About Mystical Number Theory and Pascal’s Triangle

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

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

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

About Mystical Number-Patterns

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A Hexagram is a Two Dimensional Cube

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

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

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

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

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

Star of David in The Israeli Art Genesis-2
The Fourth Day (Sun (4), Moon (5))

About the Triangular Numbers

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

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

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

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

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

The Sum of two Triangular Numbers is a Square

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

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

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

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

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

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

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

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

Star Numbers are a Combination of Two Triangular Numbers
The Square is a combination of two Triangels. It is represented by the Of Star of David, the Symbol of the Heart Chakra.
The Symbol of the Heart Chakra contains Two Triangles.

About Pascal’s Triangle

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

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

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

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

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

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

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

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

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

Triangle of Pascal

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

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

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

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

This pattern repeats itself all the time.

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

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

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

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

File:Pyramid of 35 spheres animation.gif
A Tetrahedral Number represents a 3D-version of the Tetraktys.

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

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

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

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

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

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

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

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

the Fibonacci Numbers as a Cube.
The StarTetrahedron, shows the Pattern behind the Sequence of Fibonacci.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Life is not only about Me and the Other.

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

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

LINKS

The Content of the Sepher Yesirah

About the Sepher Yesirah

About the Cube of Space

About the Tetractys

About the Cube of Space and Psychology

About the Sepher Yesirah and the I Tjing

A correspondence table of the Cube of Space

About Bereshit

About Genesis

About Patterns in the Bible

About Saturn

About the Trinity

About the Sri Yantra and Plato

About the Lo Shu and the I Tjing

All kind of strange relationships between Triangular Numbers

A website about Mystical Number Theory

About the Figurative Numbers

About Combining the Combinations

About the Golden Spiral and Plato

About the Logic of Creation

About Pascal’s Triangle and the Normal Distribution

A complete course in elementary Number Theory

About the Psychology of the Cube of Space

About the Tetraktys and the Zodiac

About the Process Theory of Paul Young

About the Theory of Dewey B. Larsson

Mysteries of the Equilateral Triangle

About Visual Patterns in Number Theory

About Pascal’s Triangle and Cell Division

About Saturn, the Son of the Sun

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

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

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

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

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

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

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

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

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

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

About the Number Seven

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

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

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

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

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

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

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

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

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

Why is Saturn the Son of the Sun?

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

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

Adam-Kadmon
The Demiurg with the Torus and the Zodiac

About  Kronos, Father Time

The Greek called Saturn Kronos, Father Time.

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

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

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

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

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

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

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

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

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

“If we then become children, would we thus enter the kingdom?” Jesus said unto them, “When ye make the two one, and when you make the inside like unto the outside and the outside like unto the inside, and that which is above like unto that which is below, and when ye make the male and the female one and the same, so that the male no longer be male nor the female female; and when ye fashion eyes in place of an eye, and a hand in place of a hand, and a foot in place of a foot, and a likeness in place of a likeness; then will ye enter into the kingdom.” (Gospel of Thomas, Logion 22).

LINKS

About the Sum of Things

About the Cube of Space

About the Myth of Saturn

About the Mother Goddess

About the Dance of Shiva

About Saturn and the Sun

About the Seven Heavens

About the Great Flood

About the Golden Age of Saturn

About the Torus and the Vortex

About Time

About the Twisted Universe

About Alchemy

About the Polar Myth

About the Sum of Things

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

lo-shu-color

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Seal of Saturn or the Dance of Yu

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

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

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

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

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

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

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

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

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

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

Lo Shu Torus

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

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

4

9

2

-5

-1

4

-3

3

5

7

-5

-2

0

2

8

1

6

-5

3

-4

1

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

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

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

About the Sum of Things

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

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

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

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

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

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

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

LINKS

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

About the I Tjing

The Calculations  behind the Number of Things

The Relationship between the Lo Shu and the I Tjing

About the Lo Shu Torus

About Saturn, the Son of the Sun

About the Trickster

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

The Sistine Chapel (Rome) and the Seal of Saturn

About the Relationship between the Lo Shu and Music

About the History of the Lo Shu

About the Wheel of Eternal Order and the Wheel of Time

About the Relationship between the Lo Shu and Chinese Alchemy

About the Great Flood

About the Orion Myth

About Plato, Pythagoras and the Lo Shu

About the Nothingness

About the Trinity

About the Heart Chakra

About the Sri Yantra

About the Lo Shu Magic Square and the Chinese Domino Game

About the Mirror Universe

About Acupuncture

About Tit for Tat

About the Prisoners Dilemma

About the Bronze Mean

About the Sheng Cycle

Everything You want to Know about Sacred Geometry

About the Influence of the Lo Shu on Recent Art

The Lo Shu Square with Imaginary Numbers

About Combining the Combinations

 

steam_engine

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

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

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

About Thermodynamics

Thermodynamics is the Science of the Transfer of Energy.

