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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 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.

320 pages, Hardcover

First published January 1, 2019

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Ben Orlin

9 books185 followers

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Displaying 1 - 30 of 97 reviews
Profile Image for Ben Orlin.
Author 9 books185 followers
August 12, 2019
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.
Profile Image for Tizzy Tizzy.
Author 2 books7 followers
July 19, 2020
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.
Profile Image for Kam Yung Soh.
757 reviews39 followers
January 15, 2020
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.
Profile Image for L.
1,063 reviews51 followers
December 8, 2022
Calculus with pictures and jokes

I recently wrote a review of Understanding Analysis, which provoked me to lament the failure of most of Earth's population to appreciate the beauty of analysis. This led me to Change Is the Only Constant: The Wisdom of Calculus in a Madcap World, which is, more or less, a book intended to extenuate that deficit. I had previously read Ben Orlin's Math with Bad Drawings, a book that is simultaneously very funny and deeply profound. Thus I bought Change Is the Only Constant and read it in the kindle app on by iPad, for the sake of the color illustrations. I was delighted to discover that the book begins with an epigraph from Octavia Butler, whose Kindred I just finished. So clearly this was MEANT TO BE!

Here is how Change Is the Only Constant begins.
“What is,” said the philosopher Parmenides, not quite a million days ago, “is uncreated and indestructible, alone, complete, immovable and without end.” It’s a bold philosophy. Parmenides permitted no divisions, no distinctions, no future, no past. “Nor was it ever, nor will it be,” he explained; “for now it is, all at once, a continuous one.” To Parmenides, the universe was like Los Angeles traffic: eternal, singular, and unchanging.
A million days later, it remains a very stupid idea.
This is accompanied by a cartoon showing several stick figures reacting to Parmenides with scorn.

The introduction explains Orlin's purpose as follows
I want to be clear: the object in your hands won’t “teach you calculus.” It’s not an orderly textbook, but an eclectic and humbly illustrated volume of folklore, written in nontechnical language for a casual reader. That reader may be a total stranger to calculus, or an intimate friend; I’m hopeful that the stories will bring a little mirth and insight either way.
If you know anything about calculus, you probably know that it is generally divided into two branches: the differential calculus and the integral calculus. The differential calculus is about change. Change Is the Only Constant is divided into two books: "MOMENTS" and "ETERNITIES", which correspond to the differential and integral calculus.

I quite liked MOMENTS. Despite Orlin's disclaimer, it does quite a good job of teaching the differential calculus, along with lots of fun stories. It is also quite good at explaining the philosophy behind much of the calculus as currently practiced, which I would describe as the mechanization of insight, so that you don't have to be Archimedes to solve tricky problems -- lesser mortals such as you and I can also do it.

I found ETERNITIES less satisfactory. The integral calculus, as Orlin is at pains to point out, is wigglier, more creative and less defined than the differential calculus. That may sound like more fun, and for some readers perhaps it will be. For me it made everything more wishy-washy -- less mathematical, in short. Your Mileage May Vary.

If you're looking for a popular exposition of Calculus, I doubt you'll do better than Change Is the Only Constant.

Blog review.
Profile Image for Denver Public Library.
642 reviews287 followers
December 1, 2022
I LOVE BEN ORLIN! I first "met" Ben when he was interviewed on the podcast, Breaking Math and then giggled my way through his blog, Math with Bad Drawings. This book in your hands, Change is the Only Constant, is his third title and includes 28 examples of life viewed through the lens of calculus. Full disclosure, I don't understand calculus and Ben makes that okay, too.
Profile Image for Jiwesh.
24 reviews
August 26, 2023
A splendid, visual exploration of calculus. The concepts are explained in bite-sized chapters, each revolving around a real-life scenario involving journalists, authors, scientists and a dog. Even the constant of integration gets a chapter, featuring Einstein and the cosmological constant.

The writing is anecdotal and witty, and the book is filled with comics, illustrations and graphs. It requires little prior mathematical background, and would be an absolute treat for a curious student.

I thoroughly enjoyed the clear explanations, sense of humour and the drawings. I was dreading finishing the final few chapters. Highly recommended.
Profile Image for Cherisevanegten.
67 reviews2 followers
November 11, 2022
Absolutely adored the book!

