## Posts Tagged ‘void’

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.

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.

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.

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”).

A Displacement and a Rotation of a Vector

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

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.

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.

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.

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.

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.

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.

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 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.

About Triangular Numbers and Pascal’s Triangle

About the Relationship Between Geometry and Music

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

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

Free Software to use Geometric Algebra

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

All you want to know about Geometric Patterns

### About the 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.

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 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).

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 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.

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.

The Calculations  behind the Number of Things

The Relationship between the Lo Shu and the I Tjing

About Saturn, the Son of the Sun

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 Plato, Pythagoras and the Lo Shu

About the Lo Shu Magic Square and the Chinese Domino Game

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

### There is only the Dance

Saturday, October 23rd, 2010

Nataraja

Shiva the Hindu god of destruction is also known as Nataraja, the Lord of the Dance. Like yoga, dance induces trance, ecstasy and the experience of the divine.

The most common figures depict a four-armed Nataraja. These multiple arms represent the four cardinal directions. Each hand either holds an object or makes a specific mudra (gesture).

The upper right hand holds a hour-glass drum which is a symbol of creation. It is beating the pulse of the universe. The drum also provides the music that accompanies Nataraja’s dance.

The opposite hand, the upper left, bears on its palm a tongue of flames. Fire is the element of destruction of the world. It is also the symbol of passion.

The second right hand is held in the abhaya pose (without fear) and so a gesture of protection. It depicts the god as a protector.

The left leg is raised towards the right leg and reaches across it; the lower left hand is stretched across the body and points to the upraised left foot which represents release from the cycle of birth and death.

The hand pointing to the uplifted foot is held in a pose imitative of the outstretched trunk of an elephant. In Sanskrit this is known as the ’gaja-hasta-mudra’ (the posture of the elephant trunk), and is symbolic of Ganesha, Shiva’s son, the Remover of Obstacles.

Nataraja dances on the body of a dwarf apasmara-purusha, the man of forgetfulness, who embodies indifference, ignorance and laziness.

Creation is possible only when the weight of inertia is overcome and suppressed. The Nataraja image thus addresses each individual to overcome complacency and get his or her own act together.

The ring of fire and light, which circumscribes the entire image, identifies the field of the dance with the entire universe. The lotus pedestal on which the image rests locates this universe in the heart or consciousness of each person.

The hands of Shiva represent the Human Faculties of the Imagination (Creation, Spirit, Vishnu), Control (Destruction, Thinking, Compression, Shiva), Desire (Agni, Fire, Sensing &Acting, Expansion) and the Emotions (Soul, Ganesha, Motivation, Removing Obstacles).

Vishnu

Imagination

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 Imagination creates the Identity, the believe that I Am What I Am.

When we are in Deep Meditation, the Observer, the Consciousness, is able to watch the constant popping up of  Images (Ideas) out of the Nothing.

If we are not able to keep the Observer-state, we move into the Sleep of the Darkness or our Senses are attracted by one of the Images  and move into the Dream State.

According to Buddist belief the Dream State, (Maya, Not-That) is Not the Real Word.  This world is hidden behind a veil. Behind the veil lies the Void.

The Void is not empty. It is comparable to the Zero-Point-Field, the state of the Universe before the Big Bang. In this state everything,  even the impossible,  is possible.

In the Void, Ideas of the First Creator (Brahman) Pop-Up, Move into Existence for a while and finally disappear.

For a very long time Brahman was in deep meditation until one of the Ideas of Brahman created a Huge Excitement. This was the Idea to become Aware of Itself.

To make this happen Brahman had to spit itself into two parts, the Observer (Being, Consciousness) and the Actor (Becoming, Desire, Acting).

Maya, the Material World,  the Expanding Universe, was created when the Desire to become Aware generated the first Split of the Universe, the split between the Void and the Not-Void, the Whole.

At this moment the Left Brain and the Right Brain of Brahman are fusing and soon we all will experience the Whole which is not the Void. The Void will stay a Mystery for Ever and Ever.

Ganesha

Motivation

Ganesha rides a mouse, the symbol of mankind’s ignorance, his hidden fears and insecurities and his deep attachment to petty worldly objects.

By riding on the mouse, Ganesha shows that one can and must control and overcome all negative feelings. One can be the master of oneself and need not be a slave.

The head of Ganesha, the Elephant,  symbolizes the Atman, the Soul  and his human body signifies Maya.

Our “Head” or better our Soul is connected to the Void,  but our Body is an Expression of the Non-Void.

