Posts Tagged ‘mount meru’

About Number and Magnitude

Monday, January 9th, 2012

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that  Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

Geometric Algebra has a strange relationship with Pascals Triangle. This Triangle, also called the Binomial Expansion, contains all the Possible Combinations of two Independent Variables. Our Universe is a Combination of Combinations exploring Every Possibility.

The last and perhaps most important Discovery in Mathematics called Bott Periodicity shows itself in Pascals Triangle.

Bott Periodicity proves that we live in a Cyclic Fractal Universe, the Wheel of Fortune, that is Rotating around the Void, the Empty Set. The Empty Set contains Every Thing that is Impossible in our Universe.

This blog is not a Scientific Article. I have tried to connect the Old Sciences and the New Sciences in my own Way.

It contains many links to Scientific Articles and even Courses in Geometric Algebra.

So if you want to Dig Deeper Nothing will Stop You.

About the One and the Dirac Delta Function

Every Thing was created out of  No Thing, the Empty Set, ɸ, the Void, the Tao. The Empty Set contains 0 objects.

The Empty Set is not Empty. It contains Infinite (∞) Possibilities that are Impossible.

Every impossibility has a probability of 0 but the sum of all possibilities (1/∞=0) is always 1. In the beginning ∞/∞ =1  or ∞x0=1.

This relationship is represented by the Dirac Delta Function. It is used to simulate a Point Source of Energy (a Spike, an Explosion) in Physics.

The Delta is reprented by the Symbol Δ, a Triangle. The Delta is called Dalet in the Phoenican and Hebrew Alphabet. Daleth is the number 4 and means Door.

The original symbol of the Delta/Daleth contains two lines with a 90 Degree Angle. Two orthogonal lines create a Square or Plane.

The Dirac Delta Function is defined as a Square  with an Area of 1,  a Width of 1/n and a Height of n where n->∞.

The Dirac Delta Function is a Line with an Area of 1.

In the Beginning a Huge Explosion took place that created the Universe.

The Dirac Delta Function δ (x) has interesting properties: δ (x) = δ (-x), δ (x) = δ (1/x). It has two Symmetries related to the Negative Numbers and the Rational Numbers.

When we move from 2D to 1D, the Number Line, the Delta Function becomes the Set of the Numbers N/N =1.

The Tetraktys of Pythagoras

The Monad (1) of the Tetraktys of Pythagoras, the Top of the Triangle, was created by Dividing the One (1) by Itself without Diminishing itself. The Monad (1/1=1)  is part of  the 1D Delta Function.

Creation is an Expansion of the 1/1 into the N/N, adding 1/1 all the time,  until ∞/∞ is reached. At that moment every Impossibility has been realized.

File:Dirac function approximation.gif

The Dirac Delta Pulse

 

To move Back to the Void and restore the Eternal Balance of  the One,  Dividing (Compression) has to be compensated by Multiplication (Expansion).

At the End of Time N/M and M/N have to find Balance in the N/N,  move Back to  1/1, Unite in the 0 and become The Void (ɸ) again.

About the Strange Behavior of Numbers

The big problem of the Numbers is that they sometimes behave very differently from what we Expect them to do.

This Strange Behavior happens when we try to Reverse what we are doing.

It looks like the Expansion of the Universe of Numbers is Easy but the Contraction creates many Obstacles.

It all starts with the Natural Numbers (1,2,3,).

When we Reverse an Addition (Subtract) and move over the Line of the Void Negative Numbers appear. Together with the Natural Numbers they are called the Integers.

The same happens when we Reverse a Division and the Fractions (the Rational Numbers) (1/3, 7/9) suddenly pop up.

An Integer N is a Rational Number divided by 1 (N/1).

The Integers are the Multiples of 1, the Fractions are its Parts.

Numbers behave even stranger when we want to Reverse a Repeating Repeating Addition (Irrational Numbers) and want to calculate a Rational Power (2**1/2).

The Complex Numbers (or Imaginary Numbers), based on the Square Root of -1 called i, are a combination of the Negative Numbers and the Irrational Numbers.

Irrational Numbers ( the Pythagorean Theorem), Fractions (a Piece of the Cake) and Negative Numbers (a Debt) are part of our Reality but the Strange Number i represents something we cannot Imagine.

About the Duality and the Expansion of Space

In the beginning the only One who was in existence was the 1.

When the One divide itself again the number -1, the Complement of 1, came into existence.

1 and -1 are voided in the No Thing, the Empty Set, 0:  -1 + 1 = 0.

The Two, the Duality, both started to Expand in Two Opposite Directions (<– and +->) both meeting in the  ∞/∞. This expansion is what we call Space.

Space is a Combination of the Strings S(1,1,1,1,1,…) and -S = (-1,-,1,-,1,-1,…) where S+S=(0,0,0,0,0,0,…).

The Expansion pattern of Space is a Recursive Function S: S(N)=S(N-1)+1 in which + means concatenate (or add) the String “,1″.

