Posts Tagged ‘duality’

About Perspective

Thursday, February 2nd, 2012
File:Reconstruction of the temple of Jerusalem.jpg

Medieval Perspective

Introduction

When we Look with our Eyes and not with our Mind we can See that Space looks very different from what we Think it is. In Our Space Parallel Lines meet at Infinity.

Around 1400 during the Renaissance Painters started to look at Space with their own Eyes and discovered the Rules of Perspective Drawing.

Between 1600-1800 Perspective Theory changed from a Theory of Art to a Theory of Mathematics called Projective Geometry.

It took 400 Years before a few Mathematicians realized that Projective Geometry was the Foundation of Mathematics and it took another 100 years before Projective Geometry started to influence Physics.

In 1908 Hermann Minkowski discovered that Einstein’s Theory of Special Relativity could be analysed using Projective Geometry. Minkowski created a 4D Space-Time Metric Geometry in which he added one Time Dimension.

Many experiments now show that 4D-Space-Time  is not sufficient to incorporate what Time Really is.

The essence of Our Universe is Movement, Expanding Space,  and Movement = Space/Time (Space Divided By Time).

Both Time and Space are 3-Dimensional and represent a Different,  Reciprocal, Complementary (Dual), View on Movement.

We can move independently in Time OR Space and in Time AND Space (The Chronotope).

The Future is Expanding Space with Infinite Potential.

Time moves behind Space and Scales Space.

About Perspective Drawing

A Mathematical Theory of Perspective Drawing could only be developed when the Renaissance freed painters to depict Nature in a way closer to what they Observed.

In the Middle Ages Social Status was very important. Important People or Buildings were always emphasized.

In the Renaissance the Artists started to look with their own Eyes and Created Pictures where the Viewer looked through the Eyes of the Painter.

The Florentine architect Filippo Brunelleschi (1337-1446) studied Greek Geometry, developed a theory of perspective and undertook painting just to apply his geometry.

The first treatise, Della pittura (1435) by Leone Battista Alberti (1404-72) furnished most of the rules.

Alberti regarded mathematics as the common ground of Art and the Sciences. “To make clear my exposition in writing this brief commentary on painting,” Alberti began his treatise Della pittura, “I will take first from the mathematicians those things which my subject is concerned”.

Alberti stressed that “all steps of learning should be sought from nature“. The ultimate aim of an artist is to imitate nature.

Perspective Machine designed by Albrecht Durer

Alberti did not mean that artists should imitate nature objectively, as it is, but the artist should be especially attentive to beauty, “for in painting beauty is as pleasing as it is necessary“.

The work of art is according to Alberti so constructed that it is impossible to take anything away from it or add anything to it, without impairing the beauty of the whole.

Beauty was for Alberti “the harmony of all parts in relation to one another,” and subsequently “this concord is realized in a particular number, proportion, and arrangement demanded by harmony“.

Alberti’s thoughts on harmony were not new – they could be traced back to Pythagoras – but he set them in a fresh context, which well fit in with the contemporary Aesthetic Discourse.

IMAGE: Leonardo's perspectograph

The Perspectograph of Leonardo Da Vinci

One of the earliest Artists to produce a book on how to draw in perspective was Albrecht Dürer. As well as discussing geometric methods, he also illustrated his book with a set of woodcuts showing practical tools for accurate perspective drawing. Other Artists like Leonardo Da Vinci developed comparable tools.

About Projective Geometry

Projective Geometry formalizes one of the Central Principles of Perspective Drawing and of Human Perception: Parallel Lines Meet at Infinity.

In Euclidean geometry, constructions are made with Ruler (Line) and Compass (Circle). Projective Geometry only require a Ruler.

In Projective Geometry one Never Measures Any Thing, instead, one Relates one Set of Points to another by a Line.

Two projections of the same object.

Different Points of View

Alberti was the first to ask what two pictures have in common if two drawing screens are interposed between the viewer and the object, and the object is projected onto both resulting in two different pictures of the same scene.

The basic idea behind Linear Perspective is simple: in every painting an artist creates a “floor” or area of the painting where the figures and/or objects will be placed. The floor ends at a horizon line, and the horizon line has a Vanishing Point or Point of Convergence on it.

The artist then draws parallel lines radiating from the vanishing point outward. Images closest to the vanishing point should appear smaller and closer together, and images farthest from the vanishing point should appear larger and farther apart, giving the impression of depth and space in the painting.

Pappus of Alexandria ( 290 – 350), one of the last great Greek mathematicians of Antiquity, proved that that given one set of points A, B, C on a line, and another set of points a, b, c on another line, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are also on a Line. This line originates at the Vanishing Point.

