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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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 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.

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.

Generalized Projective Geometry

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

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

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

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

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

Movements and not Forces are the Essence of Physics.

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

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

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

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

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

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

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

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

About the One and the Dirac Delta Function

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

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

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

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

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

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

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

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

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

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

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

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

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

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

About the Strange Behavior of Numbers

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

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

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

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

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

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

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

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

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

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

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

About the Duality and the Expansion of Space

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

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

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

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

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

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

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

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

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

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

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

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

Compressed Space is Time.

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

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

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

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

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

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

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

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

This Number System is called the Ternary Number System.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

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

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

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

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

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

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

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

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

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

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

About Numbers, Operations and the Klein Bottle

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

About Dewey B. Larson, Velocity and Time

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Universe of Numbers and Magnitudes  is Cyclic and Fractal.

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

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

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

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

About Triangular Numbers and Pascal’s Triangle

About the Relationship Between Geometry and Music

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

About Ratio and Proportion by Euclid

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

The text of the Fifth Book of Euclid

An Educational You Tube Channel called Insights in Mathematics

About the History of Geometric Algebra

Free Software to use Geometric Algebra

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

All you want to know about Geometric Patterns

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

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.

To Make Sense of the Present, Brains May Predict the Future

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

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

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

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.

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

The 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.

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.

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.

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.

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.

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.

“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 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).

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.

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).

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.

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.

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.

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).

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.

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.

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.

A few years ago (2003) somebody asked me to address the Dutch IT Architecture Congress. The subject was the Human Measure. To understand the Human Measure you have understand the relationship between the Human Being and The Human Measure System, The Emotions.

At that time I was already highly influenced by Will McWhinney so I used his model of the Four Worldviews to describe the Human. Later I discovered a Fifth Worldview (Consciousness) that was hidden in his teachings.

The consciousness is the monitor of the Whole of the Human Being. It reflects about the behavior of the parts and takes action when the Whole is not in Balance (Stressed).

According to Will McWhinney the Human can be described by The Emotions (Values), The Imagination (Ideas), The Senses (Desire, Facts) and the Expectation (Control, Rules).

The Four parts can be combined in six (or twelve = 4x3x2) Games. A Game is a strategy to solve the Conflict between the Four Independent Parts.

To me it is very clear that IT is focused on the combination Expectation/Senses. This combination is called the Analytical Game. It solves the Conflict between Facts and Rules. Will showed that this game was the dominating game in Western Culture.

In the Analytical Game the Emotions, the Consciousness and the Imagination are not important. In the Analytical Game you want to find the Absolute Truth, The Rules of the Game, by Analyzing the Facts sensed by the Eyes.

When you want to understand the Emotions you have to look at “emotional” Psychology. When you start to study “emotional” psychology the “box of Pandora” of Psychology opens up. Psychology is not a science like Mathematics or Physics. Everybody has his own theory about Emotions and everybody is defending his own “territory”. Psychology is simply a scientific mess.

One of the most helpful scientists (a friend of Will) was Rodney Cotterill. Cotteril analyzed the evolution of the Sensory-Motor System of every Organism on Earth. The Sensory-Motor System is an Interaction between the Emotions, the Motor, and the Senses.

The bacteria is drifting around, explores an inhomogeneous environment that contains all kinds of chemical structures. Some of these structures are destructive, some of them are neutral and some of them are attractive (food). When the bacteria finds (senses) food his rotator (the flagellum) moves the bacteria in a circular motion. The circular motion of the bacteria is preserved for a short time and this preservation could be called memory

The emotions are aimed at the survival of the human being. They Explore environments to find something that helps them to survive and Avoid destructive environments. When Humans have found an Attractive environment they Stay there and Store the data about the environment in their Memory. Humans are Moving Memories (E-motion means movement!).

According to Rodney Cotterill the Emotions are the basic structure, the infrastructure, of an organism. All the other structures are specializations of one of the parts (the Sensors, the Calculator (Imagination, Expectation)) of the Emotional Infrastructure.

IT is highly focused on Sensors and Calculators (the Senses and the Expectation). IT has no idea what to do with the Emotions, the E-Value-ator, the basic Measurement System of the Human Being. The main objective of the Evaluator is to find Food and to stay Alive.

