Posts Tagged ‘mathematics and physics’

About Alchemy and Logic

Thursday, April 28th, 2016


Rebis, Res Bina, Double Matter

Res Bina (REBIS), Double Matter

This blog is about Logic, Alchemy and the relationship between Logic and Alchemy.

Logic is based on the Square of Opposition of Aristotle. This square was discussed for more than 2000 years. Recently scientists detected that the Square is really a Cube. It misses an extra dimension.

The Square describes  the six oppositions (“dual combinations”) of possibility (“some”, Particular Affirmative), necessity (“all”, Universal Affirmative), not-possibility (“not some”, Particular Negative) and not-necessity (“not all”, Universal Negative).

Geometric Logic is a part of Modal Logic which is a part of Logic.

In Geometric Logic the Linguistic Representations of Logic are mapped to the Graphical Representations of Geometry.

Modal Logic works with the notion that propositions can be mapped to sets of possible worlds.

The idea of possible worlds is attributed to the famous mathematician Gottfried Leibniz (1646-1716), who spoke of possible worlds as ideas in the mind of God and argued that our actually created world must be the best of all possible worlds. Possible worlds play an important role in the explanation of Quantum Mechanics.

Alchemy is based on the Square of the Four Elements. The Four Elements are oppositions. The oppositions of Alchemy are related to the oppositions of the Square of Opposition of Aristotle in an orthogonal model. They form an arc of 90 degrees, which makes Alchemy the complex part (imaginary) of Logic.

In his work De Arte Combinatoria Leibniz developed a general theory of science that was based on a fusion between Alchemy and Logic.

The four Elements of Leibniz

The Square of Leibniz

In this blog I will explain Alchemy and Logic and show that Alchemy and Geometric Logic share the same geometry, the Hexagon (the Seal of Solomon), which is a 2D-mapping of the Cube of Space of the Sefer Yetsirah.

Leibniz calculating machine

Drawing of Leibniz’s calculating machine, featured as a folding plate in Miscellanea Berolensia ad incrementum scientiarum (1710), the volume in which he first describes his invention.

About Alchemy

When thou hast made the quadrangle round, 
Then is all the secret found. 
George Ripley (d. 1490).

One of the most complicated ancient architectures is the architecture behind Alchemy. The architecture of Alchemy is full of strange concepts and allegories.

Alchemy comes from the Arabic al-khemia meaningthe art of transformation.

Alchemy is an ancient science that was practiced all over the world. The most famous teacher was called Hermes Trismegistus in Greece and Thoth in Egypt. The old science of Hermes came back in the Renaissance.The essence of Alchemy is called REBIS (Res Bina), Double Matter. REBIS is the end product of the alchemical magnum opus or Great Work. It is the Fusion of Mind and Matter (the Body).

Double matter is sometimes described as the divine hermaphrodite, a reconciliation of spirit and matter, a being of both male and female qualities as indicated by the two heads within a single body.

The Great Work is the chemical and personal quest to create Double Matter, the Philosopher’s Stone. The stone is the agent of chemical transmutation, and the key ingredient in the creation of the elixir of life, said to heal all diseases, induce longevity and even immortality.

In current Physics  transmutation is proved at room temperature in a proces called Cold Fusion.

In Physics one explanation for the fusion between Quantum Mechanics and Gravity is called the Wheeler Feynman Absorber Theory. In this theory the Future causes the Past and vice-versa.

The Philosopher Stone

The Philosopher Stone

The aim of the Great Work is a fusion with the One (the Blazing Star, Saturn, Point) that is divided in the Two (Sun & Moon, Male & Female, Line) and the Four Planets (Square), the 12 (4×4-4) Constellations or more structures based on a power of a power (of a power….)  of 2. The Great Work moves from 2**N, …., Sixteen to Four to Two to One (or from one to two to four) in a Spiraling Spiral Motion.

Saturn is the 7th Star, connected to the 7th day of the week, Shabbath, the point of rest in the middle.

The Spiraling Spiral in Chartres Cathedral

The Spiraling Spiral in Chartres Cathedral

The One, to which the elements must be reduced, is a little circle in the center of the squared figure (the cross). The cross is the mediator, making peace between the opposition of the planets.

The Spiral of the Great Work

The Spiral of the Great Work

The winged dragon represents First Matter (Quintessence, The Fifth Element) and suggests ascension, a merging of matter (body) and spirit (Creativity). Creativity (Enthusiasm, Spirit, Inspiration, Imagination) is the engine behind the Spiral Wheel.

The First Matter is the primordial chaos comparable to what we now call the vacuum, the state of lowest energy. This state contains all possibilities.

It can be looked on as an unorganized state of energy  that is the same for all substances and exists in an invisible state between energy and matter.

The First Matter is the One, the Point in the Middle of the Circle. In current physics a point is called a singularity or a black hole.

Alchemy is about Recombination

Alchemy is about re-combination summarized in the Latin expression Solve (break down in separate elementset Coagula (coming back together (coagulating) in a new, higher form).

Solve and Coagula

Solvite Corpora et Coagulata Spiritus (“dissolve the body and coagulate the spirit”).

Earth (Body) becomes Water (Spirit) by dissolving it in some solvent. Water becomes Air (a moist vapor) by boiling, which further heating turns into Fire (a dry vapor).

Finally Fire becomes Earth by allowing the vapors to condense on a solid material (a stone).

The circulation may repeat if it is done in a reflux condenser, such as the Pelican or kerotakis.



The Pelican

The Pelican feeds its children with blood from the Heart. It is a symbol of the Upper Cycle of the Mind.

According to the early alchemists, the four elements—fire, water, air, and earth—come into existence via the combination of specific qualities, recognized as hot, cold, wet, and dry, being impressed on to the Prime Matter. For example, when hot and dry are impressed on the Prime Matter, we have fire.

