01 / A FOURTH SPATIAL DIRECTION

What is four-dimensional space?

In this game, the fourth dimension is another direction in space. It is not time.

From a line to a world.

One number locates a point on a line. Two locate it on a plane. Three describe familiar space. A fourth independent coordinate gives a point in four-dimensional Euclidean space:

W is perpendicular to X, Y and Z in the mathematical model. Our screens still have two dimensions, so the game shows a perspective view of a three-dimensional section of that larger world.

You inhabit a slice.

Imagine a flat creature living in a sheet of paper. A sphere passing through its world appears first as a point, then growing circles, then shrinking circles. In the same way, a four-dimensional sphere can intersect our three-dimensional slice as a growing and shrinking sphere.

A tesseract is the four-dimensional analogue of a cube. It has 16 vertices, 32 edges, 24 square faces and 8 cubical cells. The next field note projects its edges so you can inspect rotations; that projection is different from the solid cross-sections used for gameplay.