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Can we ever touch anything?
The distance between to articles can always be halved, so can they ever touch?

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Can we ever touch anything?

Teco
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Posted 10/13/09 - 12:30 PM:	#21
The fact is that you can always halve it, but, the limit of sum of 1/n as n goes to infinity is 1: ? 1 = 1 n->infinity n Best notation I can manage. I think this solves zeno's paradox. Eventually the rabbit will reach the turtle.

Warshed
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Posted 10/13/09 - 12:55 PM:	#22
I think the problem is that you are taking a limit or in other words you are using circular reasoning since you are assuming the consequent. I reach for my pen, we all know I will grab it since I do grab it, but in order to grab it I have to reach half of that distance, then half of the halves, and so on, so it seems I can't ever reach for my pen. So we say, well take the limit of 1/n and vioula, you got it. But that just assumes you eventually reach it, when in reality the limit never actually reaches 1, it just gets infinitely close.

kkiiji
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Posted 10/13/09 - 09:55 PM:	#23
I see the issue now, the conflict is clear. We are assuming that even with constant motion at a constant velocity, one will pass the half point, the 1/4 point, the 1/8 point, the 1/16 point and so on since you must pass all points to reach whatever you're touching. One might then think that how could we possibly pass through all the points if we can just keep halving? If we can't pass through all the points then how do we ever touch the wall? The solution is simple. Let us not look at halves for a second and look at the initial jump from the original distance to the half distance. In this first jump, we bypassed the 3/4 point, the 7/8th point, the 15/16th point, the the 31/32th point, so on and so on, we already bypassed an infinite number of points going from the full distance to 1/2 the distance. Within every amount of distance you wish to count each "jump", there are infinite number of points in between, so of course if you halve the increment of counting each time there will be an infinite number of points that must count before reaching the object. However we could just as easily choose a different increment of counting if we wish to reach the object during our lifetime. It all depends on how you want to slice up the increments. 1. There are in fact infinite number of points between you and the object, 2. The human scale of movement and increment measurement doesn't get as detailed as infinitesimal points, 3. We can pick any length of increments we like, 4. Why pick an increment measurement function that halves in size and eventually becomes infinitesimal?
Heard joke once: Man goes to doctor. Says he's depressed. Says life seems harsh and cruel. Says he feels all alone in a threatening world where what lies ahead is vague and uncertain. Doctor says "Treatment is simple. Great clown Pagliacci is in town tonight. Go and see him. That should pick you up." Man bursts into tears. Says "But Doctor... I am Pagliacci." Good joke, everybody laugh. Roll on snare drum... Curtains.

Teco
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Posted 10/14/09 - 11:18 AM:	#24
Warshed wrote: I think the problem is that you are taking a limit or in other words you are using circular reasoning since you are assuming the consequent. I reach for my pen, we all know I will grab it since I do grab it, but in order to grab it I have to reach half of that distance, then half of the halves, and so on, so it seems I can't ever reach for my pen. So we say, well take the limit of 1/n and vioula, you got it. But that just assumes you eventually reach it, when in reality the limit never actually reaches 1, it just gets infinitely close. It seems in this case infinitely close is te same as touching, or that the sum of infinite infinitesimals is a finite number. (since some infinitesimals seem to be a finite number?) For example: 10=10 (10/3)x3=10 3x3.33recurring=10 9.99.recurring=10 0=10-9.99recurring 0=0.1^?

Banno
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Posted 10/14/09 - 11:58 AM:	#25
Don't they teach calculus in what you folks abbreviate to "math"?
Davidson: We make maximum sense of the words and thoughts of others when we interpret in a way that optimizes agreement. Russel Morris: There's a meaning there, but the meaning there doesn't really mean a thing... Ned: Such is life

Wosret
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Posted 10/14/09 - 12:58 PM:	#26
I tried this defense once in court... didn't fly.
"If you've got any last words, say 'em now." - Nadie. "I am Horo the Wise." - Horo the Wise.

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