Duality in physics
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 a
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 perceive that a line has to be composed of null-dimensional parts; therefore, is subject to null-dimensional rules (though not necessarily obeying them). That’s why a line is infinite at both ends: It can start from anywhere and end up in anywhere. Then, why should it stop at the sight of some null-dimensional creature in the middle of nowhere? Point B, where the line is supposed to arrive at, is null-dimensional, too. It is the prerequisite to the line itself. The line already contains it. Half of the line, and half of the half of the line are just the same, too (Theoretically speaking, there is no difference between a line and half of a line: Both of them may expand or get shrunk infinitely). Therefore, the line can never arrive at what it already contains: It contains at least two null-dimensional points, it may also contain three, four, five… infinite null-dimensional points. It may actually contain point B, too. Then, how can we expect it to arrive at point B? we can argue that it has arrived at poin
Some topics in this essay:
Suppose I’m,
half remained,
100 meter,
half line,
spatial position,
mathematically speaking,
100 meter starting,
occupies space,
spatial positions,
remained distance,
rules properties,
meter starting,
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Approximate Word count = 1207
Approximate Pages = 5 (250 words per page double spaced)
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