Closed Loop Interval Ontology
       The Digital Integration of Conceptual Form


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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
Idealized democracy

Objectives and strategy
Reconciliation and integration

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?

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

Dimensions of set theory

What is a number?

Venn diagrams
Topology of sets

Objects in Boolean algebra
How are they constructed?

Core vocabulary
Primary terms

Core terms on the strip
Closed Loop framework

Hierarchical models

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

What does it mean?

Formal systematic definitions
Core terms

Data structures
Constructive elements
and building blocks

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

From other sources

Foundational computation

Objectives and strategy
Reconciliation and integration

Primary objectives of this project

  • Propose the interpretation and development of the Closed Loop as a universal container for all conceptual structure, including science, mathematics and philosophy
  • Define a common foundation for semantic ontology, cognitive science and the quantitative sciences
  • By defining them within a common spectrum, reconcile major competing alternative perspectives within semantic ontology and the cognitive science of categories
  • Identify related technical disciplines where foundational definitions commonly overlap, particularly when that overlap becomes confusing or fragmenting
  • Help overcome what can be perceived as fragmentation in the sciences and the humanistic disciplines, as the world of intellectual inquiry appears scattered into thousands or millions of semi-independent fragments developed from a local point of view without respect to the larger whole.

Show how this works, in a precise way that is consistent with both engineering methods and the common standards for mathematics, logic and semantics.

Clarify the basic structure of the Closed Loop

Extreme simplicity as a foundation for extreme complexity

The Closed Loop is a structure of extreme simplicity which embodies a potent array of complex interpretations. Many foundational concepts in science, mathematics and philosophy can be understood as interpretations of this simple but subtle and beguiling algebraic structure. We understand it as a "general form" that functions as a container and ordering principle for the foundational definitions of science and philosophy.

These foundational definitions include number, measurement, the relationship between quantity and quality, systematic method for defining categories and concepts, the notion of abstraction and hierarchy, and the concept of dimension as common to both quantity and quality.

A spectrum of levels

The world can be understood through a natural spectrum of levels that is innate to human thinking, and which undergird and support all human understanding, in any discipline or social sector.

Abstraction and levels of generality are or can be directly linked to specific concrete instances, as is illustrated by a common taxonomy as originally conceived by Linnaeus. But this process becomes complex, and can be understood in endless numbers of alternative and logically-independent ways, which keeps the discipline of ontology and semantics fragmented and scattered and divided by what appears to be controversy.

We propose a single integral container, a single source from which all essential definitions can be derived, a single container which links all "concepts" together within a single framework.


In some sense, the Closed Loop "stands outside of time". It contains time. It is proposed as a single framework that contains "every concept at once". All concepts can be derived from it. All concepts are held within it.

Postulate a system

The idea of the Closed Loop is a proposed interpretation. It does not "exist" as a concrete empirical observable thing in the world. It is created, it is visualized, as a way to consistently interpret the phenomena of mind and intellect and science.

It is a "human design" -- a "synthetic creation" that we can visualize as a pathway towards integration and common ground. It is a method of reconciliation. It is a way to "fit the pieces together" into a single whole.

Definitions do not stand on their own, as independent objects or discoveries. Every concept or or idea within the Closed Loop model is defined within the context of "system", and has no precise or arguable meaning outside the context of system. It is in the relationships and interdependence of concepts that mathematical ideas become meaningful, and the fragmentation of the sciences cannot be overcome without recognizing this point.

Every definition becomes meaningful in an interdependent mutually-interconnected way. The fundamental postulate that holds all of this together, as the foundation and framework and invariant container for the system, is the postulate of the Closed Loop.

This project
Creative method for this project
The wide-band method
Constructing semantics from the ground up
Reconciliation of perspectives
Assembling process
List of data structures
Units of measure

This project
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As they presently stands (April 2021), this project and database and web system are primarily creativity tools, as we explore a very ambitious possibility, and continue to gather ideas and themes that might play a role in realizing the broader objectives.

There are obviously many themes woven into this framework, generally led by the persistent notion that they can be integrated in some powerful and significant ways. Whether that is true remains to be seen, but this work continues, and is becoming increasingly sophisticated and capable, as we devise better ways to interconnect fragments.

Mon, Apr 12, 2021

Creative method for this project
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There is a tendency for this project to become a completely fragmented "free-association jump-about" - as the creative process simply moves from one interesting subject to another, without that movement making coherent sense within the context of the whole, or bearing fruit for this project.

To some degree, this is unavoidable, and probably right the thing to do. After all, we do want to embrace all these subjects, and we want to do that in an informed and documented way.

This is "brainstorming, over the long haul, with support from a fairly well-organized database system which enables us to rake this harvest into neat piles.


Bu we need to discipline this process.

Pick a central theme or "theme group" -- and go find a few or ten links and Wikipedia articles around it, and punch them into this framework.

