Sunday, May 23, 2010

Dwelling in pyramids

Martin Gardner lived life inside his own brain, and was fortunate enough to make a living playing all the time.

I have enjoyed many of Martin Gardner's books over the years, but the one that most profoundly influenced me was Aha! Gotcha. Someone gave me this book when I was young (I suppose I was eleven or twelve?) and it absolutely captivated me, I pored over its pages for many hours and with extraordinary enjoyment - the elegance and economy of its insights were absolutely delightful, and I think of it as being in the same conceptual universe as Sherlock Holmes and the stories of Isaac Asimov, other favorites of that era.

There is little evidence of it in my adult life, but as a child I was very much in love with mathematical things, and in an alternate universe somewhere I am a theoretical mathematician who does most of my work lying in bed and occasionally getting up to make a squiggle on a bit of paper. I had a very wonderful teacher outside of school - his name was Bill Cromley and he ran a sort of summer camp offering lessons in math, remedial work for those who needed it and magical work for those who wanted it for fun.

(It was odd, I later had him as a classroom teacher in high school and there was nothing magical about it at all - I thought even at the time that he should have been teaching younger children, something about drilling trigonometry into teenage minds really deadened his spirit, and he did not enjoy the give-and-take of the classroom.)

But in this funny basement room (was it in a church?) he showed those of us who liked such things some truly magical aspects of numbers and the way they work - I guess I was ten or eleven, I remember the utter delightfulness of realizing that AND and OR could be translated into columns of ones and zeros, and that the two languages were really and truly equivalent - and experimenting with ways of thinking about tetrahedrons and what other sorts of shape one might then be able to work out the volume of - and an ingenious way of doing mental multiplication in your head by visualizing the two numbers as forming the two adjacent sides of a rectangle and then adding the four different bits of it together - in any case, it was a very enjoyable and high-level form of play, and it is pretty much the spirit I hope to capture when I teach.


  1. That is what E and her best friend G do in their out-of-school math group, and it is exactly the way I think enrichment should happen: not moving kids ahead more quickly, but teaching them ways of thinking that aren't even part of the curriculum, and really don't need to be, but are, as you say, magical (you should have heard how excited they were about creating number systems in base 12 on Friday!).

  2. I think the kinds of things Gardner wrote are massively catalytic for any version of the intellectual life (though of course they have a special savor for those of us who are mathematicians in this segment of the multiverse.)