(Hot and Cold) and (Wet and Dry) are oppositions. Their fusion is the empty set.

(Hot or Cold) and (Wet or Dry) can be combined -> (Hot, Wet), (Hot, Dry), etc.

The Cold allows substances to get together. The Hot is the power of separation.

Wet things tend to be Flexible (Fluent, Movement, Self, Not-Agency) whereas Dry things are fixed and structured (Agency, Resistance, not-Movement).

When the qualities are changed, the elements themselves are changed. Adding Water to Fire substituting wet for dry; hot and dry becomes hot and wet: steam, or Air.As you can see in de picture below Hot & Cold and Wet and Dry are Binary Opposites (“lines”) that are voided by the central cross, the point of the Empty Set, The Void (A and not-A -> Empty).

Hot & Dry = Fire, Hot & Wet = Air, Cold & Wet = Water and Cold & Dry = Earth.

There are four types of Trinities the Passion-trinity (Dry, Wet, Warm), the Structure-trinity (Dry, Wet, Cold), the Resistance-trinity  (Warm, Cold, Dry) and the Movement-trinity (Warm, Cold, Wet).

The Square rotates. The wheel of the Square is driven by the four qualities. Wet on the rising side, Hot on the top, Dry on the descending side, and Cold on the bottom.

The start is powerless (Cold). By becoming more flexible (Wet) success and power comes (Heat).  At the top Rigidity (Dry) undermines the system and it falls back to a powerless state.

The Four Triangles

The Four Elements arise out of the Quintessence, The Fifth Element, The Symbol of The Heart Chakra, the Seal of Solomon

The four Elements all share the Triangle of the Holy Trinity. Every Trinity is seen from another perspective.

The two triangels, The Up-triangel and the Down-Triangel, are Opposites that are created out of two triangels that contain two Opposites that are fused. Humans are opposites in opposition.

Humans are FourFold

Humans are part of the Bilateria,  animals with bilateral symmetry.

Humans can be described as a fusion of two mirrored bilateral triangles, the Up-triangel related to the Top of the Body (Mind) and the Bottom-triangel of the lower Body both connected by the Heart. The two triangels and the separate triangels have to be balanced.

The principle of Balancing the two Triangles of Top & Bottom of the Body is represented by the Egyptian Goddess Ma’at who weights the Heart (the connector of Up and Down) of the Dead with her Feather (Nothing).

The Balance of Ma'at

The Balance of Ma'at

As you can see the Square of the Cycle of the Four Elements is visible in the picture below. The total picture shows a Hexagram with a Center (The Cross).

The points that are missing in the Square are the top- and the bottom of the two triangels which are the Whole (Up, Heaven) and the not-Whole, Emptiness, the Bottom (Hell).

The Seal of Solomon

The Seal of Solomon

A hexagon is a 2D-projection of a Cube.

The hexagon of Solomon can be transformed into the Cube of Space of the Sefer Yetsirah.

Cube of Space

Cube of Space

The Cube of Space can be transformed into the Tree of Life.

The Tree of Life also called the tree of knowledge or world tree  connects heaven and underworld and all forms of creation and is portrayed in various religions and philosophies all over the world.

The Tree of Life shows the levels/scales (three) and possible paths of the Opus Magnum, the alchemical journey.

The Cube of Space can be transformed into the Tree of Life

The Cube of Space can be transformed into the Tree of Life.

The Spiral of Alchemy is about the Chemical Transformation of the Body by the Conceptual Transformation of the Mind.

About Truths for a Fact and Truths for a Reason

People have always believed in the fundamental character of binary oppositions like Hot & Cold and Wet & Dry are used in Alchemy.

In this part we move to the Field of Logic. In this case Hot/Cold and Wet/Dry transform into Necessary /Not-Necessary and Possible/not-Possible.

Chemical Wedding (Union of Opposites)

Chemical Wedding (Marriage of Opposites)

Oppositions can be divided in:

  1. Digital oppositions, contradictories, contain mutually exclusive terms (Gender (Male/Female)).
  2. Analogue oppositions, antonyms  or contraries: contain terms that are ordered on the same dimension (Temperature (Minimum->Cold/maximum->Hot)).
Square of Opposition

Square of Opposition

The doctrine of the square of opposition originated with Aristotle in the fourth century BC and has occurred in logic texts ever since.

The logical square is the result of two questions: Can two things be false together? Can two things be true together?

This gives 4 possibilities: no-no: contradiction (A/O, E/I); no-yes: subcontrariety (I/O); yes-no: contrariety (A/E); yes-yes: subalternation (A/I, E/O) better known as implication (A->B).

The four corners of the square represent the four basic forms of propositions recognized in classical logic:

  1. A propositions, or universal affirmatives take the form: All S are P.
  2. E propositions, or universal negations take the form: No S are P.
  3. I propositions, or particular affirmatives take the form: Some S are P.
  4. O propositions, or particular negations take the form: Some S are not P.

The square of opposition was debated for many reasons for more than two thousand years.

One of the discussions is about the difference between possible and necessary. In the so called Master Argument Diodorus proved that the future is as certain and defined as the past. The essence of logic (necessaty) implies the non-existence of freedom (possibility). X is possible if and only if X is necessary.

The term ‘possible’, in Aristotle’s view, is ambiguous. It has two senses known as one-sided possibility and two-sided possibility (or contingency). Being two-sided possible means being neither impossible nor necessary, and being one-sided possible simply means being not impossible.

Leibniz distinguished between necessary Truths for a Reason, which are true for a reason—i.e, their opposite is a contradiction—and contingent truths, (Truth for a Fact) such as the fact that the president of France is François Hollande. A contingent truth cannot be proved logically or mathematically; it is accidental, or historical (based on facts (events)).

