Steven Strogatz’s “Infinite Powers”: Science Is a Story of People

“Because we tend only to see the final product of an intellectual endeavor, it is easy to forget that even titans such as Archimedes cannot know the final answer before they get their hands dirty with the problem at hand.”

A very general summary of Infinite Powers, by Steven Strogatz, might describe the book as an exposition of the history and application of calculus, one of the most fundamental branches of mathematics ever discovered by mankind. But such a clinical synopsis would miss the vibrant, personal story that Strogatz tells, reminding us that scientific, philosophical, and mathematical progress is necessarily a human endeavor. Although we stand on the shoulders of giants, those giants were as prone to ego, insecurity, fervor, and mysticism as any of us mere mortals. The stories in Infinite Powers demonstrate that the intellectual rigor by which discoveries are made—and the drama that infuses any tale of people—cannot be separated. The growth of knowledge and humanity are, and have been, forever intertwined. Strogatz reminds us that even the seemingly infallible heroes of our intellectual lineage are flesh and blood, one with the rest of us.

Archimedes (288-212 BC)

It is quite clear in Strogatz’s telling of Archimedes’ mathematical accomplishments that he admires the ancient thinker—and with good reason. The ancient Greek discovered both the principle of buoyancy and the law of the lever (the reader should consult the book for details), and he was the first to exploit what Strogatz dubs the Infinity Principle. This is the strategy whereby, in order to “shed light on any continuous shape, object, motion process, or phenomenon…reimagine it as an infinite series of simpler parts, analyze those, and then add the results back together to make sense of the original whole.” Strogatz details Archimedes’ masterful exploitation of the principle to solve problems. Successfully playing with infinity literally thousands of years before the invention of full-fledged calculus reveals the mathematician’s creative willingness to forego any previously established rules and to follow his intuitions wherever they took him. In this ancient thinker, freedom of mind reigned supreme.

Intuitions may be the stimulus of an eventual solution—or they might lead to a dead-end. The real work is everything in between.

But Strogatz does not only focus on his mathematical accomplishments. The author describes a letter that Archimedes had written to his friend, Eratosthenes. The crux of the letter, as Strogatz describes it, is that Archimedes admits to following his intuitions when trying to solve problems. Because we tend only to see the final product of an intellectual endeavor, it is easy to forget that even titans such as Archimedes cannot know the final answer before they get their hands dirty with the problem at hand. Intuitions may be the stimulus of an eventual solution—or they might lead to a dead-end. The real work is everything in between.

Archimedes gave civilization a mature science of static systems—those that remain unchanged over time. Significant progress in the study of dynamical, changing systems would have to wait well over a millennium.