Posts Tagged ‘Trinity’

About Intelligent Design

Tuesday, April 17th, 2012

Thermodynamics, the Science of Heat, became an important science in the 19th century when physicists started to improve the Steam-Machine. This blog is about a recently discovered law of Thermodynamics called the Constructal Law.

The Constructal Law describes How Intelligent Systems emerge out of the Laws of Thermodynamics.

Heat is Random Motion

According to Thermodynamics the evolution of the universe has been characterized by an on-going transformation from a simple, restricted, highly condensed, homogeneous state (the Big Bang) to an increasingly complex, widely dispersed, dynamic, multipotent, granular diversity.

Energy always moves from High to Low Temperature. This is the main reason why most of the energy of Earth comes from our Sun.

With help of the Electro-Magnetic radiation of the Sun we call Light, plants, algae and bacteria transform simple molecules into complex organic structures (Biomass = Potential Chemical Energy) and store the energy of the Sun. Bacteria and Fungi brake up these structures, produce heat, reduce the complexity, and close the Cycle.

The Input of the Heat of the Sun has to be compensated by a comparable Output of Radiation otherwise Earth would be burned instantly. The difference between the Input and Output of Energy is transformed into Movements on Earth.

The Earth’s climate is a huge flow system. It circulates air and water from the tropics to the poles and back. These flows develop as air and water move from hot to cold regions, a result of variation in the heating of the Earth’s surface by the sun.

The Earth is not only heated by the Sun. The hot kernel of the Earth is surrounded by a small crust. At certain places on Earth and the Sea the rotating pool of the magma-ocean produces a lot of energy.

The Earth with its solar heat input, heat rejection, and wheels of atmospheric and oceanic circulation, is a heat engine without shaft. Its maximized mechanical power cannot be delivered, but is instead destined to dissipate through air and water friction and other forms of heat loss. It produces maximum power, which it then dissipates at a maximum rate.

The earth is wasting a lot of energy because the transmission of  most of its energy is not contained in a Tube-like-system.

The system maximizes the sum of the work done driving the planetary circulation, and the heat rejected back to space at the cold end of the heat engine.

When the speed of the planetary circulation is low, so are the turbulent losses. As speed increases, up to a certain point the sum of work done (circulation speed) and heat rejected also increasing until the turbulence starts to interfere with the circulation and  actually decrease the total of work done and heat rejected. That is the point, “the edge of turbulence”,  at which the system will naturally run.

Every flow system tries to find the perfect balance between movement and friction.

The interesting point is that friction is movement in opposition to itself.

Clouds on the Edge of Turbulence

The biomass on Earth is direct or later (Oil, Gaz, Coal) consumed by all kinds of organisms. In Food-Webs Organisms are consumed by other organisms.

We, the Humans, describe the interaction of the organisms in the Food-Webs as a Struggle for Live, a Survival of the Fittest, but the flow of energy in the food webs could also be seen as an adaptive chain of chemical reactions that are performed in self-moving, self-reproducing chemical factories.

Energy is Potential Movement. The potential energy stored in the biomass on Earth is transformed into circular movement (kinetic energy). During this transformation Heat is produced. Heat is the waste produced by a restrained non-effective movement.

The energy of the Sun produces all kinds of movements on Earth. Examples are river-delta’s, our respiratory system and the weather-system.

Flow Systems that move from one  to many always look like a leaf or a tree

Flow Systems that move from One to Many always look like a Leaf or a Tree. Left a River Delta is shown. Right a picture of the Lungs is displayed.

According to Constructal Theory the generation of design (configuration, patterns, geometry, shape, structure, rhythm) in nature is a physical phenomenon that unites all animate and inanimate systems. Design in Nature always shows itself as systems that flow and improve themselves.  Systems improve themselves because the movement from chaos to order takes many discrete steps.

Biological organisms are flow systems. River basins are flow systems. A Tree is a flow system. The Traffic System is a flow system. The City of Paris is a flow system. The Financial Market is a flow system. The Internet is a flow system. A Proces-Manager is a flow system.

Flow Systems

All these flow systems must be structured (architecturally designed) in such a way that the currents that flow (Life Energy, Water, Air, Electricity, Gaz, People, Cars, Trains, Airplanes, Content, Money) increasingly get to where they need to go. This gives shape and structure to everything that evolves over time.

Flow Systems always remove the Resistance to the Flow themselves.

Constructal Law is formulated as follows: “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.”.

Nature always provides Resistance to Change (Heat, Erosion, Friction) and this resistance is provided by the Systems of the Past. The current Order resists the potential Chaos of Free Moving Energy.

The Paths of Change of our Universe always move in the same way. The pattern looks like a Moebius Ring, the number 8, because this is the only way to cope with the polarity of the movements. In a Moebius Ring two Opposite Cyclic Movements are perfectly United.

A Moebius Ring is a 2D-structure that operates in 3D because it needs a Twist to operate.

According to Constructal Theory the Energy of the Sun creates two types of Systems called Engines and Brakes.

Engines are the most effective and efficient states in the evolution of our Universe. They have found the best way to cope with the resistance that is provided by the Brakes. Brakes are the old systems like trees, forests and natural or constructed dams that slow down the movement so the potential energy can be stored.

If the Energy of the Sun is not stored,  the Self-Reproducing Systems are unable to evolve to a higher level of organization.  If every Resistance would be gone the Flow-Systems would Flow in a Radial Pattern to every Direction possible.

If we remove the Natural Brakes (Forests, River-delta’s) the Expansive Flow-systems will take over control and the Smart Highly Improbable Next Generation Brake Systems, the Organisms would die.

We, the Humans, are here to Resist the Engines that give the Flow-Systems the opportunity to make Everything the Same. Every Thing has to become the Same because the Universe does not discriminate. Every configuration has the same chance to be alive.

Dependent on the type of flow there are standard solutions to the dualities that are provided by the eternal battle between engine (movement) and brake (not-movement).

Paris is a Flow System

The standard solution can be calculated using the Laws of Thermodynamics. Tree (or Leaf)-shaped fractal systems are for example the best solution for a One-to-Many (or Many-to-One) Flow. The Flow Systems always converge to these Shapes.

Our Earth is rotating, spinning and moving around our moving Sun. The influx of Energy on every area on Earth is changing all the time.

This means that every Flow-System on Earth has to adapt to the short term and long term changing Energy Input of the Sun.

The stability of a Flow-System, the Resistance to Change, is highly dependent on the Resilience of the System.

According to the theory of Panarchy the Resilience of a System is dependent on the Potential and the Connectedness of a System.

In  the Exploitation/Conservation phase of the Adaptive Panarchy-Cycle the Constructal Engines become more efficient (producing more Potential) and Connected. This means that the amount of possible paths in the River-delta of the System is reduced. This amount determinates the resilience of the system.

At the state of maximum production and maximum connection (conservation) the system is spending all its potential at self-reproduction and is highly vulnerable to external disturbances. At a certain moment when a disturbance destroys the majority of the paths the system collapses (release).

Revolt: A small Wildfire can destroy a complete Ecology

The bits and pieces, the components, of the scattered ecology are reassembled sometimes in a different way (reorganization) and the system starts again most of the time on a higher level of organization.

Kleiber's law

Kleiber’s Law is an example of the Constructal Law. It shows the many levels of organization that have occured since the chemical factories of the bacteria started to work together. Kleiber’s Law can be extented to the level of the Community and the City.

The Panarchy Cycle is Self-Similar. It repeats itself on many Scales. The higher the scale the bigger the impact and the slower change takes place.

The Scales are interconnected. A huge disturbance on a lower scale (Revolt) can have an huge impact on a higher scale when both cycles are moving into the Release State.

A Slow moving High Level Cycle can help to restructure a fast moving cycle by providing the template of the way the components were originally assembled (its CommunityDNA) (Remember).

Constructal Law is a Law of Thermodynamics. Thermodynamics has evolved into a Statistical Theory called Statistical Mechanics. To calculate a probability you have to define the Space of all Possibilities of a System, the Phase Space.

When you don’t know what a system will look like it is impossible to calculate the Phase Space. To calculate the possibilities of Constructal Law you have to imagine the possible constructions of Mother Nature.

It is possible to play with Probability Theory without knowing the exact Phase Space. In this case you have to look at the probabilities of the probabilities. These probabilities are described by the Triangle of Pascal. Behind the Triangle of Pascal a new Triangular Structure shows itself. This pattern goes on and on until the primary Triangle of Creation, the Holy Trinity, is reached.

The Trinity is a combination of Desire (Mother, Female, Expansion, FLOW), Control (Father, Male, Compression, BRAKE) and the combination of both Expansion AND Compression also called the Void or the Tao. In Physics the Void is called the Vacuum or the Zero-Point-Field.

The Triangular Pattern behind the Triangle of Pascal

When we have moved back in time and have reached the state of the Trinity we are very close to the Big Bang. The Big Bang is a result of the Union of the Opposites (Yin/Yang, Male/Female, Matter/Anti-Matter, Expansion/Compression) that both came out of the Void.

The Vacuum is the Eternal Flow System of Creation. It contains everything that is possible even the impossible, the Empty Set.

The Tao is like a well: 

used but never used up.

It is like the eternal void:

filled with infinite possibilities.

It is hidden but always present.

I don’t know who gave birth to it.

It is older than God.

(Tao Te Ching 4)

According to Constructal Law every finite-size system must evolve in such a way that it provides easier access to the imposed currents that flow through it.