About Geometric Logic and n-dimensional “Squares” of Opposition 

Modal Logic is about the fusion of necessity and possibility, contingency.

Logical Hexagon

Logical Hexagon

In Modal Logic the propositions are modelled in a logical hexagon where:

  1. A is interpreted as necessity: the two propositions must be either simultaneously true or simultaneously false. A is a Proof or Law.
  2. E is interpreted as impossibility. E is an Observation that contradicts the Proof of A.
  3. I is interpreted as possibility:  the truth of the propositions depends on the system of logic being considered . I is an Idea implied by the Proof that Contradicts E.
  4. is interpreted as ‘not necessarily’. O contradicts A.
  5. U is interpreted as non-contingency: neither logically necessary nor logically impossible, its truth or falsity can be established only by sensory observation.
  6. is interpreted as contingency: propositions that are neither true under every possible valuation (i.e. tautologies) nor false under every possible valuation (i.e. contradictions). Their truth depends on the truth of the facts that are part of the proposition. Y is a possible proven theory.

The Logical Hexagon has the same geometry as the Seal of Solomon. It contains the Square of Opposition (A,E,I,O).

The Logical Hexagon can be transformed just like the Seal of Solomon to the Cube of Space now called The Cube of Opposition.

The Logical Hexagon is used in many fields of Sciences like Musical Theory or Scientific Discovery.

The Hexagon of Opposition based on Musical Theory

The Hexagon of Opposition is used in Musical Theory

Every opposite can be defined by a string of zero’s and one’s like 1010. An opposite is 0101. This means that there are 2**4/2 = 4×4/2= 16 / 2 = 8 possible opposites. This is called the Octagon of Opposites.

The Octagon contains six reachable and two unreachable points in the Center (0000, 1111), the Empty Set (the Void, the Hole, Contradiction) or its Opposite (The Whole, Tautology).

Logical Geometry

Logical Geometry

The rhombic dodecahedron RDH with the standard bitstring decoration

Octagon of Opposition

It is clear that it must be possible to create higher dimensional models based on n-based-logics.

When n becomes very big the geometry will tend to a n-Dim circle in which every point is in opposition to the point at the other side.

The big problem with n-based logics is language. We don’t have the names to articulate the many grades of opposition that are possible.

The other problem is that a negation is not a symmetric operation (A = not-not-A) but a rotation with an angle 360/n.

The n-opposite-geometries are highly related to Simple Non-Abelian Groups (SNAGs). They play an important role in biology.

The last step is to transform the static n-opposite geometries by making n very large (infinite) to a dynamic “opposition field”.

Related Models

In current Psychology Hot & Cold are called Communion and Moist & Dry, Agency. Together they create the so called Interpersonal Circumplex.

Interpersonal Circumplex

The four stages of Learning by Jean Piaget.

The mathematical model behind the theory of Piaget is called the Klein Four Group or Identity/Negation/Reciprocity/Correlation-model.


INRC-model of Piaget

INRC-model of Piaget

In the Science of Ecology (Panarchy) Agency & Communion are called Connectedness and Potential. The Panarchy model looks like a Mobius Ring.

panarchy model

panarchy model

A model that describes the Four Perspectives on Security:


The Semiotic Square of Greimas:

Semiotic Square

Semiotic Square

The Chinese Sheng-Cycle: The Chinese Five Element Model is comparable to the Western Four Element model. It contains as a Fifth Element, the Whole-Part-relationship (Earth, Observer State). Emptiness (Nothing, the Tao) is represented by the recursive Pentangle inside.

The Sheng Cycle

Tetralemma (Ancient Indian Logic)

Tetralemma (Ancient Indian Logic)

The lesson

When thou hast made the quadrangle round, then is all the secret found“.

The secret: It is impossible to move though the center because the paths that go through the center are a contradiction or a tautology (I am what I am, JHWH).

We have to move with the Cycle (making the rectangle round (a circle)), around the Singularity (the Hole of the Whole), going Up and going Down all the time.

The only way to solve this problem is to join the opposites by accepting only one thruth-value, by:

  1. Accepting everything (Wu Wei),
  2. Denying everything (Stoics) or
  3. Diminishing the amount of dimensions (“becoming Simple”, “like Children”) by moving up in abstraction (Hot & Cold -> Temperature -> Everything is Energy) to the level of zero dimensions, a point, becoming One with the First Matter (Tao/Vacuum).

“If we then become children, would we thus enter the kingdom?” Jesus said unto them, “When ye make the two one, and when you make the inside like unto the outside and the outside like unto the inside, and that which is above like unto that which is below, and when ye make the male and the female one and the same, so that the male no longer be male nor the female female; then will ye enter into the kingdom.” (Gospel of Thomas, Logion 22).


About the Geometry of Negation

About the Logic of Music

About Wu Wei

About Modal Logic

About the Cube of Opposition

About Logical Geometry

About the Square of Religion

Semiotics for Beginners

About Holonomic Alchemy

About Paths of Change

About the Sheng Cycle

How to use the Square of Opposition as a Research Tool

About the Cube of Space of  Sefer Yetzirah

About Truth of Reason and Truth of Fact

Why Humans are Toolmakers

About Chemical Transformation (Cold Fusion)

About the Ars Generalis Ultima of Ramon Lull (1305)

About the Six Domains of  the Polynomic System of Value

About the Logic of Creation

About Leibniz Calculating Machine

About Zero Dimension 

Why Innovation is Re-Combination

How to Balance the Seal of Solomon

About Interpersonal Theory 

About Panarchy

About the Hexagon of Opposition

About n-based logics

About Flow-Systems

Anti-Fragility and the Square of Opposites

An Introduction to Hexagonal Geometry

About Whole and Parts

Tuesday, December 23rd, 2008

The Whole of Reality is divided into many overlapping Parts. Most of the Humans look at Wholes and Parts (Smaller Wholes, Contexts) from a Static Perspective but the Whole is also a Dynamic Entity. The Parts are overlapping because many people don’t know how to define the right categories. Overlapping, confusing, part/whole relations are the sole cause of every conflict and war.

