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Change is the Only Constant: The Wisdom of Calculus in a Madcap World

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An exploration of the intersection between calculus and daily life, complete with Orlin's humor and bad drawings. By spinning 28 mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and dra An exploration of the intersection between calculus and daily life, complete with Orlin's humor and bad drawings. By spinning 28 mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human.


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An exploration of the intersection between calculus and daily life, complete with Orlin's humor and bad drawings. By spinning 28 mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and dra An exploration of the intersection between calculus and daily life, complete with Orlin's humor and bad drawings. By spinning 28 mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day -- love, risk, time, and most importantly, change. Divided into two parts, "Moments" and "Eternities," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human.

30 review for Change is the Only Constant: The Wisdom of Calculus in a Madcap World

  1. 5 out of 5

    Ben Orlin

    Writing this book was a five-star experience! Highly recommended. Here's what you do: 1. Study math in college. Grow to love the stuff, from the sweep of its applications down to the intricate clockwork of the deltas and epsilons. (Optional: marry a mathematician much more skilled and intellectually serious than yourself.) 2. Teach high school math. Come to see calculus through the students' eyes: a thicket of symbols, their meanings obscure. Get a little sad about that. 3. Try to rejuvenate the st Writing this book was a five-star experience! Highly recommended. Here's what you do: 1. Study math in college. Grow to love the stuff, from the sweep of its applications down to the intricate clockwork of the deltas and epsilons. (Optional: marry a mathematician much more skilled and intellectually serious than yourself.) 2. Teach high school math. Come to see calculus through the students' eyes: a thicket of symbols, their meanings obscure. Get a little sad about that. 3. Try to rejuvenate the students' spirits with stories and anecdotes. Newton's apple. Einstein's greatest blunder. A princess on the Mediterranean coast. A dog on the Michigan shoreline. The oral folklore of mathematics, the jokes and tales and tangents that mathematicians tell over tea or beer. 4. Realize that these stories aren't sidebars. They're a version of calculus in their own right. Not the textbook calculus of engineers and physicists, but a storybook calculus of poets and historians and philosophers. The calculus of human beings reckoning with a world of perpetual flux, a world that makes bananas go brown, and hair go gray, and civilizations go up and down like block towers. 5. Write down those stories, throw together some illustrations, and hey presto, a book! It'll be easy, and/or the hardest and most rewarding thing you've ever written. Could go either way. Anyway, if you're feeling pressed for time, feel free to skip all that, and just read the version I wrote. There are almost 500 cartoons *and* a photograph of a corgi, so at least you'll be getting your money's worth.

