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

# 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.

# About the End of the Stock Market (6-10-2008).

The Amsterdam Stock Exchange was the first stock exchange to introduce continuous trade in the early 17th century. The Dutch pioneered short selling and every other “modern” instrument. Until the sixties Government and the Big Companies were controlled by about 200 Rich Dutch Families (including the Royal Family). They controlled Society and took care of Stability.

In the 17th century the Dutch East India Company (VOC) was introduced by the Dutch Government. The VOC was the first multinational in the world and the first company to issue stock. It was the first mega corporation possessing quasi-governmental powers, including the ability to wage war, negotiate treaties, coin money, and establish colonies.

In the 17th century about 200 families, the so called Regenten, were in control of the Netherlands. The families promoted their members in every influential position available.

The Democracy of the Netherlands was in reality an Oligarchy. The “oligarchic way” of decision making, the Dutch Polder Model, is still the most important way to reach consensus in the Netherlands. Everything happens “behind closed doors”.

Until 1917 only the Rich people were allowed to Vote. The Rich Voted with their Money. In the beginning of the 20th century (1917) the universal suffrage for male citizens was introduced in the Netherlands. Two years later (1919) the female part of the country followed.

The Rich not only voted with their money they were also the most important owners of the Stocks. With the power of their stock and their money they helped their families to acquire important positions in the State and the Companies.

Until the Sixties the Rich maintained a very powerful social network based on reciprocity in the Netherlands. This network was not a local network. It was an international network. The influential Dutch Families were connected to comparable networks all over the world.

Around the Seventies the power of the Rich Families went down. They lost their influence in Parliament and in the Companies. The Flower Power Generation took over the Power at every Level of Society. After some time most of them lost their Ideals of Peace and Harmony.

They started to buy houses and shares and were helped by the Rising of the Economic Kondratiev Cycle. In contrary to the Regenten the Baby Boomers acted on their own. They were very Individualistic and never created a Social Network that could support Society.

Around 2000 the stock market started to vibrate and to go down. The same happened in politics. Many voters are now moving from party to party.

Who is controlling Society?

At this moment nobody is controlling Society. Society is taking its own course.

Who is controlling the Stock Market?

At this moment nobody is controlling the Stock Market. The Stock Market is taking its own course.

Not only the Stock Exchange but also the Political System and the Weather System are taking their own course.

Is there and end to this all?

I don’t think so.

Why?

We have entered the Downfall of the Kondratiev Cycle. During this Downfall the Old Institutions are destroyed and New Institutions take over the Power. We are in an “In Between State”. In this state everything is On the Move. Everything is Moving Up & Down, Left & Right. What many people don’t see that even the Center is Moving. The State and the Stock Exchange are not able to cope with the excessive amount of Movement.

What will happen at the End of the big Shake Up?

There are two possibilities. The first one is the return to an old center.  My guess is that we will move back to the State of the Renaissance.

The second possibility is “frightening” for many people. We will jump to an unknown state predicted by many Old Civilizations called the Fifth World or the Golden Age.

The Hopis call our time the “The Fourth Age of Man”. According to them the Earth has been wiped clean 3 times already. First by Fire, next by Ice, most recently by the great Flood approximately 11,000-12,000 years ago. We are now entering the last stage of the Fourth Age called “The great day of Purification“. This stage culminates either in total Rebirth or total Annihilation.

The Degree of Violence will be determined by the Degree of Inequity caused among the peoples of the world and in the Balance of Nature. In this crisis Rich and Poor will be forced to struggle as Equals in order to Survive. The beginning of the Fifth World will be heralded by the arrival of a being known as Pahana, or the lost “White Brother“.

If we believe the Prophecy of the Hopi and many other “Spiritual Movements (Gnostics, Sufi’s)” the only way that will save us from total annihilation is the Creation of Balance. We don’t have much time left. The Great day of Purification will happen . At that time the “Lost White Brother” (The Center) will return.

