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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 Future and the Past are created by the Intention of the Observer, we call Measurement.

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 is the Symbol of the Heart Chakra the connector between the Upper- and the Lower Triangle of the Body.

Kerotakis

Destillation

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

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

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.

Piaget

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:

Quaternity

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“.

When You have moved once through the Cycle you have seen Everything there is to See. The only way to move out of the Cycle is to jump into the wHole in the Middle.

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).

LINKS

About the History of Cycles (in Dutch)

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 Perspective

Thursday, February 2nd, 2012

Effective Ways To Improve Production Efficiency For Your Manufacturing Business

While all business owners should be taking measures to enhance efficiency, as this aspect of business growth is of extreme importance regardless of the industry, manufacturing businesses should take measures to boost production efficiency for several other reasons. These reasons range from improving workplace safety to saving on costs and everything in between. Manufacturing businesses that claim the lion’s share of the market are always searching for new ways to improve production efficiency with the intention of ultimately improving their bottom line.

So, to ensure your manufacturing business is constantly making notable strides towards improving production efficiency, we have rounded up five practical ways for you to achieve this. With that said, these five solutions break down the five fundamental focus points of manufacturing efficiency. Therefore, you can use these practices for years to come.

Waste in the manufacturing industry is a cost that should be avoided. And waste is also a broad term in this industry as it refers to employee hours, energy consumption, materials, and a few others. However, material waste is usually the biggest concern in the manufacturing industry. When searching for ways to reduce waste, you will need to utilize your conclusions from evaluating your production line, learn more detailed information from this top tier short cut fibers manufacturer.

When identifying waste, each of your production line processes will create some waste; identifying the processes responsible for making the most waste is the best way to reduce overall waste. However, you can also reduce waste by recycling or reusing waste instead of dumping it. You could also consider selling your waste to a business that can properly use it if you cannot eliminate the bulk of your waste.

The production line in your manufacturing business is the core of your business functions. When evaluating the production line, you should assess all the details as well, including the commonly overlooked details, such as loading dock bumper and other essential loading dock equipment your business needs. When it comes to sourcing and maintaining loading dock bumpers, you can consider Miner Corp or other leading industry service and equipment providers to ensure your production line has everything it needs to function as it should.

Throughput is another primary focal point to consider; you need this metric to measure the number of units being produced in a certain period on average. While quality equipment is crucial in ensuring your production line can run smoothly, evaluating your throughput will help you identify issues in your production line on occasions when the throughput is not entirely up to par. Capacity utilization is another element of your production line to evaluate, and this refers to calculating your factory’s total output capacity. This will allow you to determine your production line’s performance at all times.

While you are evaluating your production line, you will probably discover the most significant breakdowns in production. These are otherwise referred to as bottlenecks. Because having to shut down operations even for half a day can have a massive impact on your business’s reputation and overall profits, identifying sources of breakdowns and taking measures to prevent them from reoccurring is vital to all companies operating in the manufacturing industry.

About Plato and Harmony

Monday, January 5th, 2009
SriYantra

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.

plato

Plato

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)”

and

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”.

and

“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 …).

quasycrystal

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?

lalita

Tripura

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.

kepler_spheres-l

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.

m-brane

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

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.

LINKS

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

 

 

About The Rose

Sunday, October 21st, 2007

roseBetween 1969 and 1975 I was a student at the University of Leiden.

At that time the Flower Power Movement started. I was 18 years of age. I came out of a very protected secure environment.

My parents were very poor, totally not educated and also very religious in their own way.

My life changed in every aspect you can imagine. People were using LSD, Opium and Marihuana. I got into contact with people from all over the world, new religions and theories. We anticipated the end of all war and “peace on earth”.

The most important factor in our life was MUSIC. It was the time of Jimmy Hendrix and Woodstock. The MUSIC was connected to POETRY. We not only listened to the sound but we also listened to the Lyrics. We studied them (Bob Dylan, Leonard Cohen) and discussed them.

My favourite group was Pearls Before Swine. The music of Tom Rapp was the ultimate combination of MUSIC AND POETRY.

When I look back at that time I feel nostalgia. I want to return to the time when everything that was positive was possible. I wonder how we were able to transform an expectation of Paradise into an expectation of the Apocalyps. Let us have a look at The Song About A Rose.

