree on". Or maybe that's only my own brain regurgitating stereotypes.)
Someone's bound to suggest, "Take the male parts out, then! Don't describe rationality as 'the martial art of mind'." Well... I may put in some work to gender-purify my planned book on rationality. It would be too much effort to make my blog posts less like myself, in that dimension. But I also want to point out that I enjoyed reading Kushiel's Avatar—I was not blocked from appreciating it on account of the book being visibly female.
I say all this because I want to convey this important idea, that there is the Way and my Way, the pure (or perhaps shared) thing at the center, and the many paths we take there from wherever we started out. To say that the path is individualized, is not to say that we are shielded from criticism by a screen of privacy (a common idiom of modern Dark Side Epistemology). There is still a common thing we are all trying to find. We should be aware that others' shortest paths may not be the same as our own, but this is not the same as giving up the ability to judge or to share.
Even so, you should be aware that I have radioed back my description of the single central shape and the path I took to get closer. If there are parts that are visibly male, then there are probably other parts—perhaps harder to identify—that are tightly bound to growing up with Orthodox Jewish parents, or (cough) certain other unusual features of my life.
I think there will not be a proper Art until many people have progressed to the point of remaking the Art in their own image, and then radioed back to describe their paths.
Part of the sequence The Craft and the Community
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