Archive for the ‘History’ Category

Over Veerkracht (Resilience) (in Dutch)

Monday, April 2nd, 2012

De leer van de thermodynamica is in de 19e eeuw ontstaan uit natuurkundig onderzoek dat werd uitgevoerd om de efficiëntie van de stoommachine te verbeteren. Inmiddels heeft deze wetenschap belangrijke wetten over het Universum ontdekt.

Volgens de thermodynamica beweegt de energie in het Universum op de lange termijn zich van een onmogelijke extreem hete situatie, de Big Bang, naar een toestand van extreme kou en een hoge waarschijnlijkheid, de Big Freeze, waarin alles netjes uniform verdeeld is. Het universum beweegt van extreme chaos naar extreme ordening.

Energie stroomt daarom altijd van hoge (chaos) naar lage temperatuur (orde). Vrijwel alle energie op aarde komt van de zon in de vorm van electro-magnetische straling. Met behulp van deze zonnestraling transformeren planten, algen en bacteriën simpele chemische structuren in complexe biomassa (chemische energie). Bacteriën en schimmels breken deze structuren weer af waardoor de cyclus wordt gesloten.

Biomassa wordt door de rest van de organismen op aarde direct of soms veel later (olie/gas/steenkool) geconsumeerd. Het consumeren van de primaire zonne-energie vindt plaats in voedselketens waarin de organismen ook zelf weer worden geconsumeerd.

Vanuit ons menselijk perspectief interpreteren wij het consumeren van de participanten in een voedselketen als een competitie (“survival of the fittest”) maar we kunnen het ook zien als een uiterst flexibele keten van chemische reacties die worden uitgevoerd in bewegende zichzelf reproducerende chemische fabrieken.

 Energie is de mogelijkheid om iets in beweging te krijgen of te houden. De opgeslagen (potentiële) energie in de aarde wordt soms in meerdere stappen omgezet in beweging (kinetische energie). Tijdens deze omzetting gaat er altijd warmte verloren (dissipatie, wrijving, weerstand, erosie).

De energiestroom van de zon wekt door de rotatie van de aarde stroom-systemen (flow-systems) op. Stroom-systemen hebben een boom-structuur als de stroom van een punt naar een oppervlak of een volume gaat. Een voorbeeld zijn het weersysteem en een meanderende rivier-delta. De longen en de bloedvaten in ons lichaam hebben precies dezelfde opbouw omdat hetzelfde proces ook in ons lichaam optreedt.

Volgens de Constructal Theory van Adrian Bejan verbeteren de stroomsystemen zich steeds opnieuw en dat doen ze door gebruik te maken van de permanente slijtage (dissipatie, wrijving, weerstand, erosie) die de stroombeweging veroorzaakt.  Uiteindelijk vindt er altijd weer ergens een doorbraak plaats in de meander.

Adrian Bejan heeft de Constructal Theory volledig analytisch afgeleid uit de wetten van de Thermodynamica. Hij  beschouwt het principe van de verbeterende stroomsystemen (“construction”)  als een Hoofdwet van de Thermodynamica. Volgens hem is ontwerpen niet een intelligente actie maar een volstrekt logisch gevolg van de werking van ons Universum.

De stroom van onmogelijkheid naar uniformiteit, van hoge onwaarschijnlijkheid naar hoge waarschijnlijkheid gaat gepaard met allerlei tussenstadia waarin de bestaande structuren de nieuwe structuren de weg wijzen.

De doorbraken in de meanderende stroompatronen maken beter gebruik van de huidige mogelijkheden maar de oude paden behouden lange tijd hun functie. Hierdoor is een stroomsysteem niet afhankelijk van één pad en is daardoor ook bestand tegen calamiteiten (bijv. een sterk verhoogde regenval in het stroomgebied van de rivier).

Het systeem waar de stroomsystemen onderdeel van uitmaken bestaat uit Machines (Constructal Engines) en Barrières (Brakes).

De machines en de barrieres zorgen ervoor dat de aarde niet te warm of te koud wordt.

De machines zoeken de weg van de minste weerstand, optimaliseren de stroom, bouwen structuren op, slopen de barrieres, produceren kinetische energie en minimaliseren de slijtage. De machines slechten het pad naar de Big Freeze waarin alles gelijk zal zijn en alles stil zal staan.

De barrières bevatten potentiële energie, leveren de weerstand om de minste weerstand te vinden, slopen de machines, optimaliseren daardoor de dissipatie en produceren een maximale hoeveelheid straling met een hogere golflengte als de binnenkomende zonnestraling die de aarde weer verlaat.

Produceren (Machines) en Consumeren (Vernietigen, Slijten) houden het wankele evenwicht van Moeder Aarde in stand.

De evolutie van ecologieën, steden, organismen (wet van Kleiber), talen (wet van Zipf), organen (de longen, bloedvaten), sporten en technologieclusters voldoen aan de Constructal Theory.

In 2002 hebben Holling en Gunderson het boek Panarchy: Understanding Transformations in Human and Natural Systems gepubliceerd.

Panarchy bevat een integrale visie op de evolutie en de adaptieve cyclus van  de constructal engines die men ecosystemen noemt.

Panarchy is ontstaan door het combineren van ogenschijnlijk conflicterende theorieën. Die theorieën leken conflicterend omdat ze betrekking hadden op de verschillende fasen (Zie Plaatje Phase Space hieronder) van de adaptieve cyclus die een ecologie doorloopt.

De combinatie van de vier mogelijke fasenruimten levert een op-en neergaande cyclus op waarin op een zeker moment een sprong (bifurcatie) wordt gemaakt naar een compleet nieuwe ruimte. Nadat deze sprong heeft plaatsvonden stopt de dynamiek van de oude ecologie.

De meest herkenbare fase is de Exploitatie-fase (B).  Dit is de opgaande lijn waarin de ecologie een hoge mate van orde bereikt en overschotten (Potential) produceert.

De vier fasen van de Panarchy Cyclus voorgesteld als een landschap met een rollende bal

Aan het eind van deze fase neemt de potentie af en wordt er van alles gedaan om de levensduur van de ecologie zo lang mogelijk te rekken (C -Conservation). In deze fase zijn de structuren verouderd geraakt en zijn er op allerlei plaatsen reeds alternatieven (bypass) ontstaan die beter passen op de huidige vraag naar beweging.

De ecologie is in de conservatie-fase vrijwel tot stilstand gekomen en besteed al zijn energie aan het onderhouden  van zijn eigen structuur.

Tijdens de langzaam opgaande lijn van de Exploitatie-fase neemt de verbondenheid en vooral de afhankelijkheid (Connectedness) tussen de participanten onderling enorm toe waardoor de ecologie steeds kwetsbaarder wordt voor verstoringen.

De constructal engines in de ecologie gaan steeds efficienter samenwerken wat ten koste gaat van de diversiteit en de variatie in de ecologie.

De ecologie kan verstoringen opvangen totdat de  verschillende paden nog niet zijn dichtgeslibd maar een verstoring die alle paden tegelijkertijd raakt is dodelijk.

Op het laatst wordt de Veerkracht (Resilience) enorm op de proef gesteld en kan het gebeuren dat de Ecologie volledig ten onder gaat (Release) of na een grondige Reorganisatie weer aan een nieuwe levensloop kan beginnen.

De resilience van een ecologie wordt gemeten door de snelheid te meten waarmee een ecologie zich weer herstelt van een verstoring.

Volgens Panarchy beweegt een Ecologie zich op verschillende schalen en plaatsen en kan op die plaatsen in verschillende fasen verkeren waardoor er allerlei soorten van interactie mogelijk zijn. Hoe hoger de schaal hoe langzamer de cyclus verloopt. Hoge schalen dempen de fluctuaties van de lagere schalen.

Een snelle lokale reorganisatie kan zich plotseling heel snel verspreiden (een lopend vuur (Revolt)) terwijl een langzame geleidelijke ontwikkeling (een organisatie) een snelle ontwikkeling weer kan dempen of tot stilstand kan brengen (de organisatie van de Brandweer (Remember)).

