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Zido's paradox

truthseeker613
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4/13/2011 5:44:34 PM
Posted: 5 years ago
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated
http://www.nydailynews.com...

royalpaladin: I'd rather support people who kill spies than a nation that organizes assassination squads (Kidon) to illegally enter into other nations and kill anybody who is not a Zionist. Who knows when they'll kill me for the crime of not supporting Israel?

Koopin: LOL! I just imagine Royal sitting in here apartment at night, when suddenly she hears a man outside speaking Hebrew as sh
truthseeker613
Posts: 464
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4/13/2011 5:59:10 PM
Posted: 5 years ago
At 4/13/2011 5:48:09 PM, Denote wrote:
Zeno...

sorry you are right. thank you.
http://www.nydailynews.com...

royalpaladin: I'd rather support people who kill spies than a nation that organizes assassination squads (Kidon) to illegally enter into other nations and kill anybody who is not a Zionist. Who knows when they'll kill me for the crime of not supporting Israel?

Koopin: LOL! I just imagine Royal sitting in here apartment at night, when suddenly she hears a man outside speaking Hebrew as sh
Ore_Ele
Posts: 25,980
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4/13/2011 6:11:59 PM
Posted: 5 years ago
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.
"Wanting Red Rhino Pill to have gender"
truthseeker613
Posts: 464
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4/13/2011 6:12:32 PM
Posted: 5 years ago
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zinos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

(As an aside I would like to point out a wonderful incite I had regarding Zinos paradox. according to Jewish thinking it could be that nothing moves as it says in the Jewish daily morning prayer in the blessings preceding the recitation of the shema (hear o Israel...). "regarding god it says "the one who continually recreates the world daily". it may be said nothing moves god is just constantly recreating the world and each time he recreates the world he recreates the "moving" object in a different location.
http://www.nydailynews.com...

royalpaladin: I'd rather support people who kill spies than a nation that organizes assassination squads (Kidon) to illegally enter into other nations and kill anybody who is not a Zionist. Who knows when they'll kill me for the crime of not supporting Israel?

Koopin: LOL! I just imagine Royal sitting in here apartment at night, when suddenly she hears a man outside speaking Hebrew as sh
badger
Posts: 11,793
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4/13/2011 6:19:42 PM
Posted: 5 years ago
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?
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truthseeker613
Posts: 464
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4/13/2011 6:20:13 PM
Posted: 5 years ago
thank you orele. my problem is why continually divide. it is Zeno's paradigm/ way of looking at movement that I have difficulty with. It is somewhat more clear to me now but not fully.
http://www.nydailynews.com...

royalpaladin: I'd rather support people who kill spies than a nation that organizes assassination squads (Kidon) to illegally enter into other nations and kill anybody who is not a Zionist. Who knows when they'll kill me for the crime of not supporting Israel?

Koopin: LOL! I just imagine Royal sitting in here apartment at night, when suddenly she hears a man outside speaking Hebrew as sh
badger
Posts: 11,793
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4/13/2011 6:21:44 PM
Posted: 5 years ago
At 4/13/2011 6:19:42 PM, badger wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?

and even still you'd never reach the wall..
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badger
Posts: 11,793
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4/13/2011 6:22:39 PM
Posted: 5 years ago
At 4/13/2011 6:21:44 PM, badger wrote:
At 4/13/2011 6:19:42 PM, badger wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?

and even still you'd never reach the wall..

nah you would if you were travelling at a constant velocity :P but teleporting!
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badger
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4/13/2011 6:24:08 PM
Posted: 5 years ago
the only thing that would effectively disprove the paradox would be if there was proven to be a smallest possible unit..
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badger
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4/13/2011 6:24:57 PM
Posted: 5 years ago
At 4/13/2011 6:24:08 PM, badger wrote:
the only thing that would effectively disprove the paradox would be if there was proven to be a smallest possible unit..

no sense to be found here :)
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badger
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4/13/2011 6:27:10 PM
Posted: 5 years ago
At 4/13/2011 6:24:57 PM, badger wrote:
At 4/13/2011 6:24:08 PM, badger wrote:
the only thing that would effectively disprove the paradox would be if there was proven to be a smallest possible unit..

no sense to be found here :)

finite velocities to transcend infinite mid points lol..
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badger
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4/13/2011 6:28:07 PM
Posted: 5 years ago
At 4/13/2011 6:27:10 PM, badger wrote:
At 4/13/2011 6:24:57 PM, badger wrote:
At 4/13/2011 6:24:08 PM, badger wrote:
the only thing that would effectively disprove the paradox would be if there was proven to be a smallest possible unit..

no sense to be found here :)

finite velocities to transcend infinite mid points lol..

though.. you could keep on halving your velocity too i suppose.. so scratch that last bit lol :)
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belle
Posts: 4,113
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4/13/2011 6:29:51 PM
Posted: 5 years ago
A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t=10 , d/4 at t=20, d/8 at t=30 , and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes.
evidently i only come to ddo to avoid doing homework...
badger
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4/13/2011 6:31:53 PM
Posted: 5 years ago
At 4/13/2011 6:29:51 PM, belle wrote:
A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t=10 , d/4 at t=20, d/8 at t=30 , and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes.

haha that takes it i guess..
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PervRat
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4/13/2011 6:47:43 PM
Posted: 5 years ago
At 4/13/2011 6:24:08 PM, badger wrote:
the only thing that would effectively disprove the paradox would be if there was proven to be a smallest possible unit..

