Posts Tagged ‘fractal’

About Number and Magnitude

Monday, January 9th, 2012

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

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

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

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

Movements and not Forces are the Essence of Physics.

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

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

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

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

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

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

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

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

About the One and the Dirac Delta Function

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

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

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

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

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

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

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

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

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

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

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

The Tetraktys of Pythagoras

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

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

File:Dirac function approximation.gif

The Dirac Delta Pulse


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

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

About the Strange Behavior of Numbers

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

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

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

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

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

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

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

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

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

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

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

About the Duality and the Expansion of Space

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

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

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

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

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

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

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

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

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

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

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

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

Compressed Space is Time.

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

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

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

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

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

The Ternairy Number System is represented by the Binary Tree

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

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

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

This Number System is called the Ternary Number System.

About Ratio’s and Magnitudes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

angle between vectors in 2 dimentions

A Displacement or Bivector

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

screw theory 2

A Displacement and a Rotation of a Vector

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


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.


Combining (Adding) Bivectors creates a Trivector

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

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

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

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

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

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

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

Quaternions are rotations in 4D-space

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

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

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

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

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

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

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

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

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

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

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

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

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

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

The Hexagonal Numbers

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

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

About Numbers, Operations and the Klein Bottle

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

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

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

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

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

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

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

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

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

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


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.


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.


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.


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 Sum of Things

Thursday, September 22nd, 2011

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


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).


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.






















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.


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 the Law of KLeiber

Friday, October 29th, 2010

A power law relates one variable to another raised to a constant power. The general form takes y = xa, where y and x are variables, and a is a constant exponent.

A power law exhibits the property of scale invariance. When you multiply the Scale (x) with a factor b the function (y =  baxa) does not change its Shape.

In 1817 Goethe wrote his book ”Zur Morphologie“. This book was the start of a new science called Morphology, the Science of the Shapes.

In his book Goethe describes the so called Uhrplant, the Primal Plant, which is based on the shape of the Leaf. Goethe believed that every Plant was a Leaf within a Leaf within a Leaf.

At the time of Goethe the concept of the fractal was not known. It was developed in 1975 by Benois Mandelbrot (“The Fractal Geometry of Nature”).

A fractal is a self-similar structure. It’s shape repeats itself on every level of expansion.  Some fractals are scale-invariant.

Scale Invariance in the Leaf

The scale invariant fractal structure of the Leaf

About Kleiber’s Law

Metabolism is the process by which your body converts what you eat and drink into energy. During this complex biochemical process, calories in food and beverages are combined with oxygen to release the energy your body needs to function.

The oldest and best known Power Law is Kleiber’s law devised by the Swiss-American zoologist Max Kleiber in 1932.

Kleiber’s Law, MR = W3/4, describes the relationship of the metabolic rate (MR) to the biomass W, raised to an exponent.

Kleiber’s law means that a cat’s metabolic rate is not a hundred or 21.5 times greater than a mouse’s, but about 31.6 — 100 to the three-quarter power.

This relationship seems to hold across the animal kingdom  and it has since been extended all the way down to single-celled organisms, and possibly within the cells themselves to the internal structures called mitochondria, the cellular powerplants, that turn nutrients into energy. Mitochondria have many features in common with bacteria.

The law of Kleiber is  also applicable to super-organisms” like ant colonies, Cities and Eco-Systems.

Because of Economies of Scale, larger and more complex forms of organisms need less energy for each individual cell. They grow and reproduce more slowly and they live longer.

Kleiber's law

Kleiber's law

About Fractals and Kleiber’s Law

Kleiber’s law can be explained from a general model that describes how essentialmaterials are transported through Space-Filling Fractal Networks of Branching Tubes.

Goethe was right. The leaf is a one of the fundamental structures of Nature.

The factor 3/4 (3/3+1)  is a consequence of the fact that a Fractal Structure has to incorporate a not-Fractal Structure, 3-Dimensional Space.

One of the Bilateria: The Octopus

One of our fellow Bilaterians: The Octopus

About Bilateria

About 590 million years ago, the Central Nervous System (CNS), the Brain, appeared.

The organisms with a CNS (including the Humans), the Bilateria, are able to Act and React to a Possible Harmful Stimulus.

The CNS of the Bilateria is  a result of  an Increase in Competition between the Life Forms that came out of the Continuing Fusion of  the Cooperative Life Forms, the Bacteria. The first step in this proces was the Tube of the Sponge.

The fundamental Bilaterian Body Shape is a Tube running from Mouth to Anus, and a second Tube called the Notochord, with an especially large Sphere at the front, called the “Brain“.

The Bilateria have Five Body Spheres (1) the Brain; (2) the Spinal Cord; (3) the Heart and Lungs; (4) the Digestive Organs and Kidneys; (5) the Bladder and Reproductive organs.


About the Tiny Spheres of the Lungs

When we look at the Lungs, one of the Fractal Tube-like branching-structures of the human organism, we can see that the Branches end in Nodes called the alveoli (“little cavities“). The end-nodes of the branching system are tiny Spheres.


The Alveoli use another basic structure of Nature: The Sphere

In the tiny Spheres the Exchange takes place of Carbon Dioxide and Oxygen between the Lungs and the Blood-Vessels. Each human lung contains about 600 million alveoli.

Water diffuses from the alveoli cells into the alveoli so that they are constantly moist.  Oxygen dissolves in this water before diffusing through the cells into the blood.

The Oxygen-rich blood returns to the Heart via the pulmonary veins to be pumped back into circulation. The Carbon Dioxide is pumped out by the Lungs.

In the many million Small Spherical End-Nodes Two Circulatory Systems, the Cardiovascular System (Heart) and Pulmonary System (Lungs), are Connected.

The Big Structures of Nature are able to Scale because the Connection-Points of the Networks are Very Small.

They are reusable on Every Scale that is Bigger than the Scale of the Connection Points.

We will see that all the other Fractal Systems in our Body are based on the Same Principle.



About the Tube of the Digestive System

The Tube contains the Digestive System. It breaks-down larger food molecules into smaller ones that can be absorbed into the blood stream. This happens in the Small Intestine in the vili and microvilli.

The villi (“shaggy hair“)  are tiny, finger-like projections that are approximately 0.5-1mm in length. The microvilli are mechanosensors and have a lot in common with the flagellum (“the roter“) of a bacterium. Microvilli appear in many places in the body. They are also of importance on the cell surface of white blood cells, as they aid in the migration of white blood cells.

The Tube of our Digestive System is highly similar to the Tube of the Sponge, the first fusion of the Bacteria in a  more efficient metabolic structure.

The Output part of the Tube is called the Large Intestine (Colon). Its function is to absorb water from the remaining indigestible food matter, and then to pass Useless Waste Material from the body. The large intestine houses over 700 species of bacteria that perform a variety of functions.


The Liver Fractal

About the Chemical Factory of the Liver Cell.

The Liver is  a Fractal Branching System that detoxifies harmful substances absorbed via the Small Intestines.  It’s basic structure is the Liver Cell.

The Chemical reactions in the liver cells produces a lot of waste heat. This is carried round the body in the blood and warms less active regions.

The Liver regulates the amount of Blood Sugar, Lipids, Amino Acids.  The Liver is the Storage House of  Blood, Iron, Vitamine A, D, B12  and Clycogen, the Source of Energy of the Body.

The Liver produces Bile that is stored in the Gall Bladder. Bile is used to dissolve fat.

White Blood Cell

The White Blood Cell

About the Spleen and the Immune System

Another Fractal Branching System, the Lymphatic System ( “The Immune System“, Spleen),  maintains the health of the body by protecting it from invasions by harmful pathogens, such as bacteria, viruses, fungi, and parasites. These pathogens are the cause of many diseases, so it is necessary to detect and eliminate them rapidly.

The Lymphatic System is connected to the Blood System and produces the White Blood Cells (Lymphocites).  The Lymphocites are the Basic Unit of the Human Defense System. They look like Bacteria.

