How to Fuse Differences and Preserve Structure

In this recent blog I will explain a new way to Design based on my last blog The Computer of the Future is an Organism.

In this recent blog I showed how billions of 1-Cellular Organisms work together to support the Human Ecology we call a Body.

Summary push here

The first of this blog part repeats the Theory.

You dont need the Theory to Practice.

Push here to go to the Practice

Later in the second part I will use Examples.

I start this blog with a long citation of Nassim Taleb about Anti-fragility:

We have the illusion that the world functions thanks to programmed design, university research, and bureaucratic funding, but there is compelling — very compelling — evidence to show that this is an illusion.  

Technology is the result of antifragility, exploited by risk-takers in the form of tinkering and trial and error.  

Engineers and tinkerers develop things while history books are written by academics;

we will have to refine historical interpretations of growth, innovation, and many such things. …

The error of naive rationalism leads to overestimating the role and necessity of … academic knowledge, in human affairs — and degrading the uncodifiable, more complex, intuitive, or experience-based type”.

This is the last picture out of my blog about Anti-fragility.and Structure preserving Mappings.

It is a fusion of many theories that share the Quaternion.

Panarchy: The Patterns of an Ecology

Behind the picture above you can see the model of Panachy created by a group of scientist coordinated by Buzz Holling.

It also shows a Geometry you have to remember called the  Möbius Ring.

Part 1: Theory



“The Tao produced One; One produced Two; Two produced Three; Three produced All things.” 

The Three Pure Ones

The Trinity is the smallest Number with a Middle.


The Trinity can be balanced by linking trinities to the trinities.

The trinity is the most Efficient Number (“Balanced Ternary“) and Storage System (“Balanced Trees“)

Platonic Solids

The Platonic Solids are all the possible forms you can make with a Triangle.

You can Generate the Platonic Solids and a very simple Computer out of the Trinity.


Quick Introduction of Concepts

the Act of Creation is a Fusion of Seperate Concepts

Accordng to Arthur Koestler (1964): a new Theory is a Fusion of two previously separate Frames of Reference (“Bisociation”). 

Later (2002) Gilles Fauconnier & Mark Turner inspired by George Lakoff ( (Metaphors We Live By (1980), Philosophy in the Flesh(1999)). called the Semantic Fusion of Concepts, a Conceptual Blend

Fusion From 2->1

To save time and memory (the Human Scale) we compress Action Scenario’s into a single Concept that can be fused with another Concept to compress long Chains of actions into one word that Unwraps if needed.


The Fusion of Opposites is the Empty Set also called the Void, the Singularity or a Point.

Fusion <-> Splitting

It is not always possible to reverse a fusion of opposites unless the reverse is part of the fusion like it happens with Light and Matter.

In this case matter and anti-matter fuses into light and light splits into matter and anti-matter.

The two processes are symmetric and are related by a constraint that +1 – 1 = 0, a (Nilpotent) constraint that can be found behind every theory in Physics.

The Middle: Zero-Point

In the middle between positive and negative is the Zero, the Vacuum, the bridge between the two mirror-universes we live in. One during the Day (Sun) and one During theNight (Moon).


Two projections of the same object.

Observers (Points)

What do the two Fused Projections of two Observers have in Common?

Cross Ratio:

They share a Ratio between A,B,C,D called the Cross Ratio.


When two distinct points (dots) are connected they form a line. 



Infinity is visible from the Pole

In non-Euclidion Geometry (Projective Geometry) Parallel lines Cross (Meet) at the Horizon.



In Euclidian Geometry everything you see is seen out of a Recktangular Frame.

brown wooden dock


A non-euclidian space is Curved.

Digital vortex - Royalty-free Abstract Stockfoto

Projective Geometry started as the Art of Perspective in the Renaissance.


IMAGE: Leonardo's perspectograph

Looking Through a Hole

In this picture you can see that Leonardo Davinci is Looking with his Eye through a Hole Drawing a Sphere where theTangent is the horizon.

