These are just my idle thoughts so please shoot them down at will.  I've thought for a while now that gravity pulls in the direction of the 4th dimension. A simple example being a round planet. The 4th dimension should be perpendicular to our 3 dimensions and if we take a planets surface to be "smooth" then gravity pulls perpendicular to all surfaces. I wonder if gravity is like a magnet under paper moving iron filings around. Mass bends space-time in the direction of the 4th dimension, we try and fall in and like the iron filings we feel the force but cannot move that direction.