Panarchy is een Zelf-Refererend Cyclus-Model dat bestaat uit Vier Fasen en (minstens) drie Schaalniveaus.  De panarchische golfbeweging bestaat uit twee stappen n.l. de  positieve weg Omhoog naar de Top (exploitation, conservation)  en de negatieve weg Omlaag naar het Dal (depressie, reorganization).

Op een bepaald moment kan de golfbeweging zich splitsen waardoor een nieuw (ander) niveau van organisatie optreedt. Deze sprongen doen zich volgens een vaste regelmaat voor.

Als we kijken naar terminologie en inhoud valt het op dat er een groot verband bestaat tussen Ecologische-, Economische- en Persoonlijkheidstheorien. De natuur, de economie en de mens lijken onderhevig te zijn aan dezelfde wetten.

De theorie over de Menselijke Natuur heeft erg veel weg van de Theorie die wij over de Natuur zelf hebben ontwikkeld. De mens is een zelfstandig bewegende ecologie, een stromend stroomsysteem waaraan een groot aantal participanten deelnemen.

Bacteria wisselen DNA uit

Die participanten hebben zich in de loop der tijd verenigd omdat een samenwerkingsverband veel efficienter bleek te zijn dan een solitaire ontwikkeling.

In het begin bestond het samenwerkingsverband uitsluitend uit simpele chemische fabriekjes, bacteriën, die genetische ontwerpinformatie (DNA) van hun fabriekjes uitwisselenden. De eerste fundamentele stap in de samenwerking van de bacterien was de statische spons. De mens heeft erg veel ontwerp-informatie gemeen met de spons.

Spons

Later gingen de organismen bewegen en waarnemen. Hierdoor gingen ze als individuen samenwerken met andere organismen die genetisch op hen leken (zie Genetic Similarity Theory).  Het uitwisselen en combineren van ontwerp-informatie ging gewoon door (sex).

In volgende fasen ontstonden er hogere ordeningen, zoals lichamen die lichamen konden bevatten (huizen, steden, vliegtuigen, onderzeeboten en auto’s).

Op dit moment is de (grote) stad het hoogste niveau van koppeling maar niets houdt de “Constructal Law” (of de Entropie) tegen om een ordening te gaan scheppen op  het niveau land of aarde.

Dat betekent dat er nieuwe slagaderen moeten komen om de ontwerp-informatie en de energie die tussen de grote steden gaat stromen te faciliteren. Overduidelijk is dat het Internet de basis vormt van het zenuwstelsel van de aardse informatievoorziening.

De thermodynamica is een statistische theorie. De kansverdeling van een Systeem wordt de Entropie van het Systeem genoemd.

Om een kans te kunnen berekenen moet je de kansruimte (de Phase Space) bepalen. Die bestaat uit alle mogelijkheden.

Het aardige is dat je niet hoeft te beschikken over kennis van alle combinaties van alle componenten van een specifiek systeem om erg veel te weten te komen over een kansruimte.

Je kunt gaan spelen met willekeurige componenten (a,b,c,d,e,….), de combinaties in een matrix stoppen, gaan tellen en patronen zoeken in de getallen die er dan worden gevonden. Je bent dan bezig met de statistiek van de statistiek of beter de waarschijnlijkheid van de waarschijnlijkheid. De mogelijke patronen worden beschreven in de Driehoek van Pascal.

Wat dan blijkt is dat er achter het patroon van Pascal weer een patroon zit (zie plaatje).  Dat patroon bevat wederom driehoeken en het is zeer waarschjinlijk dat er achter de driehoeken weer driehoeken zitten. Driehoeken in driehoeken in driehoeken in…. noemt men een fractal, een zelf-herhaling.

De  (on)waarschijnlijkheid is eigenlijk heel mooi en vooral ook simpel geordend en komt voort uit een zichzelf herhalend patroon, de Drie-Eenheid, dat in iedere godsdienst op aarde voorkomt.

Wetenschap en Godsdienst gaan uiteindelijk over hetzelfde.

LINKS

Over de Big Bang

Over Thermodynamica

Over Constructal Theory

Waarom een stad een organisme is

Waarom de genen bepalen wie we aardig vinden 

Over Pan en Anarchie

Over de Wet van Kleiber

Over de orde achter de wanorde (Over de Driehoek van Pascal)

Over de Uitgebreide Driehoek van Pascal

Over de drie-eenheid.

About Perspective

Thursday, February 2nd, 2012
File:Reconstruction of the temple of Jerusalem.jpg

Medieval Perspective

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.

About Perspective Drawing

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

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

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

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

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

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

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

Perspective Machine designed by Albrecht Durer

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

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

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

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

IMAGE: Leonardo's perspectograph

The Perspectograph of Leonardo Da Vinci

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

About Projective Geometry

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.

Two projections of the same object.

Different Points of View

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

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

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

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

Pappus' Theorem

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

Desargues' theorem

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

Pascals Theorem

About the Four Points of the Cross-Ratio

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

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

The Cross-Ratio

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

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

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

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

ratios.jpg

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In Eucludian Geometry A Ruler contains a Fixed Scale

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

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

alchemy

The Expectation looks through a Small Hole.

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

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

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

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

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

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

About Space measured by Time and Space measured by Space

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

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

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

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

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

At that Time Space was measured by Time.

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

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

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

From that Time on Space was measured by Space.

Why the Future contains Infinite Possibilities

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

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

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

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

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

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

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

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

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

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

Moving Movement is the Essence of our Reality.

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

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

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

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

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

golden mean spiral2

The Spiraling Spiral of Time

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

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

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

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

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

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

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

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

Let’s Move.

LINKS

About Pythagoras and Heliopolis (Egypt)

About Pythagoras

Paul Dirac: About Physics and Projective Geometry

About the Middle Ages

About Expanding Space and Not-Euclidian Geometry

About the Renaissance

About Resistance and Mass

About the Mathematics of Perspective

About the Ether

About Clean Space

About Projective Geometry

Pictures of the Projective Plane

About Geometric Algebra

About As Within, So Without

About the Reciprocal Theory of Dewey B. Larson

A Video about Mobius Transformations

About Projective Geometry and our Senses

About Projective Geometry and Geometric Algebra

About the Cube of Space

About Time and Paranormal Experiences

About Geometry

A Textbook about Metric Geometry

About the Four Points of View

About the Void

Why the Future is Open Space

About Alchemy and the Klein Bottle

About the Human Sensory System

Stuart Kaufmann: About the Adjacent Possible

About Number and Magnitude

Monday, January 9th, 2012

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

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

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

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

Movements and not Forces are the Essence of Physics.

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

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

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

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

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

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

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

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

About the One and the Dirac Delta Function

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

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

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

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

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

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

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

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

In the Beginning a Huge Explosion took place that created the Universe.

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

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

The Tetraktys of Pythagoras

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

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

File:Dirac function approximation.gif

The Dirac Delta Pulse

 

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

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

About the Strange Behavior of Numbers

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

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

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

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

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

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

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

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

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

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

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

About the Duality and the Expansion of Space

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

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

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

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

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

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

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

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

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

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

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

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

Compressed Space is Time.

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

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

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

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

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

The Ternairy Number System is represented by the Binary Tree

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

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

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

This Number System is called the Ternary Number System.

About Ratio’s and Magnitudes

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

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

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

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

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

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

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

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

The Perfect Triangle of the Tetraktys contains 9 = 3x3 Triangels. A Triangle contains 3 Lines and 3 Points.

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

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

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

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

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

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

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

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

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

angle between vectors in 2 dimentions

A Displacement or Bivector

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

screw theory 2

A Displacement and a Rotation of a Vector

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

blades

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

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

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

add-bivectors

Combining (Adding) Bivectors creates a Trivector

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

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

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

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

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

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

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

Quaternions are rotations in 4D-space

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

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

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

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

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

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

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

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

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

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 Hexagonal Numbers

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

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

About Numbers, Operations and the Klein Bottle

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

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

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

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

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

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

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

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

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

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

SriYantra

Sri Yantra

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

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

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

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

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

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

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

About Dewey B. Larson, Velocity and Time

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

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

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

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

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

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

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

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

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

LarsonsScalarCube.jpg

Larson’s Cube, the Geometric Representation of the Octonion.

