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211 | Solo: Secrets of Einstein's Equation
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
Riemann's Theorem of Distance
Pythagoras' formula for distance is x squared plus y squared plus z squared. But Riemann says, what if you drew just x and y coordinates, but they weren't perpendicular to each other? What if you drew the y coordinate at an angle compared to where you usually draw it? Then the formula for a little length would also involve not only x squared and y squared, but x times y. These arrays of numbers tell you how to calculate distances in a completely arbitrary geometry with a completely arbitrary set of coordinates.
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