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

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

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

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

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

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

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

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

About the History of Innovation

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

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

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

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

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

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

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

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

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

About Incremental and Disruptive Industrial Innovation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

About Creativity

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

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

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

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

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

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

About Managed Creativity

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

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

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

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

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

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

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

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

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

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

About Combining the Combinations

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

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

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

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

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

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

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

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

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

Is there an End to Human Innovation?

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

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

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

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

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

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

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

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

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

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

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

What to Do?

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

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

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

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

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

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

You now have entered the Adjacent Possible.

LINKS

Why Neural Networks look like the Universe

About Creativity and High Pressure

About Self-Organized Criticallity

About Self-Organized Criticallity and Innovation

About Complexity Theory and Innovation

About Loosely Coupled Systems

About Boundaries

About Triz

Stuart Kaufmann about Radical Emergence

Advanced Systematic Inventive
Thinking

About ASIT (Advanced Systematic Inventive Thinking)

How Nature Plays

About Constructal Law

About the Origin of Good Ideas

About the Adjecent Possible

About the Law of Kleiber

Why Cities are Organisms

About the Beginning of the Universe

About  the End of the Universe

About the Law of KLeiber

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.

Lung

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.

Alveoli
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.

Villi
Villi

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.

Liver
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.

Nephron
Nephron

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
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).

Bacterium
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 be serviced 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.

LINKS

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 Entrainment

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

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

birds in sync
Birds in Sync

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

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

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

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

About Copying

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

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

About Communication

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

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

conversation1

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

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

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

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

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

About Synchronization

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

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

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

synchronization

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

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

About the Circadian Clock

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

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

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

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

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

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

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

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

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

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

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

pineal
Pineal Gland

About the Pineal Gland

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

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

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

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

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

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

About the Heart

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

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

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

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

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

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

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

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

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

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

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

Spiral Waves in the Heart

Chemical Spiral Waves
Chemical Spiral Waves

About Cymatics

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

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

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

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

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

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

The Whirpool Galaxy
The Whirpool Galaxy

About the Creation of the Universe

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

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

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

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

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

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

Quasi Crystals
Quasi Crystals

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

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

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

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

LINKS

How bacteria entrain

Steven Strogatz: About Coupled Oscillators and Biology

A lecture about Coupled Oscillators

A presentation about Coupled Oscillators

About Engagement

About Standing Waves

About Hypnosis

About the Electro Magnetic Field in the Body

About the Cardiac Pacemaker Cells

About Cymatics

About the Heart Chakra

About Stress and the Action Potential

About the Zero Point Field

About the Metallic Mean

About the Hall of Mirrors

About Good Vibrations

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

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

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

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

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

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

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

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

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

About the Svara

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

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

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

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

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

About the Aether

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

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

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

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

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

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

What is the Same?

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

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

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

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

congruent2
Two Congruent Triangels

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

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

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

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

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

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

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

Mug_and_Torus_morph
Transforming a Mug into a Torus

About the Great Breath

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

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

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

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

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

Twisted Topological Structures
Twisted Topological Structures that are Closed in Itself

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

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

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

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

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

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

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

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

About the  Number Five

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

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

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

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

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

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

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

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

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

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

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

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

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

About the Magic Square of Lo Shu

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

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

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

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

The transformed Magic Square shows an interesting symmetry.

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

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

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

About the Sheng Cycle

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

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

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

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

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

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

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

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

The Sheng Cycle
The Sheng Cycle

About Harmonics

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

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

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

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

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

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

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

About the Cyclic Universe of Paul Steinhardt

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

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

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

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

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

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

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

About Ancient Spirituality and Modern Science

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

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

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

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

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

About the Good, the Bad and the Nothing

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

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

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

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

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

The Good gives us Joy, Pleasure and Exitement.

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

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

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

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

LINKS

About the Law of Resonance

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

Why Matter is a Standing Wave

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

About the Harmonic Theory of Ray Tomes

About the Experiments of Michelson and Morley

Why God is a Topologist

About Pauli and Quantum Mechanics

About the Cyclic Universe

About the Lo Shu Square

About the Trinity

About Infinity

About the Empty Set