Posts Tagged ‘ternary number system’

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.

wom_image3.jpg

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 the Trinity

Monday, December 29th, 2008
machine fowler

The Computer of Fowler

The first fully programmable computer was Designed by Charles Babbage. Babbage failed to get enough money to Build his Analytical Engine.

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

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