CLOSED LOOP INTERVAL ONTOLOGY
       The Digital Integration of Conceptual Form
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The Many Forms of Many/One
Universal conceptual form

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The continuum and binary numbers
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Definition / description

The general thesis is

Everything emerges from the continuum (real number line) when it is differentiated in its most primal way, through binary numbers -- 0's and 1's alternating as primary differentiations.

The capacity to make any sort of distinction/differentiation whatsoever -- a "difference that makes a difference" -- a "jnd" -- a "just-noticeable difference"

All logic, all mathematics, all numbers, all description, all construction of abstract objects, begins with this definition

This project is "digital" -- which means it is inherently quantized at every point

"every point" is essentially a matrix cell -- and boundary value intersection in X and Y

  • Binary arithmetic is yin/yang
    • Yin/yang is opposites -- how do we diagram those oppositions
    • See Leibniz
    • Is the continuum "one sided"?
    • Is it "figure/ground"?
  • It is digital and quantized
  • It can construct every number
  • It can construct every word

We are lining up an approach for fundamental definitions, and this may be part of that. Natural number, binary number. How do they fit together as derived from or defined in terms of the continuum? From this basis we want to define all types of numbers -- and from there -- the quantization of synthetic dimensions -- qualitative dimensionality defined by stipulation.

Consider the Peat/Bohm discussion of category formation, and how "birds are distinguished from squirrels" -- and how are these differences noted or symbolically represented?

In what sense is the distinguishing difference binary -- or involving "opposites"? How does "figure/ground" involve "opposites"?

There emerges a line of separation -- a boundary -- maybe in many dimensions (squirrels and birds are different in many ways)

But maybe it starts very simple -- some fly, some only jump from branch to branch

How is that cognized?

Hide Placeholder Note Sketch Draft Polished

Tue, May 11, 2021

Reference

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" (zero) and "1" (one).

The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language.

https://en.wikipedia.org/wiki/Binary_number