Chuckk Hubbard wrote:
On Nov 20, 2007 5:39 PM, Frank Barknecht fbar@footils.org wrote:
For some calculations polar, for others cartesian coordinates are easier to use. To quote Miller:
The main reason we use complex numbers in electronic music is because they magically automate trigonometric calculations. We frequently have to add angles together in order to talk about the changing phase of an audio signal as time progresses (or as it is shifted in time, as in this chapter). It turns out that, if you multiply two complex numbers, the argument of the product is the sum of the arguments of the two factors.
I still don't exactly understand why one couldn't just use (x, y) vectors; why the y value has to be multiplied by something imaginary. I mean, i/j is *defined as* the square root of -1, but it can't really *be* the square root of -1... I've accepted it and moved on to more practical questions, but that is still mysterious for me.
Everything in mathematics *is* so if *definined*. You could define your own mathematics by saying "there are no two straight lines that do not subtend" (no parallels). In fact, Riemann did so, and has created a geometry different from Euklidean, which is the basis for calculation on a sphere (straight lines -> great circles).
http://en.wikipedia.org/wiki/Non-Euclidean_geometry
It does not matter, if it stresses your personal "experience", as long as it does not contradict other definitions in your mathematics. Negative numbers were a great problem to mathematicians as well:
European mathematicians however, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debits (chapter 13 of Liber Abaci, 1202) and later as losses (in Flos). At the same time, the Chinese were indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit. The first use of negative numbers in a European work was by Chuquet during the 15th century. He used them as exponents, but referred to them as “absurd numbers”.
http://en.wikipedia.org/wiki/Negative_and_non-negative_numbers#First_usage_of_negative_numbers
cu Thomas
"Prisons are needed only to provide the illusion that courts and police are effective. They're a kind of job insurance." (Leto II. in: Frank Herbert, God Emperor of Dune) http://thomas.dergrossebruder.org/