Posts Tagged ‘Tri’

About Number and Magnitude

Monday, January 9th, 2012

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that  Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

Geometric Algebra has a strange relationship with Pascals Triangle. This Triangle, also called the Binomial Expansion, contains all the Possible Combinations of two Independent Variables. Our Universe is a Combination of Combinations exploring Every Possibility.

The last and perhaps most important Discovery in Mathematics called Bott Periodicity shows itself in Pascals Triangle.

Bott Periodicity proves that we live in a Cyclic Fractal Universe, the Wheel of Fortune, that is Rotating around the Void, the Empty Set. The Empty Set contains Every Thing that is Impossible in our Universe.

This blog is not a Scientific Article. I have tried to connect the Old Sciences and the New Sciences in my own Way.

It contains many links to Scientific Articles and even Courses in Geometric Algebra.

So if you want to Dig Deeper Nothing will Stop You.

About the One and the Dirac Delta Function

Every Thing was created out of  No Thing, the Empty Set, ɸ, the Void, the Tao. The Empty Set contains 0 objects.

The Empty Set is not Empty. It contains Infinite (∞) Possibilities that are Impossible.

Every impossibility has a probability of 0 but the sum of all possibilities (1/∞=0) is always 1. In the beginning ∞/∞ =1  or ∞x0=1.

This relationship is represented by the Dirac Delta Function. It is used to simulate a Point Source of Energy (a Spike, an Explosion) in Physics.

The Delta is reprented by the Symbol Δ, a Triangle. The Delta is called Dalet in the Phoenican and Hebrew Alphabet. Daleth is the number 4 and means Door.

The original symbol of the Delta/Daleth contains two lines with a 90 Degree Angle. Two orthogonal lines create a Square or Plane.

The Dirac Delta Function is defined as a Square  with an Area of 1,  a Width of 1/n and a Height of n where n->∞.

The Dirac Delta Function is a Line with an Area of 1.

In the Beginning a Huge Explosion took place that created the Universe.

The Dirac Delta Function δ (x) has interesting properties: δ (x) = δ (-x), δ (x) = δ (1/x). It has two Symmetries related to the Negative Numbers and the Rational Numbers.

When we move from 2D to 1D, the Number Line, the Delta Function becomes the Set of the Numbers N/N =1.

The Tetraktys of Pythagoras

The Monad (1) of the Tetraktys of Pythagoras, the Top of the Triangle, was created by Dividing the One (1) by Itself without Diminishing itself. The Monad (1/1=1)  is part of  the 1D Delta Function.

Creation is an Expansion of the 1/1 into the N/N, adding 1/1 all the time,  until ∞/∞ is reached. At that moment every Impossibility has been realized.

File:Dirac function approximation.gif

The Dirac Delta Pulse

 

To move Back to the Void and restore the Eternal Balance of  the One,  Dividing (Compression) has to be compensated by Multiplication (Expansion).

At the End of Time N/M and M/N have to find Balance in the N/N,  move Back to  1/1, Unite in the 0 and become The Void (ɸ) again.

About the Strange Behavior of Numbers

The big problem of the Numbers is that they sometimes behave very differently from what we Expect them to do.

This Strange Behavior happens when we try to Reverse what we are doing.

It looks like the Expansion of the Universe of Numbers is Easy but the Contraction creates many Obstacles.

It all starts with the Natural Numbers (1,2,3,).

When we Reverse an Addition (Subtract) and move over the Line of the Void Negative Numbers appear. Together with the Natural Numbers they are called the Integers.

The same happens when we Reverse a Division and the Fractions (the Rational Numbers) (1/3, 7/9) suddenly pop up.

An Integer N is a Rational Number divided by 1 (N/1).

The Integers are the Multiples of 1, the Fractions are its Parts.

Numbers behave even stranger when we want to Reverse a Repeating Repeating Addition (Irrational Numbers) and want to calculate a Rational Power (2**1/2).

The Complex Numbers (or Imaginary Numbers), based on the Square Root of -1 called i, are a combination of the Negative Numbers and the Irrational Numbers.

Irrational Numbers ( the Pythagorean Theorem), Fractions (a Piece of the Cake) and Negative Numbers (a Debt) are part of our Reality but the Strange Number i represents something we cannot Imagine.

About the Duality and the Expansion of Space

In the beginning the only One who was in existence was the 1.

When the One divide itself again the number -1, the Complement of 1, came into existence.

1 and -1 are voided in the No Thing, the Empty Set, 0:  -1 + 1 = 0.

