# So I read this thing.

1. Oct 24, 2004

### Enceph

Ok. A guy fires an arrow at this other guy, who runs away. Now the arrow keeps getting closer and closer, but it never quite impales the second guy because the distance between him and the arrow is able to get infinitely smaller before it happens. What is happening here? The book I got it from says Calculus solved this problem. I dont know why. Anyway.

What force particle carries the action if the arrow meets the guy?

Does any theory besides string have a smallest distance?

:yuck: Heh.. eh...

-Spencer :uhh:

You Mods might want to move this I think. Sorry for that.

Last edited: Oct 24, 2004
2. Oct 24, 2004

### T@P

is this some colorful explanation of a limit...? for example a basic one limit of (1/2)^n as n goes to infinity? am i missing something...?

3. Oct 25, 2004

### spacetime

As the arrow approaches the target, the atoms of the arrow try to "mingle" with the atoms of the target. They have a higher kinetic energy, so they succeed in doing so.
They repel the atoms of target, make space for themselves and this force of repulsion acts through the electric field. So, the force carrier is photon.

4. Oct 25, 2004

### HallsofIvy

Staff Emeritus
One of Zeno's paradoxes. It has nothing to do with "force particles". It shows that the the arrow must cross an infinite number of "positions" to go any where, but the tacit assumption that that cannot be done in a finite time is incorrect.

5. Oct 25, 2004

### poolwin2001

Zeno's paradaox:Paradox is only there if we believe that all infinite series cant be finite.But that is false.So ultimately there is no paradox.

6. Oct 25, 2004

### MiGUi

Ok, I bet you to prove this. I fire you an arrow and you begin to run. If you win, I will pay you 1000 \$.

7. Oct 27, 2004

### Enceph

You're on!

Awesome explanation for the photon.

8. Oct 27, 2004

### quasar987

You probably mean "can't add up to some finite number" (i.e. converge) (?)

I got this written in the introduction to the chapter on sequences of my real analysis textbook. I believe it is how Zeno actually formulated his paradox! Thought I'd share it.

"Achille is initially 100 m apart from a turtle that he is pursuing. He runs 10 times faster then the turtle. When Achille will be at the point where the turtle was initially, it will be 10 m apart from Achille. Then it will be 1 m, 10 cm, 1 cm, ... apart. He will never catch up with it."

Here's another paradox that is fun: Let S be the serie defined by

$$S=1+2+4+8+16+...$$

Then

$$S=1+2(1+2+4+8+16+...)=1+2S \Leftrightarrow S=-1$$

So this sum of positive numbers is negative. :grumpy:

9. Oct 28, 2004

### reilly

quasar987 -- Just goes to show that you can do most anything with a divergent series.

Regards,
Reilly Atkinson