Infinite powers:The story of calculus.Review
A rare look at the history and logic of calculus, how it was invented and developed, and what it reveals about the universe, the planet, its creators — and, well, all of us
Calculus is one the most profound inventions in human history. It underlies most modern technologies such as radio, television, radar, GPS navigation, cell phones, and MRI imaging. It informs meteorology, economics, social sciences, epidemiology, biology and medicine. Thus, it is a subject that every educated person should have a conceptual understanding of, at least the very least.
In Steven Strogatz’s beautifully-written Infinite Powers: The Story of Calculus — The Language of the Universe (Atlantic Books, 2019: Amazon US / Amazon UK), we learn about the conceptual framework upon which calculus is built, we learn about its humble beginnings and how it was developed throughout the ages to address specific challenges from determining the area of a circle to making sure your space craft sticks its lunar landing.
Because calculus is a supremely human endeavor, we also learn about this discipline by learning about its people, starting with Zeno’s and Archimedes’ seminal insights, and following its development over more than three millennia by learning about critical contributions made by dedicated men and women who made it possible to study modern day abstract concepts such as chaos theory and artificial intelligence.
In this fun book, we discover that the special genius of calculus is that it’s based upon breaking down complex, seemingly intractable problems into infinitely small, solvable, pieces, which then can be computed and tamed before reassembling them into the larger, hopefully much less scary, whole. But more than breaking things into infinitely tiny pieces, this strategy has made calculus into a powerful tool that has led to all sorts of technological advances and solutions to real-world problems — solutions that most people never hear about in their maths classes, but really should. For example, I was particularly fascinated by the lucid and fascinating discussion about how calculus played a role in the universal adoption of the triple drug cocktail to combat the maddening, seemingly insurmountable mutation rate of HIV. Calculus also provided critical insights into the nature of the puzzling asymptotic stage of the HIV infection where, it turns out, there is a long-running, albeit delicate, balance in the furious battle between production of new virus particles and their destruction by the immune system (pp. 218–225).
Additionally, I was amused to learn how one can use the standing electromagnetic waves emitted by their microwave oven to calculate the speed of light with reasonable accuracy (pp. 262–264).
On a more theoretical level, Professor Strogatz’s thoughts about why synthesis is so much more difficult than analysis for problem solving was illuminating (pp. 102–103), especially when thinking about the ease of learning how to use differential equations compared to integral equations, which are more intellectually challenging.
In this book, infinity is its alpha and omega, its beginning and end, and that intellectual framing is both appropriate and aesthetically pleasing.
For readers who don’t want to immerse themselves in the actual maths but who still want to appreciate the history and the reasoning that gave rise to calculus, this is the most accessible book on those topics published in many years. In recognition of that rare achievement, this brilliant book is one of six that are shortlisted for the prestigious Royal Society Insight Investment Science Book Prize for 2019.
For serious students of calculus, Infinite Powers will give you the historical and conceptual grounding that is so often lacking in maths education these days, and in doing so, it could help you understand at a more intuitive level what the heck you are doing.