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

 

CHAPTER 5 – Shared Dimensions

SECTION A

5.1 – Any object can be defined by its outline, and/or its magnitudes, and/or its architecture, and/or its design. (2.4)

5.2 – In this Universe there exists at least two unique objects which, either instantaneously or persistently, are composed of identical outlines, and/or magnitudes, and/or architectures, and/or designs. (Definition)

5.3 – Identical outlines, magnitudes, architectures and designs can exist in more than one object. (Construction)

5.4 – Outlines, magnitudes, architectures and designs are dimensions of objects. (4.4)

5.5 – Identical dimensions can exist in more than one object. (Construction)

5.6 – A Shared Dimension is any dimension that exists in more than one object. (Definition)

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

SECTION B

5.8 - Any object can be completely defined by its outline, magnitudes, architecture and design. (2.5)

5.9 - Outlines, magnitudes, architectures and designs are dimensions of objects. (4.4)

5.10 - Any object can be completely defined by its composing dimensions. (Construction)

5.11 - Architecture determines the composition of an object within its external and internal boundaries. (2.2c)

5.12 - A Shared Dimension is any dimension that exists in more than one object. (5.6)

5.13 - If Object A is defined by dimensions 1,2,3,4, and Object B is defined by dimensions 4,5,6, then dimension 4 is a shared dimension of Object A and Object B. (5.7)

5.14 - Any definition is formed by its composing dimensions. (4.45)

5.15 - If Object 1,2,3,4 and Object 4,5,6 exist in the same definition, they form an architecture 1,2,3,4,5,6  or 1,2,3,4,4,5,6. (Construction)

SECTION C

5.16 - 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)

5.17 – Outlines, magnitudes, architectures and designs are objects. (4.27)

5.18 - Definitions are composed of defined objects. (2.16)

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

5.20 - All dimensions are defined objects. (4.6)

5.21 - All objects are defined. (4.7)

5.22 - Any definition includes each and every of its composing dimensions. (4.43)

5.23 – If Dimension A partly or wholly composes any Object B, and if the definition of an object composing Dimension A changes, then the definition of Object B changes. (Construction)

5.24 - If a dimension is shared between the definition of Object A and the definition of Object B, then exchanging that dimension of Object A for that dimension of Object B will not change the definition of Object A or of Object B. (Construction)

5.25 - The exchange of a shared dimension between objects does not change the definition of those objects. (Construction)

5.26 - If a dimension is shared between the architecture of Object A and the architecture of Object B, then exchanging that dimension of Object A for that dimension of Object B will not change the architecture of Object A or of Object B. (Construction)

5.27 - The exchange of a shared dimension between objects does not change the architecture of those objects. (Construction)

 

A shared dimension is a unique component of an object that also happens to be a unique component of one or more other objects. Common examples of this are two objects of the same color, or temperature, or length, or shape.

This chapter merely states that two distinct objects can contain an identical dimension in their definition. There is no reasoning in this chapter implying that two objects are necessarily physically joined at their shared dimension(s). If they are not physically joined, then the definition of Object 1,2,3,4 is separate from the definition of Object 4,5,6, and their architectures exist separately as definition 1,2,3,4 and definition 4,5,6. If they are physically joined at 4, then the definitions of Object 1,2,3,4 and Object 4,5,6 form a definition 1,2,3,4,5,6.

Alternatively, if a definition is composed of Object 1,2,3,4, Object 4,5,6, and Object 6,7,1, then the possible architectures are 1,1,2,3,4,4,5,6,7 or 1,1,2,3,4,5,6,7 or 1,2,3,4,4,5,6,7 or 1,2,3,4,5,6,7.

It is useful to remember that definitions can, and do change as additional dimensions are added to their structure. The statements in any chapter in this treatise are limited to what has gone before, and therefore all statements are building blocks of what is to come.

 

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