The Two, the Duality, both started to Expand in Two Opposite Directions (<– and +->) both meeting in the  ∞/∞. This expansion is what we call Space.

Space is a Combination of the Strings S(1,1,1,1,1,…) and -S = (-1,-,1,-,1,-1,…) where S+S=(0,0,0,0,0,0,…).

The Expansion pattern of Space is a Recursive Function S: S(N)=S(N-1)+1 in which + means concatenate (or add) the String “,1″.

An Addition X + Y is a concatenation of S(X) and S(Y). A Substraction X-Y is a concatenation of S(X) and -S(Y). In the last case all the corresponding combinations of 1 and -1 are voided. (1,1,1,1)-(1,1,1)=(0,0,0,1)=(1).

Multiplication XxY is Adding String S(Y) every time a “1″ of S(X ) is encountered: 111 x 11 = 11  11  11. Dividing X/Y is Subtracting S(X) every time a “1″ of S(Y) is encountered:.111  111  1/111=11 1/111. In the last example a Fraction 1/111 appears.

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

The Strange Behavior of Numbers is caused by the Limitations of our Memory System. We are unable to remember long strings that contain the same Number.

To make things easy for us we Divide Space into small Parts so we were able to Re-Member (Re-Combine the Parts).

When we want to Re-member, Move Back in Time, we have to Compress Expanding Space.

Compressed Space is Time.

Time and Space have a Reciprocal Relationship called Movement (Velocity = Space/Time).

There are  many ways ( (1,1,1), (1,1,1),..) or ((1,1),(1,1))) to Compress a String in Repeating Sub-Patterns.

In the blog About the Trinity I showed that the most Efficient Way to group the One’s is to make use of a Fractal Pattern (a Self Reference) and Groups of Three Ones.

The Trinity applied to the Trinity ( A Fractal) is a Rotating Binary Tree. Binary Trees represent the Choices we make in Life.

The rotating Expanding Binary Trees generate the Platonic Solids (see linked video!) when the (number)-parts of the Binary Tree Connect.

The Ternairy Number System is represented by the Binary Tree

When we connect Three Ones (1,1,1) by Three Lines (1-1,1-1,1-1) a 2 Dimensional Triangle Δ is Created.

If we take the Δ as a new Unity we are able to rewrite the patterns of 1′s and -1′s into a much Shorter Pattern of Δ’s and 1′s: (1,1,1),(1,1,1),(1,1,1), 1,1 becomes Δ,Δ,Δ,1,1.

We can repeat this approach when there is still a Trinity left: Δ,Δ,Δ,1,1 becomes ΔxΔ,1,1.

This Number System is called the Ternary Number System.

About Ratio’s and Magnitudes

According to EuclidA Ratio is a sort of relation in respect of size between two magnitudes of the same kind“.

A Magnitude is a Size: a property by which it can be compared as Larger or Smaller than other objects of the Same Kind. A Line has a Length, a Plane has an Area (Length x Width), a Solid a Volume (Length xWitdth x Height).

For the Greeks, the Numbers (Arithmoi) were the Positive Integers. The objects of Geometry: Points, Lines, Planes , were referred to as “Magnitudes” (Forms). They were not numbers, and had no numbers attached.

Ratio, was a Relationship between Forms and a Proportion was a relationship between the Part and the Whole (the Monad) of a Form.

Newton turned the Greek conception of Number completely on its head: “By Number we understand, not so much a Multitude of Unities, as the abstracted Ratio of any Quantity, to another Quantity of the same Kind, which we take for Unity”.

We now think of a Ratio as a Number obtained from other numbers by Division. A Proportion, for us, is a statement of equality between two “Ratio‐Numbers”.

This was not the thought pattern of the ancient Greeks. When Euclid states that the ratio of A to B is the same as the ratio of C to D, the letters A, B, C and D do not refer to numbers at all, but to segments or polygonal regions or some such magnitudes.

The Ratio of two geometric structures  was determinated  by fitting the Unit Parts of the first geometric Stucture into the Other.

The Perfect Triangle of the Tetraktys contains 9 = 3x3 Triangels. A Triangle contains 3 Lines and 3 Points.

An Example:  The Tetraktys is a Triangle (A Monad) and contains 9 Triangles (a Monad). The 1x1x1-Triangle Δ, a Part of the Tetraktys,  is Proportional to the Whole of the Tetraktys (T) and has a Ratio T/Δ = 3= Δ -> T = Δ (3)  x Δ (3) = 9.

The Mathematics of Euclid is not a Mathematics of Numbers, but a Mathematics of Forms.

