Posts Tagged ‘hypercube’

4-dimensional hypercube

July 22, 2008

I’ve been reading Michio Kaku’s Hyperspace, and it’s got me trying to visualize the fourth spacial dimension. It’s not possible to do, but it’s fun to try. Fortunately, the internet has plenty of videos on the matter, a few of which I’ll present here.

As the video I embedded in a previous post about visualizing higher dimensions said, sometimes it’s easier to imagine a higher dimension beyond the three we’re familiar with by thinking of the higher dimension as a dimension you “fold lower dimensions through” to get a desired result. For instance, as shown in the video, folding a 2-dimensional sheet through the third dimension allows the edges of the sheet to touch, so an ant can crawl from one edge to the other. If you lived on the 2-D sheet and could only see in two dimensions, it would appear to you that the ant disappeared from one edge and instantly reappeared on the other. We can’t visualize dimensions higher than three, but we can visualize how actions in these higher dimensions would would look in our 3-dimensional world, analogous to a creature who can only see in two dimensions watching an ant disappear from one place and reappear in another.

A popular 4-dimensional object to try to visualize is a tesseract, which is a 4-dimensional hypercube. We can’t picture it, but we can picture it’s projection, or shadow, in three dimensions. Here is a video of the projection of a 4-D cube rotating: