Thursday, August 28, 2014

Unreasonable effectiveness, revisited

An interesting take on the 'unreasonable effectiveness' of mathematics is formulated by Michael Barr in his book review that appeared in the last issue (August/September) of The American Mathematical Monthly, and involves the 'ubiquitous' presence of complex numbers in quantum mechanics:
Classical physics was formulated entirely with real numbers. Could quantum mechanics have even been formulated without complex numbers? What could it possibly look like? Isn’t the fact that complex numbers were created long before quantum mechanics required it, another example of the unreasonable effectiveness of mathematics?
(The Outer Limits of Reason. Noson Yanofsky. MIT Press, Cambridge, MA and London, England, 2013 - Reviewed by Michael Barr, The American Mathematical Monthly, Vol. 121, No. 7 (August–September), pp. 658-660)