Closed Loop Interval Ontology
     CLOSED LOOP INTERVAL ONTOLOGY
       The Digital Integration of Conceptual Form

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Synthetic dimensionality
Foundational recursive definition

We are exploring a universal definition and constructive method for semantic objects, based on the principle of dimensionality.

"Synthetic dimensionality" was originally defined in the early 1990's. We are beginning to gather up facets of its definition and properties and combine them in this context.

As the original vision for Synthetic Dimensionality project appeared, the claim and hypothesis emerged that "everything (all abstract objects and concepts) can be built out of synthetic dimension." This involved two major claims:

1) Every facet of conceptual structure and definition can be defined as composed from (constructed from) synthetic dimensions.

2) It Is highly desirable to do this, for many reasons

"Everything is built out of dimensions, and dimensions are built out of dimensions"

"A dimension is a facet of something"

Synthetic dimensions were seen as the universal constructive element, the universal conceptual building block, from which all mathematical and semantic objects could and should be constructed. It is the foundational concept for the universalization of language, and the interconnection of all languages. Since all languages are built from the same underling elements, and driven by the same principles and motivations -- "any language can be translated into any other language"

What is synthetic dimensionality?
Why use and develop synthetic dimensionality?
The concept of synthetic dimension
A common dimensional protocol for all description and representation
A single constructive element
Cascaded stipulative definition
Taxonomy
Measurement units
Synthetic dimensionality topic
Lists and list processing
Linear continuum
Is the unit strip a synthetic dimension?
The concept of synthetic dimension x
List of synthetic dimensions
What is a synthetic dimension?

What is synthetic dimensionality?
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A "synthetic dimension" is an algebraic form that appears to offer great generality in the description of fundamental analytic concepts.

In simplest terms, a synthetic dimension is a dimension where the values or "measurement units" of the dimension are themselves decomposable and have complex internal structure.

I like the Google response to a search for the term.

It introduces two important meanings in an intuitive way.

A dimension is about measurement -- or it can be a aspect of something.

Dimensionality is a human construction. It is a "concept" -- a analytic cognitive device that supports clear thinking and complex understanding.

Tue, May 11, 2021

Why use and develop synthetic dimensionality?
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The attraction and power of synthetic dimensionality emerges from its universality as a constructive element.

It is consistent with many fundamental definitions

  • Foundational definitions in mathematics
  • Real number line
  • Continuum
    • Define the continuum
    • How differences and new concepts emerge from the continuum
  • Measurement
  • Concept of "attribute"
  • Concept of "property"
  • Definition of "quality"
  • Definition of "class"
  • Definition of "ordered class"
  • Definition of objects in a class
  • Definition of "type" (list the distinguishing properties of the type)
  • Definition of fundamentals of geometry -- point, line, plane, coordinate frame, origin
  • Definition of hierarchy
  • Definition of taxonomy (genus, species, taxon)
  • Definition of number
  • Definition of set
  • Definition of objects/elements in a set
  • Definition of logical operations (Boolean, Arithmetic) on a set or elements of a set
  • Definition of unit
  • Definition of order
  • Definition of abstraction
  • Definition of fundamental logical operations (induction, deduction)

  • TERMS
  • Cut
  • Distinction
  • Difference
  • Boundary

  • GEOMETRY
  • Point
  • Line
  • Plane

  • MATRIX AND DATABASE
  • Row
  • Column
  • Cell

  • EPISTEMOLOGY
  • Identity
  • Equality
  • Comparison
  • Quantity
  • Quality
  • Analogy
  • Metaphor
  • Simile
  • Abstraction
  • Generalization

  • PSYCHOLOGY
  • Stipulation
  • Intention
  • Purpose
  • Motivation (?)
  • Interpretation
  • Bias
  • Creation and emergence of new ideas

  • SEMANTICS
  • Parts of speech
  • The construction of meaning
  • Making a point

  • LAW
  • Defining boundaries and "guardrails"

  • GOVERNANCE
  • Converging and optimizing collaborative decision-making

All these objects can be (are) constructed from synthetic dimensions -- and synthetic dimensions themselves are constructed from synthetic dimensions, in a bottomless recursive process that is driven by human motivation

The power to build all the basic elements of fundamental elements in ontology, epistemology, mathematics and psychology using the same constructive elements and the same fundamental language

Defining the differences between these disciplines and sectors in terms of synthetic dimensions, which can outline the entire range of similarities and differences and link these disciplines

Tue, May 11, 2021

The concept of synthetic dimension
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Notes on development -- what do we want to do with this topic?