Pappus' Theorem

Later Desargues (1591-1661) proved Pappus Theorem for Triangels. He proved that the three vertices of one triangle a, b, and c, and those of the other A, B, and C meet in a third point, and that these three points all lie on a common line called the Axis of Perspectivity.

Desargues' theorem

Later Blaise Pascal (1623-1662) proved Pappus Theorem for Conics (Circles, Parabola, Hyperbola) in his  ”Essay on Conics” (1640) when he was 16 years of Age.

Pascals Theorem

About the Four Points of the Cross-Ratio

Finally 400 years later in 1803 Lazare Carnot found the answer to the Question of Leone Battista Alberti.

In his book “Géométrie de Position” he proved that the so called “Cross-Ratio” is always preserved in a Projection with One Point of View.

The Cross-Ratio

The Cross-Ratio is the Ratio of the Ratio of the Four Points A,B,C,D lying on a Line that intersects the Four Lines defined by a,b,c,d that orginate at the Vanishing Point O.  Carnot  proved that (AB)(CD)/(AC)(BD) = (A′B′)(C′D′)/(A′C′)(B′D′).

The Cross Ratio is not only the Cross-Ratio of the Four Points A,B,C,D. It is also the Cross-Ratio of the Four Lines  and the Three Angles that originate out of the Vanishing Point. In this case (AB)(CD)/(AC)(BD)=Sin(AB) x Sin(CD)/Sin (AC) x Sin (BD).

This principle is called Duality. In 2D-Projective Geometry Connected Points and Lines, called an Incidence, are interchangeable.

There is a corresponding Duality in three-dimensional Projective Geometry between Points and Planes. Here, the line is its own Duality, because it is determined by either two points or two planes.

ratios.jpg

The Cross-Ratio k is dependent on the Order of the Four Points. It converges to 0 and infinity when k=1 and to -1/2 and 2 when k= -1.

Two examples: 2D: Two distinct Points determine a unique Line and two distinct Lines determine a unique Point. 3-D:  Three distinct Points not all on the same Line determine a unique Plane and three distinct Planes not all containing the same Line determine (meet in) a unique Point.

The 24 Permutations of A,B,C and D produce 6 possible values of the Cross-Ratio, depending on the order in which the points are given. If k = 1, the other Cross-Ratio’s are 0 and infinity. This happens when point A = point D. In this case the Geometric Entity is an Equilateral Triangle.

If k = -1, the other Cross-Ratio’s are -1/2 and 2. This is called a Harmonic Cross-Ratio. This happens when the Internal Ratio of AC determinated by B is Equal to the External Ratio of AC determinated by D. When k=-1/2 and 2 the Geometric Entity is a Square.

If the Four Points of the Cross-Ratio are on a Line or a Circle, then the Cross Ratio is a Real Number, otherwise the Cross-Ratio is a Complex Number.

Ruler (Space) and Compass (Time): The Tools of the Geometer

About the Four Layers of Geometry and the Four Points of the Cross-Ratio

In 1872 Felix Klein, published a new Mathematical Research Program called the Erlangen Program under the title Vergleichende Betrachtungen über neuere geometrische Forschungen.

In this program Projective Geometry was emphasized as the Unifying Frame for all other Geometries.

Although lines in the Projective Plane meet in one point of Infinity Klein argued that there could be two points of Infinity if the Projective Plane was a Surface Closed in Itself.

When we look at the Origin of Projective Geometry, the Artist painting A Sphere, Earth, on a Flat Surface, it is not difficult to realize that this Closed Surface is a Sphere.

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Geometry is now divided into Four  Layers. Each Layer adds a set of Assumptions that creates certain Invariants for that Layer.

An invariant is a property of a configuration of Geometric Entities that is not altered by any transformation belonging to the specific layer.

A transformation is an operation applied to a Geometric Entity. The most common transformations are Translation, Rotation and their Combinations (Reflection).

What we will see is that the Four Points of the Cross-Ratio are highly related to the Four Layers. In Every Higher Layer One Point of the Cross-Ratio is moved to the Internal Landscape, the Mind, of the Observer. This principle is called “As Within so Without“.

The First and most fundamental Layer is the Layer of Projective Geometry. This is the Layer of Human Perception and is invariant under the Cross-Ratio also called a Moebius Transformation.

The Second Layer is called Affine Geometry. In this layer Parallel Lines are preserved and the Assumption of a Plane at Infinity, the Horizon,  is created.  This Plane generates Parallel and Orthogonal Relationships between Geometric Entities by placing One of the Four Points of the Cross-Ratio in the Plane at Infinity.

Affine Geometry is Euclidean Geometry with congruence (something is the same when Shape and Size are the Same) and a metric (a definition of a Distance) left out. An affine transformation preserves straight lines and ratios of distances between points lying on a straight line.