One I want to look at right now -- is "equality". How many fertile synonyms does it have? How many threads does it open?

I want to take a little time right now to see what that thread leads to.

Equality Isomorphic Identical Identity Similarity Ship of Theseus Can't step into the same river twice

Sun, Apr 18, 2021

The wide-band method
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I have been describing this project as "wide-band" -- by which I mean "take on many interrelated subjects at the same time, without necessarily delving too deeply into any one of them, at least at the beginning."

Get a marker for the topic (theme) into the framework, and note why it is important and what's exciting about it. But don't struggle. Just get in there, try not to be stupid, and have a good reason why it's included.

All these subjects ARE important within the broad context of this project and its large objective.

It's stimulating

All these topics ARE part of the larger broad goal -- which should be defined here

we DO want to address and consider all these topics in an integral/integrated way

so yes -- we risk being "a mile wide and an inch deep" -- true. But let's take that chance.

We are sketching out the dimensions of inclusion

List of academic and scientific disciplines

List of issues approached considered addressed

Master vision and statement of the broad objective -- how dare we? well, here's the reasons we dare....

Why are we doing this, why is it important, why is it feasible, how can epistemology and categories and semantics help guide the world into something lifelike and sustainable and workable

we want "whole systems"

we want cooperation

we want efficiency

we want authenticity

we want to lift the smog -- of idiotic or mindless or ignorant philosophic confusion

Sun, Apr 18, 2021

Constructing semantics from the ground up
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In its furthest and most ambitious reach, this project might be understood as an attempt to characterize and define all semantic objects in any language in terms which are constructed from the ground up -- from an absolute lowest level -- from a simple structure of "bits" -- of simple on/off switch positions.

Supposedly, this ambition takes something like this form:

  • Bits (two-state switches, either 0 or 1, off or on) build the simplest data structures
  • Simple data structures build complex data structures
  • Complex data structures build concepts

What is the relationship between a "data structure" and a "concept"?

We are saying that a concept is a complex data structure. A concept is an intersection of dimensions, that creates something like a bounded region in N dimensions.

That bounded region is given a name, and it becomes a word meaning.

Mon, Apr 12, 2021

Reconciliation of perspectives
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Philosophical perspectives on reality -- what is real

FRISO project standards

John Sowa on basic perspectives

Theory of categories

Classical view

Family resemblance

Metaphor and analogy

Integration of alternatives by recognizing unique value and authenticity of each perspective -- they are not really competing alternatives, but methods serving slightly different purposes


There are substantial lists and systems that review and compare these alternatives in various ways. We should be familiar with them, and make sure we are actually including all the major points raised by any of these perspectives.

More or less, our idea is that yes, it does make sense that there are "contending points of view" on these issues -- but that is generally not because one point of view Is "correct" and the other "wrong" -- but that the perspective adopted depends on the purpose at hand (and perhaps some other factors, like inexperience with other purposes).

This tends to create the appearance of conflict -- and no doubt has led to actual conflict. But an "integral" perspective should be transcendent to these divisive issues -- and should "contain them as subsets of itself". We're seeing this as a realistic and desirable objective.

Thu, Apr 8, 2021

Assembling process
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We want to define precisely how it is that the closed loop (hierarchically-partitioned moebius strip) can be interpreted as a universal foundation for conceptual structure.

This is complicated ambition with a lot of moving parts, and the idea is still unproven and intuitive. List these elements here to help guide the coalescence. We need a comprehensive list of these elements, and we have to explain or justify them all individually in a consistent way.

This list is a design for project architecture:

  • The pieces that are to be combined
  • The way in which the pieces are to be combined
  • The themes and principles and methods that are brought together in one place
  • The concept of "isomorphic recursion" defined across many simultaneous objects or concepts


  • Develop a list of terms and words that are synonyms for "category" -- any dimensionally-bounded unit
  • Develop a list of terms that are synonyms -- or can be defined as synonyms -- for boundary value or "cut" -- the "line that cuts a line" to form a distinction

Type of objects that are defined through isomorphic recursion and connected to build a model of reality:

  • Abstract
  • Symbolic - representational
  • Concrete (referent?) or "actual"

"What can be done with little boxes"?

Everything is defined by a box (a bounded interval) containing some symbolic structure, composed of alphabet or numbers..

