Token Applause For Restating the Obvious


Image by cartoonist xkcd. Used under a Creative Commons license.

Given his cultural heritage (iconic cartoonist for the fiendishly brilliant nerd set) this comic by xkcd is all the more poignant. It’s not that there are no women nerds, but they are rare enough that when they do appear they appear to the predominantly male cohort as tokens of their gender rather than specific individuals from their gender.

And while this may be obvious to everyone else on the planet, and since I’m really supposed to be studying for yet another exam in my combined interpersonal communication theory / sex education / women’s studies program, I’m going to procrastinate by reinforcing (for myself) something I’d maybe sort of thought about before I began my course but hadn’t really thought about much.

In a 1993 McGraw-Hill text called Women & Gender: A Feminist Psychology, in a chapter called “Gender, Status, and Power” the authors, Unger & Crawford, discuss the issue of tokenism thusly:

Obviously a woman is much more likely to be seen as a representative of the social category “female” when she is the single person of her sex in a group. ... They are more visible and isolated than the men who, because of their numerical dominance, determine the culture of the group. They are likely to be defined in stereotypically feminine terms, and they are likely to be seen by themselves and others as representing women’s issues rather than the interests of the group as a whole.

Because of their distinctiveness within a group, tokens may be evaluated unfairly. Even expectations of differential treatment by majority-group members may, under some conditions, produce poorer performance by token than non-token individuals.

The following interesting experiment demonstrates how tokenism can be induced in anyone regardless of his or her social category. ... College students were led to believe that they were sharing their views on everyday topics with three other students (actually confederates who were present on videotape) who were either all in the same sex as the student or all of the other sex. In a later memory task, token participants remembered fewer opinions expressed in the group than did nontokens.

These individuals had not been treated differently because of their token status (the use of videotapes ruled out any possibility of differences in behavior by other members of the group). Preoccupation with their distinctiveness may have distracted their attention from what was going on within the group. The members of the majority group can, in contrast, ignore their social-group membership and attend to what is going on.

...

Tokenism, however, exerts its effects through cultural dominance, which is a constant. Those who dominate a field of action over time come to determine the rules of interaction for strangers who chance to penetrate the boundaries. Neither their culture nor their power is neutralized by [experimentally localized] numerical reshuffling.

Got that? So not only would an isolated individual (in this case the woman doing calculus or physics) be evaluated by majority-group standards (even, as in this case, when it’s a one-on-one situation) the isolated individual’s performance may suffer because of the added burden of awareness of their minority-representative status.

—-

Another personal point that’s just sunk in. While I obviously never questioned the implicit punch line of the comic, which is that the accuser is an unfair stereotyper and tokenizer. But since I haven’t studied enough math to know whether the male accuser in the comic is correct about the accusee’s math or simply full of crap I assumed his accusation is valid.

If I really was the only non-mathemetician who made that assumption then all I can say in my own defense is that the power of stereotypes is such that they get you even when you’re wary of them, antagonistic towards them, and on the lookout for them.

Bummer.

[For the record a little Googling on elements of the formula suggests the accuser is right in the sense that the integral of x squared is nowhere near pi. But my self-identified stereotype alert stands since I didn’t know that, at all, at all, when I saw the comic. —fl]

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For the non-maths people:

“The indefinite integral of x-squared is pi”

That probably means as little to you as the original notation.

To save you any further headaches:

The indefinite integral of x-squared is NOT pi, it is one-third times x-cubed. So the formula written on the blackboard is wrong.

[Good to know now, but before I definitely didn’t have that excuse. Thanks for the turtorial, SE. —fl]

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And then there’s the “stereotype threat” variation, where the speaker only has to say, “Wow, a girl doing math!” and the mere mention of belonging to a group that’s not s’posed to do well at math makes her fuck up the problem.

I’ve been thinking a lot lately about tokenism, and how different it is in the classroom now that I’ve typically got 30 to 40 percent men, as compared to 5 to 10 percent a few years ago. The interesting thing is that the men play much more nicely if they’re not feeling tokenish and thus embattled.

Snowdrop Explodes: I’m impressed. I’ve forgotten more math than I ever knew – hmmm, it seems like there ought to be a mathematical expression for that.

[Hi Sungold. Yeah, it’s been pretty nice to have maybe 20% men in the class I’m taking. —fl]

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I really like xkcd. Some male nerds are really clueless, but the xkcd guy makes anti-sexism jokes pretty regularly. Also, he makes me laugh pretty regularly.

The indefinite integral of x-squared is NOT pi, it is one-third times x-cubed.

Ooh, ooh, plus a constant! And both the “sucks at math” guy and the “sucks at math” girl forgot the dx!

