About Number and Magnitude

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.

Mount Meru (Pascal's Triangle in Vedic Mathematics)

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 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.

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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 the Vedic Square

This blog is about the Cycle of Nine implemented in the Digital Root or Modulus 9-Function. The Digital Root generates many Patterns that were used in Ancient Architectures.

One of the most important Digital Root Patterns is the Vedic Square. It is the Digital Root of the Multiplication Table of the numbers 1 to 9.

This Table contains the Harmonics of the Numbers 1 to 9. These Harmonics are highly related to the Harmonic Pattern behind the Cycles in our Universe.

The first part of this Blog is about the Digital Root. It contains the patterns that are behind the Cycle of Nine.

This part is very technical but it makes it possible to show that there is a deep structure  behind the Modulus-9.

This pattern has to do with just two numbers, 2 and 3. They generate the Spirals of Expansion and Compression of our Universe.

2 and 3 and their Sum 5  are also the Numbers behind the Harmonics of our Universe.

The Second Part is about the Vedic Square. It is called the Vedic Square because this Square is one of the most important tools in Ancient Vedic Mathematics.

Vedic Mathematics was used in many Ancient Cultures (China, Egypt, Greece) with different names. The Chinese art of Feng Shui was called Vaastu Shastra in India.

Pythagoras, trained in Egypt (Heliopolis),  used the same principles and used the same  Patterns the Ancient Vedic Scientists were using.

The last part is about the Game of Chess. This game is  just like many other Ancient Games a Simulator of the Game of the Universe.

This blog contains many links to other Blogs and Resources on the Internet. These references make it possible to dig deeper into this fascinating subject.

About the Digital Root

When  you divide a number X by a number N the Remainder of the division is called X Modulus N.  22 mod 7 = 1 because 22 = 3×7 + 1.

The Modulus-function N maps the Set of the Natural Numbers to the Numbers 0, 1, 2, ….,N-1.

One of the most famous and ancient Modulus-functions is called the Digital Root. The Digital Root is the Modulus 9 function.

Because 10 mod 9 = 1 every Power of 10 has a Modulus 9 of 1. Therefore (a10**X+ b10**Y+…) mod 9 = a + b, the Sum of the Digits of the Number. 62 mod 9 = 6+2 = 8.

Digital Roots have been recorded for thousands of years, formalized by Pythagoras in 530BC and even earlier in Indian Vedic Mathematics (Vaastu Shastra).

Digital Roots are used in Numerology. In Numerology Numbers have a Meaning.

In Gematria Letters and Words are transformed into Numbers which have a meaning.

In Ancient Languages like Hebrew Letters are also Numbers. Numerologists believe that Words with the same Digital Root have the same Meaning.

The numbers 0 to 9 of the Digital Root are the Points of the Tetraktys of Pythagoras.

The Tetraktys of Pythagoras

The Modulus 9 pattern contains 2 number groups (3,6, 9) and (1,2,4, 5,7,8).

Later we will see that the last group contains 2 subgroups (1,4,7) and (2,5,8).  Together with (3,6,9) we can map these 3 Triangels on the Modulus 9 Circle.

4 is the Middle of 1+7=8, 5 is the Middle of  2+8=10 =1 and 6 is the Middle of 3+9=12=3. 5 is also the Middle of the Middle.

The group (1,2,4,5,7,8 ) is called the Ring Z/9 in Mathematics. Z/9 is isomorphic with the Sequence 2**N mod 9 where N is positive and negative. The sequence 1,2,4,8,16(7),32(5),64(1),128 (2),256 (4),… repeats itself until infinity.

This Sequence is the Expansion and Compression Pattern of the Number 2.

The Ring Z/9 is part of the Tetraktys and forms a Hexagram. This Hexagram is a 2D-projection of the Cube of Space. When we combine the (3,6,9)-pattern with the Hexagon a (4×4) Triangle is created.

The number 2 is the Container, the Cube, inside the Tetraktys. That is the Reason why the Second letter in the Hebrew Alphabet Beth means Vessel or Container.

(3,6,9) is a Triangular Cycle that repeats itself until Infinity.  The Number 3, the Trinity, is the Mover of the Container of 2. This Rotation moves With and Against the Clock.

This is the reason why the 3th Letter of the Hebrew Alphabet, Gimel, means Camel. The Camel of Gimel carries the Water into the  2 Containers of Beth.

The Number-2-pattern contains 3 Binary Groups (called Polar Pairs) with a Sum of Nine (1,8), (2,7), (4,5). The Number-3-Pattern contains 2 Polar Pairs (3,6) and (0,9). The Polar Pairs represent the Lines of the Tetraktys.

(0,9) maps unto Itself and represents The Beginning and The End, The Now. (0,9) is a Point and a Line.

The Polar Pairs of the Z/9 create a Cyclic Pattern that contains two Squares, (1,2,4,0) and (5,7,8,0). Both of them Share the Zero, The Void.

The Sum of the Opposite Numbers of the Z/9, (4,8 = 12=3), (1,5 =6 ), (2,7=9) of the Tetraktys shows the 3,6,9-pattern again.

There are 8 Ternary Groups ((1,5,9), (1,6,8), (2,6,7), (2,5,8),(2,4,9),(3,4,8),(3,5,7),(4,5,6)) with a Sum of 15. This Ternary Group represents Triangels. All of them are part of the famous Lo Shu 3×3 Magic Square.

The 3 Triangles of (1,4,7), (2,5,8) and (3,6,9) copied from the linked Website.

When we use the number 3 as a generator 3 Triangles are created (1,4,7), (2,5,8) and (3,6,9).

The 3 Triangles move With and Against the Clock ((1,4,7) and (7,4,1)).

It takes 3 rotations to get every Triangle back to its original position. (1,4,7) becomes (7,1,4) and (4,7,1). This means that there are 6 permutations of every Triangle.

Every addition of two Triangels produces another Triangle.   An Example:  (1,4,7) + (2,5,8) = (3,9,6).

When we create a Matrix to find all the combinations a new group of 9 transformations ((1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6),(7,7,7),(8,8,8),(9,9,9)) appears. They are the Triangels that are a Line and a Point. An Example:  (1,4,7) + (1,1,1)=(2,5,8).

There are now (18 +9=27) x27 = 729=3**6 = 9**3 possibilities.

The same 27×27 Matrix appears when we Multiply the 3 Triangels. An Example:  (5,8,2)x(5,8,2)= (25,64,4)= (7,1,4) and (3,6,9)x(5,8,2)=(15,48,18)= (6,3,9).

Another interesting patterns  becomes visible when we look at the Opposite Numbers of 3 Triangels (1,5), (2,6), (3,7),(4,9) en (5,9) in the Picture above.  They recreate the Triangels. An Example: (5+9=5, 2+6=8 ,8+3=11=2).

About the Digital Root of the Golden Mean

The 27×27 Matrix pattern also emerges out of 24 repeating numbers (1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9) of the Digital Root of the Fibonacci Sequence (The Golden Ratio).

this solution gives the densest
lattice packing of spheres in 24 dimensio

When we group the Golden Ratio pattern in 2’s (2×12) the Polar Pairs appear. The 12 pattern has  a Sum of 108 = 0 Modulus 9. 108 and 24 are related to the Gayatri Mantra.

1 1 2 3 5 8 4 3 7 1 8 9

8 8 7 6 4 1 5 6 2 8 1 9

When we  group the pattern of 24 numbers (3×8) of the Golden Ration into Trinities the Triangle Pattern appears again.

1   2  3  4                  -3 -2 -1 -4 (Pattern-number)

1   1  2  3  (7)           5   8   4   3   (2)

7   1  8  9  (7)          8   8   7   6   (2)

4   1  5  6  (7)          2   8   1    9   (2)

The Pattern of the Pattern is (1,2,3,4,-3,-2,-1,-4). The last part of the Pattern (-3,-2,-1,-4) can be transformed into the first part (1,2,3,4) by adding 4.

The Digital Sum of the first 3×4 numbers is 7 and the Digital Sum of the last 3×4 numbers is 2.

When we rearange the 24 cycle in 6 groups of 4 digits another pattern shows itself: (1,4,8,5), (1,3,8,6), (2,7,2,7),(3,1,6,8), (5,8,4,1), (8,9,1,9).

The pattern of the Golden Mean copied from the Linked Website

When we combine all the different rotations of the 3 Triangels a Cyclic Flow Pattern appears that looks like the Jitterbug of  Buckminster Fuller.

The Jitterbug is a 3D projection of the 4D 24-Cell (again 24!) also called the Hyperdiamond.

The 24-cell is self-dual and is the regular polytope with no analogue among the five Platonic solids of 3-space.

The 24-cell also called the Hyperdiamond

About the Vedic Square

One of the Simple Structures of Numbers that contains a lot of patterns is the Vedic Square. The Vedic Square was called the Eight Mansions in China. The Vedic Square is the Digital Root of the Multiplication Table of the numbers 1 to 9.

The Multiplication Table is a subset of the 27×27 Matrix of the 3 Triangels.

The Multiplication Table contains the Harmonics of the Numbers 1 to 9.The Vedic Square was used to build the Pyramids, create the Chinese I Ching, the Game of Chess, Dante Alighieri used it to structure his trilogy La Divina Commedia, the Sistine Chapel was build and the frescoes and symbols were arranged according to its concepts and the first chapter of Genesis was written and imbued with its numerous concepts graphic images.

File:Michelino DanteAndHisPoem.jpg
La Divina Comedia of Dante with the Tower of Babel on the background. This Ziggurat is a Geometric Structure highly related to the Vedic Square.

