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

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