Intuitive Math

We have discussed a variety of mathematical phenomena in physics. For instance, we were able to argue that there are antipodal points on Earth with the same temperature and air pressure, based upon nothing but the principle of continuity. We showed through this example that math can put some constraints on physics, though it often does not give much information about the guts and dynamics of physics. Math can lay down the constraint regarding the existence of those antipodal points on Earth, but it does not tell you where those points are or the circumstances under which that might change.