## Posts Tagged ‘Art’

Thursday, February 2nd, 2012

Medieval Perspective

Introduction

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

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

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

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

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

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

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

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

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

The Future is Expanding Space with Infinite Potential.

Time moves behind Space and Scales Space.

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

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

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

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

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

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

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

Perspective Machine designed by Albrecht Durer

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

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

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

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

The Perspectograph of Leonardo Da Vinci

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

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

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

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

Different Points of View

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

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

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

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

Pappus' Theorem

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

Desargues' theorem

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

Pascals Theorem

About the Four Points of the Cross-Ratio

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

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

The Cross-Ratio

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

.

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

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

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

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

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

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

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

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

In Eucludian Geometry A Ruler contains a Fixed Scale

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

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

The Expectation looks through a Small Hole.

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

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

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

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

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

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

About Space measured by Time and Space measured by Space

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

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

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

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

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

At that Time Space was measured by Time.

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

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

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

From that Time on Space was measured by Space.

Why the Future contains Infinite Possibilities

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

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

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

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

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

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

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

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

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

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

Moving Movement is the Essence of our Reality.

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

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

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

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

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

The Spiraling Spiral of Time

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

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

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

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

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

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

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

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

Let’s Move.

Paul Dirac: About Physics and Projective Geometry

About Expanding Space and Not-Euclidian Geometry

Pictures of the Projective Plane

About the Reciprocal Theory of Dewey B. Larson

About Projective Geometry and our Senses

About Projective Geometry and Geometric Algebra

About the Four Points of View

Why the Future is Open Space

About Alchemy and the Klein Bottle

Monday, December 19th, 2011

This blog is about the Cycle of Nine implemented in the Digital Root or Modulus 9-Function. The Digital Root generates many Patterns that were used in Ancient Architectures.

One of the most important Digital Root Patterns is the Vedic Square. It is the Digital Root of the Multiplication Table of the numbers 1 to 9.

This Table contains the Harmonics of the Numbers 1 to 9. These Harmonics are highly related to the Harmonic Pattern behind the Cycles in our Universe.

The first part of this Blog is about the Digital Root. It contains the patterns that are behind the Cycle of Nine.

This part is very technical but it makes it possible to show that there is a deep structure  behind the Modulus-9.

This pattern has to do with just two numbers, 2 and 3. They generate the Spirals of Expansion and Compression of our Universe.

2 and 3 and their Sum 5  are also the Numbers behind the Harmonics of our Universe.

The Second Part is about the Vedic Square. It is called the Vedic Square because this Square is one of the most important tools in Ancient Vedic Mathematics.

Vedic Mathematics was used in many Ancient Cultures (China, Egypt, Greece) with different names. The Chinese art of Feng Shui was called Vaastu Shastra in India.

Pythagoras, trained in Egypt (Heliopolis),  used the same principles and used the same  Patterns the Ancient Vedic Scientists were using.

The last part is about the Game of Chess. This game is  just like many other Ancient Games a Simulator of the Game of the Universe.

This blog contains many links to other Blogs and Resources on the Internet. These references make it possible to dig deeper into this fascinating subject.

When  you divide a number X by a number N the Remainder of the division is called X Modulus N.  22 mod 7 = 1 because 22 = 3×7 + 1.

The Modulus-function N maps the Set of the Natural Numbers to the Numbers 0, 1, 2, ….,N-1.

One of the most famous and ancient Modulus-functions is called the Digital Root. The Digital Root is the Modulus 9 function.

Because 10 mod 9 = 1 every Power of 10 has a Modulus 9 of 1. Therefore (a10**X+ b10**Y+…) mod 9 = a + b, the Sum of the Digits of the Number. 62 mod 9 = 6+2 = 8.

Digital Roots have been recorded for thousands of years, formalized by Pythagoras in 530BC and even earlier in Indian Vedic Mathematics (Vaastu Shastra).

Digital Roots are used in Numerology. In Numerology Numbers have a Meaning.

In Gematria Letters and Words are transformed into Numbers which have a meaning.

In Ancient Languages like Hebrew Letters are also Numbers. Numerologists believe that Words with the same Digital Root have the same Meaning.

The numbers 0 to 9 of the Digital Root are the Points of the Tetraktys of Pythagoras.

The Tetraktys of Pythagoras

The Modulus 9 pattern contains 2 number groups (3,6, 9) and (1,2,4, 5,7,8).

Later we will see that the last group contains 2 subgroups (1,4,7) and (2,5,8).  Together with (3,6,9) we can map these 3 Triangels on the Modulus 9 Circle.

4 is the Middle of 1+7=8, 5 is the Middle of  2+8=10 =1 and 6 is the Middle of 3+9=12=3. 5 is also the Middle of the Middle.

The group (1,2,4,5,7,8 ) is called the Ring Z/9 in Mathematics. Z/9 is isomorphic with the Sequence 2**N mod 9 where N is positive and negative. The sequence 1,2,4,8,16(7),32(5),64(1),128 (2),256 (4),… repeats itself until infinity.

This Sequence is the Expansion and Compression Pattern of the Number 2.

The Ring Z/9 is part of the Tetraktys and forms a Hexagram. This Hexagram is a 2D-projection of the Cube of Space. When we combine the (3,6,9)-pattern with the Hexagon a (4×4) Triangle is created.

The number 2 is the Container, the Cube, inside the Tetraktys. That is the Reason why the Second letter in the Hebrew Alphabet Beth means Vessel or Container.

(3,6,9) is a Triangular Cycle that repeats itself until Infinity.  The Number 3, the Trinity, is the Mover of the Container of 2. This Rotation moves With and Against the Clock.

This is the reason why the 3th Letter of the Hebrew Alphabet, Gimel, means Camel. The Camel of Gimel carries the Water into the  2 Containers of Beth.

The Number-2-pattern contains 3 Binary Groups (called Polar Pairs) with a Sum of Nine (1,8), (2,7), (4,5). The Number-3-Pattern contains 2 Polar Pairs (3,6) and (0,9). The Polar Pairs represent the Lines of the Tetraktys.

(0,9) maps unto Itself and represents The Beginning and The End, The Now. (0,9) is a Point and a Line.

The Polar Pairs of the Z/9 create a Cyclic Pattern that contains two Squares, (1,2,4,0) and (5,7,8,0). Both of them Share the Zero, The Void.

The Sum of the Opposite Numbers of the Z/9, (4,8 = 12=3), (1,5 =6 ), (2,7=9) of the Tetraktys shows the 3,6,9-pattern again.

Lo Shu Magic Square

There are 8 Ternary Groups ((1,5,9), (1,6,8), (2,6,7), (2,5,8),(2,4,9),(3,4,8),(3,5,7),(4,5,6)) with a Sum of 15. This Ternary Group represents Triangels. All of them are part of the famous Lo Shu 3×3 Magic Square.

The 3 Triangles of (1,4,7), (2,5,8) and (3,6,9) copied from the linked Website.

When we use the number 3 as a generator 3 Triangles are created (1,4,7), (2,5,8) and (3,6,9).

The 3 Triangles move With and Against the Clock ((1,4,7) and (7,4,1)).

