The Digital Integration of Conceptual Form
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The Many Forms of Many/One
Universal conceptual form

Aligning the vision

Project under development
Evolving and coalescing

Guiding motivation
Why we do this

A comprehensive vision
Ethics / governance / science

Cybernetic democracy
Homeostatic governance

Collective discernment
Idealized democracy

Objectives and strategy
Reconciliation and integration

Reconciliation of perspectives
Holistic view on alternatives

What is a concept?
Definitions and alternatives

Theories of concepts
Compare alternatives

What is truth?
How do we know?

How meaning is created

Synthetic dimensionality
Foundational recursive definition

Universal hierarchy
Spectrum of levels

A universal foundation
The closed loop ensemble contains
all primary definitions

Dimensions of set theory

What is a number?

Venn diagrams
Topology of sets

Objects in Boolean algebra
How are they constructed?

Core vocabulary
Primary terms

Core terms on the strip
Closed Loop framework

Hierarchical models

Digital geometry
Euclid in digital space

The dimensional construction
of abstract objects
Foundational method

The digital integration
of conceptual form
Compositional semantics

Closed loop interval ontology
How it works

Cognitive science
The integrated science of mind

What does it mean?

Formal systematic definitions
Core terms

Data structures
Constructive elements
and building blocks

Preserving data under transformation

Steady-state cosmology
In the beginning

Semantic ontology
Domain and universal

Foundational ontology
A design proposal

Coordinate systems
Mapping the grid

From other sources

Foundational computation

Plato's republic and
homeostatic democracy
Perfecting political balance

Branching computational architecture
Simultaneity or sequence

Abstract math and HTML
Concrete symbolic representation

All knowledge as conceptual
Science, philosophy and math
are defined in concepts

Does the Closed Loop
have an origin?
Emerging from a point

What is closed loop interval ontology?

Definition / description

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.

Hide Placeholder Note Sketch Draft Polished

Mon, May 10, 2021