
The fourth dimension isn’t another place, it’s another direction to move along. We know about left, right, front, back, up, and down, but there are other possibilities. Time, for example, extends from past to future. Suppose that a cube suddenly appears floating in front of you. It stays there for one unit of time and then disappears. In the first instant of its existence, there is a cube. At the last moment of its existence, there is also a cube, but displaced in time from the first one. In between, each face of the early cube serves as the oldest face of another cube that extends through time to the corresponding youngest face of the late cube. The whole array forms a tesseract (or hypercube), a fourdimensional object bounded by eight cubes. Of course, we can only see the part of the tesseract that’s now, that happens to exist at the moment we’re looking at it.
I wondered, what does a tesseract look like when it spins? Click here to find out.
A simplexn (or nsimplex) is the simplest figure that can exist in n dimensions. Simplex2, residing in the 2dimensional plane, is a plain old plane triangle. Simplex3 is a tetrahedron, or triangular pyramid. Simplex4 is a pentatope, a 4dimensional object bounded by 5 tetrahedra. Click here to watch a tetrahedron spin in 3space and 4space, and a pentatope rotate in 4space. 