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Leopher wrote on 2012-01-09 04:40
Bringing up a rather ancient and fascinating argument for fun and thought.
Consider the following circumstance:
A creature, let's say a rabbit, wants to travel straight from point A to point B. In order to do this, it first must travel 1/2 the total distance. Once it has done this, it must then travel 1/2 the remaining distance. Next, it must travel 1/2 that remaining distance. Next, it must once more travel 1/2 the remaining distance, ad infinitum. Another way to think of this is that it first must travel 1/2 the total distance, then 1/4 the total distance, 1/8 the total distance, 1/16 the total distance, 1/32 the total distance, and so on and so forth. This means that the rabbit must complete an infinite number of tasks before reaching point B, and therefore, logically, he should never be able to reach point B. However, in the physical world we do see rabbits get from point A to point B, and therefore the physical world does not match up with the logical one, so it cannot be real.
Thoughts?
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EndlessDreams wrote on 2012-01-09 04:53
So, how about those Calculus classes? (Dealing with Limits)
If Point A and Point B is the same location, think of the mind games!
The "real" world is unknown to us. We can only see it through our senses.
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Andy-Buddy wrote on 2012-01-09 04:53
Quote from PoLkaTulK;729144:
Bringing up a rather ancient and fascinating argument for fun and thought.
Consider the following circumstance:
A creature, let's say a rabbit, wants to travel straight from point A to point B. In order to do this, it first must travel 1/2 the total distance. Once it has done this, it must then travel 1/2 the remaining distance. Next, it must travel 1/2 that remaining distance. Next, it must once more travel 1/2 the remaining distance, ad infinitum. Another way to think of this is that it first must travel 1/2 the total distance, then 1/4 the total distance, 1/8 the total distance, 1/16 the total distance, 1/32 the total distance, and so on and so forth. This means that the rabbit must complete an infinite number of tasks before reaching point B, and therefore, logically, he should never be able to reach point B. However, in the physical world we do see rabbits get from point A to point B, and therefore the physical world does not match up with the logical one, so it cannot be real.
Thoughts?
Once a situation like that is given real-world values, such as a distance measurement like meters, a circumstance like that becomes void as those infinite tasks fail to be achieved.
e.g. A rabbit moves 2 meters, halfway to its destination 4 meters away. Once it is 2 millimeters away, it has no physical ability to jump one millimeter only, nor would it have any reason to.
My conclusion is that theory must be regulated to real-world possibilities for testing and for logic's sake.
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rinaek wrote on 2012-01-09 04:53
Quote from EndlessDreams;729166:
So how about those Calculus classes? (Dealing with Limits)
∞
[SIZE="6"]Σ[/SIZE] x * (0.5)^i = 2x
i = 0
Related topic:
An infinite number of mathematicians walk into a bar. The first goes up to the bartender and says, "I'll have a pint of lager, please." Each next one says, "and I'll have half of what he's having." The bartender says, "You're all idiots," and pulls two pints.
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EndlessDreams wrote on 2012-01-09 04:56
Quote from rinaek;729168:
∞
[SIZE="6"]Σ[/SIZE] x * (0.5)^i = 2x
i = 0
That is a series.
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rinaek wrote on 2012-01-09 05:02
Quote from EndlessDreams;729170:
That is a series.
It goes to infinite. A limit didn't seem to make as much sense.
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Leopher wrote on 2012-01-09 05:08
Quote from EndlessDreams;729166:
So, how about those Calculus classes? (Dealing with Limits)
If Point A and Point B is the same location, think of the mind games!
Unfamiliar with calculus.... Sorry. Any references to it will probably be lost on me.
Quote from EndlessDreams;729166:
The "real" world is unknown to us. We can only see it through our senses.
That's quite the discussion halter.
Quote from Andy-Buddy;729167:
Once a situation like that is given real-world values, such as a distance measurement like meters, a circumstance like that becomes void as those infinite tasks fail to be achieved.
e.g. A rabbit moves 2 meters, halfway to its destination 4 meters away. Once it is 2 millimeters away, it has no physical ability to jump one millimeter only, nor would it have any reason to.
My conclusion is that theory must be regulated to real-world possibilities for testing and for logic's sake.
I'm not sure we're ever working with real world values... though I could be wrong. The talk about the rabbit is merely extracting a principle from relatively abstract math without measurements, while the conclusion of "the physical world is an illusion" is what's gained by applying the principle and saying that the physical reality does not match up with the logical one.
