At 3quarksdaily, Sam Kean has an interesting essay on the future of theoretical mathematics, whether computers capable of generating proofs will supplant human mathematicians, and what that will mean for the "beauty" of math:
There's general consensus that really genius-level mathematics is beautiful--purely and uncorruptedly beautiful, the way colored light is, or angels. More particularly, it's regarded as beautiful in a way that science is not. With a few exceptions--Einstein's theories of relativity, string theory, maybe Newton and Darwin--no matter how much science impresses people, it rarely moves them aesthetically. Science and mathematics stand in roughly the same relation as journalism and fiction--the latter in each set being more admired because it gives us the sense of having moved in a wholly different realm of being.
Computers, to be blunt, threaten that beauty. One of the four authors in the bundle of papers, Freek Wiedijk, assures mathematicians that existing computers are good for checking proofs only, simply tidying up the real work and never, never ever conjuring up original theorems. The current generation of mathematicians will continue to live by their wits alone. But beyond that ...? In a contradiction to Wiedijk, one of the other authors, Thomas C. Hales, admits in an aside that someday, who knows how soon, computers will be doing original work. Doing the work of human mathematicians.
Very interesting questions in a very well-written piece! But while I enjoyed the essay, I couldn't relate to the following passage at all:
Oddly, rigor in math is most easily recognized as a feeling--the scrotum-shrinking embarrassment that even people really, really good at college math feel upon realizing that some people are way the hell smarter.
I have no idea whatsoever how "scrotum-shrinking embarrassment" feels. Nor can I imagine the sensation, given that I, like approximately one-half of humanity, have no scrotum (horrors!). Math is a stereotypically male-dominated field, far more so than biology, chemistry or other sciences, and such a strongly gendered description only reinforces that perception. To me, the passage reads as if the "people really, really good at college math" are all male, and since I am female, I am not expected to be able to relate to their experiences (nor, apparently, to recognize "rigor in math").
I'm guessing that's not what Mr. Kean intended to imply. I think he was probably just going for an effective way to describe humiliating embarrassment, and it didn't occur to him how it might sound to a woman. But I still wish he'd chosen another wording, given that he is obviously a very gifted writer and probably had many options at his disposal. What do you think?
I think you're probably reading too much into the situation; that being said, i'm male.
Not to put too fine a point on it, but if you really wanted to you could get as many scrotums as you liked.
Frankly, I think scrotums are pretty homely and darn vulnerable to any insult or injury. Why would anybody want one in the first place? Count your blessings. And if you're not good at math, calculators are cheap these days.
He wanted to put his finger on a particular feeling and reached for his scrotum without thinking. As a male I've done the same myself. It's an unfortunate behavior and probably needs to be challenged.
Well, from what I've heard, it's a very effective description for those of you with scrotums. :) I don't think gender specific language should be off-limits at all - I just wish it wasn't used here in the context of being good at advanced theoretical math. But I may be overly sensitive.
I am with you all the way: I experienced labia-flaring dudgeon at the male-specific phrase. Of course he should have put it gender-neutrally. These things are actually important.
Well, I'm inclined to defer to the women on the appropriateness of the choice of phrase. I'd like, nevertheless, to submit the following point for consideration. Might it be the case that encouraging women to view things like this as other than harmless actually do more to discourage them from entering mathematics than the phrase itself does?
Good question. I don't think this phrase in this essay will dissuade women from entering math, nor do I think my calling attention to it does so. I think what dissuades women from entering math is being repeatedly told they're not good at it because they're female. At least, that's what I was told growing up; the constant repetition of this message by adults around me dissuaded me from taking any more math in high school or college than strictly necessary. Those are the attitudes that are harmful, and while I think we've made great strides in changing them, they're not gone. This piece is simply an example of how pervasive, unintentional, and often nearly invisible those preconceptions are.
It was unfortunate analogy, I agree. I have a scrotum, and I'm not especially good at math.
I did enjoy reading a.a. shock's phrase "labia-flaring dudgeon". Good one, a.a,! I've experienced that a few times...
I'm not at all offended by the comment, probably because I feel so deeply the sentiment that it was expressing. Even as someone who was always "the best" at math though high school and college, I nevertheless frequently felt like a complete moron in comparison to 'the greats' that I was studying.
