You Should Have Fun With Numbers!

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Today’s email is not only another advertising-supported endeavor (click! click! click!), it’s also prompted by my good friend Hugh, who asked me to write something about math, more or less. If you’ve got an idea—no matter how vague or nascent—that you want me to take on, please email me, and I’ll give it a shot.

_Yesterday morning, for whatever reason, I failed to finish the pot of coffee I’d made. When I realized what I’d done, or hadn’t done, I poured the remainder out of the Chemex into a mug, popped it in the microwave (I know: not ideal!), and set it to reheat for 44 seconds. Had it been still slightly warm instead of room temperature, I would have reheated it for 33 seconds.

This is how I do things: If I’m reheating a bowl of rice, it’s for 1 minute 11 seconds. When I butter-steam broccoli or boil corn on the cob on the stovetop, I set the timer for 3 minutes and 33 seconds. Warming up a baguette (preferably from La Bicyclette) in the oven? The temp is set at 222 degrees Fahrenheit. Roasting a chicken: 444°F. Alas, my oven only goes up to 550°F, which always bothers me when I make pizza. Those missing five degrees hurt.

Why do I do this? Mostly just because I can! We tend to think of cooking times and temperatures necessarily as very precise, but (with a few exceptions) they aren’t. A few seconds or degrees here or there will change nothing.

Far more important: It’s simply more fun to hit 3-3-3 or 1-1-1 on a keypad than, say, 3-0-0, which is just such a default, boring timeframe. Three minutes means nothing to anyone; 3:33 is a thing of beauty, a triplet of triplets that brings you right where you need to be. 3:21 would do it, too, or even 3:45, but to me, those are less attractive options. If only the oven and microwave timers offered an even greater degree of precision! Alas, three or four digits will have to suffice to amuse me for now.

The idea for this minor form of amusement did not originate with me. Rather, I cadged it from Vi Hart, a self-described “recreational mathemusician” who has a delightful, fascinating YouTube channel with videos that blend math, food, low-end paper arts, and peppy narration. Vi Hart rules, and their work is just so compulsively watchable that it feels weird to embed only one video here. Should it be the one about why τ is superior to π? The one about the turduckenen-duckenen? Okay, let’s just watch the one where Vi Hart makes a quesadilla/burrito out of a hexaflexagon:

Now let’s pause for a quick commercial break before I get into the meat of this essay:

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Math Can, and Should, Be Fun!

_Before I was a word guy, I was a math guy. Well, technically, that’s not correct—I was better at writing a few years before I was any good at math, but I was like a little kid then, anyway, so it doesn’t really matter. By the time I was a teenager, I was excelling at math—and mathy stuff like computers—more than I was at writing. I wasn’t a prodigy by any measure. Math had just started to click for me: Learning the principles and formulas and algorithms merely required a kind of conscious acceptance, a willing submission to the process, and the results just appeared thereafter, often alongside understanding. The more this happened, the more I wanted to learn more. In junior year, I took pre-calculus, then over the summer took Calculus I and II at the college in our town, and spent senior year doing Linear Algebra and Calculus III there as well. When I went off to college for real, it was as a math major.

I know this is not how it goes for most people. For most people, they do fine in math (or less fine, it doesn’t matter) all the way up to calculus—and there they hit the wall. Something about the idea of infinities, both large and small, and the conception of what happens to numbers and functions and geometries as you approach the undefinably big or tiny, just messes kids up. They don’t get it. It breaks their brains. Some of them struggle through Calc I or II, and they’re done. They’ve learned all they need about math, and now, thoroughly traumatized and unable to handle even basic calculations, they move on to economics¹.

I got lucky I guess: All that calculus made sense to me. You figure out how to calculate the volume, say, of a cone, or a complicated three-dimensional function, and you wind up with a formula, and then hey! You’ve got a formula! Now it’s just plugging in numbers if you need to.

As a college freshman, though, I didn’t want to just plug in numbers. I knew enough about math that I knew I wanted to learn… the weird stuff. Group Theory, Number Theory, Abstract Algebra.

I don’t want to explain what any of those are, partly because I can barely remember, but here’s a good way to think about things: When you’re starting out in math, you learn about numbers and arithmetic—how to add, subtract, multiply, divide. Later, in algebra, variables (x, y, z) come to stand in for the numbers, and you learn how to manipulate these stand-ins. By calculus, you’re wholly in the realm of variables, and you look at what happens when they get really big or really small. But then, past that, you’re going to another order of abstraction—you’re investigating the fundamental principles of how we manipulate not just numbers but sets of numbers, types of functions, and classes of operations on those set and types. It’s like going from sounds to words to sentences, and then leaping to the patterns of synaptic firing in Broca’s area that produce language in the first place². What happens when you look for the square root of multiplication divided by subtraction? That’s the kind of nonsense I wanted to learn as a math major.

