A maddening paradox?

x3r0

Hello

I have presented this to many people and they get mad every time i say it. theoretically, an object cannot travel the full distance from point A to point B. the reason being is because you first must travel half of the distance in order to travel the full distance, yes? well, after you accomplish this, you must travel the next half to reach the end. but after this you must travel half the distance Again to reach the end of your journey. the paradox is like cutting something in half, you can never get rid of it because you keep cutting it into halves. any thoughts or red faces about this? i understand that yes in reality you can travel a full distance, just wondering if there is any way to disprove this theory other than the obvious, such as wrong assumptions of the problem.

davee123

Well, the obvious response is what's wrong with travelling over an infinite number of points, considering that we have an infinite number of points in time in which to travel over them?

In other words, to get from point 1 to point 2, this implies that at time A I will be at point 1, and at time B, I will be at point 2. So, halfway between A and B, I'll be at point 1.5, and at half that time (1/4 between A and B), I'll be at point 1.25. Etc.

In other words, the progression of time is in itself divisible infintesimally, just as space is divisible infintesimally. Hence, no conflict!

DaveE

Proggle

This is one of Zeno's paradoxes. It troubled the greek mathematicians and philosophers of the time because they were uncomfortable with accepting the notion that something could be infinite.

In modern mathematics, this is not a real issue. You can easily show that

S=1/2+(1/2)^2+(1/2)^3...(1/2)^n converges to 1 as n tends to infinity.

If it is the physical notion that troubles you, just Google up Zeno's paradox and you'll come up to some discussion about it, but as far as I can tell, it is the general consensus that there is no issue with extending the mathematical concept I presented above into physics.

x3r0

thanks for the input, i was hoping for some reply on the mathematical spectrum. and the little history that you described above was interesting, i didnt know that.