Planck's length is believed to be the smallest meaningful measure of distance, and planck's time is believed to be the smallest meaningful measure of time. Theoretically, nothing can occur in less than a planck-time, and no measurements can be taken of anything shorter than a planck-length (which is the distance light would travel in planck-time).
Cliff.Stamp
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4/13/2011 6:49:24 PM
Posted: 5 years ago
At 4/13/2011 6:11:59 PM, OreEle wrote:

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

Slight difference, you have to go half the distance, then etc. . Thus you have to travel an infinite number of intervals and thus can never reach the wall. The answer as you noted is that the intervals get infinitesimal and thus the time is finite.
badger
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4/13/2011 7:04:38 PM
Posted: 5 years ago
At 4/13/2011 6:47:43 PM, PervRat wrote:
At 4/13/2011 6:24:08 PM, badger wrote:
the only thing that would effectively disprove the paradox would be if there was proven to be a smallest possible unit..

Planck's length is believed to be the smallest meaningful measure of distance, and planck's time is believed to be the smallest meaningful measure of time. Theoretically, nothing can occur in less than a planck-time, and no measurements can be taken of anything shorter than a planck-length (which is the distance light would travel in planck-time).

and i've heard of that somewhere before.. i'm sure i've used it even.
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PervRat
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4/13/2011 7:30:28 PM
Posted: 5 years ago
At 4/13/2011 6:49:24 PM, Cliff.Stamp wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

Slight difference, you have to go half the distance, then etc. . Thus you have to travel an infinite number of intervals and thus can never reach the wall. The answer as you noted is that the intervals get infinitesimal and thus the time is finite.

Plus, measuring and metering how fast X travels is not the same thing as X travelling. We need to be able to measure and quantify things to develop a standard, but there's no law that the way the universe operates needs to cater to a metering system.

In fact, it is widely believed in physics circles that the universe is 'curved,' and because of this curvature, some of the basic laws, precepts and concepts most of us are taught in school about distance, length and time known as Euclidean geometry does not work in the actual universe because of the curvature of space-time. Over scales of even millions of miles/kilometers, the difference between Euclidean geometry and curved space-time geometry is hardly noticeable, but on the scale of light-years the difference becomes greater and greater.

If you remember back to geometry of the Euclidean variety most of us were taught in school, you draw a triangle on a flat piece of paper, and to be a triangle, it has 3 straight sides and 3 angle; the sum of the interior angles of a triangle must always be 180 degrees -- no more, and no less; only one such interior angle may be 90 degrees (a right angle or perpendicular) or more. If the piece of paper were curved so as to be, say, the surface of a sphere, the 'laws' of Euclidean geometry fail because drawing a triangle on the surface of a sphere, all three angles can be 90 degrees for a total of 270 degrees. If you were to draw a triangle on a globe, with the equator as one edge, a line of longitude up to the north pole as another edge (the longitudinal line being a right angle), you could then draw the third edge from the poll back down to the equator on another longitudinal line that is 90 degrees of longitude from the other longitudinal line, all three angles of this globe (between the equator and each line of longitude, and between the two lines of longitude where they meet at the north pole) would be right angles.
Ore_Ele
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4/14/2011 10:35:26 AM
Posted: 5 years ago
At 4/13/2011 6:21:44 PM, badger wrote:
At 4/13/2011 6:19:42 PM, badger wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?

and even still you'd never reach the wall..

"never" implies time, therefore time is involved in the paradox.
"Wanting Red Rhino Pill to have gender"
Ore_Ele
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4/14/2011 10:42:37 AM
Posted: 5 years ago
At 4/13/2011 6:49:24 PM, Cliff.Stamp wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

Slight difference, you have to go half the distance, then etc. . Thus you have to travel an infinite number of intervals and thus can never reach the wall. The answer as you noted is that the intervals get infinitesimal and thus the time is finite.

Yes, there are infinate "intervals" however, when you say "you will never reach the end" you are bringing time, into the equation, and the limit as each interval of distance decreases, the limit approaches a constant, not infinity. And the time to travel those infinate intervals, also has a limit, which is a constant, not infinity. So the wall will be reached in a given amount of time (that constant).

In Belle's case, they were told to move every 10 seconds, and so the sum of the limit of each unit of time (in that case) is infinite.

This is really basic calculus.
"Wanting Red Rhino Pill to have gender"
Cliff.Stamp
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4/14/2011 10:45:07 AM
Posted: 5 years ago
At 4/14/2011 10:42:37 AM, OreEle wrote:

This is really basic calculus.