Scholars and Artists discovered that the various lines of the Vedic Square could be used to direct a design. By selecting a line of numbers, and using a constant angle of rotation, various designs could be produced. These designs are visible in abstract Islamic Art.

The Vedic Square is a Symmetrical Structure because AxB=BxA. This is called the Associative Property of Multiplication.  The Square is a combination of Two Triangels and contains 45 distinctive numbers.

The Vedic Square repeats itself until infinity when you extend the Square to a NxN Square.

The number pattern of the diagonal of the Vedic Square, 1,4,9,7,7,9,4,1,9,  is the Digital Root Pattern of the Square Roots. This patterns repeats itself until Infinity.

The Vedic Square contains the 5 Polar Pairs, the 8 Lo Shu Ternary Groups and the 3 Trinity Patterns ((1,4,7), (2,5,8), (3,6,9). It also contains the Star of David, The Zodiac, the Tree of Life and many other Mystic Patterns.

It is possible to transform the Vedic Square to the Lo Shu Magic Square.

The patterns of the Vedic Square Rotate. The End of a Horizontal and a Vertical Pattern connects with the Beginning of the Pattern. This means that the Vedic Square is a Torus.

This Torus is called the Rodin Torus. The Rodin Torus is a Coil that produces a Uniform Electro-Magnetic Field.

The 3-6-9 and 6-3-9 Cycle in the Vedic Square can be thought of as Clockwise and Counter-Clockwise, or as Electricity and Magnetism. They are transport-channels.

The ((3,6,9),(6,3,9)-Matrix divides the Vedic Square in 9 2×2 Squares.

The 9 2×2 Squares have a Sum of 9,18 and 27 which is 1×9,2×9 and 3×9. If we leave out the (3,6,9)-Matrix and divide by 9,  a 3×3 matrix results with 1,2,3 on the Outside  and a Cross of 2’s in the middle. This 3×3 matrix shows the Expansion of the 2 into the (1,2,3).

Patterns in the Vedic Square

The Rows and Colums of Ring Z/9 add up to 45. The Rows and Colums of the Number 3-Pattern add up to 54 which is a Mirror of 45. The (4,5)-pattern generates the Star of David and the Zodiac.

About Indian Vastu Science

The Game of Chess originated in India. It was passed on to the medieval West through the intermediary of the Persians and the Arabs.

The form of the Chess-Board corresponds to the Vastu-Mandala, the 9×9  diagram which also constitutes the basic lay-out of a temple or a city.

Hindu mythology has it that Vaastu Purusha was born of Lord Shiva’s sweat when he fought the deadly demon Andhakasura.

Vaastu Purusha himself became uncontrollable and destructive and the heavenly gods finally subjugated him and brought him down on earth with face down, with his face in the Northeast and his feet in the Southwest.

45 deities stayed there, 32 of them in the outer enclosure and 13 of them in the inner enclosure holding him in place at various points or locations on his body.

32 =64/2 and the Number of the 32 Paths of Wisdom of the oldest book of Hebrew Mysticms the Sepher Yesirah (the Book of Formation or Book of Creation, ספר יצירה).

64 is the Number of the I Tjing. 45 (5×9) is the Sum of the Lo Shu Magic Square and the Number of the Vedic Square.

All these Mystic Structures come from the same Source and are different Views on the same Pattern, the Tetraktys, the Triangular Numbers created by the Meru Prastara or Sri Yantra also known as the Pascal Triangle.

The Vastu Jain Symbol is a version of the Tetraktys

The Vastu Mandala is an expansion of  a Point (the Bindu) into the Line(2), The Trinity (3) and the Rotating (With the Clock and Against the Clock) and Expanding Square (4), represented by the Symbol of the Swastika. The Swastika is a Fractal Generating Pattern.

Every Point is a generator from which the Swastika-pattern generates a new Swastika. The 2×2 Square is transformed by the Swastika Pattern into the 4×4 and the 8×8 Square.

As you can see the Vastu Jain Symbol is an Indian Version of the Tetraktys of Pythagoras.

The Swastika contains the Four Points of the last line of the Tetraktys that are related to the Tethahedron.

About the Game of Chess

The Chess-Board symbolizes the Unfolding of Space by the Number-2-pattern and it synthesizes the Complementary Cycles of Sun and Moon.

The number 64, the sum of the Black & White (Yin/Yang) Squares on the Chess-board, is a divisor of the number 25920 (25920/64=405, 25920/9= 2880/9=320/5=72), which measures the Precession of the Equinoxes.

The Polar Pairs in the Modulo 9 Pattern are expressions of the Planets.

(1,8), the Castles, relates to the Planet Mars.

(2,7), the Bishops, relates to the Planet Venus. Venus is the Ruler of the Heart and the (2,7) is situated in the Middle of the Vedic Square.

When viewed from the Earth, the Planet Venus inscribes a near perfect five-pointed star (pentagram) around the sun every eight years. The points of a five-pointed star (pentagram) touch the circle of a pentacle every 72 degrees.  Likewise, many in Islam expect 72 virgins in heaven.

A full 360 degrees of procession takes 25,920 years, which is also seventy-two (72) 360-year cycles.

(3,6), the Knights relates to the Planet of the Messenger, Mercury. Mercury is Hermes, the Messenger God, with winged sandals. The moves of the Knights create a pattern that looks like the Swastika.

The (3,6)-number-lines are Transport-Channels (Gimel) as you can see in the Vedic Square and the Rodin Torus. The planet Mercury traces a Hexagram during its movement around the Zodiac.

(0,9) is the Planet Jupiter,  the Ruler of Modulus 9 who determinates the Rules of the Game. (0,9) is the Beginning and the End of the Game and is the cause of the Rotation of the Swastika related to the (3,6.9)-pattern.

The numbers 4 and 5 are the Moon (Queen) and the Sun (King). The Moon moves the quickest of all the planets, so does the Queen on the chessboard.

The Number 5 of the King is the Center of the 3×3 Lo Shu Magic Square and the Center of the Tetraktys.

The 8 Pawns represent  the number 2 and are connected to the Planet Saturn, the 2nd Son of the Central Sun and the Trinity (1+ 2 = 3). The Pawns start to move with 2 steps and later move 1 step. The 2 is the Center (The Son of the Sun) of the Trinity.

The 2 is also the Generator of the Expansion Pattern and the Polar Companion of the 7, the Center of the 3D-version of the Square, the Cube of Space.

The Pawn (2, Saturn) promotes into a Queen (Moon, 2×2) when he has reached the Other Side.

LINKS

About the Multiplication Table of 9

About the Tetraktys

About the Trinity

About the Vedic Square

About the Tetraktys and the Lo Shu

About the Lo Shu

About the Harmonics of the Universe

About the Hyperdiamond

About the Void

About Harmonics and Entrainment

About Good and Bad Vibrations

About the number 24

About the Jitterbug of Buckminster Fuller

A Simulation of the Jitterbug Pattern (CUBIC WONDER)

About the Game of Chess

About Plato and the Sri Yantra

About the Rodin Torus

About Vastu Science

About Gematria

About Vastu Science and the Borobudur

About Saturn, the Son of the Sun

Early astronomical traditions identify the “Primeval Sun” as the planet Saturn.

Saturn was id]]><![CDATA[entified with Osiris in Egypt and Shiva in India.  The Babylonians, the founders of Astronomy, called Saturn the "Light of Heaven, the Sun-God Shamash (or Šamaš).

Tacitus records the Jews as worshipping the planet Saturn, Shabbatai,  as their god. In Plato’s Timaeus, the word for the planet Saturn is Helios, the “Sun” god. Popular Greek traditions identified Saturn as Kronos (Father Time). At that time Saturn ruled “over the Pole“.

The Pole was seen as the Entrance to the Other World. The Shaman using his Light Body had to Climb Jacobs Ladder to get there.

In Sankrit, Suryaputrah,  “Son of the Sun”  is the name for the planet Saturn. The Medieval Alchemists called Saturn the “Best Sun”.

The Kabbalah divides the Universe  into Ten Spheres, or Sephiroth, which have Planetary and other Correspondences. The Sphere of Saturn is known as Binah (“Understanding“) and the terrestrial sphere, known as Malkuth, is said to have its foundation in Binah.

Long ago Saturn exercised the supreme power on Earth, his reign being remembered as the Golden Age, his time revered, a time which Man longed to return to. At this moment the Cycle is  ruled by Kali. The Mother Goddess Kali represents the Moon in Saturn.

Semitic civilizations referred to the god Saturn as “El”. El was the source of the Great Flood. El was represented by a Black Cube. The Kaaba (“the Cube of Space”) is a cube-shaped building in Mecca, Saudi Arabia, and is the most sacred site in Islam. The building predates Islam, and, according to Islamic tradition, the first building at the site was built by Abraham.

In Ancient History the World was ruled by the Female and  the Mother Goddess. The Vulva or the Yoni (Circle), of the Ancient Mother Goddess was always combined with a Black Stone (with a Point), the Symbol of the Phallus (Lingham) of the Male Creator. The God and the Godddess created the Universe in a short moment of Extreme Extacy.

The Pelgrims have to encircle the Black Stone of El Seven Times just like the Rings of Saturn encircle the Center.

About the Number Seven

The Blog “About the Sum of Things” is about the so called Seal of Saturn and the related 3×3 Magic Square of Saturn also called the Lo Shu in China.

Saturn is the Seventh Planet and Saturday (Sabbath) the Seventh Day of the Week.

