LAUGHED OUT OF COURT

"His second disagreeable assumption is that an infinite series doesn't have a finite sum"

I was never aware this was an assumption of Zeno.

That an infinite series has a finite sum is a premise used in an attempt to resolve the paradox but Zeno does not care about convergent series but only of the infinite intervals he has to travel. So how the infinite series convergence is related to infinite intervals to travel can only be accomplished through a supposition of a mechanism of instantaneous velocity (fluxions) that can be defined at an exact point in space(fluent), which in the first place is contradictory to the premise of infinite divisibility, that is instantaneous velocity cannot be defined without dropping the infinitesimal out of the equation, which in turn makes the use of this particular premise useless in the context of the argument, simply because it is purposely designed to self-contradict the main premise by implicitely denying the premise.

Conclusion: You cannot fundamentally explain motion using motion and prevent logical circularity and that is done with the convergent series argument.

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"His second disagreeable assumption is that an infinite series doesn't have a finite sum"

I was never aware this was an assumption of Zeno.

That an infinite series has a finite sum is a premise used in an attempt to resolve the paradox but Zeno does not care about convergent series but only of the infinite intervals he has to travel. So how the infinite series convergence is related to infinite intervals to travel can only be accomplished through a supposition of a mechanism of instantaneous velocity (fluxions) that can be defined at an exact point in space(fluent), which in the first place is contradictory to the premise of infinite divisibility, that is instantaneous velocity cannot be defined without dropping the infinitesimal out of the equation, which in turn makes the use of this particular premise useless in the context of the argument, simply because it is purposely designed to self-contradict the main premise by implicitely denying the premise.

Conclusion: You cannot fundamentally explain motion using motion and prevent logical circularity and that is done with the convergent series argument.


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The convergent series argument illustrates that you can divide any finite distance into infinite parts but the distance is still finite. I don't see how it follows that an object must have instantaneous velocity to traverse this finite distance. I suppose we would have to assume that objects have a smallest size, but that is only an inconvenience and does not prevent it from moving through space, whether the space be divided into smallest sizes or is infinitely divided into smaller and smaller sizes.

Knowing how space is divided cannot prove whether motion is possible or not. No, this is like looking at a smoothly paved road and one filled with potholes and arguing that driving is impossible in both cases. In the first, Zeno would have argued, the car would've had to drive half a mile before he reaches a mile, and half of half a mile before he drives half a mile, ad infinitum. In the second, Zeno would've said that since at each pothole, he is not on the road so he isn't really driving, so he can't drive.

He would've been wrong here as he was in his paradoxes, and mostly because he didn't care how motion was accomplished (e.g. how the car moves), but was blindly focused on the condition of the road.

The most the road- or space, can tell you about motion is on whether your ride will be bumpy or smooth.

I'm going to take a quick dip here, though I probably won't stay in the water long. I offer this only for what it's worth.

First: I think it was a mistake from the get-go to invoke an ancient philosophical theory (or whatever you want to call it), to prove or support a serious scientific hypotehesis.

Second: If I'm correct in assuming that all of Zeno's paradoxes are deductive exercises to demonstrate some properties of motion or to illustrate apparent contradictions (paradoxes) in common sense beliefs about motion; then I say this: deductions are only exercises, formulations, or formulas which prove nothing unless the premise(s) on which they are based are true (i.e. are consistant with reality). Since we do not know if matter is infinately divisable or whether there is some "smallest" (or largest) particle, instead, we do not then posess the knowledge to form the basic premises on which to proceed.

Third: My sense is that to make his points, Zeno used tricks of logic. My sense is also that many philosophical inquiries (like the ones debating this issue), are far too arcane, complicated, rationalistic, and "a priori," to be of much scientific use. That's all I'll say, except to add that the most lucid statement I've yet seen on this subject was made by 123.. to show that the paradoxes can't hold water, and is as follows.

[123...]1- In the infinitely divided space paradox, he assumes that a finite object can travel infinitesmally small distances. Another flawed assumption is that the time it takes to travel smaller distances adds up to infinity, when it's actually an inverse relationship with the distance. Or that an object cannot even begin to move because of the way the space is divided. The list goes on and on, and if we changed but one of these premises, we can show a contradiction.

2. In his arrow paradox, he assumes that a moving object is the same as a non-moving object at each instant in time. Actually, this paradox is really a semantics trick: he defines each instant of the arrow's motion as at rest and then uses this definition to conclude that since an arrow is at rest at every instant, it is not moving. What's the word for this- tautology?

