Tall, Dark, and Mysterious


Math in the news

File under: Sound And Fury, Queen of Sciences, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 1:09 pm.

Via Chris Correa via Kimberly Swygert, an article from NPR about innumeracy among journalists. It’s got some useful tips (which Kimberly discusses further) about how to interpret polls and such, though you first have to read past the rather blasé introduction about how journalists don’t really care about numbers, and that’s life, what can you do. (Hint: you can start reacting in the same way that you react toward journalists who don’t care about other sorts of facts, rather than shrug off the inability of a lot of journalists to do their damned jobs. Start setting high standards, and you just might see results.)

Another symptom of innumeracy among journalists: the fact that while they routinely fail to present math as something that’s relevant to everyone’s day-to-day life (medicine, polling data, finance), they nevertheless - to the embarrassment of many - jump at the chance to report some faux-esoteric non-story that presents mathematicians as Professor Frink wannabes:

THERE’S grim news for people who worry that if something can go wrong, it will go wrong. A new mathematical formula has proved Murphy’s Law really does strike at the worst possible time.

Ordinary people have long known that computers crash on deadline and cars break down in emergencies, while previous studies have shown the law, also called Sod’s Law, is not a myth and toast really does fall buttered side down.
But now a panel of experts has provided the statistical rule for predicting the law of “anything that can go wrong, will go wrong” - or ((U+C+I) x (10-S))/20 x A x 1/(1-sin(F/10)).

Wow, it’s got a trig function and everything, it must be true.

I’m hoping this is a practical joke, though that just means that the journalists are dupes rather than the “panel of experts” being nerds.

Where to begin? First of all, I love the contrast between “ordinary people” and the geniuses who tested their claims. But geez, mathematical equations do not prove real-life observations (what the hell does that mean? ahhh, my brain), they merely model them, and the good ones model them well. I’m not even going to go into how people will notice rush-hour traffic being bad when they’re already late but won’t notice it going well when they’re late or going badly when they’re on time; or how big projects tend to have bigger problems; or how your hot-water heater is probably working overtime in cold weather to begin with; or how IF YOU SUCK AT SOMETHING, YOU PROBABLY WON’T DO IT VERY WELL.

Some concluding tips from the department of “this guy has a Ph.D. and I don’t??”:

Project psychologist Dr David Lewis said: “…if you haven’t got the skill to do something important, leave it alone. If something is urgent or complex, find a simple way to do it. If something going wrong will particularly aggravate you, make certain you know how to do it.”

Wow, that’s some smart mathematical formula.

Women in math - the intersection of sexism with crappy pedagogy

File under: Those Who Can't, XX Marks the Spot, Queen of Sciences. Posted by Moebius Stripper at 10:26 am.

I started posting a big response to the women in math screed, but it got big enough to merit its own big post.

Joshua H. asks, How exactly do you think high-school level math ought to be reformed? I started to ask if Joshua H. (hi Josh!) meant in general, or in terms of the male/female divide - but then I realized that it’s not necessarily so easy to distinguish between those two. There’s a good post with good comments over at Learning Curves on the subject of how to educate prospective middle school math teachers that leads nicely into a lot of this. Rudbeckia Hirta describes a business math course at her school that sounds an awful lot like just about every high school math class I’m aware of: “Look at the formula. Watch me use the formula. You practice the formula. Next formula.”

And there’s half the problem with math education right there. I routinely get students cutting me short in the middle of an explanation and asking, well, sure, that’s all well and good, but what’s the formula I need to memorize in order to do this sort of problem? And my students, almost to the individual, are woefully ill-equipped to handle any math problem that doesn’t follow the very rigid templates of problems that they’ve memorized. This is the first thing I’d change. But that’s a symptom of something more serious - a cautious approach to doing things in general - “I’m not going to try anything different without permission” - which is something that’s encouraged in girls far more so than in boys:behave, and follow instructions.

Last year, there was this article in a local paper describing a pair of new, experimental, sex-segregated math and English classes at a local Island junior high school. I had no strong feelings a priori about segregating boys and girls in schools, but my jaw dropped when I read that there would be completely different approaches to teaching math to the boys and girls. “The boys’ class will be more hands-on,” boasted the principal, “while girls prefer to read about math before they do it.”

In other words, the boys get to actually think creatively about the problems they’re working on, and try to think of new approaches to questions whose structures they haven’t yet encountered. Meanwhile, the girls will never ever have to try out math problems that they haven’t had explained to them in detail beforehand. The girls will be allowed to continue learning math by learning formulas, while the boys will be taught how to deal with new concepts.

It should be pointed out that the two different curricula weren’t developed by misogynists who think that boys are inherently better than girls at math. It was developed by morons who really wanted to help the girls do better in math, but who had no idea what it meant to do mathematics. If any of the curriculum developers had any credentials in math or math education, the article’s writer didn’t see fit to mention them.

Back in the 70’s, the women’s movement was centred largely around getting women involved in male-dominated fields of study. In the decades that followed, the numbers of women in law, medicine, and science skyrocketed. Today, we’re seeing the focus shift away from getting women involved in so-called masculine disciplines and more toward valuing careers, styles of work, and interests that have been traditionally disparaged as feminine. In some ways this is good (being interested in cooking is just as valuable as being interested in automotive repair), and in some ways it’s downright idiotic (being uninterested in science is just as valuable as being interested in science). Among the most egregious examples of the latter are Carol Gilligan’s book In a Different Voice, and the similar Women’s Ways of Knowing, both of which glorify the conventionally “feminine” learning style of sitting still and being cautious and not trying anything new without near-complete context and information. Whether or not this is an accurate assessment of gender-based learning differences I am in no position to gauge; unlike the authors, I did not conduct dozens - yes, dozens - of interviews with upper-middle-class college students in order to draw my sweeping conclusions. I do know, however, that this cautions, personal, social style of learning that is highly inconducive to doing real math.

Back when I was in grade eight, my father gave me some of his old grade nine geometry notebooks. I was amazed, as well as envious of the level of work that was expected of my parents’ generation. Students were presented with problems that didn’t follow exactly the templates of the examples they’d seen in class. They got a feel for the sorts of lines they’d sometimes have to construct in order to find a certain angle or prove a certain property. Formulas were used sparingly.

When my students come into my office, I’ll guide them minimally with questions? Often they’ll say something like “well, I’d look for a common denominator but I don’t think that’s what you did in class” and then look to me for an answer. They’re looking for permission. Four times out of five, it’s the feme students who want to know if they’re allowed to do what they’re doing. They look at the steps of solving problems in terms of what they have permission to do, rather than what is mathematically correct. They don’t want to try something that might not work. “Okay,” I’ll say, “let’s try getting this over a common denominator.” Sometimes it’s the right approach (well - a right approach) and sometimes it isn’t. If so - great. If not - they’ve hopefully gained some insight into why it’s a wrong approach.

(One of my students told me that she gets confused when I don’t tell her the single correct method to solve a problem. “Often there are several, and you have a choice of which one to use on tests,” I told her. This bothered her a lot.)

So there’s this movement to get girls interested in and involved in math; there’s also a trend toward a very formula-driven mathematics curriculum. I’m above the correlation/cause conflation, but it’s worth mentioning that there are proponents of the latter who specifically mention that girls’ learning styles need to be respected in order for them to learn math.

Perhaps so. But the learning style of sitting still, being cautious, and not doing anything new without validation, is inherently inconducive to doing mathematics. It’s not a feminine learning style, it’s a deficient one, one that needs not to be respected but discouraged.


Mmm…free pie: life imitates The Simpsons

File under: Home And Native Land, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 8:03 am.

More than a third of Vancouver residents were born outside of Canada. Even when it was the bears, I knew it was the immigints.


But I just voted, dammit

File under: Character Writ Large, Home And Native Land, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 1:46 pm.

In 2000, Canada went to the polls while the US was busy trying to figure out who their president was. Now, in the middle of the US presidential debates, Parliament is split 50-50 about whether to accept Prime Minister Martin’s throne speech* - three months after he was elected, for those of you keeping track - or to force him to dissolve Parliament and call another election. Are we trying to be ignored? Show of hands - how many of my American readers knew that their northern neighbour’s government is at its most unstable in decades, and is facing the possibility of failing for the first time in a quarter century?

Mmmhmm; thought so.