In the Blog it is shown that the 3×3 Magic Square generates Two Cyclic Systems. One System, the Wheel of Karma  is a Fractal Torus and is related to the Expansion and Compression of the Universe and the number 2. The Fractal Torus contains Seven Levels associated with the Chakra’s, the Seven Heavens, The Seven Tones and the Seven Colors. The Tower of Bable and the Egyptian Pyramids are a Simulator of the Torus.

The other is a Cyclic Vortex System, the Cycle of Death, related to the number 3 and the Triangel.

The Number Seven is the Repeating Factor of the Torus System. After Seven Steps a new Fractal Level of the Expansion/Compression-Cycle is reached. On the Seventh Day a new Stage in the Creation Process of our Universe is started.

The Torus looks like a Yoni and as you can see the Lingham of Shiva is Inside the Torus. This is the reason why Saturn is associated with Binah and Shakti, the Female Part of Shiva. It also explains why Saturn is related to Fertility.

The Sequence of the Trinity (A-U-M) controls the Creation/Destruction-Cycle of our Universe.  This is the Cycle of Shiva, the Creator and Destructor.

Shiva and Shakti are the Circle (Torus, Yoni) and the Lingham (the Point, Singularity, Lingham). They are the 0 (or the 9) and the 1.

The only thing you need to Create our Universe is de Tao (0), the One, the Two and the Three and they will Generate Everything.

Why is Saturn the Son of the Sun?

There are two explanations. The first one is a Physical Explanation related to Plasma Physics. In the stage of the Golden Age our Solar System contained only Three Planets and Saturn was the Best Sun. Plasma Physics is able to explain many ancient Symbols.

The Second explanation goes back to the Numbers. The Magic Square of Saturn is the First Magic Square that can be constructed. 2×2 is not existent and 1×1 is a Point. The Magic Square of the Sun is the 6×6 Magic Square with Sum 666! and Constant 111. The 3×3 Square can be extracted (is a Son) out of the 6×6 Square.

Adam-Kadmon
The Demiurg with the Torus and the Zodiac

About  Kronos, Father Time

The Greek called Saturn Kronos, Father Time.

Most of the Souls are not aware of Cycling Cycle of the Fractal Torus of the Number Two of Duality,  the Wheel of Karma. They stay in the same Place and Their reincarnations are a Merry Go Round.

Some Souls move around the Torus and experience many experiences in the Seven Universus.

All of them are Kept in de Rotating Matrix of the Demiurg.

If you really want to be Free you have move out of Duality into the Cycle of the Divine Trinity (Shiva).

When you want to leave the Rotating Cycle (Torus) of everyday Life and move into a higher dimension (more possibilities, more perspectives), you have to Twist Yourself and Merge with Yourself.

You Twist when you Cross the Cycle of Life and Enter the Cycle of Death of the Trinity. When you join this Cycle you leave the Seven Heavens and move to the Void in the Middle of the Death Cycle.

The Void, the Kingdom,  Cleans every thing and makes every thing New.

You Merge with Yourself when you integrate the Inside and the Outside, the Up and the Down, the Male and the Female.

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

“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; and when ye fashion eyes in place of an eye, and a hand in place of a hand, and a foot in place of a foot, and a likeness in place of a likeness; then will ye enter into the kingdom.” (Gospel of Thomas, Logion 22).

LINKS

About the Sum of Things

About the Cube of Space

About the Myth of Saturn

About the Mother Goddess

About the Dance of Shiva

About Saturn and the Sun

About the Seven Heavens

About the Great Flood

About the Golden Age of Saturn

About the Torus and the Vortex

About Time

About the Twisted Universe

About Alchemy

About the Polar Myth

About the Sum of Things

The Lo Shu is a Chinese Model for Time and was used to design Cities, Temples, Cycles and Calendars.

lo-shu-color

The Lo Shu is a 3×3 Magic Square created by Fu Xi, the Founder of Chinese Civilization. Fu Xi lived around the time of the Great Flood.

The Magic Square was carried by a Turtle. The Turtle is the symbol of the Constellation Orion. Many Ancient Cultures claim that our Ancestors came from this constellation. The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos (Time).

The Chinese Pollen Path
The Duality of Fu Xi and his Sister, The Snake of the Kundalini contains 3.5 (7/2) Twists. 2x3.5 = 7. 7 = (-1,-2,-3,0,1,2,3).

According to Chinese Creation Myth  the world started with 無極 (wuji: nothingness), the Tao. Out of the Tao, the Egg of the Zero (0) and the Supreme Pure One (1) emerged. In the next step the Trinity (3), the Three Pure Ones, was created.

The Tao produced One; One produced Two; Two produced Three; Three produced All things (Lao Tsu, Tao Te Ching, 42).

SriYantra
The Sri Yantra contains 43 Triangels and is generated by the Bronze Mean.

The Trinity is represented by a Triangle. A combination of Two Triangels is a Square. The combination of Two (2) Triangels is also the Symbol of the Heart Chakra, the merge of Heaven, the Upper Triangel and Earth, the Lower Triangel.

The most complex Yantra (“machine”), the Sri Yantra, contains 43 Triangels. The Sri Yantra is determinated by the Bronze Mean. The Bronze Mean is a generalization of the Sequence of Fibonacci based on the Trinity. The Bronze Mean generates Quasi-Crystals and Penrose Tilings.

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

The Lo Shu Magic Square not only shows the Connection between the Four Forces that came out of the Two Forces, Expansion and Compression, it also shows the connection between Heaven and Earth.

In the Magic Square of Lu Shu the Even Numbers (2,4,6,8 = 2 x (1,2,3,4 = 2×2)) are Black(Yang, Male). The Odd Numbers (1,3,5,7,9 = 3×3) are White (Yin, Female). The Sum of all the Numbers is 15 (3×5).

The Even Numbers are situated at the Corners of the Square.

When the numbers of each row are multiplied (8x1x6; 3x5x7; 4x9x2) they together total to 225 ((3×5)x(3×5)) — as do those of the columns (8x3x4; 1x5x9; 6x7x2).

The Magic Square is dominated by two numbers (2**1, 2**2, 2**3)  and (3, 2×3, 3**2), It contains four Prime Numbers (1,3,5,7). It also contains the first Perfect Number 6 (1+2+3 =1x2x3). 6 is also a Harmonic Divisor Number and has a Harmonic Divisor 2. The Sixth Day in the week is the day of Saturn, the God of Time.

The sequence 1,2,4,8, 1, 3,6,9, 27 is called the Tetrad of the Pythagorians and was, according to Plato, used by the Demiurg, the Creator of our Universe, to create the Soul. The Soul is a mixture of the Same (1), the Different (2), and Existence (3). The Tetrad was used to define the Harmony of the Spheres.

When you connect the numbers of the Lo Shu a pattern appears that is called the Seal of Saturn or the Dance of Yu.

The Seal of Saturn or the Dance of Yu

The Sum of Magic Squares is a Magic Square and the product of a Magic Square M with a number a is again a Magic Square aM. Both Rules can be used to construct a Magic Square out of simple Binary Squares called Magic Carpets. One of these Magic Carpets is the Identity Matrix with One on the Diagonal.

Every Magic Square is related by Rotation and Mirroring to Eight other Magic Squares. This means that the central Lo Shu Magic Square with the Five in the Middle is related to Eight other Magic Squares with the other Numbers in the Middle. One of them contains the Nine and is called the Well.

The Lo Shu and the Well
The Sum of numbers of the Well is 18 (2×9) and the sum of all opposites across the 8 Spoke Wheel = 9 (9+0, 8+1, 7+2, 6+3, 5+4). 2×9 means that there are Two Complementary Magic Squares. One Magic Square is Rotating with the Clock and the other Against the Clock.
The Well is an Expansion and Contraction Cycle based on Powers of 2.

The Nine is the most important Number in the Magic Square. The Nine comes back in many ancient mythologies like the Egyptian Pesedjet and the Greek Ennead.

When you add the separate numbers of a number (54 = 5+ 4 = 9) the result is the Remainder when you divide the number by 9.  This number is called the Modulo 9 number.

The Powers of 2 (= Expansion) Mod 9 creates a pattern (1,2,4,8,(16)7,(32)5,(64)1,(128)2,…). This pattern is reversed when we divide by 2 (=Compression) (1/2 (0,5 =5), 1/4 (0,25 = 7), 1/8 (0,125 =8), 1/16 (0,625 = 4), 2,1).

The Expansion and Compression Pattern shows that the same pattern repeats itself when the Magic Square is expanded or compressed Six (6) Times. The 7th Step is the Same as the First Step.

After 2**6=64 (8×8) divisons of the cell a Specialized Cell is created, the stem cell. The same happens in Music.  The Game of Chess (Chiu King in China) with its 8×8 = 64 = 2**6 Playing Board contains every possible situation of the Game of Life.

The Two-Pattern does not contain the numbers 3,6 and 9. The number 9 is repeated every time when the pattern is expanded and compressed which means that Nine is the same as the Identity, the One (1+9 = 1). 3 and 6 Oscillate (1x2x3=6 and 1+2+3 =6) and  therefore represent the Duality (3+6 = 9, = the One).

If we combine the Expansion and Compression patterns a Torus (a Rotating Circle, The Wheel of Time) appears. The Zero (the Void) is in the Center and Contains the Vortex. The Vortex represents another Cycle (Black/White Hole, 3,6,9, the Wheel of Order) in which every structure/pattern is destroyed to start All Over Again.

Lo Shu Torus

If we subtract the numbers in the Square by the number of the Center, 5, a highly Symmetric Pattern emerges. This pattern shows that there are Two Mirror Universes both containing four Forces.