This the layer of  the Emotions, “the harmony of all parts in affinity to one another” of  Leone Batista Alberti.  In Affine Geometry the Frame of Reference of the Painter, the Floor,  is created. On this Floor,  the Horizon, the Plane at Infinity is drawn.  From the Point of View of the Observer, it is not possible  to Judge Distance or the-Sameness because a given Visual Object may be Large and Far away or Small and Close.

In Eucludian Geometry A Ruler contains a Fixed Scale

The Third Layer, Metric Geometry, adds the concept of Distance (Metric, Scale) to the Affine Layer. A Distance is a relation between Two Points of the Cross-Ratio. This is the Layer of the Painter, Creator, Observer, who creates his own Distance to the Distances he is Painting in the External Frame he is looking at.

Since Projective Space is the Space of Actual Perception, the true function of Metric Space is the Coordination of Various Perspectives. This is illustrated in Perspective Drawing, in which there are always Two Perspectives being Coordinated—the Vanishing Point and a Point just behind the Eyes of the Observer.  Each of these is an instance of the One Point at Infinity.

alchemy

The Expectation looks through a Small Hole.

The last, Fourth,  Layer is the layer of Euclidian Geometry. In Euclidean Geometry Distance is Fixed (not Relative) and Scaled to a Unity (Meters). This leaves us with just One Point of the Cross-Ratio, the Unity, the One.

Between  1926 and  his death in 1983 Alfred Tarski worked on the Axiomatization of Euclidean Geometry. In Tarski’s system there is only one type of Object: the One, The Point.

There are just two Geometrical notions between Points: the Ternary Relation of “in-Betweenness” and the Quaternary Relation of “Equidistance” or Congruence.  Betweenness captures the Affine aspect of Euclidean Geometry; Equidistance/Congruence, its Metric aspect.

This is the Layer of the Human Expectation who has not Distanced Itself and is Looking Outside Through a Small Hole at the Future. The Expectation considers the Future as an Extension of the Past (Memory).

In Euclidian Geometry we have to Move Outside to the Objects to Measure their Distance and the Sameness with a Pre-Defined Unity.

If we don’t move to the Object we will measure an Illusion.

About Space measured by Time and Space measured by Space

The Ancient Sumerians  knew that the Length of one side of a Hexagon is the same length as is the Radius of the Circle that circumscribes this Hexagon (See Pascals Theorem).

They also knew that the Stars of the Constellations of the Zodiac shift Counterclockwise, at the rate of 72 years/degree, because of the Precession of the Earth’s axis. One Wobble takes 25.920 years.

The length of one side of the Earth Hexagon is therefore the Distance traveled by the Constellations of the Zodiac along the horizon during 25.920/6=4,320 years.

They then subdivided this distance by 7,200  which produced the Royal Mile that was subdivided into 1,760 Royal Cubits.

Before 3.117 BC the complete Earth was covered with a uniform Geodesic System that was based on the Rotation and Precession of the Constellations of the Zodiac. This System was implemented in the Megaliths.

At that Time Space was measured by Time.

The Physical System of the Megaliths was destroyed by the Great Flood of 3.117 BC but the Metric System survived thousands of years until the French Revolution.

On the 8th of May, 1790, Charles Maurice de Talleyrand at the end of the French Revolution, proposed before the National Assembly in Paris a Change to a Decimal Measurement System.

The Academy of Science recommended that the new definition for a Meter be equal to 1/10,000,000 of the distance between the North Pole and the Equator, and this was accepted by the National Assembly in 1791.

From that Time on Space was measured by Space.

Why the Future contains Infinite Possibilities

A Painter or a Human always looks Forwards in Space. If there are Parallel Lines visible they all Converge to a Vanishing Point at The  Horizon. The Horizon is a Parallel Line at Infinity.

We all know that the Parallel Line of the Horizon is caused by the fact that the Earth is a Moving Sphere. This Moving Sphere moves around other Spheres that move around other Spheres.

The Rotation of the Spheres in Space is used as a Clock. Every time when the Cycle of the Spheres repeats itself we add one unit to a standard Time-Measure. One Sun Cycle is named a Year. One Cycle of the Precession takes 25,920 Years.

We Measure our Time by the Cyclic Movement of Objects in Space. The Cyclic Movements caused by the Rotations of Objects around Objects (around Objects) is really a Rotating Rotating Rotation, a Spiraling Spiral.

We don’t live in the Sphere but we live and Move on the Surface of a  Moving Sphere. That is why our Geometry is an Elliptic Geometry (or Projective Geometry).

