The Digital Integration of Conceptual Form
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The Many Forms of Many/One
Universal conceptual form

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

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

Closed Loop Interval Ontology
An integral model of human thinking and awareness

Notes in progress, July 2024 | July 2019

The vision

This project introduction is written for readers interested in the cognitive psychology of concepts. It suggests an interpretation of psychological ideas in terms of mathematics and computer science. An introductory bibliography of recommended readings you can download is listed at the bottom of the page.

The Closed Loop model is a general theory of conceptual structure, intended to contain or "bound" all of human thinking - including mathematics, science and deep intuition - in a single "container" that is grounded in the continuum and in the infinite. It is a topological and geometric vision, defined in algebra, and consistent with traditional or ancient ideas from mysticism and philosophy. We call this universal container "the closed loop". --list Interesting related video

This claim is grounded in our vision and doctrine of "synthetic dimensionality", which is a recursive algebraic model of dimensionality where the values (units) of dimensions are abstract objects themselves decomposable into dimensions. This approach enables us to define qualitative as well as quantitative dimensionality, while still maintaining precision measurements. The Closed Loop is connected across its hierarchical levels by synthetic dimensions.

Synthetic Dimensionality proposes that ideas are composite structures formed from "distinctions" (noticeable differences - "differences that make a difference") which become coded in various ways (images, symbols, words) in the mind, formed into complex composite wholes (concepts, ideas), and which then become the framework for shared understanding in some culture (a language, a world view). Distinctions are generally coded in terms of dimensions as a range of values, defined in ways that span the quantitative/qualitative gap (the color "red" is a qualitative and approximate value for a numeric range on the color spectrum), and which can be organized into a hierarchy of "levels". This hierarchy defines the principle of abstraction across "lower" and "higher" levels, forming a spectrum ranging from specific to general, from particular to universal, from "many" to "one".

This spectrum is proposed as a general matrix framework for conceptual structure and semantic ontology. "Intervals" are the named spaces in the row and column intersections (cells) of this matrix, which are defined and bounded like matrix cells by values. It is proposed that every mathematical and semantic structure can be defined in this way, in one consistent framework, defined by one consistent method. This means the number system, it means logic, it means semantics, it means the construction of a rational world view.

This spectrum takes a form consistent with foundational definitions in mathematics and logic, including arithmetic, set theory, Boolean algebra, and geometry. It also contains a general theory of semantics, or the theory of meaning, showing how human beings create and communicate meaning by intention, defining a shared reality that can bind together a culture.

The Closed Loop spectrum is a model of hierarchy, a cascade of levels which show the combination and synthesis of "higher levels" from elements defined at "lower levels". Logical processes (deduction/induction) run across across this (top-down/bottom-up) spectrum.

The mysterious mystical/cosmological mathematics of the project emerges as this hierarchical spectrum is defined as a "strip", which can be twisted in a mysterious process that form this foundational ideas into a "Moebius strip" - an intriguing mathematical form with "one side and one edge". We call this form the Closed Loop, which becomes a container for all ideas and all human/conceptual thinking, at any level, about anything. It becomes a foundation for mathematics and logic, and it takes on a form which can be proposed as an interpretation of "Logos", or other supreme containers and models of logic from the history of philosophy. It becomes one boundary of zero width and infinite span wrapped around everything.

The Closed Loop is a general model connecting "The Many" to and into "The One", and sealing that general form into high stability. Today as this note is written, in our continuing creative process we are still seeing the Closed Loop "through a glass somewhat darkly", as there are many details of this very complex multi-part idea that must be brought into high order before this bold promise can be kept.

The unfolding of this work continues, one fragment at a time, as our database system continues to expand and the mysterious "general form of conceptual structure", containing and organizing this project, continues to come together like a vastly complex jigsaw puzzle, guided by visionary intuition, and fed and fueled by the enormous resources available on the internet today.

The revolution

A revolution can be understood as the completion of a rotation around a circle. A revolution can be defined in terms of cybernetics and "control" and governance. It begins as a response to noticeable weaknesses or failures in some current framework, which is no longer able to meet the needs of human experience as life continues to unfold, and "the system" begins to lose control. New ideas begin to be suggested and proposed. They may be fragmented, they will be controversial or ignored, they may not be accepted, they may involve challenging significant existing investments. But if the evolutionary pressures driving them do not relent, their creation will continue on the fringes until something fundamental shifts.

We are imagining and conceiving a revolution in the structure of knowledge: an integral transformation of thousands or millions of semi-independent conceptual fragments, into a single unified and self-contained wholeness defined as a comprehensively inclusive spectrum. We believe this emerging new framework can and should be defined in "cybernetic" terms, as we define knowledge in terms of control and the emergence of stability and certainty in a global field of complex interdependency.