The Tao is the Channel of the Energy of Life. If Constructal Law is Right we have to give easier access to this Flow. We have to become the River to move to our final destination, the Sea of the Nothing.

LINKS 

A video about Constructal Theory

About the Higgs Field and the Big Bang

Why the Objects in the Universe are of Different Size

About Innovation and Thermodynamics 

About the Big Bang

About Friction

About the Big Freeze

About the Constructal Theory of David Deutsch

The Website about Constructal Theory

An Introduction into Constructal Theory

About Morphology

About Panarchy

About Kleiber’s Law

About Genetic Similarity Theory

Why a City is an Organism

About the Triangle of Pascal and the Holy Trinity

About the Holy Trinity

About Constructal Law and the Trinity

Attraction + Obstacles = Excitement 

About the Law of three & Gurdjieff

 

 

About Perspective

Thursday, February 2nd, 2012

Effective Ways To Improve Production Efficiency For Your Manufacturing Business

While all business owners should be taking measures to enhance efficiency, as this aspect of business growth is of extreme importance regardless of the industry, manufacturing businesses should take measures to boost production efficiency for several other reasons. These reasons range from improving workplace safety to saving on costs and everything in between. Manufacturing businesses that claim the lion’s share of the market are always searching for new ways to improve production efficiency with the intention of ultimately improving their bottom line.

So, to ensure your manufacturing business is constantly making notable strides towards improving production efficiency, we have rounded up five practical ways for you to achieve this. With that said, these five solutions break down the five fundamental focus points of manufacturing efficiency. Therefore, you can use these practices for years to come.

Waste in the manufacturing industry is a cost that should be avoided. And waste is also a broad term in this industry as it refers to employee hours, energy consumption, materials, and a few others. However, material waste is usually the biggest concern in the manufacturing industry. When searching for ways to reduce waste, you will need to utilize your conclusions from evaluating your production line, learn more detailed information from this top tier short cut fibers manufacturer.

When identifying waste, each of your production line processes will create some waste; identifying the processes responsible for making the most waste is the best way to reduce overall waste. However, you can also reduce waste by recycling or reusing waste instead of dumping it. You could also consider selling your waste to a business that can properly use it if you cannot eliminate the bulk of your waste.

The production line in your manufacturing business is the core of your business functions. When evaluating the production line, you should assess all the details as well, including the commonly overlooked details, such as loading dock bumper and other essential loading dock equipment your business needs. When it comes to sourcing and maintaining loading dock bumpers, you can consider Miner Corp or other leading industry service and equipment providers to ensure your production line has everything it needs to function as it should.

Throughput is another primary focal point to consider; you need this metric to measure the number of units being produced in a certain period on average. While quality equipment is crucial in ensuring your production line can run smoothly, evaluating your throughput will help you identify issues in your production line on occasions when the throughput is not entirely up to par. Capacity utilization is another element of your production line to evaluate, and this refers to calculating your factory’s total output capacity. This will allow you to determine your production line’s performance at all times.

While you are evaluating your production line, you will probably discover the most significant breakdowns in production. These are otherwise referred to as bottlenecks. Because having to shut down operations even for half a day can have a massive impact on your business’s reputation and overall profits, identifying sources of breakdowns and taking measures to prevent them from reoccurring is vital to all companies operating in the manufacturing industry.

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.

Mount Meru (Pascal's Triangle in Vedic Mathematics)

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 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 Mystical Number Theory and Pascal’s Triangle

Friday, December 2nd, 2011

The first part of this Blog is about the Triangular numbers, related to the Number 3, the Holy Trinity.

The second part shows that Pascal’s Triangle (called Meru’s Mountain in Mystics), the Binomial Expansion,  contains every Possible Mystical Number Pattern (including the Triangular Numbers) you can Imagine.

Pascal Triangle also shows that our Universe is a combinatorial miracle. It explores every possibility, is always in balance, expands and moves back to the beginning which is and was the Void, the Empty Set, the merge of Every Paradox, that is Possible.

About Mystical Number-Patterns

The Sēpher Yəṣîrâh (Book of Formation or Book of Creation, ספר יצירה) is the oldest book on Jewish Mysticism. The Sefer Yetzirah describes how the universe was created by the “God of Israel” through 32 Wondrous Ways of Wisdom.

The Number 32 is the Sum of the 10 Sephirot and the 22 Letters of the Hebrew Alphabet.

The Sephirot is related to the  Tetraktys of Pythagoras. The Tetraktys embodies the Four main Greek Cyclical (PlatonicMusical Harmonies: the Fourth (4:3), the Ffth (3:2), the Octave (2:1) and the Double Octave (1:4).

1+2+3+4 = 10. 10 is the 4th Triangular Number. The Nth triangular number is the Sum of the numbers 1 -> N. This Sum is equal to 1/2N(N+1).

Between the 10 Sephirot run 22 Channels or Paths which connect them.

The Sephirot are the Points of the Tetraktys. The Hebrew Letters are the Lines between the Points. The Lines of the  Sephirot and the Tetraktys create a Cube (6) at the Top and a Tetrahedron (4) at the Bottom.

The Letters of the Hebrew  Alphabet are divided in the 3 Mother Letters (אמש, the Trinity), the Seven Doubles (The Planets) and the Twelve Simples (the Zodiac).

The 22 letters of the Hebrew Alphabet are a combination of the Trinity, the 7 Planets and 12 Signs of the Zodiac.

When you analyse the Sepher Yeshirah the Cube of Space (the Kaaba) appears out of the Hebrew Alphabet. The Kaaba is related to the Seventh Planet, Saturn.

The 3 Axis of the Cube of Space are the Trinity, the 6 (2×3) Faces of the Cube stand for the Planets with the 7th Saturn, the Son of the Central Sun (3+1 (Center)+3) in the Center and the 12 (4×3) Boundary Lines of the Cube represent the 12 Signs of the Zodiac.

As you can see the Number Three, the Triangle,  plays an important role. It is the First Structure that is Closed in Itself and is therefore Topological related to the Circle. The Circle (and the Triangle) is able to rotate With and Against the Clock. This property is called Spin in Physics.

It is very important to realize that Everything Rotates in our Universe around a Central Object that rotates around another Central Object. The Central Object Gives Time, determinates the Rythm or Harmonics,  of the Rotation Structure.

The Trinity rotates around the Void. The 7 Chakra’s of the Human rotate around the 4th Chakra, the Heart Chakra, ((3+(1)+3)=7).

The Planets rotate around the Sun and the Sun rotates around the Central Black Hole. The arrow of Sagitarius points to this Black Hole.

On a Six Sided Dice the Sum of all the Numbers is Seven (1+6,2+5,3+4). The Sum of the Six Numbers is 3 X 7 = 21. If we add the Center (Saturn) the Number 22 appears.

22/7 is a good approximation of the number π. π relates the Square (and the Cube) to the Circle.

The Cube of Space symbolizes  the Playing Board of the Game of Life. On the Playing Board we have a Free Choice to move into the many Paths that are available. Every Path has its own Probability and this Probability can be calculated. If we don’t know what to do we could throw a Dice.

The Cube of Space contains the same six lines that exist in the I Ching. Four of the lines are of equal length, the other two, the diagonals, are longer. For this reason symmetry cannot be statically produced and the Dance (of Shiva) results.

The Circle represents the Cycles of Time of the Matrix of the Demiurg. Behind all the Probabilities of all the Possible Paths lies a Hidden Order.

A Hexagram, represented by the Star of David,  is a Two-Dimensional (Orthographic) projection of a Cube. A Symmetric Projection of the Cube creates a Cross.

A Hexagram is a Two Dimensional Cube

One of the many meanings of the first word in the Bible “Bereshit“,  is “They (Elohim) created Six” which means that in Six Stages of  the Time Cycle the Cube of Space (or the Hexagram) was populated. On the Seventh Day the Center was filled.

The book of Genesis does not describe the creation of the Trinity (They, Elohim, 1+2+3, 1x2x3) itself. This stage was later covered in the Zohar.

In my blog “About the Sum of Things” it is shown that Six Stages are part of an Expansion Pattern governed by the Powers of Two. After 2**6 (64) Expansions (or Compressions) the Same Fractal Pattern repeats itself on a higher level.

64 is the Number of the I Tjing and the Game of Chess. The number 32 of the Sepher Yeshirah is 64/2 and is a Contraction of the I Tjing.

The I Tjing is a contraction of the oldest Divination System in the Word called FA. FA is still used all over the world by the followers of the oldest wisdom-system created by the YOrubA in Africa. The Yoruba lived at the place where the ancient Paradise was situated.

Star of David in The Israeli Art Genesis-2

The Fourth Day (Sun (4), Moon (5))

About the Triangular Numbers

The Tetraktys contains the Numbers 1, 3, 6 and 10. These numbers are called Triangular Numbers.

The number 21 is also a Triangular Number because it is the Sum of  the Sixth Level of the Tetraktys,  the Numbers 1 to 6.

The Fifth Level of the Tetractys is related to the Number 15 (1+2+3+4+5). This number connects the Tetractys and the Sephirot to the 3×3 Lo Shu Magic Square also called the Seal of Saturn.

The nth Triangle number T(n) is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n.  T(n)=n(n+1)/2.

The Triangular Numbers contain the Perfect Numbers. A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. Six (1+2+3=1x2x3) is the first Perfect Number and 28 (1+2+4+7+14) is the next.

The Sum of two Triangular Numbers is a Square

The Sum of two adjacent Triangular Numbers T(n) +  T(n+1) is a Square Number because Two Triangels can be combined in a Square. 1+3=2**2 and 3+6=3**2.

