Zeno's Paradox

[bobhikes]

Is this seeing it the same way? Imagine this conversation.......
Zeno: I have a goofy way of looking at distance.
Swampy: How's that?
Zeno: I know I can walk from my chair to the bacon on the counter, but no matter how far I walk, I have another half-way to walk.
This can go on infinitely. If it goes on infinitely, then I have an infinite number of half-distances to cross. I can't do an infinite
number of things, so it would seem I could never get there. Yet here I am, munching on that bacon.
Swampy: It sounds like you're just wrestling with problems created by definitions & an inability to quantify the total distance of
your infinite number of half-way steps. Since you're eating my bacon, your model of reality must be wrong.
Zeno: That's the paradox....my model says I'll never get there.
Swampy: There is no paradox, just an error in your goofy method.
Zeno: You sure have a lot of scales for a human.
Swampy: True dat. Now you've eaten all my bacon, which proves that your infinite number of distances add up to a finite distance......reductio ad bacum.
Zeno: Fool! You've converted math from an a prior science to a posteriori. There goes civilization!
Swampy: [His tail just flits about in self satisfaction.]

My conclusion as well. From an old coach always run through the finish line. Set your goals farther then just getting there and you know what you'll get there.

 

[swamplizard]

Is this seeing it the same way? Imagine this conversation.......
Zeno: I have a goofy way of looking at distance.
Swampy: How's that?
Zeno: I know I can walk from my chair to the bacon on the counter, but after walking half-way, I still have another half-way to walk.
This can go on infinitely. If it goes on infinitely, then I have an infinite number of half-distances to cross. I can't do an infinite
number of things, so it would seem I could never get there. Yet here I am now, munching on that bacon.
Swampy: It sounds like you're just wrestling with problems created by definitions & an inability to quantify the total distance of
your infinite number of half-way steps. Since you're eating my bacon, your model of reality must be wrong.
Zeno: That's the paradox....my model says I'll never get there.
Swampy: There is no paradox, just an error in your goofy method.
Zeno: You sure have a lot of scales for a human.
Swampy: True dat. Now you've eaten all my bacon, which proves that your infinite number of distances add up to a finite distance......reductio ad bacum.
Zeno: Fool! You've converted math from an a prior science to a posteriori. There goes civilization!
Swampy: [His tail just flits about in self satisfaction.]

Yes, yes ,yes... I love it Rev !!!
Don't get me wrong, Math is a useful tool, but not the true rule; as Xeno and Bobby have pointed out here, measurement is conceptual; the universe has no song for it. I have enjoyed reading the many mathematical comments posted here by some evident minds. To surrender to the paradox of (mis)measurement is to become aware of the infinite within the one (just a fool's observation from inner space).

BTW, that ain't my tail that's satisfied in its jubilent cavorting.

best,
swampy

 

[atanu]

I was hoping that someone would bring in the time element to Xeno's Paradox. Placing these mathematical "certainties" together provides the conclusion that beginnings and endings are merely mental designs aligned with the thoughts generating finite values.

Thanks Scott,
best,
swampy

I believe that Xeno himself did that with his three paradoxes related to motion.

… that the flying arrow is at rest, which result follows from the assumption that time is composed of moments … . he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. (Aristotle Physics, 239b.30).

Zeno's Paradoxes (Stanford Encyclopedia of Philosophy)

 

[swamplizard]

I believe that Xeno himself did that with his three paradoxes related to motion.

… that the flying arrow is at rest, which result follows from the assumption that time is composed of moments … . he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. (Aristotle Physics, 239b.30).

Zeno's Paradoxes (Stanford Encyclopedia of Philosophy)

Great input atanu, thanks.

best,
swampy

 

[Tiberius]

Of course, crossing an infinitely small distance takes an infinitely short time, so one can cross an infinite number if infinitely small distances in a finite time.

 

[swamplizard]

Of course, crossing an infinitely small distance takes an infinitely short time, so one can cross an infinite number if infinitely small distances in a finite time.

Greetings Tiberius,

Is time exempt from infinite division? Is there any unit of anything that cannot be divided? I think Xeno demonstrates the futility of believing in absolute mathematical certainty.

Replace zero on the number line with arrows pointing inward.

