An effort to solve Zeno's motion Paradoxes

[Canute]

Who said anything about infinties in finite space?

 

[Mr. Robin Parsons]

Originally posted by Canute
Who said anything about infinties in finite space?

YOU posted it! I've already quoted it from YOUR post..."The whole length contains an infinite number of finite parts." that is a finite length containing an infinity (Of finite parts! too!) according to what YOU posted!


Do you Understand that?

 

[Canute]

Originally posted by Mr. Robin Parsons
YOU posted it! I've already quoted it from YOUR post..."The whole length contains an infinite number of finite parts." that is a finite length containing an infinity (Of finite parts! too!) according to what YOU posted!

Do you Understand that?

Oh yes. Your change of words confused me.

But you have completely missed the point. It is utterly absurd to think that a finite length can have an infinite number of finite parts. That's why there is a paradox, as the quote I posted quite clearly points out. Why do you then argue that it's impossible? Of course it's impossible. Everyone agrees about that.

 

[selfAdjoint]

Originally posted by Canute
Oh yes. Your change of words confused me.

But you have completely missed the point. It is utterly absurd to think that a finite length can have an infinite number of finite parts. That's why there is a paradox, as the quote I posted quite clearly points out. Why do you then argue that it's impossible? Of course it's impossible. Everyone agrees about that.

What absolute bilge. Nobody but a few cranks believes that. The real line between 0 and one, a finite length, contains points in one to one correspondence with the decimal fractions 0.a₁a₂a₃... and there are infinitely many of those.

Or you can do the dichotomy. Divide this interval in two at its midpoint. Do you say that one of these halves contains NO points? If not divide each of the halves again. Where do you stop? What evidence have you, beyond your own prejudice, that we need ever stop?

 

[Canute]

You are confusing mathematics with reality. Of course it's possible to hypothesise that there are are infinite finite points between every two points. All one need do is assume that spacetime is infinitely divisible into infinitessimal but finite quanta. The point is that this assumption is incoherent and leads to paradoxes.

You yourself said "...ha ha ha another 'self-fooly') to begin with, and you cannot have an infinity within a finite thing...except in math THEORY!".

So call it bilge when I agree with you?

 

[Mr. Robin Parsons]

Originally posted by canute
All one need do is assume that spacetime is infinitely divisible into infinitessimal but finite quanta.

Yes assume, but reality tells us very clearly about a Planck length, ergo, unless you can prove that wrong, your assumtion remains simply that, and it isn't me that it makes look like an ...assuming that is theoretical, not reality, and/so there is no 'paradox' to it, simply a self deception upon the idea of being able to number an infinity, you can, not!

The idea of (n + 1) as being representative of counting to the infinite is a self deception...no matter how large you got, measure the 'other' side, (means make it "times two" (n + 1) x 2 ...simple) none the less, you cannot 'number' an infinity, it is uncountable...so there isn't even really a paradox, just some confusing (ill)logic...

(n + 1) represents an 'activity' not a 'thing' infinity would be a 'thing'

 

[selfAdjoint]

Originally posted by Canute
You are confusing mathematics with reality. Of course it's possible to hypothesise that there are are infinite finite points between every two points. All one need do is assume that spacetime is infinitely divisible into infinitessimal but finite quanta. The point is that this assumption is incoherent and leads to paradoxes.

You yourself said "...ha ha ha another 'self-fooly') to begin with, and you cannot have an infinity within a finite thing...except in math THEORY!".

So call it bilge when I agree with you?

I have scrolled through this entire thread and can't find any post by me that fits your characterization. I posted twice before, once with my conjecture about Zeno's intent, and once to correct the belief that quantum mechanics forces space or time to be discrete. Even LQG doesn't reduce to chunks of space: they have area quantized, so when you observe it you find one of a set (which might be continuous) of eigenvalues. There is no reason in experiment or theory to assume space is discrete.

