[IAEP] Reality is a crutch (was Re: Physics - Lesson plans ideas?)
Edward Cherlin
echerlin at gmail.com
Sun Aug 16 07:29:30 EDT 2009
On Sun, Aug 16, 2009 at 12:25 AM, <forster at ozonline.com.au> 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)
More information about the IAEP
mailing list