Broader Perception and the Flatland

Broader Perception and the Flatland

Lets see an example which reveals how someone could have a broader perception of the world whereas he might be regarded as mentally unstable or a cheat. This example comes from Edwin Abbots book entitled The Flat-land.

In this short story there is a world on a plane with inhabitants which are two-dimensional shapes, that is squares, triangles etc. It is obvious that the inhabitants of this country, the Flatland, cannot perceive height. Their world has only two dimensions, length and width.

One day a creature of the three dimensional world, a sphere, for example, visits a Flatland mathematician, who has the shape of a square, with the view of revealing the secrets of the third dimension to it. The square using its vision and touch perceive the sphere as a circle since its section (intersection) with the plane is actually a circle and the square can perceive only two dimensions because this is his world. The sphere in vain tries to explain to it that there is a third dimension displaying its qualities. It moves up and down on the plane and the square can see a sign which widens into a circle that is growing as big as possible and then it is getting smaller and smaller again until it becomes a sign and disappears. This is an inexplicable phenomenon to the square because it doesnt have an immediate sensory perception and doesnt understand the dimension of height.

Nevertheless, to us it is clear that the vertical movement of the sphere on the plane leaves these traces/signs.

I wonder what image the section of a four- dimensional creature with our three dimensional world would present /create. Wouldnt it be an inexplicable phenomenon?

Then the sphere tries to explain everything geometrically to the square as it has the qualities of a mathematician. The sphere asks it to prolong a square, in an imaginary way, vertically on its plane in order to realize that it will become a cube. Its impossible. To the Flatland square there is no concept of verticality in a two dimensional object since there is not a third dimension. Can we imagine what will happen if we prolong a cube vertically in the space? What and where is the direction vertically to the cube? Finally, the sphere takes the square to the space of the three dimensions. A world even more magical than it has imagined spread in front of it . It can see the Flatland from above, understand the concept of a solid body and by climbing up and feeling it. It is so happy. It is now eager to know the worlds of four, five or even more dimensions. The sphere is displeased at its demands and deters the square from believing in these worlds. The sphere has its own sensory commitments and prejudices. Afterwards the square returns to its own world and tries to explain the concept of the third dimension to all others. It doesnt know, though, how to explain the direction upwards. Therefore, its society decides that it should be put to prison as it is a heretic and fraud.

Abbots book is a wonderful work of imagination and at the same time a biting social satire.

ACRIVITY -THE FLATLAND

What do you thing you can see from the solid on the left at the flatland. Draw your thinking at the right

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