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This is a work in progress - all rights reserved.
Copyright © 2006-2012 Anthony Giovia

 

CHAPTER 8 – Relationships

SECTION A

8.1 – A Relationship is a pathway uniting two objects or more than two objects composing a definition. (Definition)

8.2 - 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. (6.24)

8.3 - 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. (6.25)

8.4 - A relationship is a pathway uniting two objects or more than two objects composing an architecture. (Construction)

8.5 - A relationship is a pathway uniting two objects or more than two objects composing a dimension. (Construction)

8.6 - A relationship is a pathway uniting two objects or more than two objects composing a complex object. (Construction)

SECTION B

8.7 - 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. (6.24)

8.8 - 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. (6.25)

8.9 - A relationship is a pathway uniting two or more objects, and/or two or more dimensions, and/or two or more definitions, and/or two or more architectures composing a complex definition. (Construction)

8.10 - A relationship is a pathway uniting two or more objects, and/or two or more dimensions, and/or two or more definitions, and/or two or more architectures composing a complex object. (Construction)
           
8.11 - A relationship is a pathway uniting two or more objects, and/or two or more dimensions, and/or two or more definitions, and/or two or more architectures composing a complex dimension. (Construction)

8.12 - A relationship is a pathway uniting two or more objects, and/or two or more dimensions, and/or two or more definitions, and/or two or more architectures composing a complex architecture. (Construction)

SECTION C

8.13 - A pathway is a dimension shared by two or more complex dimensions composing a definition. (7.5)
           
8.14 - A Relationship is a pathway uniting two objects or more than two objects composing a definition. (8.1)

8.15 - A relationship is a shared dimension uniting two or more complex dimensions composing a definition. (Construction)

8.16 - A relationship is a shared object uniting two or more complex objects composing a definition. (Construction)

8.17 - A relationship is a shared definition uniting two or more complex definitions. (Construction)

8.18 - A relationship is a shared architecture uniting two or more complex architectures composing a definition. (Construction)

8.19 – A relationship is a dimension, and/or object, and/or definition, and/or architecture uniting two or more dimensions, and/or objects, and/or definitions, and/or architectures composing a complex dimension, and/or a complex object, and/or a complex definition, and/or a complex architecture. (Construction)

SECTION D

8.20 – A Relationship is a pathway uniting two objects or more than two objects composing a definition. (8.1)

8.21 – A Direct Relationship between Object A and Object B occurs when Object A shares one or more of its composing dimensions with Object B. (Definition)

8.22 – An Indirect Relationship between two objects occurs when:
1) Object A directly shares one or more dimensions with Object B,
2) Object A directly shares no dimensions with Object C, and
3) Object B directly shares one or more dimensions with Object C.
There are no directly shared dimensions between Object A and Object C, therefore the relationship of A and C is an Indirect Relationship. (Definition)

8.23 - An indirect relationship is composed of one or more direct relationships, and one or more indirect relationships. (Construction)

8.24 - If Object A shares a direct pathway with Object B, then A and B share a direct pathway, each to the other, A to B, and B to A. (Construction)

8.25 - If Object A shares an indirect pathway with Object C, then A must share a direct pathway to an Object B, and Object B must share a direct pathway to Object C, and A must share an indirect pathway to C, and C must share an indirect pathway to A, each to the other, A to C, and C to A. (Construction)

8.26 - Any indirect relationship is composed of one or more direct pathways and one or more indirect pathways. (Construction)

8.27 - Definitions in a relationship share a direct or indirect pathway, each to the other. (Construction)

8.28 - Dimensions in a relationship share a direct or indirect pathway, each to the other. (Construction)

8.29 - Architectures in a relationship share a direct or indirect pathway, each to the other. (Construction)

8.30 - Objects, definitions, dimensions and architectures in a relationship share a direct or indirect pathway, each to the other. (Construction)

