Tutoring my favourite nine-year-old, I was surprised at how much trouble he was having with fractions. This is a smart kid with a good number sense, but he was flummoxed as he tried to grasp the applications of halves, quarters and eighths.
I went through the stages of tutor grief — denial, anger, bargaining — before I began to realize what the problem was. Fractions represent a huge advance over everything a child has learned up to then, because they represent a relation, not an absolute. No wonder it’s a big moment.
No wonder so many have to sweat to earn it. For the first years of your life, a number is what it is. What’s the value of 7? The question is so direct it’s almost a trick. The value of 7 is 7. You multiply it by 8 and you get 56, every time. But then what is the value of 1/3? The only honest answer is, “It depends.” One-third of a fish is different from one-third of the distance to Montreal, and both are different again from one-third of the cash in my wallet.
But of course all share an element of “thirdness,” and it’s precisely the notion’s adaptability that makes it so powerful. Fractions lead you by a short road to algebra and to a Pandora’s box of tools for finding the value of unknown quantities. A few years ago I spent a month at Perimeter Institute in Waterloo, trying to understand the work of the physicists there. Most of it went right over my head, but once in a while I’d see some genius write symbols above and below a division line, cross it with symbols in a neighbouring fraction, simplify and solve, and I would realize that I was watching another application of tools that became available to that genius, as they became available to me, when we moved as children past the absoluteness of whole numbers to the contingency of relation and proportion.
At some point in almost every field you move, not without struggle, from the absolute to the contingent. In the first books you read — I’m talking little kids here — a bird is just a bird. Eventually you graduate to metaphor, and now a bird can be a stand-in for hope or freedom or death. In law you move past different readings of a statute to competing notions of the good or just. In music, harmonies become richer, relations among notes more open to interpretation, until the very notion of harmony becomes something a composer can retain or reject according to taste and need. And then you listen to Bach’s St. Matthew Passion and you wonder whether any of this change can be said to represent progress.
If there’s a place in modern society where the notions of relation, proportion and contingency are most frequently encountered and applied, it’s the university. In fact that’s a serviceable definition of the word. I can go to all sorts of places to learn something useful. At a university I spend at least some of my time struggling with the very meaning of utility. Of course this struggle is often indistinguishable from wanking.
Few places are easier to mock for their pretentiousness. (Why are campus politics so vicious? Because, Henry Kissinger said, the stakes are so low.) But at universities people are at least a little likelier, on average, to question their assumptions, to be prepared to defend or discard them, than in the rest of
the world. That’s the hope, anyway.
So it’s disappointing, while unsurprising, that these bastions of relativism — a sometimes-pejorative word that universities should more often wear with pride — have spent so much time marketing themselves as purveyors of sure value. This is the “jobs-for-tomorrow” marketing line I’ve decried at some length in previous columns. It has contributed, inevitably, to some of the pressure on universities that we’re seeing now — cuts to operating budgets in Alberta and Quebec, a national and rather onedimensional “debate” about how there are “too many BAs, not enough welders” for the available jobs.
I read one surreal column in the Huffington Post from an historian with an MA — earned in Germany — who was upset that she had not been able to find work as an historian in Canada. First of all, all the evidence suggests her job prospects as a Master’s graduate are, statistically, much better than if she’d stopped at a BA (as I did) and much better still than if she’d received a technical education. Secondly, while I wish everyone luck in the job market, I hope we’re not going to universities for job training. The ones in the humanities, especially, should be going for life training, civilization training, whatever you might call it, and they should be flexible when they leave about how they apply knowledge that is valuable precisely because it can be broadly applied.
This is a hard case to make, but since the notion of a university as absolute value is both misleading and destructive over the long term, the notion of a university as contingent value is worth making. In a world of constant, assured surprise, a university education offers the best preparation for surprises. I once suggested to a group of Western alumni that an accurate marketing slogan aimed at high-school students choosing a universityshould be something like “Western: You Have No Idea What You’re Getting Yourself Into.”
That may help explain why I didn’t make a career in marketing, but it strikes me as an honest and accurate glimpse at the real merit of higher education. And since in this world none of us really knows what we’re getting into, it may even catch on.
Paul Wells is a senior columnist for Maclean’s magazine. Follow him on Twitter @InklessPW.
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