The Phoenix (Firebird) dances the Act of Creation

a Quaternio: is a Fourfold Cycle

Paths of Change of Will Mcwhinney is a Fourfold Cycle , a Quaternio.

The Quaernio is an Invention of Carl Jung.


The four Elements of Leibniz

Leibniz fused Logic and Alchemy by Rotating the Same Fourfold Structure out of the Logic of Aristotle for 45 degrees.

Jung found the Quaternio when he researched Alchemy and the Gnostics.


The gnostics believed in Knowing we call Intuition.

Psychology, Psychiatry, Culture

Carl Jung just like Joseph Campbell with the Hero’sQuest and Mikhael Bahktin with the Chronotope, tried to find the Pattern behind the pattern.

The Fourfold Mobius pattern projected on a City.

The Fourfold Mobius pattern projected on an Ecology is called Panarchy.

A Mobius pattern has no center.

To make this possible the cycle moves in an Extra dimension.

A Pentagle is a Square + its Center (the Cross, White)

Bahktin Cycle

Every Point of View has Four connections to the other 5 Points of view.

The Pentagle repeats in the Center.

Cube of Space

Cube of Space

Quaternio Fourfold of Fourfold

The pictures show a Square divided in Squares where the four diagonals are opposites and the top-down diagonal consist of four Tetrahedra with a point (the cross) in the middle and two circles at the top (Adam, Anthropos ) and the bottom (the wheel of Fortune (Rotundum).

The wheel is Always Turning

The Seal of Solomon
The Seal of Solomon

Out of the Duality that is the Point a Process starts that is always a Balanced Cycle (circle) in which the sum of all its Potentials is Zero.

The Lo Shu Square on the back of a small turtle surrounded by the signs of the Chinese zodiac

Eudaimonia: Living the Good Life

Carl Jung

Structure Preserving Mapping

The anthropologist Alan Fiske Discovered that his model of Human Relations was compatible with the Scales of Measurement theory.


Humans Measure their Relations with Scales.


It was also clear that the model of Fiske was compatible with Paths of Change that came out of the research of Carl Jung in Alchemy he called a Quaternio.

Points of View

A Map is not the Territory (Korzibski  : General Semantics)

The higher you Climb the Scale the more Details you loose.

Zoom in <-> Zoom out

You have to Zoom in and Zoom out in the Context from the perfect Point of View when you make a Design.

A Category is a deliberately Killed Context

Will McWhinney called the measurements World Views

Yin and Yang

The world views can be classified by Agency and Communion that are the same as Yin and Yang.

Structure Preserving Mapping

The mathematician Eric Benoit  proved that the Scales are Structure Preserving Mappings.

The four Geometries of Paths of Change
  1. Projective Geometry Connect Points of View to find the Context.
  2. Find the differences
  3. Fuse the Diffrences
  4. Order them and produce a Ranking
  5. Transform the ranks in States.

When we Fuse Differences we move from Similarity Geometry to Affine Geometry.

In case of the corresponding Scales we move from the Interval scale to the Ordinal Scale or in tems of relationships from Equality Matching to Authority Ranking.

The Hierarchy of Scales

Autority ranking and the Ordinal scale share the Geometry of a Hierarchy where the most important Ranking is at the top.

Hierarchy One (Idea)->Many:

A hierarchy connects the One to the Many

To make a Ranking you need to define what > or < really means.

>=Expanding and <= is Compressing.

Mirror Universe

When you keep on compressing you reach the singularity and planck scale, a tiny black hole (Point, Bindu) that connect to a tiny white hole that connects with our Mirror universe.

Trees are Expanding Flow Sytems


In Nature every Living system contains an Expanding and a not-expanding, Inhibiting, proces that prevents expanding to Infinity.

Limited Resources

Processes are limited by the resources they use.

Structure Preserving Maps

A Theory is a 1-to-1 Mapping or Morphism between numbers perceived by the Senses and and oother numbers described by Rules (Algorithms) often related to the Mind. In Paths of Change this map is called the Analytic Game.

