Infinite Powers - Steven Strogatz

Review :

For an ordinary layperson, this is perhaps the most accessible history of the development of Calculus one could hope for. In easily readable language Strogatz has provided a fascinating narrative covering the ideas behind Calculus, its history from the earliest Greek mathematicians, its "dismissal" from the formal geometric/mathematical canon for some two thousand years, until its resurgence in the 17th-c with the work of Newton and Leibnitz, and on to its amazingly extensive application to just about every sphere of activity in modern civilisation.

Some knowledge of basic mathematics is required, but not much more than that: Strogatz is more concerned with explaining what Calculus is all about, and pointing out that certain precise questions about specific physical problems can only be best answered by its application. Calculus is the most accurate mathematical tool ever developed for answering such questions.

Some things I particularly liked about this lie in the conceptual (philosophical) matters that are implied or suggested: the idea, for example, that the modern understanding of the Space-Time continuum is maintained (for me, the "problem" between the continuum idea and the idea of infinitesimals remains, and probably should remain so); and the fact that, no matter how "infinitesimal" the divisions of differential calculus are made, there will always remain "a little bit" extra that is unaccounted for. The latter is difficult enough when dealing with the interrelationship of two "entities" or "bodies", let alone the far more complicated problem relating to three (or more) such entities, so it remains a potentially intriguing matter.

While the cynics among us might consider this enough to disparage its absolute applicability, Calculus remains our most successful, accurate and practical measurement tool so far. I like the idea that there is still the possibility for new approaches to be made: but that being said, the current "solution" to such errors will still most probably be found through the re-application and refinements of its processes.

An ironic example of this relates to Strogatz's use of the Boeing 787 Dreamliner aeroplane as a proud example of the achievements made under the auspices of this form of mathematics. This may very well be the case, but at the same time, some bad reports coming in 2019 about Boeing's 737 MAX line of planes suggested that, among other matters, computer design flaws were partly responsible for two of these planes crashing with a total loss of 364 lives: a sober reminder that the more intricate the maths, the more care needs to be taken in its applications and consequences in the physical world.

Even so, it is Calculus which is at the heart of most of the technological developments we already enjoy, and it will undoubtedly have much more to contribute, particularly in the areas of medicine, society and politics in the years to come. This book will at least provide a basic understanding of what it is that has become indispensable in our societies, whether we like it or not.


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