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Zeno had even better theory.
1. You drop a grain, what do you hear? Nothing. 2. You drop a lot of grains (like pouring them from a bag or sth) and you definitely hear them falling on the floor.
Now, what he says is that if you don't hear one grain falling and when you drop a bag of them it's just many 'one grains' fall then how come you hear it? It's just an imaginary sound ^_^
And to all that despise philosophers: Even if their theories are completly dumb you shouldn't think they are. Philosophers task is NOT to create some superb and rational theory but to force others to think. This way science goes on. (Yeah, 90% of great scientists were philosophers eq. Newton, Einstein, Darwin, La Place, Pithagoras etc.)
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He tricks you into believing that infinite additions gives infinite high numbers. That is not true, however. If the numbers get small enough - fast enough - the sum will go towards a number, never hitting it, but coming very close, and here comes the concept permit limit.
Lets assume he runs 10m/s.
After half the route he will have runned 50 m = 5s Half from 50m to the finish line = 25m = 2,5s next: 12,5m = 1,25s next: 6,25m = 0,625s next: 3,125m = 0,3125s next: 1,5625m = 0,15625s next: 0,78125m =0,078125s
Add these seconds up: 5s + 2,5s + 1,25s + 0,625s + 0,3125s + 0,15625s + 0,078125s = 9,921875s
If we continue:
next: 0,390625m = 0,0390625s next: 0,1953125m = 0,01953125s next: 0,09765625m = 0,009765625s and so on
Add these seconds up: 9,921875s + 0,0390625s + 0,01953125s + 0,009765625s = 9,990234375s
See how it gets closer to 10? If we continue it will go towards 9,99999...s
Here is permit limit useful. Without explaining it in detail the result is:
a -> 10, n ->infinite A is going towards 10, if n goes towards infinite
a = the whole sum n = times of additions
You will probably have to rewrite it because my English is quite bad. Hope you got the meaning 
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mrmin123
Korea (South)2971 Posts
Fractals anyone? Chaos theory? Koch curves? Lorenz Attractors? This thing isn't just some philosopher's ramblings anymore (not that all philosopher's ramblings are... ramblings), it's a science.
Ideas like an infinite length in a finite area (or infinitly long coastlines :F) are crazy fun.
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yea, what Kochen said:
An = 50 * 0.5 ^(n-1) where the sum of the infinite row would be Sn = A1 / (1-k) = 50 / (1-0.5) = 100
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Pffff, simple to prove Zeno wrong.
The sprinter can run 100m diestance in, lets say, 10 seconds.
Zeno divides the distane by half (infinitely), and you divide the total time by two (also infinitely). This infinite number of distances add up to 100m, and the infinite number of times add up to 10 sec.
There is a part of math which deals with sums of infinite amounts of infinite small "numbers", and it's called calculus. Using it you can easily prove Zeno wrong, and shove his "prove" up his ass.
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On July 25 2005 02:14 qux.afk wrote: yea, what Kochen said:
An = 50 * 0.5 ^(n-1) where the sum of the infinite row would be Sn = A1 / (1-k) = 50 / (1-0.5) = 100 Correct. Kochen was the first to point out the wrong assumption than a sum of infinite many numbers is always infinite. These kind of sums are called convergent sums. Try this.
Edit: Philosphers are jerks. Most of them.
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On July 25 2005 02:21 IcedEarth wrote:
cant divide with zero...
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Sweden33719 Posts
On July 24 2005 22:54 Hydrolisko wrote: Zeno is a greek philospher who thought motion is impossible. I have to write an essay to refute his argument intelligently (rationally, can't just say stuff like "wow how dumb"). I have an argument in mind but I'd like to see some more insights before I start writing. Here is his argument:
1. Zeno starts by assuming what his opponent says is possible: motion. In particular, the motion of a single body across a finite distance in a finite time. 2. To make things vivid, let’s specify the moving object, and where it is supposed to be moving: Imagine a sprinter, who starts running at one end of a 100 metre straight track, and runs to the other end. Zeno’s opponents (probably including yourself) think that it really is possible that runners can do this. (i.e. They think that it is not just an illusion.) Zeno begins by assuming that his opponents are correct, and then the fun starts. 3. Zeno points out, given that we are assuming that space is continuous, that before the runner can cover the whole 100 metres she has to cover half the distance, i.e. run 50 metres. 4. Zeno then repeats the move just made (point 4) and points out that the move can be repeated an infinite number of times: before the runner can cover 50 metres, she has to run 25, before that she must run 12.5, before that 6.25, etc. Recall that we are assuming that space is continuous, which means that any finite piece of it, such as a sprint track, can be divided into infinitely many parts, which are infinitely small. 5. Zeno then argues that to cover each of these infinitely small parts will take a certain amount of time. 6. But to take a certain amount of time an infinite number of times adds up to an infinite amount of time. So it would take the runner forever to cover 100 metres. But we were assuming that the runner could cover the distance in a finite amount of time, not that she would take forever. 7. We have run into a problem, and Zeno’s conclusion is that motion is impossible, because any finite motion would take forever.
