Naked Science Forum
General Science => General Science => Topic started by: neilep on 07/02/2004 03:51:36

I once read an explanation of my conundrum (many years ago) but have completely forgotten the reasoning to this query.....Say your hands are 100 cm apart .When you start to clap your hands, they both have to travel towards each other of course.....at some point they will be 50cms apart, then 25, then 12.5, then 6.25 etc etc ad infinitum yes?....if the distance is always halved , how do the hands eventually meet ? surely even at their closest they will never touch cos the distance towards each other is halved infinitely.....*sigh* I probably have not explained it well but hope you understand the gist of it......I'm sure it's a simple enough solution yes ?....please enlighten me !! aaaaaaargh !!!!
'Men are the same as women...just inside out !'

eeeh good question? Hand meets in halves? You see when you are clapping you are um... lmao hehehe I dunno! YOu enlighen us

It's a logical fallacy. Don't buy into it.
Your hands are not halving the distance with each successive movement, they are heading towards each other with a definite acceleration. Given that acceleration and starting points of the hands, one can mathematically show the duration of the clap and the position of the hands at that clap.
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Hands move together with the same speed, not halved per each time period. So, it's the same distance each time period so the distance will run out in a given amount of time. If it was half the distance each time period they wouldn't meet. But you've noticed when you clap your hands you don't slow down as they meet then like, hardly move at all? If that was the case they wouldn't meet, but they do because it's not half the distance per given time period ...
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Thanks Jay, Thansk Erin.....I understand and appreciate your answers.
'Men are the same as women...just inside out !'

If your hands were halving the distance every second (for the sake of simplicity) they would be traveling with an exponential deceleration. When you are clapping, they are accelerating toward each other or at least moving relatively constant velocity. Not exponentially decelerating.

John

My microbiology professor used this example in class today and I yelled at her. She was talking about how when you're picking how much time you want to autoclave something, you're killing 90% of the organisms in the first 10 minutes, then 90% of the remaining ones in the next 10 minutes, and so on. Then she used the handscomingtogetherbyhalves example. It was worse than when she tries to talk about chemistry. Why are biologists so abstracted from real science? [:P]
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If you ever did any co ordinate geometry at school, you should remember the graph of a hyperbola. The most simple one is y = 1/x which is the half by half thing ... think about the graph, then think about the graph of y=x which is what really happens. I know you've already understood it but here's just one more example just in case :P
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Thanks again Erin, and Jay and also John too.....I feel completely at ease with the clapping of my hands now....cheers..Neil
'Men are the same as women...just inside out !'

It's a logical fallacy. Don't buy into it.
Your hands are not halving the distance with each successive movement, they are heading towards each other with a definite acceleration. Given that acceleration and starting points of the hands, one can mathematically show the duration of the clap and the position of the hands at that clap.
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Hahahaha! Totally agree! Best answer though! Thanks, man (https://www.thenakedscientists.com/forum/index.php?action=post;quote=4516;topic=643.0;last_msg=4601)!

Yes, this is a logical fallacy. It is another version of Zeno's paradox.
The key to understanding this is that, while we can imagine an infinite number of points between your hands, that they must pass through during the process of a clap, the time it takes to get to each successive point also shrinks.
Let us imagine your hands closing in on each other with constant speed. If it takes half a second to reach the halfway mark, then it will take another quarter of a second to halve the distance again, and an eighth of a second to halve the distance again, and a sixteenth of a second to halve the distance again. When you add up all of those times, it turns out that it takes precisely 1 second to clap (from whatever the starting position was). This becomes obvious when we realize that it takes:
0.5 seconds to get 50% of the way through the clap
0.75 seconds to get 75% of the way through the clap
0.875 seconds to get 87.5% of the way through the clap
0.9375 seconds to get 93.75% of the way through the clap
0.96875 seconds to get 96.875% of the way through the clap
...
...
...
1.00 second to get 100% of the way through the clap

This amounts to evaluating the series 11/21/2^21/2^3********* in the mathematical world this takes an infinite number of steps to get to zero but in the physical world the separation between the hands soon comes to the Planck value of distance and can get no less.

Yes, this is a logical fallacy. It is another version of Zeno's paradox.
The key to understanding this is that, while we can imagine an infinite number of points between your hands, that they must pass through during the process of a clap, the time it takes to get to each successive point also shrinks.
Let us imagine your hands closing in on each other with constant speed. If it takes half a second to reach the halfway mark, then it will take another quarter of a second to halve the distance again, and an eighth of a second to halve the distance again, and a sixteenth of a second to halve the distance again. When you add up all of those times, it turns out that it takes precisely 1 second to clap (from whatever the starting position was). This becomes obvious when we realize that it takes:
0.5 seconds to get 50% of the way through the clap
0.75 seconds to get 75% of the way through the clap
0.875 seconds to get 87.5% of the way through the clap
0.9375 seconds to get 93.75% of the way through the clap
0.96875 seconds to get 96.875% of the way through the clap
...
...
...
1.00 second to get 100% of the way through the clap
Is that the naked scientists version of a slow hand clap ?
If they half the distance at intervals of half the time they eventually meet unless time is limited.

Yes, this is a logical fallacy. It is another version of Zeno's paradox.
The key to understanding this is that, while we can imagine an infinite number of points between your hands, that they must pass through during the process of a clap, the time it takes to get to each successive point also shrinks.
Let us imagine your hands closing in on each other with constant speed. If it takes half a second to reach the halfway mark, then it will take another quarter of a second to halve the distance again, and an eighth of a second to halve the distance again, and a sixteenth of a second to halve the distance again. When you add up all of those times, it turns out that it takes precisely 1 second to clap (from whatever the starting position was). This becomes obvious when we realize that it takes:
0.5 seconds to get 50% of the way through the clap
0.75 seconds to get 75% of the way through the clap
0.875 seconds to get 87.5% of the way through the clap
0.9375 seconds to get 93.75% of the way through the clap
0.96875 seconds to get 96.875% of the way through the clap
...
...
...
1.00 second to get 100% of the way through the clap
Is that the naked scientists version of a slow hand clap ?
If they half the distance at intervals of half the time they eventually meet unless time is limited.
As long as there is at least 1 second available (given the numbers used above), then there is no problem.

Agree  qv Zeno's paradox. Although perhaps not quite the same  I believe the clap is made by the air between the hands being compressed, then a small explosion. So you get the clap just before the hands (would) meet.

I've just remebered something re Zeno's arrow paradox. Very roughly the paradox is: that on the one hand his logic tells him the arrow will never reach its target, while on the other hand observation tells him that it does reach the target, they cannot both be true. In one translation, I read that he resolved the paradox by concluding that motion is an illusion.
Mathamaticians claimed to resolved the paradox, as has been done above following the birth of calculus and the study of infinite sequences and series, although some disputed this.
For once we can claim philosophy and science has got the better of maths  since quantum theory backs up Zeno's conclusion.

For once we can claim philosophy and science has got the better of maths  since quantum theory backs up Zeno's conclusion.
Its also psycological as we can easily accept whole can be divides into an infinate number of parts, we cannot accept that the parts are infinatley small (not my idea , just read it) Is that not the problem though, philosophy is observed in some circles as irrational, whereas the philosophy of which object is accellerating led to relativity.

There are no paradoxes, only misunderstandings. Philosophy is bunk.

Well you can tell it to descartes eh ?