Geodesics with curved time

Suppose that we are two dimensional beings living on this surface. Suppose that we want to move forward in straight lines. The equivalent of a straight line on a curved surface is a Geodesic. Here, each color represents a different Geodesic. In this first example, we are dealing with only a small amount of curvature. Here, each path is deflected by only a small amount. For example, the green and red paths start out close together, and they are deflected by slightly different amounts. The results will be completely different if we have a large amount of curvature. Here, notice how the red path and the green path start out very close together, but they end up leaving in completely opposite directions. This is shown for a curved two dimensional space and this can also be extended to higher dimensions. However, there are important considerations that need to be taken into account when applying this to the four dimensional space-time of General Relativity. In cases where we are travelling at a speed far less than the speed of light and Newtonian physics gives us accurate approximations, contrary to popular belief, the apparent force of gravity has little to do with the curvature of the three spatial dimensions relative to each other. In these cases, the apparent force of gravity is primarily due to the curvature of the "time" dimension, relative to the three spatial dimensions.