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

wom_image3.jpg

The Periodic System of Larson

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

About the Bott Periodicity

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

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

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

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

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

Bott Periodicity

The Universe of Numbers and Magnitudes  is Cyclic and Fractal.

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

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

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

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

The Star of David, the Symbol of Human Center, the Heart Chakra.

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

LINKS

About the Tetraktys (1)

About the Tetraktys (2)

About Triangular Numbers and Pascal’s Triangle

About the Empty Set

About the Relationship Between Geometry and Music

About the Trinity

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

About Number and Magnitude

About Ratio and Proportion

About Ratio and Proportion by Euclid

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

The text of the Fifth Book of Euclid

An Educational You Tube Channel called Insights in Mathematics

About the History of Geometric Algebra

About the Sri Yantra

About Geometric Algebra

Free Software to use Geometric Algebra

About Clifford Algebra

About Yantra’s

About Movement

About Topology

About the Digital Root Patterns

About the Heart Chakra

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

All you want to know about Geometric Patterns

About the Sum of Things

Thursday, September 22nd, 2011

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

lo-shu-color

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

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

The Chinese Pollen Path

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

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

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

SriYantra

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

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

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

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

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

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

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

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

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

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

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

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

The Seal of Saturn or the Dance of Yu

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

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

The Lo Shu and the Well

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

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

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

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

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

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

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

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

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

Lo Shu Torus

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

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

4

9

2

-5

-1

4

-3

3

5

7

-5

-2

0

2

8

1

6

-5

3

-4

1

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

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

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

About the Sum of Things

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

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

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

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

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

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

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

LINKS

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

About the I Tjing

The Calculations  behind the Number of Things

The Relationship between the Lo Shu and the I Tjing

About the Lo Shu Torus

About Saturn, the Son of the Sun

About the Trickster

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

The Sistine Chapel (Rome) and the Seal of Saturn

About the Relationship between the Lo Shu and Music

About the History of the Lo Shu

About the Wheel of Eternal Order and the Wheel of Time

About the Relationship between the Lo Shu and Chinese Alchemy

About the Great Flood

About the Orion Myth

About Plato, Pythagoras and the Lo Shu

About the Nothingness

About the Trinity

About the Heart Chakra

About the Sri Yantra

About the Lo Shu Magic Square and the Chinese Domino Game

About the Mirror Universe

About Acupuncture

About Tit for Tat

About the Prisoners Dilemma

About the Bronze Mean

About the Sheng Cycle

Everything You want to Know about Sacred Geometry

About the Influence of the Lo Shu on Recent Art

The Lo Shu Square with Imaginary Numbers

A City is an Organism

Saturday, February 12th, 2011

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

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

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

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

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

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

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

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

mexico-city

Mexico-City

Kleiber's law

Kleiber's law

About the Law of Kleiber

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

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

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

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

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

Bacteria exchange their DNA

Bacteria exchange their DNA

About DNA

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

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

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

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

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

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

Sponge

The Sponge, the Tube, is the Basic Structure

One of the Bilateria: The Octopus

The Octopus is a Sponge with a Brain.

About Innovation

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

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

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

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

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

Life explores every possible path.

About Cities

A City is a Combination of Houses.

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

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

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

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

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

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

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

looking-to-toledo1

Toledo (Spain)

About Synchronization

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

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

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

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

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

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

Paris

The kernels of Paris

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

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

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

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

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

chartres4

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

About the Memory Palace

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

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

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

sagrada-familia-barcelona-projection

The Sagrada Familia in Barcelona (Antoni Gaudi)

LINKS

This is a  presentation about The City as an Organism

Why the Tube is such an Important Structure

About The Law of Kleiber

Why Innovation is a Combination of Combinations

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

About Thermo-Economics

About the Autarkic City

About Cybernetics

About Synchronization

How Gaudi used a Machine to design the Sagrada Familia

About Machines that generate Architectures

How the Heart Synchronizes the Body

About Super Organisms

About Smart Technology

About Addiction

About the Master/Slave-relationship

About the Heart

Why the Cathedral contained all the Knowledge that was Needed

About the start of Civilization

About the Law of KLeiber

Friday, October 29th, 2010

A power law relates one variable to another raised to a constant power. The general form takes y = xa, where y and x are variables, and a is a constant exponent.

A power law exhibits the property of scale invariance. When you multiply the Scale (x) with a factor b the function (y =  baxa) does not change its Shape.

In 1817 Goethe wrote his book ”Zur Morphologie“. This book was the start of a new science called Morphology, the Science of the Shapes.

In his book Goethe describes the so called Uhrplant, the Primal Plant, which is based on the shape of the Leaf. Goethe believed that every Plant was a Leaf within a Leaf within a Leaf.

At the time of Goethe the concept of the fractal was not known. It was developed in 1975 by Benois Mandelbrot (“The Fractal Geometry of Nature”).

A fractal is a self-similar structure. It’s shape repeats itself on every level of expansion.  Some fractals are scale-invariant.

Scale Invariance in the Leaf

The scale invariant fractal structure of the Leaf

About Kleiber’s Law

Metabolism is the process by which your body converts what you eat and drink into energy. During this complex biochemical process, calories in food and beverages are combined with oxygen to release the energy your body needs to function.

The oldest and best known Power Law is Kleiber’s law devised by the Swiss-American zoologist Max Kleiber in 1932.

Kleiber’s Law, MR = W3/4, describes the relationship of the metabolic rate (MR) to the biomass W, raised to an exponent.

Kleiber’s law means that a cat’s metabolic rate is not a hundred or 21.5 times greater than a mouse’s, but about 31.6 — 100 to the three-quarter power.

This relationship seems to hold across the animal kingdom  and it has since been extended all the way down to single-celled organisms, and possibly within the cells themselves to the internal structures called mitochondria, the cellular powerplants, that turn nutrients into energy. Mitochondria have many features in common with bacteria.

The law of Kleiber is  also applicable to super-organisms” like ant colonies, Cities and Eco-Systems.

Because of Economies of Scale, larger and more complex forms of organisms need less energy for each individual cell. They grow and reproduce more slowly and they live longer.

Kleiber's law

Kleiber's law

About Fractals and Kleiber’s Law

Kleiber’s law can be explained from a general model that describes how essentialmaterials are transported through Space-Filling Fractal Networks of Branching Tubes.

Goethe was right. The leaf is a one of the fundamental structures of Nature.

The factor 3/4 (3/3+1)  is a consequence of the fact that a Fractal Structure has to incorporate a not-Fractal Structure, 3-Dimensional Space.

One of the Bilateria: The Octopus

One of our fellow Bilaterians: The Octopus

About Bilateria

About 590 million years ago, the Central Nervous System (CNS), the Brain, appeared.

The organisms with a CNS (including the Humans), the Bilateria, are able to Act and React to a Possible Harmful Stimulus.

The CNS of the Bilateria is  a result of  an Increase in Competition between the Life Forms that came out of the Continuing Fusion of  the Cooperative Life Forms, the Bacteria. The first step in this proces was the Tube of the Sponge.

The fundamental Bilaterian Body Shape is a Tube running from Mouth to Anus, and a second Tube called the Notochord, with an especially large Sphere at the front, called the “Brain“.

The Bilateria have Five Body Spheres (1) the Brain; (2) the Spinal Cord; (3) the Heart and Lungs; (4) the Digestive Organs and Kidneys; (5) the Bladder and Reproductive organs.

Lung

About the Tiny Spheres of the Lungs

When we look at the Lungs, one of the Fractal Tube-like branching-structures of the human organism, we can see that the Branches end in Nodes called the alveoli (“little cavities“). The end-nodes of the branching system are tiny Spheres.

Alveoli

The Alveoli use another basic structure of Nature: The Sphere

In the tiny Spheres the Exchange takes place of Carbon Dioxide and Oxygen between the Lungs and the Blood-Vessels. Each human lung contains about 600 million alveoli.

