Wednesday, November 18, 2009

"Alice in Wonderland" math

Winston Churchill sounds like such a Visual-Spatial learner to me, which may explain why he was always bottom of the school during his Harrow years, had to take English three times because he wasn't thought smart enough to advance to the Classics, and had to take his exit exams three times before he passed. His liking for grammar defined by colored underlining, his battle formations of toy soldiers (he apparently had a collection of more than 1500) and his way of thinking about math all seem to show this tendency. Even his sense of humor and his ability to see the big picture seem to me to be visual spatial traits.

In regard to Mathematics he writes:

Of course what I call Mathematics is only what the Civil Service Commissioners expected you to know to pass a very rudimentary examination. I suppose that to those who enjoy this peculiar gift, Senior Wranglers and the like, the waters in which I swam must seem only a duck-puddle compared to the Atlantic Ocean. Nevertheless, when I plunged in, I was soon out of my depth. When I look back upon those care-laden months, their prominent features rise from the abyss of memory. Of course I had progressed far beyond Vulgar Fractions and the Decimal System. We were arrived in an 'Alice-in-Wonderland' world, at the portals of which stood 'A Quadratic Equation.' This with a strange grimace pointed the way to the Theory of Indices, which again handed on the intruder to the full rigours of the Binomial Theorem. Further dim chambers lighted by sullen, sulphurous fires were reputed to contain a dragon called the 'Differential Calculus.' But this monster was beyond the bounds appointed by the Civil Service Commissioners who regulated this stage of Pilgrim's heavy journey. We turned aside, not indeed to the uplands of the Delectable Mountains, but into a strange corridor of things like anagrams and acrostics called Sines, Cosines and Tangents. Apparently they were very important, especially when multiplied by each other, or by themselves! They had also this merit—you could learn many of their evolutions off by heart. There was a question in my third and last Examination about these Cosines and Tangents in a highly square-rooted condition which must have been decisive upon the whole of my after life. It was a problem. But luckily I had seen its ugly face only a few days before and recognised it at first sight.

I have never met any of these creatures since. With my third and successful examination they passed away like the phantasmagoria of a fevered dream. I am assured that they are most helpful in engineering, astronomy and things like that. It is very important to build bridges and canals and to comprehend all the stresses and potentialities of matter, to say nothing of counting all the stars and even universes and measuring how far off they are, and foretelling eclipses, the arrival of comets and such like. I am very glad there are quite a number of people born with a gift and a liking for all of this; like great chess-players who play sixteen games at once blindfold and die quite soon of epilepsy. Serve them right! I hope the Mathematicians, however, are well rewarded. I promise never to blackleg their profession nor take the bread out of their mouths.

I had a feeling once about Mathematics, that I saw it all—Depth beyond depth was revealed to me—the Byss and the Abyss. I saw, as one might see the transit of Venus—or even the Lord Mayor's Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and I let it go!
It's interesting to me that Richard Feynman, not too different from Churchill in his irreverence and his dislike for abstraction, became a theoretical physicist while Churchill became a politician. But here, maybe family influence plays a big part. Feynman's father used to talk to him about the natural sciences, while Churchill's father was a notable political leader.

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