Stephanie V.W. Lucianovic is a Bay Area writer and editor. Her first book Suffering Succotash: A Picky Eater’s Quest to Understand Why We Hate the Foods We Hate, a humorous non-fiction narrative and exposé on the lives of picky eaters, will be released by Perigee Books on July 3.
My husband is a calculus professor and one who brings food items into the classroom with surprising regularity. No, he doesn’t bring pies on Pi day - though he can recite the string up to a couple dozen digits - but he does bring Pringles. As a teaching aid.
This afternoon when I walked into his study, I nearly tripped over a plastic Safeway bag filled with six red cans of Pringles. “Is it Pringles Day already?” I asked, nudging the bag. Pringles Day is the day Dr. Mathra lectures on the classification of critical points in multivariable calculus, and he uses the saddle-shaped Pringles to illustrate his points.
After class, the students get to eat his illustrations. It’s their favorite day.
However, this Pringles Eve, Dr. Mathra is kicking himself because in addition to stocking up on Pringles, which were invented by Proctor & Gamble & heaven in the 1960s, he also got an oblong can of Lays Stax, the parvenu potato chip that’s only been around since 2003.
Personally, I’ve never been turned on by Lays Stax. Not only are they covered with the stink of being the unoriginal upstart that is so obviously trying to rip-off the adored-for-decades potato chip, but they’re not thin and delicate enough, they’re not oily enough, and they’re not addictive enough. However, none of the above is Dr. Mathra’s complaint with them.
"It’s ridiculous!" he fumed, "They set themselves up as a Pringles competitor, but it’s an entirely different curvature!"
The shape of the Lays Stax - known as a parabolic cylinder - is way less mathematically interesting than the hyperbolic paraboloid of a Pringles, which is also known as a saddle. In math, the Pringles saddle shape exemplifies how you can stand at the flat point of a surface and not be at the highest point of your surroundings or at the lowest point of your surroundings.
Basically, you could call the saddle “the taint” of critical points. T’aint the highest point, t’aint the lowest. “Um, sure. If you wanted to be crass about it,” Dr. Mathra mumbles.
The big three types of critical points in multivariable calculus are the bottom of a bowl (aka the local min), the top of a dome (the local max), or in the middle of a saddle (saddle point).
"The Lays Stax shape isn’t even as interesting as a bowl - it’s a wishy-washy bowl. I mean, you can make the Lays shape with a piece of paper,” Dr. Mathra explains. (In my twelve years of being married to him, I have frequently found that being able to make something with paper is met with derision.) See, you can’t replicate the Pringles saddle shape with a piece of paper without cutting the paper and actually adding more paper to it and that makes it more mathematically desirable.
Sensing he has my attention throughout all of this raving, Dr. Mathra continues, “They’ve got these Lays Stax right next to the Pringles as though they are equivalent. How can they do that? One is a positive semi-definite quadratic form and the other is an indefinite quadratic form - they’re not even the same definiteness!”
When I don’t react, he insists, “Oh, come on - that will KILL in class tomorrow!”
And why should you, the non-calculus student, care about the Pringles saddle form? The principal application of calculus is optimizing, or determining whether you are at a maximum. You use calculus whenever you want to optimize, well, anything. “If you are at a local max (the top of a dome), everywhere you go moves you down. If you’re at a saddle, there’s a way you can go that will take you up.” Knowing this is important when thinking about increasing filthy lucre, precious time, diminishing resources, or a supply of Pringles.
And that, my friends, is why Pringles will always, always beat Lays Stax.
Flavor is subjective. Math is irrefutable.