Water diffuses from the alveoli cells into the alveoli so that they are constantly moist.  Oxygen dissolves in this water before diffusing through the cells into the blood.

The Oxygen-rich blood returns to the Heart via the pulmonary veins to be pumped back into circulation. The Carbon Dioxide is pumped out by the Lungs.

In the many million Small Spherical End-Nodes Two Circulatory Systems, the Cardiovascular System (Heart) and Pulmonary System (Lungs), are Connected.

The Big Structures of Nature are able to Scale because the Connection-Points of the Networks are Very Small.

They are reusable on Every Scale that is Bigger than the Scale of the Connection Points.

We will see that all the other Fractal Systems in our Body are based on the Same Principle.

Villi

Villi

About the Tube of the Digestive System

The Tube contains the Digestive System. It breaks-down larger food molecules into smaller ones that can be absorbed into the blood stream. This happens in the Small Intestine in the vili and microvilli.

The villi (“shaggy hair“)  are tiny, finger-like projections that are approximately 0.5-1mm in length. The microvilli are mechanosensors and have a lot in common with the flagellum (“the roter“) of a bacterium. Microvilli appear in many places in the body. They are also of importance on the cell surface of white blood cells, as they aid in the migration of white blood cells.

The Tube of our Digestive System is highly similar to the Tube of the Sponge, the first fusion of the Bacteria in a  more efficient metabolic structure.

The Output part of the Tube is called the Large Intestine (Colon). Its function is to absorb water from the remaining indigestible food matter, and then to pass Useless Waste Material from the body. The large intestine houses over 700 species of bacteria that perform a variety of functions.

Liver

The Liver Fractal

About the Chemical Factory of the Liver Cell.

The Liver is  a Fractal Branching System that detoxifies harmful substances absorbed via the Small Intestines.  It’s basic structure is the Liver Cell.

The Chemical reactions in the liver cells produces a lot of waste heat. This is carried round the body in the blood and warms less active regions.

The Liver regulates the amount of Blood Sugar, Lipids, Amino Acids.  The Liver is the Storage House of  Blood, Iron, Vitamine A, D, B12  and Clycogen, the Source of Energy of the Body.

The Liver produces Bile that is stored in the Gall Bladder. Bile is used to dissolve fat.

White Blood Cell

The White Blood Cell

About the Spleen and the Immune System

Another Fractal Branching System, the Lymphatic System ( “The Immune System“, Spleen),  maintains the health of the body by protecting it from invasions by harmful pathogens, such as bacteria, viruses, fungi, and parasites. These pathogens are the cause of many diseases, so it is necessary to detect and eliminate them rapidly.

The Lymphatic System is connected to the Blood System and produces the White Blood Cells (Lymphocites).  The Lymphocites are the Basic Unit of the Human Defense System. They look like Bacteria.

A lymphocite fits with a pathogen

A lymphocite fits with a pathogen

The surface of a lymphocyte is covered with a large number of identical receptors. Recognition and destruction occurs when the receptors of the lymphocyte fit like a key into the surface of the pathogen.

The Immune System is a Highly Adaptive System. It is able to generate new types of Lymphocites out of a Library of DNA-components.

Nephron

Nephron

About the Kidneys and the Bladder

The Kidneys serve the body as a natural filter of the blood, and remove wastes which are diverted to the urinary bladder. The Nephron is the basic structural and functional unit of the kidney. In humans, a normal kidney contains 800,000 to 1.5 million nephrons. Nephrons are wave-like structures. Its chief function is to regulate the concentration of water and soluble substances like sodium salts by filtering the blood.

About the Electro Magnetic System

The last  Fractal Branching System, the Meridians, is a Fast Electro-Magnetic Channel that connects to Organs to the Spine and the CNS.

The Ancient Chinese Scientists believed that this System pumps its Energy, the Chi Force, out of the Earth Magnetic Field.

The Ancient Egyptian Scientists believed the same thing. They named  the Four Cavities the Four Suns of Horus and the Spine, the Djed Pillar (Dj means “Snake”).

The Five Organs of Acupuncture

The Five Systems of Acupuncture

About the number Five

The number Five (4 +1 ) plays an important role in Ancient Chinese Medicine.

The Central Fractal System, the One (1), the Fire System, the Blood System, with its Center the Heart,  contains Four (4) Links to the Other Systems.

The Four Systems are combinations of Two Forces, Expansion and Compression.

The Two Forces came out of One Force (“The Void“).

Two Systems contain the same combination (Expansion x Expansion (Wood, Gall Bladder, Liver, Three Heater), Compression x Compression (Metal, Lungs)).

Two Systems combine Expansion and Compression in a different order (Expansion x Compression, Compression x Expansion). They create a Wave (Water, Bladder, Kidney) or Spiral -like (Earth, Immune System) structures.

The Five Spheres of the Body are incorporated in one Super Protective Sphere, the Coelum, the Skin.

In the Human Embryo the First step of Division of the Cells is between the Coelum,the Multi-Cellar Body, and the Brain, the CNS. In the first step the One was divided into the Two, the Actor and the Monitor.

The CNS  “mirrors” the activities of  the Body and acts as a “predictive simulator”.

The Shape of the CNS is a mirror (Up-Side-Down) of the Shape of the Multic-Cellular Body.

The Bilateria are a Fuse of two Organisms in which one organism changed into the Body and the other changed into the Brain.

These two structures are always competing in the Human Being.

The Brain is Looking Up at the Sky. The Body is Looking Down at Mother Earth, it’s Creator.

The Brain and the Body are United in  the Heart, the Balancer of Body and Soul and the Keeper of the Rhythm (The Pericardium).

Sponge

Sponge, The Tube

About Bacteria

The Body Shape of the Tube was inherited from the first Multi-Cellular Organism, the Sponge. The Sponge is a  Static Cluster of Amoeba, free moving bacteria, that are propelled by their flagellum (a Roter).

Bacterium

The Basic Building Block of the Body, the Bacterium

Bacteria are small chemical factories that are able to share and combine their production processes by exchanging DNA.

With their flagellum the Bacteria Explore the environment to find the chemical food they need. When they have found food the Circulation of the Flagellum moves into the Opposite Direction.

The bacterium integrates incoming chemical signals during a few-second period of its travels, and adjusts its direction of advance accordingly.

The integration is achieved through temporary chemical modifications to molecules located in the bounding membrane, which transfer nutrients to the cytoplasm, and also through changes to certain other molecules in the interior of the cell. Such integration is essentially a short-term memory mechanism.

Bacteria exchange their DNA

Bacteria exchange their DNA

At a certain moment the Bacteria got together because the Sponge is a much more Efficient Metabolic Structure than a group of Free Moving Bacteria.

Strangely enough the DNA of the Sponge already contains the complete Bleuprint of the Humans.

Scientists now believe that most species on earth are a result of a loss of DNA from the original Bleuprint that was created when the Bacteria finally fused into one Organism.

About the Nano-Level

Recently scientists have found Electric Fields as strong as 15 million volts per meter in the Nano-Parts of the Cells. These fields are as strong as those produced in lightning bolts.

It’s not clear what causes these strong fields or what they might mean but they could account for a until now unknown (by Science) or well-known (by the Old Scientists, Chi) Source of  Bodily Energy.

The nano-parts of the Cell could be the very very very small universal building blocks of Nature.

What has Happened?

In the beginning the Chemical Soup generated Self-Reproducing Chemical Factories.

These Factories combined into bigger Factories by exchanging and combining their factory-designs.

Every time when the Factories fused they became more Efficient, Bigger, Stronger, Older and therefore more Competitive.

When the Factories became more competitive they had to Protect themselves against the other Factories.

To Protect themselves the Multi-Cellular Systems started to Sense in Many Directions.

In the first step a Nerve-Net was created.

In the second step one part of the Organism turned Upside-Down and became a Specialized Predictive System (the CNS).

This part fused with the Bodily Part creating one Organism that contained Two Organisms.

The Bilateria, the Organisms with Two Complementary Parts, Body and Mind, were born.

