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Copyright © 2006-2007 Tony Giovia
28. The Construction of a Complex Context – Terminology Review
28.1 - Definitions reveal the external physical shape and internal structure of objects.
28.2 - Tools are definitions designed to analyze contexts.
As stated in the first chapter, this presentation is mainly about definitions. We can now expand that statement to say this presentation is mainly about definitions as they relate to dimensions and their relationships, and to the role of dimensions in the physical structure of contexts.
Dimensions are objects with a physical form, and there are four overlapping approaches to describing this physical form. The definition of any object can be determined by examining its outline, its magnitude, its architecture and its design. Let’s look at each of these in turn.
OUTLINE
An outline determines the external shape of an object. Because a complex context is a physical object, the term outline is used more in the context of topology than in the context of a two-dimensional tracing or representation. Topology, however, is a science concerned with physical transformations. We are only interested in the theoretical fixed shape of a dimensional object. It is important to remember that changing the shape of an object in the Geometry of Ideas either fundamentally or incrementally changes the meaning of the object, because a change in shape can only be effected by adding or subtracting dimensions.
The outline of a complex context is therefore simply its external shape. It may resemble a cube, a pyramid, a sphere, or any combination of these and other physical shapes common to our experience and mathematics. I say resemble because the Geometric Outline of a cube may or may not be in the shape of a cube. Until a working model is constructed it is best to leave the shapes of Geometric Outlines as unique and fixed, but indeterminate.
MAGNITUDE
The term magnitude has two current meanings in the Geometry Of Ideas. In its simplest sense, magnitude refers to the physical size of a Geometric Outline – which directly relates to the number and complexity of the sub-levels associated with it. Since at this point the actual physical size of a GO is a moot point absent a working model, we can only approximate the size of one GO relative to another. And even this approximation is speculation until we see how dimensions are actually arranged among associated contexts – that is, until we see how shared and logically associated dimensions configure themselves within a context. Think of the shapes of chemical compounds and you will get the idea.
The second meaning of magnitude refers to number of dimensions associated with any particular context. In a theoretical sense all contexts contain an infinite number of dimensions as you drill down from sub-level to sub-level. However, in a practical sense a context like God or Universe contains many more dimensions than a context like automobile or chair, simply because fewer dimensions are required to define these contexts in a useful way.
It is likely that soon we will be adding a third meaning to magnitude. Shared dimensions can be considered the skeleton of a complex context, acting as gateways between the contexts they connect. The relative importance of shared dimensions, versus other shared dimensions in a complex context, and versus unshared dimensions, can also be described in terms of magnitude.
ARCHITECTURE
Architecture determines the construction, internal outlines and/or internal magnitudes of an object. While a Geometric Outline defines the external shape of an object, architecture looks inside the object to define its inner structure.
The construction of a complex context refers to identifying the Dominant and Recessive Rules within the context. These rules determine the type, quantity and organization of the dimensions composing the complex context.
The internal outlines of an object refer to the pathways described by the contexts composing a complex context. The dimensions composing the Geometric Outline are organized by different sets of logical and mathematical rules, and by the dimensions shared among the rules. Each rule defines a pathway within the larger complex context.
The internal magnitudes of an object simply refer to the relative size – the relative number of associated dimensions - of the pathways we call rules, contexts and laws.
DESIGN
A design determines the intended use of an object. While architecture is concerned with details of an object’s physical construction, design refers to the Point Of View used to contextualize the object itself, or its component contexts. For example, an Axis Sub-Level has a different function in a complex context than a shared dimension or a Tributary Sub-Level.
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These four pathways – outline, magnitude, architecture and design - provide us with a direction for defining objects, but not with the tools we need to do useful work with objects like contexts. Let’s now look at the tools that will help with that work.
A complex context is a physical construction of perceivable dimensions ordered by logical and mathematical rules. The structure of a complex context, like any other physical structure, can be disassembled and analyzed.
Here is a summary of tools that will help with the analysis of complex contexts. Most of these tools were defined earlier in this presentation, however some definitions (as you may have noticed) were embellished as new concepts were introduced. These are the most current and complete definitions of those tools. In addition, a few new tools (Work, Useful Work, Elegant Work, Truthful, Falseful, Mind, Thinking, Logimathical, Meaning) are defined in the hope of providing complete clarity in our analysis.
Entity – A perceivable physical object that can be touched, smelled, heard or seen.
Idea –A logical or mathematical construction of one or more perceivable dimensions, where a dimension is a uniquely defined element of an entity or another dimension. When perceived as physical objects, Ideas are constructed with a minimum of three dimensions.
