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Copyright © 2006-2011 Anthony Giovia



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 dimensional principles. The Geometry of Ideas is not a new science; rather, it is an extension of existing sciences.

The Geometry of Ideas proposes that generic concepts can be defined in physical world terms. The purpose is to provide a scientific basis for idea organization and idea interactions. To achieve this, we must 1) establish that ideas exist as physical objects, and 2) demonstrate that physical ideas must interact via known physical laws. The actual argument for physical ideas is straightforward – 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 physical dimensions, and as such certain logical concepts (for example, “sets”) require a corresponding dimensional nature to accommodate them. This is less disruptive than it may seem. Instead of using abstract ideas to describe other abstract ideas, The Geometry of Ideas adds 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 many 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 variables, personal agendas, information awareness and honest disagreements 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 an open practical framework will predominate.

Caveat: It must be noted that a single object can and does have multiple definitions. These multiple definitions can be seen as “stages” or “levels” in an evolution to a more encompassing definition. This evolution will become apparent as definitions presented early in this treatise change as we proceed. The early definitions are still valid; however they are less comprehensive than their later incarnations.