Since time is three-dimensional, what is the total time given the time in each dimension? The answer is exactly like the total distance. Consider the times *t _{1}, t_{2}*, and

*t*. If these are the coordinates of three successive movements, then the total time is their sum:

_{3}*t = t*. But if the times

_{1}+ t_{2}+ t_{3}*t*, and

_{1}, t_{2}*t*are components of one movement, then the total time is the time displacement, which is Euclidean:

_{3}*t² = t*. If the times

_{1}² + t_{2}² + t_{3}²*t*, and

_{1}, t_{2}*t*are the components of the final point in time of a movement, then the total time is the integral of the time path taken to get to that point in time.

_{3}The metric for each axis of movement is the hyperbolic metric *ds _{i}² = dt_{i}² – dr_{i}²*. The total metric is

*ds² = ∑*with

_{i}dt_{i}² – dr_{i}²*i*= 1, 2, 3.

This raises the question whether space-time is six-dimensional or two three-dimensional geometries. In some sense 3D space and 3D time might combine to form a 6D unity. As Minkowski said, “Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. ” That’s an exaggeration but it’s basically correct.