Distance

[Welshwizard]

If there are two objects, object a and object b and the distaince between the two is 2 cm, when it is halved the distaince becomes 1 cm, dosent the laws of phisycs say that a distaince can always be halved? and if so dosen't this mean that you could infinatly half the distaince between two objects? in affect two objects can never make contact or pass each other, obviously there is an explinasion for this because objects do meet and pass all the time?

[lisaj]

Firstly, we should point out that for this to make any sense, we are talking about two points, and not two objects: A point refers to a point in space of zero size and mass. Every time you half the distance between two points, you are reducing the distance that you are subtracting. Hence they will never touch, because you end up reducing the distance between them by a mere fraction. Put the other way, if you cut a piece of paper in half, and then cut one of those halves in half, and one of those in half, ad infinitum then you will never consume all your paper: you will always have a tiny piece left over (subject to the atomic size restriction, which is of course irrelevant when dealing with points). Furthermore, the first half of your question refers to an inverse exponential approach between a and b, where as the second refers to a linear approach (and passing) of a and b.

[geofbob]

The problem you set out is one of the Paradoxes of Zeno. Zeno lived in the 5th century BC, and his paradox about continually halving distance and points never meeting has puzzled thinkers since that time. For more information on Zeno, and for a modern solution to his paradox, see http://www.utm.edu/research/iep/z/zenoelea.htm