Euclides and Pythagoras were aware of Projective Geometry (See also Pappus) but the Scientists of the Enlightenmentstarted to interpret their Theory with a Different Eye. They saw Numbers in a completely different way the Greek did.

The Scientist disconnected Number from Magnitude (Form) and created an Abstract Static Number Theory and an Abstract  Static Theory of Physics. The Movement of our Universe, the Ether, came to a stilstand.

The Theory of Perspective Drawing, based on our Real Perception of Reality, is the same theory that generated Projective Geometry. We are now back to Normal again.

In the blog about Geometric Algebra I wrote about a very Independent Thinker called Dewey B. Larson.

He reinvented Physics and Projective Geometry in his own way, Calculated all the well known Physical Constants and based his Theory on a simple well know Assumption that Space and Time are Reciprocal (A Ratio of Ratio’s , the Cross-Ratio) because Velocity= dS(pace)/dT(ime).

Moving Movement is the Essence of our Reality.

What Larson calls “Motion” is the Ether Wind (or the Higgs Field) the Velocity which was measured in the North-South (Z) direction at 208 km/s in 1933 by Dayton C. Miller.

Einstein believed the results of the Michelson-Morley Experiments in 1887 that “proved” that the Moving Ether was non-existent. Now we know that the experiments were wrong.  Einstein also did not believe that Space was Expanding. At this moment the Expanding Universe is confirmed by many observations.

When Space Expands,  Time Compresses and fills up the Space to Keep Balance. Time Scales Space.

Space moves to Infinity. Time Moves to the Inverse of Infinity, Zero. Space is measured by the Linear Visible Scalar Number-System. Time is Measured with the Rotational Invisible Imaginary Number System.

Expanding Space is Linear Motion. Time is the Spiraling Motion of the Vortex.

golden mean spiral2

The Spiraling Spiral of Time

Space is Yang and Time is Yin. Yin is feminine, Curved, Rotational, smooth or cold. Yang is masculine, Straight, Linear, rough or hot.

Space and Time are Complementary Duals that Move Around the Void.

If we look at the Human Perspective we now are able to understand what Time and Space Really are.

When we Look Forward we Experience Space. Time is always Behind our Back.

Human Senses and Conventional, Scientific Equipment can only Look Forward and therefore Measure Space (Distance) and the Change of Space (Velocity, Acceleration).

This is a Limitation of our Physical Sensory System, which evolved to measure Space, Scaled by Time, to produce what we Perceive as Causality–a Linear Ordering of Events.

Without the Cause-and-Effect System, the Sensory World of Space would just become Chaos.

Time, History, is Always Behind Us and Space, The Future, The Adjacent Possible, with Infinite Possibilities, is Always in Front of Us.

Let’s Move.

LINKS

About Pythagoras and Heliopolis (Egypt)

About Pythagoras

Paul Dirac: About Physics and Projective Geometry

About the Middle Ages

About Expanding Space and Not-Euclidian Geometry

About the Renaissance

About Resistance and Mass

About the Mathematics of Perspective

About the Ether

About Clean Space

About Projective Geometry

Pictures of the Projective Plane

About Geometric Algebra

About As Within, So Without

About the Reciprocal Theory of Dewey B. Larson

A Video about Mobius Transformations

About Projective Geometry and our Senses

About Projective Geometry and Geometric Algebra

About the Cube of Space

About Time and Paranormal Experiences

About Geometry

A Textbook about Metric Geometry

About the Four Points of View

About the Void

Why the Future is Open Space

About Alchemy and the Klein Bottle

About the Human Sensory System

Stuart Kaufmann: About the Adjacent Possible

About Old Fashioned Thinking

Monday, December 21st, 2009

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Sri Yantra Temple

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

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

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

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

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

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

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

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

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

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

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

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

Mythic

As Above, So Below

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

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

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

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

If you understand one level you understand every level.

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

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

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

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

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

The Dream of the World Clock

The Dream of the World Clock

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

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

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

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

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

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

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

yinyang

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

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

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

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

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

Sometimes the fragmented Tones of the Universe unite into one Symphony when the Strings of the many Violins are in Tune. Pythagoras, trained in ancient Heliopolis, explained the same thing a long time ago.

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

HeartChakra

The Symbol of the Heart

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ancient game

The Game of Life is played on the Square

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

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

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

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

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

The Mystery

The Mystery

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

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

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

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

humors

The Four Humors, the Four Forces of the Inner World

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

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

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

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

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

srichakra

Sri Yantra, the Machine that generates the Matrix

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

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

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

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

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

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

trickster raven

The Trickster in the Dream of the World Clock

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

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

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

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

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

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

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

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

The choice is yours.

