Math (was Re: Color terms)

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