 

[Mr. Robin Parsons]

Originally posted by selfAdjoint
I have scrolled through this entire thread and can't find any post by me that fits your characterization. I posted twice before, once with my conjecture about Zeno's intent, and once to correct the belief that quantum mechanics forces space or time to be discrete. Even LQG doesn't reduce to chunks of space: they have area quantized, so when you observe it you find one of a set (which might be continuous) of eigenvalues. There is no reason in experiment or theory to assume space is discrete.

Thats probably because part of what he quoted is from me, this part...

Originally posted by MRP
You yourself said "...ha ha ha another 'self-fooly') to begin with, and you cannot have an infinity within a finite thing...except in math THEORY!".

canute apparently ascribed it to you though, sooooo...it is mine...Ooops it isn't "ascribed" it is just posted my error, sorry! still it should have been as to avoid this kind of confu'i's'on, right?

 

[Canute]

Yeah sorry - something very strange is going on here which I can't figure out. Posts keep disappearing and swapping pages.

Self-Adjoint - I don't know why you thought my post was to you but it wasn't. from what you say I agree with you.

 

[Visitor]

Wheres the paradox? When you define the parameters to come to a certain result there is no paradox. Besides, brownian motion would eventually be greater than the distances traveled and the races would be over. Zeno never said anything about his thought experiments taking place at absolute zero.

Foolish humans.

 

[Mr. Robin Parsons]

Yikes! one last time, you cannot use a finite tool, (math) to measure an infinite "thing", or "an infinity"...to think that you can, is to indulge yourself in an absurdity...

"Ad Infinitum / Ad Absurdum"

 

[theophoretos]

zeno was not wrong

Zeno was not wrong with his paradoxes of motion. These paradoxes are meant to point up the logical flaws inherent in our everyday conception of space, time, and motion which has been quantitatively codified in the classical mechanics. Since this logical flaws have been definitively shown in relativity and quantum mechanics, it'd be productive to solve Zeno's paradoxes, not with mathematics, but simply with the principles of new physics. I think that the paradoxes up to the last one simply imply the quantized notion of space and time and the uncertainty principle (this has been vaguely stated by Peter Lynd's article), while the last, most important of statium shows that in order for space and time to be quantized, a maximum cap on velocity has to be posited, the speed of light. In other words, there is a relation of logical mutual implication between quantum mechanics and special relativity. I wrestled with this problem here:
http://www.geocities.com/therapeuter/capra7777.html

I hope no one trivalizes Zeno by positing that he was not smart enough to even understand some basic notion or that he was playing logical tricks; and the philosophical background for the paradoxes is equally important to take account of.

 

[Canute]

Good point about not trivialising Zeno. But I don't agree that his paradoxes show c to be an upper limit to velocity. How do you get that result?

 

[selfAdjoint]

It's in his discussion of the fourth case, where both space and time are discrete and objects (represented by rows of "atoms") pass each other. A paradox arises in which a speeed is seen to be twice as big as itself. And he concludes that the formula for addition of velocities must be modified. Theophoretos exhibits the familar relativistic law, but I didn't see where he proved that is the one, rather than some other variation on [tex]v_1 + v_2[/tex].

 

[Mr. Robin Parsons]

How many 'spaces' can you count in an empty space??...and to apply Xeno to it, when you arrive at any answer, divide by 2, and keep going...


Can you figure it out from there?

 

[UltraPi1]

How many 'spaces' can you count in an empty space??...and to apply Xeno to it, when you arrive at any answer, divide by 2, and keep going...

Assuming that the empty space is infinite in scale - There is an infinity of spaces possible. Whether the spaces are the size of plank, or the size of a breadbox ... Pick your poison - Then stick with it. Now if you assume that these spaces don't appear all at once - It will take forever to complete the task. In the mean time - Think of those existing spaces as moving around with laws regarding their movement of course. Therein lies our universe of discrete spaces that move in a world without halfway points to the infinite degree.

 

[Mr. Robin Parsons]

Originally posted by UltraPi1
Assuming that the empty space is infinite in scale - There is an infinity of spaces possible. Whether the spaces are the size of plank, or the size of a breadbox ... Pick your poison - Then stick with it. Now if you assume that these spaces don't appear all at once - It will take forever to complete the task. In the mean time - Think of those existing spaces as moving around with laws regarding their movement of course. Therein lies our universe of discrete spaces that move in a world without halfway points to the infinite degree.