Brief stories making mathematical functions and theories seem like elementary school calculation. The book proves that math doesn’t have to contain difficult formulas that only geniuses understand, but rather explained throughout stories, that math in fact is more comprehensible than many think.

The main focus of the book is calculus, so differential arithmetic and intergrals. Integrals, limits, functions and derivatives tell us more about our daily life than we think. Stationary moments in time contain a lot of information. Together, a series of stationary moments, contain even more. The study of the two of them, is called calculus. (This is just a brief summary of a broad study object)

Learning for a mathematical exam? Interested in mathematical ? Looking for a fun and easy to read book? I would definitely recommend this book.
Profile Image for Kend.
1,249 reviews72 followers
October 7, 2019
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.
Profile Image for Mbogo J.
425 reviews28 followers
July 21, 2022
This small gem attempts to do a near impossible task of making Calculus interesting. It did a good job and hats off to Ben Orlin for pulling it off. If you've had the misfortune of coming across Calculus especially the way its taught in most institutions then you remember the page long calculations involved for an answer to nowhere, at least I have those memories where I kept asking myself now what does this answer represent in the real world?

In this book Ben answers that question, on which derivative is instantaneous velocity or which integrand is the area under the curve, things like limits got a mention and a lot of thought experiments were put to task to explain some concepts. The tone here is chill and whimsy which might or might not work for some people. It worked well for me, my only issue with the book being too brief that at some instances you felt that you were getting the bare boned experience of a concept. This book will work well for anyone about to take an introductory class for Calculus or if you never got a chance to do calculus in life...

When I say whimsy I mean that while explaining the concept of Mean Value Theorem, Ben used as a starter story on how DFW handled it in Infinite Jest and went about explaining the concept of mean value theorem and how Wallace take maybe differs from the main line. Only Ben could do that. I am yet to finish reading Infinite Jest [it's a lifetime quest at this moment, each year I do a few more pages] but I did enjoy this short book. Not sure on who to recommend this to but if you are reading this review, you should read the book.
Profile Image for Luke Dempsey.
2 reviews1 follower
February 12, 2021
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.
Profile Image for Eric Morris.
55 reviews
June 9, 2023
Focused, substantive and fun. This book brings a lot of the humor and cultural tie-ins of Orlin’s first book (Math with Bad Drawings), while focusing on a much deeper and narrower goal: providing a geometric intuition for calculus concepts.

Overall, I enjoyed that this book scratched a similar itch for me as AP Physics B (non-calculus based physics), in that it offered an array of narratives and mental models without getting bogged down in the meat of the calculations. Definitely a good pre-read to an intro calc course.
Profile Image for Joseph Matuch.
114 reviews1 follower
March 28, 2020
Now I want to take calculus again...

Fun for mathematicians; accessible to everyone.
22 reviews
May 31, 2023
This was a fascinating read that taught me so much! Despite the influx of knowledge and the largely abstract topics, Ben Orlin presents the book in hysterical way with hilarious drawings. The humor does an excellent job of making topics that are difficult to visualize become easier to understand. Not only this, but Orlin provides easy-to-understand common analogies that allow even casual readers to visualize theoretical topics.
84 reviews1 follower
November 8, 2021
Fun and approachable read about the various real-world uses of calculus, which I never went through during high school. It won't teach you how to derrivate and integer - it's more about the general principles and interesting anecdotes concerning the topic
Profile Image for Bryan.
36 reviews
December 9, 2019
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!
780 reviews5 followers
October 29, 2019
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.
Profile Image for Rosariya Ek.
45 reviews1 follower
December 31, 2020
Interesting, funny, and extremely approachable.

This was 320 pages of stories that filled me with nostalgia and to be honest, a little bit of regret. Regret I didn't fully take the time to appreciate mathematics back when I was learning all this for the first time.
Profile Image for John Gambino.
24 reviews
March 7, 2021
So many interesting asides. Not a textbook, but would make a great supplement to engage students.
Profile Image for Nilendu Misra.
289 reviews13 followers
June 14, 2021
Joy to read, if you already know calculus. Incitement to be passionate about it, if you don’t.
Profile Image for Ahmad Rafi.
2 reviews
July 25, 2021
Absolutely love it. Easy to follow with a good sense of audience.
Profile Image for Maxwell.
21 reviews
March 23, 2022
Another wonderful blend of mathematical concepts, interesting contexts and amusing drawings.
Profile Image for Kalyan Turaga.
143 reviews13 followers
July 27, 2023
Change is the Only Constant: The Wisdom of Calculus in a Madcap World by Ben Orlin is a captivating book that takes readers on an intriguing journey through the world of calculus. As someone inclined towards mathematics, I thoroughly enjoyed this book and found it to be a sincere attempt by the author to narrate a compelling story about calculus.

