Calculus Better Explained - Kalid Azad

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So. . . What Can I Do With Calculus?

It depends. What can you do with arithmetic? Technically, we don’t need numbers. Our caveman ancestors did fine (well, for some version of “fine”). But having an idea of quantity makes the world a lot easier. You don’t have a “big” and “small” pile of rocks: you have an exact count. You don’t need to describe your mood as “good” or “great” – you can explain your mood from 1 to 10.

Arithmetic provides universal metaphors that go beyond computation, and once seen, they’re difficult to give up. Calculus is similar: it’s a step-by-step view of the world. Do we need X-Ray and Time Lapse vision all the time? Nope. But they’re nice perspectives to “turn on” when we face a puzzling situation. What steps got us here? What’s the next thing that will happen? Where does our future path lead? There are specific rules to calculus, just like there are rules to arithmetic.

And they’re quite useful when you’re cranking through an equation. But don’t forget there are general notions of “quantity” and “step-by-step thinking” that we can bring everywhere. Our primary goal is to feel what a calculus perspective is like (What Would Archimedes Do?). Over time, we’ll work up to using the specific rules ourselves.