Posts Tagged ‘Topology’

About Good Vibrations

Sunday, August 1st, 2010

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)


A Moving Standing Wave


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.


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.


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.


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

About the Void

Monday, December 1st, 2008

Infinity is a very strange concept. It is a concept we, the Humans, are unable to imagine because our Reality is Finite. Infinity is created by a division by Zero. Multiplying Zero by Infinity could be Any Number (A/∞=0, 0*∞=A). Infinity-times-Zero is an unlimited resource, the Holy Grail.

The concept 0 is not (¬) “nothing”, the empty set (Ø). The number 0 is the result of subtracting a number by Itself (A-A=0). The number 0 is the symbol of, the Middle, Balance and the Absolute Truth (A=A, I AM what I AM).

Strangely enough the name “zero” given to the symbol of the concept “0″ comes from the Arabic صفر, şafira, “it was empty” and the Sanskrit śūnya “void” or “empty”. The 0 was empty, Ø, before it was created.

The symbol of the number Zero looks like an Egg. According to many creation myths the beginning of this world non-being, one point, Ø, expanded into an egg, 0 , that was splitted until infinity (-1, 0, +1).

When we use Topology we see that Infinity is “a state we will never reach” in a linear perspective. When we create a continuous mapping of the Circle to a Line extending from “negative infinity” to “positive infinity” the line of Infinity is the line that lies parallel to the original line. Negative and positive infinity close in one “impossible” point that can easily be reached by moving through the cycle but cannot be reached by a Line.

The tragic of the Circle is that we always come back at the same point:

We shall not cease from exploration

And the end of all our exploring

Will be to arrive where we started

And know it for the first time.

(T.S. Eliot).

To learn or to get new experiences we have to jump out of the cycle. In this case the circle becomes a spiral and we move from one level of circulating to a new level of circulating.

The big problem of the spiral is that we never will reach the end. We will never find what we are looking for. We keep on moving.

But somewhere on the circle and the spiral lies the “magical zero”, the connection to the void, the gate, the primal source, our final destiny.

The great path has no gates,

Yet thousands of roads enter it.

When one passes through this gateless gate,

He walks freely between heaven and hell


The empty set, Ø, is created by paradox, I AM AND I AM NOT.

To Jump out of the Cycle and the Spiral we have to find the gateless gate.

I am fluctuating between NO(0)-THING and The ONE (1)

I am a Wave.

I am the Void, Ø, AND I am the Egg of Creation (0).

I am a Paradoxal Paradox.

I move with the River to Join the Sea(∞).

Why God is a Topologist

Saturday, November 29th, 2008

god_geometry_bigSometimes I am getting very frustrated when I read spiritual books. I am getting frustrated because those books are a very complicated mixture of many other books that are also very complicated mixtures of other books.

The most complicated spiritual books are the books that use mathematical or physical theories to proof they are Right. The main reason is of course that mathematics and physics is complicated stuff to understand.

Mathematics contains the essence of Physics. You have to understand a little bit of mathematics to understand elementary Physics. The essence of Mathematics is Geometry. When you understand Geometry the rest of mathematics is just calculation (Algebra).

Geometry started as a very practical science concerned with navigation in space and the measurement of all kinds of forms. Soon the old scientists discovered interesting and unexplainable patterns. They discovered a hidden, sacred, structure behind reality and started to find ways to proof their intuiton was right.

It was not for nothing that Einstein believed God was a Geometer. Much earlier the Mystic School of Pythagoras tried to find the Sacred Geometry behind the Numbers to understand the Whole. At this moment Geometry has advanced a lot in relation to the old days of Pythagoras and even Einstein. Geometry is now called Topology, the Science of Spaces. In terms of Einstein, God was a Topologist.

To proof the theorems of Geometry the concept of congruency was used. Two figures are congruent if they have the same shape and size, but are in different positions or in more difficult language,  if they can be transformed by a combination of translation, rotation and reflection. When two figures are congruent they are “the same” and when things are “the same” you are able to prove theorems.

During the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. In the Renaissance the perspective, looking from a different angle, was added as a “the sameness”. Circles and ellipses became part of one class.

A “the sameness” has a lot to do with Identities and Wholes. When your view on “the sameness” changes you are able to identify a different whole. The new concept of the Perspective made is possible to “see” the Sun as a persistent object instead of an ever changing object.  

During the Renaissance the Sun became the Center of the Whole. The highly confusing worldview of the Middle Ages where something was the same when it really was the same object in reality slowly faded away. The external world became the world of the Eye, the microscope and the telescope.

Topology changed this view dramatically. In topology, any continuous change which can be continuously undone is allowed. So a circle is the same as a triangle or a square, because you just pull on parts of the circle to make corners and then straighten the sides, to change a circle into a square.

In the View of Topology the Sun is nothing but a small part of an ever expanding and contracting Universe. Topology transformed the external World of the Eye into the Internal World of Moving Water, Waves and the Emotions, the Felt Sense.  Topology is the Science that prepares the Way for the Water Bearer, Aquarius.

Topology is just like Geometry not only the science of space. It is also the science of transformation and transformation is also the essence of spirituality.

The major issue of Topology is the Contraction and Expansion of forms and again the essence of spiritual transformation is the Breath of God, the Holy Spirit. Topology has also a lot to do with Harmony or Symmetry and again Realizing Harmony is one of the major issues in Spirituality.

The interesting part of Topology is that you are able to do research on a huge scientific mathematical domain by exploring just one structure which is a representative of all the other structures.


The first object of interest are the Circle and The Line. It is not possible to transform a Circle into a Line without cutting the Cycle in one Point, Infinity.

In a circular, moving world, Infinity is non existent or every Point of the Circle corresponds with Infinity. 

This is an  interesting insight because  almost nobody doubts about the fact that the space we live is a Circular Rotating Space. In the World of the Circle  The very Small and the very Big are the Same.



According to the Physicists our Space is a much stranger Space than a Circular Space.

Our Universe is highly dimensional because the complicated symmetry of our Universe simply does not fit in a lower dimensional space.

The most symmetric object, strangely called the Monster, uses 196,884 dimensions.

We, the Humans, travel a small part of the Monster, because we are not able to see enough perspectives. A perspective is a dimension.

One of the most interesting subjects is Self-Reference. The most simple Self-Referential structure is a Circle.

Topology contains very special Self-Referencial Structures like the Moebius Ring and the Klein-Bottle. The Moebius Ring is a Space without an Outside. It is closed in Its Self. You always travel the same surface.

klein bottle

A Klein Bottle is even stranger. Its surface is Closed in Itself but it has no Inside and no Outside. It simply IS. 

A Moebius Ring exists in our 3-dimensional space.

A Klein Bottle needs 4-dimensional space. The Klein Bottle has a lot in common with a very old concept, the Ouroburos, the Snake who eats Himself. The Snake is a symbol for the Kundalini, the Force of Enlightment.

knotMore complicated topological structures are Knots and to give you a quick insight, the Universe is a Web that was never Woven, a beautiful Veil that is difficult to See when you are travelling a small part of it.

I know this small blog will not help to get an insight but I assure you that when you start to explore Topology You will encounter new Concepts (or Paradigms) that will surprise You.

Topology will  give You a still small but highly extended perspective on the Creation of the One that expanded in so many Harmonic structures.


The History of Topology

About our Limited Perspective and the Limits of Reasoning

About the Topology of Art, a Short Introduction to Bahktin

About Free Will, Time and the Monster

About the Moebius Ring and the Klein Bottle in Philosophy

About Self-Reference in Physics

About Knots in Philosophy

About the Klein Bottle