__Mankind’s
Theoretical Version:__ Parallel Universes

**“VISUALIZING HIGHER DIMENSIONS
**

Our minds, which conceptualize objects in three spatial dimensions, cannot fully grasp higher-dimensional objects. Even physicists and mathematicians, who regularly handle higher-dimensional objects in their research, treat these objects with abstract mathematics rather than trying to visualize them. However, given the analogy with the Flatlanders, there are tricks we can use to visualize higher-dimensional geometric objects such as hyper cubes.

The concept of a three-dimensional cube would be alien to the Flatlanders. However, there are at least two ways in which we could convey to them the concept of a cube. First, if we were to unravel a hollow cube, we would, of course, unfold a series of six squares, which can be arranged, say, in the shape of a cross. For us, it is obvious that we can simply rewrap these squares into the shape of a cube. For the Flatlander, this is impossible. Similarly, a higher-dimensional being could convey to us the concept of a hypercube by unraveling it until it becomes a series of three-dimensional cubes, called a tesserack.

There is yet another way in which the concept of a cube could be conveyed to a Flatlander. If the edges of a cube are made of sticks, and the cube is hollow, we could shine a light on the cube and have the shadow fall upon a two-dimensional plane. The Flatlander would immediately recognize the shadow of the cube would perform geometric changes that are beyond the understanding of the Flatlanders. Similarly, the shadow of a hypercube whose sides consist of sticks appears to us as a cube within a cube. If the hypercube is rotated, we see the cube within a cube executing geometric gyrations that are beyond our understanding.

Higher-dimensional beings can easily visualize lower-dimensional objects, but lower-dimensional beings can visualize only sections or shadows of higher-dimensional objects.

First of all, a ten-dimensional being looking down on our universe could see all of our internal organs and could even perform surgery on us without cutting our skin. This idea of reaching into a solid object without cutting our skin. This idea of reaching into a solid object without breaking the outer surface seems absurd to us only because our minds are limited when considering higher dimensions, just like the minds of the Polygons on the Council.

Second, if these ten-dimensional beings reached into our universe and poked a finger into our homes, we would see only a sphere of flesh hovering in midair.

Third, if these ten-dimensional beings grabbed someone who was in jail and deposited him elsewhere, we would see that person mysteriously vanish from jail and then suddenly reappear, as if by “magic,” somewhere else. In many science fiction novels, a favorite device is the “teleporter,” which allows people to be sent across vast distances in the blink of an eye. A more sophisticated teleporter would be a device that would allow someone to leap into a higher dimension and reappear somewhere else.”

Information acquired within the quotes is from: Beyond Einstein , The Cosmic Quest for the Theory of the Universe, pages 167-170, Michio Kaku and Jennifer Thompson, 1995 copyright

Published by Doubleday