  • Introduce the concept of synthetic dimension
  • Briefly mention (?) its history
  • Mention the work on "hierarchy of abstraction" and the effort to describe this structure adequately -- and how synthetic dimension began to appear as a universal object from which we could describe or contract these hierarchies

    • What is "abstraction"?
    • Is abstraction always defined in a "hierarchy"?
    • What are "higher" and "lower" levels?
    • Is this structure in some sense universal, appearing in the same general form in many different instances and contexts?

The idea or concept of a "synthetic dimension" first appeared in this work in the early 1990's, as a consequence of a sustained study of definitions and terminology involved in the fundamental definition of terms such as "concept" or "class" or "category".

We were considering several basic terms that describe the criteria for inclusion in a category or class, including

  • Property
  • Characteristic
  • Attribute
  • Facet

If some object or item has the property, it is in the category or class.

We were working on defining "atomic levels" in the structure of these definitions. Can we ask in some broad and universal and absolute way "what these objects (class, categories) ae "made out of"?

If we are talking about computer science, these objects are indeed constructed from something.

Sun, May 2, 2021

A common dimensional protocol for all description and representation
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We want a single contructive method capable of representating all abstract objects of interest, including

  • Ideal abstract representation as an object, consistent with intuition
  • Representation in a format that is consistent with symbolic/abstract manipulation (arithmetic, algebraic)
  • All the basic terms in our epistemological language

Thu, May 6, 2021

X is a type of Y
Synthetic dimensionality

A single constructive element
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This principle -- build all abstractions from a single and identical-in-all-instances algebraic element or object -- is one of the guiding or suggestive principles prompting the development of synthetic dimensionality.

It is presumed and understood that the derivation and origination of symbolic representation is not fully understood, and that it might be possible, following ideals of modern computer science, to design or construct all abstractions from a single element, a single "building block".

A synthetic dimension is itself a composite object, with identifiable facets or aspects.

  • It is defined in two dimensions -- X (horizontal axis) and Y (vertical axis)
  • It has innate and inherent "length" (measure in X) and "height" (measure in Y)
  • It has a unit -- it is defined in multiples of something (or perhaps only one of that unit, but at least one)

Thu, May 6, 2021

Cascaded stipulative definition
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This idea is essential to understanding how meaning is "assigned".

  • It is created by humane intention
  • It is defined in cascading levels of abstraction -- from broader inclusive categories to narrower
  • This definition is stipulative, and "assigned" by the intending person/speaker
  • It is context specific
  • Because word meaning in most or all cases is subject to misinterpretation because it is not rigid and its implications are too broad, human beings can and do "drill down" across levels of specificity until an "acceptable" level of understanding is reached.

This below Wikipedia definition and discussion of stipulation does not represent this idea very clearly, and presumes that "the dictionary definition" can realistically be assumed to be authoritative. In the real world of context-specific human conversation, this is not the reality. It might work in Scrabble to resolve disputes, but not in real human relationship or negotiations.

Thu, May 6, 2021

Reference
A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context. When the term already exists, this definition may, but does not necessarily, contradict the dictionary (lexical) definition of the term. Because of this, a stipulative definition cannot be "correct" or "incorrect"; it can only differ from other definitions, but it can be useful for its intended purpose.[1][2]

For example, in the riddle of induction by Nelson Goodman, "grue" was stipulated to be "a property of an object that makes it appear green if observed before some future time t, and blue if observed afterward". "Grue" has no meaning in standard English; therefore, Goodman created the new term and gave it a stipulative definition.

