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Just as surely as (a + b) = (b + a),  mathematicians love their blackboards

  • Michael Barany before his Ph.D. defense. Courtesy


Tuesday, January 03, 2017

Movies like to depict mathematicians as weirdos, but they usually miss the one legitimately weird thing about them: an extreme love of blackboards.

Not whiteboards, not smartboards – blackboards. We’re talking chalk dust and erasers made of felt, like you had in elementary school.

“If I walk to a room and see something written on a blackboard rather than a whiteboard, I’m more likely to assume it was done by a mathematician,” said Michael Barany, a postdoctoral fellow in the Department of History at Dartmouth, whose background is in mathematics and whose research examines the sociology of the field. “There are cases of a university where the administration is doing a building renovation or moving a department, and wanted to upgrade . . . and math departments have actively protested to keep their blackboards.”

Barany knows because his research includes what strikes me as the most intriguing question I’ve heard in ages: Why do mathematicians like blackboards so much? And they surely do.

In 2015, for example, the Japanese company that manufactured Hagoromo Fulltouch Chalk went out of business, and mathematicians around the world panicked because Hagoromo is widely considered the finest blackboard chalk in the world, producing clean lines and little dust. As Gizmodo reported, a Japanese TV station came to Stanford University to do a story about frantic mathematicians, one of who had stockpiled 15 years’ worth of Hagoromo supplies.

Closer to home, ponder a casual admission that Barany made in the midst of our conversion: “I have a collection of colored chalk I carry with me. You never know if there’s going to be good colored chalk where you’re going.”

That is not something most people would say, unless they were kindergarteners or sidewalk artists. But among Barany’s publications and co-authorship of the 2014 study “Chalk: Materials and Concepts in Mathematics Research,” a 26-page analysis (with five pages of source notes) that includes sentences like “the formal rigor at the heart of mathematical order becomes indissociable from the ‘chalk in hand’ character of routine mathematical work.”

What’s behind this phenomenon? Barany has a few hypotheses, some his own and some gathered from various sources:

Tradition

Serious mathematics has always been done on blackboards, so if your proof is written on some other wall-hanging device, it must not be serious mathematics.

“There is definitely a mystique to a blackboard. Prestigious math departments prize putting blackboards in many places, as prominently as they reasonably can. A lot of places have blackboards in elevators – they don’t get used that much, part of it is just keeping up appearances of being a blackboard-y discipline,” Barany said.

“Math (departments) often have blackboard in hallways. It’s a way you mark a space as (being) a place for mathematical collaboration.”

There are even reports of blackboards in math building restrooms, although that might be rumors floated by jealous physicists.

Noise

“The sound of the chalk is loud enough, disruptive enough, sharp enough to have an active effect in turn-taking when someone’s presenting something to a group. This limits the allowable spaces for interruption; gives a certain control over the way a conversation plays out just by making a particular kind of noise,” he said. “You can talk over someone if they’re writing on a smartboard or a whiteboard, that’s a lot harder to do on a blackboard.”

This tickled my fancy. The click-click-click when writing with chalk on blackboard is like no other sound out there, and I could see it affecting group dynamics in a way that would help research mathematics, the most information-dense communication system that humanity has ever devised. In mathematics, lack of interruption is important – unlike activities such as, say, writing a newspaper column, where any random schlub can chime in.

Functionality

“It’s hard to write small on a blackboard. That forces you to limit number of symbols, to have an economy of writing,” he said.

Sounds reasonable, but Barany’s other functionality-related idea is a lot more fun: “The other thing about blackboards is that they smudge productively.”

Smudge productively! I love it – but what does it mean?

“Often a mathematical argument will involve taking some term or idea and rewriting it or rephrasing it in a fruitful way. You can do that by using an eraser or the side of your hand to rub out the thing you’ve rephrased and writing over it, but the smudge will still be visible. Being able to write over something while leaving visual evidence there was something before – is a nontrivial part of how mathematicians communicate those kinds of arguments.”

Amazing. The inherent messiness of blackboards turns out to be a feature, not a bug.

Physicality

“People say, ‘I can write more quickly on a blackboard,’ ” Barany said. “They say, ‘I have to put my body into the writing, it brings it to life some way.’ ”

And here’s a minor but non-zero benefit to using blackboards: “You can tell when chalk is about to run out in a way that you can’t tell when a whiteboard marker is about to run out.”

All these answers are intriguing, but Barany says none is the answer. As with all things involving the behavior of the universe’s most complex system, – human beings – the variables are so numerous and the interactions so tangled that it’s almost impossible to sort them out.

What’s most intriguing is that these “fuzzy” sociology and psychology factors (fuzzy to a hard-science fan, anyway) are important in the development of the purest of human activities: high-level mathematics. Math often seems to be nothing less than truth itself freed from the constraints and biases of carbon-based life forms. “Euclid alone has looked on beauty bare,” as the poet Edna St. Vincent Millay famously put it.

But Barany said that’s not really true. Math, he notes, is done by humans and should be viewed through the prism of humanity, through the realities of the person he calls “the witness,” or the mathematician who makes a finding.

“People think that it shouldn’t matter who the witness is as a person – that the character of the witness is not what makes the evidence reliable. . . . But one learns very quickly about mathematicians is that this is not how mathematicians share ideas, and it’s not how research takes place. It ends up looking a lot more like other kinds of witnessing, that are better understood,” he said.

If the witness is more comfortable or more effective or more likely to be understood when using the compressed skeletal remains of sea creatures to write on thin sheets of slate, then so be it. If nothing else, it’s a celebration of the technology’s staying power in our here-today-gone-tomorrow world.

“It’s unlikely that blackboards will be used 50 years from now in the same way they are used today, but it’s a good bet they’ll be used 50 years from now in some way,” Barany said.

One place he hopes they’ll be used, incidentally, is his new home in Dartmouth’s history department.

“I’m trying to commandeer a blackboard for the hallway.”

(David Brooks can be reached at 369-3313 or dbrooks@cmonitor.com or on Twitter @GraniteGeek)