  • In our framework, this spectrum is defined as the linear hierarchical decomposition of unity (the "unit interval") taking a form on which all intellectual structure and description can be mapped, with unbounded infinity at the top and the infinitesimal or continuum (infinitely bounded) at the bottom. This form is essentially hierarchical, taking a form like a general purpose and flexible taxonomy.
  • We are creating a series of mathematical definitions, considering all the basic concepts and principles inherent in semantic ontology and epistemology. This includes a definition of "concept', which we suggest can be usefully defined as a composite dimensional intersect, somewhat like a Venn diagram, taking varying forms depending on context. In an immediate context of communication, like a conversation between two people, the dimensions and values that define the concept can be stipulated in a flexible way by the speaker. Concepts can take a more stable form when these definitions must be consistent over time for broader or institutional use. All of these definitions can be spawned from the dimensionality of the Closed Loop.
  • This model then becomes a sealed integral unit when it is folded into the form of a Moebius Strip, a topological form which has only one boundary or edge or side, and which, under this twist of the unit interval, maps the infinite unbounded into the infinitesimal and continuous as a single straight line. All notions of larger and smaller disappear, and become only relative and "locally meaningful".
  • We show this process in the animated graphic at the upper right of the screen.

Today, we are living in a world of "silos" and specializations that are marginally consistent with one another. Too often today the right hand does not work well with the left hand. But we are proposing that this fragmentation is largely the fruit of the independent historical evolution of these elements, which today are gradually coming into closer and closer relationships. Where is the boundary of one discipline and the beginning of another? Are these boundaries more than habitual cultural artifacts? Are the deep levels of human intuition simply inscrutable to the close examination of quantitative methods and science?

We are saying "no" to these traditional and highly limiting assumptions. We are proposing that the traditionally independent elements and departments of knowledge can be fused into unity, through a common language and are seeing universal principles underlying all forms of categorization and conceptualization. We are proposing new and universal principles of measurement capable of spanning the traditional divisions (quantitative/qualitative). We are envisioning an integral form of knowledge as an essential step in the evolution of civilization and are exploring these ideas as a possible foundation for a new civilization based on wholeness and deeply shared universal principles.


This project combines deep universal mysticism with an interpretation of the classical foundations of mathematics. It is grounded in the best university-grade technical literature available, and is offered here as an opening into what seems to be a significant advance in holistic philosophy and psychology.

Closed Loop Ontology is indeed aimed at something unprecedented. But the power and breadth of its ambition and scope of inclusion does have precedent in the history of philosophy, and an example might be the "Mathesis Universalis" of Leibnitz, or in ancient explorations of the concept of "Monad".

This emerging new idea proposes that all ideas and "concepts" emerge from an enduring eternal "one" or "oneness" that is the ground of being and underlying invariant framework of all of existence and any potential for human knowledge or understanding. This idea is found in many sources, including Plotinus.

The power of this idea flows from the way this underlying framework is conceived, and depends on the notion that this relatively simple but bewitchingly tricky framework can be legitimately interpreted as containing all possible conceptual differentiations within the scope of its "bounded intervals". The notion of bounded interval begins with the unit interval - bounded between 0 and 1 on a straight line (the X axis) - and then unfolds from there as a cascade into infinite differentiations approaching the continuum, as the interval is cut up into smaller and smaller pieces. All these intervals, regardless of their "length" take exactly the same form. This model is absolutely linear and absolutely recursive ("self-similar" - like a fractal).

These ideas are fundamental to the traditional "foundations of mathematics", including ideas like "Real Numbers" and the "Dedekind Cut". We are working carefully with these same ideas - but we are blowing open some of the mysteries of the so-called "straight line". Traditional mathematical methods depend on an implict basis in Euclidean geometry - where it is presumed that it makes sense that "a line has no thickness". How can you define a "real number" on a line that can't actually exist? We say the foundational line does indeed have "thickness" -- which we can define in terms of "two edges"defined in a fundamentally digital (quanticized) space. In our model, the upper and lower edges of the line are also boundary values, within which is contained "everything" that the mind can conceive.

The entire structure of our Closed Loop can be understood as an interpretation of the concept of "unit interval" - which is normally understood as a line segment of unit ("1") length.

In the closed loop model, this segment is differentiated into parts, like decimal numbers - or in a simpler model, into binary numbers - which creates a "hierarchy" of multiple levels that extend from a unit at the top of the hierarchical cascade to any number of subsequent differentiations terminating in the infinitesimal and the principle of the continuum.

