## Posts Tagged ‘fibonacci series’

### 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

### How we Walked Around for Thousands of Years with Our Eyes Blinded

Thursday, April 24th, 2008

Pi or π is one of the most important mathematical constants. It represents the ratio of any circle to its diameter. The quest for the value of π is very old.

The oldest way to determine the value of π is to inscribe a circle within a regular polygon.

Archimedes of Syracuse (287-212 BCE) determinated that the value π was between 3 + 1/7 (22/7) and 3 + 10/71. He started with a hexagon and worked his way up to a polygon with 96 sides.

The numbers 3, 22 and 7 play an important role in the calculations of the old mathematicians. They found a relationship with music, colors and of course the planets.

The 3 stands for the “Law of Balance“, the Trinity. Two forces (Yin/Yang, Male/Female) expand and compress the center (-1, 0, 1). Everything expands and compresses.

The number 22 symbolized the circle and the cycle. This is reflected in the twenty-two letters in the cyclic Hebrew alphabet or the twenty-two cards in the cyclic Major Arcana of the Tarot.

There are 7 cycles and they are according to the law of balance divided in expansions and compressions on a “higher and lower level”.

(Mirror (-4),-1(-3(-1, 0, +1), -2(-1, 0, +1), -1(-1, 0, +1)), 0, +1(1(-1, 0, +1), 2(-1, 0, +1), 3(-1, 0, +1)), Mirror (+4)).

The 0 or the Void is the Mirror of the Mirror, the Self-Awareness, the Area, the Boundary, where the Cycle “Bounches Back“.

The relationship with music can be found when you have a look at the “Tones“. There are 7 “intervals” in an Octave (8) and 22 is the number of notes in three consecutive octaves.

The octaves contain a “deeper” pattern. Other numbers appear.

4 is the number of base-notes (Do), in three consecutive octaves. 8 is the number of fundamental notes in a single octave. The 3 octaves are each sub-divisible into 3 octaves apiece, giving an inward formula of 9 octaves, or 64 notes. So 8 is the constant and 64 is the square of it.

The deeper pattern can be understood if we look at a well-known measure, the Golden Measure. This measure can be written as F(n) = F(n-1) + F(n+1). As you see it shows the fundamental Law of Balance again.

The Golden Mean is called the Fibonacci series. The Fibonacci series can be seen in almost every part of Nature. The numbers of Fibonacci can be put into a spiral pattern (the logarithmic spiral).

Is there a Pattern that Explains Everything?

The most important concept to understand is the principle of Self-Reference. Self-reference can be seen in a Fractal but is also visible in the formula of the Golden Mean.

If “Everything is Fractal” we are able to explain everything with just two “laws”, the Pattern of the Fractal and the Enfolding of the fractal-patterns on different Scales. The Enfolding of the Fractal has to behave like the Fractal Pattern. It this way we have reached perfect Symmetry.

At this moment many scientists are looking for the “Basic Fractal Pattern“, the Grail of Science.

In essence they are rediscovering the knowledge of the “Old Mathematicians”. Many of them are aware of this. Old examples are David Bohm (“the Implicate Order”) and of course Einstein (“God is a Geometer”).

New examples are Luciano Pietronero and Laurent Nottale. They use the Logaritmic Spiral to explain the Fractal Structure behind Nature.

In February 1971 NASA (Pioneer 10 and 11) send a message to other civilizations in the Galaxy. The message was engraved on a gold anodized aluminum plague. Scientist tried to envision how they could show “What we are” and “Where we are”. They used fundamental laws to show a correlation between US and the Universe.

At this moment scientists are encrypting the message of old civilizations. More and more they discover that “The Old Ones” knew more about the fundamental laws than we know at this moment.

The idea to send a message to civilizations in the Time/Space-continuum is also not new. It was one of the major activities of the people that knew that their civilization would end by a cosmic catastrophe. They were the inhabitants of Mu and Atlantis.

They build huge structures like the Pyramids and engraved their message on Mother Earth. For thousands of years we just walked around and were unable to see them. Now finally just four years before the next catastrophe we are able to understand a little bit of what they wanted to tell us.

All of their knowledge was Encrypted and Stored in thousands of artifacts and stories. They were warning us but they also gave us entrance to their tools to survive, the Tools of Creation. They are hidden in the “Music of the Spheres” and can be translated into powerful magical incantations.

Those incantations can only be used by Magicians who have Cleaned themselves.

They have to be “Pure”, just like the White Light of the ONE hat emanates out of the SEVEN Colors of the Rainbow that are constructed out of THREE Basic Colors.