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Zeno's Paradox Concerning Time

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farid-A
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Zeno's Paradox Concerning Time

Post by farid-A » November 30th, 2019, 12:55 pm

Hi everyone,

This thread is about Zeno's paradox concerning time being impossible. Zeno claimed that time cannot exist, but merely an illusion of it. The reason for the claim is Zeno's claim that for one second to pass, half of it must pass first, and half of a half of a second must pass before half a second passes, and so on and so on ad infinitum, thus he claimed that time cannot pass.

Time is number of moments that have passed. There cannot be a fraction of a moment. The smallest unit of a moment is one. The number that the number of moments increase by is one. So, if five moments have passed, it is not true that two and a half moments first passed, and one and a quarter of moments passed before that, and so on and so on. Here is how it went, one moment passed, then two moments, then three, then four and finally five.

A second is equal to X number of moments. I, at the moment do not know how many moments are a second.

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Pantagruel
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Re: Zeno's Paradox Concerning Time

Post by Pantagruel » December 2nd, 2019, 1:48 pm

I think the classical interpretation is that what you have described is the fallacy at the heart of the paradox. Space may be infinitely divisible but time is not. Otherwise you arrive at the conclusion that motion is impossible.

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Greta
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Re: Zeno's Paradox Concerning Time

Post by Greta » December 2nd, 2019, 6:40 pm

Yes, as per above, time is not divided in itself (things keep on changing) so the infinity is a mathematical one.

Unless you are approaching the speed of light or in a black hole, time does not compress up to a stop in that way. So, for us, after the first half second passes, so does another.

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PAntoneO
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Re: Zeno's Paradox Concerning Time

Post by PAntoneO » December 3rd, 2019, 1:05 am

farid-A wrote:
November 30th, 2019, 12:55 pm
Hi everyone,

This thread is about Zeno's paradox concerning time being impossible. Zeno claimed that time cannot exist, but merely an illusion of it. The reason for the claim is Zeno's claim that for one second to pass, half of it must pass first, and half of a half of a second must pass before half a second passes, and so on and so on ad infinitum, thus he claimed that time cannot pass.


I think the reason this is a false statement is because the infinite series
1/2, 1/4, 1/8, 1/16, 1/32...
is equal to 1, not infinity.

You can demonstrate this for yourself by drawing a square. Divide it in half, then divide the half on the right in half. Then divide that half in half, and continue in this manner until your pencil is thicker than the space you're dividing. What you'll notice is that you never actually need to jump outside of the box in order to include the next half.Thus, just as we would expect at a common sense level, one second divided into infinitely many halves simply equals one second. It doesn't equal an infinite amount of time.
farid-A wrote:
November 30th, 2019, 12:55 pm
Time is number of moments that have passed. There cannot be a fraction of a moment. The smallest unit of a moment is one. The number that the number of moments increase by is one. So, if five moments have passed, it is not true that two and a half moments first passed, and one and a quarter of moments passed before that, and so on and so on. Here is how it went, one moment passed, then two moments, then three, then four and finally five.

A second is equal to X number of moments. I, at the moment do not know how many moments are a second.
I think the most logical answer would be that there are an infinite number of moments in a second--just as there are an infinite number of halves. But each half is also progressing towards being infinitely small. The moment is the conceptually actualized smallest infinite fraction.

It's a lot like saying that when you actualize [.999...] (or complete it to infinity) it is necessarily equal to 1.0. You can't really actualize [.999...], but if you could, it would necessarily have to equal [1.000...] In the same way, you can't really reach the infinitely smallest fraction, but if you could, it would be the "moment" that you speak of.

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Re: Zeno's Paradox Concerning Time

Post by Pattern-chaser » December 6th, 2019, 11:21 am

Zeno simply notes that, if you halve the interval, the distance travelled in also halved. And he carries on dividing, and the intervals and the distances carry on halving too ... and then he adds on the totally unjustified conclusion that time cannot exist. I have never worked out how this could be seen as a paradox. It's just a misunderstanding, isn't it? 🤔
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Re: Zeno's Paradox Concerning Time

Post by Pantagruel » December 6th, 2019, 11:34 am

You have to imagine time stopping, but as Greta said, thing keep on changing. It is something that looks prima facie plausible, and makes you think, so I guess it serves a purpose?

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Re: Zeno's Paradox Concerning Time

Post by Greta » December 6th, 2019, 5:40 pm

And time doesn't break into ever smaller divisions. It's like walking up to a wall, taking ever smaller steps. Since time has no wall, one can simply keep walking.

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detail
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Re: Zeno's Paradox Concerning Time

Post by detail » Yesterday, 11:34 am

Well in fact the measurement of small times smaller than 10^{30} s is somewhat difficult , if time is quantizied the could be a heisenberg uncertainty principle in it.

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