This model has several important and central interpretations. We understand it to be a) the general form of measurement; b) the general form of hierarchy and abstraction and taxonomy; c) the general form of a number system; d) the general form of an "interval"; e) a realistic definition of a "line" or the "real number line". It is a closed bounded space that contains all these foundational definitions at the same time, defined in consistent terms.

The closed loop model is extremely (or absolutely) ambitious. It's an attempt to generalize every form and type of concept - deriving them all from the same underlying process of differentiation, which cuts up the implicitly all-containing unit at the top of the cascade into every possible categorical combination - including not only numbers, but all elements (names, descriptions, measurements) that might appear in any sort of taxonomy.

Implied by this ambition are

  • A systematic and universal theory of word semantics and word meaning - one general-purpose model of word meaning that can interpret any language
  • A common framework that holds all language and conceptual form in a universal matrix that can adapt to any particular language

The topology of categories

Topology is a branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending.

This project presents a general theory of concepts and categories defined in geometrical and topological form. It presents a series of graphical models, such as the taxonomy of all mammals, which is commonly shown in graphical form.

The power of this approach depends on a simple topological deformations of basic common-sense or "3D" ways to understand categories.


  • "Closed loop interval ontology" is a universal model of the structure of concepts defined on a hierarchical spectrum of levels.
  • This spectrum takes the same form as a common measurement ruler, and enables us to define levels of abstraction ranging from empirical/quantitative to holistic/qualitative on a single consistent framework. This creates a continuous bridge across all levels of thinking and all academic and scientific disciplines.
  • This universal form can be defined on a "strip". This strip can be twisted to form a closed loop.
  • This opens the way to integrating all concepts into a single integral "master concept" that contains and organizes them all.
  • The process is grounded in a primal oneness and wholeness found in many world religions and spiritual traditions, ancient and modern.
  • This approach is entirely consistent with the foundations of science and mathematics and the great classical religions of the world. This framework enables a strong and unambiguous linkage between science and religion as an unbroken spectrum of levels.

The one

  • This project follows great classical precedents in philosophy, and grounds the derivation of all concepts and ideas in a primal "ground of being" which we call "one". It is similar to projects grounded in the concept of "monad".
  • Our definition of "one" is mathematical and based on the "unit interval", and is consistent with the foundational concepts of traditional working mathematics.
  • This framework is universal, and enables us to connect quantitative and qualitative conceptual forms in one consistent multi-level system of measurement, which enables smooth connection between empiricism and holism - or, intuitive terms, between science and religion.
The epistemology of concepts
  • Reality is understood by human beings in terms of concepts.
  • Concepts are like a map - an abstract symbolic representation of something in reality to which we are assigning a description and possibly a name (a word).
  • We are proposing that it is technically possible and mathematically correct to define "all possible concepts" on a single algebraic framework.
  • This single framework is intended to interconnect "all possible concepts" within a single "master concept" that contains them all.
  • This idea is proposed as the path to unity in human understanding - unity without uniformity, diversity and freedom in unity.
Boundary and interval
  • This project is about boundaries and how every form or shape or category in existence is defined by a boundary, in form of a minimum and maximum value
  • An interval is the space between boundaries

"The awesome hypothesis"

We propose that this general form maps all forms of measurement and defines all categories in a series of hierarchical levels

  • The range from A to B (X axis) is an unbounded interval and represents the infinite
  • The range from C to D (X axis) is the lowest possible level of differentiation approaching the continuum and represents the infinitesimal
  • The range from A to C and B to D (Y axis) represents the hierarchy of levels (increasing levels of abstraction or generality)

The closed loop

  • This master framework takes the form of a "closed loop" - a circle closed on itself to form a closed/sealed unit.
  • This closed loop is not defined on a single line - though it can be understood that way - but instead, on a "strip" that takes a hierarchical form.
  • This framework defines and universalizes the process of "abstraction" -- or the process of creating generalizations -- like the concept of "tree" which is a generalization/abstraction based on the example of many trees.
  • After we understand that all conceptual form can be mapped on this "strip", we then seal this framework by subjecting it to a topological twist, forming it into the "single-sided single-edge" topological object known as a "Moebius Strip".
  • This twist creates an astonishing integral effect that seems beyond human conceptual power, and locks the entire range of human thinking - including major sectors like science, mathematics and religion - into a single closed all-containing infinite form - where every part or level or layer can be smoothly mapped into any other, creating a comprehensive interdisciplinary and intercultural/inter-language model of reality and knowledge and language.
  • All culture and all differences among human beings reside somewhere on this framework.

What is a concept?


"Concepts are defined as abstract ideas or general notions that occur in the mind, in speech, or in thought. They are understood to be the fundamental building blocks of thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science.