LINKS

About Pythagoras

About the Trinity

Monday, December 29th, 2008
machine fowler

The Computer of Fowler

The first fully programmable computer was Designed by Charles Babbage in 1837. Babbage failed to get enough money to Build his Analytical Engine. It was never build.

The failure of Charles Babbage delayed the creation of the current computer for about a 100 years.

Nobody knows that Thomas Fowler Designed and Implemented a completely different and simple wooden computer in 1840. The big difference between Babbage and Fowler was the Number System. Babbage used Base 10. Fowler used the Balanced Ternary Number System.

About the Ternary Number Systems

The balanced ternary number system is created by balancing Ternary (Base 3) Numbers around the Centre of the Number Line, 0. A balanced ternary number is a combination of negative and positive ternary numbers.

The balanced ternary number system is a very special Number System because all the basic mathematical operations, addition, subtracting, multiplication and division are accomplished by the application of very simple operations based on very special symmetries.

Symmetries are the foundation of Simplicity, Beauty and Elegance. The Engine of Fowler was a very simple and beautiful machine made out of wood.

In 1958 a Ternary Computer, the Setun, was build at the Moscow State University. It was never used.

About Number Systems

When you want to represent a number you can start with base 1. The number 13 is represented by thirteen “1′s, “1111111111111″.

Of course you are free to use other symbols to represent the number “1″. When you want to represent 13 goats you could use 13 goat-like symbols. When you want to represent many goats the sequence of goat-like symbols becomes very long.

The next step is to group the goat-like numbers. You could group them in binary groups (11 11 11 11 11 11 1), ternary groups (111 111 111 111 1) or in every other group you want.

In every case you have to assign new symbols like “1″ → “-”, “11″→ “=” and “111″ → “≡”. The number 13 becomes “≡ ≡ ≡ ≡ -”.

When you have defined a grouping method you can repeat this method. The only thing you need is a new symbol “x” to represent repetition, a symbol that represents addition “+”, a rule how to read the sequence (left to right, right to left) and symbols (“(,”)”) that show what has to be combined. ≡ x (≡) + ≡ + – now means 3X3 + 3 + 1 = 13 (and not 3x(3+1 +1) = 21).

If you want to use a high base number you need many symbols to represent the numbers of the group. If you use a low base number you need many symbols to represent the repetition. An obvious strategy is to minimize the product of these two quantities. The result of this calculation is the number 3 (or better the number e)!

About Ternary Memory Systems

The number 3 is the most efficient way to represent numbers. There is much more to say about the properties of the number 3. One of these properties can be used in Databases and Storage systems.

A Balanced Ternary Storage system can be easily expanded because you can always add a new entrance in the middle. The Balanced Ternary Storage System (represented by the Arabic Mystical Lote Tree) is one of the simplest and efficient storing methods of data.

What is the reason behind this Blog?

knots

The Universe is a highly complicated Knot

I am writing this blog because I have spent a lot of time to research the Scientific and Spiritual Trinity. The mathematical and the spiritual theory about the Trinity have a lot in common.

The Trinity or the Ternary Number System is the most efficient, most effective and most beautiful (in terms of symmetries) way to Represent, Calculate and Store Numbers. The Trinity is therefore the most effective Way to Represent the Fractal Expansion of the Dynamic Whole.

What happened?

The beginning of the Universe is a transformation of the Void (Ø) into the Nothing (0).

In the next step,  the Egg of the 0 became the One (1) that splitted into the Duality (2) to become Aware of Itself.

In this case the first sequence of creation becomes Ø,0,1,2.

When we rewrite this sentence in balanced ternary language we read something else. In this case the beginning of the Universe is an expansion of the Void (0) into a negative (-1) and a positive part (1). The first sequence of creation becomes Ø (zero members of the set), (-1,0,1)(3 members of the set).

In the ternary balanced language the next expansion of the Universe is created by expanding the negative and positive part of the Universe in the Middle. A new expansion is created by adding the same structure in the Middle of the Middle of the Middle.

1

Ø

2

-1

0

1

-1

0

1

-1

0

1

3

-2

-1

-0

0

+0

1

2

This expansion moves on until the system has replicated itself. At that time the expansion moves faster and faster and faster. The Self-Referencing System of the Universe, the “Divine Fractal“, is unfolding itself at an ever increasing (logaritmic) speed in a spiraling spiral pattern creating many more (negative and positive) Numbers.

At a certain point the Negative and Positive numbers are Voided in the Zero and the Universe starts to expand again.

The unfolding creates many universes and one of these Universes is our own Universe. All the time the center, the 0, the Void, stayed at the middle.

At this moment the lowest level, our level, is almost finished and a new Evolution, a Jump to a new Level, has to start. This Jump will be a Jump out of the middle, the Heart Chakra.

Is this Explanation too Simple?

This explanation is much too simple because the whole creation process is now projected into one dimension, a Line,  and we are looking at the third step of the Fourty-Two (3×13 +4) Steps that have happened until now.

worldclock

The basic structure of the Material Universe, the World Clock of Wolfgang Pauli, carried by the Demiurg, The Trickster.

Every split of the universe creates a new dimension. The splitted parts of the Universe, the balanced ternary trees, are Rotating Structures that contain Rotating Structures.

They look like the image of the rotating World Clock of Wolfgang Pauli that is carried by the Raven (the Trickster, the Demiurg), the Four Beasts in the Vision of Ezekiel and the Sri Yantra.

The other complication is that the Universe is creating its own Space and is therefore closed in itself. There is no Outside of the Universe. We are not living Inside an expanding Balloon but are travelling the Inside Surface.

When the Universe has expanded for a very long time the many dimensions are still there but they show themselves in very complicated Topological Structures like (Celtic) Knots, connected Moebius Rings, the Symbol of Infinity and the Klein Bottle, the Basic Structure behind Alchemy.

It is simply impossible to show and understand the current complexity. The only thing that is very helpful is to realize that the structure behind  the Universe is a Fractal.

Balanced Ternary Tree of 43

The Balanced Ternary Tree of 43.

This means that that at every level the same structure repeats itself. When you know everything there is to know about One Level you know every thing there is to know about Every Level.

If You understand the Human Being, You understand the Universe.  This principle was called by the Ancient Scientists, “So Above, So Below” and “As Within, So Without”.

The Balanced Ternary Number System or the Trinity that contains the Trinity can be used to explain Your Self.

It can be used to explain the “strange” behavior of the Brain Trinity, a combination of a Whole, the Body, A Left and a Right Brain. The “Trinity Pattern” repeats itself in every part of your body.

The pattern of Seven (The Trinity in the Trinity) shows itself as the Seven Chakra’s. The next step, the Thirteen (3×4 +1 = 13),  shows itself in the Twelve Signs of the Zodiac (+ the Center, the Pole Star), the Twelve Apostles (+ Jesus) and the Twelve Knight of Arthur (+Arthur).

The Expansion of this pattern on a much deeper level also generates the  Acupuncture Points (Nadi’s) in Your Body.

Why is Science not Aware of this?

The main reason can be found in the story of Thomas Fowler. He invented a Very Simple computer system but he was beaten by the Complicated system of Charles Babbage.

Babbage used the 10 base to define his Engine and he needed lots of money to create this very complicated system. He never finished his analytical engine but many years later IBM almost copied his design when they developed the IBM 360. They were, like Microsoft, experts in Marketing. They sold what the Customer wanted to buy and never took time to think about the Essence.

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

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

Thomas Fowler was a very simple man. He tried to do his best and was never aware of the power structures that controlled science and the market at that time. He wanted to help people but helping people is the stupidest thing you can do in a capitalistic system.

When an infrastructure is chosen it is almost impossible to change the infrastructure because everything that is build on top of this infrastructure becomes obsolete when the foundation is wrong. We will never be able to introduce a ternary computer infrastructure unless something happens that breaks the upper layer. Some people think this time is near.

Simplicity, Elegance, Beauty and Efficiency are not the main object of Capitalism. The main object of Capitalism is Making Profit.

What is the best Way to acquire Scientific Knowledge?

Thomas Fowler was not educated in the science of his time. He just invented the mathematics he needed. When he was educated in the science of his time he could have invented the same machine but it is much more plausible that he would have invented another Analytical Engine.

Thomas Fowler used his own judgment and his own talent to create something he thought was useful to support his own banking system (he also created a Bank!).

The Balanced Ternary Database of the Universe was called the Akasha. According to the Ancient Scientists of India every memory of the past and the future is stored in the Universe. They believed we are part of a Super Mind and this Mind knows everything that has happened or will happen.

walter russell wave

The Vortex, a Painting of Walter Russell

Some people are suddenly connected to this Super Mind. They are Enlightened and find a solution for a very complicated problem in a Dream or a Trance State.

One of the most important scientists of our time, Wolfgang Pauli, found everything he wanted to know in the Akasha. There are many others like Walter Russell (The Secret of Light) and Malcolm McEwen (The Lesson of the Light).

Strangely enough all of them receive or have received the same information.

What is going to happen?

The expansion of our Universe is getting into a critical state. This state is visible in all the fractal levels of our Universe.

It is visible in the Weather System, The Ecological System, The Economic System and the Cultural System. All of them are changing.

It is also visible in many Human Beings who experience the intervention of the Super-Mind in their Lives.

The big transformation must be visible in the Seven, until now not-connected universes. The other universes are currently shielded behind a Veil but this veil is slowly lifting. The movement of the Veil could explain the huge increase of Strange Encounters with Extraterrestials.

Our universe has been expanding and but very soon it will or may appear to stop. Our Universe may even begin to appear to shrink but it is not because it is reversing, heading towards some kind of big crunch but because it is folding, connecting to Itself, the Super Mind.

In the first stages of the Universe the Light was created but now we are entering a new phase where the consciousness of the Super Mind, is opening up to all the inhabitants of all the Seven Universes.

The opening of the Super Mind to all the Souls of the Universe has been named with many names in many religions all over the World (Ascension, the Golden Age, Point Omega, The Last Judgment, the Fifth World, The End of Time).

It is not clear what the connection with the Super Mind will accomplish. Many inspired scientists and prophets have tried to describe and explain this state.

One thing is sure it will be very different from the current situation where we are all isolated souls existing in many disconnected time-lines in many disconnected universes.

LINKS

Why the number e is the best base for a modular system

About the Void

Joan Baez About Triality

Many Properties of Ternary Numbers

Many Properties of the Balance Ternary Number

Why the Balanced Ternary Numbers are Special

A Visualization of the Trinity Pattern with the Platonic Solids

The 4 Videos of Malcolm McEwen below contain a Visualization of the Trinity Pattern

McEwen, Video, The Lesson of the Light, Nr 1

McEwen, The Lesson of the Light, Video, Nr 2

McEwen, The Lesson of the Light, Video, Nr 3

About the Heart Chakra

About Plato and the New Harmony

About 2012

About the Center

About Boundaries

About Order and Chaos

About the Demiurg

About the Expansion of the Whole

How to Divide the Whole

About the Spiritual Trinity

About Alchemy

About Topology

About the Brain Trinity

About the Hermetic Principle (“As Above, So Below”).

About the Book of Triangels of St. Germain

About the Expansion of Space

Tuesday, December 16th, 2008

expand spaceThe Universe, Space, is expanding at a constant speed, the speed of Light. If we try to imagine an expanding Space we imagine something, a balloon, which is expanding in Space.

When Space is expanding, outside Space is Nothing at All. Space is just creating Space.

Imagining “nothing at all” is a big problem for many people. They believe there are always Insides and Outsides.

Expanding Space, or Movement, is the Foundation of our Reality.

Space is creating all kinds of forms but Space is also a Form.

The expanding Space conforms to “geometric expansion rules” and many people will ask the question who has created these rules.

When we have established a principle we always want to know who has created this principle. When we have solved this problem the same question is asked again and again because it is almost impossible to imagine that a Dynamic Process is not caused by a Static Cause.

The Duality of the Inside and the Outside, the Static and the Dynamic have to be resolved on a higher level. On this higher level the Outside is the Inside and the Mover is Moving Itself.

At this moment many mathematical theories of Reality are constructed that are trying to avoid the “trap” of Duality. It is not difficult to translate their physical statements into spiritual statements. Spirituality and Mathematics are exploring the same domain, the Domain of Wholeness.

It all starts with The Light.

light wavesLight is something that is moving with the same speed as the expanding space, the Akasha, so expanding space could be seen as traveling Light Waves. Space/Light is moving with the speed of Light, c, but it is not necessary that the Light that is moving inside space is traveling with this speed.

When Light is not moving in a straight line the form of Light is changed and other structures (particles) are formed. The most interesting structures are complex cyclic structures (the Vâyu). They are the basic containers of the Universe.

Space is closed in Itself but there is an absolute boundary, the Edge of Space. This edge is a Mirror. When Light bounces against this Mirror it bounces back and influences the other Light Waves.

Because the Edge of expanding Space is a circle, The Light Waves move back in a different direction and create interference-patterns. Because space is limited and closed in itself one Wave of the Light, the Svara, is sufficient to create a complete spectrum of waves.

The Frequency of the Waves determinates the levels of Space. Conscioussness appears when something is able to Observe Itself or to Moves ItSelf. So every Level in Space is consciouss.

The interference of Light Waves creates “disturbances“. Some waves are starting to move in a cyclic pattern. Within these disturbances the Light is caught. They are rotating and rotation is linear speed transformed into rotating speed. The sum of the rotating and the linear movement is always constant.

The disturbances in space are influenced by the expansion of space. When Space is expanding the disturbances are extended until they break.

Ripple in the UniverseJust like a spring (a rotating circle, a spiral) breaks when the expanding pressure is too big. When the broken structures drift away from the “front-line of space” they are put together again. When this happens some of them are twisted.

Twisted structures (Moebius Ring, Klein Bottle, Knots) are forms with are different in behavior than normal cyclic structures like the Torus. They are without an inside and an outside, they are without a surface and they expand and contract in a different way. They increase the “tension” in space.

Space itself is expanding with a constant speed but the many different forms in space react differently to the expansion. When the resistance is increasing space is rippling (“zitterbewegung”) just like our skin is rippling when we get older. During the rippling phase, space expands by folding onto itself.

The wrinkles, ripples, buckles, bends, are the many appearances of energy and matter. They can again be visualized by a balloon with knots tied on its surface. Knots that are tied on the surface of the balloon represent matter, and surface wrinkles that emerge around knots represent the electromagnetic field.

The wrinkles and knots decreases the circumference of the balloon, and while the balloon is still expanding, the inner pressure, the torsion, increases until the Balloon collapses completely into itself. The pressure is so strong that space moves through a tine hole (bindu) in the surface (the Black Hole) of the Balloon and space expands at the other side of the balloon (the White Hole). From that time on “history” repeats itself.

The Universe is Breathing.

balloonsAt this moment we have developed a very simple theory. Space is the expansion of Light. When the Light bounces against the Mirror of the Edge of Space it creates Interference Patterns.

These patterns behave differently under the stress of the expansion and the stress of the expansion starts to interfere with the other moving structures in space.

If you read the Story of the Universe one thing makes the Story rather complicated. To explain expanding space the metaphor of the Balloon is often used but the geometric structure of the Universe is not a Balloon.

We are not living Outside the Balloon but we are living Inside the Balloon. Outside the Balloon is non-existent. We are not moving Inside the Balloon but we are moving on the Surface of the Balloon. The Inside of the Balloon is non-existent.

Mathematics has used the flat structure, the Euclidian Universe, to explain reality. In this Universe all the geometric theories of Euclid were valid although one of the postulates of Euclid, the parallel postulate, was in discussion for a very long time. This postulate states that two lines intersect when the sum of their angles is less than 180°.

calibiyauWhen people found out that we are not living on a flat earth they realized that the parallel postulate was wrong. The sum of the arcs of a triangle on a sphere is not 180°.

When mathematicians started to face the facts the Non-Euclidian Geometry was born and the parallel postulate was abandoned. The flat geometry was an exception. We are living in a curved universe.

The man in the street is not educated in the curved universe and many brilliant scientists who are operating outside the area of the exact sciences don’t have an idea about non-Euclidian geometry.

Non-Euclidian Geometry has had a huge impact on Science. The curved Universe is just like the “valid” postulates of Euclid an accepted fact.

If everybody would accept the “fact” of the curved universe and realize that every system in the Universe (also the Economic System) is always expanding and compressing we could anticipate the Waves of the Life Force, the Svara.

If everybody could accept that an always expanding system in our Universe always collapses in itself we could realize that an expanding economy wil create complex knots that cannot stand the tension of the expansion. The knotted, highly related, structures in our Reality are breaking and twisting.

They stop the expansion until the singularity is reached. At that time we will move trough the Black Hole and the White Hole in another Universe, Our Twin Universe.

The most interesting part is that it is possible to develop a theory of the Universe without any idea about the real Universe. It is a direct consequence of the postulates of Euclid. The only thing that is left to interpret are the results of the Geometric Theory of the Universe in our Reality. We have to find visual methaphors in our reality that look like the concepts of the geometric theory.

black-holeThe only thing that is needed to Accept the Geometric Theory of the Universe is to Accept the Postulates of Euclid. They are more or less self-evident.

They are Visible in our Reality, but still you never know if somebody is capable of finding a new exception of the postulates. If this happens the Geometric Theory has to be adapted.

Until now nobody has a clue. The axiomes of Euclid are still the foundation of Mathematics.

The Old Scientists stated that our Reality is an Illusion. The only thing that is existent is the Movement of the Void. The Movement of the Void generated the Reflection of the Void, the Expansion of Space, The Interference Patterns of the Light and finally the final compression into The Void.

They stated that the Universe is an expansion of nothingness and the nothingness is preserved in every state of the Universe. Every duality that is constructed is voided in the nothing.

Consuming is voided by Production. The Good is voided by the Bad. The Up is voided by the Down. Life is voided by Death. Everything wants to return to the original state of the Rotating Void.

If the population of the Earth is consuming to the extremes one day the opposite will happen and we will be consumed to bring back the balance of the void.

When we lend we have to pay back our debts to the Universe.

LINKS

About Reflecting Waves at the Edge of the Universe

About Non-Euclidian Geometry

A recent Geometric Theory of the Universe

About the Moebius Ring, The Klein Bottle, Knots and Physics

About Heisenberg and the Rippling of the Universe

A very old Geometric Theory of the Universe based on the Upanishads