  2. 5 out of 5

    Kam Yung Soh

    An interesting book consisting of fascinating stories about calculus. This is definitely not a calculus textbook but if you ever want to know what calculus was, what it is used for and some interesting facts and stories involving calculus, then this would be a book to read. There are too many chapters to give a chapter by chapter summary. But the book is divided into two sections based on the two main mathematical parts that make up calculus. The first section covers "Differentiation" and the deri An interesting book consisting of fascinating stories about calculus. This is definitely not a calculus textbook but if you ever want to know what calculus was, what it is used for and some interesting facts and stories involving calculus, then this would be a book to read. There are too many chapters to give a chapter by chapter summary. But the book is divided into two sections based on the two main mathematical parts that make up calculus. The first section covers "Differentiation" and the derivative, or the idea that a derivate is an 'instantaneous change' in an object, be it time, position, and so on. It builds on that by using the example of Newton considering the moon constantly falling towards the earth sideways. Based on how much it 'falls' as it moves to remain in orbit around the earth, it's speed can be calculated. The derivative is also the rate of change of a quantity. For example, given your position over time, the 'First derivative' of it would be speed (change in position over time), the Second derivative would be acceleration (change in speed over time). Both Newton and Gottfried Leibnitz provided a notation for derivatives, but Leibnitz's notation proved to be more flexible than Newton's, showing that a proper notation can increase the flexibility for what derivatives can be used for. Examples of the powers of derivatives are also given, staring with a danger in extrapolating trends via derivatives from too little data. A fascinating example is then given, via a story of using it to determine the direction a bicycle is moving. A mystery or puzzle at the heart of derivatives is the question of how to 'approach the limits' in derivatives. Initially based on ideas from geometry, the book then shows lines and movements that cannot be differentiated (like Brownian motion), showing that there are limits to finding derivatives by geometric methods Next, the derivative is used to show how it can find the maximum or the minimum point of a curve and how it can fail when a curve has no maximum. The story of the infamous Laffer Curve is also provided, showing its influence on supply side economics and tax policies. An interesting story is then told a dog that can apparently apply calculus to the problem of find the best position to jump into the water to fetch a ball. Finally, the books shows that derivatives are used as a standard calculating tool. The next section covers the "Integral" and how it can be used to calculate the area of a circle by 'slicing' it up into tiny sections and summing them up. Tolstoy's "War and Peace" is then used as as a metaphor for integration: the sum of each tiny human experience making up the whole tapestry of history. The integral is then introduction for calculating the area under a function. It is then shown that integration and derivation are 'fundamental theorems of calculus' and opposites of each other. But despite being opposites, differentiation has well defined methods but integration does not: integration depends on a bag of tools of various ways to perform integration. Some integration problems will only yield to certain tools. One thing that integrals feature is the "Constant of Integration", an arbitary number that usually appears and is unknown without knowing an initial condition. The book then looks at Einstein's regret in introducing such a constant into his equation for General Relativity to recreate a static universe, only to discover it was unnecessary in it original form but is now needed to explain the accelerating expansion of the universe. Archimedes and his geometrical approach to integration is then shown via calculations of the volume of a pyramid and a cone. It is contrasted with using the algebraic formulation of calculus as a way to 'mechanise' calculus. The paradox of 'Gabriel's horn' is then shown, a geometric shape with finite volume but infinite surface area. Finally, unlike differentiation, some Integrals have not formal solution and is still a constant struggle for current day mathematicians.

  3. 4 out of 5

    Tizzy

    Entertaining and informative Here's the deal: I'm an engineer. Here's the other deal: I despise calculus and suck at it. Here's the reason: Colleges teach calculus in absurdly formal, mathematical ways, focusing on having students learn a bunch of formulas rather than on having them understand what any of it means anyway. On top of that, the reliance on the antiderivative as an integral method means students spend years trying to perfect this skill - even when as professionals most won't use it at Entertaining and informative Here's the deal: I'm an engineer. Here's the other deal: I despise calculus and suck at it. Here's the reason: Colleges teach calculus in absurdly formal, mathematical ways, focusing on having students learn a bunch of formulas rather than on having them understand what any of it means anyway. On top of that, the reliance on the antiderivative as an integral method means students spend years trying to perfect this skill - even when as professionals most won't use it at all, since we have calculators and software that use paradoxically more reliable numerical methods. Here's the detail about this book: It's written in the same way college classes should be taught. It focuses on helping you understand what a derivative is (other than the calculus 101 definition of "the inclination of the tangent against the curve" that means absolutely nothing) and what an integral means. Then it gives you interesting, fun examples of it. This book won't really make you good at maths or formal calculus, since it teaches no formulas or mathematical methods. It will, however, allow you to understand just what it is you're doing and why. And if I had known what I was doing and why when I was a student, my career would've been much, much, much easier. I can't recommend this enough.

