Monday, August 15, 2005

On the Road

Over the weekend, I managed to find time for the first five chapters of Roger Penrose's Road to Reality. On the spectrum from pamphlet to thick-enough-to-stun-an-ox, it's closer to the ox side, so I purchased it with a certain sense of "as if" resignation (there are too many thin books time hasn't given me the luxury of finishing).

As far as it goes, I'm really enjoying the book, its insightful examples and interesting tidbits from the history of mathematics. For example, I'd never heard the story of Girolamo Saccheri's role in the development of hyperbolic geometry.

"It would seem that Saccheri himself must have ultimately thought his life's work a failure, constituting merely an unfulfilled attempt to prove the parallel postulate by showing that the hypothesis that the angle sum of every triangle is less than two right angles led to a contradiction... But in striving for it he, in effect, found something far greater: a new geometry, different from that of Euclid." (p. 42)

I can't help thinking of this poor old chap lying on an 18th century death bed pulling a mathematical George Bailey, thoroughly oblivious to the significance of his work. Bummer.


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