- #1

- 5

- 0

The same is true with time, and as the number of divisions goes to infinite the time to cross those divisions goes to 1/(infinite) then it is easy to resolve the paradox.

Questions...comments?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Zenoman
- Start date

- #1

- 5

- 0

The same is true with time, and as the number of divisions goes to infinite the time to cross those divisions goes to 1/(infinite) then it is easy to resolve the paradox.

Questions...comments?

- #2

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,950

- 19

Then first, you need to precisely state Zeno's paradox. There are many different ways to interpret it. Some interpretations are extremely easy to refute, due to an obvious error in the argument. I've seen others interpret Zeno's paradox as one of the first arguments (by reductio ad absurdum) that that error really is an error. (It probably wasn't so obvious back then)I may have discovered an explanation to the Zeno Paradox.

What segments?If the distance traveled were divided into an infinite number of segments,

What do you mean by (infinite)? And why do you think you can divide by it? And how would the result represent a segment?then each segment could be represented by D/(infinite).

You can't add an infinite number of times. What operation are youTherefore, if each of these D/(infinite) segments were added together an infinite amount of times

What is a division? And why would there be infinitely many of them?since there is an infinite amount of divisions

What does 'infinite' mean here? And why do you think you can multiply D/(infinite) by it?then if would be D/(infinite) * infinite

And why would you think it gives this result?which would equal D.

- #3

DaveC426913

Gold Member

- 20,009

- 3,278

D/infinity*infinity does NOT result in D; it results in undefined - which means 'this has no unique answer'.

The same is true with time, and as the number of divisions goes to infinite the time to cross those divisions goes to 1/(infinite) then it is easy to resolve the paradox.

Questions...comments?

- #4

- 5

- 0

The segments that the line is divided into. If we have a line of length D and we divide it into an infinite amount of sections then each section would be the width of D/(infinite)What segments?

To answer another of your questions right off the bat, (infinite) is equal to infinite just put the parenthesis to be helpful.

Would you like me to define every word of my post to you?

What is a division? And why would there be infinitely many of them?

A division is: 1. the act or process of dividing; state of being divided.

Dividing is: 1. to separate into parts, groups, sections, etc.

There is an infinite amount of divisions because that is the paradox.

What does 'infinite' mean here? And why do you think you can multiply D/(infinite) by it?

2. indefinitely or exceedingly great: infinite sums of money.

I can multiply D/(infinite) by infinite because its the same as adding D/(infinite) and infinite amount of times.

Do me the great honor of learning basic words such as sections and dividing.

- #5

- 5

- 0

- #6

- 2,193

- 2

When dealing with points A and B of finite length, infinite segmentation is classically impossible.

To go even further, one can not segment infinity, as that would be inherently contradictory. What is one-half of infinity as opposed to infinity itself? (for example)

Anyway just some thoughts...

- #7

- 2,193

- 2

When one keeps mathematically dividing below certain levels it simply has no real meaning or effect on reality.

- #8

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 966

All you've really said here is that you do not understand the "paradox". I suspected that when I saw that this had been posted under "General Physics".

- #9

DaveC426913

Gold Member

- 20,009

- 3,278

No need to be snooty. And yes, you may need to define terms. That's what Zeno's Paradox is about - our nebulous grasp on meanings versus reality. We find that our words make a lot of assumptions, as you are finding you've done in your argument.Would you like me to define every word of my post to you?

- #10

DaveC426913

Gold Member

- 20,009

- 3,278

There is nothing in the paradox about infinity. Infinity only shows up in flawed attempts at a solution.If infinity/infinity does not equal one then I have found the other solution to the paradox. This would be that infinity is not well enough defined to solvea paradox involving infinite.

The solution to the paradox is to

- #11

rcgldr

Homework Helper

- 8,770

- 569

In the case of two objects traveling at different but constant speeds, the ratio of the change in position versus the change in time is constant for each "interval", so the rate of closure and eventually passing by remains constant, even if the limit of the number of intervals approaches infinity while the size of the intervals approaches zero at the point where the faster object passes the slower one.

Another example, is a ball bouncing with a fixed percentage loss in energy on each bounce. The total time the ball bounces is fixed, but the number of times an abstract ball bounces is infinite. (In real life, eventually the bounces become smaller than the deformation of the ball, so it stops bouncing a bit sooner).

