The Integration of Conceptual Form
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Unit interval


Coordinate frame

Project developed by
Bruce Schuman



Closed loop interval ontology

This note is a sketch in progress.

In the context of this project, we define "semantic ontology" as the philosophic and scientific study of words and word-meanings, understood in a way that includes all abstract symbolic representation, including natural language, computer language, logic, mathematics, boolean algebra, set theory, arithmetic, etc. This is a very broad array of subjects, generally thought of as interrelated, but defined without any consistent or systematic way to understand all these subjects areas as branches of one common framework.

We are exploring and unfolding an integrated ("integral") foundation for a universal semantic ontology that we describe as a "closed loop interval ontology". The objective is to define a framework that contains and helps explain all these separate areas, and also shows how they are related to one another.

We are exploring and proposing an explanatory principle of great generality.


  • isomorphic recursion -- the decomposition of the unit interval into decimal places
    • -- Check if two binary trees are Isomorphic

  • The "closed loop" is a container. It is "uncut and undivided" until some motivation arises within and distinctions begin to defined. These discintions can be combined to form composite units of distinctions

    In the evolution of thought and culture and civilzations, many of these composite distinctions become institutionalized and become the conceptual fundations for society.

  • Categories -- all categories -- defined by bounded intervals, which create "containers" for whatever is "inside" that container
    • This is created in its most basic sense by cuts and distinctions in the continuum
    • Those cuts and distinctions are defined and understood in terms of dimensions
    • Values in these dimensions are defined by cuts -- bounded ranges -- in those dimensions

  • This model is
    • An interpretation of the real number line and traditional concepts of the continuum, as defined by great mathematicians and widely accepted throughout world mathmatics and science
    • Defined on a "loop" or "circle", rather than on a closed/bounded line sgement
    • When viewed within a "normal 3-dimensionbal perspective", appears to have "two edges" -- but when tracked around the loop actually has only one edge
    • We define the Moebius loop in terms of its boundaries
    • What we are doing that seems to be unprecedented is defining a scale or transtiion of spectroum between edges of the strip, where we creae a taxonomy defined across the unit interval with top edge of the strip sseen in 3-d is a continuous undifferentiated unit interval and "purse continuity, and the bottom level (also a limit) is the "real number line" -- an impossible level but defined as a limit
    • So we create that spectrum across the two edges and differentiate that spectroum in the form of a taxonomy, which defines leels of absraction
    • Critical points of isomoprhism -- the decompsotion of decimal numbers is isomorphic to a taxonomic cascade -- genus/species each additional level of decimal decomposition is a "species" of the level that contains it


  • Decomposition of the unit interval - a recursive process
  • Universal tree: closed loop at the top, bits and continuum at the bottom, everything built up from the bottom by compositional semantics, all contained within the single bounding container, everything interconnected within the primary trunk or axis of tis tree, everything intrpretd within this framework. All parsing of this space driven by immedae local motivation ("relativistic") while the tree-frame itself define that absolute container of the entire process

We mere humans somehow know there is a perfection in reality and in nature. There is something we can see in organic form that tells us there is innate order in existence. We can see it in the stars, in the rocks, in the oceans, in the trees. There is something beautiful, something whole, something deeply true from which reality emerges, and by which somehow all natural and healthy order is maintained.