A Structure preserving mapping does not change the rules that are related with the Origin of the mapping (“Reality“).

The Secret of Alchemy

When thou hast made the Quadrangle Round, Then is all the Secret found”. George Ripley (d. d 1490).

George Ripley was a famous Alchemist.

In the statement he “gives away” the Secret of Alchemy:

History Repeats Itself:

History Repats itself all the time and the cycle is a Square, the Quaternio.

the Cycle is a Magic Square

The only thing you have to do is fill the Variable in the Beginning and turn the Wheel of Adventure where all the Four Points in the square are Opponents.

When you connect the points in the outside ring in rising order the Cycle of Saturn (Father Time) appears.

They share the same Number (5) in the Center making the square a Magic Square called the Lo Shu you can find on the back of a Turtle meaning the Constellation of of Orion.

Lo Shu Magic Square


Circle or Line?

The first Step is is the Choice between a Cycle (A->A)and or a LineInterval, A->B.

Resilience: B<-A->B

PoC advises you to choose a quaternion, a Four-fold cycle, for the reason that nothing will change because of the Third Force of the center Resilience that controls Expansion and Contraction.

The interesting point is that almost every way you chose is connected to a specific Theory of Change so you can also use your favourite approach.


That is why Will McWhinney called Paths of Change a Meta-Practise.

There are six possible Lines and many more possible cycles including a 2-step cycle and many ways to Rotate.

You can start with an Observation, a Model, a Motive, an Idea, a Vision or an Insight.

An idea is not something that pops up.

It is often a result of many Connected Cycles taking a long time.

It took Wolfgang Goethe a long time before he found the Uhrplant and it took a lot longer before his ideas about Morphology became reality.

What is an Idea?

An Idea is a Pulse that comes out of the Action Potential of the Emotions triggered by an Insight or Epiphany (Eureka-effect).

An Idea is a “product of the Imagination, something we See when we look Inside (Insight).

According to Plato an Idea is an Essential part of Reality.

Fuse Ideas into a Perfect Model

Ideas become essential by collecting a lot of look-a-likes and Fuse them into the Perfect model.

A Fuse is difficult to Split

When a fuse produces the energy of the Light of Creation it is difficult to split just like matter and anti-matter.

They can be found by looking and confronting the observations of our Reality not with a Prejudice but with an already acquired Insight (Wisdom).

The Tension between In-Sight and Out-Sight can be found in an Inventor.

Invent:Looking for Proof

Invent is the result of “Looking for Something” you already know it Exists.

Abstract concepts(Models) are not Ideas.

This can be checked by Imagining the Concept.

Abstract concepts have no image.

An Architect connects Vision and Model by making a Design (designare = draw).


2-combinations of Worldviews are called Games.

Six Archetypes

Games are controlled by an Archetypal Role in our case the Architect but we can also play the game of Inventing starting with Perceiving or the game of the Visionary or the game of the Market of the Entrepreneur.

A 2-combination of worldviews is called a Game.

There are Six games and much more Paths of Change when we combine the games into a Cycle.

A Cycle can move with- and against the Clock.

Rotation Around a Point in the Middle

In the middle of the cross of the square we find the empty set because the worldviews are Opponents.

In a Fourfold cycle there are four states to start with.

These states can be classified by the four Archetypes of Jung being the Classical Elements air, fire, earth, and water that can be replaced by the Four Seasons with the Earth in the center.

Four Seasons

In the picture below you can see a pattern that moves with the seasons and contains four “Games” and two “games” that Bridge (jump over) and two “games” that go against the flow.

Improve uses the Store created in Autumn and Make uses the Energy in summer to Expand.

Design moves against the Flow.

  • Wood/Spring (Yellow) : a period of Growth, which generates abundant vitality, movement and wind.
  • Fire/Summer (Red) : a period of swelling, flowering, expanding with heat.
  • Metal/Autumn (?Green) : a period of harvesting, collecting and dryness.
  • Water/Winter (Blue) : a period of retreat, stillness, contracting and coolness.