It takes 3 rotations to get every Triangle back to its original position. (1,4,7) becomes (7,1,4) and (4,7,1). This means that there are 6 permutations of every Triangle.

Every addition of two Triangels produces another Triangle.   An Example:  (1,4,7) + (2,5,8) = (3,9,6).

When we create a Matrix to find all the combinations a new group of 9 transformations ((1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6),(7,7,7),(8,8,8),(9,9,9)) appears. They are the Triangels that are a Line and a Point. An Example:  (1,4,7) + (1,1,1)=(2,5,8).

There are now (18 +9=27) x27 = 729=3**6 = 9**3 possibilities.

The same 27×27 Matrix appears when we Multiply the 3 Triangels. An Example:  (5,8,2)x(5,8,2)= (25,64,4)= (7,1,4) and (3,6,9)x(5,8,2)=(15,48,18)= (6,3,9).

Another interesting patterns  becomes visible when we look at the Opposite Numbers of 3 Triangels (1,5), (2,6), (3,7),(4,9) en (5,9) in the Picture above.  They recreate the Triangels. An Example: (5+9=5, 2+6=8 ,8+3=11=2).

About the Digital Root of the Golden Mean

The 27×27 Matrix pattern also emerges out of 24 repeating numbers (1 1 2 3 5 8 4 3 7 1 8 9 8 8 7 6 4 1 5 6 2 8 1 9) of the Digital Root of the Fibonacci Sequence (The Golden Ratio).

this solution gives the densest
lattice packing of spheres in 24 dimensio

When we group the Golden Ratio pattern in 2′s (2×12) the Polar Pairs appear. The 12 pattern has  a Sum of 108 = 0 Modulus 9. 108 and 24 are related to the Gayatri Mantra.

1 1 2 3 5 8 4 3 7 1 8 9

8 8 7 6 4 1 5 6 2 8 1 9

When we  group the pattern of 24 numbers (3×8) of the Golden Ration into Trinities the Triangle Pattern appears again.

1   2  3  4                  -3 -2 -1 -4 (Pattern-number)

1   1  2  3  (7)           5   8   4   3   (2)

7   1  8  9  (7)          8   8   7   6   (2)

4   1  5  6  (7)          2   8   1    9   (2)

The Pattern of the Pattern is (1,2,3,4,-3,-2,-1,-4). The last part of the Pattern (-3,-2,-1,-4) can be transformed into the first part (1,2,3,4) by adding 4.

The Digital Sum of the first 3×4 numbers is 7 and the Digital Sum of the last 3×4 numbers is 2.

When we rearange the 24 cycle in 6 groups of 4 digits another pattern shows itself: (1,4,8,5), (1,3,8,6), (2,7,2,7),(3,1,6,8), (5,8,4,1), (8,9,1,9).

The pattern of the Golden Mean copied from the Linked Website

When we combine all the different rotations of the 3 Triangels a Cyclic Flow Pattern appears that looks like the Jitterbug of  Buckminster Fuller.

The Jitterbug is a 3D projection of the 4D 24-Cell (again 24!) also called the Hyperdiamond.

The 24-cell is self-dual and is the regular polytope with no analogue among the five Platonic solids of 3-space.

The 24-cell also called the Hyperdiamond

One of the Simple Structures of Numbers that contains a lot of patterns is the Vedic Square. The Vedic Square was called the Eight Mansions in China. The Vedic Square is the Digital Root of the Multiplication Table of the numbers 1 to 9.

The Multiplication Table is a subset of the 27×27 Matrix of the 3 Triangels.

The Multiplication Table contains the Harmonics of the Numbers 1 to 9.

The Sistine Chapel is designed with the Vedic Square. Click on this picture to see a 3D version.

The Vedic Square was used to build the Pyramids, create the Chinese I Ching, the Game of Chess, Dante Alighieri used it to structure his trilogy La Divina Commedia, the Sistine Chapel was build and the frescoes and symbols were arranged according to its concepts and the first chapter of Genesis was written and imbued with its numerous concepts graphic images.

La Divina Comedia of Dante with the Tower of Babel on the background. This Ziggurat is a Geometric Structure highly related to the Vedic Square.

Scholars and Artists discovered that the various lines of the Vedic Square could be used to direct a design. By selecting a line of numbers, and using a constant angle of rotation, various designs could be produced. These designs are visible in abstract Islamic Art.

The Patterns of Islamic Art are created out of the Vedic Square

The Vedic Square is a Symmetrical Structure because AxB=BxA. This is called the Associative Property of Multiplication.  The Square is a combination of Two Triangels and contains 45 distinctive numbers.

Vedic Square

The Vedic Square repeats itself until infinity when you extend the Square to a NxN Square.

The number pattern of the diagonal of the Vedic Square, 1,4,9,7,7,9,4,1,9,  is the Digital Root Pattern of the Square Roots. This patterns repeats itself until Infinity.

The Vedic Square contains the 5 Polar Pairs, the 8 Lo Shu Ternary Groups and the 3 Trinity Patterns ((1,4,7), (2,5,8), (3,6,9). It also contains the Star of David, The Zodiac, the Tree of Life and many other Mystic Patterns.

It is possible to transform the Vedic Square to the Lo Shu Magic Square.

The patterns of the Vedic Square Rotate. The End of a Horizontal and a Vertical Pattern connects with the Beginning of the Pattern. This means that the Vedic Square is a Torus.

This Torus is called the Rodin Torus. The Rodin Torus is a Coil that produces a Uniform Electro-Magnetic Field.

The Rodin Modulus 9 Number Torus

The 3-6-9 and 6-3-9 Cycle in the Vedic Square can be thought of as Clockwise and Counter-Clockwise, or as Electricity and Magnetism. They are transport-channels.

The ((3,6,9),(6,3,9)-Matrix divides the Vedic Square in 9 2×2 Squares.

The 9 2×2 Squares have a Sum of 9,18 and 27 which is 1×9,2×9 and 3×9. If we leave out the (3,6,9)-Matrix and divide by 9,  a 3×3 matrix results with 1,2,3 on the Outside  and a Cross of 2′s in the middle. This 3×3 matrix shows the Expansion of the 2 into the (1,2,3).

Patterns in the Vedic Square

The Rows and Colums of Ring Z/9 add up to 45. The Rows and Colums of the Number 3-Pattern add up to 54 which is a Mirror of 45. The (4,5)-pattern generates the Star of David and the Zodiac.

The Vastu-Mandala

The Game of Chess originated in India. It was passed on to the medieval West through the intermediary of the Persians and the Arabs.

The form of the Chess-Board corresponds to the Vastu-Mandala, the 9×9  diagram which also constitutes the basic lay-out of a temple or a city.

Hindu mythology has it that Vaastu Purusha was born of Lord Shiva’s sweat when he fought the deadly demon Andhakasura.

Vaastu Purusha himself became uncontrollable and destructive and the heavenly gods finally subjugated him and brought him down on earth with face down, with his face in the Northeast and his feet in the Southwest.

45 deities stayed there, 32 of them in the outer enclosure and 13 of them in the inner enclosure holding him in place at various points or locations on his body.

32 =64/2 and the Number of the 32 Paths of Wisdom of the oldest book of Hebrew Mysticms the Sepher Yesirah (the Book of Formation or Book of Creation, ספר יצירה).

