Muzman on 22/11/2008 at 09:41
There's not a lot of maths nerdery here actually. Mostly I'm trying to remember if there's a name for this problem I heard about as a kid.
The problem is usually described as either a bouncing ball or a door you push closed or something: The ball bounces back after each impact to half the previous height. Calculate how long it takes to stop bouncing and it theoretically does not ever stop, but bounces to infinitely smaller heights forever (I think you have to use calculus to get around this).
I seem to remember there being a name for this problem. Searching around for similar things one mostly ends up at Zeno's paradox of dichotomous motion. But that's kind of the opposite thing isn't it? (Zeno suggesting motion doesn't really occur at all because you have to go half way before you can go the whole way, but first you must go half of the half, but first half of that half..and so on into absurdity. The door closing one probably did conform to this, now that I think about it). In the ball problem no one really disputes motion is occuring, arithemetic just can't describe when it stops.
Is that right and does this have a name all its own? (me is lower maths, hard of braining, humanities student)
Aja on 22/11/2008 at 10:16
eventually wouldn't it just get to the point where only the molecules are vibrating? And since they vibrate anyway, the height of the bounce can't get any smaller than them.
english majors breakin down the science itt
mol on 22/11/2008 at 11:51
Kolya wins the thread already at this point. lolling!
scumble on 22/11/2008 at 12:14
you'd need to account for friction and other energy losses, but calculus being what it is, based on infinitesimals, you get an asymptote and probably have to say that any motion below a certain threshold is essentially "stopped". I suppose the problem is that, as Aja suggests, you end up at the boundary between classical and quantum mechanics.
Starrfall on 22/11/2008 at 16:41
It's probably called "The Bouncing Ball Problem" or something lame.
I don't recall that paradox of Zeno's meant that motion doesn't happen, but rather that you can never reach your destination (which sounds more like the ball problem, even if it's still not exactly the same). It's been like 7 years though so I might be wrong.
ZylonBane on 22/11/2008 at 17:37
If Muzman had even bothered reading the Wikipedia article on Zeno's Paradox, he would have discovered that this sort of problem is known as a (
http://en.wikipedia.org/wiki/Convergent_series) convergent series.
demagogue on 22/11/2008 at 18:26
Quote Posted by Starrfall
I don't recall that paradox of Zeno's meant that motion doesn't happen, but rather that you can never reach your destination (which sounds more like the ball problem, even if it's still not exactly the same). It's been like 7 years though so I might be wrong.
In its original form, it was an argument supporting Parmenides' (his teacher) idea that motion is impossible -- or at least an illusion, everything is really in an eternal stasis -- with the argument running backwards: Achilles has to run 1/2 way first, but before that 1/4 of the way, etc, etc ... to the point he can't move a single inch without moving an infinite number of distances first. And another image he had was an arrow in flight; at any single moment it's not moving. But then again I also recall a lot of "too much thinking" spent on the nuance between "never arriving" and "movement never happens"...
I heard some quantum application where you can keep a particle from reaching its destination indefinitely by continuing to make observations of it, useful apparently to quantum computing, but I'm not sure of the details.
R Soul on 22/11/2008 at 18:47
If I'm ever late for work I'll just say there was a paradox in my way.
TBE on 22/11/2008 at 19:01
I'm always thinking about the car going 60 miles per hour, when it's 60 miles from the destination, and slowing by 1 mph each mile it gets closer to the destination. I need to get the formula for this one, as it drives me nuts when I'm driving down the road. I usually get distracted after about 5 miles of calculations.
