Most of us dread mathematics and its specialized branches like calculus. Few of us know the role they play in our lives without our knowing it. It would come as a surprise to most of us that our entire civilization is structured on calculus. Few know that we wouldn’t have cell phones, computers, or microwave ovens without calculus. We wouldn’t have Radio or Television. Without the knowledge of calculus, we would not have invented our ultrasound for expectant mothers or GPS for lost travelers. It was only with the help of the knowledge of calculus that we managed to split the atom, unraveled human genome, or put astronauts on the moon. So much so that we might not even have the Declaration of Independence without the knowledge of calculus. In Infinite Powers, Steven Strogatz says that it’s a curiosity of history that the world was changed forever by an arcane branch of mathematics. How would it be that a theory originally about shapes ultimately reshaped civilization? Steven Strogatz tells this amazing story of calculus in Infinite Powers.
The universe is deeply mathematical for reasons unknown to us. Steven Strogatz says that it’s a mysterious and marvelous fact that our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations. Such equations describe the difference between something right now the same thing an instant later or between something right here and the same thing infinitesimally close by. The details differ depending on what part of nature we’re talking about, but the structure of the laws is always the same. To put this awesome assertion another way, there seems to be something like a code to the universe, an operating system that animates everything from moment to moment and place to place. Calculus taps into this order and expresses it.
Isaac Newton was the first scientist to glimpse this secret of the universe. He found that the orbits of the planets, the rhythm of the tides, and the trajectories of cannonballs could all be described, explained, and predicted by a small set of differential equations. Today we call them Newton’s laws of motion and gravity. Steven Strogatz tells us that we have found since then that the same pattern holds whenever we uncover a new part of the universe. From the old elements of earth, air, fire, and water to the latest in electrons, quarks, black holes and superstrings, every inanimate thing in the universe bend to the rule of differential equations. By inadvertently discovering this strange language, first in a corner of geometry and later in the code of the universe, then by learning to speak it fluently and decipher its idioms and nuances, and finally by harnessing its forecasting powers, humans have used calculus to remake the world.
It’s often said that mathematics is the language of science. Steven Strogatz explains how it is so. Steven Strogatz says, in the case of electromagnetic waves, it was a key first step for Scottish mathematical physicist James Clerk Maxwell to translate the laws that had been discovered experimentally into equations phrased in the language of calculus. But the language analogy is incomplete. Calculus, like other forms of mathematics, is much more than a language; it’s also an incredibly powerful system of reasoning. It lets us transform one equation into another by performing various symbolic operations on them, operations subject to certain rules. Those rules are deeply rooted in logic, so even though it might seem like we’re just shuffling symbols around; we’re actually constructing long chains of logical inference. The symbol shuffling is useful shorthand, a convenient way to build arguments too intricate to hold in our heads.
Infinite Powers is startlingly revealing work that shines a light on the importance of calculus in the scheme of the universe and how we used to reshape this world. It makes our world more fascinating than it already is for us. It is written in a very clear and easy-to-understand way. Steven Strogatz has made calculus so much accessible to even high schoolers. Steven Strogatz loves mathematics and will make you love it too like you love a piece of cake. He explains the mysteries of our world in such a way that it no longer appears mysterious and chaotic. This book is for you if you want to understand how our universe was structured and function.