Month: November 2019

Enlarge / Arch-rivals Isaac Newton and Gottfried Leibniz famously fought over the credit for inventing calculus. (credit: Ben Orlin)

Math teacher Ben Orlin writes and draws the (aptly named) blog Math With Drawings and is the author of a new book, Change is the Only Constant: The Wisdom of Calculus in a Madcap World. To mark its publication, he devised this entertaining accompanying quiz. You can read the Ars interview with Orlin here.

Isaac Newton and Gottfried Leibniz have a lot in common. Birthdates in the 1640s. Fatherless childhoods. Colossal egos. Show-stopping wigs. Most of all, each had the honor of bringing calculus into the world. But when it comes to personalities, Newton and Leibniz are like night and day, or England and France, or derivatives and integrals. They’re rivals. Opposites, even. Do you belong on #TeamNewton or #TeamLeibniz? Take this quiz to find out!

What do you like to do online?

Enlarge / 28 tales make up this entertaining, illustrated exploration of the intersection between calculus and daily life. (credit: Ben Orlin)

Calculus has a formidable reputation as being difficult and/or unpleasant, but it doesn't have to be. Bringing humor and a sense of play to the topic can go a long way towards demystifying it. That's the goal of math teacher Ben Orlin's new book, Change is the Only Constant: The Wisdom of Calculus in a Madcap World, a colorful collection of 28 mathematical tales connecting concepts in calculus to art, literature, and all manner of things human beings grapple with on a daily basis.

His first book, Math With Bad Drawings, after Orlin's blog of the same name, was published last year. It included such highlights as a placing a discussion of the correlation coefficient and "Anscombe's Quartet" into the world of Harry Potter, and arguing that building the Death Star in the shape of a sphere may not have been Darth Vader's wisest move. We declared it "a great, entertaining read for neophytes and math fans alike, because Orlin excels at finding novel ways to connect the math to real-world problems—or in the case of the Death Star, to problems in fictional worlds." And now he's taken on the challenge of conveying the usefulness and beauty of calculus with tall tales, witty asides, and even more bad drawings.

Calculus boils down to two fundamental ideas: the derivative, which is a way of measuring instantaneous change, and the integral, which describes the accumulation of an infinite number of tiny pieces that add up to a whole. "The derivative is all about isolating a single moment in time, and the integral is all about gathering together an infinite stream of moments to develop a holistic picture," Orlin told Ars.

Enlarge (credit: Hubble Site)

We live on the most comfortable of planets. It may not be too visible, but the Earth's magnetic field plays a critical role in maintaining that comfort. The remaining rocky planets in our Solar System have much weaker magnetic fields and, as a result, are subject to a constant bombardment of high-energy particles from the Sun. Yes, our biosphere owes a great deal to a pool of molten iron at the core of our planet.

Yet the core presents something of a puzzle to us. The extreme conditions make it very hard to understand: we cannot conduct experiments that fully replicate core conditions, and our measurements are indirect, since no one wants to visit the core. That leaves us with computer models. Until recently, these models were rather limited. However, ever-increasing computational power is starting to reveal that the core has an interesting story to tell.

Onions not parfait

Our planet, like all planets, is born of violence. The aggregation of mass during its growth came via large impacts and oceans of molten rock. Gravity provided a kind of filter: the heavy elements like iron were pulled to the core, while light elements like silicon and oxygen were left floating on the top.