On stipulative definitions Stipulative definitions of existing terms are useful in making theoretical arguments, or stating specific cases. For example:

Suppose we say that to love someone is to be willing to die for that person. Take "human" to mean any member of the species Homo sapiens. For the purposes of argument, we will define a "student" to be "a person under 18 enrolled in a local school". Some of these are also precising definitions, a subtype of stipulative definition that may not contradict but only extend the lexical definition of a term. Theoretical definitions, used extensively in science and philosophy, are similar in some ways to stipulative definitions (although theoretical definitions are somewhat normative, more like persuasive definitions).[2]

Many holders of controversial and highly charged opinions use stipulative definitions in order to attach the emotional or other connotations of a word to the meaning they would like to give it; for example, defining "murder" as "the killing of any living thing for any reason". The other side of such an argument is likely to use a different stipulative definition for the same term: "the unlawful killing of a human being with malice aforethought" or "the premeditated killing of a human being". The lexical definition in such a case is likely to fall somewhere in between.

When a stipulative definition is confused with a lexical definition within an argument there is a risk of equivocation.

URL
https://en.wikipedia.org/wiki/Stipulative_definition

Semantics
Synthetic dimensionality

Taxonomy
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essentially the same general form as abstraction

Thu, May 6, 2021

Closed Loop Ensemble
Synthetic dimensionality

Measurement units
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units

Thu, May 6, 2021

Introduction
Synthetic dimensionality

Synthetic dimensionality topic
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Recursive definition of dimension, where values of the dimension are built from synthetic dimensions

A dimension where the values are defined in terms of dimensions

A recursive dimension, intended to define complex semantic cascades in common algebraic concept that expresses every part of the structure

A "composite" dimension

A "holistic" dimension

A "synthetic" (Put together from pieces) dimension

Thu, May 6, 2021

Core vocabulary
Synthetic dimensionality

Lists and list processing
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A synthetic dimension is a list -- an ordered list

Thu, May 6, 2021

Linear continuum
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Thu, May 6, 2021

URL
https://en.wikipedia.org/wiki/Linear_continuum

Is the unit strip a synthetic dimension?
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Just wondering. The claim is that every concept or category or taxonomic/hierarchical form can be defined on the same grid, and that the grid folds up to contain everything within it.

Synthetic dimensions are supposedly composite objects from which which any categorical structure can be created, by creating an intersection like a Venn diagram. The defined object is bound by the dimensional intersection - and the values in that dimension.

Thu, May 6, 2021

Thesis on synthetic dimensionality
Synthetic dimensionality

The concept of synthetic dimension x
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"Everything is made out of dimensions, and dimensions are linear"

Synthetic dimensionality is an exploratory interpretation of the many meanings of "dimension". A synthetic dimension is a dimension where the values of the dimension are abstractions constructed from dimensions. The original work on Synthetic Dimensionality is here: http://originresearch.com

A single best representational primitive conceptual element from which all others can be constructed

It is "utterly fluent" and can describe anything, to any degree of detail that can be conceptualized

Anything (any idea, any concept) can be constructed from it

The proper approach to this entire subject it to consider what is "the best way" to describe the phenomena

"Best" is the proper definition, the proper motivation, the proper criteria for determining the ideal

**

every facet of a decomposition cascade from highest level abstraction to lowest level components of measurement can be defined in terms of synthetic dimensions

a synthetic dimension can map a bit

if we are building semantics or syntax from the atomic level, synthetic dimension can map both

Thu, May 6, 2021

List of synthetic dimensions
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We want to make a list of important objects that can be defined as synthetic dimensions

  • Line
  • Real number line (with constraints)
  • Actual number line
  • Ordered list
  • Ordered class
  • List of natural or integer numbers
  • Taxon in taxonomy - either genus (vertical level) or species (horizontal level)

  • Attribute
  • Characteristic
  • Property

Sun, May 2, 2021

What is a synthetic dimension?
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I like the Google response to a search for the term.

It introduces two important meanings in an intuitive way.

A dimension is about measurement -- or it can be a aspect of something.

Dimensionality is a human construction. It is a "concept" -- a analytic cognitive device that supports clear thinking and complex understanding.

Mon, May 10, 2021