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Voyage from Flatland

Most of us live in Flatland. When we encounter an obstacle, it blocks our progress and we cannot go further. In the diagram below, the red circle cannot escape from the blue square. It lives in Flatland and can move only in two-dimensions. Whichever way it tries to get out it meets the blue barrier. It cannot go up or down, so it cannot get out. It thinks the whole world is the contents of the blue square! It can know no more.

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However, there are more than two dimensions. Really we live in three-dimensions (and more.) If only the red circle knew this. It would not be trapped. This is how things would look if the circle knew it had 3 dimensions - if it knew it could go up:

The Red Circle as seen from a 3-dimesnional world

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The circle isn't limited by two dimensions. It can now move up. (And down.) The blue square, which was once a barrier is no longer a barrier to the red circle that moves in 3 dimensions. It can now escape. But the red circle is no longer a circle. It is now a sphere. It has 3 dimensions and is full of existence.

Another inhabitant of Flatland would see the red circle get smaller as it rises above the barrier. It would then seem to disappear. And then it would appear on the other side of the barrier.

The Red Circle as seen from Flatland (Refresh your browser to see the animation.)

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Of course, the red circle does not really get smaller. It goes up. But in Flatland all they can see is two-dimensions. They know they can go left, right, forwards and backwards. But they do not know you can go up. So it looks like the circle shrinks and disappears. Then it seems to reappears on the other side of the barrier. At first small: it seems to grow to its normal size. To inhabitants of Flatland this looks like magic. To inhabitants of the 3-dimensional world, it just seems natural and normal.

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