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

 

CHAPTER 4 – Dimensions

SECTION A

4.1 - A Dimension is any defined component of an object. (Definition)

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

4.3 - Outlines, magnitudes, architectures and designs are defined components of objects. (2.15)

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

SECTION B

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

4.6 - All dimensions are defined objects. (Construction)

4.7 - All objects are defined. (Construction)

4.8 - Dimensions are objects. (Construction)

4.9 - Objects are composed of defined dimensions. (Construction)

4.10 – All dimensions are defined. (Construction)

4.11 – Objects are composed of dimensions. (Construction)

SECTION C

4.12 - A defined object is detectable by the human physical senses of touch, and/or sight, and/or smell, and/or taste, and/or hearing. (2.8)

4.13 - Dimensions are detectable by the human physical senses of touch, sight, smell, taste and/or hearing. (Construction)

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

4.15 - Each dimension detectable by human physical senses is itself an object defined by its outline, and/or its magnitudes, and/or its architecture, and/or its design. (Construction)

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

4.17 - A dimension is an object composed of defined dimensions. (Construction)

SECTION D

4.18 - Any dimension can be completely defined by its composing dimensions. (Construction)

4.19 - Any dimension can be completely defined by its composing objects. (Construction)

4.20 - Any object is a defined dimension. (Construction)

4.21 – Any object is a dimension. (Construction)

4.22 – Any object is defined. (Construction)

SECTION E

4.23 - 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)

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

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

4.26 – Any object is defined. (4.22)

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

4.28 – Objects composed of defined objects are themselves defined objects. (Construction)

4.29 – All definitions are defined objects. (Construction)

SECTION F

4.30 - Any definition is distinct and unique from every other definition. (2.3)
           
4.31 - Any definition distinct and unique from every other definition is composed of defined objects unique to that definition. (Construction)

4.32 - Any definition is composed of defined objects unique to that definition. (Construction)

4.33 - Any definition is composed of objects unique to that definition. (Construction)

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

4.35 – Any two definitions not composed of identical objects, each object and every object, are not Identities. (Definition)

4.36 - Each object and every object composing identical definitions must be identical. (Construction)

4.37 - Any definition is composed of each object and every object unique to that definition. (Construction)

4.38 - If any Object B partly composes or wholly composes any Object A, then Object B is "Included" in the composition of Object A. (Definition)

4.39 – Any definition includes each and every of its composing objects. (Construction)

4.40 - Each dimension detectable by human physical senses is itself an object defined by its outline, and/or its magnitudes, and/or its architecture, and/or its design. (4.15)

4.41 - Any object is a dimension. (4.21)

4.42 - Definitions are composed of dimensions. (Construction)      

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

4.44 – Dimensions composing a definition are said to “Form” the definition. (Definition)

4.45 – Any definition is formed by its composing dimensions. (Construction)

 

Any definable aspect of an object is a dimension of that object. Dimensions can be absolute, as in “There are exactly 60 seconds in a minute” or relative as in “A is greater than (heavier than, farther than) B”.

A mathematician defines a dimension as “The least number of independent coordinates required to specify uniquely the points in a space.” A physicist defines a dimension as “A physical property, such as mass, length, time, or a combination thereof, regarded as a fundamental measure or as one of a set of fundamental measures of a physical quantity.” Both of these are useful definitions completely included in our usage of the term dimension.

A key point is that every dimension detectable by human physical senses is itself a defined object. This means that each of these dimensions is itself composed of dimensions. The structure of the “dimensional universe” is a network of countless linkages. We will be looking at the phenomenon of dimensions on both a small scale and a large scale as we go along.

Objects and dimensions are for all practical purposes the same materiality, so you may wonder why we risk confusion by using two names for the same thing. The answer is… to avoid confusion. Because any object and any dimension is composed of other objects and/or other dimensions (depending on how you choose to look at it), having two names allow us to distinguish a composite object from the objects/dimensions that compose it.

 

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