(The Lyrics of Thom Rapp).

“Song About A Rose”
By Tom Rapp

This is a song about a rose

Or perhaps it’s a song about the shadow of a rose

In the morning the apple sellers congregate on corners of their own

But you and I we sing our song about a rose or perhaps the shadow of a rose

With the children of Fribourg and the good thief standing by

We consort in silent rendezvous and call the world a lie

When our song is but a candle that will one day burn away

The children of Fribourg cannot hear what we say

This is a song about a rose

Of lonely caravans whispering to God

To chain the world in prose

But people are not singers and life is not a song

And even God can only guess

Why or where or when or if

The answers all belong

And you and I we sing our song about a rose

Or perhaps the shadow of a rose

The song of the Rose of Tom Rapp is a tribute to Arabic Culture. He is unable to convince the children of Fribourg, a Swiss Town, that there were “lonely caravans whispering to God to chain the world in prose”. They were singing the Song of the Rose or the Shadow of the Rose.

The Rose is a very old mystical symbol. It is the symbol of purity and a symbol of passion, heavenly perfection and earthly passion; virginity and fertility; death and life. The rose is the flower of the goddess Venus but also the blood of Adonis and of Christ. It is a symbol of transmutation – that of taking food from the earth and transmuting it into the beautiful fragrant rose. The rose garden is a symbol of Paradise. It is the place of the mystic marriage. In ancient Rome, roses were grown in the funerary gardens to symbolize resurrection. The thorns have represented suffering and sacrifice as well as the sins of the Fall from Paradise.

Numerologically, the Rose represents the number 5, The Centre. This is because the wild rose has 5 petals. And the petals on roses are in multiples of five. Geometrically, the Rose corresponds with the pentagram and pentagon.

The Rose is the Symbol of the Heart Chakra.

The Rose is the symbol the Centre of the Whole. A Return to the Centre is not possible without Pain and Blood (Thorns). The Shadow of the Rose is the movement away from the Centre to return to the Centre (The Cycle).

That is why Scientists of the University of Fribourg “cannot hear what we say”. “They call the world a lie” and see that “our song is but a candle that will one day burn away”.

Everything will burn away and change into Ashes. Ashes can be used by A Jeweler to make Old Golden Coins Shine Again. The Jeweler cannot repair the scratches. He knows that even new coins have scratches. Nobody is perfect. The Jeweler smiles.

Ashes are also used to give the power of fertility to the Soil (Mother Earth). The Soil covers the the Seed of The Rose in Winter and gives it the Strength to Rise in Spring again. The Rose is helped by the Shining Golden Coin in Heaven, The Sun. The Rose always returns and the Song of The Rose always returns in many ways.

“The Jeweler”
By Tom Rapp

The jeweler has a shop on the corner of the boulevard

In the night, in small spectacles, he polishes old coins

He uses spit and cloth and ashes

He makes them shine with ashes

He knows the use of ashes

He worships God with ashes

The coins are often very old by the time they reach the jeweler

With his hands and ashes he will try the best he can

He knows that he can only shine them

Cannot repair the scratches

He knows that even new coins have scars so he just smiles

He knows the use of ashes

He worships God with ashes

In the darkest of the night both his hands will blister badly

They will often open painfully and the blood flows from his hands

He works to take from black coin faces the thumbprints from so many ages

He wishes he could cure the scars

When he forgets he sometimes cries

He knows the use of ashes

He worships God with ashes

At this moment Arabic Culture is highly associated with Violence and Power Plays (Oil). Many people don’t know that Western Culture really started when The Arabic World gave the old sciences and philosophy back to the West. The old sciences also contained the Secret Knowlegde of The Rose.

At that time the Arabic Culture was producing artefacts of immense beauty like the Alhambra. The walls of the Alhambra are full of calligraphic decoration, cursive and kufic writings with sentences such as “Only God is victor” (apparently by Zawi ben Zirí, founder of the Nasrid dynasty) and poems by three poets of the Court of Granada, Ibn al-Yayyab (1274-1349), Ibn al-Jatib (1313-1375) and Ibn Zamrak (1333-1393). Of course it contained a beautifull Rose Garden, the symbol of Paradise.

