I'm trying to gain a deeper understanding of gravity from a purely geometric point of view (as opposed to the more Newtonian "force" point of view). This thread is the result of a discussion that began in another thread. However, that should not cause a problem for people who are just joining. The essential question is, why (or how ) matter "chooses" one particular geodesic path over another. For example, what is the explanation for why an apple follows a geodesic back to Earth rather than following a different geodesic to somewhere else? DaleSpam has already provided some answers to get this moving. He has emphasized that I'm asking about local geodesics. A local geodesic is not concerened with a "destination" but only with maintaining a purely straight path. To define a local geodesic, all we need to know is an objects starting point and it's direction ("tangent vector"). I now understand this simple concept and can differentiate it from a global geodesic. Global geodesics are paths not defined by tangent vectors, but by the straightest way between two points. (I think global geodesics can still be defined locally if you're looking at the properties of a manifold?). At any rate, this should catch everyone up with the issue. I will make a separate post in which I've singled out one of DaleSpam's answers that will help us sort through the confusion of gravity.