A lymphocite fits with a pathogen

A lymphocite fits with a pathogen

The surface of a lymphocyte is covered with a large number of identical receptors. Recognition and destruction occurs when the receptors of the lymphocyte fit like a key into the surface of the pathogen.

The Immune System is a Highly Adaptive System. It is able to generate new types of Lymphocites out of a Library of DNA-components.



About the Kidneys and the Bladder

The Kidneys serve the body as a natural filter of the blood, and remove wastes which are diverted to the urinary bladder. The Nephron is the basic structural and functional unit of the kidney. In humans, a normal kidney contains 800,000 to 1.5 million nephrons. Nephrons are wave-like structures. Its chief function is to regulate the concentration of water and soluble substances like sodium salts by filtering the blood.

About the Electro Magnetic System

The last  Fractal Branching System, the Meridians, is a Fast Electro-Magnetic Channel that connects to Organs to the Spine and the CNS.

The Ancient Chinese Scientists believed that this System pumps its Energy, the Chi Force, out of the Earth Magnetic Field.

The Ancient Egyptian Scientists believed the same thing. They named  the Four Cavities the Four Suns of Horus and the Spine, the Djed Pillar (Dj means “Snake”).

The Five Organs of Acupuncture

The Five Systems of Acupuncture

About the number Five

The number Five (4 +1 ) plays an important role in Ancient Chinese Medicine.

The Central Fractal System, the One (1), the Fire System, the Blood System, with its Center the Heart,  contains Four (4) Links to the Other Systems.

The Four Systems are combinations of Two Forces, Expansion and Compression.

The Two Forces came out of One Force (“The Void“).

Two Systems contain the same combination (Expansion x Expansion (Wood, Gall Bladder, Liver, Three Heater), Compression x Compression (Metal, Lungs)).

Two Systems combine Expansion and Compression in a different order (Expansion x Compression, Compression x Expansion). They create a Wave (Water, Bladder, Kidney) or Spiral -like (Earth, Immune System) structures.

The Five Spheres of the Body are incorporated in one Super Protective Sphere, the Coelum, the Skin.

In the Human Embryo the First step of Division of the Cells is between the Coelum,the Multi-Cellar Body, and the Brain, the CNS. In the first step the One was divided into the Two, the Actor and the Monitor.

The CNS  “mirrors” the activities of  the Body and acts as a “predictive simulator”.

The Shape of the CNS is a mirror (Up-Side-Down) of the Shape of the Multic-Cellular Body.

The Bilateria are a Fuse of two Organisms in which one organism changed into the Body and the other changed into the Brain.

These two structures are always competing in the Human Being.

The Brain is Looking Up at the Sky. The Body is Looking Down at Mother Earth, it’s Creator.

The Brain and the Body are United in  the Heart, the Balancer of Body and Soul and the Keeper of the Rhythm (The Pericardium).


Sponge, The Tube

About Bacteria

The Body Shape of the Tube was inherited from the first Multi-Cellular Organism, the Sponge. The Sponge is a  Static Cluster of Amoeba, free moving bacteria, that are propelled by their flagellum (a Roter).


The Basic Building Block of the Body, the Bacterium

Bacteria are small chemical factories that are able to share and combine their production processes by exchanging DNA.

With their flagellum the Bacteria Explore the environment to find the chemical food they need. When they have found food the Circulation of the Flagellum moves into the Opposite Direction.

The bacterium integrates incoming chemical signals during a few-second period of its travels, and adjusts its direction of advance accordingly.

The integration is achieved through temporary chemical modifications to molecules located in the bounding membrane, which transfer nutrients to the cytoplasm, and also through changes to certain other molecules in the interior of the cell. Such integration is essentially a short-term memory mechanism.

Bacteria exchange their DNA

Bacteria exchange their DNA

At a certain moment the Bacteria got together because the Sponge is a much more Efficient Metabolic Structure than a group of Free Moving Bacteria.

Strangely enough the DNA of the Sponge already contains the complete Bleuprint of the Humans.

Scientists now believe that most species on earth are a result of a loss of DNA from the original Bleuprint that was created when the Bacteria finally fused into one Organism.

About the Nano-Level

Recently scientists have found Electric Fields as strong as 15 million volts per meter in the Nano-Parts of the Cells. These fields are as strong as those produced in lightning bolts.

It’s not clear what causes these strong fields or what they might mean but they could account for a until now unknown (by Science) or well-known (by the Old Scientists, Chi) Source of  Bodily Energy.

The nano-parts of the Cell could be the very very very small universal building blocks of Nature.

What has Happened?

In the beginning the Chemical Soup generated Self-Reproducing Chemical Factories.

These Factories combined into bigger Factories by exchanging and combining their factory-designs.

Every time when the Factories fused they became more Efficient, Bigger, Stronger, Older and therefore more Competitive.

When the Factories became more competitive they had to Protect themselves against the other Factories.

To Protect themselves the Multi-Cellular Systems started to Sense in Many Directions.

In the first step a Nerve-Net was created.

In the second step one part of the Organism turned Upside-Down and became a Specialized Predictive System (the CNS).

This part fused with the Bodily Part creating one Organism that contained Two Organisms.

The Bilateria, the Organisms with Two Complementary Parts, Body and Mind, were born.

Some of the Bilateria called Humans fused in Social Structures and the Social Structures fused and fused and became more efficient, bigger, stronger, older and therefore more competitive.

In due time they will Rule the Earth and will start to create bigger and bigger systems until they will rule the complete Universe.

To make this possible the Humans need every other part of Nature to Sustain their Growth. This will certainly result in a huge Collapse of their own Eco-System.

The main reason this is happening is that the Humans forgot to Copy the Designs of Mother Nature.

The Brain (Thinking and Sensing, Left Brain), Looking Up at the Sky,  believed it could do a much Better Job than it’s counterpart the Multi-Cellular Body (Emotions and Imagination, Right Brain), Looking Down at the Earth, the Source of All Creation.

Kleiber’s Law shows that we are now using 122 times more Energy per Person than we really would need if we would Scale in the right way.

What can we learn from Kleiber’s Law?

All organisms including the humans depend for their maintenance and reproduction on the close integration of numerous subunits.

These components need to beserviced in a relatively `democratic’ and efficient fashionto supply energy, remove waste  and regulate activity.

Natural Selection solved this problem byevolving hierarchical fractal-like branching networks, whichdistribute Energy, Information and Materials between Big Reservoirs (“Lungs”) and Small Connection Points (“Alveoli”) of other Circulatory Systems (“Blood”).

This Fractal Bottum-Up approach is highly effective and efficient.

The not-fractal, Top-Down,  machinery designed by the Humans is Scaled with a factor 1 so we can improve a lot by copying Mother Nature.


About Goethe and Morphology

About the Heart Chakra or Why the Heart connects the Brain and the Body

How to use the Heart to find Balance

About the Heart and Ethics

Why Humans look a lot like Bacteria

About Kleibers Law and the Rain Forest

About the Five Worldviews

A movie about Fractal Structures in Nature

About the Fusion of Water in the Cell

About the Number Five in Chinese Medicine

Why Humans are part of Super Organisms

How the Humans evolved out of the Bacteria

About the Left and the Right Brain

About the Void

How the Heart synchronizes the Body

About the Fast Transmisson Channel in the Body

About Kleiber’s Law

A general model to explain Kleiber’s Law

About Kleiber’s Law and the Growth of Cities

About the Immune System

About Bacteria

About the Law of Kleiber and Ant Colonies

The terrestrial evolution of metabolism and life

A movie about the origin of vertebrates

About Old Fashioned Thinking

Monday, December 21st, 2009

Many thousands of years ago human life was a far different experience to that which we enjoy today. Life for our ancient forefathers was a mixture of wonder and fear.

aboriginalsThe interesting point to notice is that the human body has not changed since the old days. The things that have changed are our environment and our language.

We see objects our ancestors could not see and therefore we talk about concepts our ancestors were not aware of.

Although our concepts have changed the way we think has not changed.

