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.
My little pandemic-lockdown contribution to the world was a series of videos called The Biggest Ideas in the Universe. The idea was to explain physics in a pedagogical way, concentrating on established ideas rather than speculations, with the twist that I tried to include and explain any equations that seemed useful, even though no prior mathematical knowledge was presumed. I’m in the process of writing a series of three books inspired by those videos, and the first one is coming out now: The Biggest Ideas In The Universe: Space, Time, and Motion. For this solo episode I go through one of the highlights from the book: explaining the mathematical and physical basis of Einstein’s equation of general relativity, relating mass and energy to the curvature of spacetime. Hope it works!
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