The Static and the Dynamic can be divided in two parts. In the first part of the Static we combine the Parts in a different way (Combine, Create). In the second part of the Static we define a Boundary around a part of the parts to protect the Territory (Control). In this case an Outside and an Inside is created.

The Dynamic can be divided in a Causal part (Time) and a Connected Part (Space). In the first part we create a Causal Network in the second part we create a Relationship Network (Social).

The Four (4) Parts of the Two (2) Parts of the Whole can be divided deeper and deeper. The Next division generates sixteen (16) Perspectives.

The big problem is to Name all the Division with a proper Term. Have a look at the Model Below.






Dynamic Whole
























































































It becomes much easier when the Names are substituted by Numbers. First we have to create a Number System. We use the same procedure.

We start with the Whole Numbers. They are used to Count. We could also use the Prime Numbers since they are the basic parts of the Whole Number System.

The Rational Numbers are the result of the operation of division. They can be represented by the harmonic series (1,1/2,1/3,1/4,..).

Irrational numbers (Pi, e, phi, sqrt(2)) capture the static relationships, the rules of the whole. They are not numbers because it is impossible to count with them. Irrational numbers can be constructed by combining the parts of the harmonic series;

Imaginary numbers capture the transitions (cyclic change) and transformations (change of form) of dynamic relationships.







Dynamic Whole
















































In the next part we have a look at a very old (5000 BC!!) Universal Rule System of the Whole Numbers. This System is called the Lo Shu. The Lo Shu is a 3×3 Magic Square. Every straight line of three numbers adds up to the number 15. The Magic, Every Sum of Three Amounts to 15, is the General Rule that keeps the Opposites together. It is a very Simple Rule with spectacular consequences.

The 3×3 Magic Square shows a very old wisdom, “Everything Comes in Three“. Two Opposite Forces are always balanced by a third Force, the Mediator.

When we subtract every number of the Lo Shu (Left) with the number in the center (5) a new Magic Square appears (Right) with a zero sum.

This Magic Square shows interesting symmetries:

1. The numbers (8,2), (9,1), (4,6), (3,7) have a zero sum. They are Opposites if we use the number 0 as the Center of the Opposites of the Whole Numbers. In this way we are able to reduce the numbers to five (0,1,2,3,4).

2. The numbers (3,2) and (1,4) add up to 5. They combine in a “strange” 2×2 Magic Quadrant. If we transform this quadrant to a base 0 (by subtracting 1), the Magic 2×2 Quadrant can be transformed into a Binary Quadrant (11,01,10,00) again with interesting symmetries. The basic forces are brought back to two, Expansion and Contraction (Yang and Yin, 0 and 1) with the “0′ in the Middle.

There are many more symmetries to be found in the basic Magic Square of the Universe but it is impossible to explain them all in this small blog. One of the most important symmetries in the Lo Shu is a Cycle. It helps you to travel the many possible combinations on every level.

The Old Chinese Scientists used the Symmetries of the Lo Shu to create a cycle called the Sheng Cycle. This Cycle is the Cycle of the Seasons but also the Cycle of the Body (Acupuncture), the Cycle of the Context (Feng Shui) and the Cycle of Astrology.

Below is a small part of a huge correspondence table that makes it possible to reuse the practice of one field  of Science (Nature, The Seasons) in a completely different practice (Medicine, Psychology).

If You are Angry You are in the Negative State (Counter the Clock) of the Spring State of the Sheng Cycle (called the Insulting Cycle) and you will have problems with your Liver and Gallbladder.

Something, an Idea You cannot Express, wants to Come out to expand in the Summer-State.

Perhaps You Have to start a Design but do you have a Plan?

What is the Whole You are Looking at?

What are the Boundaries?





























Lo Shu

Lo Shu

































Small Intestine




































Other scientists found many more relationships between the Lo Shu and Physics (Tony Smith), The I Tjing (Chris Lofting), The Tarot, Archetypes (Jung), Myths (Campbell), Historic Cycles (McKenna), Personality Types (MBTI, Enneagram), Left/Right Brain (Chris Lofting) and much more.

How to use all this knowledge

1. Always look at the Outside of the Boundary of the Context you want to analyze. If you cannot divide a Context in an Inside and an Outside you have done something wrong.

2. Always look at the Static AND the Dynamic part of the Context.

3. The Dynamic Part of the Context is related to a Cause/Effect-pattern (Time). Something is happening!

4. Look at the Social Dynamic Part of the Context. Entities, Objects, Roles, Humans are connecting the Time Lines. They are the Relations in your Static Model.

5. Always try to find New Combinations. If the Context is blocked it wants to move to another Time Line. Remove the Blockages!

6. If you want to analyze the Context one step deeper (16/25 perspectives, watch out, can you handle this?) try to make all the combinations that are possible. Use the Table in this Blog or create Your Own table (Fun). Read the PDF of Chris Lofting! Always use the Sheng Cycle!

7. Want to move much deeper? Use the Whole Numbers. Find Patterns (Irrational, Imaginary Numbers) and transform the patterns into Words. Use Fairy Tales, Myths, Archetypes, Music to explain the transformation.

8. Always Move Up in the Sky (Abstract, Fuse, Integrate) and Down to Earth (Implement, Try Out). Try to Unite what You have Divided. Keep an Overview. Reflect.

There is much more to say but I think you have enough food to digest.


Chris Lofting, How to Create Sound Categories using the I Tjing

 Tony Smith, About The Lo Shu and Physics


Why God is a Topologist

Saturday, November 29th, 2008

god_geometry_bigSometimes I am getting very frustrated when I read spiritual books. I am getting frustrated because those books are a very complicated mixture of many other books that are also very complicated mixtures of other books.