There are many relationships between the Triangular Numbers. These relationships were the focus of the research of the Mystical Group of the Mathematikoi of Pythagoras.

6 (Bereshit, the Cube, the Hexagram) + the 22 Letters of the Hebrew Alphabet = 28, the Next Perfect Number (1+2+3+4+5+6+7).

28 is like the numbers 6 and 15 also a Hexagonal Number. As you can see in the picture below 28 is the fourth Hexagonal Number. As we have seen before a Hexagon is a Projection of a Cube so 28 represents a Cube in a Cube in a Cube. A Cube in a Cube is called a Tessarect or a HyperCube.

28 is a Hexagonal Number

The Number 15 is a Cube in a Cube called a Tessarect or a HyperCube

The first sentence in Genesis (“In the beginning Elohim created Heaven and Eearth“) contains 7 words and 28 letters. This indicates that the Creation Process was already in the 7th stage of the Tetraktys and in its 2nd Fractal Expansion,  the Birth of the Material Universe.

The sum of the entire verse is the 73rd Triangular Number. The prime Numbers 37 and 73 are geometrically related. They form the third and the fourth term in the sequence of Star Numbers (1, 13, 37, 73, 121).

Hexagon/Star pairs are closely related to Triangular numbers. Their product is always a Triangle, and they can be symmetrically generated from a Pair of Triangles.

Star Numbers are a Combination of Two Triangular Numbers

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

The Symbol of the Heart Chakra contains Two Triangles.

About Pascal’s Triangle

When a number represents a Geometric Structure it is called a Figurative Number.

Every possible figurative number is generated by the Triangle of Pascal.

The Fractal Sierpinsky Triangle is the Triangle of Pascal Modulo 2.

The Triangle of Pascal was known long before Pascal (re)discovered it.

It was known in Ancient India as the Meru Prastara and in China as  the Yang Hui.  Meru Prastara relates the triangel to a Mystical Mountain called Mount Meru. Mount Meru is also implemented in the Sri Yantra.

The Triangle shows the Coefficients of the Function F(X,Y))= (X+Y)**n. If n=0 F(X,Y)=1 and if n=1 F(X,Y)=X+Y so the Coeffcients are (1,1).

Pascals Triangle is a 2-Dimensional System based on the Polynomal (X+Y)**N. It is always possible to generalize this structure to Higher Dimensional Levels. 3 Variables ((X+Y+X)**N) generate The Pascal Pyramid and n variables (X+Y+Z+….)**N  generate The Pascal Simplex.

The rows of the Pascal’s Triangle add up to the power of 2 of the row. So the sum of row 0 is 2**0 and  the sum of row 1 is 2**1 =2.

The Sum of the  rows of the higher n-dimensional versions of the Triangle is n**N where n is the Amount of Variables and N the level of expansion. So the Sum of Pascal’s Pyramid (3 variables X,Y,Z) is 3**N.

Triangle of Pascal

The most interesting property of the Triangle is visible in the Diagonals.

The First Diagonal contains only 1′s. The Ones represent Unique Objects. They are the Points in the Tetraktys.

The Second Diagonal contains the natural numbers. These Numbers are used to Count Objects that are The Same. The Natural Numbers are the Lines that connect the Points. The Natural Numbers are the Sum of the previous Ones.

The Third Diagonal contains the triangular numbers. The Triangular Numbers are the Sum of the previous Natural Numbers.

This pattern repeats itself all the time.

File:Yanghui triangle.gif

The Yang Hui is an ancient Chinese version of the Triangle of Pascal. This Triangle contains Nine (3x3) Levels.

The Fourth Diagonal contains the tetrahedral numbers (Pyramid Numbers) and the Fifth Diagonal, the pentatope numbers.

Fermat stated that Every Positive Integer is a Sum of at most three Triangular numbers, four Square numbers, five Pentagonal numbers, and n n-polygonal numbers.

The Tetrahedron with basic length 4 (summing up to 20) can be looked at as the 3-Dimensional analogue of the Tetraktys.

File:Pyramid of 35 spheres animation.gif

A Tetrahedral Number represents a 3D-version of the Tetraktys.

The Diagonals of the Triangle of Pascal contain every Possible 2-Dimensional Figurative Number (and Structure).

These Numbers are Projections of Higher Dimensional Numbers and Higher Dimensional Structures.

The Higher Dimensional Versions of the Triangle (the Pascal Pyramid, The Pascal Simplex) contain these structures.

The Rows of the Triangle Sum to the Powers of Two (2 Dimensions). These Powers control the Levels of Expansion.

Every 7th step the Fractal Pattern of the Triangle repeats itself on a higher Level.

The Figurative Numbers are the Geometric Shapes that are created by the Lines of the Natural Numbers that are connecting the Points of the One.

Pascal’s Triangle also contains the numbers of the Fibonacci Sequence (“The Golden Spiral“).

When we take the Modulo 9 (the Digital Root of Pythagoras) of the Numbers of Fibonacci a repeating patterns of 24 steps shows itself that can be represented by a Star Tetrahedron or Stella Octangula. The Star Tetrahedron is a Three Dimensional Star of David.

the Fibonacci Numbers as a Cube.

The StarTetrahedron, shows the Pattern behind the Sequence of Fibonacci.

Every Figurative Number N is the Sum of the Figurative Numbers N-1.  Every Geometric Shape is a combination of all the Previous Geometric Shapes.

This means that Every Geometric Shape is in the end The Sum of the Sum of the Sum of  …. Triangels, Trinities (Elohim) or Triangular Numbers and therefore an Extension of the Tetractys of Pythagoras.

The Expansion of the Whole is a (Fractal)  Combination of Combinations.

The Triangle of Pascal is related to the so called Binomial Theorem which is used in Combinatorics and Probability Theory to describe the Amount of Combinations of a Set of  Objects.

The rows of the Triangle of Pascal also shows the Bell Shaped Pattern of the Normal Distribution.

The Probability Distribution of the Triangle of Pascal converges to the Normal Distribution because of the Central Limit Theorem. Every Row has a Mean of N/2 and a Variance of (N**1/2)/2 which means that with every new row the Mean and the Variance become Bigger and Bigger.

The Triangle of Pascal and therefore the Figurative Numbers describe Everything that is Possible but every Expansion of the Triangle is less Likely to Occur.

The Triangle of Pascal Modulo 3

The Triangle of Pascal Mod 3 represents the Tetraktys in the Tetraktys in the .....

Because of the Fractal Expansion/Contraction Pattern The Cube of  Space, related to the Element Earth,  explains Everything there is to Know on Our Level of Existence, Mother Earth.

The interesting part of the Figurative Numbers is that they representent Visual Patterns with which we can Reason.

We don’t need complex formulas because we can See what is Possible.

The interesting part of the Triangle of Pascal is that we can See that the Complex Figurative Structures are created out of a very Simple Structure, the Triangle.

If we want to understand our Reality we have to begin with looking at the Beginning and not start somewhere in the Middle.

If we look at the Fractal Expansion Pattern of the Triangle we See that Every new Stage is an Expansion Out of the Middle.

The Expansion of the Human, the Next Step in our Evolution,  is therefore an Expansion Out of the Heart, the Balance of Father Sky and Mother Earth.

Life is not only about Me and the Other.

Life is also about the Relationship between Me and the Other.

If we don’t Collaborate the Next stage in our Evolution will never happen.

LINKS

The Content of the Sepher Yesirah

About the Sepher Yesirah

About the Cube of Space

About the Tetractys

About the Cube of Space and Psychology

About the Sepher Yesirah and the I Tjing

A correspondence table of the Cube of Space

About Bereshit

About Genesis

About Patterns in the Bible

About Saturn

About the Trinity

About the Sri Yantra and Plato

About the Lo Shu and the I Tjing

All kind of strange relationships between Triangular Numbers

A website about Mystical Number Theory

About the Figurative Numbers

About Combining the Combinations

About the Golden Spiral and Plato

About the Logic of Creation

About Pascal’s Triangle and the Normal Distribution

A complete course in elementary Number Theory

About the Psychology of the Cube of Space

About the Tetraktys and the Zodiac

About the Process Theory of Paul Young

About the Theory of Dewey B. Larsson

Mysteries of the Equilateral Triangle

About Visual Patterns in Number Theory

About Pascal’s Triangle and Cell Division

About the Sum of Things

Thursday, September 22nd, 2011

The Lo Shu is a Chinese Model for Time and was used to design Cities, Temples, Cycles and Calendars.

lo-shu-color

The Lo Shu is a 3×3 Magic Square created by Fu Xi, the Founder of Chinese Civilization. Fu Xi lived around the time of the Great Flood.

The Magic Square was carried by a Turtle. The Turtle is the symbol of the Constellation Orion. Many Ancient Cultures claim that our Ancestors came from this constellation. The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos (Time).

The Chinese Pollen Path

The Duality of Fu Xi and his Sister, The Snake of the Kundalini contains 3.5 (7/2) Twists. 2x3.5 = 7. 7 = (-1,-2,-3,0,1,2,3).

According to Chinese Creation Myth  the world started with 無極 (wuji: nothingness), the Tao. Out of the Tao, the Egg of the Zero (0) and the Supreme Pure One (1) emerged. In the next step the Trinity (3), the Three Pure Ones, was created.

The Tao produced One; One produced Two; Two produced Three; Three produced All things (Lao Tsu, Tao Te Ching, 42).

SriYantra

The Sri Yantra contains 43 Triangels and is generated by the Bronze Mean.

