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Copyright © 2006-2007 Tony Giovia

 

27. Sub-Levels

27.1– Contexts in relationships with other contexts form complex contexts.

27.2 – Complex contexts are composed of a Dominant Rule and one or more Recessive Rules. Complex contexts with identical DRs and RRs in the same pool of perceivable dimensions are identities.

27.3 – The Dominant Rule, and each Recessive Rule in a complex context, defines a level of the complex context.

27.4 - Contexts are necessarily unique in any pool of dimensions because the Dominant Rule organizing the context’s dimensions is unique to any particular pool of dimensions.

27.5 – Recessive Rules are not unique to any particular context. Complex contexts with different Dominant Rules may have identical RRs in their structure.

27.6 - Recessive Rules in one context may be Dominant Rules in other contexts.

27.7 – The Recessive Rules of a complex context are sub-levels of the Dominant Rule of that context. (Definition)

27.8 - Recessive Rules are recessive relative to the Dominant Rule of a complex context. However, Recessive Rules can be Dominant Rules in other complex contexts.

27.9 - Both Dominant Rules and Recessive Rules are Base Geometric Outlines. Therefore both DRs and RRs are complex contexts in and of themselves.

a)  Recessive Rules have the same physical structure as Dominant Rules.

27.10 - For any complex context, a sublevel of the Dominant Rule is an Axis sub-level (ASL) of that complex context. (Definition)

a)  In the case of multiple Axis sub-levels within a complex context, some Axes can exert a greater influence than other Axes on the meaning of the complex context.
b)  The influence of an Axis sub-level on the meaning of a complex context is dependent on the dimensions shared with the Dominant Rule. (Definition)

27.11 - For any complex context, a sub-level of a Recessive Rule is a Tributary sub-level (TSL) of that complex context. (Definition)

a)  In the case of multiple Tributary sub-levels within a Recessive Rule, some Tributaries can exert a greater influence than other Tributaries on the meaning of the Recessive Rule.
b)  The influence of a Tributary sub-level on the meaning of a Recessive Rule is dependent on the dimensions shared with the Recessive Rule. (Definition)

 

Contexts are physical structures composed of physical dimensions organized by logical and mathematical rules. Thus far we have identified Dominant Rules and Recessive Rules as the primary organizers of dimensions. In this chapter we look deeper into the structure of DRs and RRs.

A complex context is composed of a Dominant Rule and one or more Recessive Rules, with the Recessive Rules embellishing or supporting the structure and therefore the meaning of the Dominant Rule. By “meaning” we are saying that the RRs provide additional logical filters, and therefore additional shared dimension pathways for new dimensions entering the complex context.

However, it must be remembered that each Recessive Rule is itself a complex context, with its own Dominant Rule and supporting Recessive Rule. Every rule is a level of a context, therefore to do useful work with complex contexts we need a way to distinguish among the various types of levels within complex contexts.

We will use the term “Axis Sub-Level” (ASL) to describe a First Level Recessive Rule of a Dominant Rule. As a reminder, a First Level relationship requires one or more shared dimensions between a Dominant Rule and a Recessive Rule. The term Axis implies both a physical (“axial”) and directional (“geometry co-ordinate”) object, making it appropriate for our purpose of emphasizing the physical and spatial dimensions of a context.

We will use the term “Tributary Sub-Level” (TSL) to describe a First Level rule of a Recessive Rule within a complex context. This is easily understood by remembering a Recessive Rule can be a Dominant Rule in other contexts. In this case, the Recessive Rule is a Dominant Rule relative to its own supporting levels. The term Tributary implies a supporting context for a larger context – as a creek adds water to a river, a Tributary Sub-Level adds dimensions to a Recessive Rule that is itself supporting a Dominant Rule.

 

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