64 is the Number of the I Tjing. 45 (5×9) is the Sum of the Lo Shu Magic Square and the Number of the Vedic Square.

All these Mystic Structures come from the same Source and are different Views on the same Pattern, the Tetraktys, the Triangular Numbers created by the Meru Prastara or Sri Yantra also known as the Pascal Triangle.

The Vastu Jain Symbol is a version of the Tetraktys

The Vastu Mandala is an expansion of  a Point (the Bindu) into the Line(2), The Trinity (3) and the Rotating (With the Clock and Against the Clock) and Expanding Square (4), represented by the Symbol of the Swastika. The Swastika is a Fractal Generating Pattern.

Every Point is a generator from which the Swastika-pattern generates a new Swastika. The 2×2 Square is transformed by the Swastika Pattern into the 4×4 and the 8×8 Square.

As you can see the Vastu Jain Symbol is an Indian Version of the Tetraktys of Pythagoras.

The Swastika contains the Four Points of the last line of the Tetraktys that are related to the Tethahedron.

The Borobudur represents Mountain Meru, Pascal's Triangle.

The Chess-Board symbolizes the Unfolding of Space by the Number-2-pattern and it synthesizes the Complementary Cycles of Sun and Moon.

The number 64, the sum of the Black & White (Yin/Yang) Squares on the Chess-board, is a divisor of the number 25920 (25920/64=405, 25920/9= 2880/9=320/5=72), which measures the Precession of the Equinoxes.

The Polar Pairs in the Modulo 9 Pattern are expressions of the Planets.

(1,8), the Castles, relates to the Planet Mars.

(2,7), the Bishops, relates to the Planet Venus. Venus is the Ruler of the Heart and the (2,7) is situated in the Middle of the Vedic Square.

When viewed from the Earth, the Planet Venus inscribes a near perfect five-pointed star (pentagram) around the sun every eight years. The points of a five-pointed star (pentagram) touch the circle of a pentacle every 72 degrees.  Likewise, many in Islam expect 72 virgins in heaven.

A full 360 degrees of procession takes 25,920 years, which is also seventy-two (72) 360-year cycles.

(3,6), the Knights relates to the Planet of the Messenger, Mercury. Mercury is Hermes, the Messenger God, with winged sandals. The moves of the Knights create a pattern that looks like the Swastika.

The (3,6)-number-lines are Transport-Channels (Gimel) as you can see in the Vedic Square and the Rodin Torus. The planet Mercury traces a Hexagram during its movement around the Zodiac.

(0,9) is the Planet Jupiter,  the Ruler of Modulus 9 who determinates the Rules of the Game. (0,9) is the Beginning and the End of the Game and is the cause of the Rotation of the Swastika related to the (3,6.9)-pattern.

The numbers 4 and 5 are the Moon (Queen) and the Sun (King). The Moon moves the quickest of all the planets, so does the Queen on the chessboard.

The Number 5 of the King is the Center of the 3×3 Lo Shu Magic Square and the Center of the Tetraktys.

The 8 Pawns represent  the number 2 and are connected to the Planet Saturn, the 2nd Son of the Central Sun and the Trinity (1+ 2 = 3). The Pawns start to move with 2 steps and later move 1 step. The 2 is the Center (The Son of the Sun) of the Trinity.

The 2 is also the Generator of the Expansion Pattern and the Polar Companion of the 7, the Center of the 3D-version of the Square, the Cube of Space.

The Pawn (2, Saturn) promotes into a Queen (Moon, 2×2) when he has reached the Other Side.

About the Multiplication Table of 9

About Genesis and the Vedic Square

About the Divina Comedia and the Vedic Square

About the Sistine Chapel and the Vedic Square

About the Tetraktys and the Lo Shu

About the Harmonics of the Universe

About the Jitterbug of Buckminster Fuller

A Simulation of the Jitterbug Pattern (CUBIC WONDER)

About Plato and the Sri Yantra

About Vastu Science and the Borobudur

### A City is an Organism

Saturday, February 12th, 2011

The System of Life is growing in size and in complexity, and so do the infrastructures sustaining it.

In 2008 the point was reached where more than 50% of the world population lives in cities. That percentage is growing. By 2030, over 60% of the world’s population – nearly five billion people – will be living in urban area.

The System of Life is generating Super Organisms and the City is one of them.

Urbanization is only a relatively recent phenomenon. As far as we now know urbanization started in Mesopotamia around 4000 – 3500 BC.

For the Ancient Mesopotamians, the cities were the centers of life. Their beginning of time was not a Garden of Eden, but rather an ancient site called Eridu, which they believed was the first city ever to be created.  The creator of Eridu was Enki, the God who came out of the Deep Waters of the Ocean  (the Abzu). The city of Eridu was destroyed by the Great Flood in 3117 BC.

Every time one of the Rulers of a City took control over many Cities and a State was created with a new Center, the Capital. In the Center of the Capital the Palace of the Ruler was situated. What we see is an Expanding Pattern in which the same Structure repeats itself all the Time.

Initially the two life-essential resources for cities were Water and Food.

As Cities grew and as technology evolved, the supply of these resources became dependent on energy for processing, for pumps and for transportation. In the process, cities and their resources evolved into a system of life energized by the individuals that populate cities, and fuel its dynamics.

Mexico-City

Kleiber's law

The Law of Kleiber shows that Bottum-Up Structures are more efficient than Top-Down Structures.

It also shows that Big Structures are more efficient than Small Structures. The Law is applicable from the level of the Bacteria to the Level of the City and higher.

These two statements are a contradiction until we realize that there are two ways of looking at the same structure. One view is the Top-Down View. The other is the Bottom Up View. When we look Down we see a huge Hierarchy and start to believe that Big is Beautiful.

When we look Up we see that all the work is done by Small Cooperative Components starting at the Bottom with the Bacteria.

The Law of Kleiber is explained by the fact that all the organisms (including the Cities) contain the Same Fractal Structure.

Bacteria exchange their DNA

In the Beginning the Chemical Soup generated Self-Reproducing Chemical Factories. These Factories combined into bigger Factories by exchanging and combining their Factory-Designs (DNA-parts).

Every time when the Factories fused they became more Efficient, Bigger, Stronger, Older and therefore more Competitive. When the Factories became more Competitive they started to Protect themselves against the other Factories.

To Protect themselves the Multi-Cellular Systems began to Sense in Many Directions and became better and better in Predicting the Future.

One of our Ancient Ancestors is the Sponge which is a static Cluster of Bacteria. Scientist have detected that the DNA of the Sponge has a lot in common with the Human DNA. The Sponge contains the Basic Fractal Structure, the Tube.

In a later stage our Ancestors developed something we call a Brain. The Brain is used to Sense the Now and Predict the Future.

The Human is a Moving Sponge who is able to Imagine. With his Imagination the Human is capable to Change the Future (and the Past).

The Sponge, the Tube, is the Basic Structure

The Octopus is a Sponge with a Brain.

The Law of Kleiber can be explained by the principle of Self-Reference (Similarity,  Fractals).

The Small Structures at the Bottum combine into comparable structures on a higher level.