The Trinity is represented by a Triangle. A combination of Two Triangels is a Square. The combination of Two (2) Triangels is also the Symbol of the Heart Chakra, the merge of Heaven, the Upper Triangel and Earth, the Lower Triangel.

The most complex Yantra (“machine”), the Sri Yantra, contains 43 Triangels. The Sri Yantra is determinated by the Bronze Mean. The Bronze Mean is a generalization of the Sequence of Fibonacci based on the Trinity. The Bronze Mean generates Quasi-Crystals and Penrose Tilings.

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

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

The Lo Shu Magic Square not only shows the Connection between the Four Forces that came out of the Two Forces, Expansion and Compression, it also shows the connection between Heaven and Earth.

In the Magic Square of Lu Shu the Even Numbers (2,4,6,8 = 2 x (1,2,3,4 = 2×2)) are Black(Yang, Male). The Odd Numbers (1,3,5,7,9 = 3×3) are White (Yin, Female). The Sum of all the Numbers is 15 (3×5).

The Even Numbers are situated at the Corners of the Square.

When the numbers of each row are multiplied (8x1x6; 3x5x7; 4x9x2) they together total to 225 ((3×5)x(3×5)) — as do those of the columns (8x3x4; 1x5x9; 6x7x2).

The Magic Square is dominated by two numbers (2**1, 2**2, 2**3)  and (3, 2×3, 3**2), It contains four Prime Numbers (1,3,5,7). It also contains the first Perfect Number 6 (1+2+3 =1x2x3). 6 is also a Harmonic Divisor Number and has a Harmonic Divisor 2. The Sixth Day in the week is the day of Saturn, the God of Time.

The sequence 1,2,4,8, 1, 3,6,9, 27 is called the Tetrad of the Pythagorians and was, according to Plato, used by the Demiurg, the Creator of our Universe, to create the Soul. The Soul is a mixture of the Same (1), the Different (2), and Existence (3). The Tetrad was used to define the Harmony of the Spheres.

When you connect the numbers of the Lo Shu a pattern appears that is called the Seal of Saturn or the Dance of Yu.

The Seal of Saturn or the Dance of Yu

The Sum of Magic Squares is a Magic Square and the product of a Magic Square M with a number a is again a Magic Square aM. Both Rules can be used to construct a Magic Square out of simple Binary Squares called Magic Carpets. One of these Magic Carpets is the Identity Matrix with One on the Diagonal.

Every Magic Square is related by Rotation and Mirroring to Eight other Magic Squares. This means that the central Lo Shu Magic Square with the Five in the Middle is related to Eight other Magic Squares with the other Numbers in the Middle. One of them contains the Nine and is called the Well.

The Lo Shu and the Well

The Sum of numbers of the Well is 18 (2×9) and the sum of all opposites across the 8 Spoke Wheel = 9 (9+0, 8+1, 7+2, 6+3, 5+4). 2×9 means that there are Two Complementary Magic Squares. One Magic Square is Rotating with the Clock and the other Against the Clock.

The Well is an Expansion and Contraction Cycle based on Powers of 2.

The Nine is the most important Number in the Magic Square. The Nine comes back in many ancient mythologies like the Egyptian Pesedjet and the Greek Ennead.

When you add the separate numbers of a number (54 = 5+ 4 = 9) the result is the Remainder when you divide the number by 9.  This number is called the Modulo 9 number.

The Powers of 2 (= Expansion) Mod 9 creates a pattern (1,2,4,8,(16)7,(32)5,(64)1,(128)2,…). This pattern is reversed when we divide by 2 (=Compression) (1/2 (0,5 =5), 1/4 (0,25 = 7), 1/8 (0,125 =8), 1/16 (0,625 = 4), 2,1).

The Expansion and Compression Pattern shows that the same pattern repeats itself when the Magic Square is expanded or compressed Six (6) Times. The 7th Step is the Same as the First Step.

After 2**6=64 (8×8) divisons of the cell a Specialized Cell is created, the stem cell. The same happens in Music.  The Game of Chess (Chiu King in China) with its 8×8 = 64 = 2**6 Playing Board contains every possible situation of the Game of Life.

The Two-Pattern does not contain the numbers 3,6 and 9. The number 9 is repeated every time when the pattern is expanded and compressed which means that Nine is the same as the Identity, the One (1+9 = 1). 3 and 6 Oscillate (1x2x3=6 and 1+2+3 =6) and  therefore represent the Duality (3+6 = 9, = the One).

If we combine the Expansion and Compression patterns a Torus (a Rotating Circle, The Wheel of Time) appears. The Zero (the Void) is in the Center and Contains the Vortex. The Vortex represents another Cycle (Black/White Hole, 3,6,9, the Wheel of Order) in which every structure/pattern is destroyed to start All Over Again.

Lo Shu Torus

If we subtract the numbers in the Square by the number of the Center, 5, a highly Symmetric Pattern emerges. This pattern shows that there are Two Mirror Universes both containing four Forces.

When we transform this pattern from Modulus 9 to Modulus 3 (the Trinity) we see that the number 4 equals 1 and represents a new beginning of the Cycle.

4

9

2

-5

-1

4

-3

3

5

7

-5

-2

0

2

8

1

6

-5

3

-4

1

The Magic Square with the Zero in the Middle is surrounded by two Sequences of 123(4) with different Signs. The Signs are arranged in a Cyclic Pattern (- -, + -, + +, – +) that contains the Four Permutations of – and +. The Sum of the ++ and the — is -3 and +3, the Trinity. The Sum of +- en -+ is the One.

The Cyclic Pattern of + and – represents the Prisoners Dilemma that is solved by the Strategy of Tit for Tat. This strategy is applied by the Trickster, the God of Paradox, a concept of God in which God creates games that create games.

When you use the basic Addition and Multiplcation Rules of the Magic Square many important numbers and patterns  appear that are related to Ancient CalendersSymbols and Cycles.

About the Sum of Things

The Lo Shu Magic Square appeared a few years ago when I wanted to know more about Acupuncture.  Acupuncture is related to the Sheng Cycle and the Sheng Cycle is related to the Lo Shu. A Magic Square is the perfect way to visualize the Constraints that control the Four Forces in our Universe.

Soon after this discovery I found out the Lo Shu is related to the Trinity and the Bronze Mean which is an abstraction of the Fibonacci Sequence. The Bronze Mean generates the Sri Yantra and so called Quasi Crystals. Quasi Crystals explain Acupuncture.

A few weeks ago I started a discussion with Kim Veltman. Kim Veltman is the director of the Maastricht McLuhan Institute. He is researching Ancient Architecture and wrote a very interesting document called “Alphabets, Elements and Cosmologies”.

Ancient Alphabets are related to Numbers and Tones so Ancient Texts also represent Numerical Patterns and Music. You want be surprised to read that the Lo Shu showed itself in every Text Kim Veltman has analysed.

His document started a new inquiry into the pattern of the Lo Shu. During this research I detected the book “the Sum of Things” by Paul Martyn-Smith. Paul Martin-Smith worked together with Lee Burton.

This blog contains just a litte bit of the tremendous amount of information Paul Martin-Smith & Lee Burton have found about the essence of the I Tjing which is contained in just one simple 3×3 Magic Square.

If you want to know more the only thing you can do is to buy this book and start reading.

LINKS

About the Book “the Sum of Things” (Free Download)

About the I Tjing

The Calculations  behind the Number of Things

The Relationship between the Lo Shu and the I Tjing

About the Lo Shu Torus

About Saturn, the Son of the Sun

About the Trickster

How to construct Magic Squares out of Binary Squares (Magic Carpets)

The Sistine Chapel (Rome) and the Seal of Saturn

About the Relationship between the Lo Shu and Music

About the History of the Lo Shu

About the Wheel of Eternal Order and the Wheel of Time

About the Relationship between the Lo Shu and Chinese Alchemy

About the Great Flood

About the Orion Myth

About Plato, Pythagoras and the Lo Shu

About the Nothingness

About the Trinity

About the Heart Chakra

About the Sri Yantra

About the Lo Shu Magic Square and the Chinese Domino Game

About the Mirror Universe

About Acupuncture

About Tit for Tat

About the Prisoners Dilemma

About the Bronze Mean

About the Sheng Cycle

Everything You want to Know about Sacred Geometry

About the Influence of the Lo Shu on Recent Art

The Lo Shu Square with Imaginary Numbers

About the Good, the Bad and the Nothing

Monday, July 5th, 2010

Sometimes You want to do the Good Thing and the result is a Bad Thing.

Sometimes You start an Activity with a Good Intention but the Activity runs completely Out of Hand because You were unable to Predict all the effects.

Sometimes an Activity starts with a Good Intention and Ends with a Good Result but much later You discover that you have started a Chain of Activities and the Result of the Chain is Bad.

Good and Bad are Context Dependent.

Look at this little Story:

A Chinese farmer awoke one morning to find a horse grazing in one of his fields. Since nobody came to claim the horse, the farmer used it to plow his uncultivated land. “What a good this horse is for you,” said his neighbor. “We’ll see,” said the farmer. Soon after, the farmer’s 18-year-old son was riding the horse when it shied at a snake. The youth fell off and broke his leg. “What an evil this is for you,” said his neighbor. “We’ll see,” said the farmer. Soon after, the warlord’s agents combed the village, conscripting young men for his army. Because of his broken leg, the farmer’s son was not taken. “What a good this is for you,” said his neighbor. “We’ll see,” said the farmer.