Object – A generic term for any particular thing that exists. Entities and Ideas are objects. Essentially, an object is any logical or mathematical organization of dimensions.
Dimension – Any uniquely defined perceivable object.
Geometric Outline (GO) - A physical construction defining a unique Idea.
Base Geometric Outline (BGO) - A self-contained logical island of ideas.
Communication - The transfer of energy, in all its forms, from a sending object to a receiving object.
Pathway - A circuit along which communication occurs.
Relationship – 1) A framework for communication between two objects or among more than two objects. 2) A pathway between objects.
Perception - Any relationship between or among objects.
Rule – Any logical or mathematical relationship. Logical relationships are commonly called rules, mathematical relationships are commonly called laws. Both rules and laws are equivalent – there is no rule that cannot be expressed as a law, and vice versa.
Law - Any logical or mathematical relationship. Mathematical relationships are commonly called laws, logical relationships are commonly called rules. Both laws and rules are equivalent – there is no law that cannot be expressed as a rule, and vice versa.
Definition - A set of dimensions related by a logical or mathematical rule.
Context - Base Geometric Outlines composed of dimensions related by a logical or mathematical rule. All contexts are definitions, all definitions are contexts.
Filter – One or more Base Geometric Outlines that associate or disassociate dimensions based on the logical or mathematical laws organizing the filter. By so doing, filters associate or disassociate contexts, and associate or disassociate Ideas, and associate or disassociate GOs.
Mind – A logical or mathematical collection of contexts.
Work – Any filtering of dimensions by a rule or law.
Useful Work – Any work that includes the majority of dimensions in the perceivable pool of dimensions.
Elegant Work - Any work that includes all the dimensions in the perceivable pool of dimensions.
Truth – Elegant work.Truthful – Useful work.
Falseful - Any work that includes a minority of dimensions in the perceivable pool of dimensions.
Thinking – Work performed by a mind.
Meaning - An agreement among minds as to what dimensions and what levels to include in any definition for the purpose of doing useful work.
Point of View (POV) Context - One or more Base Geometric Outlines logically related and used as the primary filter for other Ideas. Also known as the Dominant Rule of a complex context.
Complex Context (CC) - A set of dimensions organized by a Dominant Rule and one or more Recessive Rules.
Dominant Rule (DR) – A logical or mathematical process that filters all the dimensions in a context. The Dominant Rule defines the Dominant POV of that context.
Recessive Rule (RR) - A logical or mathematical process that filters less than all of the perceivable dimensions in a context. Recessive Rules may be Dominant Rules in other contexts. Recessive Rules define the Recessive Points of View of a context. There are at least two types of Recessive Rules – Axis Sub-levels and Tributary Sub-Levels.
Recessive Point Of View – Axis Sub-Levels and Tributary Sub-Levels are Recessive Points of View within a Dominant Rule, meaning they have the potential to become Dominant Points Of View if new dimensions entering the perceivable pool of dimensions strengthen their structures while weakening the structure of the current Dominant Rule.
Level – Any particular context within a complex context.
Dominant Focal Geometric Outline (DFGO) - The BGO within any context to which other GOs in the context refer. Put another way, the DFGO is the core physical structure to which all other GOs in the context physically attach.
Recessive Focal Geometric Outline (RFGO) - When a context is not the Dominant Rule of a complex context, it is a Recessive Rule of that complex context. The DFGO of any Recessive Rule is a Recessive Focal Geometric Outline (RFGO) relative to the DFGO of any Dominant Rule.
Axis Sub-Level (ASL) - For any complex context, a sublevel of the Dominant Rule is an Axis Sub-Level of that complex context. Axis Sub-Levels are Recessive Rules of a Dominant Rule.
Tributary Sub-Level (TSL) - For any complex context, a sub-level of a Recessive Rule is a Tributary Sub-Level of that complex context.
Dimensional Nexus – The Universe of dimensions. Within this Universe a dimension is simultaneously a rule, a law, a context, a Geometric Outline, a Base Geometric Outline, a Point Of View, a level and a complex context.
Logic and Mathematics – Pathways within the Dimensional Nexus.
Logimathical - Any logical and mathematical relationship. Logimathical is a convenient combination of “logical” and “mathematical”, referring to the fact that any logical rule can be expressed as a mathematical law, and vice versa.
Meaning – A Point Of View in the Dimensional Nexus. Meaning is a logical or mathematical organization of dimensions limited by a Point Of View.
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