When we transform this pattern from Modulus 9 to Modulus 3 (the Trinity) we see that the number 4 equals 1 and represents a new beginning of the Cycle.

4

9

2

-5

-1

4

-3

3

5

7

-5

-2

0

2

8

1

6

-5

3

-4

1

The Magic Square with the Zero in the Middle is surrounded by two Sequences of 123(4) with different Signs. The Signs are arranged in a Cyclic Pattern (- -, + -, + +, – +) that contains the Four Permutations of – and +. The Sum of the ++ and the — is -3 and +3, the Trinity. The Sum of +- en -+ is the One.

The Cyclic Pattern of + and – represents the Prisoners Dilemma that is solved by the Strategy of Tit for Tat. This strategy is applied by the Trickster, the God of Paradox, a concept of God in which God creates games that create games.

When you use the basic Addition and Multiplcation Rules of the Magic Square many important numbers and patterns  appear that are related to Ancient CalendersSymbols and Cycles.

About the Sum of Things

The Lo Shu Magic Square appeared a few years ago when I wanted to know more about Acupuncture.  Acupuncture is related to the Sheng Cycle and the Sheng Cycle is related to the Lo Shu. A Magic Square is the perfect way to visualize the Constraints that control the Four Forces in our Universe.

Soon after this discovery I found out the Lo Shu is related to the Trinity and the Bronze Mean which is an abstraction of the Fibonacci Sequence. The Bronze Mean generates the Sri Yantra and so called Quasi Crystals. Quasi Crystals explain Acupuncture.

A few weeks ago I started a discussion with Kim Veltman. Kim Veltman is the director of the Maastricht McLuhan Institute. He is researching Ancient Architecture and wrote a very interesting document called “Alphabets, Elements and Cosmologies”.

Ancient Alphabets are related to Numbers and Tones so Ancient Texts also represent Numerical Patterns and Music. You want be surprised to read that the Lo Shu showed itself in every Text Kim Veltman has analysed.

His document started a new inquiry into the pattern of the Lo Shu. During this research I detected the book “the Sum of Things” by Paul Martyn-Smith. Paul Martin-Smith worked together with Lee Burton.

This blog contains just a litte bit of the tremendous amount of information Paul Martin-Smith & Lee Burton have found about the essence of the I Tjing which is contained in just one simple 3×3 Magic Square.

If you want to know more the only thing you can do is to buy this book and start reading.

LINKS

About the Book “the Sum of Things” (Free Download)

About the I Tjing

The Calculations  behind the Number of Things

The Relationship between the Lo Shu and the I Tjing

About the Lo Shu Torus

About Saturn, the Son of the Sun

About the Trickster

How to construct Magic Squares out of Binary Squares (Magic Carpets)

The Sistine Chapel (Rome) and the Seal of Saturn

About the Relationship between the Lo Shu and Music

About the History of the Lo Shu

About the Wheel of Eternal Order and the Wheel of Time

About the Relationship between the Lo Shu and Chinese Alchemy

About the Great Flood

About the Orion Myth

About Plato, Pythagoras and the Lo Shu

About the Nothingness

About the Trinity

About the Heart Chakra

About the Sri Yantra

About the Lo Shu Magic Square and the Chinese Domino Game

About the Mirror Universe

About Acupuncture

About Tit for Tat

About the Prisoners Dilemma

About the Bronze Mean

About the Sheng Cycle

Everything You want to Know about Sacred Geometry

About the Influence of the Lo Shu on Recent Art

The Lo Shu Square with Imaginary Numbers

About Combining the Combinations

 

steam_engine

Evolution means the creation of larger and larger islands of order at the expense of even greater seas of disorder in the world. In the process of evolution, each succeeding species is more complex and thus better equipped as a transformer of available energy.: Jeremy Rifkin, Entropy: A New World View (1980).

You wouldn’t enjoy a perfectly ordered universe. A wholly ordered universe would be at perfect equilibrium and would be dead. There can arise no Order unless there is a Flow of Matter and Energy which decreases in intensity as a system moves toward equilibrium. Motion, change or evolution in the Universe is driven by fluxes of energy and energy-rich matter flowing from sources of high potential to sinks of lower potential.

During the road from Being to Becoming Cyclic Auto-Catalytic Systems are created that Re-Create themselves until they Die. Islands of Order Appear and Disappear in the Sea of Chaos.

About Thermodynamics

Thermodynamics is the Science of the Transfer of Energy.

In strict Scientific terms Energy is classified into two main forms: Kinetic and Potential energy. Kinetic Energy is defined as the energy of a moving object. Potential Energy is defined as the energy in matter due to its position or the arrangement of its parts. The various forms of Potential Energy include gravitational potential energy, elastic potential energy, chemical potential energy, and electrical potential energy.

The First Law of Thermodynamics says that the total quantity of Energy in the universe remains Constant.

The Second Law of Thermodynamics states that the quality of this energy is degraded irreversibly. The Second Law predicts that our Universe will end when the Explosive Motion of the Big Bang wil stop and we will reach the Absolute Zero.

Nicolas Léonard Sadi Carnot (1790-1832) detected the Second Law of Thermodynamics when he tried to find the most efficient heating engine.

According to Carnot the Efficiency of an Engine is (T1T2)⁄T1, where T1 is the highest temparature. The Higher the Difference between the two Temperatures of the Engine the Lower the Efficiency. The Bigger the Step the Higher the Waste. If you want to build a highly efficient Engine, the Engine has to make very Small Steps when the Engine is heated.  This principle is known as Adiabatic Expansion (and Compression).

Physical, Chemical, and Electrical energy can be completely changed into Heat. But the Reverse (heat into physical energy, for example) cannot be accomplished without a loss. The irreversible increase of this nondisposable, useless, energy in the universe is measured by the abstract dimension  called Entropy (from the Greek entrope, change).

The Entropy measures the degree to which the probability of the system is spread out over different possible states. If all the possible States of the System are the Same, the System is in Equilibrium and the Entropy, the State of Order,  is on its Maximum.

In the Beginning of the Universe Every Thing was Different. In the End State Every Part of the Universe will be the Same.

About the History of Innovation

The central actor in the 19th century model of cultural innovation is the Artist, conceived, as an individual creator of works of art. Art is produced only by a handful of exceptional individuals.

The process of technical innovation in the 19th century was seen in terms similar. The central focus was on the work of individual inventors and researchers, commonly with little or no specifically scientific training.

By the early 20th century, this model was displaced by an industrialized process of innovation.

The first major step in this process was the rise of the Research University and the development of a large class of technically trained workers. In the 20th century, pure scientific research had become the preserve of universities and specialist research institutes.

The second major step was the development of corporate forms of business organization, which allowed Research and Development to become an organized business activity, operated on industrial lines.

The pattern of innovation in the 21st century is radically different. In most sectors of the economy, the rate of technological progress has slowed down substantially. Technological progress is characterised largely by Incremental Improvements to mature products.

In Computing and Telecommunications, the rate of progress has accelerated dramatically since the late 1980. The convergence of Computing and Telecommunications in the Internet has fundamentally transformed every activity it has touched. Everything that can be formalized will be formalized.

The Internet makes it possible that disjunct Networks of Isolated Innovators connect and share their Knowledge and Experience.

The Artist,  now connected with many other “exceptional individuals” all over the world,  is on its return.

About Incremental and Disruptive Industrial Innovation

There are two types of Industrial Innovation called “incremental”  and disruptive” innovation.

Japan (and now China) has made incremental improvement the cornerstone of  Technical Advancement. After months and years of gradual (adiabatic) changes, products look radically different, as happened with semiconductors, solar cells and batteries.

The US claims that it is the Champion of Disruptive Innovation.  Their “Internet”-entrepeneurs like Amazon, Google and Facebook believe in a “Statistical” model of Innovation, A Portfolio or an Innovation Ecology.

One of the many “Trials and Errors” will result in a big breakthrough that will Disrupt the Market. Behind Disruptive Innovation lies the Concept of Evolution, Survival of the Fittest, the Essence of Capitalism.

Disruptive Innovation uses Incremental Innovation to improve the Parts of the Portfolio.

Incremental Innovation (“Proces/Product/Business Model Improvement”) takes place  when an Innovation is improved until the Limits are reached.

Incremental Innovation could use the Efficient Small Steps of the Adiabatic Process to reach the Goal of the highly Effective.

Most of the time Proces/Product Improvement (“Standardization”) is not a Structured Process because People believe Innovation is about “Thinking Out of the Box”. If People “Think out of the Box” the proces will move into a Chaotic State and will Die.

Creative Incremental Innovation will produce a Lot of Waste (“Heat”, “Fuzz”) and accomplish Nothing. Managed Incremental Innovation has to remove the Waste and the Constraints.

With every step that is taken the System has to become more probable so the results of the proces will be more predictable. When the Limits are reached, we have to Restucture the System to move on.

The Second Law of Thermodynamics shows that Closed Systems finally Converge to a State of Equillibrium with a High Probability, a High Entropy.

Systems that are Isolated by a Boundary behave as Closed Systems. Systems that are Open to other Systems Merge and become Closed.

Most of the Time people don’t understand the Boundary of their System and Act in a Shared Boundary. In this Shared Boundary Competition takes place. Competition is a waste of Energy. If People could define their Boundaries they could Cooperate.

People Communicate. They  Share their Ideas, Problems and Solutions.  When a Process is well understood the Improvements of the Process are disseminated through the Human Networks and widely Copied.

Human Networks are Closed Systems that are connected to other Networks by Boundary Spanners.