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I'm going to take a quick dip here, though I probably won't stay in the water long. I offer this only for what it's worth.

First: I think it was a mistake from the get-go to invoke an ancient philosophical theory (or whatever you want to call it), to prove or support a serious scientific hypotehesis.

Second: If I'm correct in assuming that all of Zeno's paradoxes are deductive exercises to demonstrate some properties of motion or to illustrate apparent contradictions (paradoxes) in common sense beliefs about motion; then I say this: deductions are only exercises, formulations, or formulas which prove nothing unless the premise(s) on which they are based are true (i.e. are consistant with reality). Since we do not know if matter is infinately divisable or whether there is some "smallest" (or largest) particle, instead, we do not then posess the knowledge to form the basic premises on which to proceed.

Third: My sense is that to make his points, Zeno used tricks of logic. My sense is also that many philosophical inquiries (like the ones debating this issue), are far too arcane, complicated, rationalistic, and "a priori," to be of much scientific use. That's all I'll say, except to add that the most lucid statement I've yet seen on this subject was made by 123.. to show that the paradoxes can't hold water, and is as follows.

[123...]1- In the infinitely divided space paradox, he assumes that a finite object can travel infinitesmally small distances. Another flawed assumption is that the time it takes to travel smaller distances adds up to infinity, when it's actually an inverse relationship with the distance. Or that an object cannot even begin to move because of the way the space is divided. The list goes on and on, and if we changed but one of these premises, we can show a contradiction.

2. In his arrow paradox, he assumes that a moving object is the same as a non-moving object at each instant in time. Actually, this paradox is really a semantics trick: he defines each instant of the arrow's motion as at rest and then uses this definition to conclude that since an arrow is at rest at every instant, it is not moving. What's the word for this- tautology?







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Thx for the compliments. Even as a deductive exercise, I think
the Zeno paradoxes are contradictions. Zeno's conclusion- that there is no motion- is provably false, so his premises must be false also,
according to Enrico's truth table where if Q (the conclusion that there is no motion) is false, then for P-->Q to be true, p (Zeno's premises) must be false as well.

I.e., If we had started out with the premise instead that there is no motion, Zeno's logic quickly falls apart.

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Infinitesimals seem to work magically.
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That may be your opinion but it is not the opinion of many engineers and scientists the use it daily.

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Calculus, a product of Newton is not different from his laws in the sense that a total ignorance of cause and effect is clear.
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Well perhaps what you are calling ignorance is getting a system that conforms with what one actually observes versus what one believes to be false despite one's senses. I don't see how anyone can look at Newton's work and conclude that he was ignorant. Zeno contributed nothing of practical value to physics whereas Newton provided us with the beginning of gravitation theory and orbital mechanics.

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Newton and people who use infinitesimals in nowadays are not interested in causes of motion but only in practical results of motion effects, and that is ok. But many philophers and Physicists are interested in discovering the cause of motion and what space-time is made of and this is where Zeno's paradox apply.
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You repeat several statements that make no coherent sense to me. There is no "cause" to motion in a universe with an infinite past, it simply is. Every system of thought must accept certain axioms and motion is one of them. Similarly, speaking of what space-time is made of puzzles me because space and time are not PHYSICAL things with PHYSICAL properties such as composition, electrical conductivity etcetera.

The "Laughed out of Court" scenario is a different rendition of what has been called by others "The McCoin Paradox". I did propose the problem but had not named it.

It involves using three (3) clocks to test the Theory of Relativity.

Clocks
"C" is assumed at rest on Earth. v = 0
"A" is assumed traveling away from Earth at v = 0.2c
"B" is assumed traveling away from Earth at v = 0.3c

To simplify the problem and to concentrate on the pure concept that linear relative velocity produces time dilation, the test are done only at pre-stipulated velocities, for the stipulated test time and are stopped, then returned to Earth for a side by side comparison.

I just proposed this test on another web site and got numerous physicist to join in. They objected to the start/stop requirements but ultimately agreed to stipulate precise starting of the clocks by assuming instant acceleration to stipulated test velocity. That wasn't necessary but to do so simplifies doing the test.

Having done so, "They" did their calculations but immediately saw that there was going to be a problem and began making all sorts of excuses why the test couldn't be done.

I let them dig their own hole along the argument they made that "It is impossible to stop all clocks in real time at the same time"

I argued that you merely stipulate it. After all we are only testing the assumption of time dilation, not the mechanics of how to control the clocks.

