## Posts Tagged ‘lo shu’

### About the Vedic Square

Monday, December 19th, 2011

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

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

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

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

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

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

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

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

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

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

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

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

About the Digital Root

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

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

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

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

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

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

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

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

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

The Tetraktys of Pythagoras

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

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

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

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

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

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

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

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

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

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

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

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

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

Lo Shu Magic Square

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

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

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

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

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

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

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

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

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

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

About the Digital Root of the Golden Mean

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

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

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

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

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

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

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

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

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

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

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

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

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

The pattern of the Golden Mean copied from the Linked Website

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

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

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

The 24-cell also called the Hyperdiamond

About the Vedic Square

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

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

The Multiplication Table contains the Harmonics of the Numbers 1 to 9.

The Sistine Chapel is designed with the Vedic Square. Click on this picture to see a 3D version.

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

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

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

The Patterns of Islamic Art are created out of the Vedic Square

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

Vedic Square

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

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

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

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

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

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

The Rodin Modulus 9 Number Torus

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

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

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

Patterns in the Vedic Square

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

About Indian Vastu Science

The Vastu-Mandala

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

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

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

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

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

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

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

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

The Vastu Jain Symbol is a version of the Tetraktys

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

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

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

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

The Borobudur represents Mountain Meru, Pascal's Triangle.

About the Game of Chess

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

About the Multiplication Table of 9

About Genesis and the Vedic Square

About the Divina Comedia and the Vedic Square

About the Sistine Chapel and the Vedic Square

About the Vedic Square

About the Tetraktys and the Lo Shu

About the Lo Shu

About the Harmonics of the Universe

About Harmonics and Entrainment

About the number 24

About the Jitterbug of Buckminster Fuller

A Simulation of the Jitterbug Pattern (CUBIC WONDER)

About the Game of Chess

About Plato and the Sri Yantra

About the Rodin Torus

About Vastu Science and the Borobudur

### About the Sum of Things

Thursday, September 22nd, 2011

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

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

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

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

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

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

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

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

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

The Square is a combination of two Triangels. It is represented by the 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.

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

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 Heart Chakra

About the Sri Yantra

About the Lo Shu Magic Square and the Chinese Domino Game

About the Mirror Universe

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 Whole and Parts

Tuesday, December 23rd, 2008

The Whole of Reality is divided into many overlapping Parts. Most of the Humans look at Wholes and Parts (Smaller Wholes, Contexts) from a Static Perspective but the Whole is also a Dynamic Entity. The Parts are overlapping because many people don’t know how to define the right categories. Overlapping, confusing, part/whole relations are the sole cause of every conflict and war.

The Static and the Dynamic can be divided in two parts. In the first part of the Static we combine the Parts in a different way (Combine, Create). In the second part of the Static we define a Boundary around a part of the parts to protect the Territory (Control). In this case an Outside and an Inside is created.

The Dynamic can be divided in a Causal part (Time) and a Connected Part (Space). In the first part we create a Causal Network in the second part we create a Relationship Network (Social).

The Four (4) Parts of the Two (2) Parts of the Whole can be divided deeper and deeper. The Next division generates sixteen (16) Perspectives.

The big problem is to Name all the Division with a proper Term. Have a look at the Model Below.

 Static Whole Dynamic Whole Split/Merge Static Parts Static Dynamic Change Protect Space Time Create Control Connect Cause New Boundary Actors Effect Combinations Protect Time Whole Change Space Protect Time Space Change Whole Protect Control Plan Communicate Brainstorm Project Time Test Cause Invite Inspire Contract Space Dialogue Network Connect Meeting Integrate Change Design Start Meeting Connect Fuse Whole Think Sense Feel Imagine Reflect

It becomes much easier when the Names are substituted by Numbers. First we have to create a Number System. We use the same procedure.

We start with the Whole Numbers. They are used to Count. We could also use the Prime Numbers since they are the basic parts of the Whole Number System.

The Rational Numbers are the result of the operation of division. They can be represented by the harmonic series (1,1/2,1/3,1/4,..).

Irrational numbers (Pi, e, phi, sqrt(2)) capture the static relationships, the rules of the whole. They are not numbers because it is impossible to count with them. Irrational numbers can be constructed by combining the parts of the harmonic series;

Imaginary numbers capture the transitions (cyclic change) and transformations (change of form) of dynamic relationships.

