says (basically) that movement is not possible because in order to move any distance one must first move half that distance, and half that distance, etc etc. He assumes that the physical universe
in that you can divide a distance infinitely just as you can divide a number infinitely. Simply said he assumes that the universe is infinitely large
since no finite number can be divided infinitely. However, empirically Zeno's Paradox
quite obviously doesn't hold any water.
So let's look at it backwards, the reason we can't move would be, indirectly, that the universe is infinitely large. Since we can move, the universe must not be infinitely large but rather be composed of a near infinite amount of fundamental units of mass.
I'm not suggesting this is some groundbreaking idea, but I wonder if anyone has reason to dispute it? Or if some philosopher has already stated it (Zeno may have, I'm not sure).
Response to izubachi:
I'm familiar with the limit, but it doesn't really disprove what I'm saying. What we're talking about here is the limit at an asymptote However, although it will tell what number y will move towards as x goes to infinity (for a horizontal asymptote) and at what value of x, y will move towards infinity. It doesn't change the fact that the numbers never actually reach infinity or whatever number they were approaching. So if you were trying to move an infinite distance you would also never actually reach your destination. But I'm not a mathematician, so I may be mistaken.
As for relativity, I'm not sure I really see how it fits in here. It would seem, relativity and movement aside, that any distance with in the universe is a fraction of the entire size of the universe, and if the universe is infinite, then any fraction of it is infinite. Perhaps you could clarify what you mean.
Response to Halcyon&on:
Yeah, I'm not arguing that a finite number cannot be divided infinitely, it certainly can. I'm just saying that I don't think space mirrors this.
I'm gonna leave the previous argument up there as it makes more sense considering the name of the node. After discussing the issue I see that the proof is not there. I still think it's kinda interesting though. So I now say that the universe is composed of an infinite (or near infinite) number of fundamental units of mass (I still believe in those little fellas).