September 12, 2003

Geek Talk

Posted by shonk at 06:49 PM in Geek Talk | TrackBack

Let's face it, when you're studying mathematics in graduate school, you tend to acquire something of a geek vocabulary. You start getting excited about things like diffeomorphisms, quasi-manifolds and R-modules. Actually, though some of the new terms you pick up are pretty unusual, what will really throw you for a loop is the specialized meaning attributed to otherwise commonplace terms. For example, words like continuous, ideal, normal, integral, field, group, extension, map, graph, module, knot, domain, range, compact, open, closed, picture, braid, and smooth (among many others) all have specialized mathematical definitions that may or may not relate to their usual definition in some way.

And even when they do denote something similar to what we would expect, such is hardly obvious from the definition without specialized knowledge. The knots that knot theorists study, as an example, are recognizably similar to the normal conception of a knot, but they are defined to be "continuous embeddings of the circle in the 3-sphere".

That's really the uninteresting case, though. After all, some of these definitions seem totally arbitrary, leading to this inevitable comparison in junior-level algebra: "Ideals are basically just like normal subgroups, but for rings". I wish some confused English major had wandered into class just at the moment I heard that phrase sophomore year, because, as the professor said it, all of us in the class were nodding our heads, saying, "Oh, okay, that makes sense". The look of horror on the poor lad's face would have been priceless.

All of this leads me back to a conversation I was having the other day about language. I won't get into the details, but at one point I asserted that what we call things affects how we think of them, asking the hypothetical question "Would Social Security get the same kind of funding if it were called 'State-mandated Ponzi Scheme?' " But I don't necessarily think that the same reasoning applies to totally abstract concepts like those studied in mathematics. Would it make any difference for comprehension if we called it a "norring" rather than an "ideal"?

I, for one, am glad that mathematics has co-opted so much everyday vocabulary. If it hadn't, my Russian topology professor could never have said this yesterday: "If it's infinitely smooth, we just say it's simply smooth". Henceforth, then, I demand that we call Barry White simply smooth, both because that's the preferred nomenclature and because it sounds less intimidating (though my girlfriend asserts that Mekhi Phifer is much smoother than Barry White).

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