Spring is the “Creative”Artistic” step in the Cycle.

Spring starts a proces of Growth, which generates abundant Vitality, Movement and Wind.

To do that we have to Abstract the Idea into a Seed.

Seeds are eaten or planted in the Winter or Spring, Grow in the Summer and are Harvested and Stored in the Autumn.

Abstraction -> Essence

Abstract means “drag away by force meaning “splitting” and taking something out, making it more Simple, Compress,

If the idea is articulated in words, words are deleted if the idea is a picture connections are deleted, an “abstraction of a line is two points connected.

The ultimate abstraction is a Point and one Word (a State, for instance Darkness or Emptiness).

an Abstract is a summary )shorter, more Essential).

In the Beginning: Movement

The opposite proces of Expanding is complicated when the starting point does not contain a proces or the process was there before the Beginning (“Movement).

Deleting a point or the same word becomes adding a point or the same word.

Most people are not aware that many diffrent words have the same meaning.


Blue, Cold, Winter, Red, Hot, Summer, in Between Spring (Yellow), Autumn )Green).

The same Development Cycle but with different concepts.

Producer and Consumer are part of the Production and Consumption Cycle.

They are fed with the Energy of Creation (Idea) hat comes from Spirit.

The idea becomes a Seed in the Production Cycle.

The energy is Stored (Autumn, Green) in the Emotions (Action Potential)

Production and Consumption have to be Voided which means that their Sum is Zero.

A PoC-cycle based on the Business Cycle that uses the Chinese Sheng Cycle where the Cross in the middle (White) is part of the cycle creating a Pentangle in the Middle.

A Pentangle is a Fractal.

A fourfold cycle in which 2 stage of Contracton (Winter) is combined with two stages of Expansion (Summer).

Combining Expansion Compression Showing the four Patterns (Spirals) they produce.

Production/Consumption Cycle as an Expansion of the Human in the center

Starting a Cycle

The first and most difficult Question we have to ask is:

What is Different or Unique in the Context we want to Explore?

The word Context is derived from the Latin word con-textere which means Weaving (Textere) together (Con). 

A Context is Something that Surrounds Something Else, Puts Something on its Place or Relates Something to Something Else that has a stronger Foundation.

Other words that are part of the same Family are Frame of Reference, Setting, Environment, Background, Situation, Ambience, Circumstances, Fabric and Framework.

A context is a SpaceTime ( a Chronotope) with a Boundary.

Gilles de Leuze: Difference and Repetition

The Creative Force cannot be resisted.

It becomes Stronger when it is resisted.

Difference is Pressed into Forms. 

The Dialectic, of Hegel operates with Extreme Differences ( “Polarities”) alone.

Therefore Don’t use Opposites.

When a concept is already fused Split it again and reuse the Parts.

When we repeat something it has to be Essential for some reason. so

Find the repeating structures and detect the Essence or dig deeper.

sometimes cycles contain cycles and contain cycles becoming spirals or higher order torsion-fields

Higher order fields need higher dimension that are not of our world.

You can change dimensions by using different numbersystems mostly Complex like the Quaternions or the Octonions.

Unique identities can be combined with other unique entities.

Every new combination is diffrent.

Movement -> Space Divided by Time

There is only one esential concept : Movement.


Northrop Frye: Archetypes and Fearfull Symmetry

Archetypes are Essential and Unique Patterns because they are Old.

Northrop Frye lwas one of the most influential literary theorist, of the 20th century.

He uses the “same” model Mikhail Bahktin uses.

Watch this video when you want to Learn more about Archetypes

What is a Design?

Step 2: Design: From Spring to Summer


The Summer is a period of swelling, flowering, expanding with heat

Fuse the Differences

Find a way to fuse all the differences (ideas, seeds) into a Whole in the Context.

Ranking Hirarchy

Find a way to order the differences in the context.


Define what > (expand) and (compress) < mean.