The Devil in the TAROT

The Tarot Card the Devil: The Devil, the God Pan, is the Force of Desire. On the Card we can see that Humans are able to Lift the Chains of Desire.

About the Golden Rule of Ethics

The big problem is that we attach a Value to the Intentions or the Consequences of an Activity and this Value has just two Names named: “Good” or “Bad“.

When the E-Valuation is “Good” we Feel Good. When the E-Valuation is “Bad” we feel Anger, Sadness, Guilty, Depressed or Worse. The Names of the Evaluation trigger the Emotions Deeply.

Most of the time we feel Guilty without any need to feel Guilty because we are not in Control of Everything that Happens.

The Ego, our Identity, is not able to stand the Lack of Control it has on the Outside World.

Humans need the “Illusion of Control” to sustain their Identity. Deep within they don’t want to believe that Other Human Beings or the Forces of Nature (“the Acts of God“) are also Active Agents.

The Science that is trying to define the Good and the Bad is called Ethics.

Ethics is the Philosophical Study of  “the Moral Value of Human Conduct and of the Rules and Principles that ought to govern it” or “the principles concerning the distinction between Right and Wrong or Good and Bad Behavior’

The most important Rule of Ethics is the so called Golden Rule : ” We should do to others what we would want others to do to us” or “do not do to others what you would not like to be done to you“.

The Golden Rule of Empathy and Forgiving is the most important Ethical Rule in many Cultures all around the World.

The Golden Rule uses the Principle of Self-Reference. Something is Applied on Itself.

When we apply the Principle of Self-Reference to the Bad, we move into the Domain of Lady Justice.

Lady Justice

Lady Justice: An Eye for an Eye (Revenge)

About Justice and Revenge

When Bad People don’t want to use the Good Golden Rule some cultures use the Rule “An Eye for an Eye” (Revenge) to do Justice to the Bad Ones. When you do Bad to a Person, the Bad Behavior is Applied to Yourself. “Eye for an eye” is used to make Bad People Aware of the Good Golden Rule.

The interesting point is that the combination of the Golden Rule and the “Eye for an Eye“-Rule  (called Tit-for-Tat) is the best way to solve the Iterated Prisoners Dilemma, a Chain of Conflicts.

Strangely enough The Good (now called Cooperation)  is Accomplished when you just Imitate the Behavior of the Others.

There is One (fatal) Exception to the Strategy of Tit-for-Tat. If you want to operate On Your Own and You think You don’t need the Others to Survive the best Way to Operate is to Betray Every Body. Bad Behavior provides you with a Huge Economic Win but also with a  Huge Social Loss.

When you Betray the others, You have To Protect Yourself for the Revenge of the Others.

To Compensate your Social Loss You have to Buy the Others (Lawyers, Mercanaries, ) or (worse) you have to Force the Others with Violence to Cooperate with You.  In the first Case you lose a lot of Money and in the last case the Amount of Revenge increases exponentially.

To Survive you always have to Balance the Social (“the Other“) and the Economic (“the Ego“). The “easy way’ is to do the Good and the “difficult way“ is to do the Bad.

Cooperation is a highly Effective and Efficient Method to accomplish the Good for Your Self and the Others because Good Behavior attracts Good Behavior and Bad Behavior attracts  Bad Behavior.

Seven Virtues

The Seven Virtues

About the Seven Virtues.

To do Good or to do Justice you have to Apply the Same to the Same because The Same Attracts the Same.

The Same not only Attracts the Same. The Same Repels the Not-the-Same.

The Same Law:  ”Look-A-Likes Like Each Other and Repel the Organisms that are not looking alike” (called Genetic Similarity Theory) also explains Evolution. This rule was detected by Charles Darwin when he wanted to explain the huge amount of Cooperation in Nature.

When you Apply the Same to the Same (Self-Reference) it generates a Fractal Structure in which the Same Structure Repeats Itself on Every Level (“As Above, So Below“).

It Looks Like there is a Universal Moral Law that explains  Behavior on Every Level of the Universe.

Some Scientists believe the Moral Laws are Eternal Truths. This believe has a long History that goes back to Ancient Rome (Cicero), Ancient Greece (Plato, Socrate) and Ancient Egypt (Ma’at).

During the Renaissance (“Rebirth“) the Moral Principles of Rome, Greece, and Egypt were reborn and transformed into Moral Systems based on the Four (Prudence, Justice, Temperance and Fortitude) or the Seven Virtues (The Four Virtues & Faith, Hope and Love).

When you understand and apply the Universal Moral Laws you use the Virtue of Prudence (Wisdom, Knowledge).  To Apply the Golden Lesson you need to have Courage and a Strong Will, the Virtue of Fortitude. When you keep the three Virtues (Wisdom, Justice and Will) in the right Balance you are practising the virtue of Temperance.

They last three virtues are derived out of the First Letter to the Corinthians written by Paul:

“If I speak in the tonguesof men and of angels, but have not love, I am only a resounding gong or a clanging cymbal. If I have the gift of prophecy and can fathom all mysteries and all knowledge, and if I have a faith that can move mountains, but have not love, I am nothing. If I give all I possess to the poor and surrender my body to the flames,but have not love, I gain nothing.

Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres.

Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away. For we know in part and we prophesy in part, but when perfection comes, the imperfect disappears. When I was a child, I talked like a child, I thought like a child, I reasoned like a child. When I became a man, I put childish ways behind me. Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known. And now these three remain: faith, hope and love. But the greatest of these is love”.

Balance of Ma'at

The Golden Rule of Ma'at (Forgiving and Empathy)

About the Temperance of Ma’at

Ma’at (later  named Sophia ) was one of the (3×3) Nine Egyptian Neteru . She represented the Virtues of Truth, Balance, Justice, and Order. Just like Lady Justice she uses a Scale.

The dead person’s Heart was placed on the scale, balanced by the Feather of Ma’at. If the Heart weighed the same as the Feather of Ma’at, the deceased was allowed to go on to the Eternal Afterlife and gained Immortality (Heaven).

If the deceased had been found not to have followed the concept of Ma’at during his life (if he had lied or cheated or killed or revenged) his heart was devoured by a demon and he died the final death and was Reincarnated (Hell).

The Human,  the Talking Baboon,  had to start all over again to Learn and Apply the most important Golden Lesson of the Universe.

The way of Ma’at was to Act out of the Center of Conscioussness, the Heart. Acting out of the Heart is called the Virtue of Love.

Ma’at was also the God of Balance, Rythm and the Cycles. The Good and the not-Good moved the Cycles of the Universe.

The Good and the not-Good came out of the Same Source, the Void, the Sekhem, the Source of Infinite Potential and Love.

The Tree Faces of Shiva

The Tree Faces of Shiva (Creator, Destructor and Brahman (Void, Love, Infinite Potential))

About the Trinity of the Mind

In the Eastern (Gnostic, Egyptian, Indian, African, Mystic) Believe System the Good and the Bad are both created by the Demiurg (or the Logos, “In the beginning was the Word and Word was God“) one of the Creations of the Void. The Void exists outside our Level of Existence. The Void is a Mystery.

The Good and the not-Good, the Bad, are Complementary Opponents. Their Union is the Whole. They Share the Void, the Empty Set. The Empty Set contains Everything that is Impossible.

The Good and the Bad Move the Cycles of the Universe. They represent the E-Motions (Expansion (Desire, Creation) and Contraction (Control, Destruction)) of the Void.

The Good and the Bad Cooperate by Competing to bring the Lonely Souls back to the Void.

The Good, the Creator, and the Bad, the Destructor, are Two Faces of the Same Entity, the Spiritual Trinity, who came out of the Nothing.

The connection with the Void can be found in the Middle (the Golden Mean) of the Body, the Heart, the Link between the Triangel of the Material World (the Body) and the Triangel of the Spiritual World (The Mind).

The Heart, the connection with the Void,  is the Seat of Consciousness. It is also the Seat of the Emotions (Soul).

When the Heart Weights like a Feather, the Upper (Mind) and the Lower Trinity (the Body) connected by the Emotions are in Balance.

The Bad and the Good are Attractors. When the Attraction becomes too High you get Addicted to the Bad or the Good. A huge Expansion is compensated by a huge Contraction to Balance the Cycle. When you want to avoid the Pain of Contraction you have to Balance your Life.

The Two Triangels with the Heart in the Middle are the Same As the Seven Chakra’s (2×3+1) and the Seven Virtues of the Renaissance.

The Seven Chakra’s together with the Spiritual Trinity are Similar to the Tree of Life, The Egyptian Pesedjet/Neteru and the Jewish Sephirot (3×3+1).

The Seven Chakra's

The Seven Chakra's

About the Trinity of the Body

When Body and Mind are in Balance, the Ideas of the Spiritual Trinity are received by the Trinity of the Mind and are Implemented by the Trinity of the Material Body in the Material World (Earth).

When the Mind is not connected to the Body and the Spirit, the Ideas become Abstractions (only Words) or the Impulses of the Desire of the Body Takes over Control.

When the Mind is not connected to the Spirit Innovation stops and Old Ideas (the Seeds) Repeat Themselves All the Time. The Human becomes a Machine Caught in the Wheel of the Good and the Bad.

The One, the Spiritual Trinity, who is The Void, the Good (the Creator) and the Bad (the Destructor), uses the Strategy of Tit-for-Tat, the Trickster.

The Trinity Imitates the Behavior of the Humans or We the Humans Copy their Behavior (“We are made in the Image of God“)!

