March 15, 2010

How happy the lot of the mathematician!

From W. H. Auden's essay "Writing":
How happy the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavorably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.

I bet that Great Achievements in Math are debated by mathematicians, too, and not, say, by former Olympians, doctors, or journalists.


JoVE said...

Very true. Though mathematicians are in many ways similar to humanities folk. Especially in their concern with elegance and form.

I suspect it is only the fetishization of numbers by our culture that protects them from more widespread derision for their lack of concern for daily practicalities in favour of elegant abstraction.

Most people have no idea what they do but THINK that it must have something to do with the arithmetic we use in daily life and thus is useful. Little do they know.

Nicholas said...

The difference in attitude, as I see it, is that the lay public is more likely to accept an appeal to mathematicians as authority than an appeal to artists or critics. People are far more willing to defer to the expertise of mathematicians and assume they know what they're doing, in part because of a belief that mathematics is a progressive or cumulative body of knowledge. You don't see this with artists or critics at all: there's a common democratic assumption that art (from the position of the audience) is just a matter of opinion, and most people outside of the academic bubble abide by a grade-school notion of "opinion" as meaning that nobody's criticism is more valid than anyone else's. And so we've seen a rapid decline of public intellectuals in the humanities, because nobody accepts their authority.

Public awareness of mathematics isn't all that high, either. If more people were aware of the results in mathematics that come off as unintuitive to the untrained - nonstandard geometries, theorems like the Banach-Tarski paradox (where you take a sphere apart and recompose the pieces to make two spheres of the same size), and most everything involving limits or infinities - you would hear a lot more grumbling. I've had the strangest conversations with philosophy undergrads who had the hardest time comprehending that 1+1/2+1/4... = 2 (or the other canonical example, 0.999... = 1) because they flatly rejected the very notion of infinities collapsing into something finite.

You can find a lot of public grumbling about mathematics in a field that isn't even that arcane, in that you don't need to learn a lot of notation to grasp it: probability. Most people's intuitions about probability are wildly inaccurate. Look up the Monty Hall problem, which was popularized by Marilyn vos Savant (and which Mark Haddon works into The Curious Incident of the Dog in the Night-Time). It incited thousands of indignant letters from people who simply didn't accept the solution as correct.

Sam said...

Oh, that quote is Auden to a T! Loathsome, as always, and ignorant in the way only really smart people can be ignorant. What he's longing for here is for the literary arts to return to the halcyon golden days when they were conducted high atop a tower, within site but out of reach of the miserable groundlings far below (Auden deserves twenty extra years in Hell just for that bit about 'cashiers'). Golden days which of course never happened - for all his skaldic blather, Auden wouldn't know REAL literary history if it walked up and slapped him in the face.

Just look at what he's yearning for here! He wants no accountability, no pressure, and most of all no obligation to entertain ... literary tenure, in other words, based on the assumption that his particular mind is so incredible, so semi-divine, that anything it does, anything it produces at all, is worthy of study. What nonsense.

Higher mathematician live in a rarefied world because they pursue a rarefied field of study - only a few hundred people in the world can understand it. Writers deal in words, in thought transmuted to prose (and don't even get me started about verse!) - which we're all doing and understanding by age 3. So by age 20, 30, 40 yes, a well-read and earnestly-reading cashier can indeed weigh in on whether or not you're doing it publicly with any pronounced skill. Any active reader can, and you're accountable to ALL of them - that's the arena you chose to enter.

Bad enough when writers enter that arena and then act like Auden (or Jonathan Franzen, for a more modern example), like what they do is somehow hierarchical. Worse by far when, while doing that, they wistfully pine for the good old days when the slovenly public just lined up at the Muses' trough and slopped down whatever imperishable nuggets the August One decided to squeeze out that day.

Ohhh, elitism like this really gets my goat! It makes me, Sam, so furious I could punch a nun. Auden! Fah! You're lucky you wrote some fine poems, bub, because every time you published prose you embarrassed yourself!

Rohan Maitzen said...

I agree that there are a couple of illusions at stake here--the public idea that math is both objective and practical (the mathematicians I hear anything about are pretty clear that much advanced research in their fields is pretty much completely theoretical and about the problem, not, say, applications) and the implicit fantasy that offends "Sam" so much about the good ol' days of literary hierarchy. Still, I think Nick is right about the assumption that anyone who can read can be a critic--that criticism is just a matter of opinion and not susceptible to expertise. That's really what I was appreciating about this remark, as the whole Canada Reads thing irks me on a yearly basis because of this. (This year there was one real critic involved, though, and it's interesting that his book "won." Hmmm.)