Construction Of A Complex Context - Analysis

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Copyright © 2006-2009 Tony Giovia

32. The Construction of a Complex Context – An Analysis - Part 3 v2.0

32.1 Nexus points and pathway managers within a complex context.

Part 3 – Nexus Points and Pathway Managers

A complex context consists of a Dominant Rule and one or more Recessive Rules. The Recessive Rules discussed in this presentation fall into two categories – Axis Sub-Levels and Tributary Sub-Levels.

Rules with physical structures do not exist as standalone contexts. Instead, Rules are literally constructed with Geometric Architectures from other Rules. For example, a Dominant Rule is constructed of GAs contributed by its supporting Axis Sub-Levels. In turn, the Axis Sub-Levels are constructed with GAs supplied by their supporting Tributary Sub-Levels.

Rules constructed from the anatomy of other Rules are the foundation of the Geometry of Ideas. Geometric Outlines, multi-purposed to simultaneously construct multiple Rules, provide a functional understanding of the simultaneous fluidity, depth, subjective discreteness and objective unity of the Dimensional Nexus. This Dimensional Nexus is the pool of all perceivable (and not yet perceived) dimensions created by the Big Bang and the associated relationships among these dimensions.

A Point Of View – which is a logical or mathematical rule – is the organizing factor within the Dimensional Nexus. And because Points Of View are based on a perceivable pool of dimensions, POVs can change when new dimensions are added to the pool. Consider a glistening diamond – each spark of fire is another alignment of light rays and carbon molecules – each is a different Point Of View within the pool of dimensions within the diamond.

A complex context consists of a Dominant Rule and one or more Axis Sub-Levels and Tributary Sub-Levels. Because Rules are constructed with parts of other Rules via shared Geometric Outlines, there is literally no end to any context’s definition. We can continue to delve into the sub-levels that support a particular Tributary Sub-Level, then delve into the TSLs of those sub-levels, and so on. This would require detailed naming schemes – for example, Tributary Sub-Level 5 of TSL4 of TSL3 of TSL2 of TSL1 of Axis Sub-Level 2 of the Dominant Rule “Why is the Sky Blue?”

To avoid this complexity, our present analysis of a complex context will be limited to a Dominant Rule and it’s supporting Axis Sub-Levels, with the understanding that a more complete analysis would include the Tributary Sub-levels supporting the ASLs. In practice, the labels Dominant Rule, Axis Sub-Level and Tributary Sub-Level can be assigned anywhere in the Dimensional Nexus – we could rightfully call a fifth level Tributary Sub-Level a Dominant Rule just by making it the Point Of View for deeper analysis.

Looking only at a Dominant Rule and the Axis Sub-Levels used to construct the Dominant Rule will simplify our approach while still allowing us to demonstrate GA nexus points, the potential for Recessive Points of View becoming Dominant Points Of View, and common structural GAs that act as pathway managers directing energy flow through a complex context. We will further see how particular GAs within the Axis Sub-Levels create the Dominant Rule.

For clarity we will work with charts instead of dimensional images, however it would be useful to read this section twice, once as words on a page, and once as dimensional objects represented as words on a page. The Dominant Rule and Axis Sub-Levels used here are identical to those used in Step 1 above.

Chart 1 – The Dominant Rule

DIMENSIONAL THINKING DEFINES THE LOGICAL AND MATHEMATICAL RELATIONSHIPS BETWEEN IDEAS AND MATTER.
(Dominant Rule) (Complex Context)

Chart 2 – Axis Sub-Levels of the Dominant Rule

Axis Sub-Level 1 (ASL1)... A relationship is a logical or mathematical framework for communication between two objects or among more than two objects.

Axis Sub-Level 2 (ASL2)… A mind exists in logical and mathematical relationships with Ideas.

AXIS Sub-Level 3 (ASL3)… Ideas are composed of matter and therefore Ideas have a physical form.

AXIS Sub-Level 4 (ASL4) - Thinking defines objects by filtering physical dimensions into logical and mathematical relationships.

