The Geometry of Change V3

In this blog I Combine (Conformal) Geometry and Change-management

This is Version 3.

Christi Belcourt (Métis) - The Wisdom of the Universe, 2014
Christi Belcourt (Métis) – The Wisdom of the Universe, 2014

Julian Barbour (Physicist, writer of the book “The end of Time“): The only thing that Exists in our Universe are Changing Shapes. “There is no invisible river of time. But there are Shapes that you could call Instants of Time, or ‘Nows‘. As we live, we seem to move through a succession of Nows, and the question is, what are they? They are arrangements of everything in the universe Relative to each other in any moment, for example, now“.

Currently we measure Time with an artificial constructed (atom-)Clock. Before the invention of the clock time was related to the cyclical processes in the year that were related to the movement of the (Male)Sun and the (Female)Moon.

The big patterns were related to the movement of the Stars that are related to the Precession Cycle. At that time the Map of the Sky and the Map of the Earth were aligned.This means that the maps of the Earth are projections of star maps but also that the locations on earth where looking like the patterns in the sky. A good example is the Seven Cities of Paul in the Apocalypse that were aligned to the Pleiades.

The Geometry of Shapes (“Similarity Geometry“) is the most important geometry because it contains the Potential of creation. This Geometry corresponds with Mythic in paths of Change (the Creative Personality) and Equality Matching in the theory about Social Relationships of Alan Fiske. It can also be found as the Hero in the Myths of all Cultures researched by Joseph Campbell., the Fool (o) in the Tarot, Zero in the Numbersystem and Λ or in Set Theory.

The number of steps in the Hero‘s Journey corresponds with the cards of the Major Arcana of the Tarot (-> To R AT, RO T AR,..).

In the Beginning

The blog begins after a few Video’s about the current insight about the Geometry of the Universe. It looks like our Universe is without a beginning and an end but also without Time and Space. It is filled with Infinite Possibilities.

The Tao-Te Ching:

The Tao is like a well:
used but never used up.
It is like the eternal void:
filled with infinite possibilities.

It is hidden but always present.
I don’t know who gave birth to it.
It is older than God.

In Hinduism, a Kalpa. , a Cycle of a Universe, is equal to 4.32 billion years, called a day of Brahma . In Hinduism, Brahmā (Sanskrit: meaning “swelling” or “expansion”) is God in his manifestation as Creator of the universe. Brahmā is part of the Trimurti (the Hindu Trinity) alongside Vishnu and Shiva. Brahma lives on top of Mount Meru (look at the triangle on the head of Brahma) also called Pascal’s Triangle (see Chapter 9).

Lord Brahma, the Hindu God of Creation - yogalife


What is the relationship between symmetry and conservation laws. This has to do with the numbers you use for instance -1. When the rules contains a square 1**2 = (-1)**2 but also (i)**2=(-i)**2=-1.


When we push all the shapes together they will become a Black wHole. What is able to create such a Force? What lies behind the Black Hole? The Nothing, Empty Space? Is Empty space Possible? Is the Sum of Things Zero or Infinite (8)?

How small do we have to go and what energy do we need to “see” gravity? Why is gravity very different from electro-magnetism and what have we learnt from the last few years? According to Einstein Gravity is a distortion (“curvature”) of Minkowski-Space-Time but the Universe seems to be outside time and is curved in a completely different opposite way called a Anti-DeSitter Space.
In this space we live on the surface that looks like a square (not a volume). We are framed in a Black Hole that is slowly evaporating ceating a new Universe that starts with a Big Bang that is not an explosion but a slow motion expansion until the limit is reached. It looks like Ancient Indian Cosmology is right.
Phase changes are related to the closeness of the parts. What happens when parts are closely packed. What phase is this? a Bose Einstein Condensensate? Is the Universe going through phases repeating the same pattern again and again?

About the Conformal Booststrap : Geoffrey Chew, “Nature is as it is because this is the only possible nature consistent with itself,”

It is possible to unite all the different theories of the universe by playing with the the Dimensions and geometry of space which could be flat or curved in a positive or negative way.

The explanation for the data we have gathered about the beginning is that there wwas no time in the beginning which is the same explanation as the conformal bootstrap above. A universe without time is infinite but not in space. An universe without time that is not infinite in space can only be explained by an infinite converging sequenc. This is called an Anti-de Sitter-Space, a space with almost zero curvature which looks like flat space.
About the Cyclic Universe. In the beginning the Universe was so chaotic (“hot”) that their was no mass so gravity was not existent. In every stage (Kalpa) of the Universe a new Big Bang occurs that repeats the beginning.
What happens on the edge of the universe.
About Conformal Field Theory but now from the perspective of the Holographic Universe.
About the iconformal (CFT) bootstrap.CFT is a mathematical way to map many physical theories using a conformal transformation which a transformation that preserves angles (examples rotations, translations). If you are not interested in background information skip this one.
Again about Conformal Fields but now by a very good teacher Leonard Susskind.

List of Chapters

  1. The Pragmatism of Charles Sander Peirce, an Introduction into Semiotics plus an advanced application of Semiotics to determinate the beginning of our Universe by moving to Zeroness
  2. Thinking about Thinking: About the Implicate Order of David Bohm and Jiddu Krishnamurti
  3. About Hyperspace: Predicting the Future by Observing the Observer, The Mathematics of Hyperspace, about the Soul, Moving out of the Body, Healing and the Big Bang that never was
  4. The Geometry of Finite and Infinite Games, The role of the Trickster
  5. Science: Filosophy The future of Artificial Intelligence
  6. Foundations: Symmetry, Contradiction,Duality & Polarity
  7. Geometry: Spiritual, Indian, Curved Space, Topology,
  8. Theory of Measurement
  9. Mount Meru: About the Triangel of Pascal in Indian Music, Achitecture and Mathematics
  10. This blog is a fusion of blogs about Projective- and Algebraic Geometry with a blogs about Panarchy, Resilience and Anti-Fragility , the Future of the State and Complexity Theory
  11. Projective Geometry and the shared viewpoint Constructing by Connecting
  12. Introduction to Change Management
  13. Change Management and Affine Geometry
  14. Euclidian Geometry and Change Management, about the Horizon, MindScapes and Meta-systems
  15. Projective Geometry, about lines points and the shared view
  16. Similarity Geometry and Being Different, Creativity and the Holy Ghost
  17. Mappings between Geometries Moving back to Panarchy, what is a Geocology?

