Math and trap doors

December 14th, 2011

“Oh, yes,” I’ve been saying to my friends. “I’m just back from the Banff International Research Station for Innovative Mathematics and Discovery.” I feel like a kid impressing her classmates with news of a trip to Disneyland.

I toss the name off as if I could actually tell a Gaussian distribution curve from a Faustian one. This airiness conceals the huge alarm I felt that first morning, walking into a smallish classroom with the Banff mountains like bright, attentive students beyond the picture windows.

I was here through the kind invitation of Robert Moody. A mutual friend had introduced me to him when I needed to find some illustrations for my new book, Intersecting Sets: A Poet Looks at Science.  When he finally read the published book, he thought I might be interested in coming to a particular BIRS workshop on “Mathematics: Measure, Maker and Muse of the Arts.”

The invitation to Banff thrilled me, but it also tipped me through a trap door in my psyche.  I would be surrounded by people who negotiated the academic environment easily. The list of participants detailed their various affiliations, but I had to be categorized as ‘independent.’ That sounds a lot sturdier than I felt. University had been a very scary place for me four decades ago. All my fellow students seemed to know so much more than me, to be so much more sophisticated than a kid from Outer Scarberia. I never seemed to have the right answers in class, the right clothes. And at that time I was only coping with the English program – a language I could supposedly understand – not the dense math language of symbol  and equation.

So here I was. Nor could I just sit at the back of the class and absorb. At some point I was going to have to stand up and wring myself out. I’d have to talk to them. By the time I actually did so, my brain was melting jelly.

I intended to talk about metaphor, how it is an underlying mode of thought, not just a decoration, and applies to all realms of creation. Fortunately, writers can read bits of what they’ve written, and at least those sentences are coherent. I got through the outline of what I meant to say. But, in the discussion afterwards, when David Mumford asked a question about how we might teach metaphor better, I could only look at him and think, “A Fields medalist is asking me a question. What the $%@# do I say now?”

I gave some feebly irrelevant response. It was only afterwards, when the neural jelly was starting to re-set, that I thought, “For heavens sake, Alice, that whole chapter of the book is about how we can teach and learn metaphorical thinking!”

Even though this Uriah-Heep ‘umbleness had taken over my brain like an evil twin, I did manage to shake its cling aside during the week and step into that Magic Kingdom where information and ideas make their click-click-click combinations.  A number of talks concerned the area of stylometry in visual art. How can you use mathematics to identify features – brushstrokes, textural fluctuations – to decide whether a painting really is by Van Gogh or if it belongs to his Arles period? It may sound like a question that’s only interesting to art historians, but it also goes to the heart of making art. A painting is a physical object created through muscle control and repetitive modes of thought. How stuck do we get as artists into relying on our habits? Can we ever shake those patterns up at a fundamental level?

(Could I ever really write a decent haiku?)

As the week went by,  an effervescence of topics led in all directions, crossing like Venetian canals. James Wang  told us how his group has built a website to compare their computer-generated rankings of a photograph’s aesthetic quality with how much people actually like the photos. The work of trying to create computer versions of human thought is fascinating in and of itself, but in his preface to the main talk, James casually mentioned his earlier work on identifying the gender of the handprints in ancient cave paintings.

(You mean all those beautiful drawings were created by men and women? It wasn’t just a guy thing?)

Craig Kaplan showed how you can use a famous math challenge, the Travelling Salesman Problem, to create an algorithm that will draw half-tone pictures. (How does a brain assemble lines and dots into images?) Luke Wolcott used extracts from his thesis as the lyrics for a musical composition, using the phrase ‘you have to stay in this universe.’ (Mathematicians are always being told they ‘have to stay in this universe’ when they’re solving an equation. Don’t we all?)

We looked at the math of Persian mosaic designs and shoved round tables together to create large versions with blue tape. We looked at the exhibits being designed for the new Museum of Mathematics in New York and tried to twist the puzzle pieces brought by mathematical sculptor George Hart back into their neat cubes.

Now that I am home and the mountains are no longer looking over my shoulder, I have slammed the trap door shut on my evil twin and am thinking how rich the intersections of thought make us. I would answer David Mumford’s question properly now.

We don’t ‘teach’ metaphor any more than we teach people to breathe. We put a pile of different things together and encourage them to find the points of contact and the relationships between those points. It doesn’t matter whether we are in a schoolroom, a seniors’ centre or a gathering of eminent mathematicians. We just play in order to develop metaphor’s basic ‘muscle memory’ in the brain. We put a poet in a room with mathematicians, a mathematician in the room with poets.  We take ourselves to Disneyland – not the Disneyland of pre-programmed rides and candy floss, but the Magic Kingdom of collision, of discovery, of our human handprints on rock.

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