The Human Imagination has created many “abstractions” of Food and Secure Environments. They are all stored in the Memory as Symbols and Metaphors but it is not difficult to define what Humans don’t like. They don’t like the same thing IT-experts don’t like. IT-experts want to be Valued. They don’t want to be Dominated. They demand the freedom to Express their Creativity. They don’t want to play a role in a Play that was Designed by somebody else.

IT-experts love to play the Analytical Game. In this Game the Humans, called the Users play the role of the Object, the reusable Module, that has to do its Job. In the Analytic Game Users don’t have Emotions and Imagination. They have to Eat the Food that grew out of The Seeds of the Imagination of the Architect.

What is the Human Measure?

The basic measure of the Human Being is related to everything that gives him or her a feeling, an Emotion, of Security. The Human Value-System, the Emotions, is always looking for Shelter, Protection and Love. Humans Beings need other Human Beings to tell and show them that they are Value-able.

If the Human Being has an Expectation this Expectation has to be realized in the near Future.

When the Emotions of the Human Being are Dominated it wants to move away from his environment because a dominating environment could be Destructive. When something or somebody is Dominating a Human Being he/she feels worthless.

If the Imagination of the Human Being experiences No Change, (Highly Repeating Actions) it wants to Explore a new Environment.

If the Senses experience Too Much Change the Human Being becomes Confused. When you are Confused your Expectation fails and the Human starts to drift around just like the bacteria.

If the Human Being is not Conscious (Aware, Focused) it is unable to Reflect. If the Human Being is not Aware he is unable to Balance the Emotions, the Imagination, The Expectation and the Senses. If there is no balance the Body becomes Stressed. A Stressed Body slowly kills the Immune System. An Unbalanced Immune System is the Cause of many Diseases.

What is IT Doing?

IT is still creating Dominating, Always Changing, Insecure and Confusing Software.

IT is not automating the repeating activities Humans don’t like. IT is producing highly disconnected software-systems.

IT is not helping the Humans to makes senses of the complexity of the Outside World. IT is increasing the Complexity of the Environment.

IT is not supporting the Human to explore its environment. IT is shielding the outside environment and is creating an artificial outside environment. Many people believe the Imaginary World is the Real World. The most destructive artificial worlds are the Destructive Computer Games. They give the Player the Believe that Killing People is no problem at all. The destructive Games are the Games of the Military. They kill people by looking at simulators and pushing buttons.

IT is Playing the Same Game using Different Terminology all the time. If you understand the transformation of the terminology the Game is Boring. If you don’t understand the terminology the Game is Confusing. If you Mix the Terminology the Game is too Complex to Play. Almost nobody knows the Rules so many People make mistakes, believe they win the Game but in reality lose the Game.

What to do?

Perhaps somebody is able to Invent a New Game.

I have an Idea.

Why don’t we create a Game that Creates Games? According to the Theory of Will this Game is called the Game of Culture. It solves the conflict between The Imagination (The Creator) and the Emotions (The Mover). When the Mover is Inspired by the Creator the Sensory/Motor-System starts to Act with Spirit (Imagination) and Soul (Emotions). In terms of Emotional Psychology: The Human becomes Highly Moti-vated!

If we look at the theory of Will we now can see that the Analytical Game is the Complement of the Game of Culture.

If we Unite the two Games, the Games of the West and the Games of the East, we are able to connect all the parts of the Human Being in a Cycle, the Cycle of Human Innovation.

The tetramorphs are four angelic beings, drawn from Babylonian symbolism in a vision of the Hebrew Prophet Ezekiel:

As for the likeness of their faces, they four had the face of a man, and the face of a lion, on the right side: and they four had the face of an ox on the left side; they four also had the face of an eagle

The beasts are later described in the Revelation of John: “And the first beast was like a lion, and the second beast like a calf, and the third beast had a face as a man, and the fourth beast was like a flying eagle.”

The four Babylonian symbols represent the four fixed signs, the Cross of the Zodiac, Leo, Taurus (Bull), Scorpio (Eagle) and Aquarius (Human).

They are related to the four ancient elements of Air, Water, Earth, and Fire, the four evangelists (Mark/Lion, Luke/Bull, John/Eagle, Matthew/Human), the four Seasons and the four possible Views on the world (Rules (Lion), Senses (Bull), Emotions (Human) and the Imagination (Aquarius) of Will McWhinney.

