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

Invocation
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
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Objectives and strategy
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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?

Semantics
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

Set
Dimensions of set theory

Numbers
What is a number?

Venn diagrams
Topology of sets

Objects in Boolean algebra
How are they constructed?

Core vocabulary
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Core terms on the strip
Closed Loop framework

Graphics
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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

Equality
What does it mean?

Formal systematic definitions
Core terms

Data structures
Constructive elements
and building blocks

Compactification
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

Articles
From other sources

Arithmetic
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


Term
Dimension

Definition / description

What is a dimension? Why and how does it makes sense to talk about dimensions of something as its properties or attributes?

How is a dimension an attribute, and how does that interpretation relate to the traditional definition of dimension as a fundamental element of measurement?

Google's definition:

  • a measurable extent of some kind, such as length, breadth, depth, or height.

  • an aspect or feature of a situation, problem, or thing.
    • aspect
    • feature (Smith and Medin say a feature is a ---)
    • element
    • facet
    • side
    • characteristic
    • property
    • attribute

These are all properties of -- what? Models? Concepts? "Composite dimensional structures"? "A situation, problem or thing"

How do we construct a "thing" out of dimensions?

How do we construct a "situation" out of dimensions?

We have to follow the general Sowa law of picking aspects that are interesting to us for some reason.

We don't "construct the entire object". We abstractly represent aspects of the object ("dimensions of the object") that are interesting to us.

**

Poperties and attribute are composite/hollstic/assembled objects with internal structure

Is a dimension a cut or a distinction? If it is a property or attribute, how would that be true?

I used to define a dimension as an "ordered class"

So the notion of "opposite" might be generalized to define this range of variation, with a lowest and highest value in some defining attribute -- the way we might order the members of a "species" by a value in one of their defining attributes

***

Is not a dimension

Tue, Apr 27, 2021

Reference

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or SI system than in others, due to the regular 10-base in all units. Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra.

Commensurable physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are originally expressed in differing units of measure, e.g. yards and metres, pounds(mass) and kilograms, seconds and years. Incommensurable physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are originally expressed in, e.g. meters and kilograms, seconds and kilograms, meters and seconds. For example, asking whether a kilogram is larger than an hour is meaningless.

Any physically meaningful equation, or inequality, must have the same dimensions on its left and right sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility check on derived equations and computations. It also serves as a guide and constraint in deriving equations that may describe a physical system in the absence of a more rigorous derivation.

The concept of physical dimension, and of dimensional analysis, was introduced by Joseph Fourier in 1822.

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

In physics, it is important to note that a dimension is simply a measure of something, and that, for each class of features to be measured, another dimension can be added. Attachment to visualizing the dimensions precludes understanding the many different dimensions that can be measured (time, mass, color, cost, etc.). Multi-dimensional objects can be calculated and manipulated algebraically.

https://www.newworldencyclopedia.org/entry/Cartesian_coordinate_system