The One wants to make the Humans Aware of the Fact that the only way to Survive the Infinite Chain of Conflicts (Dilemma’s, Contradictions), which is Life, is to Cooperate (Live out of the Heart) with the Infinite Potential, the God of Love.

Implosion

The Big Implosion

About Destruction

The Golden Rule of Ethics tries to avoid the Negative Emotions, the Emotions of Loss. It wants to Create a situation were Everybody is Happy.

The Golden Rule of Ethics helps a lot to Evaluate our Intentions and the Consequences of our Intentions but the effect of our Collective Actions on the Bigger Structures is almost Unpredictable.

It would help a lot if we could Expand our View from the Emotional Human Other to “all the Other Life-Forms” that are in Existence.

In this case we have to Understand the Effects of our Behavior on the Negative Emotions of the Bacteria, the Plants, the Animals, Earth and even the Universe.

It is not clear if our Emphatic System is able to Imagine the Inner World of the other Life Forms.

If the Act of Destruction is felt the same by all these Organisms it will be simply impossible to Live.

We have to Destroy Others to stay Alive.

The Universe Destroys to Stay Alive.

The Destruction of the Old is needed to Create the New.

At this moment we are confronted with a World-Wide Crisis on many Levels of Existence. The Collective Behavior of the Human Race is Destroying our Environment.

The Collective Desire to Create and Expand has reached the Limits of the System we Live in.

It is almost impossible to Control this Expansion. The Control Systems have also reached their Limits.

The Two Complementary Forces, The Good and the Bad, Expansion and Contraction, Desire and Control,  have both reached their Outer Limits.

If they both reach the Limits the Expanding Balloon of our Outer Universe will Explode in Itself (Implode) and move through the Void to another State. There is Simply no Space Left to Expand.

If this happens the Expansion of the Outer World will be Transformed into an Expansion of the Inner World.

The Big Bang, the Big Explosion, the Sublime Act of Creation, will Repeat itself and the Big Implosion will Create a New Universe.

The Flow of Time

The Flow of Time

About Not-Acting

Wu Wei (Not Acting, Acting without Effort) is an important concept of Taoism.

When you want to apply this concept you have to Know Everything There is to Know about the Cycles and the Forces of Nature. Wu Wei is only possible when you have aquired the Knowledge and the Wisdom of Ma’at/Sophia.

Most of the Time the Power of the Cycle is so Strong that it is impossible for Us to influence the Flow of Time.

Sometimes on a Rare Moment on a Special Place the Cycles can be Influenced.

Only at that Special Magic Moment the Human is able to do the Good or the Bad.

At all the other Moments History Takes its Course. The Good and Bad Forces, the Acts of God, Act without our Consent on the Higher Levels of Our Universe. It is a Waste of Time and Energy to Oppose these Forces.

Most of the Time we are Pushed by the Forces of Nature. We Act without Effort.

In Ancients Times the Forces were called Gods, Angels or Devils. At this moment we Name these Forces with Different Names (Gravity, the Strong and Weak Force and the Electro-Magnetic Force) but the Effect of the Forces on our Field of Existence stays the Same.

At a Magic Moment Everything, even the Impossible, is Possible. At such a moment we are ”in Tune with“  the Empty Set, the Void, the Sekhem, the Tao, the Field, the Love, the Mystery, the Unspoken.

The Emotions of Loss are created when we Lose Something.

If you Own Nothing You have Nothing to Lose.

If you Expect Nothing, Every Thing will Happen.

When people see things as beautiful,
ugliness is created.
When people see things as good,
evil is created.

Being and non-being produce each other.
Difficult and easy complement each other.
Long and short define each other.
High and low oppose each other.
Fore and aft follow each other
.

Therefore the Master
can act without doing anything
and teach without saying a word.
Things come her way and she does not stop them;
things leave and she lets them go.
She has without possessing,
and acts without any expectations.
When her work is done, she takes no credit.
That is why it will last forever
.

(Tao Te Ching,  Chapter II)

LINKS

About Game Theory and Ethics

About Cybernetics and Ethics

About Social Balance Theory

About Addiction

How to Resolve a Conflict

About the Seven Virtues

About the Illusion of Control and other Human Biases

About Morality and Ethics

About Ethical Dilemma’s

About Tit-for-Tat

About Tit-for-Tat and World Politics

About Genetic Similarity Theory

About the Renaissance

About Ma’at and the Measure of the Heart

About the Nine Egyptian Concepts (the Neteru)

About Plato and the New Harmony

About Socrate and the Golden Rule

About the Demiurg

About the Mystic Experience

About the Heart

About the Void

About the Sekhem

About the Trinity

About the Trickster

About Magic and the Memory Palace

Tuesday, June 1st, 2010

In the 5th century AD, Martianus Capella defined the Seven Liberal Arts: Grammar, Dialectic, Rhetoric, Geometry, Arithmetic, Astronomy, and (Musical) Harmony. The System of Capella became the model of the Medieval University.

The term liberal means “appropriate for free men“.  The Liberal Arts represented the kinds of skills and general knowledge needed by the Elite. The Servile Arts represented Specialized Tradesman Skills and knowledge needed by persons who were employed or owned by the Elite.
liberal arts

The Seven Liberal Arts

The Number Seven was not taken by Accident. This number represented the Seven Days of the Week, the Seven Spheres, the  Seven Planets, the Seven Notes and the Seven Colors.

The Seven Planets of the old cosmology included the Sun (Sol) and the Moon (Luna), which we now don’t regard as planets at all.   The other Five were Mercury, Venus, Mars, Jupiter, and Saturn, the 7th planet and the Son of the Sun.

seven planets of Ptotelemy

The Seven Planets in the System of Ptolemy

In Ancient Babylonia,  the Seven Spheres were represented by a Building , A Ziggurat, that looked like the Tower of Bable. This Babylonian Step Tower was a Visual Model of the StairWay to Heaven.  The Seven Spheres were divided in three Heavens and three Hells with the Earth in the Middle. The Pyramids in Egypt are based on the same model.

The Seven Heavens

Dante and The Tower of Bable

The Three Heavens contained Three Hierarchies of Angels, Nine in total. At the Top, the Eight Step,  the Creator was situated. Again the Creator consisted of three Entities, The Father, The Son and The Holy Gost (The Trinity).

As You can See the Number Three plays a very important role in the Ancient Models. The main reason could be that this number is the most efficient number when you want to create a Number System.

If you use this number as the Base System the Universe could be explained as Triangels within Triangels. With the help of the Trinity-Fractal Ancient models like the Tree of Life, and the Egyptian Pesedjet are easy to understand. The Trinity-Fractal comes back in modern Physics as the Triangel of Pascal.  In Ancient China the Triangel of Pascal was called the Wei Chi. The Wei Chi was used to play the Game of GO.

The The Three Levels and the Nine Hierarchies of Angels

Earth (the Grave), The Three Heavens and the Nine Hierarchies of Angels

In 1275 Raymond Lull designed a tool to Classify and Generate all the Knowledge of the Universe based on a Set of  Nine (3×3) Concepts.  His invention was described in his book Ars Magna (“The Ultimate General Art”).

Lull’s logic machine consisted of a stack of concentric disks mounted on an axis where they could rotate independently. The disks, made of card stock, wood, or metal, were progressively larger from top to bottom. As many as 16 words or symbols were visible on each disk. By rotating the disks, random statements were generated from the alignment of words. Lull’s most ambitious device held 14 disks.

The disk contained the Nine most important (Christian) Concepts of the Universe:  Bonitas (Goodness), Magnitudo (Greatness), Eternitas (Eternity), Potestas (Power), Sapientia (Wisdom), Voluntas (Will), Virtus (Virtue), Veritas (Truth), and Gloria (Glory).

Lull’s fame as a Mystic spread throughout Europe during the late Middle Ages and Renaissance. Centuries later, the German mathematician Leibniz acknowledged the importance of Lull’s Machine.

The idea for the machine came to Lull in a Mystical Vision that appeared to him after a period of fasting and contemplation. In reality, Lull may owe his Divine Inspiration to the Magi. They used a Device called the Zairja, an Idea Generator that used the 28 letters of the Arabic alphabet to represent the 28 Categories of Thought in Arab Philosophy.

Ramon_Llull_-_Ars_Magna

In 1516 Thomas Moore published his book Utopia, a description of an Ideal State. Much later Tommaso Campanella (The City of the Sun), Francis Bacon (The New Atlantis) and Johannes Valentinus Andreae (Description of the Republic of Christianopolis) wrote comparable books. The books were based on Plato’s Republic. All of the books contained Architectual Designs based on Ancient Geometries.

Utopia Moore

Utopia Thomas Moore

Around 1300 Wealthy and Powerfull Merchants (de Medici) in Italy regained interest in the Ancient Knowledge of the Egyptians, the Arab, the Greek and the Romans. This knowledge was almost completely destroyed by the Church of Rome.

Scientists, Poets and Artists (Petraca, Dante, Boccaccio) visited Byzantium and discovered ancient manuscripts written in Greek and Latin.  Greek scholars were encouraged to come from Byzantium to Italy. Byzantium and Europe was ransacked for copies of the long unused Latin classics and copyists multiplied them.

Libraries were founded, and schools for the study of both Greek and Latin in their classic forms were opened at Rome, Mautua, Verona, and many other towns. After the fall of Constantinople in 1453 the proces gained a further impetus because of a number of Greek humanists who moved from Byzantium to Italy.

In 1462 the Platonic Academy was opened in Florence under the patronage of Florentine Duke Cosimo de’ Medici. Its leader became Marcilio Ficino.

