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
Cover: Infinite Powers: The Story of Calculus -- The Language of the Universe by Steven... [+]
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, 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 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.
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, much scarier, 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 heard about in maths classes. For example, I was particularly interested 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/AIDS. 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 pitched battle between production of new virus particles and their destruction by the immune system (pp. 218-225).
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 relative ease of learning differential calculus compared to integral calculus.
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. 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 what the heck you are doing.
Infinite Powers: The Story Of Calculus | @GrrlScientist
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