Just some more bogginess from the swamp,
bestest,
swampy

 

[St Giordano Bruno]

You may just keep halving the distance until you come down to a Planck length unit which would effectivly make it finite.

 

[Revoltingest]

You may just keep halving the distance until you come down to a Planck length unit which would effectivly make it finite.

Why? Is there evidence that nothing can be shorter?

 

[religion99]

Is this seeing it the same way? Imagine this Zeno: Fool! You've converted math from an a prior science to a posteriori. There goes civilization!
Swampy: [His tail just flits about in self satisfaction.]

Shortest and most accurate definition of modern math and science ( and atheism by extension )

 

[ManTimeForgot]

Why? Is there evidence that nothing can be shorter?

Plank Time is the shortest possible unit of time that the universe seems to support. A Plank Length is the shortest possible unit of distance that the universe seems to support.

One shouldn't go so far as to say that nothing can be shorter in an absolute sense; I'm quite positive that if there are alternate dimensions, then some hyperdimensional distance can be shorter, but the rules of physics as we understand them do not allow for shorter distances. And if you start asking about "Well what about outside the universe...?" We lack the scope to even speculate properly on that. Could be the hyperuniverse of giant oranges only supports larger distances...

MTF

 

[Revoltingest]

Plank Time is the shortest possible unit of time that the universe seems to support. A Plank Length is the shortest possible unit of distance....

Why is this presumed to be so?

 

[atanu]

Why is this presumed to be so?

Theoretically, the structure of spacetime becomes dominated by quantum effects only and space and time will lose meaning.

 

[Revoltingest]

Theoretically, the structure of spacetime becomes dominated by quantum effects only and space and time will lose meaning.

I still don't see why this presumption must be so.
Quantumization of electron energy levels is demonstrable.
Where is the evidence that time behaves that way too?
Or is this just speculation being proffered as fact?

 

[atanu]

I still don't see why this presumption must be so.
Quantumization of electron energy levels is demonstrable.
Where is the evidence that time behaves that way too?
Or is this just speculation being proffered as fact?

It is mathematical (I sneaked behind and am now occpying the seat of PolyHedral).

Planck time - Wikipedia, the free encyclopedia

 

[Revoltingest]

It is mathematical (I sneaked behind and am now occpying the seat of PolyHedral).
Planck time - Wikipedia, the free encyclopedia

I was already familiar with that article, which places no such restriction upon time.
It appears to simply be a unit of time, as is a "second".
I still see no reason that time cannot be continuous, ie, "smooth".

 

[atanu]

I was already familiar with that article, which places no such restriction upon time.
It appears to simply be a unit of time, as is a "second".
I still see no reason that time cannot be continuous, ie, "smooth".

That article says: for times less than one Planck time apart, we can neither measure nor detect any change.

As far as I know, at Planck length or less, the force fields are unified. Separation of fields happen at greater than Planck length.

 

[atanu]

You may just keep halving the distance until you come down to a Planck length unit which would effectivly make it finite.

No. For times less than one Planck time apart, we can neither measure nor detect any change.

Parmenides and Zeno logically show that pluralism and the reality of any kind of change are illusory. This goes down well for me. There is, IMO, no logical refutation of Zeno's paradoxes. He showed that denial of Parmenides' views lead one to absurd conclusion. If there are many things, then it leads to the conclusion that everything is both infinitely small and infinitely big. If one takes for granted that motion is infinitely divisible, then it follows that nothing moves.

A genius he was, although we may think him crazy as his conclusions are so much contrary to sensual beliefs. Logically there is no rebuttal, nevertheless. Take it or leave it.

 

[Revoltingest]

That article says: for times less than one Planck time apart, we can neither measure nor detect any change.
As far as I know, at Planck length or less, the force fields are unified. Separation of fields happen at greater than Planck length.

The inability to measure some thing does not mean that the thing itself is not there.
I'll file "quantized time" in my "fanciful speculation" folder.

 

[St Giordano Bruno]

The inability to measure some thing does not mean that the thing itself is not there.
I'll file "quantized time" in my "fanciful speculation" folder.

Have you any scientific evidence of a half a Planck length?

 

[Revoltingest]

Have you any scientific evidence of a half a Planck length?

I have none whatsoever.
I simply see no good reason to accept the belief that shorter times cannot be.