Most people don’t understand that there are other people in other Networks who are doing the Same thing they are doing. They think their activity is Unique and don’t understand that the State of Uniqueness was only there at the Beginning.

Secrecy slows down communication between the People in the Network. The result of Secrecy is that People are unable to learn from others so they are unable to reuse the solutions of others. Secrecy is again a Waste of Time.

In the end the Competitive Advantage of the Innovation is completely gone and the Entropy of the System is at its Maximum.

At that moment every Process in every Part of the System will be the Same and the Companies will Merge or will be taken over by other Companies. Winner Takes All.

The Temperature of the Industry will move to Zero and every Movement (and Innovation) will stop.

About Creativity

There are two Views on Creativity. Creativity is a Combinatorical Game and Creativity is a Spontaneous Eruption of Ideas forced by High Pressure.

At such a moment, “the Aha-Erlebnis“, two or more Frames of Reference Fuse and a new Innovative Combination is created.

The last view has a lot to do with the theory of “Self-Organized Criticallity“.

The Metaphor of this Theory is the Disaster, the Avalanche or the Sand Pile that Suddenly moves when the critical grain of sand falls. At that moment a Significant Part of the Collection of individual grains Combines and moves on its own.

When a System is reaching the Boundaries of Proces Improvement and a Huge Pressure to Innovate is experienced,  two or more Systems (“Frames of Reference”) Fuse (Combine).

When the Systems are in Equilibrium the Fusion is easy (“Connecting”) otherwise the Fusion could become a Disaster, a Disruption, a Creative Destruction and a Huge Amount of Heat (Waste) is produced.

About Managed Creativity

If Innovation  is a Combinatorial Game we have to restructure a System into a “loosely-coupled”  System of Components and combine the Components with the “well-articulated” Components of other Systems.

A Loosely Coupled System is a System where each of its components has, or makes use of, little or no knowledge of the definitions of other separate components. The components act as Black-Boxes“.

A Component is “well-articulated” if it contains Just Enough Functionality to do the job. An Under-Articulated system is Rigid. It contains Not Enough functionality to Adapt to the Changing environment. When Systems grow old they become Over-Articulated because the Designers want to add new functionality without looking at the Boundaries of the System. Over-Articulated Systems overlap and it becomes very difficult to find the Essence. Designers always want to Solve every problem with their Own System.

Genrich S. Altshuller was a Russian Patent Officer who tried to find a Pattern behind Patents.

Altshuller screened over 200,000 patents looking for Inventive problems and how they were solved. Of these only 40,000 (20%) had somewhat Inventive solutions; the rest were straight forward improvements.

Altshuller defined an Inventive problem as one in which the solution causes another problem, a Contra-Diction or Conflict,  to appear. He found that the same problems had been solved over and over again using one of only Forty fundamental inventive principles. Altshuller  named his method  TRIZ.

Humans are prone to reivent the Wheel many times because they only look for Solutions in their own Frame of Reference. The Solution of their Problem is almost all the time already available in another Domain.

Roni Horowitz has analyzed the Principles of Althuller and found a deeper structure behind TRIZ which he called ASIT.

ASIT is about Thinking Inside the Box instead of Outside the Box. The so called Closed World condition, forces the thinker to find a creative solution by heavily limiting his or hers Space of Possibilities.

The Qualitative Change Principle looks for solutions in which the influence of the main problem factor is either totally eliminated or even reversed. The System has to become Perfect. Every Component has to fullfill just one Task  (“Well Articulated”) and the Functions of the System have to create a “Closed World” which means that the System has to be Closed in Itself.

About Combining the Combinations

The Second Law of Thermodynamics shows that it is Almost Impossible to move back to an old solution when the Solution is widely used.

Nature Solves its Problems by Experimenting but the Experiments are not completely at Random. Nature uses an Established Infrastructure and Plays with all the Possible Paths that Emerge out of the Existing Infrastructure, The Adjacent Possible.

Before life emerged on Earth, the planet was dominated by a handful of basic molecules. Each of these molecules was capable of a finite series of transformations and exchanges with other molecules in the primordial soup.

According to Stuart Kauffman Life  started when the Chemical Parts of early life  started to Re-Create themselves in a Cyclic Process  called AutoCatalysis. Re-Creation of the Same Structure is one of the most important principles of a Living System. Our body is recreated all the time in an endless Cycle until we Die.

If you could Play with all the Primordial Combinations, you would end up with the Components of Life but it is impossible to create a mosquito, or a sunflower, or a human brain.They were created when the Combinations started to Combine Again and Again.

Innovation in Nature is an endless Cyclic Expanding proces of Combining the Combinations.

This process moves on until the Limits of the Expanding Space of Possibilities are reached. These Limits are reached when there is not enough “useful” Energy available.

Combining the Combination happens in Nature but also in our Culture. Old infrastructures are used in a new way and a complete new field of Combinatorics appears.

Johannes Gutenberg took the older technology of the screw press, designed originally for making wine, and reconfigured it with metal type to invent the printing press which made it possible that new ideas, concepts and procedures were better dissiminated through the Human Networks.

Is there an End to Human Innovation?

The Universe is Expanding and is Creating New Combinations of Combinations all the Time.

The Law of Kleiber shows that the Combinations of the Combinations Fuse. The Law of Kleiber is just like Self-Organized Criticallity represented by a Power-Law. Power-Laws are independent of a Scale and therefore applicable on every Level of the Universe. They show that One Principle (“a Fractal“) Repeats itself on every Level.

Every time when the Combinations Fuse they are better equipped as a Transformer of Available Energy but the Creation of larger and larger islands of Order happens at the Expense of even greater seas of Disorder. Humanity is Wasting resources at an increasing rate, and that will lead to the destruction of our civilization.

The Combinations become Bigger and Bigger AND the Big Structures Attract Each Other. The larger group of possibilities will always be the Dominant Attractor.

This is the main reason for the success of Google, Facebook and Twitter. They have aquired the Power to Control their Market by Giving away their Products for Free so the Amount of Users would grow Exponentionally. They make money by letting other companies pay for the Use of their Huge Attractor.

The Small Auto-Katalytic Chemical Factories, the Bacteria,  that were created in the beginning are now fusing into Very Big Cities and the next Step will be One Mega-City covering a Huge Area of the Earth.  These Mega-Cities will be extremely Efficient and Effective. When this happens Nature will be replaced by a Human Made Technological Structure that has to use completely new ways to produce and use energy.

The next Step is easy to imagine. The Human Race will start to create new Mega-Cities on other Planets that will fuse into Mega-Planets.

The Big Problem will of course be Energy. We have to find new Sources all the time to support the Human Need to Expand and Discover. Every time when we create a new and Bigger Source of Energy the Amount of useless Heat will increase and the End of the Universe will get closer and closer.

Human Invention is Speeding Up the End because in the End Humans want to become One with the Whole.

According to the Second Law of Thermodynamics the Universe is moving to an Equilibrium State and not to an Extremely Impossible Innovative Configuration. At a Certain Point of Time Human Innovation has to Stop because we will reach the State of Absolute Zero Temperature and every Movement will Stop.

In the End the Universe will move into a State of Infinite Sleep.

What to Do?

The most important thing you can do when you want to Innovate is to create a Deep Understanding of just One Frame of Reference.

You have to become an Expert in Something and you have to have the attitude to create the Perfect Frame of Reference.

Every time when the System is not performing you have to solve the problem Inside the Box but you have to make use of Solutions that are Outside the Box.

Every Time when you are Satisfied,  remove a Constraint and Force Yourself to Solve the problem.

At a Certain Moment your Frame of Reference will Explode and will produce many Fragments. They are the Basic Building Blocks of Your Domain.

Start to Play with the Building Blocks and new Possibilities will appear that you have never Thought off.

You now have entered the Adjacent Possible.

LINKS

Why Neural Networks look like the Universe

About Creativity and High Pressure

About Self-Organized Criticallity

About Self-Organized Criticallity and Innovation

About Complexity Theory and Innovation

About Loosely Coupled Systems

About Boundaries

About Triz

Stuart Kaufmann about Radical Emergence

Advanced Systematic Inventive
Thinking

About ASIT (Advanced Systematic Inventive Thinking)

How Nature Plays

About Constructal Law

About the Origin of Good Ideas

About the Adjecent Possible

About the Law of Kleiber

Why Cities are Organisms

About the Beginning of the Universe

About  the End of the Universe

About Entrainment

In 1665 the Dutch physicist Christiaan Huygens noticed that two pendulum clocks in his room tended to Swing in Sync. The same happens with fireflies, cardiac pacemaker cells,  menstrual cycles, birds in flight, walking, dancing, circadian rhythms in animals, quantum gravity theory, dialogues and people in a crowd.

Two connected Systems always Entrain because Every System in our Universe Vibrates and is connected.

birds in sync
Birds in Sync

When the Parts are  connected, the Rhythm of the Whole controls the Rhythm of the Parts.

The transformations of the seperate parts takes place in two steps. In the first step the variance of the frequencies of the parts is reduced but the oscillators remain incoherent, each running near its natural frequency, until a certain threshold is crossed. Then the oscillators begin to synchronize spontaneously. The effect is somewhat like the outbreak of synchronous applause after a magnificent concert.

To make the transformation possible the Parts have to adjust their behavior. They have to move with the Rhythm of the Flow of the Central Clock. At the end of the transformation from isolated Parts to the Whole the Parts are the Same. They are Copying each other.

When people are copying other people they lose their identity and move into a trance-state. The same effect can be accomplished with hypnosis.  When people are in a trance-state it is easy to manipulate them.