The Twelve parts of the Zodiac are the twelve (4×3) possible combinations of the Four Tetramorph.

The tetramorph themselves are combinations of the same aspect (the Bull = SensesXSenses).

Will McWhinney calls the twelve combinations “Games” or “Conflicts” because it is impossible to Unite the Four Tetramorphs.

They represent a Tension or a Force. We have to learn to Balance the Four Forces so they are able to Unite in the Center, The One (the Thirteen).

The Zodiac denotes an annual cycle. The constellations also move in a cycle, called the Precession, with a duration of 25,800 years. The Precession is moving retrograde (in the opposite direction) of the movement of the Sun in the yearly Zodiac.

The precession is an indicator of the cultural or religious state of our World. During the phase of the Pisces many Fish- and Water related symbols were used.

It is very interesting to see that the Roman Church is based on the worldview of a very old precessional symbol, the symbol of St Peter and St Mark, the Lion. In the Roman Church the Sins (the Senses) of the Bull have to obey the Moral Rules of the Lion.

Starting about 200 BC, Pisces, The Fish, became the ruler of the cycle of precession. Love thou Neighbor, became the object of Early Christianity. The Roman Church, an extension of the Empire of Rome, was never able to implement the Social Vision of the Fish.

It remained a hierarchical controlled structure with the Pater (Peter), the highest rank in the hierarchy of Mithras (The Killer of the Bull), at the top.

We are now moving from the State of Water into the State of Air (Imagination, Creation). The Social Structures of the Church will be replaced by Connected Individuals who want to Share and Express a Personal Mystic Experience.

The view of John the Evangelist, the view of the Mystic and the Poet, is hidden in the Inner World, the Imagination, of the Human. According to the Mystics the Outer World is an Expression of the Creative Power of this Inner World.

John the Evangelist was a disciple of John the Baptist before he became a disciple of Jesus. John the Baptist used Water when he baptized Jesus. He initiated John the Evangelist and Jezus into the Gnostic Mysteries. Jezus relates John the Baptist to the prophet Elija (Elias). (“there has not been raised of those born of women greater than John the Baptist. … if you are willing to accept it, he is Elias … the one about to come.” (Mt 11:9-14)).

The symbol of John the Baptist was not the Eagle but its antagonist, the Dove. When we look at the symbolism of the Dove we are able to detect who John the Baptist really was. John the Baptist represents Elija, Vishnu, Oannes, Enki and Ea, the Creator of our Universe, the Lord of the Waves. The Dove is represented in the Zodiac by the Pleiades, the Center of the Cross of the Universe.

In the next part I will give you a very brief introduction into the Believe System of the Mystics.

It is very important to understand that the Mystics believe that the Creator of our Universe is not the creator of the Whole, the creation itself. The process of Creation is an Act of the Imagination of the One, a formless Entity also called The Light or the First Logos, the Word. The One has delegated the process of creation to other creators who are an emanation of the One.

A creation of a creator is able to create his own reality. One of the creations is Earth and the Humans on Earth are also able to create their own reality with their Imagination which is an expression of the Imagination of the One.

The One splits itself in many parts. The first creation, the Second Logos, is the Two, The Cosmic Father and Mother (Light, Darkness, Yin, Yang). The One, The Cosmic Father and the Mother are the Trinity represented by the Letters I (I am the One), A (The Beginning) and O (the End). (Revelation 1: 8: I am, the Alpha and the Omega). IOA comes back in the name Ioa(ness),the Fish-man, John and the IOROBA of Africa.

The Human is the last step in the creation. He is a five-fold creature, a combination of the Four Forces of the tetramorphs and the Light of the One.

Our Universe is one of the creations of a creator called the Demiurge (Ea, Enki). The Human Soul is in exile in the creation of this Demiurge. There are many universes and Earth is part of one of these universes. Earth is part of the (Dark) Material Universe.

The Soul, the Sparkle of the Light, will eventually return to the One. It is helped to return to the One by other Souls (Angels, Archangels) to reach ‘the Worlds of Light’. One day the world will be saved when Oannes, Enki, Vishnu, Jesus comes back.

Our Reality is governed by a Cyclic Process. This process is created by the Demiurg to keep the Souls in the Black Material Universe. Planets and stars influence fate and are also places of detention after death.