Thinking is a bodily process. Our muscles talk and our brain processes a huge amount of data.

Current science is able to look into the living body to observe the process of thinking. Scientists think that thinking has a lot to do with seeing. A picture paints a thousand words when the objects (nouns) and the relations (verbs) between the objects are named.

Our ancient ancestors saw other ancestors, animals, rivers, mountains, trees, plants, stars, the sun and the moon. Nature was all around them and Nature was the source of their reasoning.

When you look at nature for a long time you come aware of all kinds of patterns. The Sun rises and disappears every day. The Moon shows itself in the same stages. The plants and the animals act according to these patterns. Observing Nature during day and night generates a theory of Nature and because Nature is cyclic the ancient theory of nature was a cyclic theory.

moonOur ancestors observed short and long term cycles with their eyes and created a theory of everything just like the current scientists are trying to do.

The human has not changed and his ability to define and verify a theory has not changed also.

In our time we have developed highly advanced instruments to probe in the big and the small structures of Nature. We are able to look at the beginning of the Universe and we are able to look at the very small structures of Matter.

Just like our ancient ancestors we use the data of our new eyes, the instruments, to formulate a theory. The big question is if our theory looks a lot different from the theory of our ancestors.

The images our eyes detect are interpreted by the rest of our body. Sometimes we look with our Imagination (Daydreaming, Fantasy). Sometimes we look with our Emotions. We love or dislike what we see.  Sometimes we look with our Expectation and see what we want to see  (Verification) or don’t want to see (Falsification). The objective instruments of science project our subjective theory, our belief-system, upon our reality.

Many people would say that we have advanced in our knowledge of our reality. They believe history is a progressive process. It always moves up because we are learning all the time.

Sri Yantra Temple

Our ancestors would say that history is a cyclic process. It moves Up and Down. Civilizations rise and disappear. History repeats itself all the time.

The proof of their theory is visible everywhere we go but we ignore the evidence. We, the Western people, believe our civilization will stay for ever because our supreme technology is able to solve every problem we will encounter.

The ancient people used different symbols, concepts and names to describe what they observed. We, the Western people, don’t spend much time to understand their theory because our theory of history proves that it is a waste of time to look back and learn from their experience and their comparable thinking process.

The most advanced theory of Physics is called String Theory. It was based on the so called Beta Function of Euler which describes the behavior of the string of a violin. The people that started the quest for the ultimate theory of physics highly believed in the harmony of the spheres, a concept promoted by the ancient scientist Pythagoras. Pythagoras was educated at the university of Heliopolis in Egypt.

Interesting enough the most promising variant of String Theory is called Loop Theory. It supposes that strings make close loops around flat surfaces called Branes. Just like our ancestors the creators of String Theory strongly believe in the concept of the closed cycle and there is a reason for this.

The simple reason is that you have to close our Universe somewhere. Our Universe is very big but there is a horizon, an end of the Universe, which is expanding into the nothing.

The smallest particles we can imagine also have a boundary and this boundary is closing the particle. Closing a system needs something that is closed in itself, a circle, a cycle or every other concept that returns in itself.

ouroborosOne of the most important ancient concepts of closure is the Ouroboros. It represents a snake that is eating itself. If you imagine the eating snake you will see that this snake compresses itself into a point and finally disappears into the nothing.

The modern mathematical term for the ultimate vanishing point is a Singularity, a hole in space and time, sometimes called a black hole.

A black hole is really the entrance to the singularity. It attracts matter in our space while the white hole ejects matter in a different space. The Ouroboros disappears but comes back in another world and starts to expand again. Modern theory supposes that our Universe has expanded out of the Singularity and will move back into this singularity, just like the concept of the Ouroboros is showing.

The ancient concepts are not of our days but they describe the same theory in a completely different way because the old scientists where using Nature as the Source of their concepts.

If the old scientists came with a comparable theory using different terms the big question is how they did it. They could not use the Large Hadron Collider to observe the small and the Hubble Telescope to observe the big. Their only instrument was the eye.


As Above, So Below

The ancient scientists used the rule “As Above, So Below” to make things easy for them.

If the old scientists would be asked to explain this statement in our terminology they would certainly make use of the concept of recursion. Recursion shows itself in the Russian dolls that contain dolls that contain dolls. The ancient scientist believed that the same rules repeat on every level of the Universe.

They also believed that every system is closed in itself. The Big Structures are connected to the Small Structures.

The point of positive Infinity is connected to the point of negative Infinity. The Up, the Down, Forwards and Backwards move around in a pattern called the Moebius Ring (the Symbol of Inifinity). In higher dimensional space this pattern transforms into the Klein Bottle, the basic structure behind Alchemy.

If you understand one level you understand every level.

In 1982, Benoît B. Mandelbrot formulated the same theory in his book The Fractal Geometry of Nature. In this book he coined the term “fractal” to name his recursive structures. At this moment many important physicists are convinced we live in a fractal universe.

The theory of the fractal universe implies that when you observe carefully with the human eye on our level of existence you are able to formulate a theory about every level of the Universe.

The old scientists went a little bit further and stated that our Inner Universe is also an expression of the Outer Universe (“As Within, So Without”). They united physics and psychology in one Theory of Everything.

Carl Gustav Jung (1875-1961) was a follower of the famous Sigmund Freud until he met Wolfgang Ernst Pauli (1900-1951). Wolfgang Pauli was a genius and devoted much of his time to Physics. In 1945 he received the Nobel Price for Physics. At that time Albert Einstein called him his intellectual successor.

Wolfgang Pauli started to visit Carl Jung around 1930. At that time his life was in a terrible mess and Jung started to analyze his dreams just like Sigmund Freud had told him to do.

The Dream of the World Clock

The Dream of the World Clock

Jung detected many ancient themes in the dreams of Pauli. One of the most famous dreams of Pauli is the dream of the World Clock“. This dream is a modern version of the dream of Ezekiel and the Tetramorph.

The dreams of Pauli were highly related to the hermetic alchemists of the Renaissance (John Dee, Robert Fludd, Paracelcus).  The alchemists based their theories on the Ancient Egyptian Knowledge of Heliopolis.

Pauli and Jung started a life long collaboration to explore the bridge between the Inner World of Psychology and the Outer World of Physics.

Jung was also highly interested in what was called the Pauli Effect. Wolfgang Pauli’s life was full of strange and meaningful occurrences of Telekinesis. Objects in the surroundings of Pauli started to lift without any physical explanation.

Finally Jung and Pauli were convinced that the Dream World, the Unconsciousness, was the primal source of inspiration. They also believed that this highly unknown part of the inner world of the human being was able to affect the outer world by producing meaningful signs. The telekinetic effects of Pauli were created by his own Unconsciousness.

They even believed that the force behind human creativity, Spirit, created and sustained the outside material world of our senses.

Pauli was one of the creators of a weird theory called Quantum Mechanics. The predictions of this theory were verified with the instruments of science and proved to be right all the time. The theory was weird because it detected a strange duality in physical reality. Light showed itself as a particle and a wave at the same time.


Male (White) and Female (Black) with the Black and White Hole

To explain this duality scientists moved far back in history and adopted the ancient Yin/Yang-concept as an explanation. This concept describes a constant cyclic movement of the Universe between two opposites, called Female and Male. When the two opposites are combined they are voided into Nothing. The three parts, Male, Female and the Void were called the Trinity.

The scientists of Quantum Mechanics proved that it was possible to influence this duality by the human mind of the observer when the two complementary parts of the mind unite and are voided. This happens when the human meditates or moves into trance.

In the meditative or trance state the brain resonates and entangels, becomes One, with the Electro-Magnetic Waves of Mother Earth, the Shumann Resonance, and the Waves of Life of the Universe.

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 are in Tune. Pythagoras, trained in ancient Heliopolis, explained the same thing a long time ago.

To explain Quantum Mechanics the scientists had to assume that our Universe is not the only Universe that is in existence. To solve the paradoxes they created the concept of the Parallel Universes. The only bridge between these universes is the Hole in Time/Space, the Singularity, which was there before the Duality came into existence.


