Posts Tagged ‘architecture’

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.

Classic 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 meaning the Black Soil of Egypt (or the ((Egyptian) Black Art). Alchemy is the 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 Spirit and Matter (the Body). Spirit is the Creative Part of the Human.

Double matter is sometimes described as the divine hermaphrodite, 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, Spirit in Matter.

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. We are always in the Now, the Middle between Past & Future.

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.

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, The Kingdom).

“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 Plato and Harmony

Monday, January 5th, 2009

Sri Yantra

The teachings of Ancient Civilizations are often Self-Referential.

The same knowledge is showed on many levels.

What we see with our Senses is an Illusion. Behind this Illusion lies a deeper structure.

The last and deepest level of the ancient teachings is always related to Numbers, Geometry and the Trinity.

This blog is about one of the most important geometric structures of the Trinity called the Sri Yantra.

In the ancient teachings a problem is defined and the teacher gives a clue how to solve the problem.

If the pupil has solved a problem he is able to move to a deeper level.

The whole idea is that real knowledge, wisdom, is only discovered, when the pupil has solved the puzzle of life him- or herself.

Let’s have a look at a Deeper Level.

A deep level is related to a number called Phi. Phi is called the Golden Ratio or the Divine Proportion. It is the real solution of the quadratic equation x**2-x-1.

It is also a solution of the proportion a:b=b:a+b, the sequence of Fibonacci x(n+2)= x(n+1) + x(n), the geometric structure of the Pentagram, the Fifth Element (the Quintessence, the Ether) and the Logarithmic (Golden)Spiral.

Phi is the pattern behind the Egyptian Pyramids, the Stock Market, Harmony in Music and Architecture and many other fields of science including Physics.

Let us first have a look at the way the old teachers have hidden the knowledge of the Divine Proportion in their teachings.



A beautiful example is Plato.

Plato was an initiate of the Mathematikoi, the Secret Society of Pythagoras. Pythagoras was initiated in the Secrets Societies of Egypt.

What do you think of this problem-statement:

What are the most perfect bodies that can be constructed, four in number, unlike one another, but such that some can be generated out of one another by resolution? … If we can hit upon the answer to this, we have the truth concerning the generation of earth and fire and of the bodies that stand as proportionals between them (Timaeus 53e)”


Two things cannot be rightly put together without a Third; there must be some bond of union between them. …and the fairest bond is that which makes the most complete fusion of itself and the things which it combines, and proportion (analogia) is best adapted to effect such a union”.


“For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it, and again, when the mean is to the first term as the last term is to the mean – then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one [Timaeus 31b-32a]“.

In the last citation Plato is formulating a mathematical problem related to the four bodys A,B,C,D with the three proportions A:B = C:D = (A+B) : (C+D) = (C+D) : (A+B+C+D). This problem is unsolvable if you don’t have a clue where to start.

This problem is solved when you realize that the Divine Proportion has many strange relationships that are very useful to solve the puzzle.

These relationships can be found if you know everything there is to know about Triangles and Triangles are again related to the Trinity (“Two things cannot be rightly put together without a Third“).

The Trinity comes back in the structure of the Dialogues of Plato. They are divided into Three Parts (and an introduction).

The structure of the dialogues relates to itself.

movmetatronThe knowledge of the self-reference of the Dialogues is also a clue to solve more complicated puzzles about the Dialogues themselves.

Just like the famous book of Hofstadter (Goedel, Escher, Bach) the dialogues show a new layer everytime they are read with a new aquired Insight.

The dialogues of Plato are organized according to the model he wants to teach. There are seven layers (-1,-2,-3,0,1,2,3) related to the Seven Mirror-Universes (or Hells and Heavens) of Our Universe (Eight, the Whole) in our Multi-Universe.

The Seven is a combination of Two Trinities with the Zero (The Void) in the middle. The Eight (2**3) State is the Dialog, The Whole, itself.

The Seven layers are divided into Three Sections (the Trinity) so the total amount of clues is 7×3= 21 + 1 (the Whole) = 22.

22 divided by 7 is an approximation of the number π (Pi).

Pi relates the Square to the Circle.

The Square represents the Playing Board of the Universe. On this Board we, the Humans, play our Game of Free Will.

Our Free Will is an Illusion. We are controlled by the Matrix.