Reader, I sucked at it. This shit was hard. It required a level of abstraction I could never really muster, and a devotion to studying of which I was then incapable. It just didn’t make a lot of sense, and my teachers didn’t help. When my fellow Algebra I students and I went in a group to the office hours of our professor, Georg Kempf, a filthy old man who stank of cigarettes and old denim and was frequently mistaken for a homeless vagrant on campus, to ask for assistance, he sneered at us: “I’m not teaching a class for fucking morons!”

Well.

Although this fucking moron did ace the final exam, I could tell I might not have a future in math. It was only partly the challenge of grasping the concepts. What really intimidated me was the work of mathematics: It was all about proving things.

Maybe that’s obvious to you. Mathematicians spend their careers considering how numbers, broadly defined, might work, and come up with elaborate, bulletproof explanations of why this is so. They are dedicated to finding truths so abstract and fundamental that most of us will never understand what they were even looking for to begin with. Mathematicians exist to prove theorems, QED.

Me, I’d never really thought about this. When I say I liked math, what I mean is I liked learning the math that mathematicians already knew: I liked following their train of thought, marveling at their inventions, and feeling a bit of pride that I could understand these things and make use of them in a fairly elementary way.

But when it came time to prove the concepts myself? Oh man, that was not my thing. A lot of that was that I just did not care what was true and what was false. I only cared about what was neat, what was weird, what would blow your mind, dude. And there was so much out there that fit that definition!

Want to calculate π? Actually, let’s calculate π/4:

1−1/3+1/5−1/7+1/9−1/11+…

OMG, how does that work? Obviously, there’s a proof we can walk through, but instead let’s just pause and marvel at the seemingly random elegance of that formula. You alternatively add and subtract fractions with odd numbers as denominators… and you wind up with a clear fraction of π? (Vi Hart would remind us that it’s also a fraction of τ.) That is insane.

This one’s even better. What if you were like, Hey, could you take the five most important constants in the whole universe of mathematics and combine them into one colossally simple formula? I’d be like, Dude, I gotchu:

𝑒^𝑖𝜋−1=0

It’s not just: How the holy fuck does that work? It’s: How the hell do we live in a universe—in a multiversal reality—where those all fit together so neatly?

That one’s called Euler’s Identity, and every couple of years I look up the proof to understand how it all comes together. I nod and follow along, and it all makes perfect sense, and then I promptly forget it all. I am and always have been an aficionado of math, not an artisan. To put it another way: I didn’t want to design Lamborghinis, I just wanted to test-drive them. Unfortunately, I’d enrolled in a Lamborghini-designing curriculum. Fortunately, my college also had a top-rated creative-writing program, and by sophomore year I’d switched majors³. Though I kept taking math courses through my junior year, I did not finish enough to qualify for a degree. Oh well.

Math, however, clearly left its mark on me, and not just because I’m more comfortable with computational concepts than many of my colleagues in the media world. Math is fundamentally about form, about structure—it’s about arranging ideas and variables just so, enabling a mysterious, underlying order to emerge into the light, so that what was once hazy and abstract coheres and crystallizes. It’s about balance, about rigorous thinking and rigorous expression. And math is about delight, about appreciating those moments when seeming complexity falls away to reveal a pattern of laughable elegance. As a writer, I try—and probably often fail—to bring those principles to bear with every sentence, paragraph, and story I put down. Form matters. It shapes our expectations and offers space for our emotions to play out. It connects beginnings, middles, and ends in ways we may not initially understand but that can reveal themselves with a bang of comprehension.

And still: Math is hard. I don’t know how you feel about numbers, or how they work together, and I don’t expect you to crack open that old copy of Gödel, Escher, Bach that you picked up from a Brooklyn stoop two years ago. But I would urge you to take a more playful and appreciative attitude toward them. Be whimsical with your oven timer. Figure out how high you can count with the numbers of one hand. Find the most statistically unlikely PIN for your ATM card. Marvel at the fact that mathematicians just discovered a new Mersenne prime. Choose the colors for your Beehiiv newsletter with hex codes like #FEDCBA and #ABCABC and #2D3D4D. Numbers are eternal, and math underpins the reality of our universe, but they also don’t really matter—they don’t rule us. In fact, they exist because of us, they serve at our pleasure, and we should treat them with levity, as one more unexpectedly pleasurable fact of our unlikely existence in the cosmos. Numbers should make us giggle like the kids we are all at heart. Need proof? Here’s one to get you started: 5,318,008.

Notes

1. That’s a mathematician joke. Cuz mathematicians hate economists.

2. We’ll study Wernicke next semester, okay?

3. In that junior year, I accidentally discovered that there was a branch of mathematics I had some aptitude for: analysis, and complex analysis, which deals with calculus in the realm of imaginary numbers. But by then it was too late. I knew math wasn’t for me.

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