Construction Of A Complex Context

29.1 The analysis of a complex context reveals the relationships of its composing dimensions.

The first step towards doing useful work with a rule, law, context, dimension, Geometric Architecture, Base Geometric Architecture, Point Of View, level or complex context is to analyze its construction. In the previous chapter we reviewed tools that will help with an analysis, and we will utilize those tools in this chapter.

A complex context is composed of dimensions organized via logical and mathematical laws. When a dimension is included in the definition of a logical law that dimension is said to “obey” that law.

Complex contexts are distinguishable from non-complex contexts by the number of logical and mathematical laws required to define the context. The laws within a complex context are organized in a hierarchy – one Dominant Rule and one or more Recessive Rules.

The Dominant Rule is the primary filter – the primary organizer – of dimensions in the perceivable pool of dimensions, and also for new dimensions introduced to the pool. Rules are simply logical or mathematical laws, and when we say a rule filters dimensions we mean a dimension is found to obey or not obey a particular logimathical law.

In a physical geometry such as the Geometry of Ideas, filtering means that a dimension that obeys a rule is physically added to the physical construction of the rule. A dimension that does not obey a rule is discarded but may be passed to the Recessive Rules within the complex context for further filtering. Whether or not a discarded dimension passes to Recessive Rules most likely depends on the construction of the Dominant Rule, but as discussed in a previous chapter this is still speculation.

Within any context, dimensions are further organized into other logical groupings of dimensions we call Base Geometric Architectures – essentially, BGAs are contexts within contexts. The concept of contexts existing within contexts is a key element of the Dimensional Nexus. If the Universe originated in a singular Big Bang of energy, then all parts of that energy – each distinguishable dimension of that energy – necessarily exists in a logical and mathematical relationship with every other dimension. Therefore any particular dimension requires other dimensions for its definition. Ultimately, there is only one definition of the Nexus, and that definition includes every dimension and every relationship among those dimensions.

As a practical matter, no human mind or computer has the processing power required to perceive and filter every existing dimension and every existing relationship through any particular Dominant Rule. This means that minds and computers work with a subset of the Nexus. It also means that there is some level of incompleteness to every Dominant Rule. And that means that there is no “bottom” to any particular context – no perceivable complete definition. A dimension is simultaneously a rule, law, context, Geometric Outline, Geometric Architecture, Base Geometric Architecture, Point Of View, level and complex context. “Meaning” is an agreement among minds as to what dimensions and what levels to include in any definition in order to do useful work.

We all access some subset of the Nexus every day. If indeed the Universe was created in a singular Big Bang of energy, all the created dimensions are necessarily logically related to each other. This means that the entire Nexus is accessible to us. Accessing more of the Nexus may require more processing power, or it may only require the perception of additional logical and mathematical laws.

The analysis of a complex context requires that we identify the objects composing it – the Dominant Rule, the Sub-Levels, and the Base Geometric Architectures. For simplicity we will first identify the objects composing a Dominant Rule and only one of its Axis Sub-Levels and one of its Tributary Sub-Levels. In the next chapter we will look at a more comprehensive analysis of this DR.

The notations below designating the Dominant Rule and the Axis Sub-Level are self-explanatory to anyone who has made it this far into the presentation. The Tributary Sub-Level notations refer to the Recessive Rule of the Tributary (TSL1) and the sublevels supporting that rule (1-TSL1, 2-TSL1, 3-TSL1, etc.). The final number merely identifies the particular Tributary the sublevels support - in this case Tributary Sub-Level 1 (TSL1).

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Here is a Dominant Rule, one of its Axis Sub-Levels, and the Tributary Sub-Level of that Axis Sub-Level.

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

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

Tributary Sub-Level 1 (TSL1) - Relationships are composed of energy and exist in this Universe.

1. TSL1- The Universe was created in a Big Bang of energy, therefore energy in all its forms is the sole substance of the Universe.

2. TSL1 - Everything that exists in the Universe is composed of the energy created at the time of the Big Bang.

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Organizing these objects into a chart will give us a better understanding of the dimensional nature of their relationships.

DOMINANT RULE	AXIS SUB-LEVEL 1	TRIBUTARY SUB-LEVEL 1
Relationships	Relationships	Relationships
Logic	Logic
Mathematics	Mathematics
Dimensions
Ideas
Matter
Thinking
	Framework
	Communication
	Objects	Objects
		Energy
		Universe
		Big Bang

The architecture of this complex context is beginning to take shape. One dimension – “Relationships” – is shared across the DR, ASL1 and TSL1. Dimensions have a physical aspect, therefore a shared dimension is an actual physical connection – a physical object existing in the physical structure of all three rules.

There are two ways to visualize this architecture. The easy way is to view three instances of the object Relationships – three atoms, if you will – forming a three-dimensional molecular triangle. The harder way is to try and visualize the three rules sharing one instance of an object.

This visualization of multiple instances is convenient, but it requires us to introduce a separate force to explain how the instances are logically connected - that is, how logic physically works. Are the separate instances connected by gravity, or electromagnetism, or the nuclear weak or nuclear strong forces?

On the other hand, if multiple rules share a single dimension we can clearly see the mechanics of logic. Shared dimensions provide clear nexus points for the flow of dimensions through multiple rules, and logic has a simple, definable structure. What we lose, however, is a traditional – and therefore easy to grasp - visualization of the internal and external architecture.

To be sure, one or more of the four fundamental forces must necessarily be involved in any architecture, but at this point introducing sub-atomic particles into the discussion would bring us many sub-levels away from any useful work. So we will compromise – when convenient we will use multiple instances of an object to help us visualize an architecture, with the understanding that the multiple instances are utilized only for clarity.

Most of the objects in the Dominant Rule do not appear in the ASL1 or TSL1, therefore those objects are not directly shared with them. It is interesting to note that the dimension “Objects” listed in the chart shows that it is shared by the ASL1 and the TSL1. This means that the dimensions “Relationships” and “Objects” are included in the construction of both rules. So far, our physical model includes a dimension with three axes (“Relationships”) and a dimension with two axes (“Objects”). Each rule, of course, is an axis. These minor axes are not to be confused with the major Axis Sub-Levels of the Dominant Rule.

This has been a brief introduction to the inner architecture and workings of a complex context. This example illustrates the function of shared dimensions and the function of subordinate contexts – subordinate levels – that support meaning. In the next chapter we will do a more complete analysis of a complex context, building on the principles described here.