THOUGHTS ON CHAOS
Mental Relativity describes the
between space and time,
which is called Structure.
Mental Relativity describes the
between space and time,
which is called Dynamics.
Order and chaos are not objects nor states, but
appreciations. Whenever one imposes an order, one also defines a chaos. If one were to
impose order upon the chaos, the original order must become chaos to balance time and
space. It is the nature of paradox: that one cannot order everything at once.
Fractals are not so much patterns made up of
smaller influences as frozen moments of time. When dynamics (which cannot be observed, but
only experienced) shift, the difference between what they were and what they are becomes
observable in the structural standing wave created from the interference between dynamics.
This standing wave is what we call a fractal pattern.
The nature of chaos has two sides. Looking large,
we peer at the wall of the limits of our observation. Anything that enters our limited set
appears to be a random event, as we were unable to predict it. Looking small, we peer at
the wall of the limits of our observation. Anything of a resolution below our capability
to observe that effects what we can observe appears to be a random influence. One side,
large or small will be seen as a wall of invisibility, the other as chaos. These terms are
interchangeable as long as one end is one and the other the other.
For example, when a car swerves around a corner and
nearly hits us, we see it as chaos from outside our observation. But when we scan the
heavens to discover new stars, we feel a wall of invisibility, limited by our resolution.
The car was hidden from us by space in once sense, as we could have seen it coming if not
for the building. But is was just as appropriately limited by time, as we simply had not
seen it YET. Are the stars hidden because they are too far away or because we not yet
developed strong enough telescopes? Both cars and stars are large phenomena (compared to
ourselves). One we seek, the other seeks us. Active and Passive, Space and Time. chaos and
Invisibility. All combinations are possible.
Similarly, the small phenomena, like looking for a
new molecule through a microscope or the mate to a sock in a jumbled drawer full of them:
chaos or invisibility? Time or Space? Active or Passive? It all depends on your point of
view. The point being that when large scale phenomenon are seen as one side of each binary
pair, small phenomenon will be seen as the other. This is not intrinsic to the object
being observed but to the nature of the observer herself.
Mental Relativity removes the paradox from
observation and puts it back in the mind of the observer where it belongs.
Fractals represent the contrail of the shifting of
The boundary (or transition zone) between Order and
Chaos is seen as a dimension in fractal geometry. In truth, each dimension is simply an
appreciation of the physical universe in terms of one of the following: Mass, Energy,
Space or Time. The transition zones are the psychological equivalents of Knowledge,
Thought, Ability or Desire.
So, there is not only one kind of transition zone,
there are four, just as there are four kinds of dimensions. The relationship between the
two sets is the true interface between structure and dynamics.
Order should not be seen as linear so much as a
spiral. In progressing "down the line" one eventually arrives at a point
directly above where one started. As in Random chaos vs. the Wall of Invisibility, either
Universal Relativity or Mental Relativity can be seen as linear, the other then appearing
as cyclic. It is the relationship between the linear and the cyclic (or between open and
closed appreciations of a system) that describes the full holistic truth of a system.
When one uses a linear appreciation to predict, one
must use a cyclic appreciation to understand. And vice versa. Nature is neither open nor
closed. However, depending upon our purpose, sometimes we must see it as one or the other.
Purpose cannot exist in size equal to the system in
question. If purpose was a large as that which it hopes to effect, there would be no room
to create that effect, and nothing to observe but the purpose itself. We cannot create a
purpose larger than the extent of our observation.
The universal language of art is not due to a
common appreciation of fractals and chaos so much as the common relative nature of the
human mind itself.
The technique of "iterating" or having a
linear equation double back on itself to affect earlier points in the process is still a
linear view of the function of the equation. Although referred to as a non-linear equation
because it does not respect the linear equations limitation of "progressive
exclusivity" (meaning that once an operation has been performed its function cannot
be altered) the iterative equation still falls short of true non-linearity. To be truly
non-linear an equation must process all operations contained in its function
simultaneously. It is the relativistic nature of true non-linearity that demands an
immediate response by all participants to the equation once a value is placed or changed
anywhere in the equation.
The true non-linear equation does not respond by
providing a result in the traditional sense, but by establishing a new order that reflects
the altered nature of the system described. Both linear and non-linear equations are
subject to chaos, though current thoughts see non-linear equations as describing the
impact of chaos. This is only partly correct, as linear and non-linear describe chaos to
Essential to the understanding of chaos is a
clarity of the difference between open and closed systems and how linear and non-linear
equations describe each of them. In an open system, a linear equation effectively
describes a limited system with an arbitrary head and tail. As long as the open system is
self-contained and impervious to the effects of any outside system, the linear equation
will function perfectly and predictably. But there is no single linear equation that
describes the head and tail of nature, as it must be infinitely long in order to encompass
infinity. Therefore all linear equations are subject to the interference of other linear
equations describing other portions of the Great Linearity that (in so doing) double back
across the path of the original equation.
It is in this relativistic relationship where
iterative equations fail to describe what is actually happening. It is not by seeing a
single equation that doubles back on itself that we can interpret the effects of chaos,
but by seeing one equation interfering with another. The relationship between these two
equations is the true non-linear equation. As one equation affects another, it changes
something in the operation of the affected equation, either supplying a new variable,
altering the value of a constant, or changing the relationship along the path of the
affected linear equation.
In terms of linear equations, if one knows the
first equation, the second equation, and all the arbitrators between them, the effect of
the second equation is not seen as chaos but as cause and effect. However, if the second
equation is not known, and/or the arbitrators are not fully known, no linear equation can
predict the effect of the second equation which, by definition, describes chaos. The fault
with iterative equations is their need to understand all the intervening equations,
thereby turning chaos into a manageable limitation of predictive ranges in which chaos
will operate, but only in terms of accuracy and probability.
The exact effect of chaos on a linear equation can
be determined by a true non-linear equation that sees each linear equation as a point in a
closed system. In the closed system, there is no linearity. Rather than seeing a single
equation that doubles back on itself, non-linearity sees each portion of the equation as
an element. All the elements are related in a fractal manner so that a change in one
simultaneously alters all the others. However, in a non-linear closed system appreciation,
a ripple moving down the single equation is unpredictable and appears as chaos.
In closed systems, chaos appears as an
unpredictable change in the "value" of an equation. So, open systems see chaos
as a change in the value of individual elements in the linear equation, closed systems see
chaos as a change in the value of each equation as a whole. Clearly, the two views are
describing the same phenomena from two different points of view or by two different
The open system depends upon a "flow" or
progression of time whereas the closed system depends upon a frozen time. The first
ignores the effect of spatial proximity (arrangement), the second ignores the effect of
temporal proximity (progression). It is impossible to measure space without time and time
without space; when measuring one, we must hold the other constant. What we hold constant
we cannot measure. Open systems and linear equations hold space constant, closed systems
hold time constant. Natures, both external and internal, are sometimes best understood as
open systems and sometimes as closed. It all depends on what you want to measure. Nature
itself is neither solely open OR closed nor both open AND closed. Rather, nature is
something else altogether which can be perceived in either mode. The paradox resides not
in Nature, but in the mind of the observer who must use part of her brain to look at space
in terms of time, then use another part to look at time in terms of space.
The paradox is the observers inability to see how
her own mind has been changed spatially while measuring time, and temporally while
measuring space. It is only when we see a paradox that we have perceived the deepest
understanding of a thing.