About Copying

Humans are Copiers. When we look at the Science of Coupled Oscillators it becomes clear that Copying is not an intentional act. People and other Systems are more or less forced to copy others when the frequencies of their systems are within a certain bandwith.

When people are close and are focused on a shared target (a soccer match, a concert, a conversation, a dance, a common goal) the human parts start to synchronize and become a Crowd, an entity that starts to act on its own.

About Communication

The word “communion” means “becoming a union“. All communication arises through Synchronization. All communications are dances that coordinate the rhythmic processes shared among the engaging systems.

Communication is not a transmission of information, but rather a coordination of behavior among living organisms through Mutual Structural Coupling. Just like the Crowd, a communication, starts to live a life of its own, when the exchange of the vibrations of the conversation starts to synchronize. This happens within seconds.

conversation1

In the 1960’s, William Condon of Boston University School of Medicine pioneered the empirical study of communication as coupling. In the microanalysis of a few seconds of film he was astonished to find how the voice and bodily movements of speaker and listener were coordinated within intervals as short as 20 milliseconds.

Condon introduced the term entrainment to describe the coupled behavior. He noted that: “Communication is thus like a dance, with everyone engaged in intricate and shared movements across many subtle dimensions, yet all strangely oblivious that they are doing so“.

Coupling begins with getting the attention of other organisms, or more accurately, with distracting the organisms from other engagements so they are able to discern and respond to this engagement.

When the Oscillations of two Systems are outside a certain bandwith it looks like the most powerful system takes over control. The frequency of the synchronized system is a mean and when big numbers and small numbers are added the small numbers simply disappear. This situation is called an Overload.

Overloads are able to kill small systems because the small system is unable to cope with the huge pertuberations. People with a Dominant Personality are able to force (to entrain) Dependent people to copy their behavior.

About Synchronization

A System of N coupled different oscillators creates a very complex almost unsolvable mathematical problem. In 1975 Charles Peskin formulated the conjecture  that Systems would eventually synchronize even when the parts are not identical. In 1990 the conjecture has been proven by Strogatz and Mirollo.

Systems of Coupled Oscillators show four states called Phase Locking (Synchronization), Phase Drift (“Chaos“)  and Amplitude Death (“Order“). In the last state the oscillations stop completely.  The fourth state called a Chimera is a combination of a synchronized and a drifting state.

The most important issue to notice is the fact that the state of Amplitude Death is what we call Order. It is an exceptional state that can be reached when the exchange of information between the states is “compensating” the vibrations of the states or when the System is “compressed” into a Singularity.

synchronization

Most Systems are oscillating (“Cyclic“) and are in a Phase Drift (“Chaos“) or a Chimera trying to reach some sort of Synchronicity with the other connected Systems. In Nature every System is connected to every other System because of the Electro-Magnetic (and Sound) Fields they share.

Systems of Coupled Oscillators behave differently when the connections between the parts are delayed. It this case highly identical parts start to behave as not identical parts. When a delay occurs the stable rhythm of the heart can suddenly stop, resulting in a sudden death.

About the Circadian Clock

In order to cope with and to predict 24-hour rhythms in the environment, such as light and darkness, temperature or the availability of food, most, if not all, organisms have Circadian (“Daily“) Timing Systems. These systems generate circadian rhythms in a wide range of behavioral and physiological processes.

For most animal species, a main circadian pacemaker has been identified in an anatomically defined location in or close to the brain. During the last years, however, it has become clear that circadian systems are complex and that additional oscillators exist, both within and outside the central nervous system.

The Peripheral Circadian Clocks are situated in the Heart, the Liver, the Lungs and the Kidney. These organs are the same “organs” that are used in Chinese Acupuncture which is not strange because the Aim of Acupuncture is to Balance the Electro Magnetic Field in the Body.

For a correct functioning of the circadian timing system, these oscillators should be synchronized to one another and properly phased to the environmental cycle.

Synchronization between the oscillators occurs via interactions or coupling pathways, whereas the light-dark cycle is used for synchronization to the outside world.

The most important mammalian circadian pacemaker is located in the suprachiasmatic nuclei (SCN) at the base of the hypothalamus in the brain.

From the suprachiasmatic nucleus, nerve impulses travel via the sympathetic nervous system to the pineal gland and inhibit the production of melatonin. At night, these impulses stop and melatonin production ensues and is released into the body.

In fish, amphibians, reptiles, and birds, the pineal gland appears to be directly sensitive to small amounts of light that penetrate the skin and skull.

In mammals, with increased development of the cerebral hemispheres, the pineal body came to lie deeper within the brain and indirect stimulation of the pineal gland by light via the retina came to be more important. The Suprachiasmatic Nuclei are connected to the Outer Eye and the Inner Eye, the Pineal Gland.

The Pineal Gland is called the 6th Chakra, the Third Eye (or the Eye of Horus), the Seat of the Imagination.  The Imagination, the Central Clock of our Body, is “in control” of all the other Clocks in our Body.

With the Help of our Imagination we are able to Cure and to Kill the Body.

pineal
Pineal Gland

About the Pineal Gland

The Earth is a huge magnetic sphere. The E/M field of the Earth varies in strength and consistency through the ages. Our bodies own magnetic frequencies and our bio-field patterns react to this variance of the Earth’s field.

The pineal gland is the principal structure in the brain that is directly sensitive to the Earth’s magnetic field. The Pineal Gland Senses the Field.  To sense the Field the Pineal Gland contains small calcite crystals.

Our bone structure Converts Vibrational Energy into Magnetic and Electric Energy. When the bone is bent it produces an E/M-field. This E/M-field interacts with the Pineal Gland and creates a Feed-Back Cycle.

The E/M-field of our Body, the Aura, is a combination of all kind of waves. A special type of wave-structure is called a Standing Wave.

When the E/M-field acts as a Standing Wave all the waves are in harmony and conserve structure. The Human body is in harmony when the total field of all the separate E/M-fields of the Body act as a Standing Wave.

The Standing Wave appears when the Spinal Wave of the Vertebrae of the Body is in a special Alignment.  If this happens the Standing Wave of the Spine Resonates with the Standing Wave of the Earth. At that moment the Kundalini Rises and the Pineal Gland reacts with a Huge Mystical Experience.

About the Heart

The heart beats about once a second throughout your life. These regular contractions pump blood to the Upper (Head) and the Lower part of the body and are driven by electrical impulses from a natural pacemaker inside the heart.

This pacemaker, known as the sino-atrial node, responds to signals from the Central Circadian Clock situated in the Hypothalamus that changes the heart rate according to the body’s needs (“the action potential“), making it slower when resting and faster during exercise.The rhythmic contractions of the heart are triggered by waves of electrical activity that spread from the sino-atrial node throughout the heart muscle.

There are small fluctuations in the time intervals between beats that are fractal in nature, and a loss in this variability is a sign of cardiac ill health. However, a cardiac arrhythmia, in which the rhythm of electrical waves that drive the heart is broken, can be lethal.

A loss in the synchronized rhythm of the heart causes different parts of the atrial or ventricular muscle to contract at different times, undermining the pumping action of the heart. An arrhythmia therefore leads to the mechanical failure of the heart.

The propagation of excitations in heart tissue can be described in terms of travelling waves with a velocity of about 0.5 m s-1 and an amplitude given by the action potential. Since the action potential lasts for several hundreds of milliseconds, a single wave extends over a distance of about 10 cm. This means that a normal human heart is hardly large enough to contain a single wave.

In the heart the wave propagates around a circular obstacle. The wave repeatedly travels along the same path at a frequency given by the wave velocity divided by the circumference of the obstacle.

If the radius is gradually decreased, the frequency increases until the wavefront of a new wave catches up with the tail of the previous wave. If the radius is made even smaller, the wave is forced to adopt a spiral shape that continues to rotate around a central core. Spiral  Waves have been observed in numerous chemical and physical experiments.

The Wave Structure of the Heart resembles the Wave Structure of the Universe. This could be the reason why the Heart plays such  an important role in many Religions.

When the Wave Structure of the Heart is coherent with the Wave Structure of the Whole, the Rhythm of your Life is in Sync with the Rhythm of the Universe.

The Pacemaker Cells are called the Heart Chakra, the 4th Chakra. The Heart Chakra acts as the Balance Point for all the Chakras.

The Balancing Point is the Middle of two Triangels related to  the Head and the Body that rotate With- and Counter-the-Clock creating a Moebius Ring.  The Pineal Gland, the Central Clock, is part of the Upper Triangel of the Mind.

Spiral Waves in the Heart

Chemical Spiral Waves
Chemical Spiral Waves

About Cymatics

In 1967, the late Hans Jenny, a Swiss doctor, artist, and researcher, published the book Cymatics,  The Structure and Dynamics of Waves and Vibrations. In this book Jenny showed what happens when one takes various materials like sand, spores, iron filings, water, and viscous substances, and places them on vibrating metal plates and membranes.

What then appears are shapes and motion- patterns which vary from the nearly perfectly ordered and stationary to those that are turbulently developing, organic, and constantly in motion.

When Jenny experimented with Fluids of various kinds he produced Wave motions, Spirals, and wave-like patterns in Continuous Circulation.

These patterns are the same patterns that are produced by Coupled Oscillators. This is not strange because Sound Waves are highly comparable to Electro Magnetic Waves.

With the help of simple tools it is possible to Simulate the Creation and Expansion of the Universe.

We don’t need very complicated tools to observe the Whole. The Whole shows its patterns everywhere, even in your bathtub.