The Circle represents the Wheel of Fortune, the Matrix, that Governs the Seven Universes in our Multi-Universe and the Game of Life.

What is Plato Trying to Explain?

golden ratio

The Golden Ratio

The Divine proportion is the basic concept behind Harmony.

The Divine Proportion is Not Symmetrical so Harmony is not related to Balance.

If everything would be balanced the Universe was never created.

Harmony is Balanced Unbalance.

An Architecture is beautiful when there is a slight unbalance in the Design.

This Unbalance shows the Sign of the Creator.

The Universe is created out of an Unbalance between Two Forces, the Positive and the Negative, the Good and the Bad.

The Two forces (-1,0,1) are divided into Four Forces (-2,-1,0,1,2) with the One in the Middle (Five) and are expanded into Seven Levels (-3,-2,-1,0,1,2,3). The Four Forces are “the most perfect bodies that can be constructed, four in number“.

The Seven Levels are related to the Circle. The Four Forces are related to the Square. The Universe oscillates between The Square and The Circle.

When the Square, the Game We Play with the Four Forces and the Circle (The Five Fold Cycle, Our Destiny) are in Balance the Human is in the Tao and Magic happens.

Every division is a split of the Trinity into Trinities until a state of Balance is reached. At that time the process reverses.

mt meru

Mount Meru

The unbalance of the Good (+1) and the Bad (-1) is an Illusion. They Cooperate to Create Harmony (0).

Behind the perceived Unbalance is a balancing principle, the Divine Proportion. This principle brings everything Back into the Balance of the One who is the Void (0).

What we don’t know is to be known if we understand the progression of the Divine Spiral.

The Future, the Third Step, is a Combination of Two Steps in the Past (The Fibonacci Sequence), nothing more.

Is there a Deeper Structure Behind the Divine Proportion?

golden mean spiral2

Golden Mean Spiral

The Four Forces (Control, Desire, Emotion(Compassion) and the Whole of the Trinity, Imagination) and the related sacred geometry were a guiding principle for the Imagination and the E-Motivation of many Western Scientists.

They tried to Control the Chaos of the Desires of the Senses by enforcing the Rules of Scientific Falsification.

The Proces of Falsification destroyed the Human Intuition.

The Western Scientists forgot to look at the Source of Intuition, the Center, the Quintessence (The Fifth, Consciousness).

The principle behind the Quintessence (Ether, Chi, Prana) is related to higher order symmetries and is a solution of a generalization of the generating function of the Divine proportion X**2 -X – 1

This generalization is X**2-pX-q or X(n+2) = pX(n+1) + qX(n). The solutions of this formula are called the Metallic Means.

When p=1 and q =1 the Divine proportion comes back again.

When the p=3 and q=1 a new sequence X**2-3X-1 or X(n+2) = 3*X(n+1) + X(n), the Bronze Mean appears.

The Bronze Mean generates the pattern: 1,1,4,13,43, the pattern of the Sri Yantra.

continued fraction golden meanIt shows a very beautiful pattern of “3″s when the Bronze Mean is evaluated in a Continued Fraction. The Golden Mean is a continued fraction of “1″s.

There are many more “Metallic Means” (other p’s and q’s). They are related to all kinds of symmetries and fractal patterns.

The Bronze Mean shows that behind the Trinity of the Golden Mean lies another Trinity (and another Trinity and …).


Penrose Tiling

The Bronze Mean is the generator of so called QuasiCrystals.

Quasy Crystals play a very important role in the Electro Magnetic Structures of our Body, the Collagens.  Collagens are the most abundant protein in mammals,making up about 25% to 35% of the whole-body protein content. The Collagens in our body explain the Ancient Chinese Science of Acupuncture.

Quasi Crystals are “normal” Crystals with a very complex symmetry.

They are ordered AND not-ordered.

One of the most beautiful examples of the patterns behind Quasi Crystals are the Penrose Tilings.

They were developed by the famous physicist Roger Penrose. He used the tilings to show his insights about consciousness.

Penrose believes that Our Universe is just like our Body a Quasi Crystal, a Hall of Mirrors. We the Souls travel all the Paths of this Magnificent Fluent Crystal.

Was the Bronze Mean Known by the Ancient Architects?



The most important implementation of the Bronze Mean can be seen in the Sri Yantra (“Sacred Device”).