The most complicated spiritual books are the books that use mathematical or physical theories to proof they are Right. The main reason is of course that mathematics and physics is complicated stuff to understand.

Mathematics contains the essence of Physics. You have to understand a little bit of mathematics to understand elementary Physics. The essence of Mathematics is Geometry. When you understand Geometry the rest of mathematics is just calculation (Algebra).

Geometry started as a very practical science concerned with navigation in space and the measurement of all kinds of forms. Soon the old scientists discovered interesting and unexplainable patterns. They discovered a hidden, sacred, structure behind reality and started to find ways to proof their intuiton was right.

It was not for nothing that Einstein believed God was a Geometer. Much earlier the Mystic School of Pythagoras tried to find the Sacred Geometry behind the Numbers to understand the Whole. At this moment Geometry has advanced a lot in relation to the old days of Pythagoras and even Einstein. Geometry is now called Topology, the Science of Spaces. In terms of Einstein, God was a Topologist.

To proof the theorems of Geometry the concept of congruency was used. Two figures are congruent if they have the same shape and size, but are in different positions or in more difficult language,  if they can be transformed by a combination of translation, rotation and reflection. When two figures are congruent they are “the same” and when things are “the same” you are able to prove theorems.

During the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. In the Renaissance the perspective, looking from a different angle, was added as a “the sameness”. Circles and ellipses became part of one class.

A “the sameness” has a lot to do with Identities and Wholes. When your view on “the sameness” changes you are able to identify a different whole. The new concept of the Perspective made is possible to “see” the Sun as a persistent object instead of an ever changing object.  

During the Renaissance the Sun became the Center of the Whole. The highly confusing worldview of the Middle Ages where something was the same when it really was the same object in reality slowly faded away. The external world became the world of the Eye, the microscope and the telescope.

Topology changed this view dramatically. In topology, any continuous change which can be continuously undone is allowed. So a circle is the same as a triangle or a square, because you just pull on parts of the circle to make corners and then straighten the sides, to change a circle into a square.

In the View of Topology the Sun is nothing but a small part of an ever expanding and contracting Universe. Topology transformed the external World of the Eye into the Internal World of Moving Water, Waves and the Emotions, the Felt Sense.  Topology is the Science that prepares the Way for the Water Bearer, Aquarius.

Topology is just like Geometry not only the science of space. It is also the science of transformation and transformation is also the essence of spirituality.

The major issue of Topology is the Contraction and Expansion of forms and again the essence of spiritual transformation is the Breath of God, the Holy Spirit. Topology has also a lot to do with Harmony or Symmetry and again Realizing Harmony is one of the major issues in Spirituality.

The interesting part of Topology is that you are able to do research on a huge scientific mathematical domain by exploring just one structure which is a representative of all the other structures.


The first object of interest are the Circle and The Line. It is not possible to transform a Circle into a Line without cutting the Cycle in one Point, Infinity.

In a circular, moving world, Infinity is non existent or every Point of the Circle corresponds with Infinity. 

This is an  interesting insight because  almost nobody doubts about the fact that the space we live is a Circular Rotating Space. In the World of the Circle  The very Small and the very Big are the Same.



According to the Physicists our Space is a much stranger Space than a Circular Space.

Our Universe is highly dimensional because the complicated symmetry of our Universe simply does not fit in a lower dimensional space.

The most symmetric object, strangely called the Monster, uses 196,884 dimensions.

We, the Humans, travel a small part of the Monster, because we are not able to see enough perspectives. A perspective is a dimension.

One of the most interesting subjects is Self-Reference. The most simple Self-Referential structure is a Circle.

Topology contains very special Self-Referencial Structures like the Moebius Ring and the Klein-Bottle. The Moebius Ring is a Space without an Outside. It is closed in Its Self. You always travel the same surface.

klein bottle

A Klein Bottle is even stranger. Its surface is Closed in Itself but it has no Inside and no Outside. It simply IS. 

A Moebius Ring exists in our 3-dimensional space.

A Klein Bottle needs 4-dimensional space. The Klein Bottle has a lot in common with a very old concept, the Ouroburos, the Snake who eats Himself. The Snake is a symbol for the Kundalini, the Force of Enlightment.

knotMore complicated topological structures are Knots and to give you a quick insight, the Universe is a Web that was never Woven, a beautiful Veil that is difficult to See when you are travelling a small part of it.

I know this small blog will not help to get an insight but I assure you that when you start to explore Topology You will encounter new Concepts (or Paradigms) that will surprise You.

Topology will  give You a still small but highly extended perspective on the Creation of the One that expanded in so many Harmonic structures.


The History of Topology

About our Limited Perspective and the Limits of Reasoning

About the Topology of Art, a Short Introduction to Bahktin

About Free Will, Time and the Monster

About the Moebius Ring and the Klein Bottle in Philosophy

About Self-Reference in Physics

About Knots in Philosophy

About the Klein Bottle

A Very Strange Way to Explain the Current Crisis

Thursday, September 25th, 2008

I wrote and thought a lot about Time and Time Travel. My investigations made it clear to me that Time Travel must be possible and is also happening. Most people are not aware of the Cyclic Patterns of Time.

They think Time is a Line extending into Infinity. The Cyclic Patterns are moving With the Clock and Counter the Clock. At this moment The Cycles are Reversing in Time. This explains the current Crisis.

The conclusion of my research in Time was that we are traveling through a Vibrating Static Structure, A Fluent Crystal, which contains a huge amount of possible paths. We have Free Choice to travel the many Paths but the Amount of Possible Choices is fixed.

When we are traveling and return at the same point we started our traveling, we have gone through a Cycle.

