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Bright Science is a free YouTube channel of over 1300 study videos for high schoolers (or precocious middle schoolers). Most are about five minutes (some longer, some shorter) and cover topics like chemistry, physics, calculus, geometry, biology, Algebra, trigonometry, grammar, ACT prep, and SAT prep.
The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. But what about other models of computation—like cellular automata or register machines or lambda calculus?
He’s writing a paper, he says, basically to clarify the Second Law, (or, as he calls it, “the second fundamental theorem”—rather confidently asserting that he will “prove this theorem”): Part of the issue he’s trying to address is how the calculus is done: The partial derivative symbol ∂ had been introduced in the late 1700s.
It’s not obvious that it would be feasible to find the path of the steepest descent on the “weight landscape” But calculus comes to the rescue. It turns out that the chain rule of calculus in effect lets us “unravel” the operations done by successive layers in the neural net.
Could it really be that this was the secret that nature had been using all along to make complexity? But it really wasn’t physics, or computer science, or math, or biology, or economics, or any known field. Sometimes I’ve thought of ruliology as being at first a bit like natural history. But at least it would have a home.
And if we’re going to make a “general theory of mathematics” a first step is to do something like we’d typically do in naturalscience, and try to “drill down” to find a uniform underlying model—or at least representation—for all of them. There were some areas to which I was pretty sure the methods of A New Kind of Science would apply.
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