  4. 4 out of 5

    Kend

    Pro Tip: I read this book immediately after polishing off Maulik Pancholy's The Best at It , in which the main character takes part in his school's Mathletes club. While the book isn't necessarily centered on math, it did help put me (a math-averse adult) back into the right frame of mind to consider math A) a thing that is part of daily life and B) a thing that some people do for fun (WHAT). I'm not normally much of a "math person," in that I deliberately avoided as much math as I could in sc Pro Tip: I read this book immediately after polishing off Maulik Pancholy's The Best at It , in which the main character takes part in his school's Mathletes club. While the book isn't necessarily centered on math, it did help put me (a math-averse adult) back into the right frame of mind to consider math A) a thing that is part of daily life and B) a thing that some people do for fun (WHAT). I'm not normally much of a "math person," in that I deliberately avoided as much math as I could in school and college, mostly because I have an aversion to memorization and work with no real-life application. (I took a statistics class that was great, however, because I got to DO stuff with it.) So when I say that this book is a book I *wish* had been around when I was a teenager slumping at the back of the class in frustration, I mean to say that this book manages to make math, if not fun, at least as understandable. My general resistance to math as it is taught today remains intact, but I sincerely hope that Orlin will keep publishing and inspire other educators to look at math as a subject of humor and inspiration. The anecdotes that open each chapter are witty and only occasionally esoteric, and the illustrations are, of course, an absolute delight. The ARC I received (many thanks to the publisher!) had a couple of issues (certain symbols showed up simply as blank boxes, and several explanations referred to color-coded sections of the diagrams although the ARC was in black and white), so there *were* a couple of chapters where I couldn't follow along as well—but these won't be issues readers will face with the print version, so I'd guess your reading experience will be even better than mine.

  5. 4 out of 5

    Luke Dempsey

    Lots of wonderful reference material, fun illustration, and valuable guiding principles from the history of calculus. Orlin constructed this adventure into calculus with the humor of a high school math teacher and the wit and intelligence of a seasoned scholar.

  6. 5 out of 5

    Joseph Matuch

    Now I want to take calculus again... Fun for mathematicians; accessible to everyone.

  7. 5 out of 5

    Bryan

    The book is wonderfully approachable and I would recommend it to almost anyone that might have an interest in stories behind the mathematics. Definitely does not required a calculus background at all. However, as a calculus teacher, while I enjoyed the book I think I was looking for a little more. I think most teachers who have been teaching calculus for a significant amount of time will have already been telling a significant portion of these stories. I know that is probably an unfair criticism The book is wonderfully approachable and I would recommend it to almost anyone that might have an interest in stories behind the mathematics. Definitely does not required a calculus background at all. However, as a calculus teacher, while I enjoyed the book I think I was looking for a little more. I think most teachers who have been teaching calculus for a significant amount of time will have already been telling a significant portion of these stories. I know that is probably an unfair criticism because that was exactly what Ben Orlin set out to do. To put into a book all the stories he tells around the topics he teaches in calculus. I got a few new gems to tell while teaching and to recount to friends but I would have loved to have gotten more. This book is best suited for those with an interest in math but not a strong background in calculus. For that audience, I highly recommend!

  8. 5 out of 5

    Megan

    Yay! As with the first book I managed to not only get a nostalgic tour through math, but learn something at the same time. I think it is a compliment that Orlin manages to write a book that is interesting to both a reader familiar with the subject and one who is absolutely not. (**tiny tiny wishing there was a little bit more meat in the integral calculus section.) I think we should buy a bunch of these and leave them lying around high-schools.

  9. 4 out of 5

    Aaron Zerhusen

    Entertaining, but also frustrating because it felt like it could have been so much better (especially in light of his earlier book, Math with Bad Drawings). I love his conversational writing style and the casual stick figure illustrations. Some of the chapters, especially early in the book, were great. As the book goes on it feels like he's running out of things to say and is working to satify an editor who wants x number of chapters. Unfortunately, the last chapter, talking about the integral o Entertaining, but also frustrating because it felt like it could have been so much better (especially in light of his earlier book, Math with Bad Drawings). I love his conversational writing style and the casual stick figure illustrations. Some of the chapters, especially early in the book, were great. As the book goes on it feels like he's running out of things to say and is working to satify an editor who wants x number of chapters. Unfortunately, the last chapter, talking about the integral of the PDF of the Gaussian distribution, is particularly bad and leaves a sour taste in the mouth of the reader (initially I almost left a 2 star review, and had to flip back to earlier parts of the book). This is a real shame, as underneath his story is the tension between a definite vs indefinite integral, and what it means for a definite integral to exist vs having an expression as an elemetary function. Based on his earlier writing, I think these could have been really great expositions.

