But as much as I like him, every so often he gets it terribly, terribly wrong. Consider the following:
Mathematics, rightly viewed, possesses not only truth, but supreme beauty--a beauty cold and austere, like that of sculpture.
Sounds innocuous enough, maybe even something I'd support, given my overexuberance for mathematics. But no. As you might imagine, I take no issue with the idea that mathematics possesses truth and beauty--mathematics is all about the truth and beauty (although, if you want to be picky, we have to be careful about what we mean by mathematical truth. But I don't want to be picky.). Instead, my problem is with the "cold and austere" part. Maybe I misunderstand Mr. Russell, but I think he's missed the mark.
Here we go: it's become a cliche to characterize mathematics (and mathematicians) in simultanously dismissing and reverential terms. That is, it's terribly complicated and we could never understand it and it's SO amazing that someone could, in fact, understand it. But it's also so complicated and abstruse that it's entirely disconnected from our real life, so it's ultimately unimportant and irrelevant. By extension, we do the same thing to science in general: regard it as an impressively difficult, but impenetrably tedious task better left to someone else who happens to enjoy the pointlessness. (I could go on about how harmful this idea is, how it's perpetuated by our approach to math and science education, and what it says about us as a people, but I need to get back on point.)
"Cold and austere" only serves to reinforce this idea. It suggests that mathematics, science, and even logic in general are remote and lifeless and alien to everyday existence. That logical, mathematical thought is a robotic, passionless exercise that leads to a boring and unimportant answer. Even more, it misses so much of what logical thought actually is. Your friends, your parents, and even Yann Martel all want you to believe that logic happens in a sterile, Spockian vaccum of emotion and imagination. But they are all wrong. Logic is alive and hot with argument, struggle, and discovery. It requires (not merely permits) imagination, passion, and creativity. And its results have the power to fundamentally alter how we perceive our everyday reality. (I mean this: I dare any of you to learn calculus [or maybe learn about the Cantor set] without suffering an irreversible perceptual shift.)
To be fair, probably I've significantly exaggerated Russell's meaning. Indeed, he certainly knew something of the joys of mathematical exertion. But I still argue that his imagery isolates mathematics from reality, treating it as something to be curated and admired rather than experienced. Mathematics--and logic in general--is less like appreciating a classical statue and more like creating a Jackson Pollock: an effort to find truth and beauty out of instinct and intuition; an unpredictable, even violent process that forges order from the chaos of human thought.
9 comments:
Hmmm. I think that's true. I mean with anything you need to have a passion for it. There's always debate. I may find math boring but that's probably because I haven't taken it since high school.
I think in our culture we have a fear of certain subjects like science and math and don't realize that in many other cultures it's just assumed that math and science can be learned like any other subject. Kinda like a version of the Simpson's "Don't ask me- I'm just a girl."
those links are awesome. so ... if i'm becoming increasingly uncertain, does that mean i get to count myself wise(er)?
Chad: I think that's only half the story. Yes, you need a passion for it, just like anything else. But my point is that the process itself is alive and organic, not cold and robotic, contrary to popular opinion.
g: Yes. Yes it does.
I have a degree in Mathematics, so I am no stranger to the look of shock, amazement, and bewilderment that is manifested whenever I tell people what I studied in college. I also work outside academia and am a woman - making me an even more elusive creature to the point that I sometimes feel like some sort of societal Yeti.
Because of this, I absolutely understand the frustration with people's inability to recognize how exciting and alive mathematics is. And I absolutely agree that more needs to be done to teach people how essential and beautiful it is.
That being said, I think it is a little unrealistic and maybe even condescending not to recognize how unfeeling, unforgiving, and straight up difficult mathematics can be, particularly at the levels where current advances are being made. Yes, there is inherit flexibility and there is active debate in the field, but is that evident in the manner that 95%+ of the society uses math? Not really.
I think more needs to be done to make basic math more interesting and interactive. If people can't see the excitement and life in the algebra and geometry, they can't be blamed for not sticking it out to the theory of relativity.
To that end, I think that those of us in the field have only ourselves to blame - we do a really terrible job making it interesting to the people around us. My math professors were the worst professors I had in college. I admit this freely. I think they liked being revered and feared.
This is a beautiful post, buy may I just say that I take full credit for your art analogies. Without me, you would even know what "a Pollock" is.