Some of the Bilateria called Humans fused in Social Structures and the Social Structures fused and fused and became more efficient, bigger, stronger, older and therefore more competitive.

In due time they will Rule the Earth and will start to create bigger and bigger systems until they will rule the complete Universe.

To make this possible the Humans need every other part of Nature to Sustain their Growth. This will certainly result in a huge Collapse of their own Eco-System.

The main reason this is happening is that the Humans forgot to Copy the Designs of Mother Nature.

The Brain (Thinking and Sensing, Left Brain), Looking Up at the Sky,  believed it could do a much Better Job than it’s counterpart the Multi-Cellular Body (Emotions and Imagination, Right Brain), Looking Down at the Earth, the Source of All Creation.

Kleiber’s Law shows that we are now using 122 times more Energy per Person than we really would need if we would Scale in the right way.

What can we learn from Kleiber’s Law?

All organisms including the humans depend for their maintenance and reproduction on the close integration of numerous subunits.

These components need to beserviced in a relatively `democratic’ and efficient fashionto supply energy, remove waste  and regulate activity.

Natural Selection solved this problem byevolving hierarchical fractal-like branching networks, whichdistribute Energy, Information and Materials between Big Reservoirs (“Lungs”) and Small Connection Points (“Alveoli”) of other Circulatory Systems (“Blood”).

This Fractal Bottum-Up approach is highly effective and efficient.

The not-fractal, Top-Down,  machinery designed by the Humans is Scaled with a factor 1 so we can improve a lot by copying Mother Nature.

LINKS

About Goethe and Morphology

About the Heart Chakra or Why the Heart connects the Brain and the Body

How to use the Heart to find Balance

About the Heart and Ethics

Why Humans look a lot like Bacteria

About Kleibers Law and the Rain Forest

About the Five Worldviews

A movie about Fractal Structures in Nature

About the Fusion of Water in the Cell

About the Number Five in Chinese Medicine

Why Humans are part of Super Organisms

How the Humans evolved out of the Bacteria

About the Left and the Right Brain

About the Void

How the Heart synchronizes the Body

About the Fast Transmisson Channel in the Body

About Kleiber’s Law

A general model to explain Kleiber’s Law

About Kleiber’s Law and the Growth of Cities

About the Immune System

About Bacteria

About the Law of Kleiber and Ant Colonies

The terrestrial evolution of metabolism and life

A movie about the origin of vertebrates

About Entrainment

Thursday, August 26th, 2010

In 1665 the Dutch physicist Christiaan Huygens noticed that two pendulum clocks in his room tended to Swing in Sync. The same happens with fireflies, cardiac pacemaker cells,  menstrual cycles, birds in flight, walking, dancing, circadian rhythms in animals, quantum gravity theory, dialogues and people in a crowd.

Two connected Systems always Entrain because Every System in our Universe Vibrates and is connected.

birds in sync

Birds in Sync

When the Parts are  connected, the Rhythm of the Whole controls the Rhythm of the Parts.

The transformations of the seperate parts takes place in two steps. In the first step the variance of the frequencies of the parts is reduced but the oscillators remain incoherent, each running near its natural frequency, until a certain threshold is crossed. Then the oscillators begin to synchronize spontaneously. The effect is somewhat like the outbreak of synchronous applause after a magnificent concert.

To make the transformation possible the Parts have to adjust their behavior. They have to move with the Rhythm of the Flow of the Central Clock. At the end of the transformation from isolated Parts to the Whole the Parts are the Same. They are Copying each other.

When people are copying other people they lose their identity and move into a trance-state. The same effect can be accomplished with hypnosis.  When people are in a trance-state it is easy to manipulate them.

About Copying

Humans are Copiers. When we look at the Science of Coupled Oscillators it becomes clear that Copying is not an intentional act. People and other Systems are more or less forced to copy others when the frequencies of their systems are within a certain bandwith.

When people are close and are focused on a shared target (a soccer match, a concert, a conversation, a dance, a common goal) the human parts start to synchronize and become a Crowd, an entity that starts to act on its own.

About Communication

The word “communion” means “becoming a union“. All communication arises through Synchronization. All communications are dances that coordinate the rhythmic processes shared among the engaging systems.

Communication is not a transmission of information, but rather a coordination of behavior among living organisms through Mutual Structural Coupling. Just like the Crowd, a communication, starts to live a life of its own, when the exchange of the vibrations of the conversation starts to synchronize. This happens within seconds.

conversation1

In the 1960’s, William Condon of Boston University School of Medicine pioneered the empirical study of communication as coupling. In the microanalysis of a few seconds of film he was astonished to find how the voice and bodily movements of speaker and listener were coordinated within intervals as short as 20 milliseconds.

Condon introduced the term entrainment to describe the coupled behavior. He noted that: “Communication is thus like a dance, with everyone engaged in intricate and shared movements across many subtle dimensions, yet all strangely oblivious that they are doing so“.

Coupling begins with getting the attention of other organisms, or more accurately, with distracting the organisms from other engagements so they are able to discern and respond to this engagement.

When the Oscillations of two Systems are outside a certain bandwith it looks like the most powerful system takes over control. The frequency of the synchronized system is a mean and when big numbers and small numbers are added the small numbers simply disappear. This situation is called an Overload.

Overloads are able to kill small systems because the small system is unable to cope with the huge pertuberations. People with a Dominant Personality are able to force (to entrain) Dependent people to copy their behavior.

About Synchronization

A System of N coupled different oscillators creates a very complex almost unsolvable mathematical problem. In 1975 Charles Peskin formulated the conjecture  that Systems would eventually synchronize even when the parts are not identical. In 1990 the conjecture has been proven by Strogatz and Mirollo.

Systems of Coupled Oscillators show four states called Phase Locking (Synchronization), Phase Drift (“Chaos“)  and Amplitude Death (“Order“). In the last state the oscillations stop completely.  The fourth state called a Chimera is a combination of a synchronized and a drifting state.

The most important issue to notice is the fact that the state of Amplitude Death is what we call Order. It is an exceptional state that can be reached when the exchange of information between the states is “compensating” the vibrations of the states or when the System is “compressed” into a Singularity.

synchronization

Most Systems are oscillating (“Cyclic“) and are in a Phase Drift (“Chaos“) or a Chimera trying to reach some sort of Synchronicity with the other connected Systems. In Nature every System is connected to every other System because of the Electro-Magnetic (and Sound) Fields they share.

Systems of Coupled Oscillators behave differently when the connections between the parts are delayed. It this case highly identical parts start to behave as not identical parts. When a delay occurs the stable rhythm of the heart can suddenly stop, resulting in a sudden death.

About the Circadian Clock

In order to cope with and to predict 24-hour rhythms in the environment, such as light and darkness, temperature or the availability of food, most, if not all, organisms have Circadian (“Daily“) Timing Systems. These systems generate circadian rhythms in a wide range of behavioral and physiological processes.

For most animal species, a main circadian pacemaker has been identified in an anatomically defined location in or close to the brain. During the last years, however, it has become clear that circadian systems are complex and that additional oscillators exist, both within and outside the central nervous system.

The Peripheral Circadian Clocks are situated in the Heart, the Liver, the Lungs and the Kidney. These organs are the same “organs” that are used in Chinese Acupuncture which is not strange because the Aim of Acupuncture is to Balance the Electro Magnetic Field in the Body.

For a correct functioning of the circadian timing system, these oscillators should be synchronized to one another and properly phased to the environmental cycle.

Synchronization between the oscillators occurs via interactions or coupling pathways, whereas the light-dark cycle is used for synchronization to the outside world.

The most important mammalian circadian pacemaker is located in the suprachiasmatic nuclei (SCN) at the base of the hypothalamus in the brain.

From the suprachiasmatic nucleus, nerve impulses travel via the sympathetic nervous system to the pineal gland and inhibit the production of melatonin. At night, these impulses stop and melatonin production ensues and is released into the body.

In fish, amphibians, reptiles, and birds, the pineal gland appears to be directly sensitive to small amounts of light that penetrate the skin and skull.