Is it possible to Balance the Financial System?

Yes, I think so.

The only thing we have to do is to Unite Shareholders, Customers and Workers and give them an Equal Share in a Company. They have to Share the Power, the Profit or Loss, the Spirit and the Soul. They have to become Enthousiastic about What is Happening (Spirit).

They have to take care of Nature and the Other (Soul). If we do this we will recreate the Social Power Network of the Rich on a Different Scale (Earth) with other Participants. If we Help the Other we don’t need a Pension!

I am sure You want to put Your Savings into a Shared Enterprise. I am also sure that You will Never Regain the Money you will invest in Shares at the Stock Exchange. The Era of the Stock Exchange is Gone for Ever.

# The Age of Commercial Space Exploration is Near

I am involved in a new company that is selling a new product of Richard Branson called Virgin Galactic. Virgin Galactic is selling suborbital spaceflights for the price of \$200.000.

Our principal aim behind this is not to make money. The principal aim is to reinvest any money we make into space exploration,” Branson said. “We expect to double, triple, quadruple the number of astronauts in the next few years that have currently experienced space,” he said.

To date, Branson said, about a 100 pioneers have been willing to pay \$200,000 to be the first people to go into space via Virgin Galactic. “These are the kinds of people who are going to enable us to bring the cost of space travel down,” he stated.

Space Tourism is not the primary target of the Company. It wants to be the first commercial company involved in Space Exploration.

Space Exploration is a major theme of Science Fiction. When I was young I read all the books in this Genre I could find. Science Fiction has stimulated Science extensively. Many Scientist got their inspiration out of explorations of the Future. When the Theme was set it was only a matter of time when somebody would realize the Inspiration of the Author.

The step from Idea to Realization is mostly not the issue of a Science Fiction novel. In most cases we have realized all the technology and our just “doing it”. Most of the time the final realization takes much longer than the writer could imagine. Jules Verne put a Man on the Moon about a hundred years ago.

The major theme of Space Exploration in Science Fiction is War. We meet Extraterrestrials and they or we don’t like each other. We are part of a Federation (mostly the Good Ones) and in the end we beat the Bad Ones. Interesting enough many of the Stories related to UFO’s look a lot like the Science Fiction Stories. The only difference is that THEY are visiting US.

In the Renaissance the people in the West started to explore Earth like we want to explore Space. After The Renaissance the Age of Exploitation started, The Industrial Revolution. The Industrial Revolution followed by the Age of Information made Space Exploration finally possible.

History repeats itself so I can imagine what will happen next. Both stages are part of a bigger cycle, the Cycle of Culture. It takes about 1250 years to turn around.

At this moment we are in a situation comparable to the year 758. The only thing that is different from that time is that we have moved to another Level, Earth.

What happened around 750?

At 750 we are in the Middle of the Middle Ages called the Dark Ages. It was the time when the Great Empire of Rome was collapsing because of a huge movement of hungry people. The world was struggling with a sudden change of the Climate. Everywhere States were fighting to expand and defend their territories. Around this time a new Spiritual Leader, Mohammed, created a new Religion. It was the start of the expansion of the Arab World and the Arab Empires..

Conditions in Western Europe slowly began to improve after 700 as Europe experienced an agricultural boom caused by a substantial increase in solar radiation. About 600 years later the Renaissance started.

The Great Empire of the West is currently collapsing because of a huge movement of hungry people. Just like the Roman Empire we are really not aware of the collapse. In the last days Romans spend all their time playing very expensive games and were enjoying life to the extremes. They forced all the other states to pay enormous amounts of taxes to keep the Entertainment Business running. In the End their stable infrastructure collapsed.

I hope you see the relationship.

Replace the Arab Expansion in the Middle Ages by the coming Chinese Expansion in you will know Who’s gone Win.

Millions of people are waiting for the Coming of the new Messiah, the new Spiritual Leader of the World. According to the Cycle He (or She!) will come soon.

