Oct 20, 2021 9:00 AM

The Mathematics of Cancel Culture

To add fractions, you find the least common denominator—a term that has a certain resonance in our age of mass cancellation.

Collage of images of greying hair and graphics of fractions

Even a longtime number lover like myself cringes at the memory of grade-school arithmetic—mostly boring exercises of memorization and seemingly arbitrary rules that led to often obvious answers. These number numbing years effectively murdered math for most people, who would forevermore associate the subject with answers and sums rather than questions and ideas.

The exception, for me at least, was canceling—an oddly satisfying way to slim down numbers by slicing up factors and using just what you needed. To add fractions, for example, you’d first find a common denominator to make sure you weren’t adding apples and oranges (or 6ths and 3rds). To add 1/6 and 1/3, just multiply 6 and 3 to get 18—turning the fractions into easily addable 3/18 + 6/18. Presto: 9/18!

This cumbersome answer was easy to streamline by using not just any old common denominator, but the smallest one, in this case 6. Cutting out the fat gives you 2/6 + 1/6 = 3/6 or 1/2. (Yes, it’s obvious that 9/18 is already 1/2, but that’s getting ahead of the lesson plan—a no-no if you want stay on the good side of the teacher.)

Crossing out those too-big numbers with my stubby #2 pencil appealed, I think, because it offered such a simple shortcut through complexity. The more you could cancel, the simpler and clearer things got. (That part of math just kept getting cooler.)

That thrill of x-ing out, no doubt, also plays a part in the popularity of so-called cancel culture—a default way of dealing, it seems, across the political and social spectrum. There’s none of the surgical precision of arithmetic. It’s broader and more brutal—less like math and more like the Queen of Hearts in Alice: Off with their heads!

True, “cancel” means very different things to different people in different contexts (as does “culture”). But then, in the infamous words of Humpty Dumpty, a word “means just what I choose it to mean.” Whether that’s OK isn’t the question. “The question is,” Humpty told Alice, “which is to be master—that’s all.” He added: “When I make a word do a lot of work like that, I always pay it extra!”

That seems only fair.

It’s hard to see how math or science could add (even fractionally) to this already fractious conversation; the range and scale of “cancel” is just too great. The canceled even in my small purview include books (sometimes on the basis of titles), athletes, politicians, TV shows, words, police, women’s rights, women, voting rights, fictional characters, entire ethnic groups, fields of study, people who make mistakes, yoga, vaccines, masks, nuclear energy, genetically modified foods, singing, kneeling, red wine, body odor, Afghanistan.

I should probably add seniors to this list, generally rendered invisible, or so I’m told, a different way of getting canceled. As such, we’re constantly encouraged to cancel or at least camouflage the obvious signs: gray hair (for women anyhow), wrinkles, sags, spots, splotches, spider veins, arms, necks, and oh so much more.

Still, it’s tempting to borrow a bit from arithmetic. Numbers are fun to play with, and often do add insight, so why not? (As a senior, I’ll take comfort in the fact that nobody will pay attention anyway.)

For one thing, the arithmetic canceling trick I mentioned at the outset relies on finding the “least common denominator,” a term which has a certain resonance. If that’s what we get when we cancel, that’s probably not good. In truth, the math metaphor doesn’t translate exactly to the human realm; it may, in fact, mean the opposite. When we talk colloquially about the “least common denominator,” we generally think of pandering to the basest tastes of large groups of people. (Facebook comes to mind.) So the numbers aren’t small. But canceling as a quick way to tame otherwise unwieldy problems is certainly similar in spirit. Taking someone (or something) out, so to speak, reduces the number of factors in play, simplifies the equation, trims the time it takes to solve it.

Untangling knotty problems calls for patience, and who has that these days? Faster to prune, clip, ditch. The catch is: Knotty problems, by definition, are highly entangled, and severing one strand can unravel a whole mess more than you’d bargained for. Shakespeare laid bare this conundrum brilliantly in The Merchant of Venice. Shylock demands the pound of flesh he’s owed for an unpaid debt. A pound of flesh, however, can’t be excised without also taking blood, which is against Venetian law; Shylock could lose everything.

Incisions are rarely exact, nearly always dicey. It’s not clear when to stop. I tried to fix a bad self-inflicted haircut by whittling away stray ends, but it always came out uneven. Nothing to do but keep on whittling. Suddenly, there’s almost nothing left (luckily, not a bad look).

Decisions about what has to go are rarely methodical, frequently based on ambiguous information; it’s easy to choose the wrong target, and mistakes can be fatal. The recent drone attack on Afghan civilians is a raw reminder. Some people think excising criminals from our midst requires the ultimate kind of canceling—capital punishment. The scores of known innocents executed, on death row, or recently released due to DNA evidence should give anyone pause.