When you go to work in the morning and return at home in the evening and repeat this sequence day after day you are moving through a very simple cycle. When you Repeat the Same Mistakes all the Time you are moving through a Cycle. When you are Born and Die you are moving through a Cycle called Life.

Cycles can be very complex. They are sometimes so complex that you are not aware you are repeating the same pattern all the time. You are experiencing the Feeling of Freedom of Choice because you are not Observing Your Path.

When you are Capable of Observing Your Path the Cyclic Behavior Ends. You Watch the Cycle but you are not In the Cycle. You are freed from the Cycle when you don’t make a Choice at all. This is what the Chinese Masters call the Tao.

Cycles basically move in two directions. They move With the Clock and Counter the Clock. Our Clocks move With the Clock so we assume that Time is moving With the Clock. When we move Counter the Clock we are moving Back in Time.

Cycles With the Clock, are Positive, Generating, Cycles.

Cycles Counter the Clock , are Negative, Destructive, Cycles.

The direction of a rotation is called Spin.

If we combine two Cycles that are moving With AND Counter the Clock an interesting structure appears. This Structure is called the Moebius Ring and is often used to represent the Symbol of Infinity, the Lemniscate or Ourobouros (A Snake).

The Moebius Ring is a very interesting structure because it does not have an Above and an Under. When you are traveling the Boundary you are always traveling the Same Surface. The Moebius Ring is easily constructed by connecting the two ends of a strip of twisted paper.

To Change the Direction of a Cycle you have to introduce a Twist.

To Travel Time you to have to Twist Time.

The Twist is an interesting concept. One of the Questions you could ask is if You would experience a Twist when it happened. The answer is Yes and No. Yes, when the Twist is an Up or Down Peak (An Event). No, when the Twist is a smooth path.

The most interesting Peak Experience in Life is Death. At that time the Cycle of Life is closed and another Cycle with a different Spin starts. Many cultures believe the Cycle of Death is real. In Western Society many people believe the Cycle of Death is non existent. Scientists are spending a lot of time to prove that the moment of Death is the End of Everything.

History is moving through Cycles. At some point in time many people feel History is Repeating Itself. Most of the time people believe the Cycles are moving into a certain direction. They are moving UP and DOWN. When you look at the Economic Cycles the data show that the Economic Cycles are Moving UP.

In reality the UP Cycle behind the Economic Cycle is another Cycle that is in its UP-state. Behind this Cycle is another (Long-Term) Cycle and another Cycle and …but somewhere the Cycle of Cycles (A Spiral) is Closed in Itself (A Spiraling Spiral). Just like the Moebius Ring there is no Above and Under. We are (Time-)traveling a Boundary that is closed in itself.

I don’t think many people will disagree with the concept of Cycles in History. The Theory of Economic Cycles has proven itself without any Doubt.

I don’t think many people understand that Cycles are moving in two directions. They believe the Cycles are moving With the Clock. If you believe Cycles move With the Clock it is easy to see that the Seasons are a beautiful Metaphor to understand Cyclic Behavior.

But what will happen when the Cycles of History move Counter the Clock???

If we would move through time Counter the Clock History would repeat itself just like History is Repeating Itself when we move With the Clock but the Stages of the Cycle (The Seasons) would show themselves in a Different Order.

If the Cycle With the Clock is an UP Cycle, the Cycle Counter the Clock would be a Down Cycle.

If you read the references in this Blog you will see that Western Culture is (or was) moving Counter The Clock, a CYCLE of DESTRUCTION.

The Cycle of Destruction (Capitalism, Materialism) was seen as a positive Cycle by many People but now they are becoming Aware of Reality. Western Culture is destructing Nature. It is not only destructing Nature but it is also destructing Human Culture.

At a certain point in time the Cycle HAS TO REVERSE. This TWIST is a Peak Experience, a Major Crisis. I hope You now See what is really Happening. We are Reversing the Cycle and the new Cycle is a GENERATING CYCLE. We are really Moving UP into a new state of Consciousnesa. This new state is not the state people who love materialism and capitalism (and War and Destruction and Greed and Control and Desire and …) will like.


About The Twist in History

 About the Twist in Literature

About Cyclic Behavior in History

About Cyclic Behavior in History

Using the Seasons to Understand Cycles


About Balfour and the End of Time.

Monday, July 21st, 2008

Gottfried Wilhelm Leibniz lived between 1646 and 1716. He was a universal scientist and made contributions to mathematics, philosophy, technology and social sciences. Leibniz did not believe Time and Space were real. Current developments in Physics prove that Leibniz was right. We are approaching the End of Time and Space.

The observation that time is a linear chain of events moving from the past to the future is wrong. Our believe-system makes a selection out of an infinite amount of (disconnected) Events.

The events are part of a very complex Framework, a Fluent Crystal, which is slightly out of balance. With every change of the Crystal new Shapes, or Configurations, are formed but the Crystal, the Structure, The Geometry, is not changed.

According to Leibniz Our world is the world which is at the same time the Simplest in hypotheses and the Richest in phenomena. There are many other possible worlds because there is an infinity of possible laws. Some of the laws are proper to one world, others proper to another. Each possible individual of a world includes the laws of its world in its notion.



The Universe of Leibniz is filled with Individual Monads (Souls) who are Observing. A Monad is pregnant with the future and laden with the past of his own World. Past and Future are folded up within the Monad.

A Monad is always in the Now. We are part of a Monad and the Monad is part of Us. We are One Mind that is fragmented by a Cosmic Accident. All the Minds contain the Sparkle of the Whole and are desperatly trying to Unite.

Leibniz does not believe in cause and effect (Time). They are a way to explain what we See. The Universe is What it Is. It contains a Pre-Established Harmony. We are a product of Our Senses and the Senses are creating a very Narrow View of the Universe. We Think the Universe is What We See and create Theories that prove that we are Right but all the Theories until now contain a fatal error.

