Zeno's paradox

[CountPoopoo]

A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters.

Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.

Where does the argument break down? Why?

This has been boggling my mind for a while now.

[Zerok]

How long have I been ranting about this? I love you.
Movement is a perception.

[deleted-3]

But we get to our destanation no technically we do get there so that is wrong.

[Zerok]

At 12/7/04 10:11 PM, --__-- wrote: But we get to our destanation no technically we do get there so that is wrong.

You completely failed to understand the concept.
Ignorance is bliss I guess.

Here's my example. I used a very similar setup. BUT MINE HAS DIAGRAMS! Teehee!

[Nicko9y]

At 12/7/04 10:07 PM, CountPoopoo wrote:

This has been boggling my mind for a while now.

A person with "poopoo" wrote a paradox.
LOL!

[CountPoopoo]

At 12/7/04 10:09 PM, Zerok wrote: How long have I been ranting about this? I love you.
Movement is a perception.

No you don't get it, I know its wrong i'm looking for a proof. Think about it, this includes infinite sets. Just like 0.999999.... = 1, then 1/2+1/4+1/8 is going to = 1. I just need a mathematical proof. That has been killing me. If you look at it as a series, its in terms. There must be an infinity terms if there is an infinite amount of nth terms, that means allt he other terms are added to the infinity term wich makes it infinite whcih means you'll get there because you multiply by reciprocal and you get 1=1. I just need an equation!

[StarCleaver]

Assuming a constant velocity, he moves half the distance in half the time. An eigth of the distance in an eigth of the time and so on into infinite. Nothing breaks down. It is just our incomprehension of infinite. He moves an infinitely small distance in an infinitely small time.

[Ravens-Grin]

You are confusing something that does not need to be confused. It is possible to create an infinite amount of points between two points, but these points will not change. They are definite, and will never change until a new situation arises. Therefore it is possible to derive the average velocity by doing the formula of average velocity equals distance divided by time. Distance is the difference between the two points.

No where in this formula of velocity, which is the common notion of motion in respect to an object, is it plausible to include the value of infinity.

[Zerok]

At 12/7/04 10:21 PM, CountPoopoo wrote: No you don't get it, I know its wrong i'm looking for a proof.

It's not wrong. And there is no equation. You'll never find it, even if you devote your entire life to it. Even if every living soul on this planet devoted their souls to the cause, for the next 20 billion years.

At 12/7/04 10:22 PM, Star_Cleaver wrote: It is just our incomprehension of infinite. He moves an infinitely small distance in an infinitely small time.

That's about as close as we're going to get, right there.
Infinity > us > infinity.

At 12/7/04 10:23 PM, Ravens_Grin wrote: You are confusing something that does not need to be confused.

If you'd like to continue thinking inside the box, yes. Not to say that's a bad thing, in this case.

[CountPoopoo]

At 12/7/04 10:23 PM, Ravens_Grin wrote: You are confusing something that does not need to be confused. It is possible to create an infinite amount of points between two points, but these points will not change. They are definite, and will never change until a new situation arises. Therefore it is possible to derive the average velocity by doing the formula of average velocity equals distance divided by time. Distance is the difference between the two points.

No where in this formula of velocity, which is the common notion of motion in respect to an object, is it plausible to include the value of infinity.

No you don't get it at all. Countless times have I had to explain this HAS NOTHING TO DO WITH VELOCITY! This is pure math. He was right, that you have to walk half, then half of the half and so on. However he was wrong to say that meant you would not reach point B. There are an infinity of halves between two points, but there is a point where it becomes infinitely small, and that is the nth term that stands for infinity, then it becomes infinity divided by infinity which = to 1. NOT PHYSICS, SIMPLE ALGEBRA.

[StarCleaver]

At 12/7/04 10:30 PM, Zerok wrote: That's about as close as we're going to get, right there.
Infinity > us > infinity.

Infinity > us> -infinity

Get it right. ;)

At 12/7/04 10:23 PM, Ravens_Grin wrote: You are confusing something that does not need to be confused.

If you'd like to continue thinking inside the box, yes. Not to say that's a bad thing, in this case.

He's actually had the best answer so far. He said something similar to what I said. If a guy is moving, he is moving over an infinite ammount of points. He travels in a line. A line is nothing but an infinite ammount of points.