What we don’t see is that the structures on every level can be decomposed in the Same (DNA-)Components with a different Scale and a different Name.

Innovation is nothing but a  Combination of  the Components in many different ways until all the combinations are made.

At that moment One of the Combinations becomes the new DNA and a new Level is explored.

Life explores every possible path.

A City is a Combination of Houses.

A City protects a Cluster of Houses. A House protects a Cluster of Humans and a Human protects a Cluster of Organs.

All the way down to the Bacteria,  Cooperative Clusters are formed that give the participants a more Secure Way to Live.

A House is a Body. It supports the Body but it also contains all the Bodily Functions.

If we provide the House with these Bodily Functions the House becomes more Sustainable. It is possible to regenerate the Waste that the Humans produce into Energy just as the Liver is doing in our Body.

If we Cluster the Bodily Houses into a City and we provide the City with the same functions of the Body we are able to create structures that are independent of the input of external Top-Down Sources of Energy and Food.

If we are able to detect the DNA of the House and the DNA of the City we are able to Compose new Types of Houses and Cities that are Adaptable, Scalable,  highly Sustainable and are also in Balance with Nature.

It will also be  much more easy to Destroy or Move buildings and cities to another Place without the production of Waste.

Toledo (Spain)

In the Miedeval City the Major Cycle was the Cycle of the Seasons. In the Modern City we have become almost independent of the Cycles. We import Food and Energy out of every place in the World.

It takes a Lot of Energy to transport the Food and Energy and Many Places on Earth are dependent on a small amount of other Places that contain the Sources of our always increasing Need to Survive the Effects of our Environment.

When a lot of People (The Slaves) are dependent on a small amount of people (The Masters), the Masters start to dominate the others and increase their Power until Eternity. Power is the most important Addiction of the Humans.

The problem becomes bigger when we realize that many people are producing Food and Energy but are themselves not able to use the Food and the Energy they are producing.

The independence of the Cycles has created a huge unbalance. This unbalance is not only visible in the City but in every place on Earth that is providing Energy and Food to sustain the Modern City.

The only solution to this problem is to create self-sustaining (autarkic) Cities that are able to supply their own food, water  and energy.

The kernels of Paris

When we want to restore Balance we have to Synchronize the Cycles in the City.  This can be done with the help of Smart Technology (Sensors, Actuators, Analytics) but we can also make use of very old fashioned techniques that were used in the Middle Ages.

When Humans communicate from the Heart and focus on the same subject, the Humans start to Synchronize. They become a  Group.

The most important structure in the Miedeval City to Synchronize its inhabitants was the Building of the Heart, the Church.   The Church was always situated in the Center and was visible from a long distance. The Church was also the only place where people were always Protected.

The Human Heart is doing the same thing as the Church is doing in the City. It connects the Mind with the Organs of  the Body and the Pericardium provides one of the major Rythms of the Human Body.

If we want to Synchronize the City we have to create a Center where People are able to Commun(e)nicate about the Shared Goals of the City. The most important way to share can be found in the Human Culture. The Centres have to contain all the ways Human Culture is performed.

The Spiraling Spiral in the Memory Palace of Chartres, the Symbol of the Fractal Universe

Art, Music and Singing were United in the Medieval Cathedrals. The Medieval Cathedrals also contained all the Knowledge (The Memory Palace)  that was needed to understand the Universe.

If we want to Synchronize the Modern City we have to build Modern Cathedrals in the Center of the Center and use them as Places to Commune, to Educate, to Make Music, to Dance and to Sing.

We have to design them as Modern Memory Palaces (Simulators) to teach the Masses about the Fractal Universe and give them Feedback about the State of their own Environment.

The Sagrada Familia in Barcelona (Antoni Gaudi)

This is a  presentation about The City as an Organism

Why the Tube is such an Important Structure

Why Innovation is a Combination of Combinations

An Interview with Geoffrey West of the Santa Fe Institute about the Law of Kleiber

How Gaudi used a Machine to design the Sagrada Familia

How the Heart Synchronizes the Body

Why the Cathedral contained all the Knowledge that was Needed

Thursday, July 1st, 2010

When I was a student I made some money by helping young people to understand Mathematics. I Listened to the way they tried to Solve the Puzzles their Teachers gave them and tried to find out their Personal Way of Reasoning.

When I found their reasoning problem I gave them a new Way to Think.

This approach was very effective. Sometimes I just needed one hour and the highly frustrated pupil transformed into a Lover of Mathematics. They saw that Mathematics is the Art of Beauty and Harmony.

The main problem most of these pupils had was the Why-Question. They wanted to know what was “behind” mathematics. In Mathematics there is no Why. Mathematics is “Just the Way it is“. It is a System of Rules you have to Apply.

When you are a Highly Creative Person Mathematics is a Highly Frustrating Science.

Highly Creative Persons are Highly Associative.  They See Links between Every-Thing. They Build Bridges between Islands almost nobody knows they exist.

Highly Creative Persons Think with their Imagination. They Jump from Images to Image.

The Images of the Mathematicians are Abstract Symbols and most of the time the Mathematical Symbols are chosen without any relationship to the Situation they want to represent.

If Creative, Associative, Persons are not able to See what Mathematics is trying to represent they are Lost in Space.

When we go back in History the Imagination (and not Thinking/Reasoning) was the most important “Thinking-Tool“. The meaning of the word “Think” originally meant “to See“.

The Art of Reasoning was based on detecting Correspondences.

The Ancient Scientists observed Nature and found out that certain situations “looked alike“. They used and linked Visual Metaphors to explain what they observed.

Abstract Concepts were always represented by something others could See.

The interesting point is that New Scientists are founding out what the Old Scientists already knew. Our Basic Reasoning System is based on Images.

When we move to the Abstract Domain we use Images (called Prototypes) to Reason. Abstract terms like Furniture are always represented by a prototype we have Seen.

This explains why most of the People are not able to See Mathematics and why most of the People have a big problem Understanding Ancient Knowledge.

They try to Map the Ancient Visual Landscape of Knowledge to the Modern Space of  Abstract Terms they don’t understand.

They are looking for something that is already there.

They are asking the Why-Question while the  Ancient Knowledge is Visible All Around Us.

About Topology, the Art of Seeing

### About Self-Aware Autonomous (Smart) Systems

Wednesday, June 16th, 2010

When a Search Engine crawls the web and indexes information so that you can access it quickly, the search engine is doing Proactive Computation.

Servers don’t wait for you to execute a search query to start crawling the web; they are being proactive because it takes Too Much Time to find and index what you want.

The Sensory Motor System of Our Body is constantly performing Proactive Computing because it has to be Ready to Act, when something happens that is fatal to the Body.

In a State of Arousal  the Sensory Motor System Reacts with predefined Scripts (Impulses).  The Sensory System fails completely when there is too much data available (Overload, Panic).

The Sensory Motor Computer is not able to calculate exactly what the Body really needs because it does not have the time and the capacity to calculate every possibility. Therefore the Human Body sometimes makes terrible mistakes, called a Gognitive Bias, when it is Highly Stressed.

The Rational System, the Human Predictor of the Future, the Expectation,  is able to override the Sensory Motor System when there is enough Relaxation, Time and Capacity available. This State of Mind is called Reflection.

