If you keep cutting the distance between two objects in half, would they ever touch?

Question

Is the sense of touch imaginary? If you keep cutting the distance between two objects in half, they'd never touch...SO, how do we touch things??

Answer 1

technically nothing ever touches, we just feel the force of the atoms against ours, and we have sensory neurons to pick up on these forces, as for the first part of the question, they would never touch, its a mathematical concept known as a limit

Answer 2

No, unless you cut it infinite times. let the initial distance between the object be d. then the distance after cutting the distance in half n times would be d(1/2)^n.
the function of distance approaches 0 as n tends towards infinity, but the distance could never reach zero in a finite number of cuttings.

Answer 3

No. Dividing a number other than 0 (as any distance is more than 0) by half (2) will never get to 0. You can graph this on a graphing calculator. There is a specific equation to for it.

Answer 4

If you want to be pedantic - the ever decreasing gap by division gets to the sub atomic level, and a prime number of quarks apart, you cannot divide the width of the particle so the closest your maths could get would be 1 quark apart. It would be possible to be no quarks apart and touching but not by division if the measuring was constant in unit

Answer 5

We touch because we cut the distance to zero....not in continuous half-the-distance increments.

Answer 6

Cut the distance to zero.

Answer 7

This problem was discovered by Zeno many years ago, who claimed to prove that motion was impossible because of the continuous halving. It is called the Dichotomy. Read about it here -

http://plato.stanford.edu/entries/paradox-zeno/

Answer 8

This problem doesnt really relate to us touching things

Answer 9

thats if you were to only go in half right but as we touch things we don't apply this problem

Answer 10

nope
never