You cannot try to say that the guy does not move just because of a flaw in our system to explain how he moves.

[Iceman-of-doom]

It is a limit equation. One of those calculus equations where the limit starting at infinity (or 100m in this case) approaches zero.

n
lim = sigma 100/(2^i) = x
x-->0 i=1

It's hard to draw this out on this post. I can't draw a sigma notation. I think this would be a valid equation but don't bash me if it isn't because I haven't had calculus in over a year.

[Iceman-of-doom]

At 12/7/04 10:35 PM, Iceman_of_doom wrote: It is a limit equation. One of those calculus equations where the limit starting at infinity (or 100m in this case) approaches zero.

n
lim = sigma 100/(2^i) = x
x-->0 i=1

It's hard to draw this out on this post. I can't draw a sigma notation. I think this would be a valid equation but don't bash me if it isn't because I haven't had calculus in over a year.

...................n
..lim ....= sigma 100/(2^i) = x
x-->0 .....i=1

I'm sorry for submitting this again but when the equation was posted, the spaces were deleted, shifting everything to the left, screwing up the equation. So I put periods in to take the place of the spaces. they do not have anything to do with the equation at all.

[StarCleaver]

At 12/7/04 10:35 PM, Iceman_of_doom wrote: It is a limit equation.

http://home.alltel.net/okrebs/page134.html

That explains it well.

[Zerok]

At 12/7/04 10:34 PM, Star_Cleaver wrote: Infinity > us> -infinity
Get it right. ;)

Negative infinity is infinity's evil twin godsister.

He's actually had the best answer so far.

Yeah, I was just referring the 'no need to confuse' part. It's fun to hurt your brain with this one. But so utterly pointless.

You cannot try to say that the guy does not move just because of a flaw in our system to explain how he moves.

He isn't saying the dude doesn't move, just that what we perceive as movement isn't what it actually is, due to this flaw. At least, that's what I'm saying. o_O

[CountPoopoo]

At 12/7/04 10:30 PM, Zerok wrote: It's not wrong. And there is no equation. You'll never find it, even if you devote your entire life to it. Even if every living soul on this planet devoted their souls to the cause, for the next 20 billion years.

That made me really mad. As a matter of fact I found it now, so go have anal with yourself because you ARE TEH OWNED.

BEHOLD! THE EQUATION FOR THE nTH TERM OF ZENO'S PARADOX:
2 - 1/2^(n-1) WHERE N CAN BE ANY POSITIVE NUMBER!
For the nth term = infinity. 0 = 1/infinity. 0 = 0!!!!!!!

I DID IT!!!!!!!!!! I GOT IT!!!!!!!! WOHOOO

[StarCleaver]

At 12/7/04 10:41 PM, Zerok wrote: He isn't saying the dude doesn't move, just that what we perceive as movement isn't what it actually is, due to this flaw. At least, that's what I'm saying. o_O

Why should we base our perception of reality on such a notion that can easily be explained? Like I said, a flaw in the system we use to describe reality does not change reality, it just changes the system.

[Iceman-of-doom]

At 12/7/04 10:38 PM, Star_Cleaver wrote:

At 12/7/04 10:35 PM, Iceman_of_doom wrote: It is a limit equation.

http://home.alltel.net/okrebs/page134.html

That explains it well.

Oh well, everyone makes mistakes. I haven't had calculus in over a year so give me a break. I've forgotten most of it

[Cycros]

Matter "moves" as waves of energy. Motion is just a perception. Nothing really moves...

[Kolohe]

At 12/7/04 10:07 PM, CountPoopoo wrote: Where does the argument break down? Why?

This has been boggling my mind for a while now.

When you say infinite midpoints in a finite time, you are just looking at one side of the problem. If you apply the same theory to both variables (distance & time), you would see that distance and time can be divided up in to ever smaller pieces. So, you would be moving over an infinite amount of midpoints in space over an infinite amount of increments of time. Your logic just seems kind of one sided to me because motion is not an illusion. Although it is relative to the observer, it is very real and in no way a paradox.

[StarCleaver]

At 12/7/04 10:44 PM, Cycros wrote: Matter "moves" as waves of energy. Motion is just a perception. Nothing really moves...

So if I get up and wake away from my computer, I am still at my computer, just sending out waves of energy? If that's the case, we all must still be at a singularity.