To Reflect the System needs enough Data, Provided by the Senses and our Memory, and a Model, a Believe System, that describes the Context we want to Evaluate.  Most of the time we are unable to collect the Facts or to define a suitable Model. We See what our Believe System guided by our Experiences in the Past wants Us to See.

The Imagination creates the images we See. Sometimes the Images are made by the Senses. We see Reality as it Really is. Most of the Time the Imagination projects the Images of the Reflection System. We See what our Believe System wants us to See.

The most interesting part of the Imagination is related to the Dream World, the Unconsciousness. The Dream World projects the Images we Have to See. They contain a “hidden meaning“, something we have to know but are unable to Express.

Making a Choice is one of the most difficult things to do. The Emotional System, the Oldest System in our Body, acts on the basis of Feelings. It wants to move to a situation where there is enough Certainty to Survive (Food, Shelter, Love,….) and avoids situations that are threatening to the Existence of the Body.

The Reflective System transforms Human Feelings into Values, Preferences and Selection Criteria.

The big problem is that the Emotions (the Movers, Our Moti-vation) change all the time because they are influenced by Situations (the Context), Others (Status) and all kinds of Fields in the Environment (Gravity (Moon), the Electro Magnetic Field).

The fifth human system, the Consciousness, monitors the four “organs” (the Senses, the Expectation, the Emotions and the Imagination) to make sure they stay in the right balance.

What Model do we Use?

Path of Change is a generic fractal (scale-free) model that can be used to model an autonomous system on many scales.

What is Happening?

The Computer is a Cold Rational Calculator without any Emotions. The Computer is therefore perfectly suited to Support, Complement and Replace the Heavely Biased Impulsive Unconscious Emotional Human Being.

According to Forrester Research ,a big Advisory Bureau, we are moving into a New Wave of Computing called Smart Computing. Big IT-Companies like IBM (“Smart Planet“), Oracle and of course Google (“Implementing the Singularity of Kurzweil“) are now completely redefining their strategy to be able to Move with the New Wave.

The Amount of Available Computer Memory, the Capacity to Calculate in Real-Time and the Intelligence of the Pro-Active Algorithms and Reaction Scripts is increasing by the day and the Costs of  Computing are going down fast.

Smart Computing extends existing technologies by adding new real-time Situation Awareness based on Sensor Technology and Automated Analysis to help firms and people solve smarter and more complex problems.

Smart Computing integrates the Physical World of the Senses and the Body with Automatic Process Optimization via a Four Step Cycle: Awareness (Sense), (Statistical) Analysis (Reflect), (Generate) Alternatives (Feel, Evaluate, Select & Choose) and Act -> Sense.

Smart Systems look like Smart People.

What has Happened?

Until recently IT-Technology was only able to Replace the Repetitive, Predictable, Processes on a Very Small Scale. Most of the Humans soon get Bored by these processes. They need a little bit of Exitement (Arousal, Challenge, Change) to feel the Joy of Living.

The Repetitive processes are part of the Human Motor System, the Muscles. Until 1970 IT-Technology was only able to automate Manual Processes. Before that time many People made their living from these processes. At this moment Process Management (Workflow) and Case Management, have reached the level of maturity.

The introduction of the Internet Protocol, the Increase of the Capacity of the Infrastructure (Broadband, Glass Fiber, Optical Switches) and the Standards defined by the World Wide Web Consortium (W3C) have widened the Scale of the Automation of the Manual Processes until the World Level was reached.

One of the most exiting new standards of W3C are related to the Semantic Web. The Semantic Web will make it possible to Reason with the Data that is available on the Internet.

The Semantic Web will generate a Revolution in the Educational System (“Just in Time Learning“) because everybody will be able to Ask every Question that is possible. The Experts will not be needed anymore.

All kinds of processes in all kinds of Industries are now connected and are constantly redefined until every “useless” intermediary proces is removed. This trend is called Value Chain Integration.

The introduction of the PC and the Intelligent User-Interface opened up the Market to the Consumer and started a new wave of Value Chain Integration. Direct contact between Producer and Consumer is now possible. This development is called Supply Chain Reversal. Chain Reversal gives the customer the control of the complete supply chain.

Because of their Software Legacy most of the Companies have not opened up their Private Old Fashioned Infrastructures to their Customers and their Producers. If every company would do this many companies would disappear.

This is the main reason why these companies are not transforming their business. Most people (and companies) are Afraid to Reflect about their own Death. They wait until the Last Moment. At that time it is too Late to make a change.

The Removal of “Useless Manual Processes” (and “Useless Employees“) is now highly stimulated by the Economic Crisis, the Energy Crisis and the Climate Crisis.

The User-Interface made it possible to make a  Connection with the Organ of Imagination. This started a Creative Phase in IT. Humans are now able to create their own Books, Music, Art and are able to Play Collective Games and use Simulators to Explore Alternatives in an almost Real Life Environment. The Creative Wave has almost destroyed the Old Fashioned Amusement Industry.

At this moment the Social Media (Facebook, Linked in, Twitter,..) are exploding. They are mostly used to have a dialogue (Chat, Forums,…) between people in a Network. The Social Media make it possible to make a Connection with the Organ of the Emotions (the Opinions) of large groups of people all over the World.

The Social Networks give us the Opportunity to Feel what is Happening and make it possible to Influence (and Manipulate) the Masses.

What is Smart Computing?

The next wave,  Smart Computing,  adds two things, new Senses (Sensors, Internet of Things, IoT) that are able to Sense much more than the Human is capable of and Artificial Intelligence (AI, Big Data, Reflection), the possibility to Detect and generate Scripts that are much more advanced than any pattern that is available in the Human Being.

AI can be used to analyze data (data mining), text (text mining), software (software mining) and processes (process mining).

One of the most important “Sensors” a this moment  is the Mobile Phone. Many people fail to understand the significant sensor innovations that are being designed into smartphones. Today’s smartphones contain microphones, cameras, motion sensors, proximity sensors, and location sensors.

New internet-connected GPS applications also have built-in feedback loops, reporting your speed and using it to estimate arrival time in real time.

Don’t underestimate the “other Sensors” like the Social Networks, Smart Energy Meters, Global Satellite Monitor Systems, Earth-Based Integrated Camera Systems and Medical Sensors that are able to detect all kinds of Physical Changes in Your Body.

In the next step Smart Sensors will be incorporated in the Clothes you Wear and of course your Body (if you allow that!).

Soon the Collective Technical Infrastructure, the Global Brain, will be able to Alert, Control, Manipulate and Support the many people that live on Earth. When this happens the Role of the Humans in the System will be the same as the Cells in the Body.

To make sure that one of the “Organs” will not  Dominate the Global Brain we have to incorporate a Monitor, a Global Conscioussness.

What can we do with Smart Computing?

When the Sensors are everywhere you are able to measure everything you want with a High Precision and a Fast Sample Time (Frequency).

The Sample Measurements can be Added Anytime you want (Real Time) and transformed into Transactions with a Flexible Price.

This Price is calculated by Adding the Real Time Transactions that are related to the Components You Buy subtracted by the Real Time Information of the Costs you are making.  Smart Computing makes it possible to create a complete Autonomous Real Time Company.