The Book of Destiny, the Book of Revelations, created by the Demiurg and written in the language of ancient Astrology, describes the Cycle. The Souls have to Jump out of the Cycle, through the Hole in the Universe, to reach the World of Light of the One. The Hole in the Universe is in the Centre of the Rose, The Heart.

Mysteries (Rituals, Sacraments) purify the soul, to ensure her rebirth into a spiritual body, and her ascent from the world of matter. The Knowledge of the Mysteries is hidden. The Hidden Mysteries are revealed by the Light, the First Logos, at the time when the Seeker has stopped looking for the Answer to all his Questions. At this moment of complete silence The Light Leads the Way.

John the Evangelist and his mystic woldview can be found in many old and almost extinct religions: Manicians, Coptic, Druze , Alawites, Essenes, Mandaeans, Chaldeans, Valentinians ,Cathars, Sufists and Armenians.

IOnA is a small island in the Inner Hebrides of Scotland (Scota) that has an important place in the history of Christianity. Iona formerly named Innis nan Druidhneach (the Island of the Druids) was a primary seat of learning for the pre-Christian Celtic Druid Magi until St. Columba, the Dove, was exiled from his native Ireland (Tara).

St. Columba founded a monastery on Iona with 12 companions. Iona’s fame as a place of learning and Christian mission spread throughout Europe. Iona became a holy island where several kings of Scotland, Ireland and Norway came to be buried.

St. Columba later came back to Kells, close to Tara, and created another Monastery. One of the most important relics that was taken from Iona to Kells is the Book of Kells.

The most important mystical place in Ireland is called Tara. It is, according to legend, the place where the followers of Ioaness, guarded by the prophet Jeremiah (586 BC), accompanied by his scribe Baruch, and the daughters of Zedekiah, the last king of Judah, went in exile when Jerusalem was taken by the Babylonians under Nebuchadnezzar.

One of the daughters (Tea Tepi, Scota) marries Eochaidh the high king of Ireland. Jeremiah brings many important relics to Ireland including Jacob’s Pillow, the cornerstone of the temple of Salomon.

The religion that came out of Kells and Iona was very different from the religion that came out of Rome. It was the religion of the Celtic Druids AND the followers of John the Baptist called Celtic Christianity.

Celtic Christianity was completely destroyed by the English Rulers of Ireland and Scotland. Just like the Roman Church destroyed the Cathars and Islam destroyed the Druze. Celtic Christianity went underground and came back as The Kabbalists, the Alchemists, the Rosicrucian’s and the Free Masons.

We are now entering a new phase in the Zodiac called Aquarius (Imagination). The view of John the Evangelist will become the Spirit of the Time. It is not necessary to create a New System of Rules, a Religion. The Dove is silently waiting in our Inner World to move Outside to bring Peace to the World. The Rose of the Heart will slowly open without any outside pressure.

Many people think that Charles Darwin proposed the theory of evolution but they are wrong. The predecessor of Darwin was Jean-Baptiste Lamarck (1744-1829).

In all the textbooks the evolution theory of Lamarck is highly discredited. He was totally wrong and Darwin was absolutely right. Lamarck was a fool. In his days he was blocked by the Ruling Power in Science because he attacked the major paradigm in society, “Only The Best Survive“.

Like Darwin, Lamarck concluded that species change over time by adapting to new environments. Like Darwin, Lamarck concluded that parents pass their traits on to their offspring.

He also founded the principle of use and disuse: If an organ is used, it will become stronger, and if it is not used, it will weaken and may disappear in future generations.

The big difference between the theory of Darwin and Lamarck is the flexibility of the process of evolution. Lamarck believed that evolution reacts to its environment in a much higher speed than Darwin could ever imagine.

People believe the theory of natural selection of Darwin because it fits with the general believe that “Life is a Competition“. This rule was and is the driving force behind educational theories (testing) and economic theories.

It supports the idea of the higher classes and the lower classes and it fuels racial theories (“Don’t Mix a Black and a White“). It also fits with the computer metaphor where the DNA is a database and Life is a Program that reads the Database.

Lamarck’s theory is now proved by a new field of research: Epigenetics. Epigenetics is the study of gene expression independent of DNA mutations. It contradicts the rules of Mendelian inheritance.