In mammals, with increased development of the cerebral hemispheres, the pineal body came to lie deeper within the brain and indirect stimulation of the pineal gland by light via the retina came to be more important. The Suprachiasmatic Nuclei are connected to the Outer Eye and the Inner Eye, the Pineal Gland.

The Pineal Gland is called the 6th Chakra, the Third Eye (or the Eye of Horus), the Seat of the Imagination.  The Imagination, the Central Clock of our Body, is “in control” of all the other Clocks in our Body.

With the Help of our Imagination we are able to Cure and to Kill the Body.

pineal

Pineal Gland

About the Pineal Gland

The Earth is a huge magnetic sphere. The E/M field of the Earth varies in strength and consistency through the ages. Our bodies own magnetic frequencies and our bio-field patterns react to this variance of the Earth’s field.

The pineal gland is the principal structure in the brain that is directly sensitive to the Earth’s magnetic field. The Pineal Gland Senses the Field.  To sense the Field the Pineal Gland contains small calcite crystals.

Our bone structure Converts Vibrational Energy into Magnetic and Electric Energy. When the bone is bent it produces an E/M-field. This E/M-field interacts with the Pineal Gland and creates a Feed-Back Cycle.

The E/M-field of our Body, the Aura, is a combination of all kind of waves. A special type of wave-structure is called a Standing Wave.

When the E/M-field acts as a Standing Wave all the waves are in harmony and conserve structure. The Human body is in harmony when the total field of all the separate E/M-fields of the Body act as a Standing Wave.

The Standing Wave appears when the Spinal Wave of the Vertebrae of the Body is in a special Alignment.  If this happens the Standing Wave of the Spine Resonates with the Standing Wave of the Earth. At that moment the Kundalini Rises and the Pineal Gland reacts with a Huge Mystical Experience.

About the Heart

The heart beats about once a second throughout your life. These regular contractions pump blood to the Upper (Head) and the Lower part of the body and are driven by electrical impulses from a natural pacemaker inside the heart.

This pacemaker, known as the sino-atrial node, responds to signals from the Central Circadian Clock situated in the Hypothalamus that changes the heart rate according to the body’s needs (“the action potential“), making it slower when resting and faster during exercise.The rhythmic contractions of the heart are triggered by waves of electrical activity that spread from the sino-atrial node throughout the heart muscle.

There are small fluctuations in the time intervals between beats that are fractal in nature, and a loss in this variability is a sign of cardiac ill health. However, a cardiac arrhythmia, in which the rhythm of electrical waves that drive the heart is broken, can be lethal.

A loss in the synchronized rhythm of the heart causes different parts of the atrial or ventricular muscle to contract at different times, undermining the pumping action of the heart. An arrhythmia therefore leads to the mechanical failure of the heart.

The propagation of excitations in heart tissue can be described in terms of travelling waves with a velocity of about 0.5 m s-1 and an amplitude given by the action potential. Since the action potential lasts for several hundreds of milliseconds, a single wave extends over a distance of about 10 cm. This means that a normal human heart is hardly large enough to contain a single wave.

In the heart the wave propagates around a circular obstacle. The wave repeatedly travels along the same path at a frequency given by the wave velocity divided by the circumference of the obstacle.

If the radius is gradually decreased, the frequency increases until the wavefront of a new wave catches up with the tail of the previous wave. If the radius is made even smaller, the wave is forced to adopt a spiral shape that continues to rotate around a central core. Spiral  Waves have been observed in numerous chemical and physical experiments.

The Wave Structure of the Heart resembles the Wave Structure of the Universe. This could be the reason why the Heart plays such  an important role in many Religions.

When the Wave Structure of the Heart is coherent with the Wave Structure of the Whole, the Rhythm of your Life is in Sync with the Rhythm of the Universe.

The Pacemaker Cells are called the Heart Chakra, the 4th Chakra. The Heart Chakra acts as the Balance Point for all the Chakras.

The Balancing Point is the Middle of two Triangels related to  the Head and the Body that rotate With- and Counter-the-Clock creating a Moebius Ring.  The Pineal Gland, the Central Clock, is part of the Upper Triangel of the Mind.

Spiral Waves in the Heart

Chemical Spiral Waves

Chemical Spiral Waves

About Cymatics

In 1967, the late Hans Jenny, a Swiss doctor, artist, and researcher, published the book Cymatics,  The Structure and Dynamics of Waves and Vibrations. In this book Jenny showed what happens when one takes various materials like sand, spores, iron filings, water, and viscous substances, and places them on vibrating metal plates and membranes.

What then appears are shapes and motion- patterns which vary from the nearly perfectly ordered and stationary to those that are turbulently developing, organic, and constantly in motion.

When Jenny experimented with Fluids of various kinds he produced Wave motions, Spirals, and wave-like patterns in Continuous Circulation.

These patterns are the same patterns that are produced by Coupled Oscillators. This is not strange because Sound Waves are highly comparable to Electro Magnetic Waves.

With the help of simple tools it is possible to Simulate the Creation and Expansion of the Universe.

We don’t need very complicated tools to observe the Whole. The Whole shows its patterns everywhere, even in your bathtub.

The Whirpool Galaxy

The Whirpool Galaxy

About the Creation of the Universe

In beginning the Void, the Zero Point Field,  rotated in Silence until a Huge Action Potential disturbed its Eternal Rest.

The Void was in a state of Amplitude Death until a Statistical Fluctuation, an Act of Creation, moved the System into a Chimera and later a Phase Drift.

Out of the Phase Drift Two Coupled Oscillators (Yin & Yang) appeared that moved With- and Against the Clock creating a Spiral Motion, a Vortex.

The Two Coupled Oscillators were each others Complement because two Coupled Oscillators are always Complementary.

After a while the Phase Drift generated Four and More Oscillators and Space started to Expand.

The pattern of this Expansion is governed by the Metallic Mean, which generates Fluent or Quasi Crystals. Fluent Crystals are the basic structure of the Electro Magnetic System of the Human. Scientists believe that the basic structure of our Universe is a Fluent Crystal, a Hall of Mirrors.

Quasi Crystals

Quasi Crystals

Space stops expanding when the Unbalance of the Energy of the Act of Creation is compensated by the amount of Oscillators (Strings) of Expanding Space.

At that moment the Universe will move into the State of Synchronization and all the Parts will move with the Rhythm of the Central Clock, the Tao.

When this happens the Universe starts to contract until Space has reached the Void.

In the last step the Oscillation will stop and the Void and Amplitude Death will appear again.

LINKS

How bacteria entrain

Steven Strogatz: About Coupled Oscillators and Biology

A lecture about Coupled Oscillators

A presentation about Coupled Oscillators

About Engagement

About Standing Waves

About the Electro Magnetic Field in the Body

About the Cardiac Pacemaker Cells

About Cymatics

About the Heart Chakra

About Stress and the Action Potential

About the Zero Point Field

About the Metallic Mean

About the Hall of Mirrors

About Good Vibrations

Sunday, August 1st, 2010

The Good (Creation) and the not-Good, the Bad (Destruction),  are two Waves that are moving in Opposite Directions. Together they create interference patterns called Standing Waves.

Standing Waves are Waves that preserve their Form and can be perceived as Material Particles.

If the Good is a Wave Moving with the Clock, the Bad is a Wave Moving Against the Clock.

I believe the Good is moving with the Clock because the words “Right” and “Wrong” were associated with the Right Hand and the Left Hand and the concept “moving” (wringen in Dutch).

In Magic the Left Hand Path is associated with Black Magic and in many cultures the Left is associated with Evil.

In China the Rotation with the Clock is called the Generating Cycle and the Rotation Against the Clock the Destructing Cycle.

The Standing Waves of Matter contain the Bad and the Good in a certain proportion. Therefore every part of Nature (including the Humans) contains a piece of the Bad and a piece of the Good. That’ s why it is rather difficult to make a distinction between both of them.

There is nothing either good or bad, but thinking makes it so“  (Hamlet Act 2, scene 2, 239–251)

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A Moving Standing Wave

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Two Moving Standing Waves Interfere and produce a Magnetic Field

About the Svara

The idea that our Universe is a Wave goes back a very long time. In Ancient Indian Philosophy the Wave of the Universe was called the Svara, the Wave of Life.

