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Books: Journey Through Genius
In a desperate attempt to appear "hip,' to "connect" with his teenage students, my high school math teacher compared geometry to Dungeons and Dragons. "You all love D&D, right?" he said, assuming we all did since, in 1987, it was the fad du jour. "Well, geometry is just like that: it starts as a few, basic, fundamental rules, and then builds a whole bunch of secondary rules to handle special cases. So in D&D you have basic rules for fighters, thieves, wizards and whatever, and in geometry you have rules for circles, squares and triangles. And from there you build more and more guidelines until you have an entire system!"
At the time I hated math, so I rolled my eyes at this amazingly lame analogy right along with everyone else. But now, years later, I can't help but wonder if he might have been on to something. In the decade since high school I have become fascinated both with games and math, and I now understand that the two are intimately connected. Indeed, reading Journey Through Genius: The Great Theorems of Mathematics was a lot like reading a rule book for the natural world.
Author William Dunham chose a dozen or so theorems, each of which advanced -- and, some cases, revolutionized -- the world's understanding of mathematics. It starts with the ancient Greeks and the problem of "squaring" various shapes. (One "squares" a figure by turning it into a square with sides of a known length, which, in turn, allows you to determine the area of the original shape. "Squaring the circle" was, for quite a while, the holy grail of mathemastics, until it was proven to be impossible.) The first Great Thereom demonstrates how to square rectangles, then pentagones, then hexagons, and so forth. This discovery paved the way for such other revelations as Pythegoras' Theorem (a2 + b2 = 2) and the value of pi, which, in turn, served as building blocks for still more profound insights. Journey Through Genius almost seems like a mystery novel, where clues are slowly revealed and more and more conclusions are drawn.
The most fascinating part of the book, I though, was the depiction of mathematicians as gunslingers in the 17th century. Up and coming mathematicians would challenge established scholars to "duels," where the participants would swap tests and see who could stump whom. He who could crack most of his opponent's questions would become (or remain) Mathematics Fastest Gun; the other would be shot down in ignominy. An unfortunate consequence of this institution was that mathematicians who discovered new methods of solving problems would be reluctant to share their secrets, instead hoarding their knowledge and using it to win in these gun fights. Who knew that Math Guys could be so ruthless?
I freely admit that I didn't really follow the Theorems presented in the last four chapters, although Dunham still explained the role and importance of each. Overall I found Journey Through Genius to be a fascinating read, and one -- like all the books on mathematics I read these days -- which made me wish I had cared more about this stuff when it was being taught to me to free. Criminey, if I had listened to my geometry teacher's advice and treated mathematics like D&D, I could have been a Level 13 Trigonomiter with a +2 Slide Rule of Sharpness by now. Ah, wasted youth.Posted on June 10, 2002 to Books