Right, ok, but here's the problem I'm having in conceptualizing time as the 4th dimension and including the idea of the three spacial dimensions "moving forward" through the dimension of time. Given that the three spacial dimensions are curved across the 4th dimension, namely time, and we are moving forward through time, then consider this: near a massive body, spacetime is curved more than say in deep space, such that (depending on how you orient the direction of time's arrow) future time will "arrive" at a point near a massive body before/after a point in deep space.

In other words, let's imagine the rubber sheet analogy of 2d space that is curved across the 3rd dimension of time. In this analogy, you may either think of time as something flowing across a non-moving rubber sheet, or as the rubber sheet moving across the 3rd dimension of time. Either way, if this sheet is curved through the 3rd time dimension, then the same future will "arrive" at different points in spacetime.

What do you think, am I thinking this right?