The mystic part of the Islam is called Sufism. They were the People who are “whispering to God”. They created poetry and music and knew the Secret of The Rose. The Sufis are the Gnostics of the Islam. They are comparable to the Essenes in the Judiac Religion.

Rumi was the founder of the Mawlawi Sufi order. He was born in Wakhsh (Tajikistan) under the administration of Balkh in 30 September 1207 to a family of learned theologians. Escaping the Mongol invasion and destruction, Rumi and his family traveled extensively in the Muslim lands, performed pilgrimage to Mecca and finally settled in Konya, Anatolia, then part of Seljuk Empire.

When his father Bahaduddin Valad passed away, Rumi succeeded his father in 1231 as professor in religious sciences. Rumi 24 years old, was an already accomplished scholar in religious and positive sciences. He was introduced into the mystical path by a wandering dervish, Shamsuddin of Tabriz. His love and his bereavement for the death of Shams found their expression in a surge of music, dance and lyric poems.

In The Arc Of Your Mallet

Rumi

Don’t go anywhere without me.

Let nothing happen in the sky apart from me,

or on the ground, in this world or that world,

without my being in its happening.

Vision, see nothing I don’t see.

Language, say nothing.

The way the night knows itself with the moon,

be that with me.

Be the rose

nearest to the thorn that I am.

I want to feel myself in you when you taste food,

in the arc of your mallet when you work,

when you visit friends, when you go

up on the roof by yourself at night.

There’s nothing worse than to walk out along the street

without you.

I don’t know where I’m going.

You’re the road, and the knower of roads,

more than maps, more than love.

Tom Rapp wrote “But people are not singers and life is not a song. And even God can only guess why or where or when or if the answers all belong“. We have to do it our selves. We are left alone on the street because even God does not know all the answers.

To Rumi God “Is the Road and the Knower of the roads“. He asks God to walk with him and to show him the way. The poems of Rumi are Love Poems. They apply to Godly Love and Human Love. You understand them the best when your love has left you and you are desperately looking for the answer why this happened.

The Song of the Rose is about a longing to return to the Centre of The Whole. To restore the Balance that once was. I imagine we could start this process by creating new songs about the beauty of the Whole.

Let’s start to whisper again and ask for in-spiration.

LINKS

Song about the Rose

Why Music gives Soul to the Universe and Wings to the Mind

Thursday, October 18th, 2007

I have been a lover of Music since I was born. It was a big surprise to my parents when I wanted to buy gramophone records of Opera’s when I was thirteen. My parents where not educated in music but they loved it. Everybody in my family was singing, most of them in a choir.

I was given a beautiful soprano voice when I was a young boy. It was so special that I was more or less forced to sing in theatres. I was a very shy person and the first time I was on stage I almost fainted. Later my voiced changed into a Counter Tenor.

Later, when I was about 35, Singing took me like a hurricane. I started to take singing lessons and joint many choirs. I even created my own octet. I never learnt to read notes but this was not a problem. My memory for music works perfect.

Plato framed the essence of Music in this sentence: “Music is a moral law. It gives soul to the universe, wings to the mind, flight to the imagination, a charm to sadness, gaiety and life to everything. It is the essence of order, and leads to all that is good, just, and beautiful, of which it is the invisible, but nevertheless dazzling, passionate and eternal form“.

In the old mystery schools the use of sounds were considered a very sacred science. They knew that the right sequence of sounds could change behaviour patterns and accelerate the healing process. The right toning could perform miracles.

Sound is processed by the cochlea. The word Cochlea comes from kokhlias “snail, screw and kokhlos “spiral shell“. People who have read a few of my blogs will understand that the “spiral of the ear” transforms sound into a very special spiral pattern.

This pattern travels first trough the limbic system. It is here that emotional and physical reactions are produced. The pattern than moves to the auditory cortex of the brain where we become conscious of the sound and can recognize what we are hearing.

The limbic system connects the higher and lower functions of our brains, it is called both the “Emotional Center” and the “Conscious System” of the brain. If we, as Humans, had to consider one part of our brains to be the core of our personal consciousness, it would be the Limbic System and, especially, the interaction between the limbic system and the cortex.If anything resembles the actions of a ‘soul’ in the Human brain machine, it is the interaction between the Cortex and the Limbic system.

