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by Melanie Anne Phillips

Mental Relativity describes the interface
between space and time,
which is called Structure.

Mental Relativity describes the interference
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 dynamic inertia.

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 equation’s 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 each other.

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 measurements.

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.

Copyright Melanie Anne Phillips

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