Endless elimination eventually gets us to … nothing. A void. People say nature abhors a vacuum, but actually, nature mostly is a vacuum; vacuum energy accounts for most of the energy in our universe. Nothing isn’t possible. (That is to say, “nothing” isn’t possible.) Whatever gets removed gets replaced by something else. Suck the air out of a straw and milkshake (or margarita) flows in. We all depend on pushback in one form or another. Bouncing ideas off other people. Getting rejected, sometimes for good reason. Boundaries keep us from running amok. If you’re pulling against something (or someone), and it/she suddenly lets go, you’re in for a fall. Sudden stops cause crashes, especially if you don’t take time to look out for what’s coming up behind you.

Most canceling isn’t so drastic or visible. But it goes on all the time, mostly without our noticing—a process revved up by AI. AI-driven hiring software cancels job candidates, disappears applicants from college entrance pools, culls potential mates, bans people from getting credit, insurance, parole. It even limits the options a doctor has (or sees) for prescribing drugs. No one knows exactly what these algorithms “consider” in their decisions, because the software is proprietary. We do know that AI depends on turning everything into yes-or-no questions; it’s either a relevant data point, or it isn’t. That’s digital by definition. It deals in discrete variables, not continuous change. As a geek friend recently put it: “AI murders calculus.” Mathematician Cathy O’Neil calls these systems “weapons of math destruction” (also the title of her—not yet canceled—book).

Makers of our AI-powered devices spend a lot of time canceling friction, making just about everything a no-brainer. They require less and less of us because they do more and more, whether we want them to or not. One click instead of two. They make it effortless to say things, buy things, even cancel things. We don’t need to think twice. Or think at all.

But friction is a good thing—and not just because it might slow down your ability to send that text you later wish you hadn’t or make butt dialing more difficult. We need friction to walk across the room.

Besides, deleting rarely erases things completely (your old texts included). Canceling leaves traces. In college, I received a report card (a real thing back then) with an inked A in physics crossed out, written over with a B—the ghost of the A still clear. I’d recently declined several invitations from my aged professor to meet after class for a drink. Sexual harassment didn’t even have a name at the time. But the experience canceled my interest in physics for quite a few years.

As we all know, vanquished enemies often return, sometimes in different form. Sometimes they come back to bite you. Our campaign to cancel “germs” has been so successful it’s helped to produce stronger breeds of drug-resistant bacteria.

So what’s the alternative? Bad, dangerous, and dumb things abound. If we don’t cancel them, then what?

In some obvious cases, addition can eliminate the need for subtraction—though it’s likely slower, more difficult, more expensive. For example, I read that analog clocks are being taken out of school classrooms. Why? The decision to cancel clocks was made because students no longer knew how to use them to tell time. Given that clocks are analogues to the Earth’s rotation, that’s a bigger loss than it may seem. Why not just teach kids to read hands on a clock?

Most canceling is far less trivial, of course, but options do usually exist—even if they require time and resources (and thought). We can repair, reframe, revisit, refashion, restrain, redirect, repurpose, restructure, rework, retool, reduce, revisit, refocus, retrofit, reboot, rethink, reform, and so on. The reformation of our legal system is something law professor Jody Armour has studied and lived for a lifetime and reimagines in his new book, N*gga Theory: Race, Language, Unequal Justice, and the Law. A truly progressive legal system, Armour argues, values restoration, rehabilitation, and redemption over retribution, retaliation, and revenge.

Science could not progress if it canceled old ways of understanding in favor of new. Very rarely do scientists entirely abandon even wrong and discarded ideas. Rather, the building blocks remain, but take on new meaning and context with the discovery of new knowledge, more complete theories, clearer explanations. Science is essentially additive.

I personally find it strange that most people seem to see aging as mostly a matter of cancellation. True, getting old pares away mobility of our limbs, shaves range and acuity from our senses, severs ties, shrinks stature, chisels away at memory. For me, however, what’s gained easily equals what’s lost. Sure, I’d rather do without the aches and pains, but they force me to jury-rig my way around obstacles—which is a fun challenge (sometimes). If my joints are less flexible, my outlook is more so. I remember less but know more. I have lower energy but more interests. I laugh more. Sometimes it’s the only thing you can do. Nothing wrong with that.

The biggest thing we’ve lost to cancel culture is conversation itself. We’re afraid we’ll say the wrong thing. We’re afraid we’ll get canceled. Sometimes we don’t bother even to cancel and simply “ghost”—the passive-aggressive version.

Probably needless to say, the specter of being ghosted, canceled, has haunted me all the while I’ve been writing this piece. But as I’m closer to my expiration date than most, it wouldn’t matter much. Nature will cancel me permanently, soon enough.