They are proving that Time is Linear and Space is Distance. We are unable to travel Space because we are not able to exceed the limit of Light. The prove of all these theories is based on Infinite Regress and Infinite Regress is a logical mistake. Our Universe is not “Turtles on Turtles“, “Particles all the Way Down”.The Universe is a Fixed Structure and we (the Monads) are exploring this Stucture.

Every monad mirrors the Whole of the Universe in that it expresses every other monad, but no monad has a window through which it could actually receive or supply causal influences. A monad cannot be influenced, there is no way for a monad to be born or destroyed. All Monads are Eternal. They are always Watching the Others. The only thing that changes is the Way they Watch, Their Point of View. The Monads are Alone but they are also Together because Every Monad is an Expression of the Same Principle, Harmony, Beauty or Love, The Fluent Crystal, That IS.

When a Monad is Watching it is capable of having an infinite number and complexity of perceptions. We (our Brain, Our Senses) are not conscious of all these “little perceptions” (Events), as Leibniz calls them. We connect some of them, create a “stream of consciousness” and make up a convincing story. We are constantly filtering our perceptions. The Filter is our Believe System. A huge part of What we See is not Seen but Projected on the Outside World. We See what we want to See.

The main characteristic of Our Universe is Varity. We are constantly generating new Insights of the Whole. Our Universe is a Field that is creating New Exiting Combinations that are Creating New Exiting Combinations. It always Changes because we the Observers are Changing our Point of View.  Our Universe is a Creative Universe.

The independent physicist Julian Barbour used the philosophy of Leibniz to create a completely new vision on our Universe. His vision can be found in his book “the End of Time”.

In a blog I wrote about Seth. Seth is a Monad who uses channeling (an Exchange of Energy) to explain the Physical Universe. Seth shows how we are Creating our Own Reality and what we can do to create the Reality we really want. A few days ago I found Elias. Elias is also a channeling Monad. Elias uses the Concepts of Seth to explain what is Happening at this Moment.

A small citation:

You all notice a change in consciousness of your world. Even those who are unaware notice a changing shift in consciousness“.

“The action of your shift in consciousness encompasses the entirety of your globe. It is not limited to any group, any family, any selectivity of consciousness within this dimension. It is all-encompassing”.

You have chosen, within this dimension, a new experience in creativity. You have chosen, within what you term to be your history, certain actions and experiences for long time periods, in your terms. These have been purposeful for those experiences. You presently move away from your religious era, which has continued for quite some physical time period, into a new awareness in consciousness, to allow you an expanded creativity and allow you to utilize your abilities of essence within physical focus. You are expanding your reality to encompass more of essence and more of your own creative abilities

What Elias is explaining is what Leibniz (and Balbour) are explaining but he explains Much More. He explains Why we are moving into what the Old Scientists called The Golden Age. We are moving into the Golden Age because we are bored by the Way we are looking at the Fluent Crystal.

We have explored every part we are able to See. We are blocked by all the Hierarchical Systems (Religion, Science, Politics, Banking) that are not based on a Solid Foundation. The Foundation of the World is not based on Hierarchy but on Relationship. We want something New. Something that gives US, the Monad of this Possible Universe, the Opportunity to Explore and use OUR Creativity.

The Golden Age will be a time when the Financial System of the Earth will collapse, War, Aging and Sickness will disappear and traveling Time/Space will become possible. The Doors of Perception will open wide and many new parts of the Beautiful Crystal will become visible. The most important potential of the Golden Age will be Unlimited Creativity.

The huge change in Focus on a completely New Part of the Crystal Field will destroy all our current Believe-Systems. This will create an enormous amount of Chaos and Trauma but in the end we will live in something we now would consider Paradise.


An Interview with Julian Barbour about the End of Time

An Article of Julian Barbour about the Philosophy of Leibniz

The Philosophy of Leibniz

About the Shift that is happening at this moment, The Website contains all the material of Elias


About Pan and Anarchy

Thursday, September 20th, 2007

panIn 2002 the book Panarchy: Understanding Transformations in Human and Natural Systems, (Gunderson, L.H and Holling, C.S (eds)) was published. To my knowledge this is one of the most important books of our time.

Panarchy is the first theory that is able to explain the behavior of complex ecosystems. It is an integration of many former theories in economics, biology, ecology, sociology, mathematics, psychology and other sciences.

Have a look at RA to learn more about Panarchy. You will be surprised by the amount of interesting articles and insights.

In this blog I will use long citations: “The world has not collapsed because natural ecological systems have the resilience to experience wide change and still maintain the integrity of their functions.

The world also has not collapsed because of human behavior and creativity. People do learn, however spasmodically. Change and extreme transformations have been part of humanity’s evolutionary history. People’s adaptive capabilities, have made it possible not only to persist passively, but to create and innovate when limits are reached.

The controls determined by each set of biotic structuring processes within terrestrial ecosystems are remarkably robust and the behaviors resulting are remarkably resilient. That robustness comes from functional diversity and spatial heterogeneity in the species and physical variables that mediate the key processes that structure and organize patterns in ecosystems and landscapes.

The stability domains that define the type of system (e.g. forest, savanna, grassland, or shrub steppe) are so large that external disturbances have to be extreme and/or persistent before the system flips irreversibly into another state. Except under extreme climatic conditions, Mother Nature is not basically in a state of delicate balance. If She were, the world would indeed have collapsed long ago“.

panarchy model

The books starts with a description of the five metaphors or world-views that are used to look at Nature. These metaphors are the same metaphors Bhaktin uses to describe the proces of the evolving narratives in human culture.

