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This is a work in progress - all rights reserved.
Copyright © 2006-2011 Anthony Giovia

 

CHAPTER 6 – Complexity

SECTION A

6.1 - A defined object is composed of defined objects. (2.13)

6.2 - All objects are defined. (4.7)

6.3 - If "n" is any positive integer, then any object composed of (n + 1) objects is a Complex Object. (Definition)

6.4 - If Object A is composed of Object B and Object C, then Object A is a Complex Object. (Construction)

SECTION B

6.5 - A defined object is composed of defined objects. (2.13)

6.6 - All dimensions are defined objects. (4.6)

6.7 - If "n" is any positive integer, then any dimension composed of (n + 1) dimensions is a Complex Dimension. (Definition)

6.8 - If Dimension A composed of Dimension B and Dimension C, then Dimension A is a Complex Dimension. (Construction)

SECTION C

6.9 - Any definition is composed of defined objects. (5.19)

6.10 - All definitions are defined objects. (4.29)

6.11 - If "n" is any positive integer, then any definition composed of (n + 1) definitions is a Complex Definition. (Definition)

6.12 - If Definition A composed of Definition B and Definition C, then Definition A is a Complex Definition. (Construction)

SECTION D

6.13 - Outlines, magnitudes, architectures and designs are defined objects. (2.12)

6.14 - All architectures are defined objects. (Construction)

6.15 - If "n" is any positive integer, then any architecture composed of (n + 1) architectures is a Complex Architecture. (Definition)

6.16 - If Architecture A is composed of Architecture B and Architecture C, then Architecture A is a Complex Architecture. (Construction)

SECTION E

6.17 - All definitions are defined objects. (4.29)

6.18 - All architectures are defined objects. (6.14)

6.19 - All dimensions are defined objects. (4.6)

6.20 - All objects are defined. (4.7)

6.21 - A defined object is composed of defined objects. (2.13)

6.22 - If Object A is composed of Object B and Object C, then Object A is a Complex Object. (6.4)

6.23 - Each and every Complex Object, each and every Complex Dimension, each and every Complex Definition, and each and every Complex Architecture is simultaneously a Complex Object, a Complex Dimension, a Complex Definition, and a Complex Architecture. (Construction)
           
6.24 - Each and every Object, each and every Dimension, each and every Definition, and each and every Architecture is simultaneously an Object, a Dimension, a Definition, and an Architecture. (Construction)

6.25 - Each and every Object, each and every Dimension, each and every Definition, and each and every Architecture is simultaneously a Complex Object, a Complex Dimension, a Complex Definition, and a Complex Architecture. (Construction)

 

Every object is defined in terms of other objects, and these "other objects" are in turn defined by their own "other objects". This phenomenon of interdependent definitions forms a vast architecture of objects, and similarly a vast architecture of definitions and dimensions.

An important point is that we have defined "dimensions" as the components of objects only to help us distinguish between a "whole object" and the components that make up that whole object. But in fact dimensions are themselves defined, whole objects. The designations "object" and "dimension" are merely arbitrary terms that allow us to talk discernibly about an object and its parts.

An equally suitable, and equally arbitrary mathematical nomenclature can serve the same purpose. If Ow represents a "whole object" and Oa and Ob its component parts, then Ow = Oa + Ob. In this case we can eliminate the "dimensions" terminology altogether without materially affecting the meaning.

Just as objects and dimensions are arbitrary terms, so are definitions and architectures - both terms refer to the same manifest structure of objects and dimensions. A definition is an architecture of objects/dimensions, and an architecture is a definition of objects/dimensions. The equation Ow = Oa + Ob is both a definition and an architecture.

Whether expressed logically via words or mathematically via symbols that represent words the results are the same.

No matter the nomenclature, any object can be seen as an object, a dimension, a definition or an architecture. Further, any object can be seen as a grouping of objects, dimensions, definitions and architectures.

The coherence of objects, dimensions, definitions and architectures is the framework we will be using going forward. A more fundamental justification for this framework will be discussed in a following chapter.

 

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