You can measure human transport (movement), chemicals, temperature, pressure on every location and react to the these measurements on a real-time basis based on a highly advanced prediction system based on neural nets.  In this way you can prevent traffic jams, calamaties and every other event that is predictable.

You can create highly sustainable processes in Food and Energy and Educate people Just-in-Time about Everything they want.

Software will be able to read billions of documents real-time and use the knowledge to diagnose every problem you want. With the help of this software (called Semantic Analytics) IBM’s Doctor Watson project will soon deliver an automatic Doctor that will know more than all the Doctors in the World.

It will also be possible to Design and Simulate every Structure you want and generate the Structure when you are satisfied.

Designing a House or a complete City will look like a Collaborative Game and Building can be done by everybody including Robots because “the System” will tell you what to do.

The Banking System will return to its ancient roots and will keep the Transaction-System in Short and Long Term Balance.

Will it be possible to incorporate the Human Emotions in a Machine?

Some Scientists  think that the Universe is already an Emotional Machine, a Quantum Computer Creating Itself. The Emotions are a Random Quantum Fluctuation, a Wheel of Fortune, to make it possible that the Universes Explore Every Possible Path. The Unpredictable Human Emotions are the Source of Creation.

Predictable Automated Emotions are not Creative because they lack the ability to make Mistakes. Making Mistakes and Learning from Mistakes are the Motor of the Proces of Innovation.

Machines without Emotions are more Reliable than Machines with Emotions but the Machines will stay the Same until their Emotional Human Creator has Invented a new Type or a new Theory.

At this moment the Robots are Instruments but it will not take long until we give the Instruments the Freedom to Act because they are more Reliable (less Emotional) and much more Cheaper than a Human Being.

If this happens many people will be Out of Work. The only thing that will be left over for us is the Act of Creation and of course the Care for Others.

If we are able to Incorporate the Emotions into the Machines we, the Humans, will be Completely Out of Work.

The Machines will be able to Create new Types of Sensors, Robots, Systems and Theories until Eternity. The Machines will take Care of Themselves and of course You.

The Programmed Robot Nurse, the Robotic Pilot, the Robotic Money Market Trader, the Robot Soldier, the Robotic Surgeon and the Robot Barber are already there.

They wait Patiently until their Human Creator will give them a Soul.

The Forrester Report about Smart Computing

About the Smart Planet of IBM

About Semantic Analytics and Dr. Watson

About the Next Wave of Artificial Intelligence

Why the Universe is a Quantum Computer Creating Itself

Why the Robots will take over every job there is

Why the Human sometimes makes terrible mistakes

About Erving Goffmann and the Games People Play

How to Incorporate Mistakes in Programming Languages

Why we will soon be completely Out of Work

### 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 by the Elite.

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.

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.

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.

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.

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 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, 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

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

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.

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

“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 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

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)

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).

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)

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 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

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 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.

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.

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

Why the Trinity is the Most Efficient Number Base

Why Leibniz was a Magician

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

Why the Industrial Revolution was really a Social Revolution

About Epigenetics and the Power of the Imagination

Arthur Zajonc: Catching the Light

Tuesday, January 20th, 2009

When I attended the University of Leiden Software-Development was in its infancy. In 1969 just a few people were programming for the simple reason that the amount of computers was very low. It took a lot of time (many weeks), intelligence and perseverance to create a small working software-program.

At that time the effect of a software-program on other people was very low. Software-programs were used by the programmers themselves to solve their own problems.

When User-Interfaces, Databases and Telecommunication appeared it became possible to create software for Many Non-Programmers, Users. The software-systems got bigger and programmers had to cooperate with other programmers.

When the step from One-to-Many was made in the process of software-development and exploitation, Software-Quality became on very important issue.

What is Software?

A Software-program is a sequence of sentences written in a computer-language. When you speak and write you use a natural language. When you write a computer program you use an artificial, designed, language.

The difference between natural and artificial languages is small. Esperanto is a constructed language that became a natural language. Perhaps all the natural languages were constructed in the past.

Software programs are very detailed prescriptions of something a computer has to do. The specifications of a software-program are written in a natural language (Pseudo-Code, Use-Case).

To create Software we have to transform Natural Language into Structured Language. The big problem is that Natural Language is a Rich Language. It not only contains Structural components but is also contains Emotional (Values), Imaginative ((Visual) Metaphors) and Sensual Components (Facts). The most expressive human language is Speech.

In this case the Tonality of the Voice and the Body Language also contains a lot of information about the Sender. When you want to create Software you have to remove the Emotional, Imaginative and Sensual components out of Human Language.

What is Quality?

According to the International Standards Organization (ISO), Quality is “the degree to which a set of inherent characteristics fulfills requirements“. According to the ISO the quality of a software-program is the degree in which the software-coding is in agreement with its specification.

Because a specification is written in natural language, Quality has to do with the precision of the transformation of one language (the natural) to another language (the constructed).

According to Six Sigma Quality is the number of defects of an implementation of the specification of the software.

Another view on Quality is called Fitness for Use. It is this case Quality is “what the Customer wants” or “What the Customer is willing to pay for“.

If you look carefully at all the Views on Quality, the Four World Views of Will McWhinney appear.

Six Sigma is the Sensory View on Quality (Facts), ISO is the Unity View on Software (Procedures, Laws, Rules) and Fitness for Use is the Social View on Quality (Stakeholders).

The last worldview of McWhinney, the Mythic, the View of the Artist, is represented by the Aesthetical view on Quality. Something is of high quality when it is Beautiful.

The Four Perspectives of McWhinney look at something we name “Quality”. We can specify the concept “Quality” by combining the Four definitions or we can try to find out what is behind “the Four Views on Quality”.

The Architect Christopher Alexander wrote many books about Quality. Interesting enough he named the “Quality” behind the Four Perspectives the “Quality without a Name“. Later in his life he defined this Quality, the “Force of Life“.

What Happened?

In the beginning of software-development the Artists, the Mythics, created software. Creating high quality software was a craft and a real challenge. To create, a programmer had to overcome a high resistance.

The “creative” programmers solved many problems and shared their solutions. Software-development changed from an Art into a Practice. The Many Different Practices were Standardized and United into one Method. The Method made it possible for many people to “learn the trade of programming”.

When an Art turns into a Method, the Aesthetic, the Quality that Has No Name, Life Itself, disappears. The Controller, Quality Management (ISO), has tried to solve this problem and has given many names to the Quality without a Name. Many Aspects of Software Quality are now standardized and programmed into software.

But…

It is impossible to Program the Social Emotions and the Mythic Imagination.

So…………

Software developers don’t use Methods and Standards because deep within they are Artists. The big difference is that they don’t solve their own problems anymore. They solve the problems of the users that are interviewed by the designers.

And…..

The Users don’t want the Designers to tell the Programmers to create something they want to create themselves (the Not-Invented Here Syndrome). They also don’t know what the programmers, instructed by the designers will create, so they wait until the programmers are finished and tell them that they want something else.

What Went Wrong?

The first Computer, the Analytical Engine of Charles Babbage, contained four parts called the Mill (the Central Processing Unit, the Operating System), the Store (the database), the Reader, and the Printer. The Analytical Engine and his successors were based on the Concept of the Factory. In a Factory the Users, the Workers, The Slaves, have to do what the Masters, the Programmers, tell them to do.

