Archive for December, 2011

Ivan Karamazov and Euclid

Peter Kreeft once commented (in a talk – sorry I can’t give a reference) that he tells his undergraduate students that “if your faith is weak and you don’t want to lose it then don’t read The Brothers Karamazov by Fyodor Dostoyevsky”. I can scarcely think of a better recommendation for a book. And as if you need more reason, observe this gem (page 274 of the Penguin paperback):

[Ivan:] … if God really exists and if he really has created the world, then, as we all know, he created it in accordance with the Euclidean geometry, and he created the human mind with the conception of only the three dimensions of space. And yet there have been and there still are mathematicians and philosophers, some of them indeed men of extraordinary genius, who doubt whether the whole universe, or, to put it more wildly, all existence was created only according to Euclidean geometry and they even dare to dream that two parallel lines which, according to Euclid can never meet on earth, may meet somewhere in infinity. I, my dear chap, have come to the conclusion that if I can’t understand even that, then how can I be expected to understand about God?

The Brothers Karamazov was published in 1880. Ivan is referring to the discovery a few decades earlier by Lobachevsky that Euclidean geometry is not unique, and thus it is an empirical matter whether or not parallel lines meet (or are unique) in our universe. This seems like a very minor loose thread in physics, and yet when Einstein pulled on it, 35 years after Ivan’s monologue, he was lead to General Relativity, arguably the greatest achievement of a single physicist since Newton. Gravity is geometry!

This quote came as quite a surprise to me. I hadn’t realised that non-Euclidean geometry had reached popular culture in the 1880’s.

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