Infinite Powers: How Calculus Reveals the Secrets of the Universe Paperback – April 14, 2020

Prof. R. Feynman, after an interview with a novelist who was doing research for a book about WW. II, as they were departing, asked him if he knew calculus. No, was the reply, he didn't. ''You had better learn it'' said Feynman. ''It's the language God talks''.Mr. Strogatz starts the Introduction part of his wonderful book by telling this anecdote. He continues, ''For reasons no body understands, the universe is deeply mathematical. May be God made it that way. Or maybe it's the only way a universe with us in it could be, because non-mathematical universes can't harbor life intelligent enough to ask the question. In any case, 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 and the same thing an instant later. The details differ depending on what part of nature we are talking about, but the structure of the laws is always the same... There seems to be something like a code to the universe, an operating system... Calculus taps into this order and express it.''''Isaac Newton was the first to glimpse this secret of the universe... If anything deserves to be called the secret of the universe, calculus is it.''Mr. Strogatz tells the story behind how humanity discovered this strange language, how they learned to speak it fluently and finally harnessing its forecasting powers, how they used it to remake the world.He has written this book 'in an attempt to make the greatest ideas and stories of calculus accessible to everyone'. I can say that he has greatly achieved this.First, he shows that calculus is one of humankind's most inspiring collective achievements, roots going back to Archimedes, even Zeno, to the concept of infinity. He tells the development of ideas in a comfortable, casual way, demanding only average mathematical knowledge. He gives examples of applications from our time, which is familiar to most of us. He has furnished his story with very informative drawings.What is very important is that, he tries to navigate the reader within the story of development of calculus in the historical, natural order of the development, which makes it much easier for the reader to grasp the ideas. He has added some wise, sense of humor here and there which makes the reading easy and fun. The rich bibliography at the end is very useful. I was able to meet another wonderful book 'The Calculus Gallery' of William Dunham from within that bibliography.I loved the book. No wonder it was a bestseller. I highly recommend this book to everyone who is or was scared of calculus and who wants to approach to understanding 'the language of God.'

A great dive into the history and application of Calculus. You do not need to be a mathematician in order to understand the material covered. I highly recommend this book if you are interested in the history of Calculus.

This is not intended to be a textbook on calculus. And, like a lot of calculus itself, it is and it isn’t - quite. It is, however, a book about the history of calculus, which is fascinating, and the degree to which the universe seems to have been coded in a way that calculus seems to have an uncanny ability to explain is, well, somewhat inexplicable.But as the author notes in the beginning, “For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it’s the only way a universe with us in it could be, because nonmathematical universes can’t harbor life intelligent enough to ask the question.” How often do you hear a Professor of Applied Mathematics, at an Ivy League school no less, say something even remotely so self-reflective?Steven Strogatz is a great communicator who is both a great mathematician and who, it is easy to tell, gets goose bumps every time he thinks about the wonders of calculus. I am not a professional mathematician but have always found mathematics to be both fascinating and, well, not easy, but very relatable. It’s predictable, and that’s comforting once you can see the pattern.If you don’t feel quite that way you may – spoiler alert – find this book to be a bit more like a textbook than advertised. There are plenty of equations and symbols and the like. That is, after all, the alphabet of calculus. But here’s the thing. Unless you are also a math professor, you can ignore all of that. Just go with the prose. It tells the same story, but in a far more relatable form to the average lover of the written word. Just ignore the symbols. If you do you will miss nothing and you will find the professor’s enthusiasm to be quite contagious.The beauty of the book is that it is written from a perspective of humility. Both in terms of the enormity of calculus (Most people will relate to the subject matter simply as science.), and in terms of how far we have yet to go in terms of truly understanding the universe and the reality that defines it. We’ve only explained the tip of the iceberg.Math is a human convention. It’s not hydrogen or oxygen. It’s not even dark matter, which we “know” makes up most of the universe but which no one has ever isolated, although the Chinese are close. It is very accurate at deciphering reality if getting close to the “real” explanation is close enough. But close is only close. It isn’t reality itself. Reality is, after all, by definition, real.That is, ultimately, the problem with the promise of AI. Because AI is ultimately dependent on calculus and other disciplines of mathematics, it will get very smart, but it will never be human. What it will do, however, if we let it, is dumb down what it means to be smart to a standard perfectly suited to its abilities but ignorant of its shortcomings.That’s why, despite the promises of the silicon gods, we are very unlikely to see fully autonomous vehicles for decades to come. The only way that could happen is if we take all human drivers off the road overnight (The AI isn’t the problem; it’s us. We are unpredictable.), switch every vehicle to an autonomous vehicle all at the same time, and rebuild our infrastructure to accommodate the vulnerabilities of the various disciplines of mathematics on which the technology is based. And that’s obviously not going to happen. Nor do we want it to.Pi, as but one example, despite what you were taught in school, is not a number; it’s a range. It’s a small range, to be sure, but it’s a range nonetheless. In other words, it is precise enough for most things, but it is NOT the fabric of the universe.Science is a methodology for understanding reality; it is not, in the most literal sense, reality itself. Reality is not “waiting” to be discovered. It is. And just as an artist can draw a landscape, science can draw reality. Neither, however, IS reality.The history of calculus is truly fascinating. And that, to me, as a reader, makes it entertaining. Newton and Galileo and all the rest were truly amazing people. It boggles the mind to think of what they concluded when they did.Perhaps the book’s greatest contribution, however, is that it will put Silicon Valley in perspective. You may think your smart phone has changed your life in ways that nothing else possibly could. You’re wrong. I am a great admirer of Steve Jobs but James Clerk Maxwell (a Scot in the 1860s) changed your life in ways that Steve did not come close to.And that is why this book is so timely. Calculus is changing our world, and not entirely in good ways. If ever we needed perspective we need it now. Math is elegant. It was designed that way. (Remember that it is not of the universe, like rain or sunshine.) And it does have an uncanny reliability that helps us to understand the world around us.Take GPS. We all use it. We all rely on it. But did you know that GPS is all about time, not navigation. Those GPS satellites don’t “see” you; they time you. It only works because scientists came to understand the mathematics of what we call time at a very precise level. That’s not reality, of course, because time is a concept (time, even as we understand it, varies with altitude), but it is close enough to give us GPS. And isn’t that an amazing thing.I think so. And that’s why I found this to be such an enjoyable book, beyond the fact that I am simply stimulated by really enthusiastic people and Professor Strogatz is one of the most enthusiastic people I have had the privilege to read in a really long time.If, on the other hand, you prefer a good murder mystery, or something with a little romance, at least, you won’t find it in this book. But that’s just my opinion. A little like pi, if you will. Pretty accurate, but not reality itself.Decide for yourself. You won’t be wasting your time.