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.

Mon, May 10, 2021