July 24, 2012, by Jonathan
From maths education to philosophy: what’s the story?
A report on this morning’s news claims that Britain does badly in the maths education stakes. Nothing new here really–we’ve been told how bad we are at maths education seemingly for decades now; the point today seems to be that lots of people doing engineering–and masses doing biology–have little maths in their schooling.
In part no doubt this is just another thing we are bad at–other countries do it better apparently. But it’s worth reflecting on how hard it is to get people to do maths. Here’s an analogy: our bodies are shaped for walking and virtually everyone learns to walk easily and with little instruction. Swimming is harder, is something you have to dedicate effort to compared with, and many of us make little progress. We are just not made for it. Perhaps we are not made for maths. What are we made for? Stories. Children love stories before they can understand them, while grown-ups delight endlessly in hearing about people who don’t exist and things that never happened (AKA fiction). Some Darwinians say language began with the need for stories: tales about other people were a vital currency in negotiating our way through complex social groups. And we seem to want to match big events with big stories, as anyone who’s waded through the 9/11 conspiracy literature knows.
Rightly, scholars find this interesting. They grace it with the name of narrative, and sometimes give the impression of overdoing it. There’s narrative therapy, the narrative self, and for some, science is just another narrative, with no better claim on our belief than traditional story-telling.
But science isn’t just another story, and much of it isn’t a story at all. That’s partly why the glories of the human mind are little understood, while less wonderful ideas, rich in narrative, do well in the market place. I reckon the two great intellectual achievements of the last century were Einstein’s theories of relativity, and an incomprehensible proof, by his less famous Princeton colleague Kurt Gödel, that there will always be things we can’t prove. Unless you define “story” so that everything is a story, these just are not stories. One is a general theory of the cosmos, the other-obviously–a mathematical proof.
Both have practical applications; everyone knows about Einstein and the bomb, and Gödel’s work bears on computing. But I’m focusing on their reshaping of our ideas. Einstein abandoned the intuitive notion that if two events are simultaneous from one point of view they will be from another. After that came exotics like curved space-time. But the assault on common sense paid off: successful prediction of the bending of light by gravity, the existence of black holes and other off-the-wall possibilities. It’s astonishing that someone could think in such a new way and get so much right.
I won’t even try to illustrate Gödel’s achievement, except to say that it contributed profoundly to our understanding of the limits of reason (he also and independently made a major contribution to Einstein’s physics). One reason I won’t say more is that I long ago forgot the details; indeed, I’m sure I’ve already mis-stated his result. Without that unusual commodity, mathematical talent, I struggled through college logic, quickly loosing the capacity to do even simple exercises; the same happened with physics. Where there is no story to steady us, understanding is hard to get and hard to hold.
Left to ourselves, we turn in other directions, just as we turn from vegetables to fats when they are abundant. Take psychoanalysis, for which there is an almost total lack of evidence. “While Freud had an enormous impact on 20th century culture, he has been a dead weight on 20th century psychology”, says Berkeley Psychology Professor John Kihlstrom.
Freud had a story to tell of familial conflict, reassuringly connected with myth and the literary world. His account of infantile sexuality may have challenged convention, but it suited the narrative-hungry mind very well. The effect was a stunning colonisation: “to us he is no more a person now but a whole climate of opinion” said Auden on Freud’s death. There are better theories of the mind, but with no sense-making narrative to sustain them they get comparatively little notice.
Without a Khmer Rouge of the psyche to rewire us things won’t change much. People will always be more attracted by narratives of personal greed than by theories of risk assessment when it comes to explaining the financial crisis (and yes, greed surely had a role). The most we can hope for is to make theory seem, occasionally, less forbidding and more worthwhile, without insisting that it translate into a story.
So here’s a thought. Philosophy is one activity that runs on theory without, for the most part, having to crunch the numbers. It’s full of impersonal but engaging arguments about God, about goodness, about the mind and the self. Some philosophers like narrative a lot, but they give us theories of narrative, not more stories.
There are stories in philosophy; Philippa Foot (granddaughter of US President Cleveland) gave us one about switching points on an out-of-control trolley to kill one person rather than the five currently in line. Would that be right? How about throwing a hefty bystander on the track to stop it? But the point of the story is to help us choose a moral theory.
You don’t need to be in college to get some of the benefits of philosophy: there are good books and magazines that display what’s on offer and do it in plain speech. With the current rise in university fees I’m keen to show that people should value philosophy enough to pay for it. One reason may be that it is the best defence against narrative thinking run riot–against the idea that if you are studying, say, anthropology, you are entitled to a view of the mind that no serious experimental psychologist would endorse, because what the psychologist offers is “just another story”.
But don’t hope for too much, even from philosophy. After all, I long ago forgot what Einstein and Gödel said.
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