Assume that an empty space is defined by the FACT of the NON empty space around it and, wake up!

 

[UltraPi1]

Assume that an empty space is defined by the FACT of the NON empty space around it and, wake up!

Not sure I follow. I'm curious as to where this empty space is - Certainly not in our neck of the woods. That means you have to leave the forest to the land of nada where there is no such animal as non-empty surrounding empty. I understand the point you were making, but your point is impossible to conceive by your parameters last I heard. My last post was simply conforming to the laws of reality, or non-existence if you will, where your's did not. If you want to have an empty space .. I can guarantee it won't have non-empties surrounding it. At least not by your accounts.

I replied to your post because the universe is the definition of an infinite empty space by conceptual means. It is defined with discete entities on an ongoing basis. The point I was making is that the universe will never be halved out, because you can never reach the a count of spaces within the infinite space. Not that the discrete spaces can't be halved out, but that they never will be. You choose to do so. The universe says otherwise.

Zeno is saying - If space is infinitely divisible you can never go from point A to B because first you must cross halfway point C to get to B, and so forth and so on, blah, blah, blah. One key point to be made is that there are no points in an infinitely divisible space between two points. Any attempt to do so leaves you with a finite structure by which you could never reach a conclusion as to the viability of a motion from point A to B where the space is infinitely divisible. In principle - No proof is possible for an infinitely divisible space. Either space is infinitely divisible, discrete, or both. I say it is discrete entities that are potentially infinitely divisible.

 

[Mr. Robin Parsons]

What Xeno accomplished is to use a language, math, to get you to fool yourself into thinking that you could count all of the empty spaces in an empty space...Math is a language, and a tool, and is subject to abuse, and misuse, and mis-interpretations, just like everything else, in languages.

Usually when you count, you count something, (Items, existent items) but here, in the case with Xeno's application, he has gotten you to count the "empty spaces" in an empty space, AKA "Infinity" as math attempts to reveal it...it can't, BTW...

Much past that and you are just fooling yourself...

 

[UltraPi1]

Usually when you count, you count something, (Items, existent items) but here, in the case with Xeno's application, he has gotten you to count the "empty spaces" in an empty space, AKA "Infinity" as math attempts to reveal it...it can't, BTW...

You might find this a little nutso, but I think the whole purpose of the universe is to count (create) the finite empty spaces of an infinite space. This process is ongoing and will take forever to complete. Keep in mind that I consider existence to be purely conceptual. There are no physical entities. They only come across to you as being that way.
So your existence is a hodge podge of conceptually discrete empty spaces, and each space acts in accordance with our known physical (conceptual) laws.

 

[Canute]

Hmm, do you know the 'The Jewel Net of Indra'?

 

[Mr. Robin Parsons]

Originally posted by UltraPi1
You might find this a little nutso, but I think the whole purpose of the universe is to count (create) the finite empty spaces of an infinite space. This process is ongoing and will take forever to complete. Keep in mind that I consider existence to be purely conceptual. There are no physical entities. They only come across to you as being that way.
So your existence is a hodge podge of conceptually discrete empty spaces, and each space acts in accordance with our known physical (conceptual) laws.

Nothing, well written, in a philosophy forum, should be considered "nutso", especailly not the expression, simply, of idea/concepts/and/or/thoughts...so don't worry bout that..

It begs metaphysical, inasmuch as, resolving the Idea of 'Infinite', with existence, requires understanding(s) like; "In an infinity, the center can be everywhere!" as 'material existence' and 'Infinite' seem incompatable otherwise...but Xenos is a play 'tween Theory of math (language of math) and perception(s) of reality...

In a singular 'empty space' you could count to x ? Infinity? (absurdity) the number of "empty spaces" (non-existant) you could find, in there, then, A'la Xeno, when you think you have gotten them all, halve the space that that amount of numbers 'occupies', and keep counting!

(has the absurdity become clear to you, in that example?)