Chart 3 – Shared Dimensions Among the Dominant Rule and its Axis Sub-Levels

DR

Dimensional

Thinking

Defines

Logical

Mathematical

Relationships

Ideas

Matter

ASL1

Logical

Mathematical

Relationship

Objects

ASL2

Logical

Mathematical

Relationship

Ideas

ASL3

Ideas

Matter

Physical

ASL4

Dimension

Thinking

Defines

Logical

Mathematical

Objects

Physical

Chart 4 – Pathway Connectors and Energy Directors

Verbs, adverbs and prepositions – Pathway Connectors and Energy Directors

Is, a, or, for, between, among, more, than, exists ,in, and, with, of, therefore, have, by, into

Chart 5 – Contexts dependent on Tributary Contexts

ASL1

Framework

Communication

ASL2

Mind

ASL3

Form

ASL4

Filter

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Here are the same charts, with comments.

Chart 1 – The Dominant Rule

DIMENSIONAL THINKING DEFINES THE LOGICAL AND MATHEMATICAL RELATIONSHIPS BETWEEN IDEAS AND MATTER.
(Dominant Rule) (Complex Context)

Chart 1 simply identifies the Dominant Rule under analysis. Note that within the Dimensional Nexus a Dominant Rule is simultaneously a complex context, a Dominant Point Of View, a Geometric Architecture, a Base Geometric Architecture, a Recessive Rule (an Axis or Tributary Sub-Level), a Geometric Outline, an Idea, a dimension, and a context. These terms are merely useful labels assigned to the underlying reality. The appropriate terms are dictated by the POV – the logical or mathematical rule – used to perform the analysis.

Chart 2 – Axis Sub-Levels of the Dominant Rule

Axis Sub-Level 1 (ASL1)... A relationship is a logical or mathematical framework for communication between two objects or among more than two objects.

Axis Sub-Level 2 (ASL2)… A mind exists in logical and mathematical relationships with Ideas.

AXIS Sub-Level 3 (ASL3)… Ideas are composed of matter and therefore Ideas have a physical form.

AXIS Sub-Level 4 (ASL4) - Thinking defines objects by filtering physical dimensions into logical and mathematical relationships.

Axis Sub-Levels are unique logical and mathematical rules that can be Dominant Rules in other contexts. ASLs and Dominant Rules together validate the phrase “The whole is more than the sum of its parts.”, because the “whole” of a DR is more than its organizing logical or mathematical rule, more than a listing of its component Geometric Architectures. The “whole” of a DR is a structure that also includes the logical and mathematical rules of the ASLs and TSLs used to create the DR.

Axis Sub-Levels can be deduced from a Dominant Rule, or they can infer a Dominant Rule – that is, ASLs can be constructed from an existing DR (the method used in this case), or a DR can be constructed using existing ASLs.

There is no “right” or “wrong” list of ASLs that can be used to construct a DR. This list of four ASLs could be increased to five or more, or reduced to two or three, as long as the required GAs are included. A different list of ASLs will, however, be supported by a different set of Tributary Sub-Levels. These different ASLs and TSLs necessarily affect the physical shape of the complex context in the Dimensional Nexus, and therefore affect its meaning.

Chart 3 – Shared Dimensions Among the Dominant Rule and its Axis Sub-Levels

DR

Dimensional

Thinking

Defines

Logical

Mathematical

Relationships

Ideas

Matter

ASL1

Logical

Mathematical

Relationship

Objects

ASL2

Logical

Mathematical

Relationship

Ideas

ASL3

Ideas

Matter

Physical

ASL4

Dimensional

Thinking

Defines

Logical

Mathematical

Objects

Physical

Logic and mathematics are disciplines that describe the three-dimensional world we live in, but the actual relationships among logic, math and the physical world – that is, the paths of communication between logic, math and the physical world – has never been methodically and clearly defined in any kind of empirical manner.

The Geometry of Ideas provides a logical foundation for an empirical inquiry by unifying two accepted scientific theories – the Big Bang and E= MCC. These combined theories necessitate the physical existence of Ideas. The Geometry of Ideas extrapolates the concept of physical Ideas to propose a Universe composed of Ideas logically and mathematically related to each other via the logical and mathematical laws inherent in the Big Bang. Logical and mathematical relationships in a physical world require the transfer of energy along physical pathways between the relationship partners. The Geometry of Ideas calls the sum total of these Ideas and relationship pathways the Dimensional Nexus.

This chart illustrates the shared dimensions – the shared Ideas – between a Dominant Rule and its supporting Axis Sub-Levels. Shared dimensions are the mechanics of communication in the Dimensional Nexus. We live in a Universe of energy, and shared dimensions provide the pathways along which energy travels.