  10. 5 out of 5

    Doug

    I mean, I have been teaching calculus in high school for longer than most of my students have been alive, so I'm probably a bit biased. That being said, I enjoyed the heck out of this book and think there's definitely something here for everyone, even the folks who say they are "not math people." If you come in not knowing much, you're not going to leave understanding calculus with anywhere near the rigor you'd expect from a college course or even a well-taught AP Calculus course, but you will ga I mean, I have been teaching calculus in high school for longer than most of my students have been alive, so I'm probably a bit biased. That being said, I enjoyed the heck out of this book and think there's definitely something here for everyone, even the folks who say they are "not math people." If you come in not knowing much, you're not going to leave understanding calculus with anywhere near the rigor you'd expect from a college course or even a well-taught AP Calculus course, but you will gain an appreciation for the fundamentals of calculus, the history of the subject, and the reasons it holds such a significant place in the annals of Western thought. And if you do know calculus (and especially if you teach it), you should walk out with an enriched appreciation for the many options that exist for leading others into the wild and wonderful world of derivatives and integrals.

  11. 4 out of 5

    Dale Alleshouse

    Change is the Only Constant is a thoroughly entertaining book. There aren't many authors who could juxtapose humor, history, and mathematical theory into a coherent narrative; however, Ben Orlin does so artfully. While the book clearly states that it won't "teach you calculus"(p. 17), it does provide the "whys" of calculus that are so often absent from traditional math pedagogy. Mr. Orlin showcases his masterful teaching skills by educating readers without their knowledge. Each analogy is deftly Change is the Only Constant is a thoroughly entertaining book. There aren't many authors who could juxtapose humor, history, and mathematical theory into a coherent narrative; however, Ben Orlin does so artfully. While the book clearly states that it won't "teach you calculus"(p. 17), it does provide the "whys" of calculus that are so often absent from traditional math pedagogy. Mr. Orlin showcases his masterful teaching skills by educating readers without their knowledge. Each analogy is deftly crafted to provide expert insight. The historical accounts and related stories also conspire to make the subject come alive. The final icing on the cake is the comical drawings. There isn't anything about this book that I didn't enjoy. In conclusion, I recommend this book to anyone whom enjoys witty whimsy regardless of their predilection for calculus.

  12. 4 out of 5

    Ammar

    This book entertained me to the nth power, the derivative of which is the natural log of "me" multiplied by the original function (haha), but what really made it such a good read was not the subject matter itself, but the author. You will come across many math books, but this is unlike any: rather than the dry tone utilized by many writers, he takes it upon himself to alleviate both his tone and the illustrations of the solemnity of calculus in order to beguile his readers, and succeeded he did. This book entertained me to the nth power, the derivative of which is the natural log of "me" multiplied by the original function (haha), but what really made it such a good read was not the subject matter itself, but the author. You will come across many math books, but this is unlike any: rather than the dry tone utilized by many writers, he takes it upon himself to alleviate both his tone and the illustrations of the solemnity of calculus in order to beguile his readers, and succeeded he did. Through anecdotes and elucidating examples, he teaches the (FUN)damentals of calculus to a layperson, which is a no easy task. However, he does so beautifully and makes the subject attainable and enjoyable to everyone. I especially enjoyed his discussion of history as connected to integral. The book in its entirety was remarkably thoughtful and philosophical. I highly recommend it to everyone!