The Symbol of the Heart

The old scientists agreed on the number of seven parallel Universes. They are a combination of two Trinities, the upside Triangle of the Spirit and the downside Triangle of the Material World.

They called these Universes Heavens and Hells with our Universe, the Universe of the Heart,  in the Middle.

They believed that the Shaman could travel between these universes in Space and Time with the help of his Light Body.

They also believed that the Human Soul, the Light Body, travels these universes in between the time of reincarnation.

In our Western World the Great Spirit of Creation is something many people consider a very old fashioned concept. The funny thing is that at this moment the new scientists introduce the same concepts the ancient scientists were using but with a different name. The modern Material Universe and the old fashioned Spiritual Universe are merging. The only thing we don’t want to accept is that the source of our creation could be a conscious being.

The discussion about Human Consciousness is a very complex discussion. The main reason is that scientists don’t agree about the concept itself.

Consciousness is often confused with Intelligence. Intelligence is the ability to be creative, to find simple solutions for complex problems. Consciousness is the ability to be aware of your own actions. We need our Consciousness to learn from our mistakes. We need our Intelligence to create new solutions to make new mistakes to start learning again.

The Celtic Cross with the Four Forces and the Center, The Void, in the Middle.

The Celtic Cross with the Four Forces and the Center, The Void, in the Middle.

Most people believe that Humans are the only organisms on earth that are Intelligent and Conscious. They accept the possibility that somewhere in our huge universe a comparable situation exist where extraterrestrials live. This possibility increases with the day because our highly advanced instruments are now able to detect comparable planets orbiting comparable suns in the galaxy.

The big problem is still the speed of light. According to the relativity theory of Einstein this speed is the maximum speed to travel space. Our possible companions in the universe are so far away that will be impossible to communicate with them.

Our advanced science is solving this problem too. At this moment scientists believe that the singularity now called a wormhole could make it possible to shorten the distance in space. If they are right space/time-travel will be soon a fact of life.

Some people believe animals are Intelligent and Conscious. They feel that their cat or dog or horse looks and acts a lot like the human being. Because of this believe they treat their pets just like human beings.

Scientists are already able to construct artificial humans and pets.  They are convinced it will not take a long time to produce artificial human beings that are not distinguishable from the normal human being.

Scientists are desperately trying to define a difference between a conscious and intelligent machine and a conscious and intelligent human being and they are not succeeding at all. Soon they have to admit that their experiments with artificial life show that consciousness and intelligence are the properties of a fractal system.

ancient game

The Game of Life is played on the Square

The old scientists already believed that our universe is a highly intelligent conscious fractal machine put in motion by a creator to experience all the possibilities of his own potential. The creation machine, the Matrix, gave the creator the opportunity to experience itself, to become fully conscious.

We, the Humans, are an enfolding of the Creator into a deeper level of existence. We are not created by his image we are in his image. If we look deep in the mirror of ourselves we are able to see the creator.

The old scientists even believed they had broken the code of the software of the creation machine and therefore could become an immortal being, the creator of a new parallel universe, themselves.

Consciousness is created when the self encounters the self by a short or a long feed-back loop.

If this is true the Cycles are there to become aware of the machine and to break the code of the software of the machine to become a fully creative entity. When the self encounters and accepts the mirror of the self they merge into the nothing, the state of the Universe before the singularity came into existence.

The Mystery

The Mystery

The ancient scientists did not believe that the state of the Nothing was not existent. They believed that the primal state of creation was pure potential. It was a highly fluctuating state called the zero-point-field by our scientists and the Mystery by the old scientists. The zero-point-field generates everything that is possible.

It produces mysteries, things we cannot imagine, because we as parts of the enfolding are unable to imagine every thing that could exist. Our bodily pattern recognizer, the Brain, is not capable of doing this. Imagining every thing would turn our brain into a state of pure madness.

Madness and sickness is a state of the body ancient and modern humans have experienced through history. This state has many names in our current highly specialized society. The old scientists believed that Spirit was able to help people to become sane and healthy again.

They believed in independent conscious beings with a positive and a negative attitude. The Trinity and its many enfoldings on different levels (Archangels, Angels) could be asked to erase the negative powers to let the love of the Spirit heal the body and the soul.


The Four Humors, the Four Forces of the Inner World

The ancient scientists named the force that heals the Force of Life. They believed in four other forces called the Four Elements (Air, Fire, Earth and Water) with the Force of Life, the Void, in the Center.

The first two Forces, Male and Female, are part of the first Trinity, the Spiritual World. Male and not-Male are voided in the Void. They are opposites just like expanding space, Gravity (Fire, Heaven) and not-expanding, compressing, space, the Strong Nuclear Force (Earth). Its main job is to hold together the subatomic particles of the kernel of the Atom. In the beginning God, the Void, created the Heavens and the Earth.

On the second level of Enfolding of the Trinity, the Material World, four combinations of Male and Female are possible. Two of them (Male/Male = Male, Gravity, Female/Female = Female, the Strong Force), are part of the Spiritual World and repeat their existence in the Material World.

The two other forces, the Electro Magnetic Force (“Let there be light”) of Life and the Weak Force (Radioactive Decay, Darkness) of Death are a mixture of both Male and Female and are therefore oscillating forces. They are compressing and expanding and therefore look like waves (Water and Air). These forces are also voided in the Void which shows that the potential of the Void, the Force of Life, is available at every level of existence.

The ancient system of Physics was a highly logical, mathematical system just like our current theory of Physics is. It contained just two concepts expansion (Female) and compression (Male) and showed that the spiraling vortex of creation was a repeating combination of the Expansion of just two simple dynamic concepts that were in a balance all the time. They knew that in the end everything would be Compressed to return to the Mysteriouss creator, the Void, the State of Infinite Potential.


Sri Yantra, the Machine that generates the Matrix

The ancient scientists used the terminology of Nature to explain their theory to the masses. They also used highly abstract geometric theories to calculate the movements of the levels of the fractal universe. These theories were only available for the initiates of their secret societies.

The main reason was that they were afraid of misuse of the power of their knowledge. Science was not only related to the game of invention but it was also a state of mind. Ethics, Physics, Art and Religion were expressions of the same fractal structure of the Universe, that originated out of the Love, the Attraction of the Void,  the First Creator, for his own Mirrors.

The force that heals is still there and science is again on the verge of the rediscovery of ancient practises. The weird science of Quantum Mechanics proved the power of the mind and the force of life returned when the Mystery of the Void was transformed into the zero-point-field.

The power of the mind explains the placebo-effect feared by scientists who want to cure the body with chemical structures that exist on a very low level of the enfolding of the fractal universe. The pharmaceutical industry is using conscious entities (chemical forces) with little power while the powerful forces of the Archangels are still there.

The believe of the scientists in the healing power of nature itself has disappeared. They wanted to beat Nature with brains that are part of Nature itself. They wanted to beat their selves instead of uniting the male and female parts of their brains to become whole again.

This blog is a chapter of a new book I am writing together with Steven Strong about the ancient knowledge of the Aboriginals. According to their stories one part of humanity decided a long time ago to stay close to nature.

trickster raven

The Trickster in the Dream of the World Clock

In the dreamstate they saw the consequences of the steady increase of dominance of technology when the humans would start with agriculture. They believed Nature would take care of them when they lived according to the Dreaming. I think they were right.

The move from hunter/gatherer to farmer produced the advanced civilizations of the World. Everyone of these civilizations did not survive the strange behaviors of Mother Nature, the Trickster, also called the Demiurg, represented by the Raven in the World Clock of Pauli.

I also think they forgot one thing. They forgot that the Cycles of the Wheel of Fortune of the Matrix we live in are a Machine that moves Back and Forth. It move far away from the Void into the Darkness to return back into the Light of the Mysterie.

The ancient scientists could calculate the short and long cycles of history and predicted a new Golden Age. They incorporated the predictions in their stories, buildings and artifacts. They knew that their scientific ancestors would try to explain their weird theories.