The symbols, relationships and manipulations have Physical or Geometric Objects as their referents.

You cannot work on this Mathematics without Knowing (and Seeing) the Objects that you are Working with.

About Hermann Grassman, David Hestenes and the Moving Line called Vector

Hermann Grasmann lived between 1809 and and 1877 in Stettin (Germany). Grassmann was a genius and invented Geometric Algebra a 100 years before it was invented.

In his time the most important mathematicians did not understand what he was talking about although many of them copied parts of his ideas and created their own restricted version. None of them saw the whole Grassmann was seeing.

When he was convinced nobody would believe him he became a linguist. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda were recognized among philologists.

Grassmann took over the heritage of Euclid and added, Motion, something Euclid was aware of but could not handle properly.

angle between vectors in 2 dimentions

A Displacement or Bivector

Grassmann became aware of the fact your hand is moving when you draw a 2D Geometric Structure. He called the Moving Lines, that connect the Points, Displacements (“Strecke”).

screw theory 2

A Displacement and a Rotation of a Vector

In our current terminology we would call the Displacements “Vectors”.

blades

Vector algebra is simpler, but specific to Euclidean 3-space, while Geometric Algebra works in all dimensions. In this case Vectors become Bi/Tri or Multi-Vectors (Blades).

The Trick of Grassmann was that he could transform every transformation on any geometrical structure into a very simple Algebra. Multi-Dimensional Geometric Structures could be Added, Multiplied and Divided.

The Greek Theory of Ratio and Proportion is now incorporated in the properties of Scalar and Vector multiplication.

add-bivectors

Combining (Adding) Bivectors creates a Trivector

About a 100 years later David Hestenes improved the Theory of Grassmann by incorporating the Imaginary Numbers. In this way he united many until now highly disconnected fields of Mathematics that were created by the many mathematicians who copied parts of Grassmanns Heritage.

About Complex Numbers, Octions, Quaternions, Clifford Algebra and Rotations in Infinite Space

Grassmann did not pay much attention to the Complex Numbers until he heard of a young mathematician called William Kingdon Clifford (1845-1879).

Complex numbers are ,just like the Rationals (a/b), 2D-Numbers. A Complex number Z = a  + ib where  i**2=-1. Complex Numbers can be represented in Polar Coordinates: Z = R (cos(x) + i sin(x)) where R = SQRT(a**2 + b**2).  R is the Radius, the Distance to the Center (0,0).

When you have defined a 2D-complex Number it is easy to define a 4-D-Complex Number called a Quaternion:  Z = a + ib + jc + kd or a 8-D Complex Number called an Octonion.

William Rowan Hamilton, the inventor of the Quaternions, had big problems to find an interpretation of all the combinations i, j and k until he realized that i**2 =j**2 = k**2 = ijk=-1.

What Hamilton did not realize at that time was that he just like Grassmann had invented Vector Algebra and Geometric Algebra.

Quaternions are rotations in 4D-space

This all changed when William Kingdon Clifford united everything in his new Algebra.  Clifford’s algebra is composed of elements which are Combinations of Grassman’s Multivectors.

The Clifford Algebra that represents 3D Euclidean Geometry has 8 = 2**3 components instead of 3: 1 number (Point), 3 vectors (Length), 3 bivectors (Area) and 1 trivector (Volume).

It turns out if you use combinations of these elements to describe your geometric objects you can do the same things you did before (you still have 3 vector components).

In addition, you can have additional data in those other components that let you find distances and intersections (and a lot of other useful information) using simple and (computationally) cheap numerical operations.

The most important Insight of William Kingdom Clifford was that the Complex Numbers are not Numbers all.

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

The String 1,3,3,1 of Clifford’s 3D Geometry is related to the 4th Level of Pascal’s Triangle. Level N of Pascal’s Triangle represents N-1-Dimensional Geometries.

The Sum of every level N of the Triangle is 2**N. This Number expresses the Number of Directions of the Geometric Structure of a Space with Dimension N.

A Point has 0 Direction, while a Line has 2 Directions, relative to its Center point, a Plane has 4 Directions, relative to its Center Point, and a Cube has 8 directions, relative to its Center point.

Pascal’s Triangle is also called the Binomial Expansion. This Expansion shows all the Combinations of two letters A and B in the function (A+B)**N. Level 1 of the Triangle is (A+B)**0 = 1  and level 2 is A x A + 2 A x B + B x B -> 1,2,1.

The Binomial Expansion converges to the Bell-Shaped Normal Distribution when N-> ∞.

