Math of General Relativity Part 15

You can picture Madison Square Garden from one midnight to the next, and you can picture an arbitrary real curved surface R2, so we went from there to Space-Time S4 and to a Riemann Space R4 that "represents" real space and time somehow.

To know the full and complete nature and geometric shape and form of any surface, all you need to know are 16 numbers for each point on the surface. You can arrange these 16 numbers in a 4-by-4 array, called a matrix, for convenience. These numbers are tensor numbers, because you need to give them a name, and the array is called the Matrix Tensor.

Therefore, we can abbreviate everything I just said above by stating that for any surface, if you know its matrix tensor at each point of the surface, you know how the surface looks. You know its shape, everything.