Whenever parts of a system interfere or cooperate with each other, there are nonlinear interactions taking place. Most of everyday life is spectacularly nonlinear; if you listen to your two favorite songs at the same time, you won’t get double the pleasure. The same goes for consuming alcohol and drugs, where the interaction effects can be deadly. By contrast, peanut butter and jelly are better together. They don’t just add up—they synergize.
Nonlinearity is responsible for the richness of the world, for its beauty and complexity and, often, its inscrutability. For example, all of biology is nonlinear; so is sociology. That’s why the soft sciences are hard—and the last to be mathematized. Because of nonlinearity, there’s nothing soft about them.
[…]
Sofia Kovalevskaya helped us understand how different the world appears when we finally face up to nonlinearity. She realized that nonlinearity places limits on human hubris. When a system is nonlinear, its behavior can be impossible to forecast with formulas, even though that behavior is completely determined. In other words, determinism does not imply predictability. It took the motion of a top—a child’s plaything—to make us more humble about what we can ever hope to know.
—
Steven Strogatz, Infinite Powers
(2019)
Galileo conceded that the study of pendulums “may appear to many exceedingly arid,” although it was anything but that, as later work showed.
In mathematics, pendulums stimulated the development of calculus through the riddles
they posed. In physics and engineering, pendulums became paradigms of
oscillation. Like the line in William Blake’s poem about seeing the world in a
grain of sand, physicists and engineers learned to see the world in a pendulum’s
swing. The same mathematics applied wherever oscillations occurred. The
worrisome movements of a footbridge, the bouncing of a car with mushy shock
absorbers, the thumping of a washing machine with an unbalanced load, the fluttering
of venetian blinds in a gentle breeze, the rumbling of the earth in the
aftershock of an earthquake, the sixty-cycle hum of fluorescent lights—every field
of science and technology today has its own version of to-and-fro motion, of rhythmic
return. The pendulum is the granddaddy of them all. Its patterns are universal.
Arid is not the right word for them.
—
Steven Strogatz, Infinite Powers
(2019)
