# Message #2727

From: schuma <mananself@gmail.com>

Subject: Puzzle in Minkowski Space?

Date: Thu, 02 May 2013 20:42:38 -0000

When some people try to explain the fourth dimension, they talk about time. Personally I don’t like it, because it causes a lot of confusion. And the four-dimensional puzzles here don’t have anything to do with time.

However, if one really wants the fourth dimension to be time, the space (spacetime) should be Minkowski rather than Euclidean.

http://en.wikipedia.org/wiki/Minkowski_space

In this space, spatial rotation and Lorentz boost are allowed. Because of relativity, in some sense Minkowski space is a more complete model than the common 3D space.

Since Minkowski space is so cool, my question is: can we define twisty puzzles in Minkowski space? A related question I don’t have an answer is that, what are the "regular polytopes or tessellations" in Minkowski space? I know that Minkowski space lacks the full symmetry as in Euclidean space: time and space dimensions are different. But is that a reasonable relaxation, under which there are nontrivial regular polytopes or tessellations? I did some searching, but I haven’t got any answer.

The traditional Minkowski space has 3 spatial dimensions and one time dimension (3+1). But for simplicity we may focus on 2+1 or even 1+1 dimensions. But I really don’t know how to think of regular shapes or puzzles there.

For clarity, the hyperboloid model of hyperbolic geometry is like a 2D manifold imbedded in a Minkowski space. But I don’t think a puzzle in hyperbolic geometry with an underlying hyperboloid model is what I want.

Any thought?

Nan