In a Design we move from the Visual to the Semantic making use of Words (Blends) or Schema’s, a Pattern of thought or behavior that organizes categories of information and the relationships among them.


When you observe the distinct unique objects the only thing yo can do is Count them using a unity, give a name to the numbers and put them in different orders (permutations).

Long Horn Medicine Wheel: Every Unique Stone has a unique Meaning

Rhe Medicine wheel is the oldest cycle in history. As you can see the Moebius Ring is, the model of Light is in the center. the four corners are controlled by the animals with unique characteristics like the Eagle. The four animals come back in many beliefsystems including Christianity.

Beauty of the Whole

When you observe them as a whole you could experience different types of emotions sometimes related to the concept of Beauty.

In this case I want to present the work of the recently died Christopher Alexander called the Nature of Order.

Assigning an Amount

When you have put all the different unique objects in the Chronotope it is possible to assign different quantative values (an amount) and give this amount a name to the object and create a ranking.

Nature of Order

From Summer to Autumn

a period of harvesting, collecting and dryness.


From Autumn to Winter

period of retreat, stillness, contracting and coolness.

From Winter to Spring


Using Play as the Essence of sport.

A few weeks ago I made a model of the Sports

I chose the name Spel (Play, Game) for the Unique Part of the Model

Will McWhinney called this “game”, the Game that creates Games, The Trickster or the Fool as Archetype.

James Carse called it the Infinite Game.

Business Cycle

Essential Proces Model of a Bank

Design of a the combination of Watson (IBM) and Banking (In Dutch)

Essential Model of Smart Computing




(1 Theory is split into Geometry and Semantics

Triangel, Trinity

In the geometry I explore the triangle and the many different geometries that can be made out of combining triangles.

In the semantics I explore the same trinity now called a bisocation or a Conceptual blend.

A Suare is a combination of two Triangles and contains six lines.

Square-> Quadrangle: Quaternio

A Square is a combination of two Triangles

Carl Jung discovered that the old “mystical” theories are based on squares (quadrangle)he called a Quaternio.

a Points-of-View is dependent on the Scale and the tpe of Space you live in.

In non-euclidian space everything is Curved.

In our Euclidian space we always look through a Rectangular Frame.

Preserving Structure

The new approach is based on Structure Preserving Maps that were found when the Anthropologist Alan Fiske discovered that the Types of Relationships he found worldwide in every culture were compatible with the Scales of Measurement.



(3) Step 1: Finding Uniqueness in the Chinese model of the Seasons the year starts with Spring.

What is an Idea?

An idea is an insight, and an Emotion, omething that gives a Pulse to get into Action.


(4) Step 2: From Spring to Summer called Design is not Design but Inventing in Paths of Change.

Design moves against the flow because a Hierchy is dominant over an idea or insight therefore you have to make an Anti-fragile Jump.

Paths of Change contains more “jumps” of 6 months.

Ranking: What does > mean?

We move to the Affine-Geometry, from the Interval scale to the Nominal sccale.

both are related to the Hierarchy being a rotated tree with the one at the top.

the One at the Top is Essential

The one is an essential concept so the top of a hierarchy has to be essential too.


This step is often called a Design (a drawing).

How do you draw an idea?

If it is an insight it could be a result of an outsight.

In this case you have moved from the summer the time of looking to the autumn, the time of taking store to the winter the time of reflection coming out of hybernation in Spring.

Put the difference in a whole and count them.

give a name to the numbers and a assign an amount to the unique differences.

Order (Sort) the amounts.


Unique objects can be permutated where a certain permutation could give the emotion of Beauty.

In this case you have found the Nature of Order of the recently died Meta-architect Christopher Alexander.

Transform from Levels to States.

(5) Step 3 Transformfrom Ranking Order to measuring a Distance needing a uniform measuring sStick like Hours or Money.

Use / Evaluate

(6) Evaluate (Potential)


(7) Improve


Examples of Designs.

Back to the Begin.