An Addition X + Y is a concatenation of S(X) and S(Y). A Substraction X-Y is a concatenation of S(X) and -S(Y). In the last case all the corresponding combinations of 1 and -1 are voided. (1,1,1,1)-(1,1,1)=(0,0,0,1)=(1).

Multiplication XxY is Adding String S(Y) every time a “1″ of S(X ) is encountered: 111 x 11 = 11  11  11. Dividing X/Y is Subtracting S(X) every time a “1″ of S(Y) is encountered:.111  111  1/111=11 1/111. In the last example a Fraction 1/111 appears.

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

The Strange Behavior of Numbers is caused by the Limitations of our Memory System. We are unable to remember long strings that contain the same Number.

To make things easy for us we Divide Space into small Parts so we were able to Re-Member (Re-Combine the Parts).

When we want to Re-member, Move Back in Time, we have to Compress Expanding Space.

Compressed Space is Time.

Time and Space have a Reciprocal Relationship called Movement (Velocity = Space/Time).

There are  many ways ( (1,1,1), (1,1,1),..) or ((1,1),(1,1))) to Compress a String in Repeating Sub-Patterns.

In the blog About the Trinity I showed that the most Efficient Way to group the One’s is to make use of a Fractal Pattern (a Self Reference) and Groups of Three Ones.

The Trinity applied to the Trinity ( A Fractal) is a Rotating Binary Tree. Binary Trees represent the Choices we make in Life.

The rotating Expanding Binary Trees generate the Platonic Solids (see linked video!) when the (number)-parts of the Binary Tree Connect.

The Ternairy Number System is represented by the Binary Tree

When we connect Three Ones (1,1,1) by Three Lines (1-1,1-1,1-1) a 2 Dimensional Triangle Δ is Created.

If we take the Δ as a new Unity we are able to rewrite the patterns of 1′s and -1′s into a much Shorter Pattern of Δ’s and 1′s: (1,1,1),(1,1,1),(1,1,1), 1,1 becomes Δ,Δ,Δ,1,1.

We can repeat this approach when there is still a Trinity left: Δ,Δ,Δ,1,1 becomes ΔxΔ,1,1.

This Number System is called the Ternary Number System.

About Ratio’s and Magnitudes

According to EuclidA Ratio is a sort of relation in respect of size between two magnitudes of the same kind“.

A Magnitude is a Size: a property by which it can be compared as Larger or Smaller than other objects of the Same Kind. A Line has a Length, a Plane has an Area (Length x Width), a Solid a Volume (Length xWitdth x Height).

For the Greeks, the Numbers (Arithmoi) were the Positive Integers. The objects of Geometry: Points, Lines, Planes , were referred to as “Magnitudes” (Forms). They were not numbers, and had no numbers attached.

Ratio, was a Relationship between Forms and a Proportion was a relationship between the Part and the Whole (the Monad) of a Form.

Newton turned the Greek conception of Number completely on its head: “By Number we understand, not so much a Multitude of Unities, as the abstracted Ratio of any Quantity, to another Quantity of the same Kind, which we take for Unity”.

We now think of a Ratio as a Number obtained from other numbers by Division. A Proportion, for us, is a statement of equality between two “Ratio‐Numbers”.

This was not the thought pattern of the ancient Greeks. When Euclid states that the ratio of A to B is the same as the ratio of C to D, the letters A, B, C and D do not refer to numbers at all, but to segments or polygonal regions or some such magnitudes.

The Ratio of two geometric structures  was determinated  by fitting the Unit Parts of the first geometric Stucture into the Other.

The Perfect Triangle of the Tetraktys contains 9 = 3x3 Triangels. A Triangle contains 3 Lines and 3 Points.

An Example:  The Tetraktys is a Triangle (A Monad) and contains 9 Triangles (a Monad). The 1x1x1-Triangle Δ, a Part of the Tetraktys,  is Proportional to the Whole of the Tetraktys (T) and has a Ratio T/Δ = 3= Δ -> T = Δ (3)  x Δ (3) = 9.

The Mathematics of Euclid is not a Mathematics of Numbers, but a Mathematics of Forms.

The symbols, relationships and manipulations have Physical or Geometric Objects as their referents.

You cannot work on this Mathematics without Knowing (and Seeing) the Objects that you are Working with.

About Hermann Grassman, David Hestenes and the Moving Line called Vector

Hermann Grasmann lived between 1809 and and 1877 in Stettin (Germany). Grassmann was a genius and invented Geometric Algebra a 100 years before it was invented.

In his time the most important mathematicians did not understand what he was talking about although many of them copied parts of his ideas and created their own restricted version. None of them saw the whole Grassmann was seeing.

When he was convinced nobody would believe him he became a linguist. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda were recognized among philologists.

