You are walking from point A to point B....?

Question

On your way, your distance from A to B gets cut in half, then in half again, then in half again, then in half again. It keeps getting cut in half an infinite number of times until the halves become microscopic. But no matter how small it becomes, the distance that you have remaining from where you are to where you want to be (point B) can still be cut in half again. Do you ever really get to point B or is there just too many halfway points to cross that you never really get there?

Answer 1

What you are describing is one of "Zeno's paradoxes". It sounds like you will have infinitely many "halves" to traverse. However, as you split the distance into infinite halves, the time to traverse each half also is cut in half. So if you add them all up you can travel from A to B. There is a finite sum for the distance and the time.

lim n-> infinity of (1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2^n) = 1

Answer 2

That's the old Greek thought experiment (to quote Einstein) about a warrior running in front of an arrow at half the speed of the arrow. It would seem that he would never be hit by the arrow, but in fact, we know this is not true. You will reach point B, and the arrow will kill the poor soul who is to stubborn just to step off to the right, because the velocity is not decreasing by half. This idea that you would never reach point B would only be valid if you were decelerating so that you were at half the original velocity at the midpoint between A and B, then 1/4 at the 3/4 mark, etc. Whatever percentage of the distance you have left to go, that's the percentage of your original velocity you must be traveling in order for the scenario to be true, because you would become infinitely slow before you reach point B (it's the speed of light phenomena that keeps massive objects from moving light-speed because they gain effective mass exponentially, slowing them down until they become infinitely massive as they get infinitely close to the speed of light). At a constant velocity, you'll get to and past point B.

Answer 3

This is a variation Zeno's paradox (Zeno was an ancient Greek philosopher), and the point is more to ponder the concepts (such as discrete and continuous number systems, as well as the concept of a limit) than to come up with a specific solution.

If you're thinking math with real numbers (or even just quotients), then no, you never arrive.

If you're thinking engineering eventually rounding off for measurement error will get you there ;0).

Answer 4

Mathematically, you only get close to B and never really reach it within a finite time scale.

In reality, when you get close enough in microscopic level and get over the nuclear forces that repulses matters from each other, you may get tunneled through the energy barrier, and reach B. But I can't guarantee what's left in you afterwards though.

Answer 5

You never reach point B, though B is at a finite distance from A, because it will take you infinite time to reach a finite distance.

Answer 6

Having walked from point A to point B, I conclude that yes, it is possible.

Answer 7

we never reach since there still will be many more cuts every time. logically we never reach point B

Answer 8

You will get there when you become sick and tried of walking slower and slower.

Answer 9

u mean its loci in two dimensions??

im not sure..it difficult!!

Answer 10

whatever..