Whatever we might or might not see in such a world, however, I will take it as a given that living as we do in a 3D world we can not physically picture anything higher-dimensional than ourselves. He later speaks of the wonders he saw, which he "found daily more difficult to reproduce even before my own mental vision." I maintain that even if we were somehow put in a 4D world our eyes could no more see a 4D object than Abbott's character could have seen off of his plane in the first place. In Abbott's book the main character is eventually knocked off his planar world and is temporarily able to see 3D objects directly. As 3D beings we can only see, or even visualize, objects in three or fewer dimensions. Being confined to his flat plane, however, the square can only see the part of the sphere that is crossing his 2D world: "the Sphere manifested himself to me, or to any Flatlander, as a Circle." This example illustrates the basic dilemma I'm addressing. The main character, a square, is visited by a sphere from the third dimension. All of the characters in the book have simple geometrical shapes, which makes the presentation of the ideas clearer. In his delightful novel Flatland, Edwin Abbott describes a race of beings who live in two dimensions. The purpose of this paper is not to lay first claim to these ideas, but simply to share them with anyone else who might find them fun to play with. I have, quite frankly, never bothered to look. I am quite confident that it's not original in the sense that many other people have doubtless thought of it and written about it before. This method is original in the sense that I thought of it. With a little practice you can learn to visualize objects like 5D spheres, 4D cubes, and so on, and even see what happens when you rotate them in different ways. This paper introduces a method I developed for representing objects in more than three dimensions.
#5d hypercube how to#
Viewing Hyperspheres, Hypercubes, and other 4-D Objects How to Draw a Five-Dimensional Cube Copyright (c) 2004 by Gary Felder
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