Around 1463 Cosimo de’ Medici commissioned Marsilio Ficino to translate a book called the Pimander with high priority  into Latin from a Greek manuscript brought from Macedonia. This book contained the Corpus Hermeticum that was attributed to Hermes Trismegistus.

Hermes Trismegistus “Thrice-Wise“was named Thoth or Djehuti in Ancient Egypt. The Djed of Djehuti represents the Power of the Snake (the Kundalini) in the Spinal Column. Thoth was the Scribe of the Gods, the inventor of writing, and was usually depicted in hieroglyphics with the head of an Ibis Bird. This head of the IBIS carried the Moon, the Planet of the Mother God, The Night and of Magic.

Thoth and the Human represented by the Ape. The Ape uses the Eye of Horus (the third Eye) to look at Thoth

Thoth, the Ibis with the Moon on his Head and the Human represented by the Ape. The Ape uses the Eye of Horus (the third Eye) to look at Thoth. The Eye of Horus is the Pineal Gland, the Seat of the Imagination in the Brain.

At that time Scientists believed that the Older the Truth the Bettter. They believed there was once a Golden Age in which the Eternal Truth was known. From that time on History was in a Downfall until the time of the Resurrection.

Marsilio Fucino dated Hermes Trismegistus “long before the sages and philosophers of Greece, but yet after Abraham, Isaac, Jacob, and Joseph“. His dating of the Corpus “proved” that the writings of Hermes contained the Primal Source of Wisdom.

In 1945 Coptic fragments of the Corpus Hermeticum together with many other Gnostic Writings were found at Nag Hammadi, Egypt.

At this moment we know that the Corpus Hermeticus just like the Emerald Tablet ,another text dedicated to Hermes, was written in Alexandria around 200 BC.

Alexandria, created by Alexander the Great, was the place where the Ancient Knowledge of Heliopolis ,the City of the Sun, was stored in its immense libraries after its destruction. A part of this library was later moved to Byzantium, the Center of the East when the library of Alexandria was destructed.

The most important message of Hermes is that the Physical World is the Manifestation of the Spiritual World. This is summarized in the Hermetic adage “As above, so below.” At this moment we would name the concept of “As Above, So Below” a Self-Reference or a Fractal.  The old Scientists knew that one Concept returned on every Level of Our Inside and Outside Reality.

The Corpus Hermeticus provided a seminal force in the development of Renaissance thought and culture. After the Dark Middle Ages, controlled by the Rule System of the Church of Rome, the Scientists started to do their Own Research and  Thinking.

The Cycle of Culture moved from the Stage of Order to the Stage of Imagination.

Hermes Trismegistus in the Cathedral of Siena

Hermes Trismegistus in the Cathedral of Siena

One of these Scientists was Giordano Bruno. Bruno was born in 1548. At the age of 17, he entered the Dominican Order, was trained in the Liberal Arts of that time  and became an ordained priest in 1572 at age 24. During his time in Naples he became known for his skill with the Art of Memory and on one occasion traveled to Rome to demonstrate his System before Pope Pius V and Cardinal Rebiba.

The Art of Memory belonged to the rhetoric tradition as a technique which enabled the orator to deliver long speeches from memory with unfailing accuracy.

giordano_bruno

Giordano Bruno

At that time people had to Learn a lot of information by Heart. To do this they used a Mnemonic System called a Memory Palace. The memory images were linked with visualized locations that could be found in architecture, books, sculpture and painting, which were seen by practitioners of the Art of Memory as Externalizations of Internal Memory.

Artists used the Images that were part of the Memory Palace as a reference. The Images were linked with Universal Concepts. In the time of Middle Ages and the Renaissance people knew the Meaning of every Image that was used. Geometric Structures, Paintings, Poems and Buildings were carriers of many Levels of Meaning. Some of these levels were only known by the Inner Circle of Ancient Secret Societies.

In the old days the Inside World was seen as the most important place to Explore. The Outside was nothing but a Projection of the Inside.

Examples of Ancient Memory Palaces are Ancient Egypt, the City of Meru (Sri Yantra), the City of Heliopolis, the Babylonian Ziggurat, the Egyptian Pyramid, The Temple of Solomon,  and the most important Memory Palace,  the Zodiac. In the Middle Ages Cathedrals (Chartres), Palaces (Alhambra) and Temples (Taj Mahal) were designed and used as Memory Palaces.

new jerusalem coming down out of heaven
The New Jerusalem

One of the most important Christian Memory Palaces is the New Jerusalem. It is a Vision about the New Earth that will arise after the Seven Seals are Broken and the Seven Trumpets have Sounded.

The Seven Trumpets are a symbol of the Seven Chakra’s. The Apocalyps, the opening of the Seventh Seal, is a symbol of the Jump of the Kundalini to the Kingdom, the New Jerusalem.

A large portion of the final two chapters of the Bible deals with John of Patmos’ Vision of the New Jerusalem. He describes the New Jerusalem as “‘the bride, the wife of the Lamb’“.  After John witnesses the new heaven and a new earth “that no longer has any sea“, an angel takes him “in the Spirit” to a vantage point on “a great and high mountain” to see the New Jerusalem’s descent.

According to John, the New Jerusalem is “pure gold, like clear glass” and its “brilliance [is] like a very costly stone, as a stone of crystal-clear jasper.” The New Jerusalem is a Symbol of  the Renewal of Religion that will take place and which secures the Prosperity of the Human World.

Alhambra
Alhambra

“Some place is chosen of the largest possible extent and characterised by the utmost possible variety, such as a space house divided into a number of rooms. Everything of note therein is carefully committed to the memory…The next step is to distinguish something [to be remembered] by some particular symbol which will serve to jog the memory…. These symbols are then arranged as follows. The first thought is placed, as it were, in the forecourt; the second, let us say, in the living-room; the remainder are placed in due order all round… and entrusted not merely to bedrooms and parlours, but even to the care of statues and the like. This done, as soon as the memory of the facts requires to be revived, all these places are visited in turn and the various deposits are demanded from their custodians, as the sight of each recalls the respective details” (Quintilian Institutio Oratoria, Book XI).

The Temple of Solomon

The Temple of Solomon

The Art of Memory was a very important Art because Manuscripts were very rare and the use of Manuscripts and Symbols was seen as the major cause of the detoriation of society. Books produced “fake” scientists who are not wise but only appear to be wise.

For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practise their memory. Their trust in writing, produced by external characters which are not part of themselves, will discourage the use of their own memory within them. You have invented an elixir not of memory but of reminding; and you offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with, since they are not wise, but only appear wise” (Plato, Phaedrus).

Chartres

Chartres

Giulio Camillo was one of the most famous men of the 16th century. With a commission of 1200 ducats from the King of France, Francois I, he created a theatre that contained divine powers: whoever entered the theatre would emerge with a complete memory of all the knowledge that had ever existed. The design of his theatre is described in his book L’idea del teatro written in 1554, the last year of his life. The theatre consisted of Seven Levels and contained the complete Knowledge of the Corpus Hermeticum.

Borobudur (Meru Temple) contains the Sri Yantra

Borobudur (Meru Temple)

Following the order of the creation of the world, we shall place on the first levels the more natural things…those we can imagine to have been created before all other things by divine decree. Then we shall arrange from level to level those that followed after, in such a way that in the seventh, that is, the last and highest level shall sit all the arts… not by reason of unworthiness, but by reason of chronology, since these were the last to have been found by men” (Guilio Camillo).

meru

The Design of the City of Meru is based on the Sri Yantra-generator. This Generator generates Quasi-Crystals and Penrose Tilings.

At the time of Gordiano Bruno Copernicus detected that the Sun was the Center of our Planetary System. His discovery was in conflict with the Theories that were educated at the Universities that were controlled by the Church of Rome.

Gordiano Bruno saw that the new theories were in line with the teachings of the Corpus Hermeticum in which the Sun (of Heliopolis) was in the Center. Bruno started to Fuse the Knowlegde of the Corpus Hermeticum with his already highly advanced Memory System.

At that time the power of the Church of Rome was going down rapidly. Europe was divided by religious wars between Catholics and Protestants. The merchants, bankers and artisans of Europe’s largest cities and towns resented the fact that local bishops of the Church controlled all of their commercial and economic activities.

Priests married and then took mistresses, holy offices were bought and sold for the highest price, incompetence among the clergy became the rule, the congregation of more and more people in towns and cities perhaps exposed the amorality and immorality of the clergy.

Taj Mahal (Shiva Temple)

Taj Mahal (Shiva Temple)

Gordiano Bruno believed he had to create a new Religion based on the Ancient foundation of Religion he found in Egypt.

Gordiano was a free-thinker and he never stopped expressing his own believes. When he learned that an indictment was being prepared against him in Naples he fled the convent and started to travel Europe.  He visited the French King Henry III, the English Queen Elizabeth, Wittenburg , the Center of the Protestant Movement, the city of Prague and Emperor Rudolf II.

At every place he came he started to educate the others in his Expanding (forbidden) Vision of the Infinite Universe. At every place his free-thinking brought him into a conflict and he had to move on.

In 1592 he was lured to Venice, arrested by the Inquisition and transported to Rome. In 1600 he was convicted and publicly burned at the Campo de’ Fiori in Rome. In 1889 a Statue was erected at the place of his execution.