[Kolohe]

At 12/7/04 10:44 PM, Cycros wrote: Matter "moves" as waves of energy. Motion is just a perception. Nothing really moves...

Yes, matter, space and energy are all interrelated, but not in that way. I don't know who told you that, but you should smack them upside the head with a TI-89.

[Zerok]

At 12/7/04 10:43 PM, Star_Cleaver wrote:

Why should we base our perception of reality on such a notion that can easily be explained?

That's why it's fun to think about, but futile.
I like reality. It's nice and stable. *hugs floor*

At 12/7/04 10:44 PM, Cycros wrote: Matter "moves" as waves of energy. Motion is just a perception. Nothing really moves...

If the universe is infinite, then there must be an infinite amount of energy, or else there'd be no way to gauge distances between the finite sets of energy... or the limit of energy in the universe would be approaching zero (finite / infinite).

But with infinite energy we have infinite mass (energy = mass), and that's just... uh... I have no idea where I'm going with this. I forget the brainbuster that goes with infinite mass. Woohooohoo!

At 12/7/04 10:46 PM, mastershaked wrote: it is very real and in no way a paradox.

Keyword = real.
It's not a paradox in reality. See Star_Cleaver posts.
But then reality becomes skewed, if you think about infinity too much.

[Chakra-X]

It's because the distance is dividing to an infinte number that even the slightest move will be too far right?

[Kolohe]

At 12/7/04 10:52 PM, Zerok wrote: But then reality becomes skewed, if you think about infinity too much.

Yeah, infinity is a concept that shouldn’t be taken too literally all of the time (mainly because comprehension of anything infinite is sort of impossible). It comes in handy when trying to calculate certain things, but the idea that anything is boundless can neither be proved nor disproved. That's why it's best to consider infinity as an idea, not some kind of tangible thing (number, distance, mass, energy, whatever).

[Zerok]

At 12/7/04 11:04 PM, mastershaked wrote: That's why it's best to consider infinity as an idea, not some kind of tangible thing (number, distance, mass, energy, whatever).

Yep. Stay grounded in our plane of reality. 'Why fix what's not broken?' </redundancy>

Oh, and on an unrelated (or is it?) topic:
Can you tell the shape of a drum purely from the waves it gives off when struck? Apparently, not in 3 dimensions, but you can in like, the 5th or 6th dimension...

My calculus prof told us about a lecture he went to where some guy 'proved' that and made it completely understandable in like, 30 minutes. Understandable for my prof and the grade 10's he was talking to. The guy was supposedly a master of words and this 'genius' type thinker and such. The catch was, after everyone left the lecture, their brains went *...fizzle...* and nothing made sense anymore.

This is my theory on the matter. Movement is a perception as well as measurement. If there are an infinite number of fractions inbetween 1/2 and 1/3, then there is an infinite amount of space in between 50 feet and 25 feet. It's all in how you word it.

1.298290318109238 feet.
1.298290318109287 feet.
1.298290318109286 feet.

And so on.

Measurement is only a perception that we use to give order to things. Things can become infinitely small, we just do not have the technology to view such things.

[Shrapnel]

At 12/7/04 11:10 PM, Zerok wrote:

At 12/7/04 11:04 PM, mastershaked wrote: That's why it's best to consider infinity as an idea, not some kind of tangible thing (number, distance, mass, energy, whatever).

Yep. Stay grounded in our plane of reality. 'Why fix what's not broken?' </redundancy>

Oh I get you. You're one of those people who don't listen to logic.

[Zerok]

At 12/7/04 11:15 PM, Crimson_Edge wrote: Things can become infinitely small, we just do not have the technology to view such things.

And we never will.

There are several viewpoints on this subject that I've noticed.
The purely baffled: PooPoo (and probably all of us, secretly).
Looking at reality from infinity: Myself, Cycros.
Looking at infinity from reality: Crimson here, mastershaked, Star_Cleaver, etc.

Kind of, sort of. Yeah. I like it.

[Zerok]

At 12/7/04 11:16 PM, Shrapnel wrote: Oh I get you. You're one of those people who don't listen to logic.

Huh? I thought I agreed to all the posts that said something like, "yeah, well, it's best to stick with everything that we know works and such." I even supported it...

Explain your accusation Shrap! Or I'll cry. Oh yes, I will!