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MENTAL RELATIVITY

Mental Relativity is a new theory of psychology developed by my good friend and associate Chris and myself over several years. Its impact is far ranging, offering insight in areas of justification, problem solving, and decision making.

Because it is a RELATIVITY, the theory offers no absolutes. Rather, it defines the relationship between the processes of the mind in such a way that one can objectively see what things subjectively look like from any point in the process.

Publishing the results of our work in The Subversive serves two purposes: One, it offers Chris and myself the opportunity to document our work publicly, and Two, it provides practical information that you, the readers, may find useful in exploring and understanding personal issues.

In this edition of The Subversive, I offer an article of moderate technical complexity describing the two kinds of hierarchies by which human minds can order information. Although gender considerations are outside the scope of this particular article, I am sure you will make your own discoveries as to relationship of type of hierarchy to specific Mental Sex. Future articles will draw more direct association.

HIERARCHIES: LINEAR AND RELATIVE

Linearities and Relativities are two methods of understanding the arrangement and/or functioning of a hierarchy. They are, however, mutually exclusive as to any given hierarchy.

Linearities require an appreciation in which "A" is related to "B" which in turn is related to "C". But "A" is not related to "C" except by means of "B". This is essential to a Linearity, as it is this exclusivity that orders the levels of the hierarchy.

Relativities require an appreciation in which "A" is related to "B" which in turn is related to "C", however "A" is also directly related to "C" as well. This is essential to a Relativity, as it is this multiplicity that orders the levels of the hierarchy.

For complex systems (any system of more than one dimension) a Linearity will represent a hierarchy as a "branch tree". There will b a single head which is expanded, level by level, into multiple units (or sub-divisions until the feet of the hierarchy reach the extent of the system. At this point, the linear relationships along the flow of the system have been fully described.

For complex systems a Relativity will represent a hierarchy as fractals, wherein a given matrix will serve to organize subsets of closely related elements, and more complex arrangements (equivalent to higher levels of a Linearity) will be represented as identical matrices that organize other matrices as if they were elements. When a given matrix contains all elements of a system, the relative relationships within the system have been fully described.

It is clear that in a closed complex system, a Linear Hierarchy would progress from the first unit in the chain to the last available unit in the system, at which point, the Linearity lacks an explanation for the generation of the initial unit. In fact, in a closed complex system, a Linearity doubles back on itself, inevitably reaching a paradox in which, to truly be closed, the initial unit must be equal to all the units of the final level combined.

One might try to overcome this limitation by proposing a two headed hierarchy that might b represented as two inverted pyramids, jointly sharing a common base (and overall appearing as a diamond). The apex of each triangle would be the same common point. The result would be a diamond that doubles back on itself to a single apex. This requires one more dimension than the system being represented. The hierarchy would now appear to flow in two directions from the common apex, but when arriving at the widest point, could go no further in that direction. In other word, an artificial wall of impassability would have been created in the model, separating half they system from the other half.

For this reason I propose the following principle:

MELANIE'S AXIOM: No closed system can be fully explained by a Linear Hierarchy.

In the case of an open system, a Linearity functions much better. An open system, by definition, can continue in either direction forever. The only way to understand and represent such a system is with a Linear Hierarchy. Here, the head of the hierarchy represents whatever arbitrary starting point is selected as the beginning of the system, and the feet of the hierarchy represent the arbitrary end. Whenever one needs to explain the creation of the head, one need simply move back one step and move each layer of the hierarchy down one level. Then the feet do not go far enough in detail, add another level of feet: a de facto extension of the size of the system being considered. It is this capacity to scale a system to the needs or precursors and detail that is the essence and strength of a Linear Hierarchy with regard to an open system.

This leads to my next principle:

COROLLARY TO MELANIE'S AXIOM: Any Linear Hierarchy that describes an open system has arbitrary head and feet that define the limits of the hierarchy.

Next we address the functionality of a Relativity. In a closed system, even one that appears to be linear and recursive, higher levels of understanding intrinsically exist when like progressions are compared. Like progressions MUST exist in order for the system to return to its starting point. When all like progressions have been ordered into fractal dimensions, no free units remain in a closed system. Hence:

MELANIE'S ASSERTION: Any Relative Hierarchy that describes a closed system will consist of fractal dimensions, containing like progressions, with no free units remaining.

Lastly, applying a Relativity to an open system, we can see that the head could never reunite with the feet, giving infinite resistance to any possibility of a relationship between all elements of the system. The paradox would exist that between the head and the feet there is no relationship at all, which violates the nature of a Relative Hierarchy.

Therefore, the remaining principle:

COROLLARY TO MELANIE'S ASSERTION: No open system can be fully described in terms of a Relative Hierarchy.

In Mental Relativity, we have discovered that for some purposes it is best to look at the mind as a closed system in order to understand its internal functioning. Other times, it is more fruitful to examine how the mind fits into the universe to show how we are influenced by our environment, thereby viewing the mind as an open system.

The Hierarchical matrix we employ in Mental Relativity is unique in that it allows for the same data to be organized in either a Linearity or a Relativity, depending upon the perspective of the observer. In this way, the system described is both open and closed at the same time, allowing for a unified and consistent view of its arrangement and operation, and moving the paradox back one fractal level of complexity, out of the model and into the mind of the Observer (where it belongs!)

(Copyright 1993 Melanie & Chris)

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