- #12

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,950

- 19

I would agree that your concept of 'infinite' does not seem to be well-defined. However, mathematics gives it a more than adequate treatment (even to the satisfaction of philosophers!) -- so if you're serious about reflecting about 'infinite' things, you really need to study mathematics.

- #13

DaveC426913

Gold Member

- 20,009

- 3,278

Absolutely. And therein will be an answer. But mere arithemetic - dividing and multiplying -i.e. mixing natural numbers and infinities - isn't it.Isn't infinity a part of Calculus? There are methods used to calculate infinite sums.

That's where the philosphers and the OP went awry.

- #14

rcgldr

Homework Helper

- 8,770

- 569

True, but I'm not sure of the OP's math background. If you replace "infinite" with "n", and take the limit as n approaches infinite, then the OP had the right idea.Absolutely. And therein will be an answer. But mere arithemetic - dividing and multiplying -i.e. mixing natural numbers and infinities - isn't it.

That's where the philosphers and the OP went awry.

- #15

- 1,550

- 0

The right idea to prove what? Was Zeno right or wrong in what he was trying to prove?True, but I'm not sure of the OP's math background. If you replace "infinite" with "n", and take the limit as n approaches infinite, then the OP had the right idea.

The OP seems to think Zeno was claiming any length is equal to an infinite length and any time duration is equal to an infinite duration of time. Or that that is true and thus negates what Zeno was trying to claim.

I cannot tell because the OP never says what Zeno was claiming to prove.

But neither does anyone else here which makes me think no one in this argument really knows what Zeno was trying to prove.

- #16

rcgldr

Homework Helper

- 8,770

- 569

This might help:But neither does anyone else here which makes me think no one in this argument really knows what Zeno was trying to prove.

It's a paradox, which could mean that the author already knew the solution, but still considered it an interesting exercise for a potential reader.

- #17

- 5

- 0

Zeno claimed that movement wasn't possible because there was an infinite number of divisions to overcome. What I am saying is that because the number of devisions gets infinitely large, the time to cross those would be infinitely small. So these infinities would cancel.

If you can't figure out if I am proving or disproving the paradox perhaps it would be helpful to read the Paradox in full from the link Jeff provided. I was mistaken not have added that in my OP.

- #18

DaveC426913

Gold Member

- 20,009

- 3,278

Yes.Infinity/Infinity does not equal one in some cases... true. Such as 5x/x as x-> Infinity. However in this case, the n/n as n-> infinity does equal one..

No.Zeno claimed that movement wasn't possible because there was an infinite number of divisions to overcome. What I am saying is that because the number of devisions gets infinitely large, the time to cross those would be infinitely small. So these infinities would cancel.

- #19

- 2,193

- 2

Your assuming, and thus calculating, that infinity resides between two finite points.

- #20

- 2,193

- 2

This is not possible.

- #21

rcgldr

Homework Helper

- 8,770

- 569

Or that an infinite number of points exist between two finite points, similar to the fact that an infinite number of real numbers exist between any two real numbers.Your assuming, and thus calculating, that infinity resides between two finite points.

- #22

- 264

- 1

Your comment seems out of the blue. How do you get "...an infinite number of points exist between two finite points," from [tex]\frac{\infty}{\infty}[/tex]?Or that an infinite number of points exist between two finite points, similar to the fact that an infinite number of real numbers exist between any two real numbers.

I think what you're trying to say is that as x approaches 0, t also approaches 0.

Zeno's paradoxes are nonsense anyways...

- #23

rcgldr

Homework Helper

- 8,770

- 569

Your assuming, and thus calculating, that infinity resides between two finite points.

Or that an infinite number of points exist between two finite points, similar to the fact that an infinite number of real numbers exist between any two real numbers.

No, just a response to the comment that infinity resides between two "finite" points. A better analogy to the OP's paradox is that an infinite number of events (the location where the faster object reaches a point where the slower object was at the the previous event), can exist within a finite distance and/or time.Your comment seems out of the blue. How do you get "...an infinite number of points exist between two finite points," from [tex]\frac{\infty}{\infty}[/tex]? I think what you're trying to say is that as x approaches 0, t also approaches 0.

Zeno's paradoxes are nonsense anyways...

- #24

- 1,550

- 0

Zenoman;

You and others are continuing to argue as if Zeno thought things like motion, finite points, distance, or things at distances were real things.