The World-Views are connected to Mathematical Models that are commonly used in Science to explain an Ecology. The authors show that every model has its consequences. The most beautifull thing they show is that these models are not wrong. They are needed to keep the Cycle of the Ecology running.

panarchy levels

What they also show is that a Panarchy-cycle uses a memory when the Ecology is collapsing. Somewhere a small area is preserved. It contains the “seeds” of the new Cycle. We have to look back when we want to move foreward. We also have to look back to learn form our mistakes. “People do learn, however spasmodically”. Learning is not copying. We have “to create and innovate when limits are reached”.

Somewhere in History the Seeds of the New Cycle are available. A beautifull example is the Sacred Groove. It is a place where very old trees are preserved by the local community. They need the trees to aquire medicine to cure deseases or snake bites.

Because the new Cycle has to be based on Harmony I feel you have to have a look at China. China is not only the Economy Power that is able to destroy the World when it moves on the way it moves. It is also the Culture where Harmony was the basic Concept. When you read my blogs you will see that I use many Chinese Concepts to explain.

The theory is a Self-Referencial (“Fractal“) theory and uses the Moebius Ring as the central concept. You understand why I was flabbergasted when I found Panarchy on the Internet.

The last thing that made me very enthousiastic is the name Panarchy. It is based on the name of the Old Greek God of Joy and Nature, Pan.

Pan was “Goat-legged, enthusiastic, a lover of ectacy, dancing among the stars, weaving the harmony of the Cosmos into playfull song” (The Orphic Hymns). The myth was told in Early Creece that he had left the Earth. It is of a high urgency that we ask Pan to come back. We can only save Mother Nature when we become enthusiastic again to weave Harmony all over the World.

Pan is also the God of Dance and Rythm:

Complex natural systems work in rhythms – with a front-loop phase of slow, incremental growth and accumulation, and a back-loop stage of rapid reorganisation leading to renewal, to, collapse. The front-loop phase is more predictable with higher degrees of certainty.

In both the natural and social worlds, it maximises production and accumulation. The consequence of this is an accumulation and concentration of wealth, but also emergence of greater vulnerability, due to the increasing number of interconnections that link that wealth, and those that bear it, in efforts to sustain it.

Little time and few resources are available for alternatives that explore different visions or opportunities. Emergence and novelty is inhibited. This growing connectedness leads to increasing rigidity in its goal to retain control, and the system becomes ever more tightly bound together. This reduces resilience and the capacity of the system to absorb change, thus increasing the threat of abrupt change.

We can recognise the needs for change but become politically stifled in our capacity to act effectively. Wealth and broadening wealth accumulated to lead to our present vulnerability on a world stage.

We are entering the back loop of re-organisation that entails the collapse of accumulated connections, the release of bound up knowledge and capital. But it also opens a creative potential and the opportunity for ‘creative destruction“.

The World and Our Society is now in the non-predictable back-loop stage of rapid reorganisation, creative destruction, collaps and renewal. It will soon jump back to an early stage where the Seeds of the New Cycle of Creation are Stored.

Because the Long Term Cycle of Earth is now Collapsing we have to look back for a long time to find the Seeds. The most impressive collaps of our World happened when the Great Flood appeared at 3117 BC.

Strangely enough 3117 BC is the start of the Mayan Calendar and the Indian Kali Yuga (“The Dark Age“).  Before that time the Humans lived in the Green Sahara also called Paradise. At that time Pan, the God of Nature,  was still there.

Do we have to move back to Paradise to Start All over Again?


About Panarchy

About the Great Flood

About Social Cohesion

About World View

About Chinese Concepts

About the Fractal Universe

About the Green Sahara and Paradise

Catching the Light: About Steiner, Goethe and The Placebo Effect

Wednesday, June 6th, 2007

When I was working at ABN-bank I was doing a project to reorganize the Archives of the bank. One of my colleagues was heavily inspired by the work of Rudolph Steiner. He was very busy to create a new type of bank based on his ideas (now The Triodos-Bank). 


At the same time I met people that were practicing his ideas in the process of automation and organizational change processes. I loved what they were doing so I started to read his Books. 


Steiner came back in my life when I wanted to know more about Colors. I bought the Color Theory of Goethe and I found out that Goethe was the person that inspired Steiner the most. 


Goethe and Steiner became a force of Inspiration for Me and my Wife. She started to do Art-courses and I saw that she loved it. She even considered to become an Art-Therapist. We visited the Goetheaneum in Dornach (Zwitserland). We found an Antroposophic general practitioner. She uses Homeopathic medicine. I practiced Eurhythmics and lately I got a treatment to strengthen my “boundaries” where they use the Essential Oil of Flowers.


Arthur Zajonc is a well known Professor of Physics. He is also inspired by Rudolph Steiner and Goethe. Many people think the ideas of Steiner are weird and non-scientific but as you see even a professor of Physics knows that what he is saying to the world is of tremendous value. 


Arthur Zajonc wrote a beautifull book called “Catching The Light”. The book tries to explain Light.  It uses two perspectives. The perspective of Physics and the perspective of Steiner.


Zajonc shows that Science and Spirituality are basically telling the same story. Mind, Spirit and Soul are seeing the same thing but use different words to describe the same phenomenon.


 The most interesting part of the book is about the Imagination. Experiments show that we don’t see with our eyes. We see the world through our Imagination. 


Experiments in Physics show also that our Imagination (Our Creative Power) is controlling the Material world. Matter (Photons) is doing what the Imagination wants them it to do. We Get what we See.


Many people don’t understand the impact of this. They Think we are controlled by an outside Force (Fate) and they don’t realize that everything they are encountering in Life is created by Themselves. They don’t want to see that the Outside World is reflecting their personal creative process. If things go wrong they don’t realize that they want them to go wrong.


How can we make things go right? It’s simple. Imagine they are going right. Think positive.

Do you know why Medicine is working? 

Because we Believe its Working. 

I Love the Placebo effect!