The Whirpool Galaxy
The Whirpool Galaxy

About the Creation of the Universe

In beginning the Void, the Zero Point Field,  rotated in Silence until a Huge Action Potential disturbed its Eternal Rest.

The Void was in a state of Amplitude Death until a Statistical Fluctuation, an Act of Creation, moved the System into a Chimera and later a Phase Drift.

Out of the Phase Drift Two Coupled Oscillators (Yin & Yang) appeared that moved With- and Against the Clock creating a Spiral Motion, a Vortex.

The Two Coupled Oscillators were each others Complement because two Coupled Oscillators are always Complementary.

After a while the Phase Drift generated Four and More Oscillators and Space started to Expand.

The pattern of this Expansion is governed by the Metallic Mean, which generates Fluent or Quasi Crystals. Fluent Crystals are the basic structure of the Electro Magnetic System of the Human. Scientists believe that the basic structure of our Universe is a Fluent Crystal, a Hall of Mirrors.

Quasi Crystals
Quasi Crystals

Space stops expanding when the Unbalance of the Energy of the Act of Creation is compensated by the amount of Oscillators (Strings) of Expanding Space.

At that moment the Universe will move into the State of Synchronization and all the Parts will move with the Rhythm of the Central Clock, the Tao.

When this happens the Universe starts to contract until Space has reached the Void.

In the last step the Oscillation will stop and the Void and Amplitude Death will appear again.

LINKS

How bacteria entrain

Steven Strogatz: About Coupled Oscillators and Biology

A lecture about Coupled Oscillators

A presentation about Coupled Oscillators

About Engagement

About Standing Waves

About Hypnosis

About the Electro Magnetic Field in the Body

About the Cardiac Pacemaker Cells

About Cymatics

About the Heart Chakra

About Stress and the Action Potential

About the Zero Point Field

About the Metallic Mean

About the Hall of Mirrors

About Good Vibrations

The Good (Creation) and the not-Good, the Bad (Destruction),  are two Waves that are moving in Opposite Directions. Together they create interference patterns called Standing Waves.

Standing Waves are Waves that preserve their Form and can be perceived as Material Particles.

If the Good is a Wave Moving with the Clock, the Bad is a Wave Moving Against the Clock.

I believe the Good is moving with the Clock because the words “Right” and “Wrong” were associated with the Right Hand and the Left Hand and the concept “moving” (wringen in Dutch).

In Magic the Left Hand Path is associated with Black Magic and in many cultures the Left is associated with Evil.

In China the Rotation with the Clock is called the Generating Cycle and the Rotation Against the Clock the Destructing Cycle.

The Standing Waves of Matter contain the Bad and the Good in a certain proportion. Therefore every part of Nature (including the Humans) contains a piece of the Bad and a piece of the Good. That’ s why it is rather difficult to make a distinction between both of them.

There is nothing either good or bad, but thinking makes it so”  (Hamlet Act 2, scene 2, 239–251)

Doppler_div
A Moving Standing Wave
proton10
Two Moving Standing Waves Interfere and produce a Magnetic Field

About the Svara

The idea that our Universe is a Wave goes back a very long time. In Ancient Indian Philosophy the Wave of the Universe was called the Svara, the Wave of Life.

It is the manifestation of the impression on matter of the Power Which Knows Itself (Atman). The Atman arises out of the Emptyness (Brahman). The Emptyness is a Mystery. It is impossible to Reason about it.

The Svara consists of Five Types of Waves called Tattvas. They represent distinctive Forms and Vibratory Motions and are the five modifications of the Great Breath, Prana, of  the Atman. Prana is called Chi in China.

The first Wave that came out of the Atman is called the Âkâsha (Spirit, Egg, Black). After this came  the Vâyu (Air, the Circle, Blue), the Tejas (Fire, the Triangle, Red), the Apas (Water, the Crescent of the Moon, Silver) and the Prithivi (Earth, the Square, Yellow).

The Svara has two different States,  the Bright Sun-Breath  and the Dark Moon-Breath. In the first state the Svara expands, away from the Void. In the second state it contracts and moves back to the beginning.
At a certain moment we will experience the spectacular Twist of the Svara. This is the moment when Time will move back and the Apas (Aquarius, Water) will dominate the Fire (Bull) of the Tejas.
The Âkâsha and the other Four States of the Svara are the States of what Western Scientists call the Aether, the Carrier of the Standing Waves of the Universe.
The Five Tattvas
The Five Tattvas

About the Aether

Until the experiments of Michelson and Morley in 1887 every Physicist believed in the existence of the Aether. Everybody was very surprised when the experiments showed that the Aether was moving with a constant speed, the Speed of Light, in both directions of measurement.

Nobody questioned the experiments so a completely new theory had to be created to explain the strange behavior of Light. This new theory was the Relativity Theory of Albert Einstein.

The situation became even stranger when Niels Bohr (and others) invented Quantum Mechanics and showed that Light could be interpreted as a particle, a Photon, and a Wave.

At that time almost nobody understood the Concept of the Standing Wave. A Standing Wave is a Wave that preserves its Form and therefore shows itself as a Particle.

It is now proved that Michelson and Morley made a fatal mistake. The Unification of the Theories of Einstein and Bohr is going on but two foundations of the Theory of Einstein, the non-existence of the Aether and the Constant speed of Light, are gone.

The concept of the Aether, the Svara,  is back and new theories of the Universe based on Standing Waves are produced and verified. These theories are much simpler than the old theories.

What is the Same?

The Ethical Law of Resonance states that “The Same attracts the Same and Repels the Not-the Same“.  The Good  attracts the Good and the Bad attacts the Bad but the Good also repels the Bad and the Bad repels the Good.  If we are able to define the Same we are able to define the Good and the Bad.

When you want to find out if some Thing is the same as another Thing you have to define the concept of “the-sameness“.

Every thing is different from any other thing when you collect enough different data about both of them. When you ignore every detail every thing  is the same (A = A). When two objects are literally “the same” we call this relationship an equality (A=B).

The same objects can appear differently when we Look at them differently. In this case a “the sameness” (now called a congruency) appears when we are able to create the same object when we move (translate), rotate or reflect the other object.

congruent2
Two Congruent Triangels

To find an independent reference framework for an Observer who is “not moving” and a constant Speed of Light Einstein had to abstract from Translation, Rotation, Reflection and Movement (Speed and Acceleration). Einstein’s friend Minkowski solved his problem by creating a new type of “curved” space now called Minkowski Space.

The Ancient Scientists of India not only abstracted the Aether from the Eyes like Einstein did. They abstracted the Aether from the other Four Senses too.

Every Tattva represents another Sense Organ and a related Wave pattern. The interesting point is that the Waves of the Tattva of the Eyes, the Light Waves, the Tejas, behave, exactly the way the current scientists describe.

The current Scientists ignore the fact that Humans observe their Environment with their Five Senses. The ancient Scientists not only detected five types of Waves. They also found a way to combine the Five Wave-Types into one Wave Model.

In general Objects are “the same” when we are able to find a Structure Preserving, isomorphic, transformation (F) from Object A to Object B. F(A)=B and G(B)= A and FG=Identity. With the help of an Isomorphic Transformation you are able to map a structure A to another structure B  and move back to the same structure A.

Every Isomorphic transformation can be seen as a “specialized Organ“, that  “looks” at Reality in its own way.

The mathematical field of Topology is concerned with the “the sameness” of objects that are Expanded and Compressed. Topology represents the Organ of the Emotions. With this organ we are able to  research the effects of the Great Breath of the Prana.

Mug_and_Torus_morph
Transforming a Mug into a Torus

About the Great Breath

With the help of isomorphic  “topological” transformations it is possible to make the huge Diversity of Forms in our Universe the Same. It is even possible to compress every structure in our Universe into one structure, the structure of the Void.

In this case there are a few topological possibilities depending on the dimensions of space. In two dimensions we can choose out of the Point and the Circle, a Closed Line. In higher dimensions strange twisted structures appear such as the Moebius Ring and the Klein Bottle.

If the Universe is compressed into a Rotating Circle,  The One who is in the Centre always Returns on Itself.  The Universe is expanding and compressing until Eternity. At a certain time even after a huge expansion the Power of Creation is able to “Knows Itself”. This concept is called the Cyclic Universe.

If the Universe is compressed  into a point, called a singularity, we live in a “Big Bang-universe“, the standard cosmological model, which will expand into Eternity.

It will be clear that the structure in the beginning determinates the way the Waves of the Universe expand.

Twisted Topological Structures
Twisted Topological Structures that are Closed in Itself

If the Universe is Closed in Itself the Outbound Waves of the Beginning  will meet the Inbound Waves of the Utmost Boundary and will create Interference Patterns that look like Standing Waves.

When the Universe was small the Interference Patterns came up almost immediately. When the Universe expanded it took more time to Close the Loop.

If the Universe is a Closed System, the Waves of the Past and the Waves of the Future will meet in the Now.  At every moment in Time we are able to look into a possible Future and a possible Past.

At every moment in Time we can Change the Past and the Future if we are able to start a Powerful Negative (Destructive, Bad) or Positive  (Creative, Good) Wave of our Own.

According to the Ancient Scientists the Forces of the Tattvas at a certain Level of Enfolding represented Consciouss Beings (Angels, Devils) who could be Called to help to influence the Standing Waves of Matter.

In the strange terminology of Quantum Mechanics this state is called a Quantum Superposition and the union of the waves is called Quantum Entanglement. Quantum Entanglement moves with a speed much higher than the Speed of Light.

Sometimes the fragmented Tones of the Universe unite into one Symphony when the Strings of the many Violins of the Individual Standing Waves are in Tune.

