Tesseract

Tesseract

In such interdimensional contemplations, we need not be restricted to two dimensions. We can imagine a world of one dimension, were everyone is a line segment, or even the magical world of zero-dimensional beasts, the points. But perhaps more interesting is the question of higher dimensions.

We can imagine generating a cube in the following way: take a line segment of a certain length and move it an equal length at right angles to itself. That makes a square.

Now move the square an equal length at right angles to itself, and we have a cube. We understand this cube to cast a shadow, which we usually draw as two squares with their vertices connected. If we examine the shadow of a cube in two dimensions, we notice that not all the lines appear equal, and nota all the angles are right angles.

The three dimensional object has not been perfectly represented in its transfiguration into two dimensions. This is the cost of losing a dimension in the geometrical projection. Now let us take our three-dimensional cube and carry it, at right angles to itself, through a fourth physical dimension: not left-right, not forward-back, not up-down, but simultaneously at right angles to all those directions.

Could there be a fourth physical dimension or a tesseract? (Quotations from M. Jorgensen). Image: © M. Jorgensen (Elena)

We cannot show what direction that is, but we can imagine it to exist. In such a case, we would have generated a four-dimensional hypercube, also called a tesseract.

It is impossible to show a tesseract, because we are trapped in three dimensions. But what we can show is the shadow of a tesseract. It resembles two nestled cubes, all the vertices connected by lines. But for a real tesseract, in four dimensions, all the lines would be of equal length and all the angles would be right angles.

If a fourth-dimensional creature existed it could, in our three-dimensional universe, appear and dematerialize at will, change shape remarkably, pluck us out of locked rooms and make us appear from nowhere. It could also turn us inside out. There are several ways in which we can be turned inside out: the least pleasant would result in our viscera and internal organs being on the outside and the entire Cosmos – glowing intergalactic gas, galaxies, planets, everything – on the inside. Hum… we cannot be sure we like the idea.