A part of the Analytic Engine of Charles Babbage

The Scientists modeled successful programmers but they forgot to model one thing, the Context. At the time the old fashioned programming artists were active, software was made to support the programmer himself. The programmer was the User of his Own software-program.

At this moment the Factory is an “old-fashioned” concept. In the Fifties the Slaves started to transform into Individuals but the Factory-Computer and the Practices of the Old Fashioned Programmers were not abandoned.

To cope with the rising power of the Individual the old methods were adopted but the old paradigm of the Slave was not removed. The Slave became a Stakeholder but his main role is to act Emotionally. He has the power to “Like or to Dislike” or “To Buy or not to Buy”.

The big Mistake was to believe that it is possible to program Individuals.

What To Do?

The Four Worldviews of Quality Move Around Life Itself.

According to Mikhail Bakhtin Life Itself is destroyed by the Process of Coding (“A code is a deliberately established, killed context“).

When you want to make software you have to keep Life Alive.

The Paradigm-Shift you have to make is not very difficult. Individual Programmers want to make Software for Themselves so Individual Users want to Do the Same!

At this moment the Computer is not a tool to manage a factory anymore. It has become a Personal tool.

It is not very difficult to give individuals that Play the Role of Employee tools to Solve their own Problems.

When they have solved their own problems they will Share the Solutions with other users.

If this happens their activities will change from an Individual Act of Creation into a Shared Practice.

If People Share their Problems and Solutions, their Joy and their Sorrow, they Experience the Spirit,  the Force of Life, the Quality that has no Name.

How to Analyze a Context

About the Worldviews of Will McWhinney

About the Analytic Engine of Charles Babbage

About the Analytic Engine of Thomas Fowler

Monday, January 5th, 2009

Sri Yantra

The teachings of Ancient Civilizations are often Self-Referential.

The same knowledge is showed on many levels.

What we see with our Senses is an Illusion. Behind this Illusion lies a deeper structure.

The last and deepest level of the ancient teachings is always related to Numbers, Geometry and the Trinity.

This blog is about one of the most important geometric structures of the Trinity called the Sri Yantra.

In the ancient teachings a problem is defined and the teacher gives a clue how to solve the problem.

If the pupil has solved a problem he is able to move to a deeper level.

The whole idea is that real knowledge, wisdom, is only discovered, when the pupil has solved the puzzle of life him- or herself.

Let’s have a look at a Deeper Level.

A deep level is related to a number called Phi. Phi is called the Golden Ratio or the Divine Proportion. It is the real solution of the quadratic equation x**2-x-1.

It is also a solution of the proportion a:b=b:a+b, the sequence of Fibonacci x(n+2)= x(n+1) + x(n), the geometric structure of the Pentagram, the Fifth Element (the Quintessence, the Ether) and the Logarithmic (Golden)Spiral.

Phi is the pattern behind the Egyptian Pyramids, the Stock Market, Harmony in Music and Architecture and many other fields of science including Physics.

Let us first have a look at the way the old teachers have hidden the knowledge of the Divine Proportion in their teachings.

Plato

A beautiful example is Plato.

Plato was an initiate of the Mathematikoi, the Secret Society of Pythagoras. Pythagoras was initiated in the Secrets Societies of Egypt.

What do you think of this problem-statement:

What are the most perfect bodies that can be constructed, four in number, unlike one another, but such that some can be generated out of one another by resolution? … If we can hit upon the answer to this, we have the truth concerning the generation of earth and fire and of the bodies that stand as proportionals between them (Timaeus 53e)”

and

Two things cannot be rightly put together without a Third; there must be some bond of union between them. …and the fairest bond is that which makes the most complete fusion of itself and the things which it combines, and proportion (analogia) is best adapted to effect such a union”.

and

“For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it, and again, when the mean is to the first term as the last term is to the mean – then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one [Timaeus 31b-32a]“.

In the last citation Plato is formulating a mathematical problem related to the four bodys A,B,C,D with the three proportions A:B = C:D = (A+B) : (C+D) = (C+D) : (A+B+C+D). This problem is unsolvable if you don’t have a clue where to start.

This problem is solved when you realize that the Divine Proportion has many strange relationships that are very useful to solve the puzzle.

These relationships can be found if you know everything there is to know about Triangles and Triangles are again related to the Trinity (“Two things cannot be rightly put together without a Third“).

The Trinity comes back in the structure of the Dialogues of Plato. They are divided into Three Parts (and an introduction).

The structure of the dialogues relates to itself.

The knowledge of the self-reference of the Dialogues is also a clue to solve more complicated puzzles about the Dialogues themselves.

Just like the famous book of Hofstadter (Goedel, Escher, Bach) the dialogues show a new layer everytime they are read with a new aquired Insight.

The dialogues of Plato are organized according to the model he wants to teach. There are seven layers (-1,-2,-3,0,1,2,3) related to the Seven Mirror-Universes (or Hells and Heavens) of Our Universe (Eight, the Whole) in our Multi-Universe.

The Seven is a combination of Two Trinities with the Zero (The Void) in the middle. The Eight (2**3) State is the Dialog, The Whole, itself.

The Seven layers are divided into Three Sections (the Trinity) so the total amount of clues is 7×3= 21 + 1 (the Whole) = 22.

22 divided by 7 is an approximation of the number π (Pi).

Pi relates the Square to the Circle.

The Square represents the Playing Board of the Universe. On this Board we, the Humans, play our Game of Free Will.

Our Free Will is an Illusion. We are controlled by the Matrix.

The Circle represents the Wheel of Fortune, the Matrix, that Governs the Seven Universes in our Multi-Universe and the Game of Life.

What is Plato Trying to Explain?

The Golden Ratio

The Divine proportion is the basic concept behind Harmony.

The Divine Proportion is Not Symmetrical so Harmony is not related to Balance.

If everything would be balanced the Universe was never created.

Harmony is Balanced Unbalance.

An Architecture is beautiful when there is a slight unbalance in the Design.

This Unbalance shows the Sign of the Creator.

The Universe is created out of an Unbalance between Two Forces, the Positive and the Negative, the Good and the Bad.

The Two forces (-1,0,1) are divided into Four Forces (-2,-1,0,1,2) with the One in the Middle (Five) and are expanded into Seven Levels (-3,-2,-1,0,1,2,3). The Four Forces are “the most perfect bodies that can be constructed, four in number“.

The Seven Levels are related to the Circle. The Four Forces are related to the Square. The Universe oscillates between The Square and The Circle.

When the Square, the Game We Play with the Four Forces and the Circle (The Five Fold Cycle, Our Destiny) are in Balance the Human is in the Tao and Magic happens.

Every division is a split of the Trinity into Trinities until a state of Balance is reached. At that time the process reverses.

Mount Meru

The unbalance of the Good (+1) and the Bad (-1) is an Illusion. They Cooperate to Create Harmony (0).

Behind the perceived Unbalance is a balancing principle, the Divine Proportion. This principle brings everything Back into the Balance of the One who is the Void (0).

What we don’t know is to be known if we understand the progression of the Divine Spiral.