We are able to change the Past and the Future when we are in Tune with the Waves of the Universe.

About the  Number Five

The symbol of the number Zero (“0”) looks like an Egg, the Âkâsha. The Âkâsha represents Space.

The name “zero” comes from the Arabic صفر, şafira, “it was empty” and the Sanskrit śūnya “void” or “empty”. The 0, Space, was Empty, Ø, before it was created.

According to many creation myths the beginning of this world,  Non-Being, Ø, the Empty Set, expanded into an Egg, 0.

The Egg started to Rotate (Air, Vayu, Movement) and was splitted into the Duality (-1,1), the Crescent of the Moon (Apas), the In-Between-Moon or Half Moon (1/2).

The negative part of the Duality started to move in the Opposite Direction. At that moment the Good (Creation) and the Bad (Destruction) were created.

The Apas are the force of Contraction (Control), the Opposite of the Tejas, Fire (Desire), the Force of Expansion. The Apas wants to bring the System back to the Void.

In the Beginning the Good (Fire) was much stronger than the Bad (Water). Therefore the Universe started to Expand.

The Trinity, the Triangel (Tejas, Fire), contains three numbers (-1, 0, +1). When the first Trinity was created the Force of Fire and Desire, the Tejas, started to Expand the Trinity into more Trinities. The production of Trinities in Trinities is a Fractal Pattern (“So Above, So Below“).

The first two Triangels, the Triangel of the Trinity of the Mind of the Atman and the Trinity of the Material World, are combined into a Square (Prithivi, Earth). The Prithivi are seen as the Force of Resistance, the Opposite of Âkâsha, Space.

The Prithivi, the Square of the Four Forces, the Human,  resists the movement back to the Void. The main reason is that the connection between the Spiritual World and the Material World is very strong.

The Spirit of the Human, situated in the Heart Chakra,  needs Matter to create all the possible combinations of the Becoming Trinities to Experience the Fullness of Being.

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

The number Five can be found in the Middle of the oldest Magical Square on Earth, the Lo Shu Square. The Lo Shu Square was given to Emperor Yu the Great after the Great Flood (3117 BC) by a Turtle, the symbol of the Star System Orion.

About the Magic Square of Lo Shu

The Lo Shu Magic Square contains the numbers 1-9 (3×3). In every direction they add up to a total of 15 (3×5).

The Magic Square Constraints the Expansion of the Force of Fire and makes it possible that the Cycle moves back to the zero, the Void, the Mystery.

The Lo Shu Square in the Middle of the Mystic Tablet from Tibet
The Lo Shu Square in the Middle of the Mystic Tablet from Tibet
-1 4 -3
-2 0 2
3 -4 1

When we subtract all the numbers in the Magic Square with the number 5,  the Zero of the Egg of the Âkâsha appears in the Middle.

The transformed Magic Square shows an interesting symmetry.

On the six “crosses” the same negative and positive Tattvas are found. The Four Tattvas are Balanced in the o, Space, the Âkâsha.

On the straight lines  two symmetric patterns emerge ((-1,4,-3) and (1,2,-3)) again both positive and negative. In these patterns the 4 balances the 1 and the 3 and the 2 balances the 3 and the 1.

When we follow the Numbers of the Square from -4 to +4, the Sheng Cycle appears.

About the Sheng Cycle

The Sheng Cycle not only contains the Cycle of the Five Tattvas. It also contains Five Triangels in which One Tattvas Balances Two other Tatvass.

The number Five is the same as the Number Zero when we accept that there are Two Structures (or Two Universes). One structure rotates in the Positive Domain, The Sun, and one in the Negative Domain, The Moon.

The Square represents the Four Force of Nature who are the Four Combinations of the Two Forces of the Duality, Compression and Expansion, Yin and Yang, the Apas and the Tejas, Fire and Water, Control and Desire.

The Sheng Cycle is the major Cycle in Chinese Philosophy. It was used to explain and control the many levels of existence (State, Family, Environment, Body,..).

The Sheng Cycle moves in two directions, With the Clock (Generating, +1) and Against the Clock (Destructing, -1).

When we combine the two Cycles a 9(3×3)-fold Twisted Moebius Ring is created with the Earth in the Middle. This Cycle is represented by the Symbol of Infinity (). This Cycle is comparable to the Tree of Life, the Jewish Sephiroth and the Ancient Egyptian Pesedjet (the Nine).

In the Bright (positive) Part of the Moebius Ring we are in the Sun-State, Life. In the Dark (negative) Part we experience the Moon-State , Death, the Underworld (Our Twin Universe), the place where the Souls exist when they Die.

Now it becomes very clear what the Ancient Indian Scientist meant with the Dark Moon-State of the Svara. When the Wave of Life moves back to the Center, the Void, Death will become Life  (“the Death will be raised“), Time will Reverse, the Universe will Compress and the Good will become the Bad.

The Sheng Cycle
The Sheng Cycle

About Harmonics

In 1931 the US Department of Commerce assigned Edward Dewey the task of discovering the cause and underlying dynamics of the Great Depression. The US Government created a special institute the Foundation for the Study of Economic Cycles. The Institute contains a huge database of the times-series of almost every Cycle there is.

The most interesting observation of Edward Dewey is that Cycles restore themselves all the time and are influenced by other Cycles. The Cycles Resonate.

Ray Tomes, a statistical mathematician, started to do research on the time-series of the Institute. He confirmed the Insights of Dewey but with the much more powerful tools of his time he was able to dig a lot more deeper into data.

Tomes detected a relationship between the Cycles and Music, the Âkâsha. Tomes also developed a  method to find the basic structure behind the Waves of the many Cycles.

Tomes found one Basic Standing Wave that generates other waves by producing Overtones. Tomes rediscovered the Svara and could also explain why the “numbers” behind the Svara are the way they are.

The explanation can be found in the so called Highly Composite Numbers (HCN). The HCN are “social” numbers with many divisors. They represent the major “harmonic” connectors in the Universe. The HCN are the opposite of the “lonely” Prime Numbers who only contain themselves.

The structure behind the HCN is self-referencial and is based on the numbers 2, 3 and 5.

About the Cyclic Universe of Paul Steinhardt

The Cyclic Univere of Paul J. Steinhardt
The Cyclic Universe of Paul J. Steinhardt

Paul Steinhardt has created a new theory about the Universe based on the Four Forces of the Square and the Void in the Center. In his theory the Universe is Cyclic. It is expanding and contracting.

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

The two Branes are higher dimensional flat surfaces that are in parallel. The Left and the Right Brains split into many similar Cell-like Structures. We live in one of the Cells of the Cyclic Universe.

When the Universe expands the constraints of the Flat Surface (the Lo Shu Square) create a huge tension and the flat surfaces start to Ripple. The Ripples are waves that are closed in themselves (loops).

When you use your imagination you can see that the Cyclic Universe of Paul Steinhardt has a lot in common with the ancient theories of India and China with only one difference.

In the Ancient theories the creator of the Universe was “Aware of Itself” in the new theories Awareness is a Feed-Back-Loop, a Cycle.

About Ancient Spirituality and Modern Science

This blog started with the Ancient Spiritual Indian Concept of the Svara , the Wave of Life. It ends with the Modern Material Cyclical Universe of Paul Steinhardt.

In between I have tried to show that the old theories of the Self-Aware Universe and the new theories of the Endless Feed-Back Loops in Our Universe have a lot in common.

The Ancient Spiritual Scientists developed a Theory of Everything based on the principle of the Fractal Universe (“So Above, So Below“).

If the Universe is a Fractal Structure,  the only thing the Modern Sciences have to do is to find the Right Level of Observation (Cells, Body, Family/Group, Culture, State, Earth, ..) of the Fractal Expansion of our Universe and the Same Laws will appear again and again.

The Levels in our Universe
The Levels in our Universe (Calculated by Ray Tomes)

About the Good, the Bad and the Nothing

If the Good and the Bad are Standing Waves that move With the Clock and Against the Clock it will be much more easier to determine what is Right and what is Wrong (Left).

With the Clock moves With the Flow. It generates new structures until the Limits of the Universe are reached.

Against the Clock moves Against the Flow. It destructs new structures until the Limits of the Universe are reached.

The Bad wants to Control Everything. It Fears the Good and the Future.

The Bad does not (want to )understand that The Good and the Bad are moving to the same Destination, The Nothing.

The Good gives us Joy, Pleasure and Exitement.

The Bad moves Back in Time. It wants to restore what was already there. Its final aim is the Zero, Empty Space.

The Good moves Forwards in Time. It creates new Perspectives about a Bright New Future. Its final aim is Every Thing, the Many, Infinite Space filled with an Infinite Amount of Forms.

The Bad and the Good move Back and Forth around an Unknowable Center, the Nothing, that makes Every Thing possible.

Some day the One and the Infinite, will merge, into the Impossible. When this happens the Nothing will return for a very short  (1/∞) moment.

LINKS

About the Law of Resonance

About the History of the Laws of Nature (The Website of Milo Wolff. It contains everything you want to know about the history of the concept of the Standing Wave).

Why Matter is a Standing Wave

About the Svara (This Website  contains a (big) Complete Book written in 1894 about the Ancient Theory of the Svara.  A Must Read, when you want to understand Ancient Physics).

About the Harmonic Theory of Ray Tomes

About the Experiments of Michelson and Morley

Why God is a Topologist

About Pauli and Quantum Mechanics

About the Cyclic Universe

About the Lo Shu Square

About the Trinity

About Infinity

About the Empty Set