One of the highlights of this book is the incorporation of interesting stories, such as the tale of the mathematician in Michigan and his extraordinary dog, Elvis, who apparently has a talent for calculus. These anecdotes added a delightful touch of humor and uniqueness to the overall narrative, making the book a pleasure to read.

Moreover, the brevity of the book is commendable, as it stays concise and to the point without sacrificing the depth of its content. Ben Orlin has a talent for presenting complex mathematical concepts in a clear and accessible manner, making it suitable for readers of varying levels of mathematical understanding.

In particular, I believe this book would be an excellent read for teenagers who have an interest in mathematics. It has the potential to captivate young minds and inspire them to delve deeper into the world of calculus and its applications.

I would like to extend my gratitude to Ben Orlin for penning this book. It fills a niche in the literary world by combining storytelling and mathematics, and I appreciate the effort and thoughtfulness put into its creation.

In conclusion, Change is the Only Constant is a captivating and enjoyable read for anyone with an interest in mathematics, and I wholeheartedly recommend it to those seeking a unique perspective on calculus.
Profile Image for Jessica.
397 reviews4 followers
April 12, 2021
I love the title of this book. It cleverly uses the word Calculus in a funny way that lets you know the subject won't be taken too seriously. As promised by the title, I found myself laughing out loud more than once. My favorite was on page 182: "Historians tend to pluck out a handful of occurrences - coronation, battle, dance-off, treaty - and examine them as if they tell the whole story." For some reason, I pictured a historian writing a serious record about the results of a dance-off and I laughed so hard I had tears. That kind of humor is throughout the book and if the right section sneaks up on you at just the right time, like that line did for me, you will find you have tears too.

So the important question is, do you need a degree in math to read this book? Well to give you an idea, I left my last and only Calculus course about 20 years ago with a very hard-earned B, a vague idea that it all had to do with the area under a curve, and a plan to forget it all as soon as possible. Still I would say that I followed the vast majority of this book. There's no need to wait until you take Calculus to read it. In fact, it may even help you if you read it before.
Profile Image for Aaron Zerhusen.
9 reviews2 followers
February 14, 2021
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.
Profile Image for Shu.
445 reviews3 followers
August 6, 2021
Ben managed to turn me into a “kid who always scramble[d] to get the inside joke” in every one of his “bad” drawings, even down to those relegated to the endpaper and pastedown. I savored the bibliography section (which is a goldmine, BTW), not wanting the enjoyment to end. Five full stars, despite a couple of graphical printing errors I found. Wish I had this book when I was taking AP Calc, and will gift it to kids taking the course now.

What I loved the most was how the mathematicians honored in the book all came alive on the pages; the cute portraits didn’t hurt, either. I especially felt grateful to have learned about Maria Gaetana Agnesi and already bought her biography so that I can donate it to my public library. Thanks, Ben, also, for convincing me that I should just DNF DFW’s Everything and More and pick up Eugenia Cheng’s Beyond Infinity instead.

“Math is a weave of many threads: the formal and the intuitive, the simple and the profound, the momentary and the eternal. Love the thread you love. But never mistake it for the tapestry.”
Profile Image for Dana Nourie.
34 reviews7 followers
August 16, 2023
This book was sooooooo fun! Calculus confused me for years. I knew it was essential to astronomy and other sciences, but when I tried to read calculus textbooks they made my head spin. It was really hard for me to see the utility of it.

Then came this book. It doesn't teach you how to do calculus, but it explains how it's used, why it's used, and supreme examples. The best part of the book, though, is Ben Orlin's sense of humor and his wonderful diagrams. I so much a appreciated this book. When I learn things, I have to know the context, the high level overview, and the WHY. This book did this for me, so I could then go to calculus books or courses and understand what the equations are telling you about a system.

This book is fun even if you don't have any interest in math. I also read Ben's book Math with Bad Drawings, which was wonderful! And the drawings aren't bad. His humor is so refreshing in a book about math!
Profile Image for Doug.
260 reviews9 followers
November 12, 2019
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.
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