Closed Loop Interval Ontology
       The Integration of Conceptual Form


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Project under development
Coalescing and evolving

Closed Loop Interval Ontology
How it works

Objectives and Strategy
Reconciliation and integration

Core Vocabulary
Primary terms

A Universal Foundation
The closed loop ensemble contains
all primary definitions

Core terms on the strip
Closed Loop framework

Reconciliation of perspectives
Holistic view on alternatives

Closed Loop Interval Ontology
How it works

The "Project for Closed Loop Interval Ontology" is our exploratory development and architectural design for the integration of semantic ontology and our response to "The Tower of Babel Problem."

Major dimensions and implications
What is closed loop interval ontology?
Assembling process
A single line of descent from absolute measurement
Unit interval

Major dimensions and implications
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We are postulating a master containing and aligning principle, from which we propose all conceptual form is derived, and within which all conceptual form is contained. This structure has a central axis across its descending levels that guides participating collective decision-making towards a common center

  • Foundation for conceptual form -- all form derived from this structure
  • Universal container for conceptual form - all form contained within this structure
  • Integrating (global and local) center-point for convergent decision-making

There is an implicit ethics contained within this framework, defined as link between global and local, where global well-being is instantiated and replicated at the local level. This concept is sometimes known as "glocalism" (ie, the global in the local).

The well-being of the whole is defined by balance (homeostasis) and that same balance is replicated at the level of local community.

The integrity of this connection forms a guiding universal ethic active at all levels (from local to global).

What is closed loop interval ontology?
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We are proposing a new model of the continuum, which we define as a closed loop -- a circle -- but in this case taking the form of a "Moebius Strip".

We are proposing that "an ontology" can be defined within (bounded by) and on (as a strip) a "closed loop". By "ontology", we mean a system or framework of definitions or terms or concepts ("words"), where the distinctions and specifics characterizing those terms are defined within intervals created by distinctions and boundary values.

  • What is a "closed loop?"
  • What is an "interval?"
  • What is an "ontology?"

We are exploring the hypothesis that the two "edges" of the strip -- which are actually only one continuous edge -- can define an "interval" across the width of the strip - somewhat as is shown in the animated graphic in the header.

In addition to this basic concept of bounded interval (bounded by top edge and bottom edge), we define a range of values nested "between the edges" of this form, which we propose takes the general form of a taxonomy or "hierarchy of abstraction". This hierarchy of nested levels extends from a "top level" (from the top edge), which is an unbounded interval ("the infinite") to a "bottom level" (to the bottom edge) ("the infinitesimal").

This decomposition is analogous to ("isomorphic to") the decomposition of the unit interval into the decimal number system.

The exploratory hypothesis is that this simple general form can interpret any special-case instance, and that all taxonomies take this same general form, taking a specialized configuration in service to particular purposes arising in particular contexts. The power of this model emerges from the way we interpret it.

  • The "closed loop" is a container. It's like a cell in a spreadsheet or database table. It has boundaries (or boundary) and something inside those boundaries (or boundary).
  • We understand those boundaries to be defining cascades of nested distinctions, or, at the bottom the cascade (the hierarchy of abstraction), perhaps a single element or instance.

    • How do the purposes defining a taxonomic cascade influence or shape the structure of the cascade?
    • How does the general form interpret any special case instance?
    • Why is this important?

  • Those boundaries can be defined as "boundary values" -- lower and upper limits on some dimensional range.

  • The objective is to understand how it is that "everything is contained within it." This concept is proposed as an absolute bound on the conceivable. Every idea, it is proposed, every concept, every term or category, emerges as a distinction or a "cascaded nest of distinctions" defined within this framework.

  • The entire structure can be understood as a "unit interval" - which we see as a foundation concept for defining the notion of "unit" -- "one of anything".

    The unit interval can be "decomposed" -- like a taxonomy. A series of levels - like a taxonomy - is shown in the animated graphic.

  • So, this decomposition is similar to (identical to, isomorphic to) the decomposition of decimal numbers -- or any other numbers -- into decimal places and finer and finer (smaller and smaller) measurement distances or units (10ths, 100ths, 1000ths, 10000ths, etc.)

    The power here emerges when we understand that this entire process can be contained across the limited width of the moebius strip -- the distance between the two edges. One edge of the strip is the open undefined unbounded infinite interval with no end-points -- because it is a circle -- and the other edge is defined as something like the real number line, the finest differentiation possible, and an approach to continuity as a limit.

Assembling process
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We want to define precisely how it is that the moebius strip can be interpreted as a universal foundation for conceptual structure.

This is complicated with a lot of moving parts, and the idea is still unproven and intuitive. List these elements here to help guide the coalescence. We need a comprehensive list of these elements, and we have to explain or justify them all individually in a consistent way.

This list is a design for project architecture:

  • The pieces that are to be combined
  • The way in which the pieces are to be combined
  • The themes and principles and methods that are brought together in one place
  • The concept of "isomorphic recursion" defined across many simultaneous objects or concepts


  • Develop a list of terms and words that are synonyms for "category" -- any dimensionally-bounded unit
  • Develop a list of terms that are synonyms -- or can be defined as synonyms -- for boundary value or "cut" -- the "line that cuts a line" to form a distinction

Type of objects that are defined through isomorphic recursion and connected to build a model of reality:

  • Abstract
  • Symbolic - representational
  • Concrete (referent?) or "actual"

"What can be done with little boxes"?

Everything is defined by a box (a bounded interval) containing some symbolic structure, composed of alphabet or numbers..

Everything is matrix

matrix can define everything -- to within some error tolerance

A single line of descent from absolute measurement
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We want to define an aligning axis as a guide to interpretation across levels ranging from global to local, from "infinite" to "infinitesimal"

It's a guide to interpretation, and is a guide to convergence towards common center


Unit interval
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the top level in the strip – the undifferentiated “one” at the top of the hierarchy of layers, defined in a recursive way like a “holon”, such that every nested interval is also a unit interval

In mathematics, the unit interval is the closed interval [0,1], that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted I (capital letter I). In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology.

In the literature, the term "unit interval" is sometimes applied to the other shapes that an interval from 0 to 1 could take: (0,1], [0,1), and (0,1). However, the notation I is most commonly reserved for the closed interval [0,1].