In the West we are playing Games. Leslie Benzies, the producer of Grand Theft Auto IV recently revealed in an interview that the amount of money spent on the development of the game was right around \$100 million. The budget of the movie Pirates of the Caribbean was \$300 million. The development costs of all the movies and games exceeds the budget of the World Food Organization with ease.

Why do we need to move into Space?

The first reason could be to escape Earth. We need another place to live because life on earth is not the way it was. If we do this and Science Fiction is Right at the long term we will move into a comparable situation, Competition on the Level of the Galaxy. We have to learn who are our friends and who are our enemies.

The second reason could be “Spin-Off”. Space Exploration has boosted Science and Technology.

The last reason could be to see Earth as it is. A Beautiful Blue Slowly Turning Globe without any Borders. From Space Earth looks like a Paradise. I imagine the Extraterrestials are seeing this also! This could be the reason they are here!

The Cycle of Civilization is a slow cycle but there are cycles with a much longer periodicity. Many “Old Civilizations” found the Cycle of the Precession of the Equinox and “calculated” the Center of this Cycle, The Mother Goddess situated in the Pleiades.

The coming Years the Very Long Cycle and the Cycle of Civilization are coming into a Conjuction. The Effect of this Conjunction is unknown. Human Civilization has not gathered enough data to make an understandable prediction. The only thing we know is that we are living in a Very Special Time of History.

One of the people that analyzed the very Long Cycle (Terrence McKenna) predicted Time/Space-Travel as a major Novelty that would soon appear. Just like the Mayas and many other Civilizations he knew there is a very cheap alternative, DMT (a psychedelic drug).

The Old Civilizations predicted a return of the (Virgin!) Mother Goddess of the Pleiades (Ises, Mary Magdalene, The Black Madonna, Alcyone). Perhaps She is the New Spiritual Leader many religions are waiting for. I hope the Male Religions don’t mind She is a Female!

Perhaps Richard Branson should start a new Company soon, Virgin TimeTravel. She Will Love It.

Wait and See.

The Renaissance was a Cultural Movement that spanned roughly the 14th through the 17th century. It started in Italy in the late Middle Ages and later spread to the rest of Western Europe.

After the Dark Middle Ages, controlled by the Church of Rome, aimed at the Inside (Spirit and Soul), many people wanted to discover the Outside.

The Renaissance is the Age of Discovery. It is the time of Columbus.

The printing press, invented in 1450, made it possible to distribute all the new knowledge all over the known world.

The new knowledge is in reality very old knowledge. Renaissance means re-birth and the Renaissance is the re-birth of the knowledge (and wisdom) of the Greek and the Romans.

This knowledge was forbidden and destroyed by the Rulers in Rome. It came back because of renewed contacts with the Arab Culture. At that time Arab Culture was at the top of its cycle.

Art (Leonardo Da Vinci) and Science (Copernicus (1514)) exploded. Both of them were funded by the rich merchants (Medici, Venice).

Scientists started to experiment and used advanced tools (Microscope, Telescope) to study the external world and the internal world (the Body). They looked with their own Eyes and not with the Eyes of the Bible.

In the Arts the Perspective was invented. Artist used advanced tools (“camera’s) to support their own eyes to project the outside world on a flat surface.

Another Re-Birth was the Reformation (Luther, 1517). The Bible was translated in many languages and distributed by the printing press to many people.

For the first time people outside the Church could read and study Religious documents and compare them with Scientific Evidence  from Greece, Arabia and Rome.

The need to convert others to the Christian faith was huge. Many expeditions, Crusades,  were send out to unknown territory to find convertible humans.

The missionaries used the old fashioned trick learned from the Huns to force people to accept  the Faith by violence. Millions of people were tortured and killed.

At the outside of the Christian Empire the Arabs were attacking all the time. They were also very wealthy.

The search for Gold stimulated the weapon-industry of the west.