Heather: thanks for chiming in--it's nice to have the perspective of another mathematician. But I have to disagree with you, at least a little bit. Of course I concede that mathematics can be difficult and unforgiving (although I do reject "unfeeling"), but that's true of any discipline taken far enough. Language, for example, is simple enough: most of us can string nouns, verbs, and adjectives together to form complete sentences. The specifics of grammar and usage get a little more complicated, and when you start looking at modern linguistics things become impenetrable in a quick hurry.
But we don't usually say things to a linguistics student like "Man, that's so unbelievable; I could never do anything like that!" (with subtext: "Man, why would anyone ever want to do anything like that?"), at least not the way we do with math. We do something special with math (and, to a lesser degree, any hard science): we de-humanize it. We like to think that mathematical problem solving is primarily mechanical: take the problem, and if you are smart enough, you heartlessly follow the recipe until you're finished.
My point isn't that people should feel bad about themselves if they don't, say, appreciate the implications of the Riemann hypothesis. That'd be unrealistic AND condescending, as you say. My point is that mathematical/logical reasoning is alive with imagination and discovery. To point out that, often enough, the solution comes to a mathematician the same way a writer might find just the right way to phrase his ideas--inexplicably, and without method.
I fully agree with your second-to-last paragraph. I think that much of the problem is in how we teach these subjects, particularly at the primary and secondary level. My experience was different than yours: math was boring and tedious until college, when the subject was treated as a process to understand instead of a set of methods to memorize (to be fair, much of my mathematical training was in the engineering department, but I've had several excellent instructors in math departments). And I don't think there's any reason why that emphasis can't work before college.
In fact, that would go along way towards helping that 95% realize the life and flexibility in the mathematics that they experience. No, they don't see the still-debated frontiers of mathematics, but--as you point out--there is excitement to be found even in the math we all saw in high school.
Amanda: Yes, you may. Credit granted.
The T-Rex was funny. I resent the Yann Martel statement. That being said, I agree with you. At least I really want to (I have never been good at math; my mind doesn't work that way. I suppose I could train it to, but, honestly, I don't feel like it). I can see how math and science are both very beautiful things (without being cold) and I wish I understood them more than I do. Surprise: I love biology and wish I had a better understanding of it because it would make my poetry much more interesting. Perhaps I will take it up. One of my favorite professors was a beautiful poet and before she taught literature she taught an anatomy class which I think enhanced what she was able to do artistically. I was always a little jealous of our friend Ashley Mackay because before she started studying English she was a Neuroscience major. The things she is able to write with a math and science background will probably be 100 times better than anything I write. This is why I love people like Jackson Pollock and Arnold Schoenberg. Their stuff is a little weird, for sure, but their use of math makes what they did incredibly interesting. I think that to be a good artist, you have to be well-rounded and have an understanding not only of feelings and beauty but of math, science, logic, philosophy, etc. This is why I will most likely never be any good. Again, perhaps I should take some of these things up.
I am feeling this tremendous amount of love for math right now. Whoa. Maybe there is a mathematical equation that can describe this love. I don't know.
Probably there isn't. Mathematics is too precise to describe something as fluid and organic as your love (and suddenly this post self-destructs from internal contradiction!). I fully appreciate your appreciation for fully-integrated well-roundedness. Ironically, though, I'm not a big fan of Schoenberg, although I respect the quality, innovation, and craftsmanship in his work. But at the end of the day it's just not accessible enough to communicate meaningfully with an audience most of the time. But I still wish I were as good as he was.
I stand by my Yann Martel statement. In fact I've delayed responding to your post because my blood pressure goes up every time I look at his quotes to think about my response. He makes me so angry sometimes.
So: I'll rant briefly. "Life of Pi" is basically a treatise on the triumph of imagination over rationality. Rationality gives us "dry, yeastless factuality" whereas imagination brings us the "more beautiful story". Of course I acknowledge the power of imagination, but I ask: do we really need to abandon factuality to inject moisture and leaven into life? I say "(hell) no", and I further argue that doing so is so very harmful. Believing in something just because you like that something--or because the idea of it makes you happy or comfortable--is a lazy and soul-destroying approach to belief, and Martel's effort to ennoble that approach does a disservice to believers everywhere who feel they have legitimate, defensible justifications for their faith.
(By the way, thanks everyone for your input. Only the Prop. 8 post has more comments. Hooray for controversy!)
Post a Comment