Did any of you look at the Wiki link Jeff gave? With other links there it does a reasonable job of explaining Zeno did not believe those were real.

And creating an infinity from something that does not exist proves nothing to Zeno.

The reduction to the absurd – was not the method used to falsify Zeno’s conclusions as some seem to indicate in this thread.

It was the method Zeno used to prove his point that the idea that any “thing” real moves at all was false.

Zeno’s argument was with the “pluralists” (pluralism at the time believed things really do move within a plenum similar to what Newton centuries later called absolute space and absolute time)

The point of Zeno’s arguments is he was used the logic of those that believe things do move “pluralists” to construct a paradox based on their own pluralist rules of movement that reduces to an absurd result; therefore refuting as absurd the idea that anything moves at all;

Thus supporting Zeno’s monism (what today we would call “Absolute Monism”) which believe that all is just one thing within which we and everything only exist as essentially an idea with nothing real actually moving.

As the Wiki info states in pure logic no one since then though the 20th Century has yet to falsify the Zeno Dichotomy Logic with out first assuming in principle that things move; And that in logic terms incorrectly “begs the question” posed in the first place.

Nothing in this thread certainly not the OP brings something new to resolve the issue as raised by Zeno.

Science seems to do just fine though by ignoring the Dichotomy and like paradoxes as meaningless sophist arguments. They quite literally were put forward by sophists, the problem is justifying with logic that sophist ideas are meaningless.

If you wish to resolve Zeno’s Dichotomy, it needs to be done in the context it was presented without “begging the question”.

Extra note:

Also since “Science”, (General Physics included) can be said to include as a principle foundation that Sophist agreements are not useful;

it is only logical that science cannot resolve a sophist problem.

That is this is more of a Logic and Philosophical issue; it might be better placed in the Philosophy Forum.

You and others are continuing to argue as if Zeno thought things like motion, finite points, distance, or things at distances were real things.

Did any of you look at the Wiki link Jeff gave? With other links there it does a reasonable job of explaining Zeno did not believe those were real.

And creating an infinity from something that does not exist proves nothing to Zeno.

The reduction to the absurd – was not the method used to falsify Zeno’s conclusions as some seem to indicate in this thread.

It was the method Zeno used to prove his point that the idea that any “thing” real moves at all was false.

Zeno’s argument was with the “pluralists” (pluralism at the time believed things really do move within a plenum similar to what Newton centuries later called absolute space and absolute time)

The point of Zeno’s arguments is he was used the logic of those that believe things do move “pluralists” to construct a paradox based on their own pluralist rules of movement that reduces to an absurd result; therefore refuting as absurd the idea that anything moves at all;

Thus supporting Zeno’s monism (what today we would call “Absolute Monism”) which believe that all is just one thing within which we and everything only exist as essentially an idea with nothing real actually moving.

As the Wiki info states in pure logic no one since then though the 20th Century has yet to falsify the Zeno Dichotomy Logic with out first assuming in principle that things move; And that in logic terms incorrectly “begs the question” posed in the first place.

Nothing in this thread certainly not the OP brings something new to resolve the issue as raised by Zeno.

Science seems to do just fine though by ignoring the Dichotomy and like paradoxes as meaningless sophist arguments. They quite literally were put forward by sophists, the problem is justifying with logic that sophist ideas are meaningless.

If you wish to resolve Zeno’s Dichotomy, it needs to be done in the context it was presented without “begging the question”.

Extra note:

Also since “Science”, (General Physics included) can be said to include as a principle foundation that Sophist agreements are not useful;

it is only logical that science cannot resolve a sophist problem.

That is this is more of a Logic and Philosophical issue; it might be better placed in the Philosophy Forum.

Last edited:

- #25

DaveC426913

Gold Member

- 20,009

- 3,278

While I don't doubt that you're making a valid point, I cannot understand what you are saying, especially in the above. It is grammatically so poorly-formed as to be unintelligible.The point of Zeno’s arguments is he was used the logic of those that believe things do move “pluralists” to construct a paradox based on their own pluralist rules of movement that reduces to an absurd result; therefore refuting as absurd the idea that anything moves at all;

Thus supporting Zeno’s monism (what today we would call “Absolute Monism”) which believe that all is just one thing within which we and everything only exist as essentially an idea with nothing real actually moving.

Share: