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Tue Aug 18 12:06:01 EDT 2020

            ART MATRIX  PO 880  Ithaca, NY  14851-0880  USA
                   (607) 277-0959, Fax (607) 277-8913
            'The Paths of Lovers Cross in the Line of Duty.'
                         THE CELL AND THE WOMB.
                Copyright (C) 1985 by Homer Wilson Smith
     Consider the fertilized cell in the womb.  When it divides, two
identical cells are formed.  When they divide, four identical cells are
formed.  And when each of them divide, eight identical cells are formed.
The question is, since every cell is an exact duplicate of the cell
before it, how come eventually some cells become skin cells and some
become bone marrow cells?  Or some become blood cells and some become
brain cells?  They are all, every last one of them, merely future
perfect duplicates of the original cell in the womb.
     The answer is, up to the moment when there are eight identical
cells they are all in the same environment.  They form the corners of a
cube.  No cell is in a special or different environment from the others
except maybe for the one that touches the womb wall.  However with the
next division of each cell into two identical cells there are now 16
cells.  Eight are on the inside and eight are on the outside.  They form
two cubes of 8 cells each, one cube on the inside of the other cube.
The cells on the outside form a tight well controlled environment for
the cells on the inside.  Each cell knows what environment it is in.  As
the cells divide they change their own environment and the environment
of their fellows by adding the presence of their sister cell.  It is
these different environments that cause cells to develop different
     When a cell divides in two, each half is smaller but identical.
There is a time for growing before the cell is allowed to divide again.
A cell grows by two way interchange of chemical substances across the
cell wall.  The cell grows by taking in MASS from the outside world.  In
different environments it 'eats' different masses so it becomes
something different.  The cell wall demarks the inside of the cell from
the outside of the cell which is the entire rest of the universe.  How
the cell grows and into what it becomes is determined by the nature and
substances of the environment.  Identical cells become very different
when allowed to grow in different environments.  The human body is
living proof of this.  The internal genetics do not change, but the
external manifestation changes dramatically.
     This immediately suggests a simple mathematical model.
     Define a number as any number on the complex plane and define two
different complex planes called the INSIDE PLANE and the OUTSIDE PLANE.
Remember these are two complete and different complex planes, not two
parts of the same plane.  Both the inside and outside complex planes
contain all possible integer, rational, irrational and transcendental
complex numbers from infinity to minus infinity.
     Each number in the inside plane represents the internal state of
one cell at one time.  The entire inside of a cell is represented by one
number.  Likewise each number in the outside plane represents the
                                                                  PAGE 2
environment of that same cell at that same time.  The entire outside of
the cell is represented by one number.  The outside of a cell is the
entire rest of the universe.  The inside of a cell is finite.  The
outside may not be.
     A cell can do two things:  grow and divide.  Division results in
two identical but smaller cells each in the new environment of its own
sister.  Division takes place over a very short period of time and the
cell does not eat during the division process.  Growth takes place over
a longer period of time and consists mainly of eating and incorporating
into its body the material which it has absorbed.  Growth results in a
bigger but very different cell.  Also important is that while the cell
is taking IN mass, it is also exchanging mass OUT into its surroundings
creating a unique environment for any of its neighbors.  What the cell
puts OUT is of course affected by what it takes IN, so in different
environments the cell will then CREATE even more different environments
from its own effluence.
     Thus as a cell absorbs different masses, it grows into a different
cell.  From this inflow it also creates new and unique outflows that act
as inflows to other cells in its vicinity which then, absorbing this
different environment, become different in their own turn.  They in turn
generate a new outflow which acts as a new environment for the first
     This might seem to be hopelessly confusing, but it becomes simpler
if we study the grow and divide cycle of just one cell.
     One ITERATION is one cycle of grow and divide in the on going life
of a cell.  Cells can live or die.  If they live they continue to
iterate: grow and divide.  If they die they stop iterating.  Usually
they die while trying to grow.  Cells often will not divide unless they
have grown enough, that is attained a large enough mass through eating.
If they do not have enough proper food they will not grow to the
dividing stage and so die of starvation or poisoning.  If they make it
to the divide stage, they usually have enough food energy to make it all
the way through the division.  Cells do not eat while they divide.
     The purpose of creation is trade in expressions of discovery.
Cells that do not discover how to iterate by trading stuff properly with
their environment are selected out.  It is hoped something would be
selected in, that would iterate forever.
                            The JULIA PLANE.
    (First thing, let's get something straight.  The Mandelbrot set is a
statement about all possible Julia sets, so if you are studying the
Mandelbrot Set and don't know what a Julia Set is, you are lost.)
     The progress of a cell and what it becomes (its STATE) can be
plotted on the inside plane as a red dot jumping around.  This is
because the inside plane is a numerical representation of every possible
state the inside of a cell could be in.  As long as the red dot stays
within a finite reasonable arena of operation on the inside plane, the
cell can be considered to be alive and functioning.  (See 'Do Fractals
Explain Everything' for a more detailed explanation of this idea.)  If
the red dot goes to infinity, the cell dies.
     The inside plane is a STATE SPACE of every possible internal state
the cell could be in.  A STATE SPACE is a SPACE of ALL STATES.  As the
cell changes over time, its internal state changes also and its
representative value on the plane of all possible insides also changes.
                                                                  PAGE 3
SURVIVAL is obtained when there is no change at all, or when there is
change within reasonable bounds.  Infinite change is death.  You can't
change EVERYTHING about you and still expect to be you.  If you were to
change EVERYTHING about you, chances are you would be a perfume bottle
or a turtle or Dust in the Wind (which might be considered a state of
maximum change).
     The JULIA PLANE is the STATE SPACE of the INSIDE of the CELL.
                           The OUTSIDE PLANE.
     Cells live forever because of what they are.  But what they are
results from what they were and what their environment was too.  So the
environment plays a determining role in what a cell becomes and if it is
able to live.
     One finds that
     1.) For SOME ENVIRONMENTS,     NO CELLS live forever.
     2.) For NO   ENVIRONMENTS, do ALL CELLS live forever.
     3.) For SOME ENVIRONMENTS,   SOME CELLS live forever.
     First this says that some environments are so DEADLY nothing can
expect to survive.  The inside of a super nova might be an example.  A
nitric acid bath would be another.  The air over Los Angeles would be a
third.  Electrical Engineering classes at Cornell would be a fourth.
     Secondly it says that there is no environment that is conducive to
life for every possible kind of cell no matter how malformed or unsuited
for life it may be.  What this means is that if you are going to survive
you must bring a modicum of your own personal survivability to the
situation in which you wish to live.  Then if you should find an
environment amenable to your particular life form, you have a going
     Lastly it says that biological immortality, at least for a species,
is possible as long as there is a correct match between the nature of
the cell and the nature of the environment.
     As for individual BIOLOGICAL immortality, remember that for
entities that survive by dividing and growing, there must be some
mechanism of individual death or else the system will over populate and
THAT is one of the most deadly environments there is.  The resulting
death and disease from over population and excessive numbers of dead
bodies lying around can kill EVERYTHING.  It is always better to have a
famine cut back the population, for then the few and the strong almost
always survive and with them the species.  In a famine situation the
number of dead bodies lying around is much less than in an
overpopulation situation, as the dead bodies tend to get eaten by other
hungry animals who are also starving, and thus disease has less of a
chance to take hold.
     In this case too much food is much worse for a population than too
little food.  There is almost always enough food for SOME and the BEST
to survive.  But if there is too much food, then animals start to drown
in their own excrement and the bugs that love excrement and dead bodies,
and THIS can infect the entire population forever or wipe it out over
night.  The point being that an endlessly affluent environment is not
always the most conducive to good survival.  Instead an environment that
                                                                  PAGE 4
has a measure of roughness and toughness will far better serve
biological immortality.  Biologically speaking, endless wealth means
certain death.  This is true because SPACE is limited.
     One might consider recent experiments wherein mice that were 30
percent underfed vastly outlived their well fed compatriots.  Nature has
learned that endless affluence must be checked against by an early death
rate to avoid the total annihilation consequent to overpopulation.
                     The CELL and its ENVIRONMENT.
     As the cell grows and divides it changes its own environment.  It
does this by adding the presence of its sister cell after division and
also by emitting material into the environment for other cells to absorb
which then in turn re-emit new material back out into the environment
for the first cell and others.
     As long as the cell changes its own environment to one that is
supportive of its functioning it will continue to survive and iterate.
If it doesn't it will be selected out (die) in a finite number of
     The outside plane is a STATE SPACE of every possible outside or
environment a cell could be in.
     The OUTSIDE plane is the MANDELBROT PLANE.
     The MANDELBROT plane is the STATE SPACE of the OUTSIDE of the CELL.
     It should be obvious that with the Julia Plane and the Mandelbrot
Plane we have the universe covered.  This is no small point.  If we
become well versed in Mandelbrot Sets and Julia Sets, we will have a
descriptive mechanism to help us deal with, well, everything.
Everything where insides are affected by outsides, and outsides are
affected by insides.  A DESCRIPTIVE MECHANISM mind you, not necessarily
a PREDICTIVE mechanism.  (See Mandelbrot and Julia Survivability Maps
for a further discussion of this idea.)
                     Coloring the MANDELBROT PLANE.
     Assume for a moment that as the cell divides it does NOT change its
own environment.  Then a starting cell can be placed in each and every
possible starting environment represented by each point on the
Mandelbrot plane, and allowed to grow and divide until dead.
     If it dies then that spot on the outside plane is colored according
to the number of divisions the cell made before it choked.
     If the cell never dies in a particular constant environment then
that position on the outside plane is colored black.  Color measures how
long until the cell died.  Black means it never died or took so long we
could not wait to find out.
     Since a cell DOES change its environment when it divides, as the
red dot jumps around on the inside plane, representing the changes
inside one cell over time, a green dot is also jumping around on the
outside plane.  The green dot on the OUTSIDE plane traces the time
evolution of the changes to the ENVIRONMENT of the same cell whose own
INNER evolution is traced by the red dot on the INSIDE plane.
                                                                  PAGE 5
     The position of the red dot on the inside plane specifies the
entire inside state of the cell at that moment; specifically whether it
is a blood, skin, brain or dead cell.  The position of the green dot on
the outside plane specifies the entire outside state of the cell at that
moment; specifically the environment that the cell is growing in
immediately after division.
     The green dot makes one move on the outside plane because the cell
divides creating a new environment for itself.
     The red dot makes one move on the inside plane because the freshly
divided cell grows in its new environment and so becomes a different
cell just before it divides again.
     Thus the two dots move one after the other.  First the cell grows
creating a new inside for itself (red dot moves), then the cell divides
creating a new environment for itself (green dot moves).
     GROWTH is a form of CHANGE.  DIVISION is a form of SURVIVAL.
CHANGE is a form of NON SURVIVAL.  What you were then is not what you
are now.  What you were did not survive.  SURVIVAL is a form of NO
CHANGE.  What you were then is still what you are now.  What you were
did not change.
     The cell CHANGES  because of its OUTSIDES during the GROW   phase.
     The cell SURVIVES because of its INSIDES  during the DIVIDE phase.
     What this means is that two cells that start off identical (because
they both just resulted from a division of a common cell) will quickly
CHANGE into different cells as each feeds in a different environment.
Hence CHANGE happens during the GROW phase BECAUSE OF differing
     Division however is the sign of SURVIVAL, a sign that the cell made
it.  After division there are two of them after all and surely that
means it survived.  But it made it because of the correctness of its
INSIDES in their ability to function properly in the environment given.
Division is sort of a reward for having successfully made it through the
growth phase to maturity.  Thus division is a sign of survival.  Thus
SURVIVAL happens during the DIVIDE phase BECAUSE OF viable INTERNAL
CONSTRUCTION (INSIDES).  However the result is two IDENTICAL cells.  No
CHANGE takes place (except in size) during the division process in the
internal nature of the cell.  Thus GROWTH is associated with CHANGE
which is a form of NON SURVIVAL, and DIVISION is associated with
SURVIVAL which is a form of NO CHANGE.
     When CHANGE takes place during DIVISION a mutation occurs.  What
was is no longer, although it might fare better.  When SURVIVAL takes
place during GROWTH, the cell has failed to differentiate properly due
to its surroundings.
     In this sense CHANGE and SURVIVAL are dicoms, DIchotomies of
Comparable and Opposite Magnitude.  Change is a form of non survival,
you are no longer what you just were.  What you just were did not
survive because it became what you are now.  Survival on the other hand
is a form of no change.  It means you persisted as you were without
change across a span of time.
     Of course in biological systems, the overall cycle of change and
survive should SURVIVE as this is the process of life going through
time.  But notice that during GROWTH the cell SHOULD CHANGE, if it
doesn't then something is very very wrong.  At the same time during
                                                                  PAGE 6
DIVISION the cell had BETTER NOT CHANGE, because the purpose of division
is to exactly replicate the DNA structure within.  If the DNA changes
during a division then a mutation has occurred, which means the original
blue print definitely did not survive.  In general this can mean the end
of the cell.  If you don't believe me, try eating some radium some time.
SOMETIMES the non survival of one chain of DNA and the continued
survival of the mutant is GOOD for the ongoing cycle of life as a whole,
but the original cell that did not divide properly definitely did not
survive even if it improved the chances for its offspring.
     Thus the iteration and movement of the red dot on the inside plane
happens during the growth phase and tracks the changes in the cell
brought on by the environment.
     The iteration and movement of the green dot on the outside plane
happens during the divide phase and tracks the changes in the
environment brought on by the cell.
     The red dot is allowed to go anywhere but infinity.  Infinity means
too much change in the cell and this means death.
     The green dot is allowed to stay in the black forever or wander in
the colored areas for a while but not so long as to cause the cells
fatality.  The green dot staying in the black areas of the outside plane
MEANS the red dot DID NOT go to infinity and so survived.  This is true
by the definition of how we color the outside plane in the first place
according to whether or not the cell lives or dies.  But the coloring of
the outside plane represents a CAUSAL quality of the environment namely
how it affects the longevity of an initial cell.  The red dot goes to
infinity BECAUSE the green dot stayed in a colored area too long.  The
green dot in a colored area means that the red dot WILL GO TO INFINITY
after N number of iterations and so WILL die if the green dot does not
get back into a black area quickly.
     It is possible that if the green dot stays in a colored area for
too long, the red dot will go infinity even if the green dot gets back
into a black area before the red dot does got to infinity.  Thus there
is a point of no return, and point of no RECAPTURE.
     In more lay terms, it is OK to smoke a cigarette every once in a
while (bad environment) but don't chain smoke.  Likewise it is OK to
visit Los Angeles (or downtown Ithaca for that matter) but don't move in
for the long haul.  (Please see 'The Theory Behind The Cell and the
Womb' for a more detailed explanation of RECAPTURE.)
     Life functions in the high iteration areas bounding the black and
colored areas of the outside plane.
     The Mandelbrot plane does not determine how a cell will evolve but
demarks how a cell can evolve and still be viable.  The evolution IS
determined by what a cell does with its present environment to make
itself a new environment through division.
     If the cell creates environments in the colored areas of the
outside plane it will cause its own demise.  If it creates environments
in the black areas of the outside plane it will survive forever.  Since
survival forever is equivalent to death forever through over population,
the ideal survival for the SPECIES is obtained by the cell creating
environments for itself that wander around the chaotic boundaries of the
outside plane where color and black, death and survivability intermix
and swirl around each other in and endless array of beauty, confusion
and amazement.  This guarantees the death of the individual cell but the
                                                                  PAGE 7
survival of the ongoing process.
     Individual death of old age is the result of intentional failed
recapture.  The offspring are injected into the system where recapture
is relatively secure.
                     Z = Z*Z + C  and  C = C/2 + Z
                           Please see Fig 1.
     If Z stands for ZYGOTE which is the cell in the womb, and if C
stands for (external) CONDITIONS, then the equation  Z = Z*Z + C  says
that what the zygote becomes is what the zygote was squared plus the
number representing its environment.  This iteration represents the GROW
phase of the zygote as it changes and prepares itself for its next
divide phase.  We know this because this equation represents the
iteration of the zygote (Z).  Z appears both on the left and the right
of the equal sign, thus it is the zygote that is being iterated.  It
shows that the zygote changes from what it was before, to what it is one
iteration later.  The zygote CHANGES while it GROWS not while it
divides.   Thus Z = Z*Z + C models the growth phase starting just after
division and ending just before its next division.  During this process
the environment (C) does not change.  Z changes.
     The second equation, C = C/2 + Z says that the environment
(external Conditions) becomes what the environment was divided by 2 with
the new sister zygote added in.  This iteration represents the DIVIDE
phase of the zygote as it changes its environment by adding the presence
of its sister cell during division.  We know this because C is on both
the left and the right of the equal sign, therefore it is the
environment (C) that is being iterated.  This equation says that C
changes from what it was before division to what it is after division.
The zygote does not change during this phase (even though it is the
zygote that is dividing!).  C (the environment) changes.
     Z is the red dot jumping around on the Julia plane.  C is the green
dot jumping around on the Mandelbrot plane.  Assume an initial zygote
called Z0 in an initial environment called C0.  Then during the growth
phase Z0 grows into a new and different zygote called Z1 but it does
this growing in the original environment call C0.  Then as the new and
fully matured zygote Z1 divides, it produces two smaller but identical
versions of itself, both still called Z1, but now the environment C0
that the first Z1 was in now includes the presence of the second Z1, so
becomes C1.
     Recognizing that any equation may be used to model the growth and
division of a cell, we may write this in general mathematical terms as
follows.  Let Z1 = Z0*Z0 + C0 be generalized to Z1 = f(Z0,C0) and let C1
= C0/2 + Z1 be generalized to C1 = g(C0,Z1).  The iteration of Z1 =
f(Z0,C0) relates to the GROWTH of the cell in environment C0 from the
smaller Z0 to the bigger but different Z1.  The iteration of C1 =
g(C0,Z1) relates to the change in environment from C0 to C1 caused by
the DIVISION of cell Z1 from the larger Z1 to two smaller but identical
Z1's.  The sister copy of Z1 becomes part of the new environment C1 of
the first copy of Z1.
                        The MOTH and the FOREST.
                                                                  PAGE 8
     The question naturally arises, is it reasonable to represent the
entire inside state of a cell by one number?  Or even more ridiculous
the entire rest of the universe by one number?  Consider a population of
moths in a forest.  Here the inside is the system of moths trying to
survive in the forest environment which is the outside.  The number of
moths in the forest at any time is a function of the number of moths
just prior plus the environment.
     Clearly the population of moths in the forest at any one time can
be represented by one number.  But can the entire rest of the forest be
represented in this same way?  The forest is a large system of
interacting subsystems, like the number of trees, the number of birds,
the number of oxygen molecules in the air.  It would seem that if you
broke the forest into its parts you might be able to represent the
forest as a system of things each of which can be represented by one
number.  Hence representing the entire forest at any one time as a
function of many single numbers resulting in one overall number is not
so wild. Just so with the inside and outside of a cell.  Of course the
arrangement of things can be important too.  But in large systems, the
DENSITIES of things can be more important that exact positioning.  And
where positioning becomes important, it would be taken into account by
the number representing the environment 7containing the particular
object it was positioned next to.
                         The DNA and the SOUP.
     Consider the primordial sea.  This is an all pervasive environment
that contains all the parts for a DNA molecule to start building itself.
DNA molecules survive by perfectly duplicating themselves.  They can not
see ahead and so do not 'plan' their own changes.  A DNA molecule that
is different after it has duplicated has NOT survived.  The environment
of the DNA molecule is constantly trying to destroy it and scatter its
well collected parts back into the soup.
     DNA molecules also tend to eat each other and eat each others
parts.  The ones that survive are the ones that can continue to
perfectly duplicate in spite of an environment that is trying to destroy
them.  Thus survival is always measured by no change in inside state.
The outside environment is directed towards changing the inside state.
The environment is not trying to intelligently build a better DNA
molecule.  But if a better DNA molecule should happen to form via
environmental influences then it will begin to out survive the
environmental destruction.  Thus is obtained a classic case of insides
surviving in the presence of outsides.  Clearly all of life has evolved
because of the ability of insides to out survive the changes brought on
by the outsides.
          What is a FRACTAL and why is there one in every PAW?
     Every equation of the form M = f(M,F) has two questions that can be
asked of it.  If M stands for Moths, and F stands for Forest, clearly
the number of Moths in the Forest depends on the number of Moths just
prior and also on the Forest.  One would want to know therefore what
happened to the number of Moths for every possible starting number of
Moths given a constant Forest, and also what happened to the number of
Moths, for every possible Forest given a constant starting number of
                                                                  PAGE 9
   The first question is for each and every possible starting M and a
constant F, what happens to M?  This is the Julia plane.  The second
question is for each and every possible F and a constant starting M,
what happens to M?  This is the Mandelbrot plane.  A fractal is thus the
pictorial representation of either one of these questions.  There are
Julia fractals and Mandelbrot fractals.  And of course there are hybrid
fractals like the Tarantula resulting from iterating equations in both M
and F.
     Fractal math is a way of looking at equations and physical
phenomena.  Just like calculus is a way of looking at equations and
physical phenomena.  Calculus deals with related rates.  Fractals deal
with insides and outsides.  Fractal math has been called the most
important discovery since calculus and has been rated with Relativity
and Quantum Mechanics as one of the three great discoveries of the 20th
century.  Calculus is important to all of life.  So are fractals.
     What in existence does not have to do with insides and outsides?
     Fractal math has to do with any system of insides trying to survive
in a system of outsides.  Even a hurricane depends on and feeds upon the
surrounding atmosphere where there is no hurricane.  If you were to
vanish all the rest of the CALM air on the planet surrounding the
hurricane, the hurricane would vanish too.
     Fractals ARE a description of whether or not insides survive in
various outsides of interest.  From that point of view they underlie
every operating system in existance.  -HWS
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