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Tackling A Paradox: Do We Or Don't We Arrive At The Destination?

1240 words - 5 pages

Suppose I'm to walk on a straight road from A to B: I wear a pedometer, (as well as my sneakers) and set off. The distance (AB) is 100 meter. I come to a place where my pedometer shows 50. "Half of the way", I think and keep going, roughly estimating the remained distance: I'm going to walk half of the remained 50, then half of the remained 25, then half of the remained 12.5, then half of the remained 6.25, then half of the remained 3.125, then... Will I really arrive at B? Mathematically speaking, NO! I may get so so close to B, but never arrive at B itself. Then, why I really do arrive at B?It's perhaps not that easy to answer. However, I just try to afford some rough conjecture: Focusing on the different nature of Bs (arriving points) may shed some light upon the dilemma: Realistically speaking, B is a place, not a single point. It's a tree, or stone, or a cottage at the end of the road, where is 100 meter away from the starting station, A. Why we arrive at B? Well, because we take B as some visible, concrete spatial thing. B occupies some space; it has a three-dimensional nature NOT comparable to the mathematical B which is just a point, consisting of no dimension. I can claim that I actually never arrive at point B (some invisible theoretical thing) at the end of my journey, but I do arrive at that B (a stone, or a tree, or even an extremely narrow upright beam) which is placed right 100 meter away from the starting point A. Before launching into any further inferences, let's discuss the very nature of point itself: Mathematically speaking, what is a point? Is it some quantum concept? If it cannot be reduced to any sub-parts, if we take it as the ultimate constituent of a line (the first dimension), if it is null-dimensional in itself, something never actually "there", but something I must just go toward, then it is quite plausible that I may never "arrive" at it. You see the point (not that point, of course)? We take B as something "there", quite plausible, then we try to calculate half of the remained distance from it, and half of the remained half, and so on, after that, strangely enough, we come to the conclusion that we will never ever arrive at it, no matter how far we go!Let's play a little game: Assume that I could reduce myself to some null-dimensional traveler point, set off to see my fellow point B who is supposed (apparently) to reside at somewhere 100 meter away. How can I be sure of this, in the first place? 100 meter means there is a line - and only a straight line - between me and my fellow. Now who am I? I got no dimension, neither has my fellow point. Then how is it possible for some poor line (or any other creature!) to find me and my fellow bro there? Besides, what is a line in itself? In mathematical terms, it is a combination of points. What sort of a combination? There should be at least two points (in Euclidian geometry) to compose a line: Even if we define a line as "a set of at least two inter-dependent points", we...

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