 Whole Numbers Dynamic Whole Operation Split/Merge Primes Primes Operation Split/Merge Create Rules Connect Cause Imaginary Irrational Multiplication Addition Numbers Numbers Division Subtraction Irrational Whole Numbers Primes Imaginary Rational

In the next part we have a look at a very old (5000 BC!!) Universal Rule System of the Whole Numbers. This System is called the Lo Shu. The Lo Shu is a 3×3 Magic Square. Every straight line of three numbers adds up to the number 15. The Magic, Every Sum of Three Amounts to 15, is the General Rule that keeps the Opposites together. It is a very Simple Rule with spectacular consequences.

The 3×3 Magic Square shows a very old wisdom, “Everything Comes in Three“. Two Opposite Forces are always balanced by a third Force, the Mediator.

When we subtract every number of the Lo Shu (Left) with the number in the center (5) a new Magic Square appears (Right) with a zero sum.

This Magic Square shows interesting symmetries:

1. The numbers (8,2), (9,1), (4,6), (3,7) have a zero sum. They are Opposites if we use the number 0 as the Center of the Opposites of the Whole Numbers. In this way we are able to reduce the numbers to five (0,1,2,3,4).

2. The numbers (3,2) and (1,4) add up to 5. They combine in a “strange” 2×2 Magic Quadrant. If we transform this quadrant to a base 0 (by subtracting 1), the Magic 2×2 Quadrant can be transformed into a Binary Quadrant (11,01,10,00) again with interesting symmetries. The basic forces are brought back to two, Expansion and Contraction (Yang and Yin, 0 and 1) with the “0′ in the Middle.

There are many more symmetries to be found in the basic Magic Square of the Universe but it is impossible to explain them all in this small blog. One of the most important symmetries in the Lo Shu is a Cycle. It helps you to travel the many possible combinations on every level.

The Old Chinese Scientists used the Symmetries of the Lo Shu to create a cycle called the Sheng Cycle. This Cycle is the Cycle of the Seasons but also the Cycle of the Body (Acupuncture), the Cycle of the Context (Feng Shui) and the Cycle of Astrology.

Below is a small part of a huge correspondence table that makes it possible to reuse the practice of one field  of Science (Nature, The Seasons) in a completely different practice (Medicine, Psychology).

If You are Angry You are in the Negative State (Counter the Clock) of the Spring State of the Sheng Cycle (called the Insulting Cycle) and you will have problems with your Liver and Gallbladder.

Something, an Idea You cannot Express, wants to Come out to expand in the Summer-State.

Perhaps You Have to start a Design but do you have a Plan?

What is the Whole You are Looking at?

What are the Boundaries?

 4 9 2 -5 -1 4 -3 3 5 7 -5 -2 0 2 8 1 6 -5 3 -4 1 Lo Shu Lo Shu Step Name Season Feeding Controlling Process Positive Negative Number Number Organs Organs Emotion Emotion 3/-2 7/2 1 Wood Spring Liver Gallbladder Protect Love Anger 2/-3 8/3 2 Fire Summer Heart Small Intestine Time Joy Hate 5/0 0/5 3 Earth Indian Spleen Stomach Balance Fulfillment Obsession 1/-4 9/4 4 Metal Autumn Lungs Colon Space Hope Grief 4/-1 6/1 5 Water Winter Kidney Bladder Change Will Fear

Other scientists found many more relationships between the Lo Shu and Physics (Tony Smith), The I Tjing (Chris Lofting), The Tarot, Archetypes (Jung), Myths (Campbell), Historic Cycles (McKenna), Personality Types (MBTI, Enneagram), Left/Right Brain (Chris Lofting) and much more.

How to use all this knowledge

1. Always look at the Outside of the Boundary of the Context you want to analyze. If you cannot divide a Context in an Inside and an Outside you have done something wrong.

2. Always look at the Static AND the Dynamic part of the Context.

3. The Dynamic Part of the Context is related to a Cause/Effect-pattern (Time). Something is happening!

4. Look at the Social Dynamic Part of the Context. Entities, Objects, Roles, Humans are connecting the Time Lines. They are the Relations in your Static Model.

5. Always try to find New Combinations. If the Context is blocked it wants to move to another Time Line. Remove the Blockages!

