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'The Paths of Lovers Cross in the Line of Duty.'
THE LAST LAUGH
Copyright (C) 1990 by Homer Wilson Smith
A Mandelbrot fractal is a statement of how well something survives
in a given environment. If it does NOT survive well you give the
environment some color of the rainbow specifying how quickly the thing
died. If the item in question DOES survive well or lives forever you
color that environment black.
Mathematically speaking infinity does not mean infinite survival.
Infinity means infinite change, which means death. Thus in the
Mandelbrot plane (C) if the iterated variable Z goes off to infinity
that means it died and you give the environment (C) some color
representing that fact, and how long it took to go out of bounds.
What the variable does in most of the black area of the Mandelbrot
set is not much better as far as survival is concerned. In much of the
black area the iterated variable attains a steady state of no change at
all, or a periodic change from one state to another and back again.
This too is not life.
Life is not a rock or a statue. It is a constantly changing
system. You grow, you change, you shed your entire skin every so often,
you replace broken parts, you age, you split in half, or you procreate
and then die.
This is very unlike the behavior of the variable going off to
infinity and it is very unlike the variable hanging out at a fixed point
or fixed period cycle. Life much more resembles the iterated variable
involved in a chaotic attractor, those areas of constant change within
These areas of constant change, of chaotic attraction, happen for
environments (C) that are on the boundary of the Mandelbrot Set. But
they also happen if the environment (C) is constantly changing from
iteration to iteration. A fixed point for one value of (C) will not be
a fixed point for another value of (C). So if Z is zooming in on a
fixed point or dull periodic cycle for a particular value of (C) and you
keep changing (C), you will change the value of the fixed point out from
under the variable that is homing in, and it will attain a state of
constant change within reasonable bounds never settling down to a dull
or rigid cycle. This is life.
One last point should be made here. Once the iterated variable (Z)
reaches a fixed point or cycle, it stays there BECAUSE the environment
(C) is NOT changing. But in real life the environment is always
changing and in fact it is often changed by the very production output
of the iterated item in question. The cell that splits in two while
iterating CREATES a new environment for itself consisting of its newly
formed sister cell. Thus what may be a fixed point during one iteration
may no longer be a fixed point during the next iteration because the
environment variable (C) has changed. Thus the iterated variable, the
inside trying to survive in an outside, may constantly skit around
looking for stability to find it always eluding its grasp. This keeps
you from becoming a rock or a statue. This is the constant ebb and flow
of biological life, and keeps the wheels of progress, production and
consumption, always turning.
This can have a negative side too. People trying to find health
and happiness by DRIVING to work everyday may be foiled by the
productive output of their automobile engines.
A lot of people laugh at 'The Cell and the Womb' or the idea that
fractals have anything to do with insides surviving in outsides.
However the equation Z = Z*Z + C directly says that what happens to Z is
a function of what Z was just a moment before and EVERYTHING ELSE IN THE
WORLD THAT IS NOT Z. If that is not something 'surviving by changing'
in an environment not itself, then I don't know what is.
You got to remember something about fractals. A long time ago Ben
Franklin was playing around with electricity and he came up with some
interesting theories to explain some very interesting phenomenon. They
really knew how to zap people in those days, what with Leyden jars and
kites on strings and all. Everyone had to 'feel the spark', that was
part of their initiation into the inner conclave of Electricians. If
you failed the initiation, either by accident or otherwise, they buried
you and found someone else.
No joking, Leyden jars ganged in parallel could store millions of
volts and throw sparks 2 feet long. But they still thought electricity
was a liquid that you could dissolve in water. That's HOW they
discovered the Leyden jar. ZAP!
This was all very impressive to everyone involved, but does this
mean that Ben was right? No of course not, Ben's ideas of electricity
were near ridiculous. It took a guy by the name of Faraday to make any
real sense out of the matter, but to hear HIM talk of it Ben was a
That's because before Ben's time people were pretty much passing
banana's back and forth in the trees as far as electricity was
concerned. Ben made the first bold steps towards making electricty a
respected and controllable subject of knowledge.
Just so today with fractals. Chaotic dynamical systems is a VERY
VERY NEW field of math and it is VERY DIFFERENT from anything that has
gone before. People have no idea what is to be found there, and people
have no idea what it could be used for. They might as well be passing
bananas back and forth in the trees when it comes to fractals.
So you could say that these ideas about the 'Cell and the Womb' and
so forth are in the Ben Franklin stage of discovery. No one has even
proven them wrong yet. They are still LAUGHING at them, don't you see?
The Faraday stage of development, where they get ripped apart and put
back together again correctly, is still way down the road. But in 200
years people will know what this was all about and not only will they be
able to prove that their understanding is correct they will be able to
use it to incredible ends.
Of course we may not be able to recognize these original ideas in
the final useable version, just as Ben's original ideas have been lost
in the upgrades. But the people who LAUGHED at Ben were not the ones to
make the upgrades, and Ben himself would have been the first to embrace
the improvements even if it had meant leaving his own name in the dust.
And with that attitude you can be sure his name never will be left
in the dust.
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