'minus' infinity

[Potatoman]

Heres something that got me thinking... All numbers can be halved - 100; 50; 25; 12.5 etc... Now, assume that 2 marbles are rolling towards each other - 1 meter apart - 50cm - 25cm etc. At what point do they touch? you can have 1mm, 0.5mm all the way to 0.00000000000000001mm - you get the idea. There will never be exactly 0 distance. Even with thousands of decimal places. So when they touch, surely the distance is 0.infinate 0's then 1 (if you know what i mean).
Ill never forgive my old science teacher for giving us that one...

[brachiopod]

(2nd attempt to post - lost 1st answer. Grrrr.....!!)

Two marbles would definitely collide since they have a velocity (ie speed and direction) that describes their paths and the collision between them.

Don't confuse this with the old conundrum;

"I am travelling from A to B.
If I cover half the distance today, and half the remaining distance tomorrow - then half the remaining distance the day after etc etc. When will I reach B?"

The answer is "never".

This is the opposite of infinity (a very big number) in that it is a very small number. In fact it is the reciprocal of infinity, or 1/∞.

Just as � (being 1 divide by 2), is larger than than � (1 divide by 4) - then the larger the denominator (the bottom number), the smaller the 'value' of the fraction. Hence, 1 split an infinite number of ways, (ie 1 divided by ∞), is a very small number indeed.

For this to apply to your colliding marbles, they would (for some reason) have to be decelerating in a frictionless environment, at an exact, perfectly proscribed geometric rate.
In all other situations, they bang into eachother.

[Loosehead]

As Brachiopod explains very well they will collide for the reasons explained. Note though that as you get to the ever small distances you get to the first atoms comming together as their respective electron orbits collide initially, so athough we deem them to have touched they still have the vast space between the orbits and the nucleus to go but that would still result in the energy of the collision to make the "Click" and rip millions of atoms/molecules from the surface.

[dawkins]

Wouldn't Heisenburg's uncertainty principle apply so that errors in measurement of time or distance would prevent the observer from saying with certainty when the marbles collided? or am I talking rubbish?

[heathfield]

This comes under Zeno's Paradox.

And yes, Dawkins, you're right, though it's also referred to as the 'quantum Zeno effect'.

[jake-the-peg]

Heisenbergs uncertainty principle is very definately not to do with errors in measurement.

It stses that there are pairs of quantities that cannot be known with infinite precision. This is not because of errors or our technical capacity but a fundamental limit.

One of these pairs is position and momentum another is energy and time. It is therefore possible to know exactly when a collision occurs providing you are not also attempting to measure the energy of the collision.

However attempting to extend Heisenberg to a large scale structure like a marble is somewhat questionable.

The question is one of Zeno's paradoxes http://en.wikipedia.org/wiki/Zeno's_paradoxes known as the dichotomy paradox

It is resolved by calculus showing that the ininte geometric series can converge.

http://mathworld.wolfram.com/ZenosParadoxes.ht ml

[jake-the-peg]

Post overlap.

The Quantum Zeno effect is to do with surpressing radioactive decay with contant measurement.

Not too sure how that fits in with the HUP - can you explain?

[dawkins]

ok badly worded Jake, but given that the marbles will collide and Potatoman's comment that there will never be exactly zero distance Is it not the case that we cannot calculate the exact moment when the marbles collide because of the uncertainty principle?

[mibn2cweus]

Has anyone else failed to take an exam after speeding the entire time wondering exactly when "now" is? I'm still not sure if it's part of the "n" or maybe in the precise centre of the "o" or perhaps at one of the points in the letter "w"? Just my luck I would guess wrong and be given detention for cheating . . .
Which ever it is, I also deliberated over whether the propagation delay of sound was why the smartest kids sat at the front of the class.

[Peter Pedant]

You science nerds cant pass Zeno's paradox - well I never found it much of one - without the ancient answer

solvitur ambulando

[it is solved by walkiing]