The DNA contains many genes that are not used. Until recently they were seen as a sort of waste. They were dumped by the selection process. Recent research shows that these genes are used when the environment changes. The reaction to the environment is much faster than anybody imagined.

In the theories that are educated the controlling mechanism of life is DNA. It contains the code and the code is “clean” and “effective”.

Every time when a new cell has to be created the same procedure is repeated all over again and again. This has proved to be wrong.

The controller of life is not a database and a standard program but a highly differentiated database used by an “intelligent” processor. This processor reacts to the internal and external environment of the organism. It sends out messengers and reacts to messengers.

The most influential messengers are related to the “human imagination”. Our “theories about the inside and outside world”, our belief systems, determine an important part of the adaptive cycle.

The now widely accepted Lamarckian view on evolution in Molecular Biology has a huge impact on science.

The current theories about diseases and aging have to be adapted. In this theory Genes determine diseases, aging and are a very important tool to diagnose and therapy. When genes are adaptive we have to support the process of adaptation instead of interfering in this process.

You can imagine that epigenics disturbs the whole medical profession and of course the pharmaceutical industry. They will use the same tactics that were used to stop the ideas of Lamarck.

# How to Create Human Scale Tools: About Movers, Memories and Comparators

Humans are the most advanced toolmakers in nature. The main reason is that they are the less specialized organisms. They need tools to survive. People are also the most complex organisms in nature. This complexity makes it possible to invent new possibilities and to work with specialized tools and animals (horse, cow, hammer, car, computer).

All the time people have tried to make a better living by inventing new tools. If the basic needs were met (food, housing, health, safety), people got the time to get their emotional system into balance (love, self-esteem) and satisfy their imagination (play, explore, self-actualization).

At this moment, the amount of leisure-time to enjoy family life, relax, play and explore is going down. The number of people with heavy levels of stress is growing. The pressure on the emotions is increased by the current state of technology. The tools have overlapping functionality, take too much of the attention, do not communicate with each other and dominate the human being.

Tools have to be integrated completely in the cognitive system of the human being. If a tool takes over a part of the sensory-motor system (glasses, hammer, car) the imagination has to learn a new way to create the outside world. In the end, after practicing, people become united with their hammer or their car. They are not aware that they are carrying their glasses. If people have to practice too long or the tool is constantly intervening in their workflow the emotions get involved. They get frustrated and angry.

Tools were first invented to support basic human activities like talking, moving, looking,  hearing, remembering and learning.

In a later stage of development, the use of the tools generated a new space of exploration. In this space, new tools emerged.

The invention of symbols started the exploration of Mental Space. Program Languages, Telecommunication and especially the Internet has opened up a new space to explore, called Cyberspace.

Advisors and masters involve the emotions. An advisor helps to make a choice or to set priorities. A master (e.g. a physician, teacher, manager) makes a choice for a person. The Cyberspace version of the master and the advisor is the Expert System. It uses advanced ways of pattern-recognition (e.g. Neural Networks).

• Simulator

Simulators stimulate the imagination. Theaters and movies are examples of passive simulators.  Games are actively involving many people. The Cyberspace version of the active simulator is the Collaborative Computer Game. The passive form can be seen in the Movie and the Television-program.

• Memory

A memory archives the results of an internal or external dialogue. In the beginning, human communication was only verbal. Important issues to remember were incorporated in stories that were told from one generation to the other. When people specialized their activities, they needed a method (bookkeeping) to keep track of all the transfers. People invented symbols and the external memory to do this.  The writing-symbols made it possible to share and exchange memories (letters, books) without talking. Writing enabled the movement of memories. The library was invented to store the external memories and protect them from fading away. Cyberspace is filled with the versions of static and moving memory called the Electronic Message (Email, Transaction) and the Database.

• Mover

Movers were the first tools used in human society. A mover is an extension of the muscles. The first generation was invented to help the human move in physical space. Examples are hammers, cows, horses, steam-machines, cars, bicycles and robots. The next generation supported the movement of symbols (e.g. moving numbers) in mental space. The Difference Engine of Charles Babbage was invented to automate the calculation of mathematical tables. The most advance version of the mover, the telecommunication network, enables the movement of external memory’s in cyberspace.

