Advanced Bash tutorial

[dougsweetser at gmail.com (Doug)]

> Wow, I wish that I could grasp the relationship
> Jay

Hello Jay:

With the power of email communication, it is not possible to
accurately gauge your level of sarcasm.  I'll presume it is high,
saying this observation is trivial.  The issue has to do with complex
numbers and how they are currently represented in a 2D spatial plane.
There is no difference visually between the real and the imaginary
numbers.  If someone did not label the real or imaginary axis, there
would be no way to tell if a reflection was over the real or imaginary
axis.

By representing the real axis with time, and the imaginary axis as
space, there is a difference.  Space reflections involve pairs of dots
moving like mirror reflections.  If there is a pair of dots moving
like synchronized swimmers in a mirror, a space reflection is going
on.  Time reflection require that an observer remembers how a dot
moved, so when it moves the opposite way, that can be noted.

The animation of trig functions is not what I had guessed.  I am used
to the unending speed bumps.  With quaternions, all the events move in
the same line.  What changes is when they happen.  It is a different
representation of the same function, but it looks quite different to
me as an animation.

doug

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