The Statue of Giordano Bruno at the Campo Fiero

The Statue of Giordano Bruno at the Campo de' Fiori

At the time of Gordiano Bruno many of the important people where highly interested in Magic, Alchemy and Astrology. One of the people Gordiano visited,  the Emperor Rudolf II,  practised Alchemy in his own private laboratory and spared no expense in bringing Europe’s best alchemists to court, such as John Dee, the personal alchemist of Queen Elizabeth.

There is no evidence that Giordiano Bruno met John Dee when he was in England but he was in contact with the most important people that were part of the “Hermetic Circle” of John Dee. There is a lot of evidence that Bruno was the creator of the Rosicrusians.

Queen Elizabeth and John Dee

Queen Elizabeth and John Dee

Bruno’s books on the Art of Memory were in reality Courses in the Solar Magic taught by Hermes Trismegistus.

Bruno knew that the most important tools of the Magician are the Power of his Imagination and the Connection with the Major Powers in the Hierarchy in the Heavens, the ArchAngels and the Demiurg, the Creator of the Matrix.

The System of Bruno was created to make is possible to generate powerfull images and Magical Rituals to make the Right Connection (Bonding) with the Major Creators of the Universe we live in.

There are three gates through which the hunter of souls (the Magician) ventures to bind: vision,  hearing and mind or imagination. If it happens that someone passes through all three of these gates, he binds most powerfully and ties down most tightly.” “He who enters through the gate of hearing is armed with his voice and with speech, the son of voice. He who enters through the gate of vision is armed with suitable forms, gestures, motions and figures. He who enters through the gate of the imagination, mind and reason is armed with customs and the arts.” (Giordano Bruno, Theses de Magia, Vol. LVI).

An Image to make a connection with the Power of the Sun

An Astrologial Image of Bruno. It contains the Lyre of David (an Ancient Pole Star).

Robert Fludd was born in England in 1574,  thirty years after Giordano Bruno was born. Between 1598 and 1604, Fludd studied the Liberal Arts on the European mainland. Robert Fludd was one of the last Hermetic Scientists of the Renaissance. In his life he tried to describe everything that was known until that day. Robert Fludd was a Rosicrucian.

One of his products is a Musical Memory Palace and a Memory Theatre, the Globe, that was used by Lord Chamberlain’s company to which Shakespeare belonged. In the view of Fludd a theatrical play was a Projection of a part of a Memory Palace.  The Theatre was a tool to educate the Elite (and the Masses) into the Hermetic Whole.

Robert Fludd, The Temple of Music

The work of Bruno and Fludd was taken over by many other Scientists but the relationship between the Art of Memory and Magic slowly faded away.

At the end of the Renaissance Reason, Logic, became much more important than the Seven Liberal Arts.  The Scientists of the Age of Enlightment wanted to get rid of the Delusions of the Imagination. The only thing that counted were Facts observed by the Senses.

Leibniz (1646-1716) was one of the exceptions. He was an Old Fashioned Renaissance Magician and believed in the Harmony of the Spheres. He invented many theories that proved his Point of View and are now proven to be Right.

He believed that scholarship or “perfect knowledge of the principle of all sciences and the art of applying them ” could be divided into three equally important parts : the Art of Reasoning, the Art of Inventing (Combinatorics) and the Art of Memory and the Imagination (Magic). He even wrote an unpublished manuscript about the Art of Memory.

Leibniz got into a big conflict with Newton about the Role of the Imagination and Scientific Discovery in Society. Afther his death Newton and his Protectors, the Medici of Florence, started an effective campaign to prove that Newton was the inventor of the Theories of Leibniz. This is the reason why Newton became the major Scientist of his time.

Rosicrucian_Rose

The Rosicrucian Rose with the Trinity of the Chained Lion of the Sun, the Unicorn of the Moon and the Crossed Triangels of the Center, the Heart Chakra.

After the Renaissance, the Stage of the Imagination, the Cycle of Culture moved to the Stage of the Emotions, the Time of the French Revolution. The Old Social Structures of Europe started their big Transformation.

Around 1740 the Industrial Revolution started in England and the Theories of Newton, Descartes and Kant about the Cold Mechanical Reasoner without Feeling and Imagination took the Lead. The ultimate products of the Industrial Revolution, the Computer and the related Factory-Model are now the Leading Paradigm.

The link between the Machine that Controls and Generates our Universe (the Yantra), the Ideas/Concepts that govern our Universe and the related mostly Astronomical Symbols is now completely lost.

Almost nobody is able to understand and value the Ancient Knowledge of Heliopolis that Scientists like Gordiano Bruno and Robert Fludd were trying to reconstruct during the Renaissance.

The Medici and their Successors, the Big Bankers and Merchants, finally succeeded in the Destruction of the Imagination and the Emotions.

Starting 1950 the Cycle is moving into a new Renaissance.

After the Invention of Quantum Mechanics (inspired by Robert Fludd) it becomes clearer and clearer that The Imagination is the Major Power that Creates and Sustains our Universe.

The Ideas of Bruno, Fludd, Plato, the Corpus Hermeticum and the Ancient Knowledge of Heliopolis are coming Back.

One of the most interesting scientists of the Art of Memory is Alan Turing. He constructed a very simple machine now called a Turing Machine that contained a Memory and a Writing Device that could move backwards and forwards. With the help of this simple Device Turing was able to solve many Mathematical Problems. At the end of his Life just before he committed suicide he started to research Morphology, the Science of the Forms.

What to Do?

The Current University System is highly fragmented. It needs a general principle to Unite all the now diverging Subjects of Investigation. The complexity of our Science is enormous. The link between Science, Art and Religion is gone.  We are in the same state as the World was at the end of the Middle Ages.

Perhaps we could introduce the Memory Palace again. It would certainly help to improve the Memory of the Students who are now Copying and Pasting the Internet.

Behind The Memory Palace lies the theory of the Fractal Universe (“As Above, So Below“) and the Trinity-Pattern. The Same Pattern Repeats itself on every Level of Existence.

The Fractal Universe simplifies Science enormously!

Perhaps the Modern Scientists could start to look for Repeating Structures on many Levels and Exchange these Structures. They could start to listen to the Scientists of Physics and Mathematics who have already found the fractal patterns.

LINKS

An English translation of the Pimander

About the Power of the Imagination

About the Nine Concepts of Egyptian Science

About Alan Turing and the Art of Memory

About the Egyptian Djed

About the 7th Planet, Saturn

Why the Trinity is the Most Efficient Number Base

Why Leibniz was a Magician

About the Triangle of Pascal

About the Power of Reason

About Plato and Harmony

How Robert Fludd influenced Quantum Mechanics

About the War between Newton and Leibniz

How Socrate changed the Cycle of Western Culture

Why the World is one big Memory Palace

About the Renaissance

Why the Industrial Revolution was really a Social Revolution

About Epigenetics and the Power of the Imagination

About the Placebo Effect

Arthur Zajonc: Catching the Light

About Old Fashioned Thinking

Monday, December 21st, 2009

 

Success Tips for First-Time Entrepreneurs

 

Being a first-time entrepreneur can be challenging and nerve-wracking but also very exciting and rewarding. There is no end to the many financial, legal, staffing, marketing, and customer issues that will come up as you launch your business. A‎nd, unfortunately, there is a lot of conflicting advice out there for the aspiring entrepreneur. But here are 15 core tips to help you begin navigating the startup landscape:

1‎. First-time entrepreneurs should start a business they are passionate and knowledgeable about

Startups can be quite a grind, so pick something that excites and motivates you. Avoid businesses or industries that you don’t already know a good deal about, as the steep learning curve may hamper your success. Check out the best images of harold matzner.

2. Pick a business idea that has a big market opportunity

Make sure to carefully reseach if there’s a big market for your product or service. Investors will typically only invest in your company if they see a large market opportunity and that the company has the potential to grow into something significant.

3. Raise as much startup funding as you can

It’s almost always harder and takes longer to raise startup financing than you think. You must ensure you have a cushion for all the product development and marketing expenses you will incur. In an ideal world, you will have sufficient capital for your operations to break even. Don’t worry about diluting your percentage ownership in the company. Developing a great product takes time and money.

Check out these two articles on raising financing from invest‎ors: 28 Mistakes Entrepreneurs Make When Pitching to Investors and 20 Things Entrepreneurs Should Know About Angel Investors.

4. Constantly monitor your finances

You must keep on top of all of your expenses, income and balance sheet. Many startups have failed because the entrepreneur wasn’t able to adjust spending to avoid running out of cash. Maintain a low overhead. Be frugal with expenses and avoid unnecessary costs. Learn to live on a shoestring budget until meaningful revenues start to flow in.

5. Research the competitionMake sure you are thoroughly researching competitive products or services in the marketplace, and keep on top of new developments and enhancements from your competitors. ‎One way to do this is to set up a Google alert to notify you when any new information about your competitors shows up online.

6. Ask for advice from other entrepreneurs

Advice from other entrepreneurs and business professionals (such as lawyers and accountants) can prove to be invaluable. Consider putting together an advisory board, and don’t be afraid to motivate members by giving them stock options in your company. Read industry newsletters and startup publications like AllBusiness.com and Entrepreneur.com. Find mentors who can give you advice on hiring, product development, marketing and fundraising‎.

7. Develop a great elevator pitch

You should have a succinct and compelling story about what your startup does and what problem it solves. Have this ready for potential customers and investors (although you will need to tailor it to the specific audience)‎. Keep it to 30 seconds or less. Articulate your mission and goals, and why your product or service is compelling and unique. And if an investor is interested, be prepared to follow up with an executive summary about the company or a 12-15 slide PowerPoint “deck” that dives into more detail about the company and the market opportunity.