• Sensor

Sensors transform and filter data. Glasses and hearing aids were invented to support people when they get old.  Humans looked at the stars and invented the telescope. In a later stage very advanced sensors were developed (Radio-telescope, MRI). They use complex statistical calculations to filter and transform the sampled data into pictures or sounds.

• Comparator

Human survival and learning is based on comparing data and acting on the result. A comparator acts on an exception. To compare data a measurement instrument is needed and a agreement about the object of measure.

Human beings started to measure time and space a long time ago. It was needed to navigate and to predict the movement of the stars. In the first phase, the human body was used as a measure-instrument of space and the cycle of the sun and the moon as a measurement for time. The big problem with this approach was that every person and every place on earth came up with a different measurement and a different time.

When the human networks started to connect, standardization on a global level became necessary.  The process of standardization of time and space took many ages. It needed numerous inventions in technology to support the process. The measure-instruments changed from mechanical devices (the clock) to software-devices.

• Servant (Operating System)

A servant coordinates the activities of sensors, comparators and memories. Servants take over repetitive patterns.  Humans find these activities boring (not imaginative). A servant has to act invisible (a black box).

When the use of a servant is prohibited, humans get frustrated. It has to be there all the time and do its job inconspicuous. With the help of the comparator and the sensor, the servant has to detect events and take appropriate action (coordinated movements, action patterns).

The big problem at this moment is the visibility and the interference of the servant in the human activity. People have to fill in the same form all the time. Processes stop in the middle of a company. The customer has to handover the data to the other processes.

Humans do not like to be emotional involved in boring activities.  Therefore, the needs (their wishes) have to be defined in a very simple way. It must be possible to imagine the behavior of the complete system without knowing how the system is operating.

A good example of a perfect servant is the central heating system. People define their needs (a temperature) and everything works. The temperature is a control variable that represents the performance of the total heating system. People are able to imagine the effect of adjusting the thermostat (a comparator) on the environment they live in. They do not need to know how the servant works. His behavior is hidden. The central heating system is a black box, loosely coupled with another invisible servant-system, the utility-system (gas, electricity).

The servant and its associates were in the first era of IT locked into the physical space of the general-purpose computer controlled by its general purpose operating System. The servants had to stay close together because of the speed of communication. The speed and the capacity of the telecommunication network is going up fast.  This makes it possible to distribute, specialize and connect Servants (now called Appliances).

# How to Create Cooperative Networks by Playing Complementary Roles

People have to cooperate to survive. Children need their parents to nurture and teach them. Parents need the help of their children when they are old. The basic principle behind cooperation is long-term reciprocity. People give something voluntary and sometimes for free to others or help the other trusting they get something of the same value back in the future.

To survive people have to have a long-term perspective. They have to sustain their environment and the supporting infrastructures to make sure that there are enough people and tools to help them when they are old.

The need to survive created the basic level concept of cooperation (the tribe). The tribe transformed into higher and more complex levels of cooperation (town, guild, state, corporation) when human society evolved.

To coordinate the complex structures the mental concept of the many leveled hierarchy was formed. This concept fails when the environment of the organizational structure becomes turbulent.

Hierarchies adapt too slowly to their environment. At this moment, hierarchies are falling apart in cooperating self-sustaining specialized network. The networks are gaining control over many activities that are now taking place at the level of the big corporation and the state.

A specialized network produces activities and products that are consumed by other specialized networks. To realize the output people have to play complementary roles.

When we can distinguish six basic roles:

• Craftsmen (Senses, Patterns)

A craftsman has acquired experience by practicing. Craftsmen do not like too much change. Change requires new practicing and keeps him from producing.  A craftsman loves to make what he sees. He learns by copying. Examples are carpenters, painters, musicians, technicians and programmers. The craftsmen are the producers in the network. In many cases, programmable machines can replace their activities. Craftsmen use specialized tools. If their processes are standardized a process-model can be used to coordinated their activities.

• Entrepreneur (Senses, Emotions)

An entrepreneur feels what preferences people have. Examples are retailers and brokers. Entrepreneurs sell the products the network is producing and buy products the network needs. They also are the people that negotiate contracts and make connections to other specialized networks. Entrepreneurs use technologies like relationship-management-tools and procurement-systems.

• Politicians (Emotions, Patterns)

A politician structures collective emotions by creating consensus. He feels the opinions of the collective, has the gift to influence opinions, and gets people into collaborative action.   A politician looks after the social cohesion in the network. He uses opinion polls and media.

