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#93027 01/23/03 01:49 AM
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Asymptote
(spelling according to my Merriam Webster Collegiate Dictionary, but I've seen it without the "p", as well)

I've had a fondness for this word for many years, not because of its mathematical application but because of its potential applicability outside that field. I've never used the word in other than a physical science context nor have I seen it used otherwise by anyone else. But it seems to me that the idea of describing a social or political situation as "asymptotic" is quite descriptive and worthy of something George Will might write.
One might say, "His approach to acknowledging error is asymptotic" (meaning, he comes close, but never quite gets there). Or, "The administration's asymptotic treatment of the homeless problem leaves much to be desired."
I'd be interested to hear your views on the subject--particularly if you've ever run across the word outside the realm of mathematics or physics.


#93028 01/23/03 02:31 AM
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Dear JH: A really good airliner landing seems aymptotic until pilot cuts power.


#93029 01/23/03 02:47 AM
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Well, both of you know more than I do. Atomica gave a couple of diagrams, but they didn't help me at all. The def. consisted of "A line whose distance to a given curve tends to zero." Okay-y-y...if somebody would give me an explanation starting from scratch, I would be most grateful. I have NO idea what this means! There is distance between the line and the curve, so I surmise that the line is not the curve. I am envisioning a straight line, going on for infinity, and some curve somewhere above, beside, or below it. But how do they decide from what part of the curve they want to measure this distance? The part closest to the line? I guess it would have to be pretty darned close, to be nearly zero distance. And what in the world did they mean by "tends to"?? Tends toward?
(By the way, I guess this might be taken as once-and-for-all proof that I am pretty literal-minded!)


#93030 01/23/03 04:26 AM
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Before those really smart math guys start throwing equations at you, think of a person who is told to stand in front of a wall and told to move half the distance to the wall every hour. Intuitively, you can see that he will never reach the wall, although he is constantly approaching it. A graph of this would show a curve approaching an axis but never touching it.
(My apologies to the real math guys out there--I was just a pre-med student).


#93031 01/23/03 06:42 AM
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http://www.mathnstuff.com/math/spoken/here/1words/a/a28.htm

to tell you the truth i haven't even known there is quadratic asymptote. i always thought it must be straight line ..


#93032 01/23/03 09:17 AM
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I like your suggestion regarding asymptotic JH, but have never encountered it.

Hyperbole and parable have the same roots as hyperbola and parabola and give us hyperbolic and parabolic to describe either the rhetorical or the mathematical use. So why not use asymptote and asymptotic similarly? I guess tangent and tangential are the most widely used examples of this linking of curves with language. Are there others? How about a hyperparable for an allegory that really takes things beyond credibility, matched with hyperbolicparaboloid?



#93033 01/23/03 11:07 AM
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For starters, the distance of the curve to the line (I don't like the way it was termed, A line whose distance to a given curve, even though it amounts to the same thing) is measured in a distance perpendicular to the line.

Next, it is not true that the curve can never touch the asymptote. A sine wave, e.g., that is decreasing in amplitude by some amount, say 1/x, can be said to be asymptotic to the x-axis. It will "touch" the x-axis at 0, pi, 2pi,... It is said to be asymptotic to the x-axis because the envelope enclosing the sine wave is asymptotic to the x-axis, where the envelope would be equal to the pair of curves y=1/x and y=-1/x. See Ex. 1 in rav's link.


#93034 01/23/03 11:24 AM
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It's a good word that I use not infrequently (maybe once every year or so), but I think you and I use the term in slightly different ways.

For example, I'm not sure what the intended effect of this statement is:
"The administration's asymptotic treatment of the homeless problem leaves much to be desired."

As you know, but for the benefit of the others, if the locus of points approaches a line asymptotically, then it is 1) headed in approximately the right direction and 2) constantly getting closer to the goal, the distance between the curve and the asymptote becoming vanishingly small.

If the administration's treatment of the homeless problem were asymptotic, I might interpret this that the solution is always short of the mark, but that it was zooming in - eventually becoming quite good, and so the part about "leaves much to be desired" seems out of place to me. (Well, that's just the way I would interpret it.)


Other really good technical words I use all the time, because I think they make at least as much sense as the alternatives:

1) Heuristic - a solution method to a problem that is close enough most of the time, at least to start off with. Also known as a "rule of thumb" or a "general rule" in the vernacular. Interesting that this is not implied by the MW definition of the term, but in most computer science books, they explicitly call a heuristic a "rule of thumb."

"Drinking 8 glasses of water a day should not be treated as an absolute rule, but as a heuristic."


2) Orthogonal - meaning two things are independent, or unrelated. "Some people believe that wisdom and intelligence are orthogonal qualities, but I don't."


I've heard a few very nontechnical people use signal-to-noise ratio and bandwidth - these terms are almost mainstream.

k



#93035 01/23/03 11:43 AM
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You left me behind at "decreasing in amplitude by some amount", Faldo.

But I have seen asymptotic used outside physics and math. I know this, although I can't give you a reference, because I don't read physics or math books/articles/journals. Except by accident in dentists' waiting rooms and the like.

- Pfranz

#93036 01/23/03 12:53 PM
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