Grassmann took over the heritage of Euclid and added, Motion, something Euclid was aware of but could not handle properly.

angle between vectors in 2 dimentions

A Displacement or Bivector

Grassmann became aware of the fact your hand is moving when you draw a 2D Geometric Structure. He called the Moving Lines, that connect the Points, Displacements (“Strecke”).

screw theory 2

A Displacement and a Rotation of a Vector

In our current terminology we would call the Displacements “Vectors”.

blades

Vector algebra is simpler, but specific to Euclidean 3-space, while Geometric Algebra works in all dimensions. In this case Vectors become Bi/Tri or Multi-Vectors (Blades).

The Trick of Grassmann was that he could transform every transformation on any geometrical structure into a very simple Algebra. Multi-Dimensional Geometric Structures could be Added, Multiplied and Divided.

The Greek Theory of Ratio and Proportion is now incorporated in the properties of Scalar and Vector multiplication.

add-bivectors

Combining (Adding) Bivectors creates a Trivector

About a 100 years later David Hestenes improved the Theory of Grassmann by incorporating the Imaginary Numbers. In this way he united many until now highly disconnected fields of Mathematics that were created by the many mathematicians who copied parts of Grassmanns Heritage.

About Complex Numbers, Octions, Quaternions, Clifford Algebra and Rotations in Infinite Space

Grassmann did not pay much attention to the Complex Numbers until he heard of a young mathematician called William Kingdon Clifford (1845-1879).

Complex numbers are ,just like the Rationals (a/b), 2D-Numbers. A Complex number Z = a  + ib where  i**2=-1. Complex Numbers can be represented in Polar Coordinates: Z = R (cos(x) + i sin(x)) where R = SQRT(a**2 + b**2).  R is the Radius, the Distance to the Center (0,0).

When you have defined a 2D-complex Number it is easy to define a 4-D-Complex Number called a Quaternion:  Z = a + ib + jc + kd or a 8-D Complex Number called an Octonion.

William Rowan Hamilton, the inventor of the Quaternions, had big problems to find an interpretation of all the combinations i, j and k until he realized that i**2 =j**2 = k**2 = ijk=-1.

What Hamilton did not realize at that time was that he just like Grassmann had invented Vector Algebra and Geometric Algebra.

Quaternions are rotations in 4D-space

This all changed when William Kingdon Clifford united everything in his new Algebra.  Clifford’s algebra is composed of elements which are Combinations of Grassman’s Multivectors.

The Clifford Algebra that represents 3D Euclidean Geometry has 8 = 2**3 components instead of 3: 1 number (Point), 3 vectors (Length), 3 bivectors (Area) and 1 trivector (Volume).

It turns out if you use combinations of these elements to describe your geometric objects you can do the same things you did before (you still have 3 vector components).

In addition, you can have additional data in those other components that let you find distances and intersections (and a lot of other useful information) using simple and (computationally) cheap numerical operations.

The most important Insight of William Kingdom Clifford was that the Complex Numbers are not Numbers all.

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

The String 1,3,3,1 of Clifford’s 3D Geometry is related to the 4th Level of Pascal’s Triangle. Level N of Pascal’s Triangle represents N-1-Dimensional Geometries.

The Sum of every level N of the Triangle is 2**N. This Number expresses the Number of Directions of the Geometric Structure of a Space with Dimension N.

A Point has 0 Direction, while a Line has 2 Directions, relative to its Center point, a Plane has 4 Directions, relative to its Center Point, and a Cube has 8 directions, relative to its Center point.

Pascal’s Triangle is also called the Binomial Expansion. This Expansion shows all the Combinations of two letters A and B in the function (A+B)**N. Level 1 of the Triangle is (A+B)**0 = 1  and level 2 is A x A + 2 A x B + B x B -> 1,2,1.

The Binomial Expansion converges to the Bell-Shaped Normal Distribution when N-> ∞.

The Diagonals of Pascal’s Triangle contain the Geometric Number Systems (Triangular Numbers, Pyramid Numbers, Pentatonal Numbers, ..) and the Golden Spiral of the Fibonacci Numbers.

Pascal’s Triangle is a Repository of all the Possible Magnitudes and their Components.

The Normal Distribution shows that the first level of the Triangle (the Tetraktys) is much more probable than the last levels.

The Hexagonal Numbers

The first four Levels of the Triangle of Pascal contain the Tetraktys of Pythagoras.

The Tetraktys  is an Ancient Vedic Mathematical Structure called the  Sri Yantra, Meru Prastara or Mount Meru.

About Numbers, Operations and the Klein Bottle

The Complex Numbers are not “Numbers” (Scalars) at all.

They are “Operations” (Movements) that can be applied to Magnitudes (Geometries) and Magnitudes are Combinations of the Simple Building Blocks of the Tetraktys, Points and Lines.

The Tao of Ancient China was not for nothing represented by a Flow of Water. According to the Ancient Chinese Mathematicians Every Thing Moves.  In the Beginning there was only Movement.

In the Beginning only the One was Moved but when the Duality was created the Two moved around each other never getting into contact to Avoid the Void.

When we look at the Numbers we now can see that they are the result of the Movements of  the first Diagonal of Pascals Triangle,  the 1′s (Points) or better the Powers of  the One: 1 **N (where N is a Dimension).

