Sunday, September 27, 2009

Daffy

From Professor William Dunham's lecture on the mathematician Leonhard Euler (1707-1783), delivered September 17 at The Philoctetes Center for the Multidisciplinary Study of Imagination. Professor Dunham, describing the polynomial (below), said:

"It looks daffy."

He spoke particularly about the square roots of the square roots, suggesting these were perhaps the best illustrations of daffyness.

When I looked at this solution, daffy did not come to
mind. In fact, no words at all came to mind.

Certainly math has never looked daffy to me, but it never occured to me that it would look daffy to anybody--even to a mathematician.

My favorite of Euler's formulas, or discoveries, is the Euler Line, which is drawn once one determines the orthocenter, centroid, and circumcenter of any triangle. His Polyhedral Formula is also appealing (and was the starting point for topology and algebraic topology, and a theory of surfaces).

Nothing in these, still, struck me as daffy. Even the idea of his finding so many amicable numbers, which he did, did not rate as daffy.

That a hive in Switzerland (according to Prof. Dunham) is still publishing Euler's papers at the Swiss Institute: this qualifies as daffy. . . . How steadily have they been working? (Those monks copying the Bible for Queen Elizabeth come to mind--they've been working on that for a while, too. . . . Oh to be calligrapher to the Queen. Miles above dish soap and digestive biscuits. But I digress.)

What Prof. Dunham, a noted mathematics professor originally trained in topology, accomplished by describing the above formula (solution?) as daffy provided a bridge between math and English that allowed me to understand (if only in that instance) one mathematician's taste--in language anyway.

If I had to come up with one word to describe all those signs and numbers, I would say "hair caught in the wrong end of a hairdryer, although on a beautiful fall day in a green valley, and with lots of crisply drawn right angles." Honestly, one word just wouldn't be enough. It's a lot of sound, visually speaking. I do like the square roots of the square roots idea, though. That's quite nice.

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