You can conceive of a shared dimension as a single dimension shared by multiple Points of View (as in Illustration 2). Remember that a Dominant Rule and each of its Axis Sub-Levels are logical or mathematical rules with their own unique POVs, their own unique ordering of the dimensions in the perceivable pool of dimensions. Because dimensions are physical objects, it may be difficult to visualize the actual physical structure of multiple contexts converging at a single dimension. However, in a multi-dimensional Universe this scenario is a reasonable avenue of investigation.

You may also conceive of a shared dimension as not a single object but as exact copies of one object. But this scenario introduces a complication - additional pathways are needed to connect the copies. One obvious solution is that copies may form regular structures – think of crystals - providing both multiple “docking stations” and built-in pathways between the copies. The spatial orientation of these copies will affect the final physical design, and therefore the meaning of the complex context.

In our chart the dimensions “Logical” and “Mathematical” are shared among four of the five POVs. In terms of the Dimensional Nexus, these dimensions form the core structure of this complex context.

This core structure should give you a sense of the mobile nature of POVs. Dimensions consistent with a logical or mathematical rule are added to the physical structure of the rule – this structural annexation is what we mean when we say a particular phenomenon “obeys” a logical or mathematical rule. Adding or removing dimensions from the pool of perceivable dimensions can strengthen some POVs while weakening others.

Everyone who has read The Adventures of Tom Sawyer by Mark Twain remembers Tom and Huck Finn walking in on their own funerals. This event removed the dimension that they had passed on, and added the dimension that they were still alive. This changed the Dominant Rule from “Tom and Huck are gone.” to “Tom and Huck are here.” It is obvious, but I will mention that one of the ASLs or TSLs of the funeral DR necessarily defined “gone” by contrasting it with “here”. That ASL or TSL became the new Dominant Rule when they strolled in.

Chart 4 – Pathway Connectors and Energy Directors

Verbs, adverbs and prepositions – Pathway Connectors and Energy Directors

is, a, or, for, between, among, more, than, exists, in, and, with, of, therefore, have, by, into

Complex contexts are physical circuits along which energy travels. Verbs, adverbs, prepositions and other grammatical objects take on a new meaning (that is, a new Point Of View) in the Geometry Of Ideas. Grammatical objects are pathway connectors and energy directors in the physical world of the Dimensional Nexus.

The list above contains obvious energy directors – “is’, “for”, “between”, “among”, “into”, etc. Articles (“a”, “an” ‘the’) are also directors, aiming the flow of energy in a context to a particular GO.

Chart 5 – Contexts dependent on Tributary Contexts

ASL1

Framewok

Communication

ASL2

Mind

ASL3

Form

ASL4

Filter

Just as a Dominant Rule is constructed of GAs contributed by Axis Sub-Levels, the Axis Sub-Levels are constructed of GAs contributed by Tributary Sub-Levels. And just as the Axis Sub-Levels of a Dominant Rule must contain all the GAs necessary to construct the Dominant Rule, Tributary Sub-levels must contain all the GAs necessary to construct the Axis Sub-Levels.

In this example, there are five GAs in the structure of the Axis Sub-Levels (Framework, Mind, Form, Filter and Communication) that are required to complete the structure of the ASLs, but which do not exist in the structure of the Dominant Rule. The Tributary Sub-Levels constructing the ASLs must contain all the GAs necessary to construct the ASLs (which in turn construct the Dominant Rule). TSLs are distinguished from ASLs because they contain all the GAs necessary to define an ASL, while an ASL contains all the GAs necessary to define a Dominant Rule.

The construction of ASLs and TSLs, especially at the complexity of the complex context presented here, is more art than science. As more complex contexts are constructed, we can expect ASLs and TSLs to become more like standardized modules than can be “plugged into” new complex contexts.