SECTION E

8.31 - A Definition determines the outline, and/or magnitude, and/or architecture and/or design of an object, such that any definition is distinct and unique from every other definition. (2.2)

8.32 - If Object A is composed of dimensions 1,2,3 and Object B is composed of dimensions 4,5,6, then Object A and Object B are distinct and unique definitions. (Construction)

8.33 - If Object A is composed of Object B and Object C, and Object B is composed of dimensions 1,2,3,4, and Object C is composed of dimensions 4,5,6,  then dimension 4 is a shared dimension of Object A and Object B, and of Object A and Object C, and of Object B and Object C. (Construction)

8.34 - A relationship is a pathway uniting two objects or more than two objects composing an architecture. (8.4)

8.35 - If Object A is composed of Object B and Object C, and Object B is composed of dimensions 1,2,3,4, and Object C is composed of dimensions 4,5,6, and if they form an architecture 1,2,3,4,5,6, then 4 is a relationship uniting Object B and Object C. (Construction)

8.36 - Any two definitions composed of identical objects, each object and every object, are Identities. (4.34)

8.37 - Any two definitions composed of identical dimensions, each dimension and every dimension, are Identities. (Construction)

8.38 - All dimensions are defined objects. (4.6)

8.39 - If Object A is composed of Object B and Object C, and Object B is composed of dimensions 1,2,3,4, and Object C is composed of dimensions 4,5,6,  then 4 is an identical dimension in the composition of Object A and Object B and Object C. (Construction)

8.40 - If Object A is composed of Object B and Object C, and Object B is composed of dimensions 1,2,3,4, and Object C is composed of dimensions 4,5,6, and they form an architecture 1,2,3,4,4,5,6, then the exchange of 4 between Object B and Object C, will not change the definition of Object A. (Construction)

SECTION F

8.41 – An Indirect Relationship between two objects occurs when:
1) Object A directly shares one or more dimensions with Object B,
2) Object A directly shares no dimensions with Object C, and
3) Object B directly shares one or more dimensions with Object C.
There are no directly shared dimensions between Object A and Object C, therefore the relationship of A and C is an Indirect Relationship. (8.22)

8.42 - 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. (6.24)

8.43 – Objects in a relationship “Exist” in a relationship. (Definition)

8.44 – Objects, dimensions, definitions and architectures in a relationship exist in a relationship. (Construction)

 

For the purposes of Dimensional Thinking, a relationship is constructed when two or more objects share a dimension directly, or share a dimension indirectly via a logical operation. Similarly, any relationship can also be viewed as an architecture of dimensions, or an architecture of definitions, or a complex architecture of architectures. Shared dimensions, pathways and relationships are aspects of each other.

Relationships are composed of objects, therefore they are simultaneously objects, dimensions, definitions and architectures in and of themselves – that is, they can stand alone as unique entities. In addition, relationships act as pathways within more complex objects, dimensions, definitions and architectures.

A non-numerical example of a shared dimension is, “A sunrise is the end of nighttime and the beginning of daytime.” Sunrise is a shared dimension used once in the architecture of this sentence. We could re-write the sentence to include “sunrise” twice: “A sunrise is the end of nighttime and a sunrise is the beginning of daytime.” The exchange of the first “sunrise” with the second “sunrise” does not change the architecture of the sentence.

Note that capitalizing one of the sunrise objects, as in “Sunrise is the end of nighttime and sunrise is the beginning of daytime.” adds a hierarchy - an extra level, an extra dimension - to the Sunrise object. In that case they are different objects with different definitions and are not interchangeable. Sentence components “the”, “of” and “is” can of course exchange places with their identities without changing the architecture.

The definitions and constructions in this chapter are only intended to lay the groundwork for further investigation. It is useful to remember that thus far we have been discussing objects, dimensions, definitions and architectures detectable by the human physical senses – touch, sight, smell, taste and hearing. For example, our usage of the term “definition” is synonymous with a physical architecture, not with language.

 

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