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This is a work in progress - all rights reserved.
Copyright © 2006-2009 Tony Giovia

 

25. Shared Dimensions Define the Physical Structure of Logic and Mathematics v2.0

25.1 – A context is composed of logically or mathematically related Geometric Architectures.

a)  The mechanical processes of logical operations and the mechanical processes of mathematical operations are indistinguishable from each other. Any logical operation can be executed and described mathematically, and vice versa.

25.2 - Geometric Architectures are entirely composed of dimensions. Dimensions are composed of energy. Geometric Architectures are therefore entirely composed of energy.

a)  Via the big Bang Theory, this Universe was created in a burst of energy, and everything in the Universe is necessarily composed of energy.

b)  Perceivable objects necessarily exist. Objects that exist must exist in this Universe of energy. Perceivable objects are therefore composed of energy.

c)  Dimensions are perceivable. Therefore they exist and they are composed of energy.

d) Geometric Architectures are entirely composed of dimensions, therefore Geometric Architectures are entirely composed of energy.

25.3 – A relationship is a framework for communication between two objects or among more than two objects.

a)  A pathway is a circuit along which communication occurs. Pathways within a relationship consist of dimensions shared, directly or indirectly, between or among objects.

25.4 - A dimension can be viewed as a Base Geometric Architecture, a logical island of Ideas.

a)  Ideas require dimensions for their definition.

b)  Dimensions are perceivable objects, and therefore dimensions necessarily exist.

c)  Objects that exist in this Universe are composed of energy.

d)  Via E=MC2, energy, mass and the speed of light squared are logically and mathematically related to each other.

e)  Energy, mass and the speed of light squared are ideas.

f)  A dimension is a logical island of Ideas.

25.5 - Communication requires 1) a physical medium that is, or contains, the message, and 2) a physical pathway that directs the medium.

a)  Via the big Bang Theory, this Universe was created in a burst of energy, and everything in the Universe is necessarily composed of energy.

b)  All modes of communication existing in this Universe must necessarily be composed of energy.

25.6 – Influence is a communication of energy between two objects or among more than two objects.

a)  For any object to influence another object, it must exist in a relationship with it. Therefore objects in a relationship can influence each other.

25.7 - Logical and mathematical laws and processes have a physical structure.

a)  Via the Big Bang Theory, this Universe was created in a burst of energy, and everything in the Universe is necessarily composed of energy.

b)  Energy has a mass component, and mass is a measure of a quantity of matter. Mass therefore requires matter for its definition. Energy therefore has a matter component.

c)  Energy and matter share the dimension mass in their definitions.

d)  Energy is logically and mathematically related to mass via E=MCC.

e)  Mass is logically and mathematically related to matter via the definition of mass as a quantity of matter.

f)  Energy is logically and mathematically related to matter via their shared dimension mass.

g)  Matter is a physical entity.

h)  Logical and mathematical processes exist in the Universe and therefore are composed of energy and have a physical existence.

i)  Logical and mathematical processes have a physical existence, and therefore a physical structure.

25.8 - Logical and mathematical laws and processes influence physical objects.

a)  Influence is a communication of energy between two objects or among more than two objects.

b)  For any object to influence another object, it must exist in a relationship with it. Therefore objects in a relationship can influence each other.

c)  Logical and mathematical processes exist in a relationship with physical objects.

d)  Logical and mathematical processes influence physical objects.

25.9 Shared dimensions define the physical structure of logic and mathematics.

a)  Logical and mathematical processes influence physical objects.

b)  Communication requires a physical medium that is, or contains, the message and a physical pathway that directs the medium.

c)  A shared dimension is a physical pathway between Geometric Architectures.

d)  Contexts are Geometric Architectures composed of dimensions related by a logical or mathematical rule. A rule is a logical or mathematical process, and therefore a rule is a physical structure.

e)  Shared dimensions provide physical pathways within logical or mathematical structures.

25.10  The mechanics of meaning is the flow of energy – the flow of dimensions – across shared dimensions.

 

Contexts are the repositories of meaning in a mind. For example, comparing and contrasting contexts allows us to discern fact from fiction; allows us to find new relationships among Ideas; allows us to align or refute new dimensions with existing goals. To do useful work with contexts we need to look into their structure, and just as important, we need to look at how information is processed within that structure.

The common dominator for all things contextual is the substance used to construct contexts and the components of contexts. That substance is energy, in all its forms. When we say energy is the sole substance of the Universe, we are simultaneously saying that mass, matter and the speed of light squared are equivalent forms of energy, via Albert Einstein’s equation E=MC2.

Traditionally we think of logical and mathematical laws as Ideas somehow existing separate and apart from the objects they describe. But in fact laws (rules, processes, relationships, etc.) are perceivable to a mind, which is a proof that they exist. And if they exist, they exist in this Universe, a Universe where everything is composed of energy. And anything composed of energy can be viewed as matter – as a physical entity.

In this light, logical and mathematical laws are physical entities. Far from merely describing a physical phenomenon like motion, laws are included in the physical structure of motion. Communication in a physical Universe is necessarily physical, and logical and mathematical processes influence physical objects because logical and mathematical processes are themselves physical.

Communication requires a pathway along which the communication occurs. Pathways within a logical or mathematical relationship consist of dimensions shared, directly or indirectly, between or among contexts. Dimensions are composed of energy, and the flow of dimensions through contexts is equivalent to energy flowing along the pathways of shared dimensions. The directed flow of energy across shared contexts is the electrical equivalent of the meaning of those contexts.

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