  13. 5 out of 5

    Zhi Chen

    Similar to the previous book, Math With Bad Drawings, Change is the Only Constant reveals the many relationships between mathematics (calculus in this case) and the world. I would expect that the book would be more enjoyable for those with exposure to calculus, but most readers will still be able to appreciate how the chapters aim to bridge the two realms, revealing not only mathematical beauty ("What the Wind Leaves Behind" - limits, "The Green-Haired Girl and the Super-Dimensional Whorl" - der Similar to the previous book, Math With Bad Drawings, Change is the Only Constant reveals the many relationships between mathematics (calculus in this case) and the world. I would expect that the book would be more enjoyable for those with exposure to calculus, but most readers will still be able to appreciate how the chapters aim to bridge the two realms, revealing not only mathematical beauty ("What the Wind Leaves Behind" - limits, "The Green-Haired Girl and the Super-Dimensional Whorl" - derivatives, "Calculemus!" - calculus, "A Great Work of Synthesis" - Fundamental Theorem of Calculus) but also insights into human experience ("War and Peace and Integrals" - history through mathematical integration, "If Pains Must Come" - utilitarianism and moral calculus).

  14. 5 out of 5

    David

    As an engineer I'm kind of a fan of math, so I really enjoyed this book. The author did a great job explaining some of the major concepts of calculus at a level that doesn't require much if any familiarity with math to understand. I don't know that I would recommend the book to non-math people, but it at least wouldn't be over their heads. The first half of this book was very enjoyable, but I was a little disappointed with the second half. It didn't feel as cohesive as the first. Several of the c As an engineer I'm kind of a fan of math, so I really enjoyed this book. The author did a great job explaining some of the major concepts of calculus at a level that doesn't require much if any familiarity with math to understand. I don't know that I would recommend the book to non-math people, but it at least wouldn't be over their heads. The first half of this book was very enjoyable, but I was a little disappointed with the second half. It didn't feel as cohesive as the first. Several of the chapters seemed to be more about general calculus or history than about integrals. I don't believe that any of the chapters didn't belong in the book, but perhaps rather than two sections (derivatives and integrals) there should have been three.

  15. 5 out of 5

    Sanjith Senthil

    Ben explains to us calculus in the way it should be taught. With stories, paradoxes, pictures, and the occasional punchline. This book won't teach you how to do calculus, but help you what it's for and how it works. Conveying math into a non-technical writing with incredible organization and elegancy is no easy task, but Ben has done it again. "Change is the only constant" is a brilliant book, and I would recommend it to anyone that would like to learn math as it originally was, exciting and inc Ben explains to us calculus in the way it should be taught. With stories, paradoxes, pictures, and the occasional punchline. This book won't teach you how to do calculus, but help you what it's for and how it works. Conveying math into a non-technical writing with incredible organization and elegancy is no easy task, but Ben has done it again. "Change is the only constant" is a brilliant book, and I would recommend it to anyone that would like to learn math as it originally was, exciting and incredible.

  16. 5 out of 5

    Heather

    Overall, enjoyable and enlightening book. I learned several new ways to see core math concepts, and am really glad I read it. My one complaint is that it uses little-known English words often, e.g. “trenchant” and “reviled”, and that interrupted the flow of the book as I don’t know those words. It makes it a book really only for the most intellectual people, which is ironic, especially given the chapter on David Foster Wallace and big math words. I wish it were more accessible.

  17. 4 out of 5

    Kevin Saunders

    I really enjoyed this book, although maybe not as much as his previous book, Math with Bad Drawings. Spending some time with calculus brought back memories of my time going through Calc 1-3 in college, and while I enjoyed the journey occasionally it would butt up against my own knowledge and I was left wanting a little more concrete math in among the metaphors. Probably a great introduction to thinking about calculus if you’ve never encountered the subject before.

  18. 5 out of 5

    Joy

    As the author states in this book, this book will not teach you calculus. However, it will show you how calculus relates to everyday life. I found myself giggling and smiling often while reading this book, and while learning to look at things a whole new way. I definitely would recommend this, even to those who dislike math. Thanks to Black Dog & Leventhal Publishers for the advanced copy.

  19. 4 out of 5

    Alex

    This is a good and interesting book. But I liked Ben's previous book a bit more. This one felt a bit less insightful. A few chapters could use a bit more detail, for example, the 5==7 thing wasn't fully explained or named (it's called "staircase paradox" as I found later). The War&Peace chapter seemed a bit unnecessary and a stretch as it was fairly tangential to the book's topic. This is a good and interesting book. But I liked Ben's previous book a bit more. This one felt a bit less insightful. A few chapters could use a bit more detail, for example, the 5==7 thing wasn't fully explained or named (it's called "staircase paradox" as I found later). The War&Peace chapter seemed a bit unnecessary and a stretch as it was fairly tangential to the book's topic.