The Future, the Third Step, is a Combination of Two Steps in the Past (The Fibonacci Sequence), nothing more.

Is there a Deeper Structure Behind the Divine Proportion?

Golden Mean Spiral

The Four Forces (Control, Desire, Emotion(Compassion) and the Whole of the Trinity, Imagination) and the related sacred geometry were a guiding principle for the Imagination and the E-Motivation of many Western Scientists.

They tried to Control the Chaos of the Desires of the Senses by enforcing the Rules of Scientific Falsification.

The Proces of Falsification destroyed the Human Intuition.

The Western Scientists forgot to look at the Source of Intuition, the Center, the Quintessence (The Fifth, Consciousness).

The principle behind the Quintessence (Ether, Chi, Prana) is related to higher order symmetries and is a solution of a generalization of the generating function of the Divine proportion X**2 -X – 1

This generalization is X**2-pX-q or X(n+2) = pX(n+1) + qX(n). The solutions of this formula are called the Metallic Means.

When p=1 and q =1 the Divine proportion comes back again.

When the p=3 and q=1 a new sequence X**2-3X-1 or X(n+2) = 3*X(n+1) + X(n), the Bronze Mean appears.

The Bronze Mean generates the pattern: 1,1,4,13,43, the pattern of the Sri Yantra.

It shows a very beautiful pattern of “3″s when the Bronze Mean is evaluated in a Continued Fraction. The Golden Mean is a continued fraction of “1″s.

There are many more “Metallic Means” (other p’s and q’s). They are related to all kinds of symmetries and fractal patterns.

The Bronze Mean shows that behind the Trinity of the Golden Mean lies another Trinity (and another Trinity and …).

Penrose Tiling

The Bronze Mean is the generator of so called QuasiCrystals.

Quasy Crystals play a very important role in the Electro Magnetic Structures of our Body, the Collagens.  Collagens are the most abundant protein in mammals,making up about 25% to 35% of the whole-body protein content. The Collagens in our body explain the Ancient Chinese Science of Acupuncture.

Quasi Crystals are “normal” Crystals with a very complex symmetry.

They are ordered AND not-ordered.

One of the most beautiful examples of the patterns behind Quasi Crystals are the Penrose Tilings.

They were developed by the famous physicist Roger Penrose. He used the tilings to show his insights about consciousness.

Penrose believes that Our Universe is just like our Body a Quasi Crystal, a Hall of Mirrors. We the Souls travel all the Paths of this Magnificent Fluent Crystal.

Was the Bronze Mean Known by the Ancient Architects?

Tripura

The most important implementation of the Bronze Mean can be seen in the Sri Yantra (“Sacred Device”).

The Sri Yantra is related to the Red Triple Goddess of Creation, Tripura also named Lalita (“She Who Plays“).

The Sri Yantra is generated out of the FiveFold Pattern or Creation and the Four Forces of Destruction.

It contains  9 interlocking isoceles triangles. 4 of them point upwards and represent the female energy Shakti, while the other 5 point downwards, representing the male energy Shiva.

The standard form of the Sri Yantra  constitutes a total of 43 triangles. The centre of the Yantra has a Bindu which represents the Void.

The FiveFold Pattern of Creation moves with the Clock. A pattern that moves with the clock is a  generating pattern.

It moves away from the void and generates space. The FiveFold Pattern is the pattern of the Universe. It creates Universes, Galaxies and Planets. The Pattern moves around the Cellestial Center of Creation,  the Black Hole.

The FourFold Pattern moves Against the Clock and is a destructing pattern. It dissolves space and moves back to the void.  The FourFold pattern is the pattern of the Human Being and Earth.

The combination of both patterns is a Moebius Ring (the symbol of infinity) with the celestial Centre in the Middle. The FiveFold/Four Fold pattern resembles the Ninefold Egypian Pesedjet and the Ninefold Chinese Lo Shu Magic Square.

From the fivefold Shakti comes creation and from the fourfold Fire dissolution. The sexual union of five Shaktis and four Fires causes the chakra to evolve” (Yogini Hridaya (Heart of the Yogini Tantra)).

In Pakistan the Mother Goddess (Sharika) is represented by a diagram that contains “one central basic point that represents the core of the whole cosmos; 3 circles around it and 4 gates to enter, with 43 triangles shaping the corners“.

The Penrose Tilings and many other quasi crystals can also be found in Ancient Roman, Islamic and Christian Architecture (Pompei, Alhambra, Taj Mahal, Chartres). The tilings are an expression of the Game of Life and were used to build Educational Buildings (Pyramids, Cathedrals,..) to teach and show the old teachings.

Keplers Model of the Solar System

Kepler (1570-1640), a German Mathematician and Astronomer (The Cosmographic Mystery) and Albrecht Durer (1471-1528), a German Painter, knew about the Penrose Tilings but until the discovery of the Penrose Tilings nobody knew that they knew.

The new scientists (re)discovered old patterns that were known by the old scientist

What is the Meaning of the Bronze Mean?

The Bronze Mean shows the effect of a continuous division of the Universe in Trinities.

It shows that the Universe (and other levels) is suddenly moving from an ordered state to a chaotic state.

This chaotic, not predictable, state is not chaotic at all when you understand the patterns behind chaos.

In our Universe chaos is always ordered. Chaos is an effect of something that is happening in a higher (not Sensible) Dimension or A Higher Consciousness.

The Two Brains of Paul Steinhardt

The writer of an important article about Penrose Tilings and Islamic Art, Paul Steinhardt is like Roger Penrose a well known physicist.

He has created a new theory about the Universe based on Four Forces AND the Quintessence.

In this theory the Universe is Cyclic. It is expanding and contracting.

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

The membranes are higher dimensional Squares that are in parallel.

The Braines at both sides split into many similar cell-like structures. We live in one of the Cells of the Universe.

The Others, our Twins, live on the other membranes and are not aware of our existence until the Brains are getting into Balance.

At that moment the Twin Universes are Connected.

Scientists don’t know when this will happen but the Old Scientists who could travel the Multi-Universe with their United Brains knew.

It would happen at a very special Alignment of the Five Fold Center of Creation of the Milky Way with the FourFold Cross of the Destruction of Earth.

The Bronze mean is the Master-Pattern of our Multi-Universe.

The pattern 1,1,4,13,43 is in its 42nd enfolding and soon we will experience the 43th step, a Merge of the Left and the Right Brain of the Super Conscioussness, Adam Kadmon.

How to Raise the Djed

About the Nine-Fold Pattern of the Egyptian Pesedjed

Everything you want to know about the Divine Proportion

About The Indefinite Dyad and the Golden Section: Uncovering Plato’s Second Principle

About the Self-Referential Structure of the Dialogues of Plato

About the Law of Three of Gurdjieff

Paul Steinhardt, About Penrose Tilings and Ancient Islamic Art

About Penrose Tilings and the Alhambra

About the Geometric Patterns in Ancient Structures

An interview with Roger Penrose about the relationship between Conscioussness and Tilings

A lot of information (including simulations) about the Cyclic Universe of Paul Steinhardt

A simple model for the formation of a complex organism

How life emerged out of one Quasy Crystal

About Quasy Crystals and Sacred Geometry