Even in the most simple Number System, the Unary Number System, Concatenation is an Operation, An Algorithm.

The Mathematician John Conway recently invented a new Number System called the Surreal Numbers that contains Every Number you can Imagine.

The Surreal Numbers are created out of the Void (ɸ)  by a simple Algorithm (Conway calls an Algorithm a Game) that describes Movements (Choices of Direction: Up, Down, Left, Right, ..)  that help you to Navigate in the N-Dimensional Number Space.

The Ancient Chinese Mathematicians played the same Game with the Numbers.

Algorithms were already known for a very long time by the Ancient Vedic Mathematicians. They called them Yantra’s.

SriYantra

Sri Yantra

Geometry is concerned with the Static Forms of Lines and Points but there are many other more “Curved” forms that are the result of  Rotating Expansion and Compression. These forms are researched by the modern version of Geometry called Topology.

The most interesting 4D Topological Structure is the Klein Bottle.  The Klein Bottle is  a combination of two Moebius Rings. It represents a Structure that is Closed in Itself.

It can be constructed by gluing both pairs of opposite edges of a Rectangle together giving one pair a Half-Twist. The Klein Bottle is highly related to the Ancient Art of Alchemy.

The movement of the Duality around the Void can be represented by a Moebius Ring the Symbol of Infinity ∞.

Later in this Blog we will see why the Number 8 is a Rotation of ∞ and the symbol of Number 8 is a combination of the symbol of the number 3 and its mirror.

First we will have a look at the Reciprocal Relation between Space and Time.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

About Dewey B. Larson, Velocity and Time

Dewey B. Larson (1898 – 1990) was an American Engineer who developed the Reciprocal System of Physical Theory (RST).

Larson believed that the failure to recognize that Motion is the most basic physical constituent of the universe has handicapped the progress of the traditional study of physics, which focuses on Forces.

The definition of Motion stems from the Equation of Velocity, v = ds/dt.

Instead of depending upon the change of the location of an object to define an arbitrary “quantum” of space per “quantum” of time, such as miles per hour, or meters per second, the RST assumes that the observed universal passage, or progression, of time is one aspect of a universal motion that necessarily must be accompanied by a universal “passage,” or progression, of space.

The Units of Time fill up the Units of Space. Space and Time are Duals.

Space is not-Time and Time is not-Space. Time is Non-Local, Cyclic and represented by the Rotating Imaginary Numbers. Space is Local, Linear and Represented by the Scalar Numbers. Space is the Vacuum and the Nothing and Time is the non-vacuum, the Every Thing, the Solids represented by the Cube of Space.

The Cube of Space is the structure behind the Tetraktys but also behind the Book of Genesis.

Our Reality contains two Reciprocal 3D-structures related to Space and Time. Space and Time are related by the Simple Formula N/N=1/1=1, the Formula of Diracs Delta Function.

We are able to perceive the Real 3D-Structure of Space. The 3D-Structure of Time is Imaginary. It is situated in the Imaginary Number Space of i.

LarsonsScalarCube.jpg

Larson’s Cube, the Geometric Representation of the Octonion.

Larson, a Self Thought Genius like Grassmann, developed Geometric Algebra without knowing anything about Geometric Algebra but he also invented String Theory long before String Theory was invented.  The Mathematics of Larson is also the Mathematics of the Tetraktys of Pythagoras without even knowing anything about it.

wom_image3.jpg

The Periodic System of Larson

Larson was able to Calculate all the important Physical Numbers without any problem and was also able to Calculate Chemical Structures and Reactions.

About the Bott Periodicity

The fourth line of Pascals Triangle and the Tetraktys contains 8 Directions in the Four Geometric Dimensions: 0, 1, 2, and 3.

Mathematicians are intrigued with this number 8, because they find it popping up unexpectedly in advanced mathematics.

In fact, expanding the Binomial Expansion to 8 dimensions just creates an inverse copy of these first Four Dimensions, and then the pattern just repeats itself with a half-twist and back from there, ad infinitum.

This is called Bott Periodicity discovered by the mathematician Raoul Bott (1923-2005).

The mathematician John Baez wrote an article in which he relates this 8-fold Periodicity to the Scalars (1), the Complex Numbers (2), the Quaternions (2×2), and the Octonions (2x2x2 = 2**3).

Bott Periodicity

The Universe of Numbers and Magnitudes  is Cyclic and Fractal.

Our own Reality, symbolized by the Tetraktys,  repeats itself in Higher Dimensions until Infinity.

The Tetrad, represents Completion, because it contains all its Previous Numbers, the 1, 2, 3, and itself, 4, in One Number, 10 = (The One) +  9 (= 3 (Trinity)x 3 (Trinity) = Tetraktys).

As you can see in the Picture above the Fractal Pattern of 8 contains two kinds of Trinities/Triangles, an Upside and a Downside (Rotated by 180 Degrees) Triangle. When you Rotate by 180 Degrees the 1 becomes -1 and 1 + -1 =0 is the Void.

