I read an SF yarn once where the time-traveling protagonists were trying to determine the curvature of time. The curvature is negative if even a tiny change in the past cascades to a colossal change in the future--the old "stopping a Jurassic butterfly wing flap causes birds instead of mammals to develop space travel by the 20th century" gag.

A positive temporal curvature implies that there is an inertia to time; that even an enormous cataclysm in the past will eventually damp out and if you wait long enough things will settle down and wind up in the same place after all. Even destroying the earth altogether would not affect, say, the future history of the solar system.

The radius of curvature describes the rapidity with which the small change evolves into a big one (in the case of negative curvature), or the amount of time it takes for the induced change to return to a stable state (positive curvature). We can even postulate that the curvature may vary at different temporal scales, i.e., perhaps negative in the short run but positive in the long view. This implies that at some temporal scale the curvature is flat, whatever that means. And of course, space may play some role in all this, and the speed of light as well.

I guess I've strayed off-topic somewhat, but that's the thought-train your comments provoked.