The Diagonals of Pascal’s Triangle contain the Geometric Number Systems (Triangular Numbers, Pyramid Numbers, Pentatonal Numbers, ..) and the Golden Spiral of the Fibonacci Numbers.

Pascal’s Triangle is a Repository of all the Possible Magnitudes and their Components.

The Normal Distribution shows that the first level of the Triangle (the Tetraktys) is much more probable than the last levels.

The Hexagonal Numbers

The first four Levels of the Triangle of Pascal contain the Tetraktys of Pythagoras.

The Tetraktys  is an Ancient Vedic Mathematical Structure called the  Sri Yantra, Meru Prastara or Mount Meru.

About Numbers, Operations and the Klein Bottle

The Complex Numbers are not “Numbers” (Scalars) at all.

They are “Operations” (Movements) that can be applied to Magnitudes (Geometries) and Magnitudes are Combinations of the Simple Building Blocks of the Tetraktys, Points and Lines.

The Tao of Ancient China was not for nothing represented by a Flow of Water. According to the Ancient Chinese Mathematicians Every Thing Moves.  In the Beginning there was only Movement.

In the Beginning only the One was Moved but when the Duality was created the Two moved around each other never getting into contact to Avoid the Void.

When we look at the Numbers we now can see that they are the result of the Movements of  the first Diagonal of Pascals Triangle,  the 1′s (Points) or better the Powers of  the One: 1 **N (where N is a Dimension).

Even in the most simple Number System, the Unary Number System, Concatenation is an Operation, An Algorithm.

The Mathematician John Conway recently invented a new Number System called the Surreal Numbers that contains Every Number you can Imagine.

The Surreal Numbers are created out of the Void (ɸ)  by a simple Algorithm (Conway calls an Algorithm a Game) that describes Movements (Choices of Direction: Up, Down, Left, Right, ..)  that help you to Navigate in the N-Dimensional Number Space.

The Ancient Chinese Mathematicians played the same Game with the Numbers.

Algorithms were already known for a very long time by the Ancient Vedic Mathematicians. They called them Yantra’s.

SriYantra

Sri Yantra

Geometry is concerned with the Static Forms of Lines and Points but there are many other more “Curved” forms that are the result of  Rotating Expansion and Compression. These forms are researched by the modern version of Geometry called Topology.

The most interesting 4D Topological Structure is the Klein Bottle.  The Klein Bottle is  a combination of two Moebius Rings. It represents a Structure that is Closed in Itself.

It can be constructed by gluing both pairs of opposite edges of a Rectangle together giving one pair a Half-Twist. The Klein Bottle is highly related to the Ancient Art of Alchemy.

The movement of the Duality around the Void can be represented by a Moebius Ring the Symbol of Infinity ∞.

Later in this Blog we will see why the Number 8 is a Rotation of ∞ and the symbol of Number 8 is a combination of the symbol of the number 3 and its mirror.

First we will have a look at the Reciprocal Relation between Space and Time.

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.

About Dewey B. Larson, Velocity and Time

Dewey B. Larson (1898 – 1990) was an American Engineer who developed the Reciprocal System of Physical Theory (RST).

Larson believed that the failure to recognize that Motion is the most basic physical constituent of the universe has handicapped the progress of the traditional study of physics, which focuses on Forces.

The definition of Motion stems from the Equation of Velocity, v = ds/dt.

Instead of depending upon the change of the location of an object to define an arbitrary “quantum” of space per “quantum” of time, such as miles per hour, or meters per second, the RST assumes that the observed universal passage, or progression, of time is one aspect of a universal motion that necessarily must be accompanied by a universal “passage,” or progression, of space.

The Units of Time fill up the Units of Space. Space and Time are Duals.

Space is not-Time and Time is not-Space. Time is Non-Local, Cyclic and represented by the Rotating Imaginary Numbers. Space is Local, Linear and Represented by the Scalar Numbers. Space is the Vacuum and the Nothing and Time is the non-vacuum, the Every Thing, the Solids represented by the Cube of Space.

The Cube of Space is the structure behind the Tetraktys but also behind the Book of Genesis.

Our Reality contains two Reciprocal 3D-structures related to Space and Time. Space and Time are related by the Simple Formula N/N=1/1=1, the Formula of Diracs Delta Function.

We are able to perceive the Real 3D-Structure of Space. The 3D-Structure of Time is Imaginary. It is situated in the Imaginary Number Space of i.

LarsonsScalarCube.jpg

Larson’s Cube, the Geometric Representation of the Octonion.

