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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.
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Carpal Tunnel
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Dear JH: A really good airliner landing seems aymptotic until pilot cuts power.
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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!)
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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).
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Pooh-Bah
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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?
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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.
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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
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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
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WW, what are you using obiter dictum to mean? I've only ever heard it in the plural (obiter dicta) meaning parenthetical remarks made by a judge expressing his opinion but not actually part of the judgement he's giving.
Bingley
Bingley
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'Nother query--obiter means 'in passing'; why isn't it orbit? If obiter is where orbit came from, how'd the r get in there?
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rare individuals
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They're not related near as I can figure. Orbit is from orbis, ring, circle; obiter means in passing as has been said before. Can't trace orbis past Latin nor could I find any details about obiter although I suspect some connection to it as the 3rd person singular of the verb ire, to go.
Quick edit: Seems to be no verb obire. There is a preposition ob meaning in front of, before; in return for; because of, on account of.
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[bold]
obiter dictum
[/bold]
I've heard this before, but never understood it or been inclined to look it up.
Useful term, though. I'll make an effort to find occasions to use it.
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Dear Bingley: here is what Wordsmith posted quite a while ago:
Date: Tue Mar 20 00:02:10 EST 2001
Subject: A.Word.A.Day--obiter dictum
X-Bonus: I'm proud to pay taxes in the United States; the only thing is, I could be just as proud for half the money. -Arthur Godfrey, radio and television entertainer (1903-1983)
obiter dictum (OB-i-tuhr DIK-tuhm) noun, plural obiter dicta
1. A passing comment.
2. An observation or opinion by a judge that is incidental to the case in
question, and not binding as precedent.
[From Latin, literally, saying by the way.]
"`Abstract Expressionism was being deployed as a cold war weapon,' (Frances
Stonor) Saunders jauntily asserts. ... Obiter dicta like Saunders's
pronouncement above highlight her irreducible problem."
Josef Joffe, America's secret weapon, New York Times Book Review, Apr 23,
2000.
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left me behind at "decreasing in amplitude by some amount"
The function y=sin(x) is a sine wave with an amplitude of 1. If you have the function y=sin(x)/x it will be undefined at x=0 but beyond that it will be a sine wave of decreasing amplitude. At x=2 it will be a sine wave of amplitude 1/2 and at x=3 it will be amplitude 1/3. This sine wave would be said to be asymptotic to the y-axis since its amplitude would be approaching 0 as x increases without bound. It will never reach 0 because, for any finite x, 1/x>0.
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That should settle it! Thanks, Dr. Bill.
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Thanks, Faldage. Much appreciated.
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I am very sensitive about this thread, since I am teaching a course about "teaching Mathematics", so I am deeply interested in what people think - more or less consciously -about maths.
The first comment is about the relation
maths= equations
A lot of maths is done without equations or numbers at all, and usually mathematicians don't like to computate - indeed, there are a lot of attempts to let the computer computate even algebraic calculus, to avoid mistakes, and boring computations
All the greek geometry was developed without equations...
Just after Descartes, and the cartesian coordinates, they have been used, as a powerful tool. but even now, a proof made without coordinates is considered somehow more elegant.
In this context, we could say that an asymptote to a given curve is a "tangent" to the curve in a point "at the infinity".
The second comment is about "really smart math guys"
I know that it was not intended to say anything not polite, (please, please, don't be offended) but it seems express the idea that maths is a Male stuff. I deeply disagree with that.
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"The second comment is about "really smart math guys"
I know that it was not intended to say anything not polite, (please, please, don't be offended) but it seems express the idea that maths is a Male stuff."
First, Im not offended. And I'm aware that the connotation of "guys" is "generally" masculine. However, I was using it, as I often have, in a neutral sense. I have been guilty of saying to a class of students of both genders, things such as, "You guys better not be late." No one thought I was excluding the ladies from this warning. It may be generational or regional, but I've also heard the term "fellas" used in the same way.
Mrs. Rice, my 10th grade algebra teacher, would speak on my behalf, if she were here.
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Dear emanuela: I'm not sure how you define "equation". Geometry has many
statements of equality, there is addition, subtraction, amd division (I think), just
no algebra.
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I never use the term "fellas" at all, much less to address a gender-mixed group, but my m-i-l always announced dinner that way ("You fellas ready to eat?"), and it was clear that the question was addressed to everyone.
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http://www.cut-the-knot.org/ctk/pww.shtml
http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html
Just two examples, to explain what I was meaning.
And, JohnHaway, thank you for the explainations.
Not having English as a mother tongue, I can miss subtilities... for example, I learnt "guys and gals" here in Awad, but never encountered "guys" in a mixed sense.
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This thread is pretty much beyond my comprehension, but I must tell you, emanuela, that to me it's usually OK to use 'guys' or 'fellas' to mean both sexes. It depends on the context -- but I use it myself, all the time. Ciao, bello!* ~~~ *this is a joke. 
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etymology of "fellow" interests me.
fellow - O.E. feolaga "partner," from O.N. felagi, from fe
"money" + verbal base denoting "lay." Sense is of "one who
puts down money with another in a joint venture." Used
familiarly since M.E. for "man, male person," but not
etymologically masculine. University senses evolved from
notion of "one of the corporation who constitute a college"
and who are paid from its revenues. At one fell swoop is
from "Macbeth." Fellow-feeling (1613) attempted to
translate L. compassio and Gk. sympatheia. First record of
fellow-traveller "one who sympathizes with the Communist
movement but is not a party member," is from 1936,
translating Rus. poputchik.
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etymology of "fellow"
My Concise Anglo-Saxon Dictionary lists feolaga as masc. Being a Germanic language, English gives the gender of the last element in a compound word to the word as a whole. The word laga, law is masculine and feoh, cattle specifically, or property or money in general is neuter. Whether or not it is related to any verbal base denoting "lay" is not addressed.
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I never use the term "fellas" at all, much less to address a gender-mixed group, but my m-i-l always announced dinner that way ("You fellas ready to eat?"), and it was clear that the question was addressed to everyone.
Ny experience is similar. In my case it's my daughter-in-law, who has kept her maiden name after marriage and yet uses "you guys" to be gender-inclusive. ("Emerson!") I have found "you folks" to be an acceptable workaround.
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I have found "you folks" to be an acceptable workaround.
Nothing beats "y'all."
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old hand
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For the record, and back to the original question, there's an interesting architecture firm called Asymptote. ( http://www.asymptote.net) that is very cutting edge. Their website, which is very Flash-intensive, demonstrates this. I haven't read too much about them (because I keep getting caught up in the design of the site) but I suspect their name comes from the idea that their designs are approaching the future infinitely, but never quite there (because, duh, when you get there, the future has moved.)
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"What do I think about the future? Well, it's not here yet, is it?"
"Welcome to the future. It's starting just now!"
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Yeah, yeah, "Today is the first day of the rest of your life" ...
Very faldaginacious of you, matey!
- Pfranz
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