★★★★☆ Calculus with pictures and jokes

Change Is the Only Constant: The Wisdom of Calculus in a Madcap World

Ben Orlin

I recently wrote a review of Understanding Analysis, which provoked me to lament the failure of most of Earth's population to appreciate the beauty of analysis. This led me to Change Is the Only Constant: The Wisdom of Calculus in a Madcap World, which is, more or less, a book intended to extenuate that deficit. I had previously read Ben Orlin's Math with Bad Drawings, a book that is simultaneously very funny and deeply profound. Thus I bought Change Is the Only Constant and read it in the kindle app on by iPad, for the sake of the color illustrations. I was delighted to discover that the book begins with an epigraph from Octavia Butler, whose Kindred I just finished. So clearly this was MEANT TO BE!

Here is how Change Is the Only Constant begins.

“What is,” said the philosopher Parmenides, not quite a million days ago, “is uncreated and indestructible, alone, complete, immovable and without end.” It’s a bold philosophy. Parmenides permitted no divisions, no distinctions, no future, no past. “Nor was it ever, nor will it be,” he explained; “for now it is, all at once, a continuous one.” To Parmenides, the universe was like Los Angeles traffic: eternal, singular, and unchanging.
A million days later, it remains a very stupid idea.

This is accompanied by a cartoon showing several stick figures reacting to Parmenides with scorn.

The introduction explains Orlin's purpose as follows

I want to be clear: the object in your hands won’t “teach you calculus.” It’s not an orderly textbook, but an eclectic and humbly illustrated volume of folklore, written in nontechnical language for a casual reader. That reader may be a total stranger to calculus, or an intimate friend; I’m hopeful that the stories will bring a little mirth and insight either way.

If you know anything about calculus, you probably know that it is generally divided into two branches: the differential calculus and the integral calculus. The differential calculus is about change. Change Is the Only Constant is divided into two books: "MOMENTS" and "ETERNITIES", which correspond to the differential and integral calculus.

I quite liked MOMENTS. Despite Orlin's disclaimer, it does quite a good job of teaching the differential calculus, along with lots of fun stories. It is also quite good at explaining the philosophy behind much of the calculus as currently practiced, which I would describe as the mechanization of insight, so that you don't have to be Archimedes to solve tricky problems -- lesser mortals such as you and I can also do it.

I found ETERNITIES less satisfactory. The integral calculus, as Orlin is at pains to point out, is wigglier, more creative and less defined than the differential calculus. That may sound like more fun, and for some readers perhaps it will be. For me it made everything more wishy-washy -- less mathematical, in short. Your Mileage May Vary.

If you're looking for a popular exposition of Calculus, I doubt you'll do better than Change Is the Only Constant.

Amazon review

Goodreads review

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