It is the manifestation of the impression on matter of the Power Which Knows Itself (Atman). The Atman arises out of the Emptyness (Brahman). The Emptyness is a Mystery. It is impossible to Reason about it.

The Svara consists of Five Types of Waves called Tattvas. They represent distinctive Forms and Vibratory Motions and are the five modifications of the Great Breath, Prana, of  the Atman. Prana is called Chi in China.

The first Wave that came out of the Atman is called the Âkâsha (Spirit, Egg, Black). After this came  the Vâyu (Air, the Circle, Blue), the Tejas (Fire, the Triangle, Red), the Apas (Water, the Crescent of the Moon, Silver) and the Prithivi (Earth, the Square, Yellow).

The Svara has two different States,  the Bright Sun-Breath  and the Dark Moon-Breath. In the first state the Svara expands, away from the Void. In the second state it contracts and moves back to the beginning.
At a certain moment we will experience the spectacular Twist of the Svara. This is the moment when Time will move back and the Apas (Aquarius, Water) will dominate the Fire (Bull) of the Tejas.
The Âkâsha and the other Four States of the Svara are the States of what Western Scientists call the Aether, the Carrier of the Standing Waves of the Universe.
The Five Tattvas

The Five Tattvas

About the Aether

Until the experiments of Michelson and Morley in 1887 every Physicist believed in the existence of the Aether. Everybody was very surprised when the experiments showed that the Aether was moving with a constant speed, the Speed of Light, in both directions of measurement.

Nobody questioned the experiments so a completely new theory had to be created to explain the strange behavior of Light. This new theory was the Relativity Theory of Albert Einstein.

The situation became even stranger when Niels Bohr (and others) invented Quantum Mechanics and showed that Light could be interpreted as a particle, a Photon, and a Wave.

At that time almost nobody understood the Concept of the Standing Wave. A Standing Wave is a Wave that preserves its Form and therefore shows itself as a Particle.

It is now proved that Michelson and Morley made a fatal mistake. The Unification of the Theories of Einstein and Bohr is going on but two foundations of the Theory of Einstein, the non-existence of the Aether and the Constant speed of Light, are gone.

The concept of the Aether, the Svara,  is back and new theories of the Universe based on Standing Waves are produced and verified. These theories are much simpler than the old theories.

What is the Same?

The Ethical Law of Resonance states that ”The Same attracts the Same and Repels the Not-the Same“.  The Good  attracts the Good and the Bad attacts the Bad but the Good also repels the Bad and the Bad repels the Good.  If we are able to define the Same we are able to define the Good and the Bad.

When you want to find out if some Thing is the same as another Thing you have to define the concept of “the-sameness“.

Every thing is different from any other thing when you collect enough different data about both of them. When you ignore every detail every thing  is the same (A = A). When two objects are literally “the same” we call this relationship an equality (A=B).

The same objects can appear differently when we Look at them differently. In this case a “the sameness” (now called a congruency) appears when we are able to create the same object when we move (translate), rotate or reflect the other object.

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Two Congruent Triangels

To find an independent reference framework for an Observer who is “not moving” and a constant Speed of Light Einstein had to abstract from Translation, Rotation, Reflection and Movement (Speed and Acceleration). Einstein’s friend Minkowski solved his problem by creating a new type of “curved” space now called Minkowski Space.

The Ancient Scientists of India not only abstracted the Aether from the Eyes like Einstein did. They abstracted the Aether from the other Four Senses too.

Every Tattva represents another Sense Organ and a related Wave pattern. The interesting point is that the Waves of the Tattva of the Eyes, the Light Waves, the Tejas, behave, exactly the way the current scientists describe.

The current Scientists ignore the fact that Humans observe their Environment with their Five Senses. The ancient Scientists not only detected five types of Waves. They also found a way to combine the Five Wave-Types into one Wave Model.

In general Objects are “the same” when we are able to find a Structure Preserving, isomorphic, transformation (F) from Object A to Object B. F(A)=B and G(B)= A and FG=Identity. With the help of an Isomorphic Transformation you are able to map a structure A to another structure B  and move back to the same structure A.

Every Isomorphic transformation can be seen as a “specialized Organ“, that  ”looks” at Reality in its own way.

The mathematical field of Topology is concerned with the “the sameness” of objects that are Expanded and Compressed. Topology represents the Organ of the Emotions. With this organ we are able to  research the effects of the Great Breath of the Prana.

Mug_and_Torus_morph

Transforming a Mug into a Torus

About the Great Breath

With the help of isomorphic  “topological” transformations it is possible to make the huge Diversity of Forms in our Universe the Same. It is even possible to compress every structure in our Universe into one structure, the structure of the Void.

In this case there are a few topological possibilities depending on the dimensions of space. In two dimensions we can choose out of the Point and the Circle, a Closed Line. In higher dimensions strange twisted structures appear such as the Moebius Ring and the Klein Bottle.

If the Universe is compressed into a Rotating Circle,  The One who is in the Centre always Returns on Itself.  The Universe is expanding and compressing until Eternity. At a certain time even after a huge expansion the Power of Creation is able to “Knows Itself”. This concept is called the Cyclic Universe.

If the Universe is compressed  into a point, called a singularity, we live in a “Big Bang-universe“, the standard cosmological model, which will expand into Eternity.

It will be clear that the structure in the beginning determinates the way the Waves of the Universe expand.

Twisted Topological Structures

Twisted Topological Structures that are Closed in Itself

If the Universe is Closed in Itself the Outbound Waves of the Beginning  will meet the Inbound Waves of the Utmost Boundary and will create Interference Patterns that look like Standing Waves.

When the Universe was small the Interference Patterns came up almost immediately. When the Universe expanded it took more time to Close the Loop.

If the Universe is a Closed System, the Waves of the Past and the Waves of the Future will meet in the Now.  At every moment in Time we are able to look into a possible Future and a possible Past.

At every moment in Time we can Change the Past and the Future if we are able to start a Powerful Negative (Destructive, Bad) or Positive  (Creative, Good) Wave of our Own.

According to the Ancient Scientists the Forces of the Tattvas at a certain Level of Enfolding represented Consciouss Beings (Angels, Devils) who could be Called to help to influence the Standing Waves of Matter.

In the strange terminology of Quantum Mechanics this state is called a Quantum Superposition and the union of the waves is called Quantum Entanglement. Quantum Entanglement moves with a speed much higher than the Speed of Light.

Sometimes the fragmented Tones of the Universe unite into one Symphony when the Strings of the many Violins of the Individual Standing Waves are in Tune.

We are able to change the Past and the Future when we are in Tune with the Waves of the Universe.

About the  Number Five

The symbol of the number Zero (“0″) looks like an Egg, the Âkâsha. The Âkâsha represents Space.

The name “zero” comes from the Arabic صفر, şafira, “it was empty” and the Sanskrit śūnya “void” or “empty”. The 0, Space, was Empty, Ø, before it was created.

According to many creation myths the beginning of this world,  Non-Being, Ø, the Empty Set, expanded into an Egg, 0.

The Egg started to Rotate (Air, Vayu, Movement) and was splitted into the Duality (-1,1), the Crescent of the Moon (Apas), the In-Between-Moon or Half Moon (1/2).

The negative part of the Duality started to move in the Opposite Direction. At that moment the Good (Creation) and the Bad (Destruction) were created.

The Apas are the force of Contraction (Control), the Opposite of the Tejas, Fire (Desire), the Force of Expansion. The Apas wants to bring the System back to the Void.

In the Beginning the Good (Fire) was much stronger than the Bad (Water). Therefore the Universe started to Expand.

The Trinity, the Triangel (Tejas, Fire), contains three numbers (-1, 0, +1). When the first Trinity was created the Force of Fire and Desire, the Tejas, started to Expand the Trinity into more Trinities. The production of Trinities in Trinities is a Fractal Pattern (“So Above, So Below“).

