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

 

Preface v1.1

The Geometry of Ideas, Contextual Geometry, and Dimensional Thinking are nomenclatures for related sets of principles. It is convenient to use The Geometry of Ideas as an umbrella term, Contextual Geometry when considering idea designs, and Dimensional Thinking when applying learned principles.  The Geometry of Ideas is not a new science; rather, it is an extension of existing sciences.

The Geometry of Ideas seeks to clarify the definitions of generic concepts by defining them in physical world terms, thereby providing a scientific basis for idea organization and idea interactions. The goal is two-fold – 1) establish a physical basis for ideas, and 2) show how physical ideas interact via known physical laws. The actual argument for physical ideas is quite simple – if everything in the Universe originated in a Big Bang of energy, then everything in the Universe is a product of the Big Bang and is composed of energy. Albert Einstein showed us that energy has a mass component – therefore ideas have a mass component.

Physical ideas - like all objects with mass - have surfaces and dimensions, and therefore certain logical concepts (for example, “sets”) require a corresponding dimensional nature to accommodate them. This is less disruptive than it may seem at first glance. Instead of using abstract ideas to describe other abstract ideas, The Geometry of Ideas introduces a physical dimension to examine the possible ways logic actually associates one idea to another.

All ideas are defined in terms of other ideas, but along the way the definitions of abstract terms have lost their physical world roots – it is difficult to navigate down and discover how a word like “abstract” relates directly or indirectly to the existence of a real object for its meaning, or, for that matter, for its own non-abstract existence. The Geometry of Ideas re-defines these and other difficult concepts and shows how they co-exist in a more general nexus of physical ideas.

Initially, the lack of standardized definitions will lead to multiple geometries because the wording of definitions is the very basis of any Geometry of Ideas. Language issues, personal agenda issues, information awareness issues as well as simple disagreement issues all influence the wording of definitions. But it is the Darwinian nature of thought organizations to settle on the most efficient structures, and over time a single open practical framework will predominate.

The following text refers to Entities, Ideas, Objects and Elements, defined as follows:

• Entity -  A physical object that can be touched, smelled, heard or seen.
• Idea -  A perceivable dimension, where a dimension is a uniquely defined element of an entity or another dimension.
• Object -  A generic term for any particular thing that exists. Entities and Ideas are objects.
• Element - A generic term indicating a single object existing in a relationship with another object or objects.

 

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