The Sri Yantra is related to the Red Triple Goddess of Creation, Tripura also named Lalita (“She Who Plays“).

The Sri Yantra is generated out of the FiveFold Pattern or Creation and the Four Forces of Destruction.

It contains  9 interlocking isoceles triangles. 4 of them point upwards and represent the female energy Shakti, while the other 5 point downwards, representing the male energy Shiva.

The standard form of the Sri Yantra  constitutes a total of 43 triangles. The centre of the Yantra has a Bindu which represents the Void.

The FiveFold Pattern of Creation moves with the Clock. A pattern that moves with the clock is a  generating pattern.

It moves away from the void and generates space. The FiveFold Pattern is the pattern of the Universe. It creates Universes, Galaxies and Planets. The Pattern moves around the Cellestial Center of Creation,  the Black Hole.

The FourFold Pattern moves Against the Clock and is a destructing pattern. It dissolves space and moves back to the void.  The FourFold pattern is the pattern of the Human Being and Earth.

The combination of both patterns is a Moebius Ring (the symbol of infinity) with the celestial Centre in the Middle. The FiveFold/Four Fold pattern resembles the Ninefold Egypian Pesedjet and the Ninefold Chinese Lo Shu Magic Square.

From the fivefold Shakti comes creation and from the fourfold Fire dissolution. The sexual union of five Shaktis and four Fires causes the chakra to evolve” (Yogini Hridaya (Heart of the Yogini Tantra)).

In Pakistan the Mother Goddess (Sharika) is represented by a diagram that contains “one central basic point that represents the core of the whole cosmos; 3 circles around it and 4 gates to enter, with 43 triangles shaping the corners“.

The Penrose Tilings and many other quasi crystals can also be found in Ancient Roman, Islamic and Christian Architecture (Pompei, Alhambra, Taj Mahal, Chartres). The tilings are an expression of the Game of Life and were used to build Educational Buildings (Pyramids, Cathedrals,..) to teach and show the old teachings.


Keplers Model of the Solar System

Kepler (1570-1640), a German Mathematician and Astronomer (The Cosmographic Mystery) and Albrecht Durer (1471-1528), a German Painter, knew about the Penrose Tilings but until the discovery of the Penrose Tilings nobody knew that they knew.

The new scientists (re)discovered old patterns that were known by the old scientist

What is the Meaning of the Bronze Mean?

The Bronze Mean shows the effect of a continuous division of the Universe in Trinities.

It shows that the Universe (and other levels) is suddenly moving from an ordered state to a chaotic state.

This chaotic, not predictable, state is not chaotic at all when you understand the patterns behind chaos.

In our Universe chaos is always ordered. Chaos is an effect of something that is happening in a higher (not Sensible) Dimension or A Higher Consciousness.


The Two Brains of Paul Steinhardt

The writer of an important article about Penrose Tilings and Islamic Art, Paul Steinhardt is like Roger Penrose a well known physicist.

He has created a new theory about the Universe based on Four Forces AND the Quintessence.

In this theory the Universe is Cyclic. It is expanding and contracting.

The expansion of the Universe ends when the Two Major Structures (-1,0, 1) in the Universe, called Membranes or Branes, are in Balance with the Center (0, the Void).

The membranes are higher dimensional Squares that are in parallel.

The Braines at both sides split into many similar cell-like structures. We live in one of the Cells of the Universe.


Adam Kadmon

The Others, our Twins, live on the other membranes and are not aware of our existence until the Brains are getting into Balance.

At that moment the Twin Universes are Connected.

Scientists don’t know when this will happen but the Old Scientists who could travel the Multi-Universe with their United Brains knew.

It would happen at a very special Alignment of the Five Fold Center of Creation of the Milky Way with the FourFold Cross of the Destruction of Earth.

The Bronze mean is the Master-Pattern of our Multi-Universe.

The pattern 1,1,4,13,43 is in its 42nd enfolding and soon we will experience the 43th step, a Merge of the Left and the Right Brain of the Super Conscioussness, Adam Kadmon.