Note it was actually solved long before calculus, though that is the obvious solution to it now. The race problem is the same thing in a different form.
Ore_Ele
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4/14/2011 10:54:13 AM
Posted: 5 years ago
At 4/14/2011 10:45:07 AM, Cliff.Stamp wrote:
At 4/14/2011 10:42:37 AM, OreEle wrote:

This is really basic calculus.

Note it was actually solved long before calculus, though that is the obvious solution to it now. The race problem is the same thing in a different form.

Of course, but calculus is perfectly designed for such a question, and makes it so easy. There are, of course, other ways to solve it.
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badger
Posts: 11,793
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4/14/2011 12:12:00 PM
Posted: 5 years ago
At 4/14/2011 10:35:26 AM, OreEle wrote:
At 4/13/2011 6:21:44 PM, badger wrote:
At 4/13/2011 6:19:42 PM, badger wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?

and even still you'd never reach the wall..

"never" implies time, therefore time is involved in the paradox.

ah yeah.. i meant to say speed there :)
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Ore_Ele
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4/14/2011 12:52:23 PM
Posted: 5 years ago
At 4/14/2011 12:12:00 PM, badger wrote:
At 4/14/2011 10:35:26 AM, OreEle wrote:
At 4/13/2011 6:21:44 PM, badger wrote:
At 4/13/2011 6:19:42 PM, badger wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?

and even still you'd never reach the wall..

"never" implies time, therefore time is involved in the paradox.

ah yeah.. i meant to say speed there :)

if you are traveling, you are traveling at a speed (since speed is distance traveled over time, and we know there is a distance involved and there is a time involved).

Typically, this paradox is done with a constant velocity, however, you can really look at it with any kind of velocity (and function you want). And then, pending on your velocity function, you may or may not ever reach the wall.
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badger
Posts: 11,793
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4/14/2011 2:26:25 PM
Posted: 5 years ago
At 4/14/2011 12:52:23 PM, OreEle wrote:
At 4/14/2011 12:12:00 PM, badger wrote:
At 4/14/2011 10:35:26 AM, OreEle wrote:
At 4/13/2011 6:21:44 PM, badger wrote:
At 4/13/2011 6:19:42 PM, badger wrote:
At 4/13/2011 6:11:59 PM, OreEle wrote:
At 4/13/2011 5:44:34 PM, truthseeker613 wrote:
I have yet to understand zidos paradox of movement. in his question of when does the arrow move, it seems logical to me to say it moves in between interval a and b. you can keep braking it down but there will always be a "Between interval a and b". (Regarding the race every time runner b reaches were runner a was, runner a has moven forward. of all them this seems strongest. but again it boils down to the fact that an infinitely small unit of time before they meet runner a went an infinitely small distance but b did an infinitely small distance more then a.). the last paradox I simply don't understand, granted to move 1 you must move 1/2 and so on and so forth. but there for what I don't begin to understand? help is appreciated

much of it (the race ones, and the walking to a wall) are precursers to limits in calculus.

Zeno says that if you go half the distance to the wall (1/2*x), then half of that (1/4*x), then half of that (1/8*x), and so on, you'll never really reach the wall.

x= starting distance to the wall

Basically we have...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

simplified
x*(1/2 + 1/4 + 1/8 + 1/16 + ...)

If you do the sum of those fractions, you find that they get closer and closer to 1, but never quite reach it (reaching x would mean reaching the wall), so it seems that they never quite reach x, and so you never quite reach the wall.

However, there is an unseen side of this equation. And that is time. unlimited steps =/= unlimited time.

Lets say you are moving towards that wall at a constant rate of speed, we'll call "v".

So the time it takes to travel a distance of "x" at velocity "v" is x/v, and we'll call that "t"

So lets look at each unit that we are traveling.

1/2*x, that section would take 1/2*t time to travel.
1/4*x, that section would take 1/4*t time to travel.
1/8*x, that section would take 1/8*t time to travel.
and so on.

so the time to travel...
1/2*x + 1/4*x + 1/8*x + 1/16*x + ...

would take a time of...
1/2*t + 1/4*t + 1/8*t + 1/16*t + ...

simplified as
t*(1/2 + 1/4 + 1/8 + 1/16 + ...)

From this we can see that the time taken approaches a fixed amount of time "t" rather than an infinite amount of time. So, mathematically, we can see that we will reach the wall in time "t," and the notion that we will never reach it, is effectively disproven.

you can't do that.. time has nothing to do with the paradox.. let's say you were teleporting from each half distance to the next.. would you reach the wall ever?

and even still you'd never reach the wall..

"never" implies time, therefore time is involved in the paradox.

ah yeah.. i meant to say speed there :)

if you are traveling, you are traveling at a speed (since speed is distance traveled over time, and we know there is a distance involved and there is a time involved).

Typically, this paradox is done with a constant velocity, however, you can really look at it with any kind of velocity (and function you want). And then, pending on your velocity function, you may or may not ever reach the wall.

but you don't even have to be travelling for this paradox.. you could just be taking endless mid points along a line.. which i suppose would be fairly impossible for us.. but theoritically.
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