They refused to so stipulate. When I told them it was possible they shifted the burden for the test to me to prove that I could devise a method of synchronizing the clocks. After due delay and declining to do so, allowing them to all gang upon me saying that was because it was impossible and therefore the calculated results "WHICH THEY MADE" were invalid. I posted the following.

*****************
Sync
1 - Velocity is stipulated from clock C.

2 - Each observer sees his clock function normally but in accordance with relativity it should dilate relative to C

3 - You have already agreed to stipulate instant acceleration to test velocity so as to simplify the test analysis and the starting of the clocks.

4 - You are testing time dilation by relavistic velocity and you are testing a formula that predicts that relative to clock C.

5 - You simply set each clock to the calculated test time per clock C.

Clock C Set to 10 hours

A Set to 9 hours 47.88 minutes

B Set to 9 hours 32.36 minutes

Now if you would like to argue that the clocks will not all stop at the same time relative to clock C (the master test clock)? What can I say?


So tell me now what are the clock dials for each observer case below.


1 - Observer C: Delta A/B
2 - A: Delta A/B
3 - B: Delta A/B
4 - A: Delta C/B

**********
Here is the type of responses I got(some I can't repeat here<img src=icon_smile_big.gif border=0 align=middle>. Like this one which has been editied by managesment:


QUIT AVOIDING MY QUESTION, ****: SHOW ME HOW YOU CAN DESIGN A PHYSICAL MECHANISM FOR STOPPING THE CLOCKS "AT THE SAME INSTANT."

The *** went something like "YOU F______ IDIOT", all in 1 1/12 inch high bold print.<img src=icon_smile_big.gif border=0 align=middle>



****
Warren

Moderator edit: Personal insults add nothing useful to the discussion.


Edited by James R on 02-22-03 at 05:55 AM

**********

Here was my final post:

Trapped
chroot,

You are trapped and you know it. You can't have it both ways.


quote:
****************
This is a joke. If you stipulate that the clocks stop at some particular reading, then you no longer have an experiment. The effect you seek to measure, time dilation, will not be measured.
****************

Stop trying to confuse the people. If the clocks didn't stop at those times they would not according to your precious Relativity stop simultaneously. Now you want to object to the use of Relativity to conduct the test. the very theory you say works.

You have already done all the calculations so since you seem to want to resist posting your own results and since I have succeeded in meeting all the terms of the test stipulation, I guess I will have to post the data for you.

**************************************:Hours
1 - Stipulated test time by clock C************:10.000
2 - C's view of Clock A:**********************9.798
3 - C's view of Clock B***********************9.539
4 - Differential predicted by C for (A-**********0.259
5 - Differential predictied by A for (A- :*********0.048

Since #4 and #5 are not in agreement your physical clock must be capable of possessing two different time losses simultaneously.

Seems to me you lose. And I don't even need to resort to the other impossible conclusions where even more clock errors exist by looking at what B predicts.
************************
Another Response:
************
You can't be this stupid... you aren't testing a damn thing except that the clock isn't broke. If you stop all the clocks when the clock says a specific time, of course they will all be the same when brought back together.
*************

quote:
****************
Listen, Mac... if you can't come up with a mechanism to MAKE (not INFER) the clocks stop at the same instant, just let it go. Maybe you learned something from this experience.
***************

So you refuse to trust Relativity to stop the clocks? That is strange indeed.

I think it is you that learned something from this experience. At least I would hope so.

Personally I thought using Relativity to prove Relativity has conflicts was pretty damn neat.

And I thought making you deny Relativity or accept clock timing was also not bad for a crackpot. Especially since you mouthed off so loudly that timing the clocks was impossible.

You know what your problem really is? You think memorizing what others have figured out before you makes you smart but you have never learned to think for yourself.

That is the difference between being educated and intelligent.
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One (the only one favorable response I received back). No need to post the many other response I got back. I think you can guess what they were like.<img src=icon_smile_big.gif border=0 align=middle>

You have him trapped, but you know that he'll never admit it. Neither will any of the other relativists on this forum, but they will remember it. Rest assured that there are a lot of people watching from the sidelines, and what they saw is what really matters. They will be the ones that will spread the "three clock paradox".

Tom

*********************

Thought the group might need a few laughs. This went on for three days building to the conclusion. I have re-read the string and my sides are still hurting and got to wipe the tears of laughter out of my eyes.
****************

"IF ONE MERELY ASSUMES RELATIVITY IS VALID THEN YOU CAN PROVE IT IS INVALID"

Any comments?