The Square is a combination of two Triangels. It is represented by the Of Star of David, the Symbol of the Heart Chakra.

The Star of David, the Symbol of Human Center, the Heart Chakra.

The Multi Dimensional Rotations of the Octonions always Come Back to Square 1/1=1, the One and keep Rotating around the Center, the Nothing,   Until Infinity.

LINKS

About the Tetraktys (1)

About the Tetraktys (2)

About Triangular Numbers and Pascal’s Triangle

About the Empty Set

About the Relationship Between Geometry and Music

About the Trinity

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

About Number and Magnitude

About Ratio and Proportion

About Ratio and Proportion by Euclid

A book of Augustus deMorgan about “The Connection between Number and Magnitude”

The text of the Fifth Book of Euclid

An Educational You Tube Channel called Insights in Mathematics

About the History of Geometric Algebra

About the Sri Yantra

About Geometric Algebra

Free Software to use Geometric Algebra

About Clifford Algebra

About Yantra’s

About Movement

About Topology

About the Digital Root Patterns

About the Heart Chakra

A Video that shows how the Platonic Solids are created out of the Trinity Numbers

All you want to know about Geometric Patterns

About Mystical Number Theory and Pascal’s Triangle

Friday, December 2nd, 2011

The first part of this Blog is about the Triangular numbers, related to the Number 3, the Holy Trinity.

The second part shows that Pascal’s Triangle (called Meru’s Mountain in Mystics), the Binomial Expansion,  contains every Possible Mystical Number Pattern (including the Triangular Numbers) you can Imagine.

Pascal Triangle also shows that our Universe is a combinatorial miracle. It explores every possibility, is always in balance, expands and moves back to the beginning which is and was the Void, the Empty Set, the merge of Every Paradox, that is Possible.

About Mystical Number-Patterns

The Sēpher Yəṣîrâh (Book of Formation or Book of Creation, ספר יצירה) is the oldest book on Jewish Mysticism. The Sefer Yetzirah describes how the universe was created by the “God of Israel” through 32 Wondrous Ways of Wisdom.

The Number 32 is the Sum of the 10 Sephirot and the 22 Letters of the Hebrew Alphabet.

The Sephirot is related to the  Tetraktys of Pythagoras. The Tetraktys embodies the Four main Greek Cyclical (PlatonicMusical Harmonies: the Fourth (4:3), the Ffth (3:2), the Octave (2:1) and the Double Octave (1:4).

1+2+3+4 = 10. 10 is the 4th Triangular Number. The Nth triangular number is the Sum of the numbers 1 -> N. This Sum is equal to 1/2N(N+1).

Between the 10 Sephirot run 22 Channels or Paths which connect them.

The Sephirot are the Points of the Tetraktys. The Hebrew Letters are the Lines between the Points. The Lines of the  Sephirot and the Tetraktys create a Cube (6) at the Top and a Tetrahedron (4) at the Bottom.

The Letters of the Hebrew  Alphabet are divided in the 3 Mother Letters (אמש, the Trinity), the Seven Doubles (The Planets) and the Twelve Simples (the Zodiac).

The 22 letters of the Hebrew Alphabet are a combination of the Trinity, the 7 Planets and 12 Signs of the Zodiac.

When you analyse the Sepher Yeshirah the Cube of Space (the Kaaba) appears out of the Hebrew Alphabet. The Kaaba is related to the Seventh Planet, Saturn.

The 3 Axis of the Cube of Space are the Trinity, the 6 (2×3) Faces of the Cube stand for the Planets with the 7th Saturn, the Son of the Central Sun (3+1 (Center)+3) in the Center and the 12 (4×3) Boundary Lines of the Cube represent the 12 Signs of the Zodiac.

As you can see the Number Three, the Triangle,  plays an important role. It is the First Structure that is Closed in Itself and is therefore Topological related to the Circle. The Circle (and the Triangle) is able to rotate With and Against the Clock. This property is called Spin in Physics.

It is very important to realize that Everything Rotates in our Universe around a Central Object that rotates around another Central Object. The Central Object Gives Time, determinates the Rythm or Harmonics,  of the Rotation Structure.

The Trinity rotates around the Void. The 7 Chakra’s of the Human rotate around the 4th Chakra, the Heart Chakra, ((3+(1)+3)=7).

The Planets rotate around the Sun and the Sun rotates around the Central Black Hole. The arrow of Sagitarius points to this Black Hole.

On a Six Sided Dice the Sum of all the Numbers is Seven (1+6,2+5,3+4). The Sum of the Six Numbers is 3 X 7 = 21. If we add the Center (Saturn) the Number 22 appears.

22/7 is a good approximation of the number π. π relates the Square (and the Cube) to the Circle.

The Cube of Space symbolizes  the Playing Board of the Game of Life. On the Playing Board we have a Free Choice to move into the many Paths that are available. Every Path has its own Probability and this Probability can be calculated. If we don’t know what to do we could throw a Dice.