They knew that one day ancient science and modern science would converge because the cycles predicted that.

They knew that independent minds would return in every step of the cycle to repeat the same story again and again with different words and different concepts. They knew that history repeats itself all the time.

The only thing that is left for us is to take the consequences of our current understanding of our Universe.

Do we want to fight Nature with our technology until Nature fights back to create a new balance or do we want to return to the old knowledge of the Aboriginals and start again to cooperate with our Mother Earth.

The choice is yours.


About Pythagoras

About Morphology or How Alan Turing Made the Dream of Goethe Come True

Tuesday, November 17th, 2009

The Ancient Greeks believed that the images of waking life and dreams came from the same source, Morpheus (Μορφέας, Μορφεύς), “He who Shapes“.

The Science of the Shapes, Morphology, was created and named by Goethe in his botanical writings (“Zur Morphologie“, 1817).

Goethe used comparative anatomical methods, to discover a primal plant form that would contain all the others-the Urpflanze. Goethe being a Romantic Idealist hoped that Morphology would Unify Science and Art.

The Uhrplant shows itself also in the Lungs and Riversystems

The Uhrplant shows itself also in the Lungs and Riversystems

“The Primal Plant is going to be the strangest creature in the world, which Nature herself shall envy me. With this model and the key to it, it will be possible to go on forever inventing plants and know that their existence is logical”. Nature always plays, and from which she produces her great variety. Had I the time in this brief span of life I am confident I could extend it to all the realms of Nature – the whole realm“.

Goethe (wikipedia)

Goethe (wikipedia)

Hundred years later in the 1920s Goethe’s dream came true. Morphology moved outside Biology to other parts of Science due to the works of D’Arcy Thompson’s On Growth and Form, Oswald Spengler Morphology of History, Carol O. Sauer Morphology of Landscape, Vladimir Propp, Morphology of the Folktale and Alfred North Whitehead Process and Reality.

Goethe observed nature and reflected on similar structures. He believed that there was something behind this similarity, an archetypal plant.

According to Goethe the archetypal plant was the leaf (“While walking in the Public Gardens of Palermo it came to me in a flash that in the organ of the plant which we are accustomed to call the leaf lies the true Proteus who can hide or reveal himself in all vegetal forms. From first to last the plant is nothing but leaf“).

At this moment scientists know the reason why the leaf is the most important structure of the plant. It is a solar collector full of photosynthetic cells.

The energy of the sun provides the energy to transform water from the roots gathered by the leafs and carbon dioxide out of the air also gathered by the leafs, into sugar and oxygen. Plants are structures with many leaves. These leafs shield other leafs from collecting sunlight and water.

To solve this problem a plant has to optimize its structure to collect enough Sunlight and Water. The process of Optimization is not a Central Coordinated action. Every leaf tries to find the best place in the Sun on its own. This place determinates the growth of the next level of branches and leafs.

Goethe observed a pattern and deduced a structure, the leaf, the Uhrplanze. What Goethe really observed was not a Static Uhrplant but the Dynamic Process of the Branching of all kinds of leaves in all kinds of plants (Morpho-Genesis).

The leafs of the plants are not the main target of the morphogenesis of the plant. The visible External and the invisible Internal Forms or Organs are one of the many solutions of an equation with many variables and constraints. The optimal solution is reached by experimenting (“Nature always plays”).

Many solutions fail but some survive (Evolution of the Fittest). When a solution survives it is used as a Foundation to find new rules for more specific problems (Specialization). When the environment, the context, changes old rules have to be replaced by new rules (a Paradigm Shift).

The Fractal Geometry of Nature

The Fractal Geometry of Nature

New mathematical paradigms in the field of the Machines and Languages (Alan Turing, The Chemical Basis of Morphogenesis) and the Self-Referencial Geometry of Nature (Benoît Mandelbrot, The Fractal Geometry of Nature) have stimulated further investigation in the Field of Morphology.

In 1931, in a monograph entitled On Formally Undecidable Propositions of Principia Mathematica and Related Systems Gödel proved that it is impossible to define a theory that is both Self-Consistent and Complete. The paper of Gödel destroyed the ambitions of the Mathematicians at that time to define one theory that explains everything.

In 1936 Alan Turing produced a paper entitled On Computable Numbers. In this paper Alan Turing defined a Universal Machine now called a Turing Machine. A Turing machine contains an infinite tape that can move backwards and forwards and a reading/writing device that changes the tape. The Turing Machine represents every Theory we can Imagine.

Turing proved that the kinds of questions the machine can not solve are about its own Performance. The machine is Unable to Reflect about Itself. It needs another independent machine, an Observer or Monitor to do this.

It can be proved that Turing proved the so called Incompleteness Theorem and the Undecidability Theorem of Gödel in a very simple way.


The Eniac

In 1943 Turing helped to Crack the Codes of the Germans in the Second World War. At that time the first computers were build (Eniac, Collossus).

It was very difficult to Program a Computer. This problem was solved when Noam Chomsky defined the Theory of Formal Grammars in 1955 (The Logical Structure of Linguistic Theory).

When you want to define a Language you need two things, an Alphabet of symbols and Rules. The symbols are the End-Nodes (Terminals) of the Network of Possibilities that is produced when the Rules (Non-Terminals) are Applied. The Alphabet and the (Production- or Rewriting) rules are called a Formal Grammar.

If the Alphabet contains an “a” and a “p” the rules S→AAP, A→”a” and P→”p” produce the result “aap”. Of course this system can be replaced by the simple rule S→”aap”. The output becomes an infinite string when one of the rules contains a Self-Reference. The rules A→a and S→AS produce an Infinity String of “a’-s (“aaaaaaaaaaaaaaaaaa….”).

The system becomes more complicated when we put terminals and rules (non-terminals) on the Left Side. The System S→aBSc, S→abc, Ba→aB and Bb→bb produces strings like, “abc”, “aabbcc” and “aaabbbccc”. In fact it produces all the strings a**n/b**n/c**n with n>0.

The inventor of the theory of Formal Grammar, Chomsky, defined a Hierarchy of Languages. The most complex languages in his hierarchy are called Context-Dependent and Unrestricted. They represent complex networks of nodes.

A language where the left-hand side of each production rule consists of only a single nonterminal symbol is called a Context Free language. Context Free Languages are used to define Computer Languages. Context Free Languages are defined by a hierarchical structure of nodes. Human Languages are dependent on the context of the words that are spoken.

It is therefore impossible to describe a Human Language, Organisms, Organisations and Life Itself with a Context Free Computer Language.

Context Free Systems with very simple rule-systems produce natural and mathematical structures. The System A → AB, B → A models the Growth of Algae and the Fibonacci Numbers.

A Recognizer or Parser determinates if the output of a formal grammar is produced by the grammar. Parsers are used to check and translate a Program written in a Formal (Context Free) Language to the level of the Operating System of the Computer.

grammarRegular and Context Free Grammars are easily recognized because the process of parsing is linear (causal, step by step). The stucture of the language is a hierarchy.

The recognizer (now called a Push-Down Machine) needs a small memory to keep the books.

Context Dependent (L-systems) and Unrestricted Grammars are difficult to recognize or are not recognizable in practice because the parser needs a huge sometimes Infinite Memory or Infinite Time to complete its task.

To find the Context the Recognizer has to jump backwards and forwards through the infinite string to detect the pattern.

If the network loops the recognizer will Never Stop (“The Halting Problem“).

Turing proved that the Halting Problem is Undecidable. We will Never Know for Sure if an Unrestricted Grammar contains Loops.

The Rules and the Output of Unrestricted Grammars Change and never stop Changing. Our Reality is certainly Context Dependent and perhaps Unrestricted.

Parsing or Recognizing looks like (is similar with) the process of Scientific Discovery. A theory, a Grammar of a Context-Free Systems (“aaaaaaaaaaa…”) is recognizable (testable) in Finite Time with a Finite Memory. Theories that are Context Dependent or Unrestricted cannot be proved although the Output of the Theory generates Our Observation of Nature. In this case we have to trust Practice and not Theory.

cellular automata

A 3D Cellular Automaton

In 2002 the Mathematician Stephen Wolfram wrote the book A New Kind of Science.

