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Math (was Re: Color terms)

From:Yoon Ha Lee <yl112@...>
Date:Sunday, November 19, 2000, 17:43
On Sat, 18 Nov 2000, H. S. Teoh wrote:

> Nov 18, 2000 at 04:08:22PM -0500@ > > On Sat, Nov 18, 2000 at 04:08:22PM -0500, Yoon Ha Lee wrote: > > I can visualize Menger sponges but alas, nothing of higher-dimension. I > > do love looking at two-dimensional renditions of three-dimensional > > "slices" of four-spheres, though. Quite lovely. > > I think I've seen some computer-generated snapshots of a few 3D slices of > a 4D sphere showing how it's turned inside-out. And no, I do not know > *how* you can turn a sphere inside-out in 4D (even though I like to give > people the impression that I do know) :-P
I think Ivars Peterson attempts to describe sphere eversion for a lay audience in one of his books (either _The Mathematical Tourist_ or _Islands of Truth_). I haven't seen a rigorous mathematical description, so I can't comment on his efforts other than to say that his books made me stop hating math because of all the cool ideas that he tries to introduce.
> [snip] > > "Gut feeling" has rarely worked for me in math. :-/ I "internalize" > > things when I'm learning language with relative ease. My German class is > > a joke, and I'm doing pretty decently with teaching myself Latin out of > > Wheelock. For some reason my mind assimilates language-forms far more > > easily than math-forms. (I don't claim to be a language genius; I'm > > better than average, but "genius" would go to people like my friend Abby, > > who's fluent in Arabic, Spanish, English, French and Korean and last I > > heard was working on Chinese due to a certain boyfriend.) I'm loath to > > classify this as either "rational" or "intuitive." > > Hmm, interesting. I find that I'm better at internalizing math (esp. > calculus) and scientific stuff, although I do have some ability to > internalize foreign languages -- eg., English has practically become my L1 > now; I think in English, speak to myself in English, and do everything in > English. Only vestiges of Chinese remains in my everyday thinking process, > such as the multiplication table since I learned it in Chinese, or certain > words/idioms in my L1 untranslatable to English. Of course, this is just > English; I still find it hard to learn other languages. Much harder than > I'd find a new subject in math/science, for example.
Different aptitudes. :-) My boyfriend is brilliant at math/physics. I am good but will never be brilliant. OTOH German is practically a joke class for me, and I get away with absurdly little work in most history classes. Last month I was getting really depressed over graduate school, because I had originally intended to go for a doctorate in math, and if honors algebra and topology are burning me out right now, I figured that even if I could get into a good math grad program (my advisor thinks I could), the workload would just be too much. And then I realized: hey, you can't be good at everything. I am pretty darn good at writing and language, all things considered. And while I'll never be a mathematician, I am going to get a master's in education so I can *teach* math and communicate its beauty to others (since writing is all about communication and entertainment). So I feel much less bad about not being ready for a math doctorate program. Silly, but it takes me a while to realize such things.
> > You are fortunate to have the ability to "follow your nose" in math. I > > can sometimes come close (when I can't solve a proof, I write down an > > outline of approaches I might take; TA's sometimes give partial credit > > for such things) but it doesn't come naturally. :-p But that's why I'm > > a math major: so I can learn something from professors that I would find > > terribly difficult to learn on my own! And I find that I know material > > best about a year *after* I've learned it, mainly because my mind has > > given up resisting it. <laugh> > > :-) On the contrary, being the lazy bum that I am, I've always avoided > courses that I know I'm not good at, in my undergrad years. For some > reason, I just *cannot* grok certain subjects (probability and statistics > come to mind; biology used to be an old enemy although that may not be > true now). It's so bad that during one assignment in a CS advanced data > structures course, I got perfect on every other question but nil on the > one question that was related to probability :~(
Oh gosh, on the GRE Math I took a couple weeks ago I left every probability and statistics question *blank.* I've never grokked those either, yet in IB Math, I was whizzing through infinite series, which every else hated, while when we hit probability & statistics I nearly flunked a prelim while everyone else thought it was the easiest subject yet. :-p It was the first time I saw people being good or bad at different *areas* of math, as opposed to elementary & middle school binary good or bad at math. If I only took "easy" subjects I'd have a sickening GPA. <wry g> But a) you can't get much of a job with a history degree (though you can argue teaching high school math isn't much better), which is important because I need to be able to support my "writing habit" and b) it's not as fun that way....
> Hmm... *I* like writing stuff inductively... even in the odd math system > that I sometimes work on, in my free time. I like the suspense :-) I find > deductive-mode essays quite boring, because to me, you're just making some > (possibly outrageous) claim and then twisting... ermm, discreetly picking > the right facts to make your claim sound plausible. Inductive-mode essays, > OTOH, presents the (hopefully) unbiased facts, and then show you how these > facts lead to the thesis. To me, it's better to let the facts guide your > conclusion than conversely.
<wry g> Yeah--I've seen deductive essays that I could tell were flawed because they didn't account for the opposing point-of-view(s) in subjects I knew about. OTOH, the beauty of the deductive essay is that it lets you pick some thesis, as long as there's decent evidence for it, and write away *even* if you disagree heartily with your own thesis. I did this numerous times in English lit classes, and in a couple history classes as well; one time the prof wrote, "Excellently argued, but I'm not sure I agree with your thesis." I sat there giggling because I *completely* disagreed with my thesis; it just happened to be the easiest for me to write about and support.
> Disclaimer: I've never actually gotten away with *submitting* an > inductive-mode essay, so I hereby disclaim any liabilities associated with > the loss of grades and grade-point averages, mental trauma, insomnia, and > any other loss resulting from the use of my advice. ;-)
I wrote an inductive-mode essay (before I knew there was a term for it) for a take-home AP U.S. history final. It killed my 2nd-semester grade. To this day I still believe it was a decent if not earthshattering essay. And then I got revenge by being the only one in the class to get a 5 on the AP exam. <snicker> YHL