The Cube of Space contains the same six lines that exist in the I Ching. Four of the lines are of equal length, the other two, the diagonals, are longer. For this reason symmetry cannot be statically produced and the Dance (of Shiva) results.

The Circle represents the Cycles of Time of the Matrix of the Demiurg. Behind all the Probabilities of all the Possible Paths lies a Hidden Order.

A Hexagram, represented by the Star of David,  is a Two-Dimensional (Orthographic) projection of a Cube. A Symmetric Projection of the Cube creates a Cross.

A Hexagram is a Two Dimensional Cube

One of the many meanings of the first word in the Bible “Bereshit“,  is “They (Elohim) created Six” which means that in Six Stages of  the Time Cycle the Cube of Space (or the Hexagram) was populated. On the Seventh Day the Center was filled.

The book of Genesis does not describe the creation of the Trinity (They, Elohim, 1+2+3, 1x2x3) itself. This stage was later covered in the Zohar.

In my blog “About the Sum of Things” it is shown that Six Stages are part of an Expansion Pattern governed by the Powers of Two. After 2**6 (64) Expansions (or Compressions) the Same Fractal Pattern repeats itself on a higher level.

64 is the Number of the I Tjing and the Game of Chess. The number 32 of the Sepher Yeshirah is 64/2 and is a Contraction of the I Tjing.

The I Tjing is a contraction of the oldest Divination System in the Word called FA. FA is still used all over the world by the followers of the oldest wisdom-system created by the YOrubA in Africa. The Yoruba lived at the place where the ancient Paradise was situated.

Star of David in The Israeli Art Genesis-2

The Fourth Day (Sun (4), Moon (5))

About the Triangular Numbers

The Tetraktys contains the Numbers 1, 3, 6 and 10. These numbers are called Triangular Numbers.

The number 21 is also a Triangular Number because it is the Sum of  the Sixth Level of the Tetraktys,  the Numbers 1 to 6.

The Fifth Level of the Tetractys is related to the Number 15 (1+2+3+4+5). This number connects the Tetractys and the Sephirot to the 3×3 Lo Shu Magic Square also called the Seal of Saturn.

The nth Triangle number T(n) is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n.  T(n)=n(n+1)/2.

The Triangular Numbers contain the Perfect Numbers. A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. Six (1+2+3=1x2x3) is the first Perfect Number and 28 (1+2+4+7+14) is the next.

The Sum of two Triangular Numbers is a Square

The Sum of two adjacent Triangular Numbers T(n) +  T(n+1) is a Square Number because Two Triangels can be combined in a Square. 1+3=2**2 and 3+6=3**2.

There are many relationships between the Triangular Numbers. These relationships were the focus of the research of the Mystical Group of the Mathematikoi of Pythagoras.

6 (Bereshit, the Cube, the Hexagram) + the 22 Letters of the Hebrew Alphabet = 28, the Next Perfect Number (1+2+3+4+5+6+7).

28 is like the numbers 6 and 15 also a Hexagonal Number. As you can see in the picture below 28 is the fourth Hexagonal Number. As we have seen before a Hexagon is a Projection of a Cube so 28 represents a Cube in a Cube in a Cube. A Cube in a Cube is called a Tessarect or a HyperCube.

28 is a Hexagonal Number

The Number 15 is a Cube in a Cube called a Tessarect or a HyperCube

The first sentence in Genesis (“In the beginning Elohim created Heaven and Eearth“) contains 7 words and 28 letters. This indicates that the Creation Process was already in the 7th stage of the Tetraktys and in its 2nd Fractal Expansion,  the Birth of the Material Universe.

The sum of the entire verse is the 73rd Triangular Number. The prime Numbers 37 and 73 are geometrically related. They form the third and the fourth term in the sequence of Star Numbers (1, 13, 37, 73, 121).

Hexagon/Star pairs are closely related to Triangular numbers. Their product is always a Triangle, and they can be symmetrically generated from a Pair of Triangles.

Star Numbers are a Combination of Two Triangular Numbers

The Square is a combination of two Triangels. It is represented by the Of Star of David, the Symbol of the Heart Chakra.

The Symbol of the Heart Chakra contains Two Triangles.

About Pascal’s Triangle

When a number represents a Geometric Structure it is called a Figurative Number.

Every possible figurative number is generated by the Triangle of Pascal.

The Fractal Sierpinsky Triangle is the Triangle of Pascal Modulo 2.

The Triangle of Pascal was known long before Pascal (re)discovered it.

It was known in Ancient India as the Meru Prastara and in China as  the Yang Hui.  Meru Prastara relates the triangel to a Mystical Mountain called Mount Meru. Mount Meru is also implemented in the Sri Yantra.

The Triangle shows the Coefficients of the Function F(X,Y))= (X+Y)**n. If n=0 F(X,Y)=1 and if n=1 F(X,Y)=X+Y so the Coeffcients are (1,1).