I know that probably goes over the had of some of the people reading it, but I felt a sudden compulsion to be pedantic about it. (Also “plus a constant” the punch line of my favorite anti-sexist math joke, which involves a waitress one-upping two mathematician dudes who have made a bet about whether she can integrate x to the fourth. Excruciating details on request.)

[I only had one quarter of calculus-for-non-science-students (while involved with a hard-core math major no less) and so no way I’d have remembered that without a major refresher. Thanks, P. —fl]

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oops – but, in my defence, it’s about 19 years since I did maths seriously.

(I’m very curious to know the rest of the joke, now!)

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God(s) bless you, Mrs Easton, wherever you are.

That’s a little devotional ritual I do when things like this come up – perhaps, if she’s still alive, someday someone who knows her will see one, and tell her.

Y’see, Mrs Easton was my math teacher in grades 3-4. I thought I hated math – but she had the perceptivity to see the truth: I was bored with basic arithmetic. She spent many after-school hours coaching me, showing me the delights of math and nurturing my hidden above-average ability. In the process, she immunized me against “girls are bad at math and science” messages – I was probably told that, but I didn’t hear it; it had nothing to do with me.

As I get older, I keep discovering more ways in which this affected me – f’ex, just now, I was scratching my head about that study, because I seldom even notice when I’m the only, or one of the few, women in a mostly-male group other than based on what flavor of nice scenery is around. I think that, too, traces back to Mrs E’s influence.

The world – still, dammit – needs more Mrs Eastons.

Incidentally, Figleaf, I think the ratio of women in geek settings is quite a bit higher in younger generations. Certainly, among younger folks, the guy-geek who believes there are few girl-geeks is considered to be quaint, amusing, and inobservant beyond standard “geek oblivion”.

Sunflower

[Agreed that it’s higher, Sunflower. And as Sungold points out elsewhere in comments there’s also enough movement of men into traditional women’s areas that people are able to climb down off that “wow [random whole demographic]‘s sucks at [traditional other demographic baliwick.]” —fl]

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This is straying off the point, but I’ve often wondered why being unable to read is something not not often admitted to, something shameful, whereas people are perfectly happy to say they can’t add up, even finding it amusing. It’s OK to be innumerate but not OK to be illiterate.

[Hi, A. At least here in the states I think it has something to do with associating math with keeping one’s checking account balanced. It’s obviously not tedious, and, worse, almost completely unnecessary to do, so even though it’s scarcely math at all and even though the worst parts aren’t related to math, it intimidates people enough that it’s become a metaphor, and almost a point of pride. So yeah, off point but an excellent point. —fl]

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Good post, figleaf.
Sunflower – agreed. I was encouraged at school not to feel being good at maths was “unfeminine” – my school had extension classes for science geeks :-) and we were also encouraged to enter a national essay competition.
This is kind of important.

I knew the formula was nonsense. But forgot about the dx :-( in my defence, haven’t done maths since A-level!

[Hi Butterflywings. Thanks for stopping by. I agree that telling girls they’re bad at math is as… emotionally amputating as telling boys they mustn’t cry. It just complicates their lives without really providing any benefit… beyond maybe never having your stereotypes confronted. Which really just isn’t worth the cost at all, at all. —fl]
Sa

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So, two mathematician dudes are out eating lunch together, and one of them starts holding forth about how the general public is shockingly ignorant about math, can’t even take a simple integral, etc. The other objects: true, not everybody is cut out to be a mathematician, but mathematics education has made great strides in the last couple of years. Surely, most folks aren’t so benighted as to be ignorant of basic calculus! They argue back and forth for a while, until the first mathematician dude excuses himself to go to the bathroom.

While he’s gone, the second mathematician dude waves the blonde waitress over to the table. “Could I ask you to help me win a bet?” he says. She raises her eyebrows. “All I need you to do,” he says, “is to say ‘one third x cubed’ the next time I ask you a question. And here’s twenty dollars for your trouble.” The waitress smiles, takes the $20, and walks away.

When the first mathematician gets back, the second mathematician says to him, “Look, I bet you fifty dollars that even that waitress over there can take a simple integral: say, x squared dx.” The first mathematician says, “You’re on.” So the second mathematician calls the waitress over to the table, asks her to integrate x squared dx, and gets the response “one-thur-decks-skubed”.

As the first mathematician is forking over his money, the waitress smiles and says, “Oh, plus a constant”.

[I love those kind of “gotcha” jokes. Thanks for telling it, P. —fl]

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If you read the comic on the original xkcd page, you may know that often the funniest part is the alt text that you get when you hover over the image. In this case it says, “It’s pi plus c of course.” Although, apparently that’s not quite right either.

[I actually am dimly aware of that, Miz_Geek. I remember going through and checking them out, but I keep forgetting to go check the hover text on new ones. —fl]

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