xfl12.memo
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'The Paths of Lovers Cross in the Line of Duty.'
THE WHY IS GOD
Copyright (C) 1990 Homer Wilson Smith
All Rights Reserved
One of the great discoveries of the 19th century is that everything
in the physical universe (except maybe consciousness) follows
mathematical laws. All of the relationships between objects in space
and time can be measured in terms of numbers, and all of the causal
influences between them can also be described in terms of equations and
mathematical relationships.
Apparently God was a mathematician first, and a purveyor of
damnation second.
Thus the study of math becomes of paramount importance in the
process of understanding and controlling the universe around us.
It goes without saying that if the universe is controlled by
mathematical laws then the qualities and conditions found in those
mathematical laws will be manifest in the universe that is controlled by
them.
Thus the study of pure mathematics is beneficial to us all, for as
we gain deeper insight into the nature of the math we use, we are more
able to find these same things manifested in the exterior physical
universe. If it were not for the mathematician making the discovery on
the purely theoretical level, these manifestations would go forever
unnoticed or unexplained in the physical universe.
It is quite apparent that the mathematics that governs the macro
scale world is based mostly on the simple force laws of Gauss, Maxwell
and Co. namely the 1/R*R laws that relate to the propagation of force
lines through out the surface of a surrounding sphere. This one idea
alone brought science into the 20th century and with good reason. It is
basically correct enough.
We find this simple mathematical equation expressed not only in the
laws of gravity, but also in electromagnetism and electricity without
which our world would still be cold and dark.
Thus it would seem that if the mathematicians are to stay ahead of
the game they should spend some time studying the ins and outs of the
1/R*R laws and their related equations, such as derivatives and
integrals.
For the longest time, the missing part to this whole story was the
concept of iteration. For example in the force law F = GMM/R*R we see
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Force expressed as a function of mass and position, but we do not see
POSITION expressed as a function of mass and POSITION. Thus the use of
the F=GMM/R*R law is strictly on an evaluation basis. You find the
inputs and you get one output. There is no place to stick the output
back into the input because the Force term is not in the input, and the
input terms are not in the output.
Most of physics went this way for eons although it need not have.
People have long known of differential equations wherein the present
CHANGE in state is a function of the present state. But really it took
some very bright people looking into living biological systems to start
coming up with equations that expressed the PRESENT STATE directly in
terms of the PRESENT STATE (just a moment before!)
This of course gives the needed conditions for ITERATION, or
repeated evaluation of the equations involved.
It is quite possible to then go back to all the old familiar stuff,
like planets moving around the sun, and REWRITE the equations in terms
of iteration, wherein the present position is a function of past
position. In fact the rocket guys do it all the time, as simple
algebraic solutions to multi bodied planetary systems are either
impossible or difficult. Actually the use of iterated differential
systems has been with us for a long time.
So if we go back and look at the world in this new light, all of a
sudden we find we have a plethora of iterated expressions with little to
no understanding of what their MATHEMATICAL nature is.
So once you start looking into the matter you find a wonderful
world of structure and 'nature' in the subject. You find there are
fixed points, and period cycles, and chaotic cycles, there are repulsive
and attractive things with basins of attraction, and there are open and
closed Julia Sets which give rise to all sorts of fantastic Mandelbrot
Sets. One finds that all these things depend on the values of the
parameters involved in the equations, and that all equations manifest
these things in one form or another.
One also finds that for many of them the various boundaries
surrounding basins of attraction or what have you are quite FRACTAL, an
incidental but very important new thing to know about the matter.
IT COULD NOT BE SO PROMINENT AND NOT BE IMPORTANT, DON'T YOU SEE?
Not as long as the equations which manifest such things are key
causal descriptors in the physical universe in question.
First you find out what is true MATHEMATICALLY, and THEN you find
out where those things are applied in the real universe. I assure you
these things do not exist in a vacuum of vanity. If they exist
mathematically, they ARE applied.
Now the important equations of the physical universe have not
changed, Y = X*X + C is still Y = X*X + C, but the CONCEPT of what you
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are going to DO with it has changed, from simple evaluation which
produces parabolas, to multiple iteration which produces Mandelbrot Sets
and Julia Sets. And all of a sudden this entire new landscape of
structure and nature appears to unfold as if out of nowhere.
It may seem like it is new, but you and I know it has been there
all along.
AND YOU CAN BET THE PHYSICAL UNIVERSE KNOWS IT TOO.
The physical universe has been using these same equations to march
its wheels of time forever, and you can be sure that if these equations
show some inner structure or 'nature' then that same nature will be
manifested outwardly in the physical universe expression of that
equation.
The physical universe is basically an iterated system, so actually
it is surprising we have made the progress we have, using only simple
evaluation. The equations have been around forever. The physical
universe has been USING them almost forever. The equations have as part
of their nature things like fixed points, period cycles, chaotic cycles,
basins of attraction, etc., so you can be sure all these things are
manifested in the physical universe INCLUDING FRACTALNESS.
To say therefore that fractals have nothing to with anything and
have not explained or proven useful in our understanding of the universe
is more a statement about the people who are working with fractals
rather than a statement about the pertinence of fractals to the world at
large.
Fractals are so pertinent to the universe no one can see it yet.
Long time ago, they thought math did not pertain either. The 'why'
was God.
The 'why' may still be God, but if it is, then clearly God is a
mathematician of significant merit, and no doubt a fractal enthusiast.
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