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DR	Dimensional	Thinking	Defines	Logical	Mathematical	Relationships	Ideas	Matter
ASL1				Logical	Mathematical	Relationship			Objects
ASL2				Logical	Mathematical	Relationship	Ideas
ASL3							Ideas	Matter		Physical
ASL4	Dimension	Thinking	Defines	Logical	Mathematical				Objects	Physical

Chart 3 – Shared Dimensions Among the Dominant Rule and its Axis Sub-Levels
DR	Dimensional	Thinking	Defines	Logical	Mathematical	Relationships	Ideas	Matter
ASL1				Logical	Mathematical	Relationship			Objects
ASL2				Logical	Mathematical	Relationship	Ideas
ASL3							Ideas	Matter		Physical
ASL4	Dimensional	Thinking	Defines	Logical	Mathematical				Objects	Physical
Logic and mathematics are disciplines that describe the three-dimensional world we live in, but the actual relationships among logic, math and the physical world – that is, the paths of communication between logic, math and the physical world – has never been methodically and clearly defined in any kind of empirical manner. The Geometry of Ideas provides a logical foundation for an empirical inquiry by unifying two accepted scientific theories – the Big Bang and E= MCC. These combined theories necessitate the physical existence of Ideas. The Geometry of Ideas extrapolates the concept of physical Ideas to propose a Universe composed of Ideas logically and mathematically related to each other via the logical and mathematical laws inherent in the Big Bang. Logical and mathematical relationships in a physical world require the transfer of energy along physical pathways between the relationship partners. The Geometry of Ideas calls the sum total of these Ideas and relationship pathways the Dimensional Nexus. This chart illustrates the shared dimensions – the shared Ideas – between a Dominant Rule and its supporting Axis Sub-Levels. Shared dimensions are the mechanics of communication in the Dimensional Nexus. We live in a Universe of energy, and shared dimensions provide the pathways along which energy travels. You can conceive of a shared dimension as a single dimension shared by multiple Points of View (as in Illustration 2). Remember that a Dominant Rule and each of its Axis Sub-Levels are logical or mathematical rules with their own unique POVs, their own unique ordering of the dimensions in the perceivable pool of dimensions. Because dimensions are physical objects, it may be difficult to visualize the actual physical structure of multiple contexts converging at a single dimension. However, in a multi-dimensional Universe this scenario is a reasonable avenue of investigation. You may also conceive of a shared dimension as not a single object but as exact copies of one object. But this scenario introduces a complication - additional pathways are needed to connect the copies. One obvious solution is that copies may form regular structures – think of crystals - providing both multiple “docking stations” and built-in pathways between the copies. The spatial orientation of these copies will affect the final physical design, and therefore the meaning of the complex context. In our chart the dimensions “Logical” and “Mathematical” are shared among four of the five POVs. In terms of the Dimensional Nexus, these dimensions form the core structure of this complex context. This core structure should give you a sense of the mobile nature of POVs. Dimensions consistent with a logical or mathematical rule are added to the physical structure of the rule – this structural annexation is what we mean when we say a particular phenomenon “obeys” a logical or mathematical rule. Adding or removing dimensions from the pool of perceivable dimensions can strengthen some POVs while weakening others. Everyone who has read The Adventures of Tom Sawyer by Mark Twain remembers Tom and Huck Finn walking in on their own funerals. This event removed the dimension that they had passed on, and added the dimension that they were still alive. This changed the Dominant Rule from “Tom and Huck are gone.” to “Tom and Huck are here.” It is obvious, but I will mention that one of the ASLs or TSLs of the funeral DR necessarily defined “gone” by contrasting it with “here”. That ASL or TSL became the new Dominant Rule when they strolled in.

Chart 5 – Contexts dependent on Tributary Contexts
ASL1	Framewok	Communication
ASL2	Mind
ASL3	Form
ASL4	Filter
Just as a Dominant Rule is constructed of GAs contributed by Axis Sub-Levels, the Axis Sub-Levels are constructed of GAs contributed by Tributary Sub-Levels. And just as the Axis Sub-Levels of a Dominant Rule must contain all the GAs necessary to construct the Dominant Rule, Tributary Sub-levels must contain all the GAs necessary to construct the Axis Sub-Levels. In this example, there are five GAs in the structure of the Axis Sub-Levels (Framework, Mind, Form, Filter and Communication) that are required to complete the structure of the ASLs, but which do not exist in the structure of the Dominant Rule. The Tributary Sub-Levels constructing the ASLs must contain all the GAs necessary to construct the ASLs (which in turn construct the Dominant Rule). TSLs are distinguished from ASLs because they contain all the GAs necessary to define an ASL, while an ASL contains all the GAs necessary to define a Dominant Rule. The construction of ASLs and TSLs, especially at the complexity of the complex context presented here, is more art than science. As more complex contexts are constructed, we can expect ASLs and TSLs to become more like standardized modules than can be “plugged into” new complex contexts.