Quote from rinaek;729168:
∞
[SIZE="6"]Σ[/SIZE] x * (0.5)^i = 2x
i = 0
That looks awesome. Though I have no idea what it means.
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EndlessDreams wrote on 2012-01-09 05:30
Quote from rinaek;729179:
It goes to infinite. A limit didn't seem to make as much sense.
If the movement from point A to point B was taken as a function. As you get infinitely close to point B, it will be get closer and closer to be being point B since the value of point B lies on the function. Of course, when it is on point B, the value is point B.
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Chiyuri wrote on 2012-01-09 15:52
Simple: It is possible do jump over the infinite amount of task once they reach the "insignificant" barrier.
The rabbit doesn't think "have to travel 1/16 of this distance, have to travel 1/32" and so on.. The rabbit think. "Gotta do a jump there, and a jump there, and a jump there, ah.. I just arrived."
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Osayidan wrote on 2012-01-09 19:34
Even logically it works out.
How big is the rabbit? How many halves of the distance you can travel before the distances become irrelevant is relative to the size of the traveler. Once the distances are much smaller than the traveler, he would technically be touching point B due to his size.
It's like trying to cut a pie in half an infinite number of times. With a knife you can only go so far, then you need something thinner and sharper than a knife, then maybe a laser, then even smaller lasers, eventually you're down to individual molecules of pie, then the atomic and quantum levels. I don't think anything exist allowing us to cut that in half so you would say you went as far as you can go, because our cutting tools are too big.
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Leopher wrote on 2012-01-09 20:54
Quote from Chiyuri;729632:
Simple: It is possible do jump over the infinite amount of task once they reach the "insignificant" barrier.
The rabbit doesn't think "have to travel 1/16 of this distance, have to travel 1/32" and so on.. The rabbit think. "Gotta do a jump there, and a jump there, and a jump there, ah.. I just arrived."
Quote from Osayidan;729757:
Even logically it works out.
How big is the rabbit? How many halves of the distance you can travel before the distances become irrelevant is relative to the size of the traveler. Once the distances are much smaller than the traveler, he would technically be touching point B due to his size.
It's like trying to cut a pie in half an infinite number of times. With a knife you can only go so far, then you need something thinner and sharper than a knife, then maybe a laser, then even smaller lasers, eventually you're down to individual molecules of pie, then the atomic and quantum levels. I don't think anything exist allowing us to cut that in half so you would say you went as far as you can go, because our cutting tools are too big.
Hmm... I think I see the point, and I think it's an important one to raise. However, I also think that we are dealing with a 1 or 2 dimensional example. The use of the rabbit is deceptive, so I apologize, but the point is that a thing of unspecified size is travelling an unspecified amount of distance. It's abstract, and we're not concerned with the size of things but only the idea that something can be continually halved, which is what the example attempts to illustrate.
Please note that I do not support the argument, but am arguing for it nonetheless.
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Osayidan wrote on 2012-01-09 21:24
Mathematically you can half something infinitely. But to go with the example of traveling 1 half the distance each time you have to take into account the size of the traveler, unless the traveler is nothing more than a point on a number line, in which case it doesn't actually exist and just serves to illustrate that you can indeed half something infinitely.
Realistically you would have a distance from point A to B of say 8
and a traveler of size 1
you would keep halving 8, then 4, 2, 1, 0.5
once the traveler's size is equal to (or maybe greater than if you want to look at it that way) the distance remaining between A and B, he is physically at his destination. So in this case, once the distance remaining is also 1 (or 0.5).
Now if people want to get philosophical about it, physical reality can be argued about until the end of the world. That subject is interesting and fun but it's more a place of ideas and speculation and I'm not sure the human race has the scientific/mathematical capacities yet to properly express it.
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Sumpfkraut wrote on 2012-01-09 21:31
Well to be fair you can't strictly reduce length more than the smallest actual physical entity spans, the rest would be de facto indivisible, so the mathematical world would provide the illusion, not the physical world.
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Osayidan wrote on 2012-01-09 21:52
Quote from Sumpfkraut;729907:
Well to be fair you can't strictly reduce length more than the smallest actual physical entity spans, the rest would be de facto indivisible, so the mathematical world would provide the illusion, not the physical world.
Forgot about that too. So once you divide something into two units of 1
Planck length each, according to our understanding of the universe at the moment, that's where it ends.
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Excalibuurr wrote on 2012-01-09 22:19
I thought of the Matrix when I read this, and I mean the movie. We could all be living under some mental infrastructure and we could not be aware of it. Well, nothing to do about it, though it's always good food for thought.