In this book he tells about his long term Experiments with his own Mathematical Program Mathematica. Wolfram defined a System to Generate and Experiment with Cellular Automata.

Wolfram believes that the Science of the Future will be based on Trial and Error using Theory Generators (Genetic Algorithms). The big problem with Genetic Algorithms is that they generate patterns we are unable to understand. We cannot  find Metaphors and Words to describe the Patterns in our Language System.

This problem was adressed by the famous Mathematician Leibniz who called this the Principle of Sufficient Reason.

Leibniz believed that our Universe was based on Simple Understandable Rules that are capable of generating Highly Complex Systems.

It is now very clear that the Self-Referencial Structures, the Fractals, of Mandelbrot are the solution of this problem.

The Scientific Quest at this moment is to find the most simple Fractal Structure that is capable of explaining the Complexity of our Universe. It looks like this fractal has a lot to do with the Number 3.

It is sometimes impossible to define a structured process to recognize (to prove) a Grammar. Therefore it is impossible to detect the rules of Mother Nature by a Structured process. The rules of Mother Nature are detected by Chance just like Goethe discovered the Uhrplanze. Science looks a lot like (is similar with) Mother Nature Herself.

When a Grammar is detected it is possible to use this grammar as a Foundation to find new solutions for more specific problems (Specialization, Add More Rules) or when the system is not able to respond to its environment it has to Change the Rules (a Paradigm Shift). All the time the result of the System has to be compared with Mother Nature herself (Recognizing, Testing, Verification).

Turing proved that if Nature is equivalent to a Turing machine we, as parts of this machine, can not generate a complete description of its functioning.

In other words, a Turing machine, A Scientific Theory, can be a very useful tool to help humans design another, improved Turing Machine, A new Theory, but it is not capable of doing so on its own – A Scientific Theory, A System, can not answer Questions about Itself.

The solution to this problem is to Cooperate. Two or more (Human) Machines, A Group, are able to Reflect on the Other. When the new solution is found the members of the Group have to Adopt to the new solution to move on to a New Level of Understanding and drop their own Egoistic Theory.

Each of the individuals has to alter its Own Self and Adapt it to that of the Group. It is proved that Bacteria use this Strategy and are therefore unbeatable by our tactics to destroy them.

Turing proved that Intelligence requires Learning, which in turn requires the Human Machine to have sufficient Flexibility, including Self Alteration capabilities. It is further implied that the (Human) Machine should have the Freedom to make Mistakes.

Perfect Human Machines will never Detect the Patterns of Nature because they get Stuck in their Own Theory of Life.

The Patterns of Turing

The Patterns of Turing

The Only ONE who is able to Reflect on the Morphogenesis of Mother Nature is the Creator of the Creator of Mother Nature, The Void.

Gregory Chaitin used the theory of Chomsky and proved that we will never be able to understand  The Void.

The Void is beyond our Limits of Reason. Therefore the first step in Creation will always be  a Mystery.

At the end of his life (he commited suicide) Alan Turing started to investigate Morphology.

As you can see the Patterns of Alan Turing are created by combining many Triangels. The Triangel is called the Trinity in Ancient Sciences.

According to the Tao Tse King, “The Tao produced One; One produced Two; Two produced Three; Three produced All things”, which means that the Trinity is the Basic Fractal Pattern of the Universe.

In modern Science this pattern is called the Bronze Mean.

It generates so called Quasi Crystals and the Famous Penrose Tilings.

The Bronze Mean is represented by the Ancient Structure of the Sri Yantra (“Devine Machine”).

Goethe was not the real discoverer of Morphology. The knowledge was already there 8000 years ago.


About the Observer and Second Order Cybernetics

A PDF About the Morphology of Music.

The origins of life and context-dependent languages

A Website About the Morphology of Botanic Systems

A Website About the Morphology of Architectural Systems

A Plant Simulator using Morphology

About Intelligent Design

The Mathematical Proof of Gödel of the Existence of God

About Bacteria 

About the Bronze Mean

About the Trinity

About the Logic of Creation

Monday, October 12th, 2009
The Big Bang Inflation Field

The Big Bang Inflation Field

The Way the Universe was Created has generated an ongoing discussion for more than 6000 years. In this Blog I give you a way to solve this problem with the use of Logic.

When we use Logic you will see that the concept of Creation out of Nothing leads to a Strange Contradiction.

This Contradiction looks a lot like the Zero-Point-Field of Quantum Mechanics.

The theory of Quantum Mechanics is a Statistical Theory. Statistical Theories are an approximation of a Theory.

Behind this approximation lies a hidden structure called the Tree of Life. The Tree of Life is an expansion of the first Creation, the split of the Void.

Perhaps the most important conclusion of this blog is that what most people call the Spiritual World is really the Material World which can be explained by Mathematics and Physics.

The only part of our Universe that is truly Spiritual and is without any Duality lies outside our Universe. This Part, The Void,  prevents Our Universe for Total Annihilation.

To describe the process of Creation out of Nothing we have to define the Void (Ø) and the Whole (○). The Void is the Empty Set. The Empty Set is a Set with Zero Members. An example is the Set of months with more than 31 days. In this case the Empty Set is the result of an impossible selection.

The Tao is like a well:
used but never used up.
It is like the eternal void:
filled with infinite possibilities.

It is hidden but always present.
I don’t know who gave birth to it.
It is older than God.

The empty set is not the same thing as nothing. It is a set with nothing inside it. In Logic there is no concept that describes “nothing”. We have to assume that there was something in the Beginning and that something is the Empty Set.

The Empty Set contains everything that is impossible.

In the Beginning an impossible selection was not possible because there was nothing to select from. This means that in the Beginning the Empty Set was the only Set in the Universe.

In the beginning the only thing that was possible was the impossible.

The Void is the Opposite of the Whole. To define the Void and the Whole we have to make use of a Distinction.

A Distinction is something that divides a Set into Two parts, X and its Opposite not-X (Yin/Yang).

A Set  that is divided into Two Parts Suddenly contains Four parts A, not-A, the Division and the Set itself (the Whole): Yin, Yang, Yin AND Yang (Division), Yin OR Yang (Whole).

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

X and not-X have only the Void in common. When we bring the two sets together they become Nothing just like the combination of Matter and Anti-Matter results in the Annihilation of Both Parts and the production of a Photon (“Light”) and Kinetic Energy (Movement). To avoid annihilation Matter and Anti-Matter have to Stay Apart.

The Fusion of Matter and Anti-Matter produces Light

The Fusion of Matter and Anti-Matter produces Light and Movement

When you Fuse the two parts X and not-X the Whole appears again. In the Beginning there was Nothing to Fuse and the commonality of the Empty Set with its Opposite, the Not-Empty Set, the Whole, was the Empty Set. In the Beginning the Whole was the Empty Set because there was only the Empty Set.

All is possible when emptiness is possible.
Nothing is possible when emptiness is impossible.

Nagarjuna, Chapter 24 verse 14 of the Mūlamadhyamakakārikā

In Logic the commonality of two sets is represented by the term “and”. The fusion of two sets is represented by the term “or”. The not is represented by the symbol “~”. Using these Symbols we can write down the “laws of Logic” as follows:

Ø = ~○

X and ~X = Ø

X or ~X = ○

At the beginning of the beginning, even nothing did not exist (Chuang-tse)

At the Beginning the Universe was the Void and the Void was the Whole.

This implies the following:

Ø and ~ Ø = Ø

Ø or ~ Ø = ○

Ø = ~ Ø

Form is no other than emptiness; emptiness no other than form (Diamond Sutra)

The First Distinction in the Universe is the Choice between Distinction (~ Ø) or Non-Distinction (Ø). The Choice between the two is the Whole (Ø or ~ Ø = ○). Non-distinction is the state of Union of Every Thing in the Universe. The Union of Every Thing is No Thing at all.