About the Divine Trinity Pattern

How to Raise the Djed

About the Nine-Fold Pattern of the Egyptian Pesedjed

Everything you want to know about the Divine Proportion

About The Indefinite Dyad and the Golden Section: Uncovering Plato’s Second Principle

About the Self-Referential Structure of the Dialogues of Plato

About the Law of Three of Gurdjieff

About Sharika, the Mother Goddess

About the Metallic Means

Paul Steinhardt, About Penrose Tilings and Ancient Islamic Art

About Penrose Tilings and the Alhambra

About the Geometric Patterns in Ancient Structures

An interview with Roger Penrose about the relationship between Conscioussness and Tilings

A lot of information (including simulations) about the Cyclic Universe of Paul Steinhardt

A simple model for the formation of a complex organism

How life emerged out of one Quasy Crystal

About Quasy Crystals and Sacred Geometry



Too Many Insights about IT-Architectures and IT-Strategy

Monday, November 19th, 2007

I have been responsible for IT-Architectures and IT-Strategy between 1984 and 1997. From 1997 until now I have reviewed many Architectures and Strategies when I was part of Meta Group (now Gartner).

An IT-Architecture is a System that describes the components of a Software System on an Abstract Level.

An IT-Strategy is a Process that contains Stages. In every Stage a new version of the IT-Architecture is implemented.

A Well-Formed IT-Strategy is able to Adapt the Old Version of the Architecture. When you’re Strategy has failed You have to Start All over Again.

There are two types of Systems. The first type contains Systems. The second type I call a Foundation. It is the level where we think “the Real Things are Happening”. The major problem is to define the Level of the Foundation.

If you look at your Own computer the Foundation lies deeper than you think. It depends on “What You Understand About a Computer“.

We could define the Foundation as the Operating System of Your Computer (most likely a Microsoft Operating System) but below this Foundation other Foundations are in Existence.

At a more abstract level you can see the real Problem. The problem is Containing.

If you use the Containing Metaphor you Never Stop but You Have to Stop Somewhere.

The level where you Stop is the level where you give the responsibility to An-Other. This can be an Organization, A Person or when we dig deep enough even Nature.

When you give the responsibility for something to an-other you have to Trust the Other and the Other has to take Care of You.

The reason why Architectures fail is that they are based on a Foundation that is not stable on the long term.

Suddenly somebody starts to tinker with the Foundation and suddenly everything goes wrong. This happens all the time. The others leave you alone and you have to take care of yourself.

A solution was to create a Foundation that was able to withstand every Change at the Lower level.

This layer was called Middleware. It is situated somewhere between the UP and the DOWN of all the Layers. History has proven that this solution is not helpful.

Everything changes all the time.

I want to give you a Model to understand the complexity of the problem. I use a Horizontal and a Vertical layer, A Matrix. Layered architectures can be mapped on a Matrix, a Cube or a higher dimensional Structure, N-Dimensional Space.

Every component can be described by a point that is connected to N-variables. The links between the components are lines connecting the points.

The first thing we could do is use one dimension to describe the “type” of the component (software, hardware, database, form, etc). If we create a picture of this dimension we have created a System Diagram. There are many types of System Diagrams invented. They were called a Method or a Modeling Language. Every new Method created a “Method War” because the Users always thought that their Method was the Best.

I participated in many activities of the IFIP (International Federation for Information Processing). We tried to find a way to find the “Best Method” to Improve the Practice. It was proven that there was no best method.

Many roads lead to Rome. See “Information Systems Design Methodologies: Improving The Practice“, T.W. Olle, H.G. Sol and A.A. Verrijn-Stuart, (Eds.), North-Holland.

At the end the major Method Wars ended with a Compromise, UML. Compromises are always the worst solution for a problem. UML is a very complicated method.

If we start the Diagram with an Event and we have chosen the right Modeling Language, now called a Programming Language, we are able to “simulate” the System or to “generate” the software. There are many Tools, Modelers, Simulators, Languages and Generators developed.

They also created wars (called Competition) between all kinds of Vendors. In the end many Tools were taken out of the market by the Vendors and the Users got stuck. They were unable to convert the old tools to the new tools or they simply did not take the time to do this. This problem is called the Legacy Problem.

The Market invented something to solve this problem called Reverse Engineering. Reverse Engineering proved to be a failure because the semantics, the meaning, of the software was gone.

When you deconstruct a car and you show an engineer all the parts he knows the parts belonged to a car. When you do this with something nobody ever knew it existed the only engineer that is capable to reconstruct the original is the engineer who constructed it.