Pascals Triangle is a 2-Dimensional System based on the Polynomal (X+Y)**N. It is always possible to generalize this structure to Higher Dimensional Levels. 3 Variables ((X+Y+X)**N) generate The Pascal Pyramid and n variables (X+Y+Z+….)**N  generate The Pascal Simplex.

The rows of the Pascal’s Triangle add up to the power of 2 of the row. So the sum of row 0 is 2**0 and  the sum of row 1 is 2**1 =2.

The Sum of the  rows of the higher n-dimensional versions of the Triangle is n**N where n is the Amount of Variables and N the level of expansion. So the Sum of Pascal’s Pyramid (3 variables X,Y,Z) is 3**N.

Triangle of Pascal

The most interesting property of the Triangle is visible in the Diagonals.

The First Diagonal contains only 1′s. The Ones represent Unique Objects. They are the Points in the Tetraktys.

The Second Diagonal contains the natural numbers. These Numbers are used to Count Objects that are The Same. The Natural Numbers are the Lines that connect the Points. The Natural Numbers are the Sum of the previous Ones.

The Third Diagonal contains the triangular numbers. The Triangular Numbers are the Sum of the previous Natural Numbers.

This pattern repeats itself all the time.

File:Yanghui triangle.gif

The Yang Hui is an ancient Chinese version of the Triangle of Pascal. This Triangle contains Nine (3x3) Levels.

The Fourth Diagonal contains the tetrahedral numbers (Pyramid Numbers) and the Fifth Diagonal, the pentatope numbers.

Fermat stated that Every Positive Integer is a Sum of at most three Triangular numbers, four Square numbers, five Pentagonal numbers, and n n-polygonal numbers.

The Tetrahedron with basic length 4 (summing up to 20) can be looked at as the 3-Dimensional analogue of the Tetraktys.

File:Pyramid of 35 spheres animation.gif

A Tetrahedral Number represents a 3D-version of the Tetraktys.

The Diagonals of the Triangle of Pascal contain every Possible 2-Dimensional Figurative Number (and Structure).

These Numbers are Projections of Higher Dimensional Numbers and Higher Dimensional Structures.

The Higher Dimensional Versions of the Triangle (the Pascal Pyramid, The Pascal Simplex) contain these structures.

The Rows of the Triangle Sum to the Powers of Two (2 Dimensions). These Powers control the Levels of Expansion.

Every 7th step the Fractal Pattern of the Triangle repeats itself on a higher Level.

The Figurative Numbers are the Geometric Shapes that are created by the Lines of the Natural Numbers that are connecting the Points of the One.

Pascal’s Triangle also contains the numbers of the Fibonacci Sequence (“The Golden Spiral“).

When we take the Modulo 9 (the Digital Root of Pythagoras) of the Numbers of Fibonacci a repeating patterns of 24 steps shows itself that can be represented by a Star Tetrahedron or Stella Octangula. The Star Tetrahedron is a Three Dimensional Star of David.

the Fibonacci Numbers as a Cube.

The StarTetrahedron, shows the Pattern behind the Sequence of Fibonacci.

Every Figurative Number N is the Sum of the Figurative Numbers N-1.  Every Geometric Shape is a combination of all the Previous Geometric Shapes.

This means that Every Geometric Shape is in the end The Sum of the Sum of the Sum of  …. Triangels, Trinities (Elohim) or Triangular Numbers and therefore an Extension of the Tetractys of Pythagoras.

The Expansion of the Whole is a (Fractal)  Combination of Combinations.

The Triangle of Pascal is related to the so called Binomial Theorem which is used in Combinatorics and Probability Theory to describe the Amount of Combinations of a Set of  Objects.

The rows of the Triangle of Pascal also shows the Bell Shaped Pattern of the Normal Distribution.

The Probability Distribution of the Triangle of Pascal converges to the Normal Distribution because of the Central Limit Theorem. Every Row has a Mean of N/2 and a Variance of (N**1/2)/2 which means that with every new row the Mean and the Variance become Bigger and Bigger.

The Triangle of Pascal and therefore the Figurative Numbers describe Everything that is Possible but every Expansion of the Triangle is less Likely to Occur.

The Triangle of Pascal Modulo 3

The Triangle of Pascal Mod 3 represents the Tetraktys in the Tetraktys in the .....

Because of the Fractal Expansion/Contraction Pattern The Cube of  Space, related to the Element Earth,  explains Everything there is to Know on Our Level of Existence, Mother Earth.

The interesting part of the Figurative Numbers is that they representent Visual Patterns with which we can Reason.

We don’t need complex formulas because we can See what is Possible.

The interesting part of the Triangle of Pascal is that we can See that the Complex Figurative Structures are created out of a very Simple Structure, the Triangle.

If we want to understand our Reality we have to begin with looking at the Beginning and not start somewhere in the Middle.

If we look at the Fractal Expansion Pattern of the Triangle we See that Every new Stage is an Expansion Out of the Middle.

The Expansion of the Human, the Next Step in our Evolution,  is therefore an Expansion Out of the Heart, the Balance of Father Sky and Mother Earth.

