Mathematicians are aware that a form that penetrates itself in a given number of dimensions can be produced without cutting a hole if an added dimension is available. The point is nicely illustrated by mathematician Rudolf Rucker. He asks us to imagine a species of “flatlanders” attempting to assemble a Moebius strip. Rucker shows that, since the “physical” (externally experienced) reality of these creatures would be limited to two dimensions, when they would try to make an actual model of the Moebius, they would be forced to cut a hole in it. Of course, no such problem of the Moebius intersecting itself arises for us human beings, who have full access to three external dimensions. What is problematic for us is the making of the Klein bottle, requiring as it would a fourth dimension. Try as we might, we find no such dimension “out there” in which to execute this operation.

(back to chapter 5)