Honestly, though, it makes no sense to me to have Parliament vote on whether or not they’re down with the Prime Minister’s promises, when he’s only marginally more accountable for what he actually does than he would be under a majority government. If this government survives, and Martin doesn’t follow through on anything he’s promised, there’s no precedence for holding a confidence vote over that. Here in Canada, talk can be expensive.

* which doesn’t seem to exist on the official Canadian government website. This is really the sort of thing that should be available, and easy to find, in HTML - I shouldn’t have to go to some random MP’s homepage to find it in pdf form.


The women in math screed

File under: Righteous Indignation, Sound And Fury, XX Marks the Spot, Know Thyself. Posted by Moebius Stripper at 2:57 pm.

Last month, a writer from Seed Magazine wrote to me for my thoughts on women in math, and the barriers that women mathematicians face today. I haven’t heard back from her (LM - are you there?), so I don’t know if my comments will ever make their way into a real, live magazine, but there’s no reason I can’t toss ‘em up here. What follows is an adaptation of the email I wrote to her.

To begin: no meaningful or productive discussion of this topic can take place without acknowledging that there are far, far fewer women than men who are both interested in, and qualified to do, higher mathematics. Unfortunately, no discussion of that fact can take place - at least not in my presence - without someone pointing that the likely culprit is socialization, not biology - as though this is some profound insight that only those enlightened, self-proclaimed gender experts have ever considered - and one that renders any further discussion on the topic of women in mathematics completely moot. Social problem, not biological, the absence of women in math is a result of sexism, not hormones, nothing to see here.

Baloney. This fact - and it is a fact - is relevant in light of the reality that mathematics is a highly cumulative subject: if a student is lost or disinterested in mathematics in high school, they’re not going to be able to catch up in university without a lot of effort and a lot of motivation. If biology is responsible for the dearth of women in math, then there’s nothing to do; to the extent that it’s socialization, then by the time a girl is ready to apply for university - never mind grad school - then it’s between five and fifteen years too late to be thinking about how to get her interested in math and able to do it at a high level. Which is why, despite the abundance of scholarships and such available to women university and graduate math students, the numbers of both have remained nearly constant in many schools in years. (Compare this to the number of law degrees and such, in which women are neck-and-neck with men.) It’s also why I (cynically, perhaps) see the efforts geared at bringing university-level females into math programs as being little more than self-back-patting on the parts of those who support them: they’re certainly too late, if not too little. If any progress is going to be made countering the anti-math socialization that females experience, it needs to be done with children, not with adults.

Yet, “we must increase the numbers of women in math!” has become the dominant battle cry of mathematicians and feminists alike - the former of whom (mostly men, mostly older) typically have limited understanding of the life experiences of girls, and the latter of whom typically know next to nothing about math. The former accept the latter’s simplistic notion that the women-in-math problem would be solved if only we consciously countered our latent sexist beliefs and actively tried to recruit adult women into math programs and positions. I’ve been party to hiring committees and places of study in which this philosophy was applied. It’s almost always the same story: competent but sub-par female applies for position; hiring committee points out that she obviously has some skill and that we should really hire her, women-in-math thing and all; competent but sub-par female gets hired, and does competent but sub-par job.

When people express the belief that men are better than women at math, that’s not a conclusion they’ve drawn from unthinkingly assimilating stereotypes perpetuated by their teachers, their families, and The MediaTM. It’s a conclusion they’ve drawn from observing, with their own eyes, women who work alongside them or above them in math programs. And this in turn increases the pressure on the stronger female mathematicians to be better, faster, stronger than their peers, in order to prove that women can do math.

A number of times, I’ve asked people who accepted as axiomatic that we should try to get more women in math, why they held that belief. The conversations - which tend to catch people very much off guard - are illuminating. The fashionable talking point these days is one of diversity - women in math make the department more diverse. “Diverse how?” I’ll ask. Well, I’m told, women are more sensitive, more attuned to people’s emotions… Oh, yeah, I’ll comment. More sensitive, more emotional…less logical… Look, I didn’t say THAT…

Whatever. Due to the small number of mathematicians who are women, and the even smaller number of math/science people in gender-policy think-tanks, women in math are, for the most part, seen but not heard when it comes to dealing with the issue of women in math and related disciplines. The divide between the official policy of sensitivity toward women mathematicians’ concerns, and the actual involvement of said women in the issues that apparently affect them, is a sight to behold. It’s telling that the line that “women are sensitive!” is the one that comes up most often when I press people to tell me how women add diversity to the math department. Women are sensitive, see. Their male colleagues just plain aren’t emotionally attuned to their concerns; that’s women’s work. In other words, once women have been admitted to the math department, their male colleagues’ responsibility toward them has ended.

There was a male prof at my old school who routinely invited his postdocs and grad students - all men - to parties where they’d watch the Oscars or other somesuch and analyse in detail which of the young starlets were, and I quote, “the most fuckable.” I heard this from an attendee, who was quite outspoken against the sexism that excluded women from the department. It didn’t occur to him that the department had a responsibility to actually include its female students in its activities . To give what may seem at first a silly example on this subject: the only women’s washroom in one of the math buildings was frequently closed for repairs. When this happened, women were told to use the washrooms in another building. It never seemed to occur to anyone to temporarily designate one of the two men’s rooms in that building a women’s room, or even a co-ed room - thereby marginalizing the female students and faculty, who would have to leave discussions and classes to go to another building to pee. This has happened many times. Once I sent out an email asking one of the men’s washrooms to be temporarily reassigned. My email was ignored.

On the academic front: long hair aside, there are few ways in which I am conventionally feminine. One way, however, in which I adhere closely to my biological (or socialized?) fate is that I am interested in, and good at, distilling my subjects of interest to non-experts. This is something that study afer study has revealed that females of all species excel at, compared to males: teach a male a skill, and he uses it. Teach a female a skill, and she uses it, and teaches it to her mate, her kids, her friends. My interest in teaching and writing math books for a semi-general audience was summarily dismissed by all but one of my professors - no! you should do RESEARCH! If you’re not interested doing pure research, what are you doing pursuing a graduate degree in math? I understand that my alma mater is a research school, not a teaching one, but none of the faculty - save one - could even point me to schools or resources that would help me achieve my goal of writing about math. In other words, mathematicians want women to be women (be sensitive, and such), but when those women do something conventionally feminine, it’s dismissed. Teaching? Writing for an audience of non-experts? That’s stupid girly stuff. We want diversity, but we reserve the right to dismiss you for embodying it.

One of the most common arguments in support of affirmative action is the notion of “critical mass” : the more women there are around, the more comfortable people are with them, and the less of a boys’ club the math department becomes. This used to be an argument I (generally opposed to AA as typically applied to adults) found somewhat compelling, but over time I realized that it is just another side of the diversity coin, allowing its supporters (who aren’t sexist, of course!) to deflect responsibility onto the women they purport to help. Why should we need 25%, 30%, 50% female enrolment in order to the department to become less of a boys’ club - particularly since said boys are the ones talking about the value of sensitivity and such? And once we attain 25%, 30%, 50% enrolment, is it then our responsibility to organize our own Oscar parties? Or will the men’s parties end? Will the assholes stop being assholes? Or will it just matter less if they continue?

Bottom line - I’m unmoved by the bean-counting approach to measuring and dealing with discrimination in math and other male-dominated fields. It’s a policy that requires next to zero effort on the parts of the people who support it, and that achieves next to nothing in terms of dealing with any sexism that does exist - either the sexism that results in girls (high school and younger) losing interest in math and hence not pursuing it, or the sexism that sees male university students and professors generally being assholes and hence driving away their female colleagues. Men who publicly bemoan the dearth of women in math, and proclaim that we need to recruit, recruit, recruit, are always taken aback when I challenge them, or even ask them to elaborate or clarify. How could I not agree with them - I’m a woman, after all, and they’re expressing the Official Women’s Point of View. Shouldn’t I be grateful that they hold the right belief? Doesn’t that in itself make them virtuous? What gives?

In other words - shouldn’t I be sensitive to their feelings, and quietly listen to them without argument? After all, that’s the sort of diversity we’re aiming for, and it’s my responsibility to provide it.


Still tweaking.

File under: Meta-Meta. Posted by Moebius Stripper at 6:13 pm.

I still need to fiddle with the colours; these are a bit too monochromatic for my liking. And if anyone can tell me how to get rid of that little space to the right of the header, I’ll…eh, I shouldn’t finish that sentence in my current state of desperation.

But this is cleaner than the last layout and doesn’t have a horizontal scrollbar on my machine, so I’m happy. For now.

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