I should mention that I was also not particularly offended by Larry Summers' comment about women perhaps having less innate ability at higher mathematics than men. I think it's a viable hypothesis, although I'm not sure how it can be satisfactorily studied given the possibility that women who could have been really, really good at math could have been dissuaded from pursuing it (as Jessica Palmer describes above).
In my personal experience, that never happened. From a young age, my gift was recognized and strongly encouraged. In math classes where I was one of a very small number of female students, I felt like I was always given extra encouragement because being female and very good at mathematics made me somehow "special" because I was the exception. Perhaps that's patronizing in its own way, but it certainly didn't discourage me from pursuing mathematics.
The majority of, say, college math majors, are not people who are great at math - they are people who are good enough at math (which is still pretty damn good) and (usually) find it interesting. What I've seen happen frequently is that the women in this group lose interest. They realize during their first or second years of college that they're also very good at philosophy or sociology or biology or Celtic literature, find it easier or more interesting, and decide to pursue that instead. The male math majors, while in general no better at math, tend to be a bit more "one-dimensional" in their talents and therefore stick with it (usually straying no further than physics or computer science). In my conversations with young females who are good at mathematics, it is usually very difficult to convince them to stick with it, not because they feel unwelcome, but because they see so many things that look more interesting that they know they'll also be great at.
However, even though there are lots of females who are good at math, I've certainly noticed that the very best math students tend to be male. There have been exceptions, but that's the trend. I have no idea whether this due to innate differences or conditioning, but I think both hypotheses are worth considering.
Aren't you overreacting? I'm female, but I can easily understand the feeling the author refers to by using the phrase. Besides, the actual text uses the phrase to refer to the people that are less smart; perhaps the guys should be complaining about bias?
I think you are right about that kind of thing reinforcing the notion that, of course, anyone who would even consider comparing himself to a great mathematician must be male.
Krilu, I am impressed with your powers of imagination! I really don't have a clue what a shriveling scrotum feels like and I don't know where to begin imagining it. I do know what sudden, humiliating embarrassment feels like - nausea, flushing, chills, a feeling of vertigo in the pit of the stomach, for example; but since the author didn't use any of those, I get the feeling he's going for another, more specific feeling. (I now kind of wish I could get in a VR chamber and experience a shriveling scrotum - I'm getting really curious why it is such an effective description.)
When you jump into really cold water, your testicles retract into your abdomen to keep them from getting too cold. I suspect this is the feeling being referred to.
Indeed, but I'm not sure I have any way of appreciating what that feels like, any more than you know what I mean when I say I'm having severe menstrual cramps.
This is getting way too metaphysical for me! I'm just a simple physiomotherfuckinologist!
But it really does emphasize the point that there is good reason to use gender-inclusive metaphors.
Let's say robots choose to start painting. That's art. People would look at it and appreciate it for what it is and hate it for what it isn't.
Real math will require human function or it isn't very real at all. It is just sybolic manipulation.
I think you are right to call him on this gendered phrase; the fact that many comments don't agree suggests to me that many people do not have a problem with the 'default' human being male. I'm female and a physicist, so happen to have more mathematics than the average person. I think this sort of thing has a lot more subconscious impact than is recognized. I recall being grateful in a Quantum Field Theory class when the professor described an observer as "she". As a woman in a male-dominated field, I find that having one's existence denied (actively, passively or even accidentally) is tiring and discouraging.
Also, I think 'beauty' is far more common in science than acknowledged in the passage quoted. It is not isolated in mathematics. Though I think beauty is over-rated; it is, after all, nothing more than a BIAS. We have no objective reason for presupposing that 'correct' theories possess 'beauty'. (But then, I switched from particle physics to geophysics, and the earth is a messy place).
When one writes in the first person it is very important to consider different viewpoints and not to alienate some readers. The phrase would be interpreted differently(less critically as well) if it were written in the third person then I would have understood it as context specific - meaning those specific group of guys experience that specific emotion that way, but now it reads as the kind of experience that everyone should be familiar with. And then yes it definitely excludes all women.