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Already the steam-engine works our mines, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grain, spins and weaves our cloths, transports the heaviest burdens, etc. It appears that it must some day serve as a universal motor, and be substituted for animal power, water-falls, and air currents.
Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”
Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities.
In the end—after all sorts of philosophical arguments, and an analysis of actual historical data —the answer was: “It’s Complicated”. A test example coming soon is whether I can easily explain math ideas like algebra and calculus this way.) OK, so that’s a lot of projects.
Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930). At the level of individual events, ideas from the theory and practice of computation are useful. One is so-called Böhm trees.
Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930). At the level of individual events, ideas from the theory and practice of computation are useful. One is so-called Böhm trees.
But what about other models of computation—like cellular automata or register machines or lambda calculus? And we can trace the argument for this to the Principle of Computational Equivalence. We’ve talked about building up the ruliad using Turing machines. A very important claim about the ruliad is that it’s unique.
It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). Richard Feynman and I would get into very fierce arguments. Ed was a serious (and, by all reports, exceptionally good) pilot—with an airplane transport pilot license (plus seaplane and glider licenses).
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