Thoughts? Eh.. So what if there's an infinite number of distances over the course of a 100 metre track, once you reach the end of it, you have covered them all --
Or am I not getting something ._.?
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On July 25 2005 02:49 ygor wrote:Show nested quote +On July 25 2005 02:14 qux.afk wrote: yea, what Kochen said:
An = 50 * 0.5 ^(n-1) where the sum of the infinite row would be Sn = A1 / (1-k) = 50 / (1-0.5) = 100 Correct. Kochen was the first to point out the wrong assumption than a sum of infinite many numbers is always infinite. These kind of sums are called convergent sums. Try this. Edit: Philosphers are jerks. Most of them.
Not quite, as you see, a provocing philosopher has evedently made us all think twice about a lot of things. Another of Xeno's paradoxes are the flying arrow:
An arrow flys from A to B In between these to there is a third point C. In order to occupy space in point C it is requiered to momentarily be at rest in this particular instant of time. However, imagine an infinate number of points like C inbetween A and B. The arrow is then requiered to stay still in every single of these, thus moving at the same time it is at rest.
This is all supposing i remember the paradox correctly, but the point of it all is that the thought of momentary motion is impossible. That motion is allways measured between two places that indeeed can be very close to one and other but not momentarily. Thus in Xenos' opinion making the thought of motion a contradiction to itself. Not that I agree, but you have to realise that he does have a point.
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MURICA15980 Posts
I think you worded it wrong, because I totally disagree and can't even see where the "thinking" part of it is... unless I'm blind at 3:30am :O
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On July 25 2005 03:35 Klogon wrote: I think you worded it wrong, because I totally disagree and can't even see where the "thinking" part of it is... unless I'm blind at 3:30am :O
Imagine instantaneus motion. Then try to think outside the box.
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This is the same kind of crap an old greek guy pulled out of his behind about how a rabit could never catch up with a turtle who had a little head start (even tho the rabit is 10 times faster). But as we all know this is just a way of playing with words and math.
Instead of adding up all these infinitely small numbers into an infinite time, what about this?
The runner runs 100 meter in 11 seconds. And now we want to know how long it takes for him to move one of those infinitely small bit forward (1 divided by infinity). The answer is that it takes him no time at all and no matter how long we keep adding these up we see that it takes 0 second to move an infinitely amount of infinitely small distance. So what do we get? The answer is that the runner runs 100 meter in 0 seconds.
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An infinite amount of intervals that are getting infinitly small equals a finite lenght
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On July 25 2005 01:10 Klogon wrote:Show nested quote +On July 24 2005 22:57 imRadu wrote:On July 24 2005 22:54 Hydrolisko wrote: Many times when I am driving or even a passenger in a car, I imagine a little elf-like man jumping from tree-top to tree-top right along with my car. Thoughts? *fixed WOW~! I can't stop laughing haha ;D
I do the same thing, only it's a snowboarder usually grinding the fences along the road and jumping and stuff.
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On July 25 2005 04:29 Chaso wrote: This is the same kind of crap an old greek guy pulled out of his behind about how a rabit could never catch up with a turtle who had a little head start (even tho the rabit is 10 times faster).
lol, it IS the same thing.
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u gotta be kidding u retard
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why are you all responding to this? and don't point out that i'm responding too
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On July 25 2005 04:40 WOstick wrote:Show nested quote +On July 25 2005 01:10 Klogon wrote:On July 24 2005 22:57 imRadu wrote:On July 24 2005 22:54 Hydrolisko wrote: Many times when I am driving or even a passenger in a car, I imagine a little elf-like man jumping from tree-top to tree-top right along with my car. Thoughts? *fixed WOW~! I can't stop laughing haha ;D I do the same thing, only it's a snowboarder usually grinding the fences along the road and jumping and stuff.
holy shit i do the same thing except its a skateboarder and i imagine him grinding all the road fences. he holds onto a car then lets go to jump up and grind the border and when he dismounts he grabs onto another coming car bahaha
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Belgium6772 Posts
Achilles and the turtle. It wasn't a rabit.
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