Everything is matrix

matrix can define everything -- to within some error tolerance

Mon, Apr 5, 2021

Closed loop interval ontology
Objectives and strategy

List of data structures
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In progress, taken straight from Wikipedia as a strong starting point for a comprehensive list. We might not need all these types, but they are an interesting study. What are the fundamental constructive objects ("basic building blocks") and what are the more composite objects -- complex structure built from simpler structures

  • Data types

    • Primitive types

      • Boolean, true or false.
      • Character
      • Floating-point numbers, limited precision approximations of real number values.
      • Including Single precision and Double precision IEEE 754 Floats, among others
      • Fixed-point numbers
      • Integer, integral or fixed-precision values.
      • Reference (also called a pointer or handle), a small value referring to another object's address in memory, possibly a much larger one.
      • Enumerated type, a small set of uniquely named values.
      • Date Time, value referring to Date and Time

    • Composite types or non-primitive type

      • Array (as an example String which is an array of characters)
      • Record (also called Associative array, Map, or structure)
      • Union (Tagged union is a subset, also called variant, variant record, discriminated union, or disjoint union)

    • Abstract data types

      • Container
      • List
      • Tuple
      • Multimap
      • Set
      • Multiset (bag)
      • Stack
      • Queue (example Priority queue)
      • Double-ended queue
      • Graph (example Tree, Heap)

      Some properties of abstract data types:

      Structure Order Unique List yes no Associative array no yes Set no yes Stack yes no Multimap no no Multiset (bag) no no Queue yes no Order means the insertion sequence counts. Unique means that duplicate elements are not allowed, based on some inbuilt or, alternatively, user-defined rule for comparing elements.

      Linear data structures A data structure is said to be linear if its elements form a sequence.

      Arrays Array Bit array Bit field Bitboard Bitmap Circular buffer Control table Image Dope vector Dynamic array Gap buffer Hashed array tree Lookup table Matrix Parallel array Sorted array Sparse matrix Iliffe vector Variable-length array Lists Doubly linked list Array list Linked list Association list Self-organizing list Skip list Unrolled linked list VList Conc-tree list Xor linked list Zipper Doubly connected edge list also known as half-edge Difference list Free list Trees Main article: Tree (data structure) Binary trees AA tree AVL tree Binary search tree Binary tree Cartesian tree Conc-tree list Left-child right-sibling binary tree Order statistic tree Pagoda Randomized binary search tree Red–black tree Rope Scapegoat tree Self-balancing binary search tree Splay tree T-tree Tango tree Threaded binary tree Top tree Treap WAVL tree Weight-balanced tree B-trees B-tree B+ tree B*-tree B sharp tree Dancing tree 2-3 tree 2-3-4 tree Queap Fusion tree Bx-tree AList Heaps Heap Binary heap B-heap Weak heap Binomial heap Fibonacci heap AF-heap Leonardo Heap 2-3 heap Soft heap Pairing heap Leftist heap Treap Beap Skew heap Ternary heap D-ary heap Brodal queue Trees In these data structures each tree node compares a bit slice of key values.

      Tree (data structure) Radix tree Suffix tree Suffix array Compressed suffix array FM-index Generalised suffix tree B-tree Judy array X-fast trie Y-fast trie Merkle tree C tree Multi way trees Ternary tree K-ary tree And–or tree (a,b)-tree Link/cut tree SPQR-tree Spaghetti stack Disjoint-set data structure (Union-find data structure) Fusion tree Enfilade Exponential tree Fenwick tree Van Emde Boas tree Rose tree Space-partitioning trees These are data structures used for space partitioning or binary space partitioning.

      Segment tree Interval tree Range tree Bin K-d tree Implicit k-d tree Min/max k-d tree Relaxed k-d tree Adaptive k-d tree Quadtree Octree Linear octree Z-order UB-tree R-tree R+ tree R* tree Hilbert R-tree X-tree Metric tree Cover tree M-tree VP-tree BK-tree Bounding interval hierarchy Bounding volume hierarchy BSP tree Rapidly exploring random tree Application-specific trees Abstract syntax tree Parse tree Decision tree Alternating decision tree Minimax tree Expectiminimax tree Finger tree Expression tree Log-structured merge-tree Lexicographic Search Tree Hash-based structures Bloom filter Count-Min sketch Distributed hash table Double hashing Dynamic perfect hash table Hash array mapped trie Hash list Hash table Hash tree Hash trie Koorde Prefix hash tree Rolling hash MinHash Quotient filter Ctrie Graphs Many graph-based data structures are used in computer science and related fields:

      Graph Adjacency list Adjacency matrix Graph-structured stack Scene graph Decision tree Binary decision diagram Zero-suppressed decision diagram And-inverter graph Directed graph Directed acyclic graph Propositional directed acyclic graph Multigraph Hypergraph Other Lightmap Winged edge Quad-edge Routing table Symbol table See also Purely functional data structure

      Mon, Mar 15, 2021


      Objectives and strategy
      Data structures

Units of measure
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We want to explore conversion systems between units of measure, considering the question of whether or not there are "optimal" ways of organizing conversion.

As we look around at that issue, we will post some links to places and systems that are doing unit conversion

Please visit us at We support unit conversions for all units sharing the same dimensionality.

There is DRUM (Digital Representation of Units of Measure) -

Thu, Apr 8, 2021