On Sun, Aug 16, 2009 at 12:25 AM, <[email protected]> wrote: > Alan > > We study complex numbers and transfinite numbers even though they aren't real > world. Root(-1) isn't real world but its a useful abstraction to study.
This turns out not to be the case. Complex numbers are required in classical electricity and in all parts of Quantum Mechanics, where the imaginary part of a wave is necessary to represent its phase, where probabilities of states are represented by the product of the wave function with its complex conjugate, and where state-change operators (such as _i_ times partial derivative with respect to spatial coordinates) routinely involve complex values. Infinities and infinitesimals appear as real-world values in the theory of games of perfect information. See Conway, On Numbers and Games, and Berlekamp, Conway, and Guy, Winning Ways for Your Mathematical Plays. -- Silent Thunder (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) is my name And Children are my nation. The Cosmos is my dwelling place, The Truth my destination. http://earthtreasury.org/worknet (Edward Mokurai Cherlin) _______________________________________________ IAEP -- It's An Education Project (not a laptop project!) [email protected] http://lists.sugarlabs.org/listinfo/iaep
