Infinite Powers: How Calculus Reveals the Secrets of the Universe

by Steven H. Strogatz

This is what Einstein marveled at when he wrote, “The eternal mystery of the world is its comprehensibility.”

That’s the big idea behind calculus. Everything becomes simpler at infinity.

That annoying hum is the sound of sine waves bobbing up and down sixty times a second. It’s the telltale sign of alternating current produced by generators in the power grid whose machinery is spinning at that same frequency. Where there is circular motion, there are sine waves.

Three drugs in combination, however, would be hard for the HIV virus to overcome. The math suggested that the odds were something like ten million to one against HIV being able to undergo the necessary three simultaneous mutations to escape triple-combination therapy.

From this point of view, calculus is the sprawling collection of ideas and methods used to study anything—any pattern, any curve, any motion, any natural process, system, or phenomenon—that changes smoothly and continuously and hence is grist for the Infinity Principle.