6. If you want to analyze the Context one step deeper (16/25 perspectives, watch out, can you handle this?) try to make all the combinations that are possible. Use the Table in this Blog or create Your Own table (Fun). Read the PDF of Chris Lofting! Always use the Sheng Cycle!

7. Want to move much deeper? Use the Whole Numbers. Find Patterns (Irrational, Imaginary Numbers) and transform the patterns into Words. Use Fairy Tales, Myths, Archetypes, Music to explain the transformation.

8. Always Move Up in the Sky (Abstract, Fuse, Integrate) and Down to Earth (Implement, Try Out). Try to Unite what You have Divided. Keep an Overview. Reflect.

There is much more to say but I think you have enough food to digest.

Chris Lofting, How to Create Sound Categories using the I Tjing

Tony Smith, About The Lo Shu and Physics

### About the Chinese Domino Game and the Magic Square of Lo Shu

Tuesday, April 29th, 2008

Old Games always contain a Mystical meaning. They contain a Code. Over and over again the same Code is implemented in many games.  This blog is about the Chinese Domino Game.

The Old Chinese Masters made a distinction between the Square and the Circle. The Square was related to Human Creativity (Playing the Infinite Game of Life). The Circle was related to the Cycle and the Spiraling Spiral, the Fundamental Laws of the Universe.

The meeting of the Square, The Game,  and the Circle, Fate, generates Luck, Coincidence or Synchronicity.

The Chinese Domino Game Set is created by a throw of two six-sided dices. There are therefore 21 unique patterns. The 22nd pattern , the whole, closes the circle.

A tile is divided into two suits called Military and Civilian. The Civilian tiles are the Upper Triangle in the Matrix generated by the 36(6X6) throws of the dice. We find the same division in the Old version of Chess. The Civilian tiles are named and ranked according to their Level (Heaven, Earth, Human).

Each civilian tile has a Chinese name : The 6-6 is tin (天 heaven), 1-1 is dei (地 earth), 4-4 is yan (人 man), 1-3 is ngo (鵝 goose or 和 harmony), 5-5 is mui (梅 mei, flower).

The six symmetrical tiles (1-1, 2-2, ..) are the Basic Powers in the Universe (Earth, HuMan, Fire (Growth), Heaven, Center,..). The other Tiles are Connectors between the Powers and the Levels.

Chinese language is a Pictorial language. The Pictures are related to Sounds (morphemes). The oldest version of Chinese consisted of only Four Tones. The meaning of the language is highly Context-Dependent.

Numbers are also Context-Dependent. You have to know the modulus to understand what a number means. In the West we are accustomed to the use of 10. The number 13 means 10+3. In the “Old Days” other numbers where used.

When we move back to the Domino-Game we see that the base-number is 6. 1-3 (meaning Harmony) is really 6+3=9 in our notation based on 10.

A Magic Square is combination of numbers where the numbers in all rows, all columns, and both diagonals sum to the same constant. One of the oldest Magic Squares is the Lo Shu Square. It was given after the Great Deluge to the Mythical Emperor Lo Shu by a Magical Turtle. The Turtle is the Symbol of the Star System Orion.

 4 9 2 3 5 7 8 1 6

The Lo Shu Square is a Code. If you follow the “numbers” 1-9 a Pattern emerges called the (generating) Sheng Cycle. When the numbers are added the number 15 (3X5) appears. The number 15 represents Three Times the Center which again indicates that there are Three levels. The three levels enfold into 7 levels when we apply the movement, the Spin, of the Cycle (Left-Handed, Right Handed).

The Sheng Cycle

The Left-Handed cycle is called the Destructive Woe Cycle. The Generating Cycle is voided by the Destructing Cycle (-1 + 1 = 0). The number 7 is 2X3+1 (-3,-2,-1, 0, 1, 2, 3).

The division of the numbers 22 and 7 generates an approximation of the number pi, the Squaring of the Circle. It binds the Game of Life (Square) to the Laws of the Universe (Circle).

The 5 represents the Center and is called the Force of Life (Chi). Chi was called Ether in the West and Prana in India. Ether is called the Vacuum in Modern Physics.