So Music (Tones) are a direct connection between the Outside World and our Consciousness, The Emotions.

If you read this blog you will understand that Sound makes a connection to another physical space, Our Twin or Mirror Space (“Dark Matter or Mirror Matter“).  .

Out if this space we are fed by the Force of Life (Qi, Prana). With Sound we are able to connect to every Whole by something called “quantum superposition”. It is a term used in Quantum Mechanics and it defines a state of “Harmony”, “Coupling” or “Entrainment” . If we produce the right sound waves we are able to “entrain” the Body to a Whole (A higher level in the Universe) that is able to heal the body (Qi).

If you read the last blog You will also discover that not only our Ears but our whole body through the connective tissues of our body (skin, bones) is able to resonate.

When people are producing sounds in a group they start to resonate and become a whole. An example is a soccer-match. When the sounds and the movements of the body (the Wave) become entangled the people in the Stadion become a Whole.

Not only the people but also the Architectual Structure of the Stadion plays a very important role. That is why some of the new developed Stadions and Concert Halls are not able to generate the “Right Atmosphere”. They are not able to give the right Feed-Back between Limbic system and the Cortex.

The same applies to Offices. When people are working they need to “hear” the “Humm” of the Others. When the “Humm” is a positive sound they start to feel good and productivity rises. They are connected to the Whole of the Company they are working for. When the “Humm” is a negative sound productivity goes down. When this happens they become sick. The “Acoustical” Structure of a Building is able to transform a positive “Humm” into a negative “Humm” (The Sick Building Syndrome).

If you want to know more I advice you to read the beautifull books of Christopher Alexander about Architecture.

How Socrate changed the Cycle of Western Civilization

Tuesday, October 16th, 2007

SocrateMany people Project their Knowledge of the Now to History. They Think that People Thought the same Thoughts many years ago.

To understand the Spirit of The Time we have to understand the Historical Context People lived in. One way of doing this is to look at a shared foundation and study the Historical Variations on the Central Theme.

This idea corresponds with the Insights of Micheal Bahktin. He called the central theme The Chronotope, “The place where the knots of narrative are tied”. I used his theory to have a look at the Cultural Cycle of History.

I combined the theory of Bahktin with the Economic Cycle Theory of Kondratiev. To my big surprise Kondratiev and Bahktin use a different periodicity (50, 250 years) of the Cycle but the stages of the Cycle were the same.

What surprised me more what that the periodicities of the Cycles where related by the factor Five. When you know the basic periodicity the only thing you have to do is multiply or divide by five and the same pattern, the Basic Fractal of History, emerges. The Five or the Pentagram shows itself in every culture on Earth. When we transform this structure in three dimensions it shows itself as a Spiral or a Moebius Ring.

A beautiful example of a projection of the Now on History was a visit to the Cave of Lascaux in France. An anthropologist was explaining to us what we were seeing.

The Cave contained many Spiraling Abstract Paintings. She told us that the Cave was used for rituals and the many pictures we saw had a symbolic meaning. I did not believe that because the theory of symbolism was “invented” by de Saussure (1857-1913).

The people that lived in the Cave had no idea of Symbolisms and Symbols. They just painted what they “saw” in the Outside World and the Inside World. If I place myself in their Context I cannot Imagine they were Thinking a lot. I feel they were Experiencing Nature in all his states of Wonder and Terror. Imagine what a beautifull Sky they were experiencing every Night and you will understand why the Sky Father was the major Force they felt.

The people that lived at the time of the Cave of Lascaux always situated their Holy Places at the crossings of important Ley Lines. These Ley Lines represent the Spiraling Knots of the Electro Magnetic Field of the Earth (the Earth Grid) .

Highly sensitive people can still feel the PowerPlaces and it is not strange to assume that the sensitive people at that time (“the Sjamans”) could do the same. Just like the Current Sjamans they could travel Space/Time by performing Rituals (Spinning, Chanting the Sacred Tones), Lucid Dreaming or by eating Sacred psychoactive plants like the Peyote and the Amanita Muscaria (the Soma).