When the software is old the original programmer is gone and nobody is able to understand what he was doing. Sometimes the software contains documentation. The programmer has written a Story about the Meaning of the Software. Programmers never took (and take) the time to do this.

I want to get back to N-Dimensional Space. I hope you understand that we when we use enough dimensions we are able to Model Everything.

We are also able to MAP Everything to Everything. Mapping or Converting could solve many problems.

There were Systems on the market that helped you to MAP one Structure to another Structure. An example was Rochade. I implemented Rochade when I was responsible for IT-Architectures and I know Rochade solved many problems with Legacy Systems.

Rochade used something called a Scanner or Parser. A Parser is a “piece of software” that translates a “piece of software” into another “piece of software”. It stored the data of the software (the meta-data) in a “general” format that could be translated to other formats.

When you program in a Software Language the code is translated to another Language. This happens many times until the software reaches the Lowest Level, The Processor or the CPU.

The CPU uses a Cycle to process a very simple language that consists of binary numbers. These numbers are real numbers or operations. The simplest operations are operations on a Set.

The whole concept of the CPU was invented by John von Neumann and is therefore named the Von Neumann Architecture.

The architecture of von Neumann has a big disadvantage called the Von Neumann bottleneck. The CPU is continuously forced to wait.

The Von Neumann Computer is Wasting Time and Energy.

An alternative is the Parallel Architecture. Parallel computing has recently become the dominant paradigm in computer architectures. The main reason is the Rise of the Internet.

The Rise of the Internet started the Fall of Centralized IT-Architectures and Centralized IT-Strategy.

At this moment we need another approach to Manage or Control the sofware-production of a big company.

This approach can be found in the Open Source Movement.

If we use the Matrix Approach we can answer interesting questions.

First I introduce a Rule.

When we increase the amount of Dimensions we are able to make every point and connection between a point Unique. If we do the opposite we are able to make every point and connection The Same.

When people talk about the Reuse of a Component we are looking for a Dimension were some points and their connections are the Same.

I hope you see that it is possible to Reuse Everything and to Reuse Nothing. The Choice is Yours.

This also the Practice in Software. When I discovered that the Year-2000 problem could lead to a disaster I started a research-project with the CWI. The CWI develop a very intelligent parser that could create Software-Maps.

When we studied the maps we saw that some pieces of software came back all the time. These were “citations”. One programmer invented a new construct and others reused the construct all the time. The major difference with the Theory of Reuse was that MANY Parts were the Same.

When you dig deep enough you always find “The Same”.

The CPU is handling binary codes and when you would come from another planet you would not understand why all these zero’s and 1′s are creating a DIVERSITY. They create a DIVERSITY because Something is Interpreting the Sequence. This Something is also a Program. This program uses a Theory about Languages. Most of the time it supposes a Context Free Language. A Context Free Language is a language where the interpretor always moves in one direction. It processes a List.

The Diversity a Computer Produces is based on one long List of Binary patterns. If we could analyze all the possible patterns we could find all the possible software-programs that could be build until Eternity. Because the binary codes can be mapped to the Natural Numbers. We need only one dimension (A line) to classify all the possible software-components in the World.

In 1931 Gödel’s stated the so called incompleteness theorems. He uses the Natural Numbers to prove that a part of our Human Reality cannot be described by a Computer Program.

There is something “left for us” that the Machines cannot take over. This part is related to the Emotions and the Imagination. We cannot Automate them. If we do this we stop Innovation and Commitment.

Now I want to come back to IT-Architectures.

When You start an IT-Architecture Out of Nothing you start with a Small Amount of Dimensions. The world looks very simple to you. When you add detail you have to increase the amount of dimensions. The effect of this is that Everything Changes. New Possibilities arise. If you go on using the Top-Down Approach you will move into a State of Huge Complexity. Always start in the Middle!

At a certain moment You have to move to Reality.This means Programming Software. At that moment You encounter something you never thought of. The Software Legacy!!!!!!!!!!!!

When you increase the Scope of your System and you leave the Boundaries of Your Company (the World of the Internet) the Complexity increases also.At that moment You encounter something you never thought of, Open Source. Millions of Possibilities arise and You don’t Know what to do!

Behind the Software are People. Some of them are creating Small Companies and they are doing things you’re company is also doing but they do it much cheaper and faster.

What to do?

If You Can’t Beat them Join Them.