Chapters 1-12 are about Geometry, Mathematics and Physics.

In chapter 3 I will show you how a new concept of Space is able to produce a Theory of Everything that explains the Para-Normal.

From chapter 10 on I describe the relationship between geometry and change. I will show that our Embodied language already contains everything we have to know about geometry.

As an example, reflect on what we are projecting on What when we design(“ont-werp“) and what Scape we See when we are projecting.

IMAGE: Leonardo's perspectograph
The Perspectograph of Leonardo Da Vinci

This blog is still under Construction.

1 The Pragmatism of Charles Sanders Peirce

Writing chapter 12 has generated (as always) many issues I never thought about before. The major cause is Charles Sanders Peirce , (1839-1914) the “inventor” of Semiotics and the first Pragmatist in the Us. He believed that science is finished when the theories are working in Practice but also that the Laws and Constants of Nature are changing all the time.

 In this blog you wil find out that current science has moved far away from he path of converging because it lost its foundation. This foundation lies behind the imagination in the nothing.

After my encounter with Peirce I stumbled upon The theory of J. W.Dunne who experimented with predicting the Future and discovered Hyperspace.

Looking for Hyperspace gave the link to ANPA, an organization of scientists who try to understand the Paranormal. After that I rediscovered (New) Thinking Allowed (NTA), a YouTube-channel of Jeffrey Mislowe, a wellknown para-psychologist.

I (re)discovered NTA because I have always been interested in the paranormal because I was ” paranormal” since I was a child. Ghosts visited me when I was young and when I was older I became “enlightened” (“a terrifying experience”).

Looking for an interesting issue on NTA I rediscovered Alien Abductions and the Grays (our descendants out of the Future), an issue I also encountered when I met the medium Judith Moore. by accident. She helped me to understand what was happening to me after my Jump of my Kundalini that caused many strange effects. Through Judith I discovered that I was of the lineage of the Persian Magi.

As you can see this Blog grows by accident because I Explore (a connection between the Imagination and Action) every Possible paths just as Nature is doing.

Introduction in Semiotics

If we are to proceed in a logical and scientific manner; we must; in order to account for the whole universe; suppose an initial condition in which the wholeuniverse was non  existent; and therefore a state of absolute nothing:…We start; then; with nothing; pure zero: But this is not the nothing of negation: For not means other than; and other is merely a synonym of the ordinal numeral second: As such it implies a first; while the present pure zero is prior to even first: The nothing of negation is the nothing of death; which comes second to; or after; everything: But this pure zero is the nothing of not having been born: There isno individual thing; no compulsion outward nor inward; no law: It is the germinal nothing; in which the whole universe is involved or foreshadowed: As such; it is absolutely undefined and unlimited possibility  boundless possibility There is no compulsion and no law: It is boundless freedom:(Collected papers of S. Peirce, 1931)

This is a Very compact explanation of Semiotics. Peirce uses a model with 3 components that he calls first-ness (1), second ness (2) and thirdness(3).

1stness is the Senses, 2ndness are the Emotions (Social in PoC, the Other). They are a power, force, a resistance but also a Relation (Duality).
3rdness is the Mind (Unity in PoC), patterns, habits. Interesting is that Peirce forgets the Imagination which could be the influence of the Enlightenment.

When you look at he 2 pictures below who are taken out of the second link about Semiotics you can see that the Representamen is an intermediary beween the Duality of the Object (Event, Outside) and the Subject (Inside, Square, (Mind<-> Senses)<-> (Emotions<->Imagination).

Observe that it is possible to substitute the first picture in the second picture at he place of the Human. In this case the sequence becomes Nature->Object->Human-Interpretant ->Culture. You can extend the chain as long as you want by filling in new Trialities.

Peirce has produced an enormous amount of documents that still need a lot of specialized scientists to interpret what he meant.

It is very clear that Peirce used a “fractal” model without knowing what fractal (Recursive) meant.When you look at Paths of Change Peirce used connected triangels as you can see in the Path of the Human Hero a model of the MetaMyth.and the Trickster who plays the role of God always teasing and stimulating us to Explore and Create because we are the real Creators made in the image of God.

In the third picture below you see that the Triangel is a Connection of 3 Dualities.

About the Semiotics of Physics.


The metamyth is a model that contains all the myths in every culture. This myth is defined by Joseph Campbell in his book The Hero with a thousand Faces.

The Metamyth defined with the model of Paths of Change.
Observe that it is possible to define more triangels when you connect Unity (Modelling) and Social (Values) or break open the four Squares who are connections of two Triangels. In this case the amount of Possible Paths explodes.
Defining possible paths between ” virtual particles” (“Temporary States“) is the essence of modern Physics that is caused by the invention of the Path Integral by Richard Feinmann.
The model of Paths of Change containing Four Independent Worldviews that make 12 combination because all of the connections are Bilateral.

2 Thinking about Thinking

David Bohm, the successor of Albert Einstein came into contact with the Indian philosopher Jiddu Krishnamurti chosen by the Theosophical Society as the new Maitrea . They started to find out what lies behind Thinking what they called the Implicate Order. In this blog you will learn that the Implicate order is the Vacuum(“Empty Space”) sustained by our Imagination.
Freeman Dyson about the Path Integral of Richard Feinmann.
Sheldrake is a follower of Peirce.
When you start to study Science you have to start with Rupert Sheldrake a scientist who came with a highly ignored theory that reality is influenced by the majority of the behavior of others. This implies that bbehavior spreads in TimeSpace without Direct physical contact and is picked up elsewhere. You can also explain this by believing that Structure is a Field and just as in Quantum Mechanics parts that are connected stay connected using “bridges” in space-time that are Magic to us just as Einstein called them “spooky action at a distance”1.
The return of American Pragmatism.

