Infinite Powers: How Calculus Reveals the Secrets of the Universe

This is an interesting history of calculus. The writing is entertaining and the historical facts are enlightening. I would point to some considerations on the discussion of Xeno and whether space and time being distinct would mean that movement wouldn't be possible. The author explains that in computer science and in video production, we see pixels moving and thus Xeno is wrong. But, what the author is saying doesn't conflict with Xeno's prediction and in fact supports it. You don't see pixels move. You see new pixels be drawn and give the illusion of them moving but they aren't the same pictures and in fact, each image is still, motionless and while infinity is cool, it doesn't give us any support here. One is still not two even if there are infinite many points between them and so no matter how many still images you draw (changing what we call the frame rate), you won't change the fact that with time and space being distinct, as is the case in video production and pixelated animation, that there is no motion but only a trick of your eyes to make it seem like there is. That said, this book is an interesting read and gives many insights about the math world that we all should learn. Later, there is a discussion of Bolt and getting his speed at instances. That further demonstrates Xeno's point. The reason you can ascertain Bolt's speed at an instance is that it's Bolt that is moving in space time. If space and time were distinct, you could no longer do that because Bolt wouldn't be Bolt anymore. There would have to be a bunch of individual Bolts and each one of them would occupy a space on a time line but none of them would be the previous Bolt whereas Bolt is the previous Bolt since he lives in spacetime and not in a space and a time. I get the sense, however, that the author is either joshing or there's something more that must be missing from the equation as I'm quite sure everyone knows that pixels don't move (they are static is another way to say it) and only have the illusion of movement. What is very fascinating, though, is that Xeno had figured out something that wasn't very intuitive before Einstein. In any case, this is the sort of thought the book provokes and the sort of history it presents as it takes you from the early days of algebra to the sort of calculus that Newton developed and beyond.

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.'

It is a delicious narrative about the origin of calculus and its importance in our daily life. It is a great book for those not familiar with mathematics.

Just great, fun like a novel, insightful like a math book.

This book is much more than just a history of a branch of mathematics. It's a framework for thinking about calculus. I was mind blown at how Strogatz explains calculus; like I had been blind all those years and now I saw. His 'breaking down and reassembling' analogy may not be the best explanation to the more mathematically inclined, but to me it made perfect sense, at last. This book provided me with a mind model to think about calculus. A gem. "To shed light on any continuous shape, object, motion, process, or phenomenon - no matter how wild and complicated it may appear - reimagine it as an infinite series of simpler parts, analyze those, and then add the results back together to make sense of the original whole."

El autor de este libro te explica cálculo diferencial e integral de una manera mucho más clara que mi profesor de primero de carrera en ingeniería. Te deja claro su historia, de donde vienen los conceptos, su utilidad, todo sin usar muchas fórmulas. Este libro no es para aprobar un examen sino para entender de verdad de que va ésta útil herramienta de las matemáticas. Lo recomiendo para cualquiera que quiera comprender de verdad sus bases y no solo memorizar una serie de fórmulas y gráficas, como pasó en mi curso.

I bought this on Kindle a year ago on a whim. I was dabbling with getting back into a math after a couple of decades away from school. I've been pretty successful in many fields in which math deeply underlies but doesn't explicitly require mastery. Nevertheless it always bugged me that, despite mastering these fields, I never had a firm mathematical foundation, and always relied on workarounds and intuition given that my mathematical skills were artificially slowed during my early education. Due to my consistent successes in learning varied topics, I never made much sense to me that math should be looked at as this special field that requires unique skills to understand and be proficient in. Like any other field, it is honed through lots of practice, practical applications, and attention. Steven's book really inspired in me that that hunch was more than just a hunch, and a year later I have gone well beyond my stunted grade school math education and can see myself learning math for the pure love of it for the rest of my life. Saying nothing of the fact that I know it will improve my hard skills across every domain I work in today and into the future. Steven really has a gift not only for doing math itself, but for expressing exactly how and why learning math is, like any skill or topic worth devoting effort to, one of the deepest and most beautiful struggles. And, regardless of our learning stage or status, that struggle and its rewards belongs to all of us equally.