If you’re still reading this, thank you. Not sure I could write a more off-putting title. I envision a somewhat less-than-engaged response. Here I want to show a little love for math. Come on with me, might be all right.
Arithmetic is most of the math we experience. There is really nothing fun about learning arithmetic for most of us. Memorizing tables and 20 homework problems just does not excite. Even arithmetic, so obviously a significant part of daily adult life, could trigger the ugly question, “Why do I have to learn this?” And the ugly answer, “Because I said so.” We got so wrapped up in the numbers we missed the point of math, that there are tactics that prove things, and describe truth.
I worry that as a culture we’ve forgotten the arithmetic of ratios. I have no idea if it’s true, but there’s a story about the 1/3 pounder hamburger falling to the 1/4 pounder because customers thought 1/4 was bigger than 1/3. Seems sadly possible to me.
Which sounds bigger: 2x, 100% increase, or doubling? We’re good with miles per hour, maybe price per pound, but I find lots of cases strongly argued that describe some statistic not well understood.
In political discussions especially we cherry-pick numbers to defend a bias, with little care about what that number really says because we don’t carefully consider how it’s defined. The pandemic was rife with numbers thrown around higgledy-piggledy, so much so that I found myself largely throwing up my hands.
Without considering the right ratio; deaths per capita (of course New York City had more deaths than Pittsburg), deaths per infection, serious illness per vaccinated patient, per patient with co-morbidities, which co-morbidities, it was easy to be confused and stressed and eventually call each other liars.
All those metrics are important in helping us understand what’s happening around us but they don’t really help us decide if it’s safe to go to my aunt’s funeral. So yes, our children need to learn arithmetic (and we all need to use it better). It’s gonna be on the test, the real test. Not because I said so, it just is.
Calculus is where I first learned that I wasn’t as smart as I wanted to be. I could hang with the principles, but putting them into practice, like on a test, was humbling, and still painful. I’ve read a lot more about Isaac Newton and the nearly magical insights he had that created calculus and maybe that’s where my love of math began.
Though I still can’t do it, calculus describes the world we live in, that we understand in everyday experience, and makes it rigorously true. It translates how to catch a fly ball into a language that is as precise and self-consistent as arithmetic. The James Webb Telescope works. We shot that thing up there, way beyond the moon into the dark of the Earth’s shadow, to a discrete spot where the gravity of Earth and sun balance just so and it will stay there. The spot even has a name: the second Lagrange point or L2. We didn’t just shoot the telescope up there blindly— we talk to it, tell it what to look at and how, and it tells us what it sees. Lots of calculus has to work pretty well for that to happen, so yeah. That’s amazing and true.
But around the turn of the 20th century, the math of physics changed everything, and now I am sure I do not really understand anything. I wish I could drag you through the details but I don't understand them well enough. It's all about this "wave versus particle" description of light. Guy named Planck proved something, de Broglie showed that it was true about everything, Einstein showed that it fits with everything, Schrödinger mapped it statistically, and together they carried us into the era of quantum mechanics.
We now live in a post-Newtonian world, where calculus describes things pretty well, but only for the tiny range of space and time that we happen to live in. The very small and the very large and the very cold and the very fast worlds are not obvious in Isaac Newton’s garden. The math we use to describe the quantum world is pretty deep; the folks I’ve met who navigate it are special people. There’s an interesting discussion about whether math is invented or discovered, either way, I’m forced to admit that time and space are beyond me. I don’t really understand bricks.
The math that got us here, arithmetic, algebra, geometry, calculus, is all still true, but our view is broader and we can see limitations and now math is marching us into some strange territories. The fact that math evolves doesn’t make it wrong, only that the more we learn, the more it gets refined. We build stuff all the time now using our understanding of the math of these new worlds, even though it baffles us. It’s that lesson from second grade, that there really are truths, that can be proven (and disproven) and used to make stuff or to understand stuff. There are three categories of knowledge: correct, incorrect and “dunno.” We can sift through all the noise bravely, with conviction and humility. It’s on the test.
Jack Dunne lives gratefully in Lakebay.
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