Symbolism was a theme of the Spirit of the Time of a stage in the development of the Kondratiev Wave that operated between 1890 and 1940. It was the time of Standardization (Control, Plan).

The stage before this stage (1850-1890) was related to Energy (Ego, Self, Desire, Fire). It was the time when the Steel Mills were created, the research in Chemistry started and Alexander Noble invented Dynamite. I was able to map every phase of the Kondratiev Cycle to the Cycle of Bahktin.

The 5 phases of the Kondratiev Cycle (5×50 =250 years) could be summarized at a higher level, the Industrial Revolution. I found out that the Industrial Revolution was a Social Movement. A Social Movement is always preceded by a Spiritual Movement, the Renaissance.

I started to map the Cycle again with a periodicty of 250 years. The time-interval between 1450 and 1700 is called Renaissance. It is the stage of the Spirit and Ideas. The model fitted.

I went back 5×250 years (200-450). In this time Christianity was created by the Roman Emperor Constantine I. He used the widespread Cult of Mithras to introduce Christianity in the Roman Empire. Again we are in the stage of the Spirit. The Model fitted.

I jumped to a higher level of the Cycle (The Cycle of Civilizations) and travelled further back in time. I arrived at the time of the Cave of Lascaux. At that time many caves contained “abstract pictures”. The pictures look like Spiraling Spirals.

Later the spirals where placed in a Medicine Wheel and connected to Animals (Eagle, Bull). The same animals appear in the Medieval Cathedrals but now they are related to the Apostles. Even the medicine wheel (a labyrinth) can be found there.

If you walk this wheel in the Cathedral it will point you to all the important stories that are told. Just like the Medicine Wheel the Cathedrals (build by the (Free) Masons) where an educational tool to tell about the Spiral of Life. Suddenly I saw the big picture.

Every step in the Cycle was nothing but a new way to show the “same thing” again and again. The spiralling spiral came back all the time but on a different level.

What happened around 550 BC?

At that time an Innovation in Religion came into the World. This innovation can be summarized by the famous statement of Socrate Know Thyself. The same statement can be found in the Gospel of Thomas and is also the central theme of the teachings of the Buddha. The Gospel of Thomas is a part of the Dead Sea Scrolls, a Gnostic Library of the Essenes, dated 50 BC.

Jesus said: Whoever knows the All but fails to know himself lacks everything . . . But the Kingdom is within you and it is without you. If you will know yourselves, then you will be known and you will know that you are the sons of the Living Father. But if you do not know yourselves, then you are in poverty and you are poverty“.

Boeddha became an Inspiration in the East. Socrate and Jezus were killed. From that time on an enormous amount of people were killed in the West when they wanted to Know Themselves, find the Whole in their Inner World.

They could not experience the Roman Religion through A System. Know Thyself was a huge threat to the Rulers of Western Civilization. Constantine simply took over Christianity to preserve the power and made it into a Roman System. A system of Laws to Obey. He practiced the old Roman trick of Divide and Conquer to save his Empire.

Between 1450 and 1700, the Renaissance, the tides started to turn. It took another 250 years (1950) before the people in Europe started to find their own Identity again. We are now in the Stage of Individuality of the Cycle and are slowly entering the state of Empathy. It shows itself in the many attempts to create Networks (Communities). The Internet is one of the major Western technological inventions to support this.

The Cycles of East and West (and North and South) are coming together. The Eastern Cultures embrace Western Culture and the Western Culture embraces Eastern Culture. We can create Harmony by a fuse of everything the Human Race has Learnt when a new cycle started around 550 BC.

The Cycle of The Earth is almost at The Breaking Point. According to many environmental scientists we will soon experience a very fast Reorganization on the Level of Earth. The long term cycle of Earth is restoring itself.

Not only Earth will restore itself. The original Spirituality of the civilization of MU, will be restored. An ancient Bhuddist prophesy speaks of the darkest hour of the Dark Age, when the rivers of materialism burst their banks, and plague, famine, greed and warefare beset desperate people everywhere.

That Dark Age will soon end and the new Golden Age will appear. Many living buddhas are now here to bring the precious healing Dharma to anyone ready to receive it.