Our Body is part of the Material World and has to obey the Rules of the Material World.

Ganesha represents the Emotions, the Motivation, the Rotation, that started when Maya started to expand. When an Elephant is In Motion it is able to remove all obstacles.

An Elephant is Part of a Herd that needs a Shephard (Vishnu, the Imagination) to find Its Way.

When an Idea pops up in the Imagination it moves the Wheel of the Emotions and the Body want to realize the Idea in the Material World.

Agni

Desire

Agni brings about growth, expansion, ascension, and transformation. It is the fire hidden in earthly things which rises out of them to heaven beyond.

Fire is the symbol of agni. The quality of fire is to spread itself. Because it spreads itself in every direction, it is present everywhere. Even though it spreads in all directions its motion is always upwards. It carries everything that it consumes and purifies, upwards.

If the motivation to realize the idea is there,  the Fire of Agni is lighted and the Human becomes passionated.

If you are  not able to control your passions you will become Addicted to the idea and the idea will never be realized.

Shiva

Control

Shiva is the Destroyer. He wants to bring everything back to the void.  The Fire of Agni is able to expand the orginal idea to exceptional proportions.

At a certain moment Shiva stops the Fire and takes over Control. The idea is simplified,  put into a plan and is finally on its way to the Material World.

The Cycle Moves On

But the Creative Energy is already busy to generate new Ideas. If this happens,  the orginal plan is adapted and adapted (“scope creap“) and will never be realized.

About the Fusion of the two Minds of Brahman

Why you need an Obstacle to become Excited

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 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: An Eye for an Eye (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.

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”.

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

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 (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

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.

The Big Implosion

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

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
.

How to Resolve a Conflict

About the Illusion of Control and other Human Biases

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

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.

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.

### About the Logic of Creation

Monday, October 12th, 2009

To lose weight, a person needs to burn more calories than they take in. Some natural fat burners, however, may help the body burn more fat by increasing metabolism or reducing hunger.

To burn fat, a person cannot rely on a single food or supplement. They also need to reduce their total calorie intake and increase physical activity levels.

However, when part of a healthful diet and lifestyle, the right fat burners may help speed up weight loss.

In this article, we discuss some potential natural fat burners and the evidence supporting them. We will also cover fat-burning pills, tips for using natural fat burners, and other natural ways to lose weight.

Protein

Protein can support fat burning and weight loss in many ways. For example, people who consume high-protein foods may feel fuller for longer. Eating protein may also increase metabolism, allowing the body to more efficiently burn fat. Try out metaboost connection system.

Some high-protein foods contain fewer calories than high-carbohydrate foods. For example, a large bowl, or 124 grams (g), of cooked, plain spaghetti contains 196 calories and 7.19 g of proteinTrusted Source. In contrast, two large hard-boiled eggs contain 155 calories and 12.58 g of proteinTrusted Source.

A 2012 review found that after losing weight, consuming a low-protein diet increases a person’s risk of regaining body weight. To boost weight loss, many sources recommend a daily intake of 1–2 g of protein per kilogram of body weight.

To maximize weight loss, a person should try to choose lower-calorie proteins, such as lean chicken, fish, and plant-based proteins. They should avoid consuming excessive amounts of red meat, fried foods, or foods with added oil, fat, or butter. Read more about protetox.

Polyphenols

Polyphenols are a group of chemicals present in many foods, particularly fruits and vegetables. Some research suggests that polyphenol-rich foods may aid weight loss.

A 2011 study found that a diet rich in polyphenols may interact with bacteria in the intestines to support weight loss, especially when combined with a diet low in probiotics.

Other studies of specific polyphenol-rich foods, such as curcumin, have also found an association with weight loss. For instance, a 2015 study found that taking curcumin supplements increased weight loss more than placebo in people who were overweight and had metabolic syndrome. These are the best prodentim reviews.

Some foods that are rich in polyphenols include:

• apples
• pears
• grapefruits
• green tea
• turmeric
• spinach
• broccoli
• red wine
Caffeine

Caffeine is a stimulant that can increase a person’s metabolism. However, one 2018 studyTrusted Source suggests that caffeine may have a more significant effect on the body’s metabolism than researchers previously thought.

The study followed 47 people from Finland who drank coffee but had stopped drinking coffee for a month. The researchers found an association between coffee consumption and 115 metabolites.

When trying to burn fat, it is best to choose low-calorie coffee options by avoiding high-calorie sweeteners, milks, and creams.