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This is a work in progress - all rights reserved.
Copyright © 2006-2012 Anthony Giovia
CHAPTER 9 – Networks
SECTION A
9.1 – A Direct Relationship between Object A and Object B occurs when Object A shares one or more of its composing dimensions with Object B. (8.21)
9.2 – 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)9.3 – 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. (8.19)
9.4 – Objects in a relationship compose an architecture of dimensions. (Construction)
9.5 - Objects in a relationship compose an architecture, and/or dimension, and/or definition, and/or object of complex architectures, and/or complex dimensions, and/or complex definitions, and/or complex objects. (Construction)
9.6 - An indirect relationship is composed of one or more direct relationships, and one or more indirect relationships. (8.23)
9.7 - Architectures in a relationship directly or indirectly share dimensions. (Construction)
9.8 - Architectures, and/or dimensions, and/or definitions, and/or objects in a relationship directly or indirectly share architectures, and/or dimensions, and/or definitions, and/or objects. (Construction)
SECTION B
9.9 - A Network is an architecture of direct or indirect relationships completely or partially composing an object. (Definition)
9.10 - A network is an architecture of direct or indirect relationships completely or partially composing a definition. (Construction)
9.11 - A network is an architecture of direct or indirect relationships completely or partially composing a dimension. (Construction)
9.12 - A network is an architecture of direct or indirect relationships completely or partially composing a complex architecture. (Construction)
9.13 - A network is an architecture, and/or object, and/or dimension, and/or definition of direct or indirect relationships completely or partially composing a complex architecture, and/or complex object, and/or complex dimension, and/or complex definition. (Construction)
SECTION C
9.14 - 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)
9.15 - Outlines, magnitudes, architectures and designs are defined objects. (2.12)
9.16 - 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)
9.17 - Any definition includes each and every of its composing dimensions. (4.43)
9.18 - Any definition includes each and every of its composing objects, dimensions, definitions and architectures. (Construction)
9.19 - Any definition is composed of objects unique to that definition. (4.33)
9.20 - If Object A is composed of Object B and Object C, then the definition of Object A is composed of the definition of Object B and the definition of Object C. (Construction)
9.21 - If Object A is composed of Object B and Object C, then the definition of Object A is different from the definition of Object B alone, and different from the definition of Object C alone. (Construction)
9.22 - If Object A is composed of Object B and Object C, then Object A, Object B and Object C are three differently defined objects. (Construction)
SECTION D
9.23 - If Object A is composed of Object B, Object C and Object D, Object A is simultaneously an object, a dimension, a definition and an architecture, Object B is simultaneously an object, a dimension, a definition and an architecture, Object C is simultaneously an object, a dimension, a definition and an architecture, and Object D is simultaneously an object, a dimension, a definition and an architecture. (Construction)
9.24 - A Shared Dimension is any dimension that exists in more than one object. (5.6)
9.25 - A shared dimension is any dimension, object, definition and architecture that exists in more than one object, definition, architecture and complex dimension. (Construction)
9.26 - If Object A is composed of Object B and Object C, then Object A, Object B and Object C are three differently defined objects. (9.22)
9.27 – A Direct Relationship between Object A and Object B occurs when Object A shares one or more of its composing dimensions with Object B. (8.21)
9.28 – 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)9.29 - If the architecture of Object A is composed of the dimensions of Object B, Object C and Object D, and if B shares one or more of its composing dimensions with C and with D, then B, C and D are directly related, each to the other. (Construction)
9.30 - If the architecture of Object A is composed of the dimensions of Object B, Object C and Object D, and if B shares one or more of its composing dimensions with C but not with D, then B and C are directly related, and B and D are indirectly related. (Construction)
9.31 - If the definition of Object A is composed of the dimensions of Object B, Object C and Object D, and if B shares one or more of its composing dimensions with C and with D, then B, C and D are directly related, each to the other. (Construction)
9.32 - If the definition of Object A is composed of the dimensions of Object B, Object C and Object D, and if B shares one or more of its composing dimensions with C but not with D, then B and C are directly related, and B and D are indirectly related. (Construction)
9.33 - If Object A directly shares one or more dimensions with Object B and one or more dimensions with Object C, then some or all of the dimensions of B and C are directly or indirectly shared with A. (Construction)
9.34 - If Object A directly shares one or more dimensions with Object B, and Object B directly shares one or more dimensions with Object C, and Object A directly shares no dimensions with Object C, then the definitions of B and C directly and indirectly share the definition of A. (Construction)
9.35 - If Object A is composed of the definition of Object B and the definition of Object C, then the definitions of B and C directly share the definition of A. (Construction)
9.36 - If Object A is partly or wholly composed of Object B and Object C and Object D, then B, C and D directly or indirectly share the composition of A. (Construction)
SECTION E
9.37 - Any definition includes each and every of its composing objects, dimensions, definitions and architectures. (9.18)
9.38 - A network is an architecture, and/or object, and/or dimension, and/or definition of direct or indirect relationships completely or partially composing a complex architecture, and/or complex object, and/or complex dimension, and/or complex definition. (9.13)
9.39 - All objects are defined. (4.7)
9.40 – Networks are defined objects. (Construction)
9.41 - Networks are defined objects, and/or dimensions, and/or definitions, and/or architectures. (Construction)
9.42 - A defined object is composed of defined objects. (2.13)
9.43 - If Object A is composed of the definition of Object B and the definition of Object C, then the definitions of B and C directly share the definition of A. (9.35)
9.44 - If Object A is partly or wholly composed of Object B and Object C and Object D, then B, C and D directly or indirectly share the composition of A. (9.36)
9.45 - Definitions are networks of objects. (Construction)
9.46 - Definitions are networks of objects, and/or dimensions, and/or definitions, and/or architectures. (Construction)
9.47 - Definitions are networks of direct or indirect relationships. (Construction)
9.48 – Definitions, objects, dimensions and architectures are networks of direct or indirect relationships. (Construction)
9.49 - Definitions, objects, dimensions and definitions are composed of direct or indirect relationships. (Construction)
An object is defined by its composing dimensions and the relationships among them. The relationship between an object’s definition – that is, the object itself - and its composing dimensions and relationships is absolutely aligned, because any alteration of the composing elements changes the definition of the object and therefore the object itself.
The dimensions composing an object’s physical definition exist in direct and indirect relationships with the dimensions of other objects, and these relationships determine the uniqueness of any object.
The Geometry of Ideas is no more than a tool designed to examine the structure of the innumerable relationships composing our Universe. The fact that we contextualize Wholes and Parts into manageable chunks is a reflection of the mechanics of human perception, and not of the breadth and depth of actual interconnections.
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