The Magic Square is a representation of a Topological Structure called the Moebius Ring. The Ring is a Cyclic Structure without a Boundary. The Ring is the Basic Fractal pattern. The Universe is a Closed Self-Referencial structure, a Spiraling Spiral. The Ring enfolds in a Ring and the Enfolding is a Ring.

The Magic Square can be expanded to the 64 (8X8, the Checker Board) hexagrams of the I Tjing.

In the Game of Chess the Pawns are moved along the lines of The I Tjing. They create a Pattern just like the Game of Domino creates a pattern.

Both Games were played by Four Players, The Four Forces. The Games are a simulation of Life (or Earth or the Universe).

The Seven Heavens represented by the Tower of Babylon

The Magic Square is also the basic pattern behind Acupuncture, Feng Shui and Astrology. The Magic Square Forces the Forces to Cooperate. They have to stay within the Limits of 15, the Upwards Spiral.

To move back to the Center (The Void) they travel back by the Downward Spiral. The Up/Downward Spiral is the basic Fractal Pattern of the Universe.

Again we move back to the game of Domino.

The Domino Stones can be seen as Numbers with a base 6, Characters with a meaning (1-3 (=9, the end state) means Goose and Harmony), Sounds, Colors and connectors in the Magic Square. In this case there is a relationship to the Human Body, The Living Context (Feng Shui), The Planets and the Galaxy.

The 21 unique throws of the two six-sided dices can be rewritten in a combination of two Lo Shu 3×3 Magic Squares in which one square is the negative of the other and the zero is in the middle ((-1,-2,-3,0,1,2,3) x (1,2,3)). It represents a combination of a left- and righ hand turn of the Cheng Cycle.

The Old Masters believed in a self-referential Universe. The “Fractal” pattern repeates itself on every Level. At this moment Scientists start to believe the same.

Thoth and the Human represented by the Ape. The Ape uses the Eye of Horus (the third Eye) to look at Thoth

The Magic Square was given to mankind after the Great Deluce by a Mythical Entity, Half Man, Half Serpent. He came from an old civilization that was situated in MU. His Knowledge came from the Star System Orion (The Turtle).

The Egyptian name of this Magical Entity is Thoht, Tehuti or Djehuti. The Greek named him Hermes “Three Times Great” (Trismegistus) which relates him to the number 15 (3X5) of the Magical Square. Thoth was the keeper of the Secrets of Osiris (The Planet Sirius). Thoth was the Moon-God and is represented in old paintings as ibis-headed with the disc and crescent of the Moon. Hermus Trismegustus inspired the Magicians in the Middle Ages (John Dee) and new “mystical” groups like the Rosecrusians and the Free Masons.

Thoth came to Earth to teach mankind. He made all kinds of calculations about the Heavens, the Stars and the Earth. When he was finished he returned to Heaven (Orion?). When Earth is in a huge crisis he will come back. His knowledge and calculations were put into the Sacred Books of the Temple put unto 36535 scrolls that were enclosed in the Hall of Records. The Keys of Thoth were put into a Calendar. The Egyptian calendar was based on the Moon Cycle. They synchronized the Moon Cycle with the Cycle of Sirius. Sirius in the star system Orion rose every 365 days. The Egyptian Year started when Sirius appeared (June 21th).

The Playing Board of the Egyptian Game Mehen

Thoth came from Sirius (Al Shira, The Shining One). Interesting enough all the other Serpent-Kings came from the same Star System. All the Serpent Kings created Pyramids (even in China!) and the Pyramids are a “Simulator” of the Orion System.

Thoth will Return. We will be warned about the Rebirth of Thoth when something happens with Sirius. In a Hopi Myth Sirius is called the Blue Kachina. When the Blue Kachine drops its mask (or veal) the Fifth World will appear.

Let us move back to the Game of Domino.

Vladimir Pakhomov wrote a book called the Message to the Unborn. He used the Game of Domino to encrypt the Code behind the Code. The book contains more than 500 pages to explain his theory.

When he placed the Chinese Domino game in a Magic Square of Lo Shu and used the Orion System as the Central Code the code behind the code showed itself.

He named his book Message to the Unborn because he shows that our Ancestors from the Stars not only gave us a warning. They also gave us Tools to Save Mankind. The Tools are Magical Incantations (Tones and Sounds). Perhaps it is Very Easy to Save Mankind!

A website about the Lo Shu

About Mehen, the Spiral Game