• Creators (Imagination, Patterns)

A creator visualizes the whole of a structure. A creator can balance variety (his imagination) and predictability (the patterns). Examples are composers, architects and designers. A creator designs the machines and the products the network is producing.

• Motivator (Emotions, Imagination)

A motivator visualizes what makes people move forward. Motivators develop concepts.  Many of them operate in the media (actors, writers, poets and movie-directors). Motivators cannot live without variety. Other examples are coaches and psychiatrist. A motivator looks after the long-term perspective of the network by creating and implementing a shared vision.

• Inventors (Senses, Imagination)

An inventor makes sense of his imagination. Inventors generate ideas and create prototypes (R&D). They use brainstorming tools and analyze trends.

The roles are not evenly distributed in the network. The majority of the people play the role of the producer, the craftsman.

In the current situation, the basic roles are concentrated in specialized corporations (e.g. media, retail, production-plants) or   staff-department of big corporations. Many high talented people are already leaving the big corporations and take part of specialized networks. The amount of one-person-companies is increasing.

People can cooperate with persons that share with them one of their basic cognitive components. An entrepreneur can convince a craftsman what products people he has to sell. They are both practical people (the senses). A creator (e.g. an architect) can show a craftsman what to make. They share a focus on structure (patterns).

When complementary roles are working in a cooperative environment, they join their forces in an open dialogue. This dialogue has many stages ranging from brainstorming (inventors take the lead) to realizing material structures (craftsman work together with creators).

Politicians, entrepreneurs and motivators can only perform if they are able to observe and express emotions (visual expressions, gestures). To ensure a successful cooperation they have to meet. New technologies like video-conferencing make it possible to cooperate anytime, any-place and anywhere.

To collaborate people have to communicate face to face. In a competition patents (legal actions) and secrecy (rules and walls) shield ideas to prevent the competitor to take the lead.  In cooperation, ideas are shared to sustain the network.

The most used model in communication is the sender/receiver-model.  People send and receive content (e.g. email, documents, pictures, plans, designs) Specialized networks need advanced content-management systems to support this model of communication.

The sender/receiver-model supposes that the brain converts ideas directly into words and that another person can easily draw out the meaning of the ideas from the words. It assumes little effort to understand or interpret what is being conveyed.

The sender/receiver-model only works if there is a high level of common conceptual understanding (a shared model) between all the people involved in the communication process.

In reality, this is mostly not the case especially when experts (inventors, craftsman and creators) are communicating with laymen (entrepreneurs, motivators and politicians).

The dialogue between an expert and a layman is often a monologue. The expert confuses the layman with all his knowledge and the layman is not capable of asking the right questions. In the end, the layman stops asking questions and accepts the situation.

The sender/receiver-model reduces a specialized network to a production-process. The model lowers the social cohesion (politicians), reduces the external cooperation (entrepreneurs) and removes the long-term perspective of the network (motivators).

People have to invest time to understand (ask unsophisticated questions) and explain their ideas (inventions) in many ways. It also takes time to generate trust. Ideas of others have to be tried out (in the imagination or in the real world) to understand them.

People have to have the opportunity to fail and learn from their mistakes. Sometimes they generate personal inventions that can be given back to the others to create reciprocity.

Eventually ideas create new personal patterns that can be shown and praised by others.  Collaboration does not take place instantly but evolves in a cycle where the pleasure of finding things out is the motivator.

When people are pessimistic and afraid the other becomes the enemy. They shield themselves from the outside world by creating fixed boundaries (walls).

To make sure that they get something in return they use a threat (e.g. physical force, the legal system). Before they start, they have to spend time to prevent a possible conflict (making contracts, detailed specifications). When people trust each other, they cannot wait to start.

The fear of losing something (possessions, status, existence) changes a collaborative relationship into a battle.

In a competition, the focus is on winning and selfishness. Fear has a negative impact on the senses (tunnel view), the emotions (stress) and the imagination (creativity block).

In a competition, priority is given to stay in front and to prohibited possible actions of the enemies. To win one has to predict and control by defining strict rules and make sure that people obey the rules. Internal and external competition finally kills a cooperative relationship.

To prevent the move from cooperation to competition people have to sustain a free and open communicate-process.