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This is a work in progress - all rights reserved.
Copyright © 2006-2008 Tony Giovia

 

 

2. Dimensions v1.1

2.1 - A dimension is a particular, uniquely definable element of an object’s outline, magnitude, architecture or design. (Definition)
                                                                                   
2.2 - A dimension or collection of dimensions define an object. (Construction)

2.3 - Particular dimensions can be shared among multiple objects. (Construction)

2.4 - An idea is a unique definition of a perceivable dimension. (Construction)

2.5 - A context is a unique collection of ideas. (Definition)

2.6 - A mind is at least a collector and organizer of ideas and contexts. (Definition)

2.7 - Tangible dimensions are dimensions perceivable by the senses and which are ultimately capable of perception and definition by a mind. (Definition)

2.8 - Intangible dimensions are ultimately definable by an idea or context, and capable of collection by a mind. (Definition)

2.9 A valid idea definition must uniquely describe a perceivable dimension. (Definition)

 

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.

In this section we are introducing the terms idea, context and mind. Ideas are definable objects. Certainly some ideas can be defined to a more exact degree than others, but all ideas, to be considered as ideas, must be uniquely definable. Further, for the purposes of this discussion, we will define a practical baseline for idea definitions: a valid idea definition must describe a perceivable dimension.

Initially, the lack of standardized definitions due to cultural differences and reasoning abilities will result in multiple geometries. But it is the nature of things that a common language will evolve, and conflicting definitions will present opportunities for more precise definitions.

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You will note the introduction of the term “construction”. Euclid, The Father of Geometry, used “Common Notions” as building blocks to create his geometric proofs. He called these proofs “Propositions”, and used the Propositions to create more complex Propositions. In a similar manner we will use certain definitions as our “Common Notions”, and like Euclid, use these definitions as the foundation for creating more complex definitions. Because definitions are composed of dimensions, the terms definition and dimension are interchangeable in this context.

We will be discussing Euclid in greater detail in the Applications section of this presentation. For now we can say that where Euclid used the term “Proposition” to describe the product of logical reasoning, we will be using the more direct – and more obvious – term “construction”. Euclid primarily focused on ideas as abstract objects – points, lines, planes and so on – and applied these abstract ideas to physical objects. Our approach differs in that we see ideas as physical objects – not as abstractions. When we use the term “reason” or “logic” we are referring to the physical connections and relationships between physical dimensions that ultimately define an object – that is, the physical dimensions used in the construction of an object.

 

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