Lance Mannion writes real gud, so I usually enjoy reading his essays, but this time he struck a nerve and for the first time I have to deeply disagree with him. He’s writing about math. He, personally, thinks he’s not good at math, so he regards it as unnatural.
Personal prejudice: Most people can’t do math. What we call math is actually simple arithmetic. Adding, subtracting, multiplying, and dividing. Calculating. What Jethro Bodine in his pride at his sixth grade education called cipherin’. Nobody does math, and can do math, until they understand why multiplying two negative numbers together produces a positive number. I’ve never understood that one. So I can’t do math.
I can cipher like a wiz, though. Like a sixth grader, at any rate.
This Paley Center panel discussion on Hidden Figures was interesting and I can’t wait to see the movie but I was a bit disgruntled by the way people on the panel who know better talked about math as if it’s all arithmetic and anybody can do it and do it well if they put their mind to it and get over the idea it’s too hard.
OK, that part I agree with. He’s right: math isn’t about the kind of number games you can play on a calculator. Mathematics isn’t about arithmetic, except for those parts of a big field that are. But then, after correctly stating that math is something more, he doesn’t really get it and ends up criticizing it for things it isn’t.
But I didn’t like it that learning to do math got implicitly compared with learning how to write a sentence that parses.
As the son of a physicist and computer scientist who, hard as he tried, never could get me to follow his math when he helped me with my homework, and as someone who was an A student in math in grade school but was stymied by ninth grade algebra and defeated in eleventh grade by calculus, and as the father of someone who has struggled with a severe math learning disability—dyscalculia they’re calling it these days—and is two daunting math courses shy of completing his degree, I’m here to tell you…
Math ain’t natural.
We don’t think in numbers. We’re not good at holding them in our heads. Most of us count “One, two, three, many” and then, if we’re forced to go higher, “Many more, and a lot!” and that’s as high or as complex as our numbers get.
That’s irrelevant, as he should know. Mathematicians aren’t necessarily thinking in numbers, either: they’re thinking about patterns, or relationships, or logic, or even geometry. Somehow, being unable to visualize numbers greater than, say, seven in our heads doesn’t seem to be an obstacle to considering infinity.
The thing that raises my hackles, though, is that word “natural”. I hate that word. It’s usually used to vaguely mean “the good things that I like” rather than “those unnatural abominations that perverted libertine over there likes”…like math. Or football.
And then, uh-oh, he abuses the “E” word. My wrath is immediately stoked.
Some of this is the result of biology, anatomy, and evolution—the evolution of bodies, and then the evolution of culture.
Evidence suggests that humans were talking to each other from the start, putting words to their feelings, coming up with ideas that could only be created with words, naming things. Naming things is what made us human. We evolved to speak and we evolved from speaking. Culture, art, and society are the result of words. We didn’t start counting until later when societies became more complex and more things needed to be sorted out. We can see our ancestors inventing math.
We don’t know precisely when language arose, so it’s hard to place it in relationship to other aspects of culture. Did the hominins who lacked language also lack art? We don’t know. So it’s hard to say that one is the prerequisite for the other. It’s also a definitional problem.
Did the first being we’d recognize as human speak? Or are we going to use speaking as the criterion for defining humanity? Maybe the first True Human was the bipedal ape who rose up from the grass with a rock in his hand, computed (without words, obviously) the parabola it would follow when thrown, and estimated the intersection of his rock’s path with the racing path of that tasty looking rabbit over there. Note that this isn’t the math of counting things, which Mannion unfortunately lapses into assuming here, but a different kind of understanding of the nature of motion that’s more physics than poetry (although I have noticed a tendency for poets to claim movement as an act of poetry; maybe scientists need to fire back and claim meter and rhythm as acts of physics and sensory biology).
But to return to the previous point: everything is natural, or nothing is. If we’re going to start labeling human specializations as unnatural, well then, singing ain’t natural. Dancing ain’t natural. Writing novels…what a weirdly unnatural thing for an animal to do.
All that stuff doesn’t just come “naturally”, whatever that means. People have to train to do it, they have to practice and practice, and there’s also an aspect of talent that you have to be born with. I can’t sing, unless you call off-key croaking “singing”, but I wouldn’t seriously declare that singing ain’t natural. Of course it is, because we do it.
Hey, who knows, maybe singing — something with a rhythm and tones — preceded language, even. Perhaps australopithecines got together in great choruses and hummed and beat drums and sang to express their mood, all while calculating what frequencies went together best to make pleasing chords. Don’t know. Wouldn’t past ’em. Humans are weird, and the first ones wouldn’t have been constrained by any expectations, you know?
So please, avoid trying to justify your prejudices by claiming your preferences are “natural”. It turns out we’re all capable of whipping that one right back at you, so it’s a poor argument.
But I do usually agree with Mannion, so I’ll conclude on one point we both share. He’s not a fan of the current STEM fad.
I hate the word neo-liberal. But I only know it as an online epithet. Progressives use it as an all-purpose insult for liberals and Democrats who don’t adhere to any point of their programmatic political doctrine, and as such it has whatever meaning the user gives it because it suits his purposes or feelings at the moment. Which is to say it has no real meaning. But if it does have any meaning in the real world, it’s when it describes the self-interested principle that social good is best achieved by letting capitalism take its natural course. If it saves money or makes money and some of that money is used to promote the general welfare, then hooray! And if that’s what it means, then our colleges and universities have become hotbeds of neo-liberalism.
STEM is a neo-liberal dream.
Promote STEM and the government will throw money at your school. Promise the kids good jobs and they’ll flock to your school and more government money will follow. Target minorities and girls in particular and even more money sluices in. And look at the good you’re doing while you build the endowment and hire more administrators. Those kids get a first class education (Never mind that most of their classes are taught by grad students and adjuncts.) and will likely get good jobs when they graduate. They’ll become productive members of the wealth producing elite and isn’t that the whole purpose of education and of life, in general?
I’m a STEM guy in a STEM field teaching students STEM who personally benefits from the parent/student bias for STEM degrees, but I agree, STEM alone is a terrible idea. We should be promoting a balanced education, where scientists-to-be need to learn some history and language and music and all that social science/humanities stuff. I deal with students all the time who regard all those requirements outside science and math to be a waste of time, and are focused entirely on zipping through their education as quickly as possible so they can get a job in a science- or engineering-related occupation. It’s a terrible attitude. Didn’t they pay attention to Alexander Pope?
A little learning is a dang’rous thing;
Drink deep, or taste not the Pierian spring
Oh, right, they’re STEM majors, and they would never even hear of Pope unless we forced them to take those literature courses, which they think are a waste of time. They don’t know what the Pierian spring is, either, because they’re all hoping to grow up to be David Gelernter.
You know Gelernter, the guy who might be Trump’s science advisor.
In Gelernter’s view, the future of higher education will involve a focus on STEM subjects while “throwing out” the arts and humanities. Online courses will become commonplace, but not without evolving, and students will need a “digital guides or mentors” to carry them through online education.
Degrees themselves will become a thing of the past, Gelernter writes as they’re “gradually be replaced by certified transcripts.” Rather than a university conferring the degree, a “transcript” — that is, coursework showing that a student has successfully learned a given set of material — will be “vouched for” by a trusted institution like a think tank, newspaper, museum, or research lab.
Jebus. Throwing out the arts and humanities is a great way to build a generation of short-sighted, unimaginative, uneducated blockheads who might be able to code or mix reagents, but that’s about it.
How about if we do it all, balanced and in moderation? Or would that be too “unnatural”, especially when it requires an alliance of mathy people and non-mathy people?