3 About HyperSpace

Predicting the Future by Observing the Observer in Hyperspace

in 1924 J.W. Dunne detected that he and his friends where able to look in the Future and the Past by moving into a state of Lucid Dreaming. He discovered that there are 3 levels of SpaceTime in which an observer is observing an observer that could be the same observer. The big problem, of this theory is called infinite regress. The model has no end. In the next video you learn how you can transform an infinite series into a converging series that simulates Space.

The Mathematics of Hyperspace

Louis H. Kaufmann About Spacetime Algebra. Sometimes Algebra starts with No Thing that could be not a thing but also be nothing or the void. By using a tautology A=B Kauffman develops numerical patterns that start with the beginning (void, nothing, zero) and move into infinity. These patterns contain meta-patterns (orders) that can be interpreted as a rhythm that look like a wave that connect cycles in cycles that contain particles that are the anti-particle of itself that can be described by a Clifford Algebra (also called Geometric Algebra) which is an extension of the Imaginary (i) numbers i with j and k where i.j.k.=-1.
Doug Matzke Hyperdimensional Reality. How Intelligence can be explained by points that are “close” in a hyperdimensional Space (“synchronicity“) and the experiments by Robert Monroe (leaving the body) , William Tiller (the Placebo Effect) and others.
Interview with Robert Monroe about Out-of-the-Body Experience .
What is a hyper-Space? This is a visualization.

4 Infinite Games

This is Version 2. In this version I have finished the Educational part of this blog (Chapter 1) and I have started to write about the Geometry of Change. in chapter 12.

In this part I advice you to spend some time on a video of George Lakoff one of the Leading Scientists in Embodied Cognition . This part of Cognition Theory is based on the Fusion of Complementary concepts (“Bisocation“).

Will McWhinney gave me a book of J.P. Carse called Infinite Games. Infinite games are the opposite of the Finite Game that ends when somebody has won. The Infinite Game is a Game that Creates Games. It is the game of the Trickster. The same Dichotomy can be found in the difference between a Vocation and a Career. In a career (a Racetrack) you Win or Lose.

Hopi Raven Trickster . Raven Steals the Light. Famous Flemisch Trickster Tijl Uilenspspiegel (Mirror of the Owl) .
The Trickster Tijl Uilenspiegel with the Owl in his Left (Magic) Hand and the Mirror of Cycle of Life (the Zodiac) in his Right Hand.

In this blog you will find that the Finite Game of the Controllers is related to Affine Geometry (Order, Ranking, Being the Same) and the Infinite Game of the Trickster to the Similarity Geometry (Being Different). There are two more Geometries that are related to Measures (Euclidian) and Connections (Projective).

Why Science is an Infinite Game.

5 Science

This is a Part of a long series about the Philosophy of Science in which you see the Perspectives of Paths of Change come back united with an idea about How to Do Science in which we learn from our Mistakes.

Artificial Intelligence

We are witnessing the birth of Artificial Intelligence (AI). AI has nothing to do with Intelligence. It is producing Artificial Humans that beat humans in many area’s (Chess, GO) but still not in Mathematics. Just like you’re calculator you have the choice to be dependent on a machine or to become an exception a human who is able to calculate by Head. Every new Technology makes us more dependent from this new technology (“the so called Automation Paradox)

This a Generator of Cycles where the Stages of the Cycle are determinated by Paths of Change The generator is a Fractal pattern. The (meta-)model behind the Generator is the Chinese Lo Shu (a 3×3 Magic Square) that turns into the Sheng Cycle when you connect the points.
The Cycle Generator applied on Technology shows that we are approaching a new Era in which we will see a Global Brain emerging.

6 Foundations


This is one of the most interesting documents about the Foundations of Physics and Mathematics I have read for a very long time. It shows what I already wrote down a few years ago about Geometric Algebra that the Number system opens up new number systems when to want to Reverse what you did.

The Positive numbers end by zero and move over to the negative numbers. When you standardize repeating adding and call it multiply dividing ends when you reach zero. Repeating multiplying generates the square roots that end with the negative numbers generating the Imaginary numbers (i=SqRT-1) but this is not the end. Generalizing the imaginary numbers (the Quaternions) created numbers nobody understood until it was found that they are Rotations in N-Dimensional Space.

Peter Rowland surprises by showing that the symmetries in the symmetries show the Implicate Order of David Bohm and more important that zero (“truly empty) is the Beginning (“alpha”) and the end (“omega”). Which means that the universe is always in balance.

Duality & Polarity

If a statement is true its Negation is also true. In geometry Points also called incidents are lines that Meet and Lines are unions of Points. A point is not-Space and is empty and Flat space is a union of lines. True Statements can be rephrased with different components that create new truths about existing components. The next step is Category Theory in which you can reason with theories (called Functors) as objects called Types.

Marvin Minsky About Triality.
Marvin Minsky: About Artificial Intelligence.
An Alternative view on the reason why there is Dark Matter based on the theory of Peter Rowland. Rowlands asserts that physics and mathematics are even more intertwined than we commonly believe, and that quaternions together with the assumption that zero is the natural start and end state of all physical reality is enough to derive all of quantum mechanics including Dirac’s and Schrödinger’s equations.
A presentation about the Theory of Peter Rowland.
In 1972, Frank Wilczek was 21 years old. He and his thesis adviser, David Gross, discovered the basic theory of the strong force — the final pillar of the Standard Model of particle physics. Their work revealed the strange alchemy at work inside the nucleus of an atom. It also turned out to underpin almost all subsequent research into the early universe. Wilczek and Gross went on to share the 2004 Nobel Prize in Physics for the work. Frank wrote a new book about Complementarity which looks a lot like duality and polarity. Deep below the universe two forces are creating a subtile equilibrium in which energy is given and taken.
Frank Wilczek explains Physics with the help of the same insights of Maxwell who detected the Electromagnetic Field. Maxwell used a model based on the 3 colors we use to make all the colors we see by mixing and adding intensity. Frank shows that Physics can be explained by so called property-fields in which complementary forces combine to make other complementary forces that keep Balance. Stangely enough this is the same as the model of Panarchy that describes an ecology. Is the Universe an Ecology of different shapes?
Time crystals
A Time-Chrystal When time crystals were first proposed in 2012 by physicist Frank Wilczek they seemed like an exotic consequence of quantum mechanics in systems of many interacting particles. Wilczek argued that such systems broke symmetry in time, changing so as to return periodically to the same state just as ordinary crystals exhibit periodicity in space.
Subsequent experimental work has found that quantum time crystals can exist in systems maintained out of equilibrium by some driving force. Now Norman Yao of the University of California at Berkeley and colleagues suggest that time crystals can arise without the need for quantum physics at all.


The third video is about the emerging Global Brain. The first two video’s are about the Foundation of Mathematics which is based on Contradiction . The fourth video is about the Human Relationship theory of Alan Fiske.THis theory is a Bridge between Geometry and Change Management.

About Global Brain. By connecting many specialized local Brains we will reach a higher level of AI.
A design of a highlyDistributed Adaptive computer that is based on the Wave Function of Quantum Mechanics that could become Conscious when it moves above a certain level of complexity.
How Godel proved that it is impossible for a System to Observe Itself. This was also proved by alan Turing . He invented what is now called a Turing Machine a model of a Computer that is able to Represent a Theory.
Gregg Zuckerman About the Mathematics of Consciousness based on Non-russell Sets. Consciousness is based on Contradiction.
Alan Fiske has developed a widely accepted and used theory about how people coordinate and cooperate. This theory is compatible with Paths of Change. The theory is also compatible with the results (see chapter 8) of Measurement theory where the types of measurement are called Scales. Scales can be related to Geometries. In the blog I start with explaining geometries and move in Chapter 12 to the field of change Management where I Apply the Geometries.
When I studied Mathematics I found the Dutch Mathematician Brouwer who believed what I now still believe and George Lakoff later proved that you have to See Mathematics otherwise it is wrong.

History of this Blog

The reason behind this blog is explained in the last chapter of my blog About the Ecology of the State.

In the blog about the Ecology of the State I reused a blog about Anti-Fragility, a new name for Resilience. Resilience is a major variable in the theory of Panarchy which is a theory about Ecologies.

I combined Panarchy with Paths of Change also a Theory about change and the theory of Alan Fiske about Human relationships. This combination gave me the insight that there is a shared Geometry behind many of the theories tabout Change.

This blog gives you an opportunity to combine the theories yourself. I also will show you that this geometry was known for a very long time ago mainly starting in India (See “Vedic Mathematics“). In the interpretation of the Theory of Alan Fiske the Scales of Measurement play an important role. I have created a special Chapter 8. for this subject.

In this blog I want to explore the Geometry of Change. To make it possible that others are also able to think about Geometries this blog contains many Educational Videos’.

7 Geometry

The four Geometries of Paths of Change
A projection of the model of Panarchy on the model Paths of Change.
Model of Vitality projected on Paths of Change.
The Model of Panarchy projected on Paths of Change using the colors of PoC.
The ridel of Alan Fiske projected on Paths of Change using the colors of PoC.

As you can see in this Chapter Geometry is very old. It was the Foundation of Art, Architecture , the State and Religion. People have been fascinated by Patterns like the visible patterns Up in the Sky of the Sun, Moon Planets and the Zodiac but also the patterns in numbers. Out of Geometry many sciences have grown that were grouped in schools sometimes called a University. Behind he patterns music was found and music was also created using patterns. The most important Music was the Music of the Spheres . This chapter is Big. It contains many Video’s that contain simulations. The main reason is that you have to See (“insight”) the Theory to understand the Practice.

How Physics, Movement, Symbols and Sound are supported by Geometry

Richard Feynman was able to recreate every theory at will and was therefore able to explain what the theory was about. His lectures are famous. This is a recontruction with a Simulation of his Last Lecture. It is a lecture about Geometry. Below you see a comparable lecture about a comparable genius Riemann who lived a short life but was able just as Feynman to see (Imagine) a lot. This shows the Power of Mathematics. It is not about Reasoning but about Insight. That’s why I have selected many video’s and will find more. Enjoy.
Why the Prime Numbers lie on a line but nobody knows why. A nice present of Quanta Magazine. about the Hypothesis of Riemann. Riemann comes back later when he solves another problem, the problem why geometries are different. He proved that this has to with the Curvature of space. Something you see below when you see the solution of Einstein to the problem of Gravity solved before that time by Newton who stole it from Leibniz, one of the last Magicians before the Golden Dawn (see video below about Mystic Geometry.) Einstein got the solution for his problem of his friend the Mathematician Minkowski.
The curved space of Einstein.
The role of Higher Dimensions in Physics and Mathematics. It started with Albert Einstein. He used a new 4D curved geometry to explain gravity. Kaluza found that Gravity and Electro-magnetism could be united by adding an extra 5th Dimension. This solution was improved by Oscar Klein by introducing Imaginary (2D) numbers . This solution transformed much later into 10 dimensional (vibrating) String /theory to integrate quantum mechanics, . As you can see in the next video the extra dimensions are put into a Very Small Closed in itself (“circular”) area in Space.
About Kaluza Klein Theory.
Part of a long series of lectures and simulations about symmetric shapes that played an important role in ancient physics and mathematics which was at that time related to the Order of phytogoras.
Transforming a flat structure into a 3D projection of a higher order structure made of Pentacles.

The Physicist Sean Carrol About Geometry and Topology in particular Riemannian non-Euclidean geometry, and topological invariants called “Homotopy groups.

The geometry of our space has zero curvature. In spaces with positive or negative curvature other rules are valid. George Bernhard Riemann developed a new geometrical concept by imagining a 2-dimensional bookworm living on a 3D crumpled sheet of paper.

The surface of the paper would seem to be flat and undistorted. Because the worm can only perceive two dimensions it would not be able to detect that his own body crumples with the paper in the higher dimension. The “force” that would keep the bookworm from moving in a straight line was not a mysterious “action at a distance”, but a result of the unseen warping from the third dimension.

You can imagine a similar experience by walking a straight line on a rotating platform. To you the shortest connection is a straight line while you move with a curve when observed by someone outside the platform. The geometry changes the idea that the shortest distance between two points is a straight line.

It even changes the idea that we return on the same point when we move in a loop (“circle”). This happens when our space contains one or more holes (“singularities”, “dividing by zero”).

With this example you can learn that it makes a lot of Difference when you are In (Intrinsic) or Outside (Extrinsic) the Context.

Geometry and the Riemann Space
Space Harmony: The work of Rudolf Laban about Movements. The same geometry can be used to make letters, sounds and meaningful symbols.
Kim Veltman about the history and geometry of Letters.


System Theory related to Buddism. A speedy introduction of system thinking leading to chapter Eleven. .
How to transform an infinite proces into a finite proces
A very rich source about Mystic Geometry. About India, Soemer, Egypt, Magic Kabbalah, the Rosicrucians , Blavatsky and of course the Golden Dawn.

8 Theory of Measurement

Measurements can be made through the human Senses or through the use of a measurement Instruments.

Measurement is the assignment of Numerals to a system according to a set of rules.  These rules are called a Theory.

Our senses or the instruments that are used to measure the system also represent a theory. This theory has a sometimes unknown impact on our measurement.

To avoid the Bias of the Theory behind our Measurement Systems a theory has to be a Structure Preserving mapping, a homomorphism. The Structure of the system has to stay the same when the rules are applied.

If the theory does not preserve structure the theory introduces its own theory and we are not measuring the original system.

Not only the primary theory has to be a homomorphism. The complete chain of theories we use has to preserve the structure (The Uniqueness Axioma) of the original system.

To avoid Bias a System of Measurement Scales is defined.

A video about Scales.
The Hierarchy of Scales
The Hierarchy of Measurement Scales. Observe that the scales are Nested.THis means that every scale is Part of a “higher” scale and all the constraints have to be valid on a higher level. This means that C4 contains C3 etc.

a Nominal Scale defines Sets. Sets contain the Same elements. When we want to preserve structure  we have to satisfy the constraint If s1 = s2 ⇔ f(s1) = f(s2) (“the Same stays the Same”). This is called the Symmetric group, the group of all Permutations of the objects in the Set.

The Ordinal Scale is part of the nominal scale. The relational structure preserved during the measurement process preserves equality and order. The set of admissible transformations are relations that satisfy the constraint If s1 < or >s2 ⇔ f(s1) < or >f(s2). This is called the Order-Preserving Group and is the group of monotonic increasing functions.

Monotonic Functions Increasing and Decreasing
Monotonic Increasing and Decreasing functions,

The Interval Scale has to satisfy the constraint  If s1−s2 = s3−s4 ⇔ f(s1)−f(s2)=f(s3)−f(s4).This is called the General Linear Group (or Affine Group).  Differences can only be preserved when the transformation is a Linear transformation Ax + B where A is a Rotation and B is Translation (Displacement).

The Ratio Scale has to satisfy the constraint If s1/s2 = s3/s4 ⇔ f(s1)/f(s2) = f(s3)/f(s4). This is called the Linear Group.The only transformation that satisfies this constraint is the functions f(x) = Ax. This means that the only tranasformation that is left is muliplication and division (“not by zero!). which is transl;lated in Expansion and Compression the object of Topology.

A short Seminar about the history of Topology and a few highly interesting applications that show you for instance why we have to leave thinking in Hierarchy and move to Topological Structures with a higher Betti-Numbers (Loops).
Mathematician Prof. Norman Wildburger About the History of Mathematics focusing on geometry. . Norman has made thousands of video’s explaining everything you don’t know but want to know. THis video is about History.
An introduction to Group Theory. Group theory is about “being the Same“. This is a visualization.

Geometry, the Art of Transformation Size, Shape and Symmetry.

Figures shown in the same color are similar. A similar structure can be transformed by Rotation, Translation (Displacement) and Scaling (Multiplication), “blow up/down”).

Groups can be compared to numbers. Just like the primes the Simple Groups can be used to create other groups. The Biggest group is called the Monster.
The Geometry of the Space we live on, the Sphere, where Parallel Lines Cross at the Poles. This video contains nice visualizations.
Affine Geometry, The Geometry of Linear Transformations.


Projective Geometry is about Perspective and the projective plane, the space of one-dimensional subspaces of a three dimensional vector space (lines through the origin). This view leads to Hyperbolic and Eliptic Geometry finally framed in the language of Geometric Algebra . Affine geometry is the “world” of Linear Algebra and Vector Spaces leading to Euclidean and Einstein’s (Minkovski) ,Relativistic geometry.

With Geometric Algebra you can Calculate with Shapes. Geometric algebra is a very convenient representational and computational system for geometry. It is going to be the way computer science deals with geometrical issues. It contains, in a fully integrated manner, linear algebra, vector calculus, differential geometry, complex numbers and quaternions as real geometric entities, and lots more.

Geometric Algebra brings us back to the Tetractys of Pythagoras which shows the Fourth triangular number which is part of the Triangle of Pascal.also called the Yang Hui in China and Mount Meru in Sanskrit. The Triangle of Pascal contains many Fractal structures that were used a very long time ago in Music (Rythms), Art & Architecture (Proportions) and Numerology (“The Art of interpreting Patterns in Numbers).

Triangular Numbers.
The Tetractys (1+2+3+4=10 = 1 MOD 9) in a Mystical Vision of Jakob Böhme. In the center of the Heart you can see the Hebrew letter/numbers that are a copy of the comparable Sanskrit symbols. See the video of Kim Veltman above.

9 Mount Meru

the roots of all the geometries can be found in Ancient Indian Mathematics.

The five central towers of Angkor Wat symbolize the peaks of Mount Meru; Angkor, Cambodia.
Mount Meru Prastaara. When you Want to know more about the history of Sanskrit (“krit” = the Practice) and “sans = Speaking and the influence on many cultures (~f.i. Hebrew) of the culture of ancient India look at the Video of Kim Veltman above.
Theory of ALan Fiske explained by Steven Pinker.

It all comes back to Breathing

Realize that the 3D version of Panarchy is also a 3D version of the Movement of the Relational Models of Alan Fiske and their related Geometries in Cognitive Space and the movement of many Concepts that share the same Worldviews of Path of Change.

Also Realize that Panarchy is a result of a theory (Cultural Theory) that is based on the same Worldviews of PoC and of Alan Fiske that can be explained by a 2×2 Matrix containing the variables Agency and Communion that are the same as Yin and Yang.

Agency and Communion also determine the Big Five the most used Personality Classification (and many others)

Yin and Yang are also represented by 0 and 1 and therefore the Triangle of Pascal represents the many combinations of possible personalities on earth but is also a result of a completely different System (Geometries) to calculate Combinations. Think about (X>Y)**n (Affine) or (X-Y)**n (Euclidian) as an example (X>Y)**n is a Program (“Protocol”) to n times create all the possible combinations of X>Y.

It is therefore also not strange to call the total process of the movement of Expansion (Yin) and Compression (Yang) in space the Cosmic Breath named the Svara in Sanskrit. Svara स्वर (svara and svāra): Voice, musical note, sound; note of the musical scale, tone in recitation, accent in grammar, symbolic expression.


The Ished Tree | Egyptian gods, Egyptian art, Ancient egyptian
Ished Tree in Egypt. Thot with the moon on his head (“the inventor) and Seshat with the wheel of the Seven Stars (Pleiades) and the symbol of the Bull, the daughter of Ma’at the Goddess of
Balance aquire the Magic leafs of the tree.The names of the ascended ones are written on its leaves.
The Benu Bird (Phoenix, the Fire Bird) lives on the top of the ished tree. in Heliopolis. The Phoenix is recreated by the Fire of the Kundalini also represented by the Snake of Ouroboros being a Cycle that connects to itself. This fire was wellknown in antiquity.
Yggdrasill, Old Norse Mimameidr, in Norse mythology, the world tree, a giant ash supporting the universe. One of its roots extended into Niflheim, the Underworld; another into Jötunheim, land of the Giants; and the third into Asgard, home of the Gods. Asgard was according to Kim Veltman situated in Tomsk Russia.


The Egyptian Goddess Ma’at was later called Sophia (Wisdom). Ma’at is the keeper of the Underworld. She is also the keeper of the Harmony in the universe. Ma’at weights the Heart (“the center”) with her feather which carries the symbol of the nothing (“the empty set”). When the Heart weights light as a feather the human was balanced in the Heart Chakra meaning that he lived a “Good Life” and was allowed to enter Heaven. Observe that the Heart is the Controller of the Upper (Head) and the Lower (Body) Cycle of Blood (“=Life“). Observe that the human is represented by an Ape with the moon of Thot on his head.

11 About Perspectives and Projective Geometry

Projective Geometry PG)is a result of Perspective Drawing

IMAGE: Leonardo's perspectograph
The Perspectograph of Leonardo Da Vinci

As you can see in the picture above PG makes use of drawing Lines that connect the Point of the Eye (the Sensor) with the \Planes and Points of the Object of the Drawing. Observe that the object is a Sphere. and that the two lines connect with the sphere at the Horizon which is a line we often confuse with Infinity(“the point we will never reach”).. Also observe that the rear-end of the Sphere is invisible.

The pole of the Sphere can be connected to Parallel Lines that Never Cross. The lines connected to the eye of the artist and the Pole always have an Angle>0.

PG Connects many Points(“people”) by Lines (“Connectors“) and is there fore highly comparable with Communal Sharing of Fiske and Social of PoC.

What Perspectives have in Common.

What is a Point of View?

Two projections of the same object.
Alberti was the first to ask what two pictures have in common if two drawing screens (Planes) are interposed between the viewer and the object, and the object is projected onto both resulting in two different pictures of the same scene. Leone Battista Alberti (1404-72) was the writer of the irst treatise, about Perspective  Della pittura (1435). The solution to this problem was found in 1803 by  Lazare Carnot
In his book “Géométrie de Position” he proved that the so called Cross-Ratio is always preserved in a Projection with One Point of View.
The Cross-Ratio is the Ratio of the Ratio of the Four Points A,B,C,D lying on a Line that intersects the Four Lines defined by a,b,c,d that orginate at the Vanishing Point O. Carnot proved that (AB)(CD)/(AC)(BD) = (A′B′)(C′D′)/(A′C′)(B′D′).
How to unite all the geometries using a General Way of describing Lines and Points in higher dimensions. In this way the Horizon becomes a circle.
Cross-ratios are invariant under Möebius transformations. THis is a visualization.A Moebius transformation is a combination of many transformations, a reflection, a rotation, an inversion a translation and a homothety, a homogeneous dilation .
Geometries are types of Transformations (Rotation, Translation, scaling, projection and )and Things that Stay the same -> Invariants (Length, Angle, parallel lines, incidence (“crossing lines”, points) and the Cross-Ratio ( a complicated way to relateLlines or Angles that have the Same Point of View) ).

about Meta Geometries

Moving one step Higher in Abstraction.

About 4D Space and Quaternions : Quaternions are the Imaginary Numbers (x, i,j,k) of 4 D Space. The Imaginary Numbers are Rotations in 3D space (x,i) . This video gives you a way to train your 4D-view by starting in Flatland being an imaginary world in 2D. A Line is a projection of a Circle that starts at Infinity which is a point at the North Pole of the Sphere.

In 1872 Felix Klein, published a new Mathematical Research Program called the Erlangen Program under the title Vergleichende Betrachtungen über neuere geometrische Forschungen.

In this program Projective Geometry was emphasized as the Unifying Frame for all other Geometries.

Although lines in the Projective Plane meet in one point of Infinity Klein argued that there could be two points of Infinity if the Projective Plane was a Surface Closed in Itself.

When we look at the Origin of Projective Geometry, the Artist painting A Sphere, Earth, on a Flat Surface, it is not difficult to realize that this Closed Surface is a Sphere. This sphere is projected on a plane that contains the imaginary numbers that are solutions of the cross-ratio when the 4 points 𝐴𝐵𝐶𝐷 are not on a circle.

COnformal mappings are mappings that preserve angles. This video shows why the cross ratio is complex when the points are not on a circle.
About Kleins erlangen Program

12 Using The Geometry of Change

Refresh and Surprise

First I present a few Slides to refresh your knowledge about the Background of the Blog or to surprise you.

In chapter 13 start to talk about the Geometries of Change.

The issue of this chapter is to help you to think about related issues like Machines, Cybernetics, the Anticipatory System of Rosen but also about Semiotics.

You don’t have to understand everything and you can also skip as many issues as you want.

I hope you become inspired to look at the geometry with another view (“I hope the Mythic“) and see the Magic (“have you looked at . the video about “Mystic Geometry in Chapter 1″?).

The engineering method COLLIN Looks like Paths of Change.
This is a >4 times Expansion of Paths of Change with the Human in the Middle and the Four types of humans that surround him/her.
Here you see four types of Social Networks with a Production and Sales Cycle moving With- and Against the clock.
The four Communities correspond with the four Relationship types of Alan Fiske.
Remember that the four Relationships are related to four types of Geometries. This was proven by relating the Relationships to Scales of Measurement.
Measurement theory (Chapter 2) is based on the idea that measurement has to be based on Structure-preserving maps from the outside (what we think we see with our senses) to the inside (what we see with our imagination which is related to an inner sensor (“the third eye”) which is the Pineal Gland).

Keep your Third Eye Open - Foods That Activate And Decalcify Your Pineal Gland of the Endocrine System — MOT MAG

Observe that explain means making something plane (flat) which is a projection from Knowledge (Affine Geometry) to the (flat) Image of the Imagination (Similarity Geometry).
Observe also that Design (in Dutch Ont-Werp) is related to Throwing (projection) something at the right moment (ont).
What target (Goal (Plan) ) do you want to hit? Realize that the energy for the projection comes out of the fusion of Complementary (Different) concepts. What is different? Not-the same. Not is a Negation.

Mind, Machines and Anticipatory Systems

Professor of Cognitive and Computational Neuroscience Anil Seth looks at the Neuroscience of Consciousness and how our biology gives rise to the unique experience of being you
.This presentation is mostly about the so called the Bayesian Brain. In this theory the brain is a prediction machine that produces a “best guess” combining internal “memory” / “imagination” and external data produced by the senses.
Damasio: ” Living systems are not static, but they act in the world in order to minimize surprise and persist in a future shaped by uncertainty” but humans Need Surprises to find life exiting.
“Organs are not machines” : The defining property of a living system is that it has organisational closure: every efficient cause (why, Aristotle) ) that is necessary for its continued existence must be in turn generated from within the system.
The presentation We looks at organisational theories of the organism from Aristotle, via Kant, to Robert Rosen, who provided a basic relational diagram for a system with closure to efficient causation. The reason for its existence has to come from within the system and the paths that are connected by the “causes” have to connect and close.
Mathematical Foundations of Anticipatory Systems | SpringerLink
Robert Rosen: Anticipatory System.Observe that this picture can be mapped to Paths of Change by mapping a Natural Systems to the Sensory Worldview and the Formal System to the Unity Worldview. Final Cause is the Why Question which is the Mythic Worldview. The material cause is the Social Worldview. Closure is what Will Mcwhinney called a Path.


The model of Cybersemiotics.
Humans (We = I (Sensory) and/or The Other(s, Social) Exchange our models being personal interpretations of the Natural Systems we sense or are part in.
This exchange can take place using a “communication-model” being the Conduit Metaphor (we exchange containers) or the Toolmaker Metaphor in which we exchange our experiences about using the models.
We are an organism and we communicate using the expiriences of our outer or inner body. In t he last part we are specialized and therefore talented to experience our Inner Eye or we get insights without knowing how.
Cybersemiotics uses the Semiotics of Peirce. Peirce uses a “simple” model in which he uses 3 Stages in te proces of Meaning, The Sign , the “cause” of the Sign and the Interpretation of the Sign in the Mind.
About 1st, 2nd and 3rdness x 1st, 2nd and 3rdness = 9 correlates.
Peirce's Triadic Model – Interpreting Signs
The basic Trinity of Peirce.

A lot of Questions and Observations of Soren Brier trying to find a new foundation for the sciences. It will not help you to find certainty. Perhaps it wil sharpen your questions or doubts.
Another presentation of Soren Brier: The Cybersemiotic star: A diagram of how the communicative social system of embodied minds‟ four main areas of knowledge arises.
Physical nature is usually explained as originating in energy and matter, sometimes also information.
living systems as emerging from the development of life processes (such as the first cell).
Social culture is explained as founded on the development of meaning and power in language and practical habits, and, finally, our inner mental world is explained as deriving from the development of our individual life world and consciousness,
in spiritual and religious framework often ultimately from an objective transcendental spirit or as a soul coming from a personal creator God.


An interview with Niklas Luhman in German but translated into English. Luhmann has tried to incorporate the idea of autopoiesis (self-reproduction) in sociology. He proves that Social Systems reproduce themselves and are therefore highly resistent to change.

Autoiesis is about Self-Reproduction or Repair during Production. Neil Theise loops from makro-levels to micro-levels of what we call reality. He explains complexity, autopoiesis,positive &negative feedback-loops, cancer and how all that relates to us in the universe and the universe in us? Why ants move away from their territory to come back when they have found the food that is needed.

Simulation of the Human Cell.


The presentation behind the link above explains the theory of Robert Rosen in combination of the theory of George Lakoff. For the last one move below. For the first one explore this blog about Meta-Engineering. As you will see is that the presentation tells a comparable story as Chapter 2 about measurement in the way that it explains that a model is a mapping from something we experience outside with our senses (A natural system) or with our instruments and we have to make a structure preserving mapping to avoid that we introduce a bias with our measurement instruments.

Paths of Change mapped on Kolb Learning Styles In this picture you can see what a Closure means, a path connecting the four worldview. Know that the arrows can also move the other way around and every Box is a PoC-model in itself. Thats way PoC is a Fractal System of Change.
Body and Mind are connected by the Heart and are centers of cycles where the four views/types move around. The four views with one shared view create the “magic” number seven (3+1+3) . Observe that the cycles move with and against the clock creating the well known Moebius Ring (8). This model maps on the Indian Model of the Chakra’s and the Chinese Median Points. Service above Self is the motto of the Rotary where ROTAR is a permutation of TAROT.
Paths of Change mapped on the minor Arcana of the Tarot.
The path of the Hero (Fool) connects 2 triangular paths
The history of the Tarot. Rob Doctors van Leeuwen was visited by an Angel who asked him to do research about the pattern of the Tarot. He (and his brother Onno) detected two new cards called Truth (Blue) and Intuition (Yellow)
Paths of Change used in a model about the Production Cycle.
A picture out of my Blog about a new Ecology of the State that unites Panarchy, ALan Fiske and Paths of Change. It is an application of the Geometries. The most important Worldview is Yellow and was called Mythic by Will McWhinney in his book Paths of Change.
Mythic relates to Intuitive in the myers Briggs Model: “Intuitive people live in the future and are immersed in the world of Possibilities. They process information through patterns and impressions. Intuitive people value inspiration and imagination. They gather knowledge by reading between the lines. Their abstract nature attracts them toward deep ideas and concepts”

The first thing you have to realize is that you have been looking at pictures that describe the same subject with different names. All of them are about Change and Change looks like Breathing <-.-> (Contract/Expand). Below you see the Expansion Pattern of “nothing”/. This pattern is controlled by the Trinity, the number 3 and the Triangel. This pattern is called the Bronze Mean. It is a specialization of the Golden mean. The bronze mean contains a very important number 43.

The center is the Empty set (Yellow), the Nothing, the Foundation of creativity. Desire (Female) and Control (Male) create a child (Communion) Left you see Adam Kadmon the first Human and the Tree of Knowledge.
By playing with the Arrows (->) Expansion (Red) and Compression (Blue) are reproduced. The other 2 combinations create The Emotions (Green) and Creativity (Yellow).

The first picture of this paragraph contains a Cycle connected to another Cycle where both cycles move in opposite direction showing the well known Moebius Ring (8). The model contains a center that contains the model of the whole. This is called a fractal. When you compare this model with other models look at the colors. I have used the same colors of PoC all the time.

13 About Affine Geometry, Maps, Metaphors and Mappings

In the model of the Geometry of Change you see that Blue, named Unity in PoC and Knowledge in other models is called an Affine Geometry and is connected the concept Rank and the Constraint If s1 < or >s2 ⇔ f(s1) < or >f(s2) which is called the Order-Preserving Group. Knowledge is an Order but what order?

The solution to this puzzle can be found at the beginning of this blog where you read the sentence “The role of Higher Dimensions in Physics and Mathematics”. The concept Dimension is used to define a Ranking of Spaces.

Basic spatial dimension
Higher Dimensions are represented as Projections on a Plane. This 2D plane could be called a Scape (taken out of out of Land-scape).
George Lackoff researched the brain and detected that the Brain is based on the Body (“Embodiment”). When we are young we learn that it is difficult to learn to find balance to stand right up and to move. Thats why Up (Higher) is better dan Lower (Down). Thats why Heaven is Up and Hell is Down. Thats why a Tree is a Symbol of Knowledge. George also discovered that we always make represent ations of what we think. When we try to represent an abstract concept we use a prototype (one out of the set). He also found out that Our brain uses Frames to interact with the outside world: About Framing. This is also the subject of Goffman.

14 About Euclidian Geometry, Distance and the Horizon

beach birds calm clouds

In the picture above you see the Horizon. Horizon is related to Horizontal, a line that is perpendicular to a line that moves from Up to Down or Back. the horizon is an Illusion because we live on a Globe. Behind the Horizon we see nothing but we know that there is something behind the Horizon. In our Perspective the Horizon is the place where parallel lines Cross. The word horizon derives from the Greek “ὁρίζων κύκλος” horizōn kyklos, “separating circle”,[3] where “ὁρίζων” is from the verb ὁρίζω horizō, “to divide”, “to separate”,[4] which in turn derives from “ὅρος” (oros), “boundary, landmark. The horizon is a symbol for infinity (“the place we never will reach” but also something we can find wen we keep on moving at the right direction.

About Deep Learning & Euclidian and Non-Euclidian Shapes.

This video explains Neural Networks using Graphs that are able to recognize Non-Euclidian Objects.

About Scapes and Meta-Systems.

Below you see a picture and a presentation of Kent Palmer. He found out that the term Scape (Schap in Dutch) we use in Landscape is used to imagine a “flat plane” . In dutch and english scape is also translated into ship (“Friendship, vriendschap) being a relationship that carries as a tray, something to hold something.

Perspectives are about seeing something but seeing is used as an insight. We look at our personal frame.

A Few years ago I gave a presentation about Context to Software-architects about Mikhail Bahktin: The Wordwide Carnival: A Short Introduction into the World of Mikhail Bakhtin. He was a Russian Philosopher that was put into a Goelag-camp by stalin. He was an expert in Dialog and what he called the Chronotope: “The place where the knots of narrative are tied” or “the intrinsic connectedness of temporal and spatial relationships”.

Exploring Intelligent Enterprise System Limitations Incose 2007 Palme…