CLOSED LOOP INTERVAL ONTOLOGY        The Digital Integration of Conceptual Form
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Loop definition

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 We are exploring this "foundational form", which we are interpreting as a universal basis for all mathematical and cognitive science definitions. The objective of this project is to discover and learn and show how this form and its interpretations, such as the closed loop, become foundational to the understanding of language, concepts, and the principles of mathematics.
 Design overview | Foundational form PROJECT DESIGN OVERVIEW INTRODUCTION We are following a vision for the integration of knowledge, which we propose to describe and define on an algebraic structure we call "The Closed Loop" This is an ambitious objective, involving many ideas that are not in common knowledge or widely accepted, so our immediate objective is to develop a careful and precise method to describe this process, and show how its widely diverse elements can be interpreted as a single idea The "Closed Loop" is a topological structure which is formed by twisting a simple topological object we call "the strip" and then connecting it back to itself, in the form of a "Moebius Strip", which takes the form of a closed loop "The strip" is a simple algebraic generalization of the concept of hierarchy defined as "the many/one relationship", as "the one" is partitined into "the many" by a process of discriminating stipulative definition This is interesting because there many definitions from a wide array of traditionally independent subjects that can be defined on this single structure This seems to open open a powerful and promising pathway towards establishing a solid common foundation for the collective human exploration or truth -- in all fields of inquiry and expertise PROJECT DESIGN Outline project vision and general dimensions Begin exact definition of "the strip" in all its facets and interpretations The strip is defined in (is composed of) "intervals", and every facet of it is defined as an interval Many of the basic/foundational idea of mathematics and ontology can be defined on the strip These definitions can be universalized. Show the closure of the strip into a loop VISION Existence/being prior to all analysis is a neutral/unmarked/undifferentiated space with no characteristics This idea has many precedents and interpretations in the history of philosophy This "prior to all form" space is analogous to "the continuum", and might be consistent with or a definition of the continuum This space may be consistent with or the same thing as the concept of "upper ontology" This unmarked space is "the common blackboard" on which all semantics and conceptual structure is written/defined In human beings, "motivation arises" (from somewhere, somehow) to define distinctions on this space, creating ways to conceptualize and encode similarities and differences with a system of labels As distinctions and motivation arise, this unmarked space can take any form, and describe any "thing" These distinctions take the form of words, letters, numbers and symbols, creating a semantics and system of categories This process can be defined with digital mathematical precision Any abstract object at any level of complexity can be defined by this process It may be possible to define a "generic algebraic object" (like a "synthetic dimension") for defining all abstract construction, including quantitative and qualitative properties All of mathematics, all of language and all of logic can be constructed in this way, working with a basic motivation function creating distinctions and assigning abstract structure and labels (words, sounds, labels, gestures, "signs", etc.) This project could emerge as a collaborative network across multiple sectors, each with their own motivation, contributions and issues THE CLOSED LOOP This project is defined on a topological structure that can be described as a "strip" (when seen in the flat 2-dimensional plane) or as a "loop" when subjected to a twist connecting point A and D and points C and B. This form is known as a "Moebius Strip", which is described as a continuous loop with one side and one edge. We are defining our basic "strip" hierarchy in this way because it forms a closed space that functions as a "container" for everything within it THE TECHNICAL/PHILOSOPHIC CHALLENGE When defined in classical mathematical and scientific/philosophic terms, this process involves a "massive simultaneity" of interdependent concepts and facets fitting together into one structure This process is a convergence or a fusion These generic definitions are suitable for "interdisciplinary mediation", because the broad principles are applicable for study or development across the complete sciences/humanities spectrum THE STRIP/LOOP MODEL IS INTENDED TO BE CONSISTENT WITH Basic well-understood mathematics Classical models of "the whole" or "the one" Classical theology from a variety of traditions (Judeo-Christian/Indic/Buddhist) THEORY OF MEANING The closed loop project includes and implies a theory of meaning, that considers How meaning is created, through intention, assertion and stipulation The structural composition of meaning The definition of words and concepts - how meaning is constructed Exploratory thesis: meaning may involve "making a point" (in a n-dimensional space) where "the point" is a bounded range defined in semantic rather than standard dimensional terms PRINCIPLES OF OPTIMIZATION It is clear that there are "many ways" to define or construct most or all of these objects and elements independently, and this multiplicity can appear to be "controversial", since there is no apparent basis for agreement among these methods, and no active connection or collaboration between schools of thought We argue that defining algebraic and semantic terms independent of some comprehensive system of definitions is misleading. Terms only have a meaning within a system where they play a well-defined role We are supposing that there is "one best method" for combining all of these elements into one common/shared framework, and the principles that govern this process why it is "the best way" can be clarified and made precise These principles certainly do include "Occam's Razor" and many other principles of good design involving simplicity and minimalism We are supposing that there are criteria for "linearly optimizing" the dimensions and features of this project, using "shortest path" principle that maximize processing speed and minimize complexity COSMOLOGY The entire idea can possibly be understood as a cosmology, or a framework with implications for cosmology It might be related to Sir Arthur Eddington's argument that physics can be deduced from epistemology The approach might be based on the principle that all science and physics and cosmology is actually defined in "concepts", which are disembodied models of reality, reinforced by mathematics and empirical observation COLLABORATIVE BRAINSTORMING Build breadth of scope and application: Collect and organize similar and related visions from all over the world and throughout the history of civilization Reduce redundancy: List and organize processes and methods that appear to be highly analogous (similar) in some way Explore consistency with existing domain-specific ontologies and consider methods of generalization. Can domain-specific models be understood as special-cases instances of broader principles? INTERVALS The Loop/Strip model is constructed in all dimensions and regards in terms of "bounded intervals". Every facet of the structure is defined by or as an interval. THIS STRUCTURE IS A SIGNIFICANT ANALOGY WITH Basic structure of abstraction Basic structure of hierarchy Basic structure of taxonomy Basic structure or meronomy - part/whole relations Basic structure of holism Hierarchy of value types (statistics, Stanley Smith Stevens) Binary or decimal number system and systems of measurement SCIENTIFIC MACHINE-COMPATIBLE EPISTEMOLOGY This model supports a complete mathematical theory of epistemology, including definitions of all basic terms from epistemology These terms include concepts like metaphor, similarity, analogy, simile, difference, equality, abstraction, generalization, and many others Many common pairs of "opposites" from epistemology can be given definitions on this framework, including pairs like "abstract/concrete" or "universal/particular" or "inductive/deductive" or "synthetic/analytic" or "bottom-up/top-down" Many types of "variables" can be defined on this framework, including the common terms from statistics "ratio, interval, ordinal and nominal" A COMPLETE THEORY OF MEASUREMENT AND DIMENSONAL ANALYSIS Define dimension Define unit Define comparison with a template COMPUTER-SCIENCE GROUNDED CONSTRUCTIVISM It may be possible to avoid many confusing or controversial issues from traditional philosophy by enforcing a "machine compatible constructivism" over terms and definitions. LINKS https://www.cs.uleth.ca/~fitzpat/apex-calculus/sec_continuity.html https://www.cs.uleth.ca/~fitzpat/apex-calculus/sec_limit_def.html https://www.cs.uleth.ca/~fitzpat/apex-calculus/sec_limits_one_sided.html https://www.apexcalculus.com/ https://www.cs.uleth.ca/~fitzpat/apex-calculus/index-1.html -- index of terms
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