"Concepts can be organized into a hierarchy, higher levels of which are termed "superordinate" and lower levels termed "subordinate". Additionally, there is the "basic" or "middle" level at which people will most readily categorize a concept. For example, a basic-level concept would be "chair", with its superordinate, "furniture", and its subordinate, "easy chair".

"When the mind makes a generalization such as the concept of tree, it extracts similarities from numerous examples; the simplification enables higher-level thinking. A concept is instantiated (reified) by all of its actual or potential instances, whether these are things in the real world or other ideas.

"Concepts are studied as components of human cognition in the cognitive science disciplines of linguistics, psychology and, philosophy, where an ongoing debate asks whether all cognition must occur through concepts. Concepts are used as formal tools or models in mathematics, computer science, databases and artificial intelligence where they are sometimes called classes, schema or categories. In informal use the word concept often just means any idea."

Examples of concepts: number, numbers, measurement, measurements, names, labels, units, sizes, colors, structures, properties, attributes, characteristics

"Concepts are built up from measurable distinctions - differences that make a difference"

Also see
"Concepts are the building blocks of thoughts. Consequently, they are crucial to such psychological processes as categorization, inference, memory, learning, and decision-making. This much is relatively uncontroversial. But the nature of concepts -- the kind of things concepts are -- and the constraints that govern a theory of concepts have been the subject of much debate (Margolis & Laurence 1999, Margolis & Laurence 2015). This is due, at least in part, to the fact that disputes about concepts often reflect deeply opposing approaches to the study of the mind, to language, and even to philosophy itself. In this entry, we provide an overview of theories of concepts, and outline some of the disputes that have shaped debates surrounding the nature of concepts. The entry is organized around five significant issues that are focal points for many theories of concepts. Not every theory of concepts takes a stand on each of the five, but viewed collectively these issues show why the theory of concepts has been such a rich and lively topic in recent years. The five issues are: (1) the ontology of concepts, (2) the structure of concepts, (3) empiricism and nativism about concepts, (4) concepts and natural language, and (5) concepts and conceptual analysis."

Information structures

Peter Wegner - Programming Languages, Information Structures and Machine Organization, 1968
A concept is an "information structure" - a concept from basic computer science diagram

  • What is an information structure?
  • How can everything we know about concepts be defined in terms that constitute an information structure?
  • Why is that a great thing to do?
  • Why hasn't it happened?

Types of concepts

    "A concept is a way to classify the world in your mind. The hierarchical model of concept classification includes three levels of concept: the most general is the superordinate concept, followed by the basic concept, and the most specific is the subordinate concept."
    In the simplest terms, a concept is a name or label that regards or treats an abstraction as if it had concrete or material existence, such as a person, a place, or a thing. ... For example, the word "moon" (a concept) is not the large, bright, shape-changing object up in the sky, but only represents that celestial object.
    The human nervous system is capable of handling endless streams of information. The senses serve as the interface between the mind and the external environment, receiving stimuli and translating it into nerve impulses that are transmitted to the brain. The brain then processes this information and uses the relevant pieces to create thoughts, which can then be expressed through language or stored in memory for future use. To make this process more complex, the brain does not gather information from external environments only. When thoughts are formed, the mind also pulls information from emotions and memories (Figure 1). Emotion and memory are powerful influences on both our thoughts and behaviors.

    In order to organize this staggering amount of information, the mind has developed a "file cabinet" of sorts in the mind. The different files stored in the file cabinet are called concepts. Concepts are categories or groupings of linguistic information, images, ideas, or memories, such as life experiences. Concepts are, in many ways, big ideas that are generated by observing details, and categorizing and combining these details into cognitive structures. You use concepts to see the relationships among the different elements of your experiences and to keep the information in your mind organized and accessible.

    This Wikipedia page outlines many of the most important type of thinking -- all of which are included in our simplifying holistic model.

    Interesting/long list of types

Hierarchical graphics

two shall become one


Introductory readings
Click to download

1. Categories and Concepts, , Douglas Medin, 1981
Clarifying survey of concept theory as it was emerging at that time. Provides clear insight into dimensionality of features, and comparison of various alternative interpretations and models of concepts. A landmark paradigm for concept theorists, still very helpful.
2. Women, Fire and Dangerous Things, What Categories Reveal About the Mind, George Lakoff, 1987
Powerful and detailed review of the theory of concepts from the point of view of metaphor, analogy and family resemblance
3. No Boundary, , Ken Wilber,
Chapter 2 of integral philosopher Ken Wilber's pioneering account of boundaries and distinctions and categories, and his thesis that "where the line is drawn, there the battle begins"
4. Number: The Languages of Science, , Tobias Dantzig,
"This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands.
- Albert Einstein

The basic structure of "hierarchical levels" is shown in the definition of whole numbers, displayed here in decimal and in binary.