Think about the dimensionality of a balloon with surface waves. Say these waves are of small amplitude compared with the radius of the balloon. Two coordinates label points on the balloon and a third labels radial position. Creatures who lived on the surface could make measurements that determined the curvature of their space. Let us say they would also be able to detect the waves that went about their space. They would say their space is two dimensional but they needed a real field to describe the waves on their surface. To we who live in 3 space dimensions we would say, what field, they live on a two dimensional surface that can vibrate. They need three coordinates to describe their world. Giving our spacetime extra dimensions seems natural even if wrong. Thanks for any thoughts, and apologies if this post is in the wrong place.