Not only the weapon industry flourished also the transport industry (Maps, Navigation, Big Ships) made a lot of progress.

The combination of both of them (The Navy, “War-Ships”) helped the West to Rule the Sea.

Production in the Renaissance was carried out by the Guilds, a Cooperation of Craftsman. They were almost in total control of every craft in the big cities.

The Renaissance (Creation) is part of the Cycle of Western Culture.

In this Cycle it was preceded by the rule of Roman Church (Control) and followed by the Industrial Revolution (Social).

The rebirth was fuelled by an Expansion Phase (Fire).

In this phase not only Arabic Culture expanded and rose to a high point also the new rulers of the West (Celts, Germans), the descendants of the Huns, created new Kingdoms and build the Cathedrals. The Cathedrals contained all the occult knowledge of that time (Sacred Geometry, The Spiral, The Light, The Four Forces,.).

On a macro level we see an interesting pattern.

The phase of Fire (Expansion, Practice, Summer, Sensory, …) fuels the phase of Creation (Up, Spirit, Idea, Eye, Winter, Mythic,…).

Ideas are put into Practice or Practice generates Ideas. The combination of Sensory and Mythic (A Game) is called Invention or Exploration by Will McWhinney.

The game of Exploration is an Infinite Game. Infinite games are about continuing the Game.

Going Back to Jump to another Level is also a pattern that is visible in the most advanced theory about ecologies promoted by the Resilience Alliance (RA).

The Ecology of the Roman Church dominant in the Dark part of the Middle Ages collapsed. It collapsed because of many factors.

In this time the Plague killed millions of people. The Climate was very instable (An Ice-Age) and the new Kingdoms of the Huns and Celts were heavily expanded. They started to fight for dominance.

According to the theory of RA a collapsing ecology reverts to a previous stage to rise again.

What does this say about Innovation?

Innovation is fuelled by an earlier (expansion) stage in history. It is triggered by a collapse of an Ecology.

If we look at the current state of the world we see a Collapse (a Compression) of the World Wide Ecology. It will certainly generate a stage of Ideas and Creativity.

This is needed to solve the current problems. In contrary to many ideas about Innovation the only way to solve the problems is to Look Back and Learn from History.

We can learn from the Control Stage of the Middle Ages where one paradigm was enforced. At this moment Science is enforcing again one paradigm, the paradigm of Control, Abstraction, Technology, the Computer, Statistics and the Factory.

They were created during the Industrial Revolution that was aimed at creating Unity (Every Thing is the Same).

At this moment we are moving into the stage of the Center, Balance and Harmony.  In this stage we always jump to a new level of Conscioussness. In the last Center-Stage the Religion of the Islam was born so the chances are high that a new World Religion will appear or re-appear.

People that explore contradicting paradigms are excluded from the scientific community. This community controls the world of Inspiration just like the Guilds were controlling the crafts in the Renaissance. To innovate we need Freedom of Paradigm.

We can learn from the Idea stage of the Renaissance. It teaches us that a Union of Art, Science and Spirituality is needed to support real innovation.

We can also learn from a comparable phase in the Cycle, the phase of Harmony. In this phase the old is completely destroyed by an invasion of people outside its territory (The Huns).

The West is trying with all its force to block a huge part of the Earth (the “Under-Developed” countries) to take part in its innovation. It creates (Economic and Legal) Walls just like the Roman Empire and the Chinese Empire created Walls to protect their territory from the Huns and The Celts when they were in their end-stage.

The Under-Developed countries are of a Lower Culture. Perhaps these cultures carry something the West desperately needs. In these cultures the collective is more important than the individual. In these cultures the sick, the poor and the old are still taken care of.

Funny.

I believe this was the message Christianity wanted to bring to the World.

Something went wrong in the West don’t you think?

Lectures about the Renaissance part 1

Lectures about the Renaissance part 2

Lectures about the Renaissance part 3