The first two Triangels, the Triangel of the Trinity of the Mind of the Atman and the Trinity of the Material World, are combined into a Square (Prithivi, Earth). The Prithivi are seen as the Force of Resistance, the Opposite of Âkâsha, Space.

The Prithivi, the Square of the Four Forces, the Human,  resists the movement back to the Void. The main reason is that the connection between the Spiritual World and the Material World is very strong.

The Spirit of the Human, situated in the Heart Chakra,  needs Matter to create all the possible combinations of the Becoming Trinities to Experience the Fullness of Being.

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

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

The number Five can be found in the Middle of the oldest Magical Square on Earth, the Lo Shu Square. The Lo Shu Square was given to Emperor Yu the Great after the Great Flood (3117 BC) by a Turtle, the symbol of the Star System Orion.

About the Magic Square of Lo Shu

The Lo Shu Magic Square contains the numbers 1-9 (3×3). In every direction they add up to a total of 15 (3×5).

The Magic Square Constraints the Expansion of the Force of Fire and makes it possible that the Cycle moves back to the zero, the Void, the Mystery.

The Lo Shu Square in the Middle of the Mystic Tablet from Tibet

The Lo Shu Square in the Middle of the Mystic Tablet from Tibet

-1 4 -3
-2 0 2
3 -4 1

When we subtract all the numbers in the Magic Square with the number 5,  the Zero of the Egg of the Âkâsha appears in the Middle.

The transformed Magic Square shows an interesting symmetry.

On the six “crosses” the same negative and positive Tattvas are found. The Four Tattvas are Balanced in the o, Space, the Âkâsha.

On the straight lines  two symmetric patterns emerge ((-1,4,-3) and (1,2,-3)) again both positive and negative. In these patterns the 4 balances the 1 and the 3 and the 2 balances the 3 and the 1.

When we follow the Numbers of the Square from -4 to +4, the Sheng Cycle appears.

About the Sheng Cycle

The Sheng Cycle not only contains the Cycle of the Five Tattvas. It also contains Five Triangels in which One Tattvas Balances Two other Tatvass.

The number Five is the same as the Number Zero when we accept that there are Two Structures (or Two Universes). One structure rotates in the Positive Domain, The Sun, and one in the Negative Domain, The Moon.

The Square represents the Four Force of Nature who are the Four Combinations of the Two Forces of the Duality, Compression and Expansion, Yin and Yang, the Apas and the Tejas, Fire and Water, Control and Desire.

The Sheng Cycle is the major Cycle in Chinese Philosophy. It was used to explain and control the many levels of existence (State, Family, Environment, Body,..).

The Sheng Cycle moves in two directions, With the Clock (Generating, +1) and Against the Clock (Destructing, -1).

When we combine the two Cycles a 9(3×3)-fold Twisted Moebius Ring is created with the Earth in the Middle. This Cycle is represented by the Symbol of Infinity (). This Cycle is comparable to the Tree of Life, the Jewish Sephiroth and the Ancient Egyptian Pesedjet (the Nine).

In the Bright (positive) Part of the Moebius Ring we are in the Sun-State, Life. In the Dark (negative) Part we experience the Moon-State , Death, the Underworld (Our Twin Universe), the place where the Souls exist when they Die.

Now it becomes very clear what the Ancient Indian Scientist meant with the Dark Moon-State of the Svara. When the Wave of Life moves back to the Center, the Void, Death will become Life  (“the Death will be raised“), Time will Reverse, the Universe will Compress and the Good will become the Bad.

The Sheng Cycle

The Sheng Cycle

About Harmonics

In 1931 the US Department of Commerce assigned Edward Dewey the task of discovering the cause and underlying dynamics of the Great Depression. The US Government created a special institute the Foundation for the Study of Economic Cycles. The Institute contains a huge database of the times-series of almost every Cycle there is.

The most interesting observation of Edward Dewey is that Cycles restore themselves all the time and are influenced by other Cycles. The Cycles Resonate.

Ray Tomes, a statistical mathematician, started to do research on the time-series of the Institute. He confirmed the Insights of Dewey but with the much more powerful tools of his time he was able to dig a lot more deeper into data.

Tomes detected a relationship between the Cycles and Music, the Âkâsha. Tomes also developed a  method to find the basic structure behind the Waves of the many Cycles.

Tomes found one Basic Standing Wave that generates other waves by producing Overtones. Tomes rediscovered the Svara and could also explain why the “numbers” behind the Svara are the way they are.

The explanation can be found in the so called Highly Composite Numbers (HCN). The HCN are “social” numbers with many divisors. They represent the major “harmonic” connectors in the Universe. The HCN are the opposite of the “lonely” Prime Numbers who only contain themselves.

The structure behind the HCN is self-referencial and is based on the numbers 2, 3 and 5.

About the Cyclic Universe of Paul Steinhardt

The Cyclic Univere of Paul J. Steinhardt

The Cyclic Universe of Paul J. Steinhardt

Paul Steinhardt has created a new theory about the Universe based on the Four Forces of the Square and the Void in the Center. In his theory the Universe is Cyclic. It is expanding and contracting.

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

The two Branes are higher dimensional flat surfaces that are in parallel. The Left and the Right Brains split into many similar Cell-like Structures. We live in one of the Cells of the Cyclic Universe.

When the Universe expands the constraints of the Flat Surface (the Lo Shu Square) create a huge tension and the flat surfaces start to Ripple. The Ripples are waves that are closed in themselves (loops).

When you use your imagination you can see that the Cyclic Universe of Paul Steinhardt has a lot in common with the ancient theories of India and China with only one difference.

In the Ancient theories the creator of the Universe was “Aware of Itself” in the new theories Awareness is a Feed-Back-Loop, a Cycle.

About Ancient Spirituality and Modern Science

This blog started with the Ancient Spiritual Indian Concept of the Svara , the Wave of Life. It ends with the Modern Material Cyclical Universe of Paul Steinhardt.

In between I have tried to show that the old theories of the Self-Aware Universe and the new theories of the Endless Feed-Back Loops in Our Universe have a lot in common.

The Ancient Spiritual Scientists developed a Theory of Everything based on the principle of the Fractal Universe (“So Above, So Below“).

If the Universe is a Fractal Structure,  the only thing the Modern Sciences have to do is to find the Right Level of Observation (Cells, Body, Family/Group, Culture, State, Earth, ..) of the Fractal Expansion of our Universe and the Same Laws will appear again and again.

The Levels in our Universe

The Levels in our Universe (Calculated by Ray Tomes)

About the Good, the Bad and the Nothing

If the Good and the Bad are Standing Waves that move With the Clock and Against the Clock it will be much more easier to determine what is Right and what is Wrong (Left).

With the Clock moves With the Flow. It generates new structures until the Limits of the Universe are reached.

Against the Clock moves Against the Flow. It destructs new structures until the Limits of the Universe are reached.

The Bad wants to Control Everything. It Fears the Good and the Future.

The Bad does not (want to )understand that The Good and the Bad are moving to the same Destination, The Nothing.

The Good gives us Joy, Pleasure and Exitement.

The Bad moves Back in Time. It wants to restore what was already there. Its final aim is the Zero, Empty Space.

The Good moves Forwards in Time. It creates new Perspectives about a Bright New Future. Its final aim is Every Thing, the Many, Infinite Space filled with an Infinite Amount of Forms.

The Bad and the Good move Back and Forth around an Unknowable Center, the Nothing, that makes Every Thing possible.

Some day the One and the Infinite, will merge, into the Impossible. When this happens the Nothing will return for a very short  (1/∞) moment.

LINKS

About the Law of Resonance

About the History of the Laws of Nature (The Website of Milo Wolff. It contains everything you want to know about the history of the concept of the Standing Wave).

Why Matter is a Standing Wave

About the Svara (This Website  contains a (big) Complete Book written in 1894 about the Ancient Theory of the Svara.  A Must Read, when you want to understand Ancient Physics).

About the Harmonic Theory of Ray Tomes

About the Experiments of Michelson and Morley

Why God is a Topologist

About Pauli and Quantum Mechanics

About the Cyclic Universe

About the Lo Shu Square

About the Trinity

About Infinity

About the Empty Set