Needle which is almost touching a pane of glass

1. Aug 30, 2009

kkapalk

I am a little confused by movement. It is difficult to explain, but here goes. Say I have a needle which is almost touching a pane of glass, so close if fact that the smallest movement toward the pane would result in the needle touching it. My confusion is, if the needle has to move to touch the pane then is has some distance to travel to get there. The distance can always be divided down. The point when it is not touching does not seem to naturally flow to the point when it is. You could say 'one more billionth of a millimetre movement this time and it is there'.But that would not be the case, as first it has to travel half that, and half that distance before that. I picture moving anything in my mind's eye and always feel that the initial movement is going to be 'jerky', or missing some initial movement out. Can anyone understand what I mean, I do find it hard to elaborate properly. I just feel movement, and time also, do not flow properly.
Kev.

2. Aug 30, 2009

Re: Movement

This has nothing to do with quantum physics. You are confused about open sets, the fact that the dimension of the surface is one lower than the dimension of the volume, and that such a surface than has a measure of zero.

In quantum physics things don't touch in single points.

3. Aug 30, 2009

ZapperZ

Staff Emeritus
Re: Movement

Thread moved from the Quantum Physics forum.

Zz.

4. Aug 30, 2009

A.T.

Re: Movement

Yes you can divide a finite positive number up into an infinite amount of greater than zero numbers:
1 = 1/2 + 1/4 + 1/8 .... and so forth
It would be 'jerky' if the movement would always stop at half of the remaining distance. But if it moves continuously it is not 'jerky'.

5. Aug 30, 2009

DaveC426913

Re: Movement

This is almost an exact analogy of Zeno's Achilles and the tortoise paradox.

The solution to the paradox is the http://en.wikipedia.org/wiki/Convergent_series" [Broken], as A.T. points out above.
The infinite sequence: 1/2 + 1/4 + 1/8 + 1/16... converges on the very finite number 2.

Last edited by a moderator: May 4, 2017
6. Aug 30, 2009

A.T.

Re: Movement

I said 1

7. Aug 30, 2009

Integral

Staff Emeritus
Re: Movement

Consider:

$$S = \frac 1 2 + \frac 1 4 + \frac 1 8 + ...$$

$$S = \frac 1 2 ( 1 + \frac 1 2 + \frac 1 4 + ....$$

$$2S = 1 +S$$

$$S = 1$$

8. Aug 30, 2009

DaveC426913

Re: Movement

My mistake. The sequence I meant to post starts as 1/1 + 1/2 + 1/4 ...

9. Aug 30, 2009

Integral

Staff Emeritus
Re: Movement

The difference of course is one sequence is :
$$\Sigma _{n=0} ^ \infty 2^{-n}$$

vs

$$\Sigma _{n=1} ^ \infty 2^{-n}$$

Easy detail to miss.

10. Aug 31, 2009

kkapalk

Re: Movement

Thanks for the replies guys. I have been to Zeno's Paradox and it is indeed the same as my problem. I do understand that if I divided any space down infinitely it would still be the same size, and also understand that I must be seeing the issue slightly askew. I just find the initial first movement very hard to comprehend. Whatever we decide is the initial distance moved must always be incorrect, as we will have to pass through an infinite number of smaller distances to get to that distance. I get the same confusion with time. To me it seems the present is very elusive, as it is just the point when past and future meet. Each event that occurs in time is infinitely short, in fact no event can exist for any length of time at all. So how can it exist at all? I suppose I am trying to look too deeply into time and motion, and as we all know it is very baffling. Thanks again for the replies,
Kev

11. Aug 31, 2009

A.T.

Re: Movement

They "exist" in the same sense as points on a line: they have no extend. Keep in mind that math is just a bunch of abstract concepts made by humans for practial use. It doesn't matter if you consider things like numbers as "really existing" or not. They are just usefull to describe existing things.

12. Aug 31, 2009

DaveC426913

Re: Movement

Why?

Why does the abstract concept of passing through an infinite number of smaller distances cause you to think, that, in reality, it can't be done?

13. Sep 1, 2009

kkapalk

Re: Movement

I didn't say it cannot be done, I said I found it difficult to understand the measurement.
A.T, thanks for your post. I think you have hit the nail on the head with the comment about numbers and maths just being used by us humans. I think my problem is trying to understand the very complex time and motion with my own limited forms of measurement.