On Thu, Sep 13, 2012 at Roger Clough <rclo...@verizon.net> wrote: > would it make any sense to do comp using complex numbers, where the real > part is the objective part of the mental the imaginary part is the > subjective part of the mental >

The names "real" and "imaginary" are unfortunate because imaginary numbers are no more subjective than real numbers, but for historical reasons I guess we're stuck with those names. From a physics perspective think of the real numbers as dealing with magnitudes and the imaginary numbers as dealing in rotations in two dimensions; that's why if you want to talk about speed the real numbers are sufficient but if you want to talk about velocity you need the imaginary numbers too because velocity has both a magnitude and a direction. The square root of negative one is essential if mathematically you want to calculate how things rotate. It you pair up a Imaginary Number(i) and a regular old Real Number you get a Complex Number, and you can make a one to one relationship between the way Complex numbers add subtract multiply and divide and the way things move in a two dimensional plane, and that is enormously important. Or you could put it another way, regular numbers that most people are familiar with just have a magnitude, but complex numbers have a magnitude AND a direction. Many thought the square root of negative one (i) didn't have much practical use until about 1860 when Maxwell used them in his famous equations to figure out how Electromagnetism worked. Today nearly all quantum mechanical equations have an"i" in them somewhere, and it might not be going too far to say that is the source of quantum weirdness. The Schrodinger equation is deterministic and describes the quantum wave function, but that function is an abstraction and is unobservable, to get something you can see you must square the wave function and that gives you the probability you will observe a particle at any spot; but Schrodinger's equation has an "i" in it and that means very different quantum wave functions can give the exact same probability distribution when you square it; remember with i you get weird stuff like i^2=i^6 =-1 and i^4=i^100=1. All the rotational properties can be derived from Euler's Identity: e^i*PI +1 =0 . John K Clark John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.