| beauty of infinity -
03-03-2006, 06:15 PM
The beauty of complex numbers is, in the first place, that they use the imaginary numbers, i.e., numbers that somebody, somehow, had to invent when he ran out of resources to try to explain certain solutions. The complex analysis we learn in high school, as much of the math, doesnīt have anything to do with the real use of these little invented fellows. Complex analysis can be used to solve equations that wouldnīt have an answer in the real plane and, for our special interest in TOE, it is significantly usefull that the complex sphere with the union of the infinite forms a space where solutions can be solved algebraically easier. Then we can use projections to return to the original space. This allow us to work with several dimensions and, even though we can not visualize them, they make sense mathematically.
So, letīs think that math uses a lot of imagination. In the other hand, if the results of an operation yield to different results, we are facing a fallacy. I would like to take a look to that fake operation you guys are trying to solve.
In the meantime, letīs enjoy the power of imagination.
regards,
or |