Life is not only about Me and the Other.

Life is also about the Relationship between Me and the Other.

If we don’t Collaborate the Next stage in our Evolution will never happen.

LINKS

The Content of the Sepher Yesirah

About the Sepher Yesirah

About the Cube of Space

About the Tetractys

About the Cube of Space and Psychology

About the Sepher Yesirah and the I Tjing

A correspondence table of the Cube of Space

About Bereshit

About Genesis

About Patterns in the Bible

About Saturn

About the Trinity

About the Sri Yantra and Plato

About the Lo Shu and the I Tjing

All kind of strange relationships between Triangular Numbers

A website about Mystical Number Theory

About the Figurative Numbers

About Combining the Combinations

About the Golden Spiral and Plato

About the Logic of Creation

About Pascal’s Triangle and the Normal Distribution

A complete course in elementary Number Theory

About the Psychology of the Cube of Space

About the Tetraktys and the Zodiac

About the Process Theory of Paul Young

About the Theory of Dewey B. Larsson

Mysteries of the Equilateral Triangle

About Visual Patterns in Number Theory

About Pascal’s Triangle and Cell Division

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 Tree of Life

Sunday, April 20th, 2008

The Tree of Life is a concept that can be found in almost every culture. The Tree of Life describes the Process of Creation.

enneadLet’s begin with Egypt. The Tree of Life is constructed out of nine entities. That’s why the tree of life is called Pesedjet (Nine) later translated in Ennead.

The top of the tree is called Atum. Atum masturbated and gives birth to two children called Shu (Air) and Tefnut (Moisture). Shu and Tefnut give birth to Geb (Earth) and Nut (Sky). Geb and Nut produce four children Isis, Nephthys, Osiris, and Set.

The sequence of the process of birth of all the deities generates a structure. The first step is a triangle. The second step is a square and the last step is also a square. If we connect all the stages a patterns of 22 connections emerges that is visible in all the other trees of life.

luriaThe Jewish tree of life is strongly related to the Kabbalah. The Kabbalah originated in the middle ages (the 12th Century) but the source of the Kabbalah is much older. Perhaps it originated in Egypt when Ra-Moses moved the priests of Aten (inspired by Ra) to the Holy Land.

The top of the structure in the Kabbalah is called Keter (Crown), “the most hidden of all hidden things“. The concept of the Keter has a lot in common with the concept of Atum. Atum and Kether are both “self-reproducing structures”.

In the Yggdrasil the top is called Asgard. It is the place where Odin(Ygg) lives. Asgard contains Walhalla (“heaven“). At the bottum of the tree we find Hel located in Niflheim. Midgard or Middle Earth, the world of mortals, is located in the middle.

It is very clear that the story of the Yggdrasil contains many distortions caused by influences of Christianity (Hell) and many authors who gave their “artistic interpretations” without knowing the “old” foundation.

Yggdrasil2The Axis Mundi is perhaps the oldest representation of the Tree of Life. It is represented by a mountain (Mount Meru, Mount Olympus) surrounded by other “impressive” structures of nature. Meru has a lot in common with the Old Continent of Mu. Many stories that are connected with the Tree of Life tell about the disaster of the Great Flood and predict a comparable end of the world (the Gotdammerung).

What happened?

It is very clear that many stories are “mixed up”. The story of Mu and Atlantis are mixed up with the knowlegde about the origin of creation (the self-reference that is closed in itself), interference of the Church of Rome (Heaven and Hell), the creative power of poets and old knowlegde of the Sacred Geometry of Life.

The Kabbalah and especially the Zohar contains (in my opinion) one of the purest representations of first stage (the Triangle) of the Tree of Life.

Read this poem and you know everything you have to know! It is about the Ein Sof, The Primal Void.

 

Know

Before the beginning of creation was only the Highest

All full filling light

Free

Fulfillment, no emptiness

Only endless, equal light

Circled everything

Then He decided to create worlds and creatures

So that He revealed His perfection

Reason for creating the worlds

He restricted Himself in His center

Pressed the light together and withdraw

Free place stood behind, empty space filled with endless

Around the center

Equally pressed

So this empty place became a circle

So the light restricted Him self

And see

After compressing

In the central of the space filled with endless light

Forms His self a round emptiness

Then

A place appeared

Where creation and creatures can exists

And see

A strait forward ray forms itself from endless light

From above to below descended He in the empty place

Reached out His self, descended per ray to below

Endless light

All the worlds were perfect

In this empty space

For the worlds the Endless was

In His perfection outstanding

No creature has strength to grasp His perfection

Concrete form cannot reach Him

For Him there is no place, no border, no time

And via the ray the light descended

To worlds

In black empty space were everything is

And each circle

Of each world

Near the light – is worthy

To our world of material in the center

Within all circles in the center of endless emptiness

Expelled from endless – further then all the worlds

Material so eternal low -

He is within all the circles -

In the middle center of the endless emptiness…..