Imagine a world where you could do miracles - become invisible, walk across walls, change your shape, have x-ray vision and so on...
Let me take you on a journey to such a World, where you can be God-like, and do all these things. Are you ready? Ok... Let us go!
Oh wait! but before going, we need to do some Math. Let us quickly recollect our Geometry. A point has no dimensions, a line has single dimension of length, a rectangle has two dimensions length and breadth, a cube has three dimensions - length, breadth and height. We perceive space in three dimensions.
OK, lesson over, now let us go and play some miracles.
Let me introduce my friends from this new World - Mr. Square Flat and Mrs. Circle Flat. This is their home, and this table top is their World. As you can see they are Flatlanders, and their World is two dimensional. The words, above and below, up and down do not mean anything in their world. They can only move in the plane of Flatland.
How do you think they would be seeing each other? Any guesses? Right, they can only see each other as lines. If I tell Mr. Flat that his wife is beautiful, round and pink in colour, he would not understand. He sees her only as a line. And he cannot see any color. He married her because from wherever he looked at her, she was always of the same length. It is difficult to get another person of such inimitable proportions. And of course she had a sweet voice. As for Mrs. Flat, she would see Mr. Flat as a line that grows in length and then shrinks as she goes around him.
If I put my finger into the Flat land, what would they see? They would see the cross section line of my finger appear in their World out of nowhere. I put two fingers and they see two new people. I put my arm in, and they would see a handful of people entering their World and then Merging into a single big person. When I pull out my hand from the plane, they would see that I have disappeared. Obviously we could play the Vanishing act in their World.
The Flats cannot see beyond their walls, but we can see both inside and outside their walls. See, we have X-ray vision.
The Flats are talking to each other and I suddenly yank Mr. Flat out of his plane. For Mrs. Flat, it would appear as if Mr. Flat disappeared into thin air. Now I place Mr. Flat outside their home. He rings the bell, and Mrs Flat would have the shock of her life, seeing Mr. Flat materialize outside, as if he had gone through the walls.
We can have lot of fun, playing such mischief in the Flatland. But let us get back to our World and extrapolate the Flatlanders' plight with our own. Our physical perception is limited by 3 dimensions. What if there is a 4th Spatial dimension? Would a person in 4th dimension be able to play God with us, just as we did in the Flatland?
Now, what would you say, if I said there are 10 dimensions?! Can you imagine that? Modern physicists are working on the SuperString theory for the Universe, and their studies have shown that Universe has 26 dimensions, out of which at least 10 are of consequential importance. Can you imagine that? It is fascinating and at the same time too bewildering for our minds.
I hope that the demonstration of the 2 dimensional flatland has made you understand dimensions and how our perception defines our World for us. We feel proud of our progress, but at the same time we should also feel humbled by the Unknown.
Maybe the physicists, by unlocking the secrets of the multiple dimensions, would chance up on God, who may be playing with us from His or Her 10 dimensional World?
If you are interested, you could watch the movie “Flatland” or read the book written by Edwin Abbot. Another reference is Hyperspace by Michio Kaku.
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