There is in reality neither truth nor error, neither yes nor no, nor any distinction whatsoever, since all — including contraries — is One (Chuang-tse)

The One. . .is there before every oneness amid multiplicity, before every part and whole, before the definite and indefinite, before the limited and the unlimited. It is there defining all things that have being, defining being itself. . .It is there beyond the one itself, defining this one. (Dionysius)

The One transcends all antithesis, rises above all relation, is pure from all duality (Proclus)

Everything is of the nature of no thing (Parmenides)

The Tao that can be told is not the eternal Tao. The name that can be named is not the eternal name. The nameless is the beginning of heaven and earth. The named is the mother of ten thousand things. These two spring from the same source but differ in name; this appears as darkness. Darkness within darkness. The gate to all mystery (Lao Tzu)

In the Beginning when the Laws of Logic, the Logos, came into existence two Empty Sets were produced, the Empty Set and its Opposite, the Not-Empty Set. In the Beginning the Void was not the Void.

In the Beginning the Void has Negated Itself. This Negation started the Proces of Creation out of Nothing.

By Negation itself the Void created a deep Passionate longing to move back to the Sea of the Nothing.

The One is a Negation of Negations (Meister Eckhart)

The not-Void has a choice (Ø or ~ Ø). One choice is to merge with the Void (Ø and ~ Ø) and return back into Emptiness. The other choice is to avoid Annihilation. In this case the not-Void, ~ Ø, has to stay apart from the Void, Ø. Therefore the Not-Void, ~Ø, has to Move Away from the Void, Ø.

Gravity Waves

Gravity Waves

When this happened The Not-Void transformed from the State of Being into the state of Becoming and started to Rotate and Expand in a Spiraling motion. The Moving Void, the Second Distinction, Expanding Space, was created. When the Second Distinction was created the Void came to Rest but to keep the Balance of the Void, Not-Expanding, Compressing Space, Ø and ~ Ø, came into Existence too.

Expansion (The Strong Force) has to be compensated by Compression (Gravity) to bring the Universe back to the Void. The amount of Time this will take is dependent on the Power, the Potential, of the not-Void when it was disconnected from the Void. When the Potential of the disconnection is small, the Void and the Non-Void will merge soon and start a new process of disconnection to solve their Eternal Contradiction.

Expanding Space (Ø or ~ Ø ) and ~ Expanding Space(Ø or ~ Ø) = Ø

Gravity and The Strong Force  = Ø

Gravity or The Strong Force = ~ Ø

The whole process of logical reasoning from the Void to Space/Time is based on a Contradiction that occurs when we define what happens when Logic (Consciousness, the Two, the Self and the Observer of the Self) came into existence (“In the beginning was the Logos“) and the Void was the Whole.

When we look at the current theory of creation called the Big Bang Theory we find the same contradiction formulated in a different way.

The Gravitational Singularity

The Gravitational Singularity

In the theory of the Big Bang the Void that is the Whole is called a Gravitational Singularity (GS). A GS is a situation where the current laws of Physics break down because one of the variables moves to Infinity. When such a contradiction happens scientists know there is something wrong with their theory.

In the Big Bang Theory, the Universe is compressed (moved back in Time) into an extremely small space, a point, a singularity, and is therefore infinitely hot.

The Void that was the Whole, Empty Space, is extremely cold (0 degrees Kelvin). This condition is called the Zero-Point-Field. It is the State of the Universe that was there before the Big Bang.

According to Quantum Mechanics, the Zero-Point-Field, the Vacuum State, is not truly empty. It contains fleeting electromagnetic waves and particles that pop into and out of existence. It is not strange to define this popping up of No-Thing by the statement: ~ Ø = Ø (Sometimes there is nothing and sometimes there is not nothing).

The only thing we have to look for is the reason why the State of Rest of the Zero Point Field was disturbed. The answer of this question is simple: “It just happens“. A statistical fluctuation can be very small or very big.

Shiva and Shakti Create the Universe

Shiva and Shakti Create the Material Universe

In the Beginning the Quantum Fluctuations of the Zero Point Field, the Phoenix,  generated a huge Fluctuation represented by a “Cosmic Orgasm (Shiva and Shakti made Love)” and a real particle, a Photon (“In the Beginning was the Light“), came into existence. This Single Photon, One Wave of Light, bouncing against the expanding walls of the Universe, was enough to Create the Whole Universe.

Quantum Fluctuation is a Statistical Theory. Statistal Theories don’t explain the Universe. They are an approximation of a deeper structure we still don’t know. The ancient scientists used a metaphor out of Nature to explain this deeper structure. This metaphor was called the Tree of Life.

When we use Logic, the first step in Creation generates a Trinity. This Trinity consists of Gravitation (Expansion), the Strong Force (Compression) and the Void, the Empty Set. The concept of the Trinity with different names comes back in every Ancient Religion.

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

tree of life

The Tree of Life

The first Trinity is the Top of a structure called the Tree of Life. This structure can be found in almost every Ancient Culture.

The Tree of Life consists of Nine Concepts with the Void (10=0)  at the top. The Nine Concepts of the Tree of Life are created by Multiplying the Trinity by the Trinity (3×3 =9 + the Void = 10 = 0).

The duality (-1,1) is represented by two Trinities (-3,-2,-1,0,1,2,3) with the Void in the Middle. In this case the Pattern of Seven appears.

The real enfolding  is created when we apply the Trinity to the Trinity. In this case the sequence becomes 1, 1, 4 (1+ 3×1), 13 (1+3×4), 43 (4+3×13), the Bronze Mean.

Every number in this sequence represents an important Stage in the enfolding of our Universe and has its own Mystical Meaning (The Void, The Duality, the Four Forces, The Zodiac (with the Sun in the Center), The Sri Yantra (The Kingdom)).

The fractal patterns moves deeper and deeper into the Material World, father away from the Beginning, the Void. At this moment our Universe contains fourty-two levels.

At some point (43) the pattern of enfolding will finally reach the Kingdom and the pattern will reverse and moves back to the Void. From that moment  we will move backwards in Time.

When you apply the Trinity to the Trinity you use a principle that is called Self-Reference. In modern mathematics this principle is called a Fractal and the theory associated with Fractals is called Chaos Theory. Fractals play a very important role in the new String Theories of the Universe.

It is possible to generate the many levels of the Universe out of one Fractal Pattern, the Trinity. In modern Physics one of the candidates for the Fractal Pattern of the Universe is the Sierpinski Triangel. This fractal pattern generates the well known Mystical Geometries and is based on Trinities.

Physics and Mystics show that Our Universe and every part of it (including the Human Being) are part of the first Trinity that came out of the non-Void, the negation of the Empty Set that came into Being.


The Second Trinity Brahmā, Vishnu, and Shiva is created out of Brahman (The Void)

If the Void and the Trinity are concepts that represents the concept of God, we are all part of the enfolding structure, God, the Not-Void.

One part of God, the “Real Void“, the Mystery (Brahman), is not part of our Universe. It stays outside to prevent total annihilation of Every Thing.

We cannot understand The Mystery because we cannot Reason, don’t have a Distinction, about the Beginning of the Beginning. It lies Outside our System of Understanding called Logic. The only thing that is left for us is to Experience and Keep Silent.

Gravity is the root of lightness; stillness, the ruler of movement (Lao Tsu, Tao Te Ching, 26).

The Void is also the power that Attracts every part of our Universe. The farther away we expand from the Void the stronger the Strong Force becomes. At a certain point in Time this force will force us to Move Back. When this happens the Compression of the Universe, back to the Void, cannot be stopped. When we move Back, Time will be Reversed.

The Universe Closed in Itself

The Universe Closed in Itself

In the End the Spiral of Enfolding will be Closed in Itself and the not-Void will merge with the Void. At that moment the State of Stillness of the Zero Point Field will be restored waiting for a new Fluctuation to occur. The Universe is Breathing. It is recreated time after time until the Void and the Non-Void finally fuse into the Nothing, the Mystery.