Larson, a Self Thought Genius like Grassmann, developed Geometric Algebra without knowing anything about Geometric Algebra but he also invented String Theory long before String Theory was invented.  The Mathematics of Larson is also the Mathematics of the Tetraktys of Pythagoras without even knowing anything about it.

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The Periodic System of Larson

Larson was able to Calculate all the important Physical Numbers without any problem and was also able to Calculate Chemical Structures and Reactions.

About the Bott Periodicity

The fourth line of Pascals Triangle and the Tetraktys contains 8 Directions in the Four Geometric Dimensions: 0, 1, 2, and 3.

Mathematicians are intrigued with this number 8, because they find it popping up unexpectedly in advanced mathematics.

In fact, expanding the Binomial Expansion to 8 dimensions just creates an inverse copy of these first Four Dimensions, and then the pattern just repeats itself with a half-twist and back from there, ad infinitum.

This is called Bott Periodicity discovered by the mathematician Raoul Bott (1923-2005).

The mathematician John Baez wrote an article in which he relates this 8-fold Periodicity to the Scalars (1), the Complex Numbers (2), the Quaternions (2×2), and the Octonions (2x2x2 = 2**3).

Bott Periodicity

The Universe of Numbers and Magnitudes  is Cyclic and Fractal.

Our own Reality, symbolized by the Tetraktys,  repeats itself in Higher Dimensions until Infinity.

The Tetrad, represents Completion, because it contains all its Previous Numbers, the 1, 2, 3, and itself, 4, in One Number, 10 = (The One) +  9 (= 3 (Trinity)x 3 (Trinity) = Tetraktys).

As you can see in the Picture above the Fractal Pattern of 8 contains two kinds of Trinities/Triangles, an Upside and a Downside (Rotated by 180 Degrees) Triangle. When you Rotate by 180 Degrees the 1 becomes -1 and 1 + -1 =0 is the Void.

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

The Star of David, the Symbol of Human Center, the Heart Chakra.

The Multi Dimensional Rotations of the Octonions always Come Back to Square 1/1=1, the One and keep Rotating around the Center, the Nothing,   Until Infinity.

LINKS

About the Tetraktys (1)

About the Tetraktys (2)

About Triangular Numbers and Pascal’s Triangle

About the Empty Set

About the Relationship Between Geometry and Music

About the Trinity

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

About Number and Magnitude

About Ratio and Proportion

About Ratio and Proportion by Euclid

A book of Augustus deMorgan about “The Connection between Number and Magnitude”

The text of the Fifth Book of Euclid

An Educational You Tube Channel called Insights in Mathematics

About the History of Geometric Algebra

About the Sri Yantra

About Geometric Algebra

Free Software to use Geometric Algebra

About Clifford Algebra

About Yantra’s

About Movement

About Topology

About the Digital Root Patterns

About the Heart Chakra

A Video that shows how the Platonic Solids are created out of the Trinity Numbers

All you want to know about Geometric Patterns

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)

Doppler_div

A Moving Standing Wave

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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.

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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.

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Transforming a Mug into a Torus

About the Great Breath

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

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

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

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

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

Twisted Topological Structures

Twisted Topological Structures that are Closed in Itself

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

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

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

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

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

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

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

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

About the  Number Five

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

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

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

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

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

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

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

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

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

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

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

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

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

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

About the Magic Square of Lo Shu

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

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

The Lo Shu Square in the Middle of the Mystic Tablet from Tibet

The Lo Shu Square in the Middle of the Mystic Tablet from Tibet

-1 4 -3
-2 0 2
3 -4 1

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

The transformed Magic Square shows an interesting symmetry.

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

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

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

About the Sheng Cycle

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

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

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

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

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

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

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

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

The Sheng Cycle

The Sheng Cycle

About Harmonics

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

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

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

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

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

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

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

About the Cyclic Universe of Paul Steinhardt

The Cyclic Univere of Paul J. Steinhardt

The Cyclic Universe of Paul J. Steinhardt

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

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

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

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

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

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

About Ancient Spirituality and Modern Science

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

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

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

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

The Levels in our Universe

The Levels in our Universe (Calculated by Ray Tomes)

About the Good, the Bad and the Nothing

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

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

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

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

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

The Good gives us Joy, Pleasure and Exitement.

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

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

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

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

LINKS

About the Law of Resonance

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

Why Matter is a Standing Wave

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

About the Harmonic Theory of Ray Tomes

About the Experiments of Michelson and Morley

Why God is a Topologist

About Pauli and Quantum Mechanics

About the Cyclic Universe

About the Lo Shu Square

About the Trinity

About Infinity

About the Empty Set