Thursday, January 6, 2011

'Nother M&M

 [“Bite-sized essays for the busy businessman” ®]

A. D. Aleksandrov, in his splendid  essay on Non-Euclidean Geometry for the Soviet Mathematics overview (vol. II, p. 177, of the English translation published by the MIT Press), is quite concerned to defend mathematics from any charge of being a “just-so story”, or abstraction for its own sake; and this, for motives rather opposite to those that move mé. He, in the service of orthodox Marxism; I, in the service of orthodox Christianity.  But in this case it comes to the same thing:

Riemannian geometry has its applications as a method of abstract-geometrical description of physical phenomena.  This description is not at all arbitrary, and is not an idle play of the mathematical mind; it reflects the real mechanism of the phenomena in question, but reflects it in an abstract form.

I greatly look forward to meeting Aleksandrov in the next life.  (Eventually.  I reckon we’re both headed for an extended stint in purgatory, though for different reasons.)

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