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

(Gospel of Thomas, Logion 22).

When we look at the Logic of Creation we can see that the only part of Our Universe that is Truly Spiritual is the Void. The Not-Void and all its expansions are part of the Material World (Maya) that can be explained by Mathematics and Physics.

The Void, the Infinite Potential with Infinite Possibilities, lies Outside our System of Reasoning and is Nameless, Formless and not Dividable. It is truly One.

We are Nothing but a Rare Fluctuation of the One, who is the Void.


About the Mathematics of Distinctions of Spencer Brown

About Boundaries

About Boundary Mathematics

About the Tree of Life

About the Void and Atman

About the Seven (3-1-3) and the Nine (3×3)

About the 42 Levels in the Fractal Universe

Why Time is a Chain of Nows

About the Holy Trinity in Mathematics

How to create Mathematics out of the Void

Why Quantum Fluctuation could have created the Universe

How the Universe was created out of one Photon

About the Productivity of Knowledge Workers

Monday, August 10th, 2009

blue collar workerIn the 19th Century The Blue Collar Workers were replaced by Machines operated by White Collar Workers.

When the White Collar Workers were replaced by the Software of the Programmers a new Type of Work was created, called Knowledge Work.

It is very difficult to measure the Productivity of the Knowledge Worker.

In this Blog I will show you that the Problem of the Productivity of the Knowledge Worker can be solved when you Realize that the Business Cycle is a Self-Referring Object (A Fractal).

Work is a Process and is part of a Business Cycle. Work has a Result and it uses Resources.

When the Result of the Process is accomplished somebody has to Use the Results. The process of Use is called Consuming.

When a Requirement is Transformed into a Result and the Result is Sold (Sales) and Used somebody starts to Think, gets Ideas, about Adapting the Requirements and the Cycle of Work is Closed.

When the Requirements are Satisfied we call the process Effective. The process is Efficient when Waste is minimized.

In the Business Cycle the Four “Organs” of the Human, Control, Desire (Consume), the Emotions (E-value-ate) and the Imagination (Create) are Dominating a Phase. The task of the fifth Organ, Conscioussness, The Monitor, is to Balance the Four Organs to make sure that one Human Faculty is not dominating the Cycle. The Business Cycle is Self-Referring.

This means that we are able to apply the Business Cycle in every part of the Business Cycle. A Salesman makes the Requirements of a Sales Plan, Executes a Sales Plan and Improves his Sales Cycle when he gets new Ideas about the effect of his efforts.

What we see is the process of Specialization resulting in the Division of Labour.

Every time when a new specialization of the Business Cycle is created the Level of the Process changes and the Speed of the Movement of the Cycle, the Periodicity, changes. Every Time when a new Division of Labour occurs the Business Cycle Speeds Up.

The Division of Labour not only Accelerates the Business Cycle. The New Roles in the Cycle behave like an Independent Unit. They want to Dominate Cycles on other Levels and most of all they want to expand their Activities.

The Personal Assistant who was helping the Manager to Hire and Fire Personnel transforms into a Human Resource Management Department.

At some point in time the specialized Units disconnect from the Whole and start a Life of their Own. Designers start Design Bureaus. Teachers unite in a School. Scientists cluster in Universities.

All of them are still payed by the Primary Processes in Society (Agriculture (Food), Industry, ..) but the Secundary (or higher order) processes don’t want to hear that. They think they are the Most Important Processes in Society.

When the new Wholes are created they start to Divide again and again. The Result of the Split of the Work Cycles, the endless Division of Labour, is an Incomprehensible, not Effective, Inefficient Network of Competing Work Processes Clustered in many Institutions.

The Business Cycle is Breathing.

When the process of Splitting has gone too far, the process of Union and Integration starts.

Splitting, Expansion, occurs when the Economic Cycle is going Up.

Integration, starts when the Economic Cycle is going Down.

We are now again in an Integration Phase which means that many secundary and higher order processes will be destroyed until the Essence of Society is visible again.

What is a Knowledge Worker?

A Blue Collar Worker works in a Factory and is doing Manual Labour. The people who are part of the Staff Departments of the Factory (Sales, Planning, Design,) are called White Collar Workers. White Collar Workers are more Educated as the Blue Collar Workers. They Earn more money and are doing Intellectual Work. The Knowledge Worker Uses and produce Knowledge. Examples are: Programmers, Systems Analysts, Lawyers, Teachers and Scientists. Examples of processes are: planning, acquiring, searching, analyzing, organizing, storing, programming, distributing and marketing.

What is Productivity?

The Concept of Productivity implies that an organization works as a Physical System with variables and their inter-relationships amenable to precise definitions. The basic reliance is on the acceptance of a Stimulus-Response model of Causality that an Input causes an Output.

Productivity is the ratio of Outputs (Goods and Services) divided by one or more Inputs (Labor hours, FTEs, Capital, Expenses). Using money as a measure of value makes it possible to compare dissimilar inputs and outputs.

Productivity is only applicable in the Production Phase of the Business Cycle. In the other Phases other Measures are used like Customer Satisfaction in the Consuming Phase. Customer Satisfaction is a measure of the Effectiveness of a Production phase.

The Business Cycle is a Self-Referencial Object. Every Phase of the Business Cycle can be divided in the Phases of the Business Cycle. This means that the Productivity of the Knowledge Worker can be Measured when he is Producing Something (A Design, A Research Document, A Plan).

If the Knowledge Worker is not Producing anything there is nothing to Consume in the next Phase. In this case the Knowledge Worker is not Effective. If this happens the  Knowledge Worker has to Reflect, Use his Consciousness, to detect his Added Value to the Whole he is part of.

To Define the Productivity of a Blue of White Collar Worker, the Process has to be Standardized. To standardize a process you have to define the Flow of the Components (Bill of Materials) and of course the Product, the Result.

If the Process is Standardized it is very easy to get rid of the Waste in the Process (Process Improvement). When this happens the process becomes more Efficient (now called Sustainable).

Standardization results in a Decrease of the Workers, a Lowering of the Waste (Costs) and an Increase in Rules. The Process Rules are implemented in Machines and Software.

What are Knowledge Workers Really Doing?

The Designers and Implementers of the Rules, the Knowledge Workers, are the people who are Destroying the Work of the Blue and White Collar Workers in a Factory. They are also the Creators of New Factories (Business Development) and connect Old Factories (Value Chain Integration).

How to Measure the Productivity of Knowledge Workers.

Knowledge Workers are part of the Business Cycle. They Analyze Work Processes to minimize Waste, Evaluate the Results of the Consuming of the Result of a Work Process (the Product) , Imagine and Test new Ways to Satisfy the Needs of the Consumer, Design New Work Processes or Change Existent Work Processes.

The Business Cycle is Self-Referring. This means that you can organize the Work Processes of the Knowledge Workers just like the Work processes they Analyze.

If you measure the Productivity of the Work Process of the Blue and White Collar Workers in a certain way, it must be possible to measure the Productivity of the Knowledge Worker in the same way. Knowledge Workers also have to make plans and have to evaluate their own products to Learn and to Improve their Performance.

This approach has a great advantage. If you treat the Knowledge Workers just the way you treat the Blue and White Collar Workers they will understand that some day the Controller will Standardize Knowledge Management, Reduce the Waste, Focus the Process on a Clearly Defined Target, Eliminate the Knowledge Workers and Replace them by a Very Intelligent and Creative Software Program.

These Software-Programs are already there (Expert Systems, Artificial Intelligence, Pattern Recognition) and are constantly improving their behavior. One of the most interesting examples is Wolfram Alpha.

When the Fractal Pattern Recognizers are fully operational the Knowledge Workers will Realize that the White and Blue Collar Workers are also Humans. They will know that every Human has the ability and the need to Control his own Process of Life.

They will see that Every Human has Desires, Emotions and Imagination.

They will become Aware (Consciouss) of the Fact that every Human is Able to Improve his Own Work Processes.