Math of General Relativity Part 17

First, we relate a point and time in Madison Square Garden (for instance, a chair at 123 seconds) MSG to a geometric point on the four dimensional surface. Then we relate the value of the gravitation field at that point and time (or that space-time point) to the value of the Matrix Tensor at the correspondingly mapped point on the surface R4.

Notice what I just claimed: that gravity in real space and time DETERMINES the way the 4D surface will look. That is, gravity in MSG will create the shape of the surface. From there, we can analyze how gravity works by using the mathematical methods developed by Riemann and his work on Differential Geometry.

In more concrete and visual detail, let me show you how to "map" a space-time point into a surface point, and then how to map the Metric Tensor back into Madison Square Garden so that you know the gravitational field inside the stadium.