  20. 5 out of 5

    Matt

    An interesting, funny, and approachable read about the beauty of calculus. It's not overly informative for anyone who has studied math, but it's not trying to be. For anyone with a slight aversion to math who has ever wondered why math nerds say things like "Math describes the world", this is a great place to start. An interesting, funny, and approachable read about the beauty of calculus. It's not overly informative for anyone who has studied math, but it's not trying to be. For anyone with a slight aversion to math who has ever wondered why math nerds say things like "Math describes the world", this is a great place to start.

  21. 4 out of 5

    Madhukara

    Really interesting book which teaches ideas of calcus with stories and history. The book does not focus much on the application of calcus it's ubiquitous by now, but it gives historical reasoning behind some of the discoveries. It also talks about dichotomy of pure maths vs approximate maths of statistics. Overall nice read Really interesting book which teaches ideas of calcus with stories and history. The book does not focus much on the application of calcus it's ubiquitous by now, but it gives historical reasoning behind some of the discoveries. It also talks about dichotomy of pure maths vs approximate maths of statistics. Overall nice read

  22. 5 out of 5

    Bobby Wales

    Fantastic read. I like algebra and statistics, but I’ve avoided calculus like the plague. Ben Orlin masterfully reduces the barriers to the topic and uses bits of history, science, and humor to explain complicated concepts (similar to Mihir Desai’s book on finance: The Wisdom of Finance, also a great read).

  23. 5 out of 5

    Anish Morakhia

    Such an interesting perspective. Its a little bit random and could use a better flow of thought. Also, this was a bit less intuitive than his first book. Nevertheless, read it for the analogies ( History is an integral )

  24. 5 out of 5

    Josh

    A few interesting bits jumped out to me but mostly I had already heard most of these stories in one form or another. I admire the author for attempting to write a math book that appeals to non math loving people and perhaps he did succeed in capturing that audience.

  25. 5 out of 5

    Michael Wallace

    A really good book on calculus, makes it much more approachable and very understandable. As a calculus tutor, I find it difficult to explain concepts like these to people, so this makes it easier to explain them in concrete words and stories.

  26. 4 out of 5

    Bernard

    Exactly as excellent as expected This is not a book to teach you how to do calculus. It’s a book exploring why you might want to. Orlin combines a breezy prose with his trademark stick figures to illuminate mathematical stories. It’s wry, engaging, and highly readable.

  27. 5 out of 5

    Nick

    Personally this book didn't land. It tries to explain the fundamentals of calculus, derivatives and integrals, using non-technical anecdotes and humor. I didn't enjoy the humor very much, and a few times the concepts were oversimplified for myself. Personally this book didn't land. It tries to explain the fundamentals of calculus, derivatives and integrals, using non-technical anecdotes and humor. I didn't enjoy the humor very much, and a few times the concepts were oversimplified for myself.

  28. 4 out of 5

    Christine

    Super fun read! The drawings were hilarious and informative, and the chapters wonderfully bite sized while still managing to convey the concepts in a fairly thorough way. I will definitely be picking up Math with Bad Drawings.

  29. 4 out of 5

    Jenna

    A funny, fun read. And a fascinating look at the practicality of calculus which has been an abstract and confusing subject for the last 37 years and which I still don’t understand. Fortunately higher math skills are not needed to enjoy this book - or the pictures

  30. 5 out of 5

    Davic Vielma

    It's a great book, full of examples that make it easier to understand very ambiguous concepts, really wish to have star reading it when I started to learn calculus, several years ago; soo if you want to learn or are about to, I strongly recommend it. It's a great book, full of examples that make it easier to understand very ambiguous concepts, really wish to have star reading it when I started to learn calculus, several years ago; soo if you want to learn or are about to, I strongly recommend it.

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