Posts Tagged ‘unity’

Over de Paradoxen van het Leven (in Dutch)

Tuesday, August 14th, 2012

Op  heb ik een verhaal verteld over Path of Change in het Dialoques House van ABN AMRO in Amsterdam ZO.

Hierbij de plaatjes van de presentatie. Als er vragen zijn stel ze gerust via het contact-formulier.

Paths of Change gaat over veranderen en is ontwikkeld door Will McWhinney.

Recent is er een boek “Faciliteren als tweede beroep” verschenen van Jan Lelie dat een eigen interpretatie van Paths of Change bevat. Mensen die meer over Paths of Change willen weten wordt aangeraden in ieder geval dit boek te lezen.

Het Egyptische Spel Mehen

Jan Lelie heeft Paths of Change (POC) toegepast op Faciliteren terwijl ik het vooral heb gebruikt bij het Ontwerpen van Systemen.

POC kan op alle terreinen worden toegepast die je maar kunt bedenken omdat het een Meta-Praxis is, een Theorie over de Praktijk van het Veranderen.

THEORIE

POC gaat er vanuit dat mensen een eigen onafhankelijke perspectief op de wereld hebben en dat het mogelijk is om die verschillende kijken te classificeren met behulp van vier zogenaamde wereldbeelden (“Worldview”). Veranderingen gaan altijd samen met veranderingen van wereldbeeld.

De oneindige varieteit aan menselijke kijken kan worden afgeleid door het toepassen van de wereldbeelden op zichzelf. Ieder mens leeft in zijn eigen universum maar er bestaat een fractaal patroon waardoor ze elkaar kunnen begrijpen.

Het patroon kan worden gevonden  door de regelmaat in de regelmaat (in de regelmaat…) te onderzoeken. Wat dan blijkt is dat die regelmaat een zelf-referentie is. Hetzelfde patroon blijft zich herhalen.

Veranderingen zijn Cyclisch en Fractaal. Dezelfde veranderingen komen altijd weer terug op iedere Schaal die er bestaat. Ze springen in de tijd van Schaal (bijv. Mens) naar Schaal (Organisatie) en zelfs de Schaalsprongen zijn weer onderdeel van een Cyclus.

Het is zoals de Sufi’s zeggen: Alles draait om Alles.

Alles draait om Alles

Alles draait om Alles

Hierdoor is Alles uiteindelijk in zichzelf gesloten en roteert rondom het centrum van het centrum (van het centrum…..), de Leegte.

De “mystieke” leegte heeft exact dezelfde eigenschappen als de wiskundige leegte die de lege verzameling wordt genoemd. Dat is niet zo raar als het klinkt als je beseft dat wat de Christenen in het Evangelie van Johannes de Logos noemen (“In den beginne was het Woord (Logos)”) dezelfde principes vertegenwoordigd als wat wij nu de Logica noemen.

De lege verzameling die de Leegte wordt genoemd staat voor alles wat nu nog onmogelijk is. In China wordt ze de Tao genoemd.

Alles is niet-Niets

Alles is niet Niets

De schepping, Alles wat  Is, is de ont-kenning van de Leegte. Die negatie ging gepaard met een enorme explosie in de vorm van een Dirac Delta-puls waardoor het Alles tot op heden permanent aan het expanderen is volgens de regel Space/Time, waarbij de tijd de inverse is van de ruimte. Alles spiraleert rondom het onmogelijke, het Niets. Als we alle schillen van de ui hebben afgenomen blijft er niets over.

Nothing is an opportunity to imagine something. Absolute nothing is the most powerful opportunity of all to imagine anything at all. Because there is really absolutely nothing, the contrast with even a flickering thought of something is enough to make that something seem real! (Law of Forms, Spencer Brown).

The Spiraling Spiral in Chartres Cathedral

De Spiralerende Spiraal in de Kathedraal van Chartres

Het betekent ook dat er altijd sprake is van een paradox, een onlogische situatie, die we steeds maar weer proberen op te lossen maar in zijn wezen onoplosbaar is.

Will McWhinney’s meest wijze woorden zijn dan ook “Our task is not to resolve the paradoxes, but to manage them”. Het heeft geen zin om de uiteindelijke logica achter de werkelijkheid te zoeken want die bestaat niet.

Decentralisatie roept Centralisatie op en een streven naar Menselijkheid tendeert uiteindelijk in On-Menselijkheid. De enige manier is om van alles het midden te vinden en van daar uit te gaan balanceren net als een koordanser. Vandaar de andere favoriete uitspraak van Will “There is only the Dance” (van Shiva).

Veranderingen lopen vast als het pad van de cyclus tegen het pad van een andere cyclus opbotst. Die botsing kan worden vermeden of het conflict kan worden opgelost door een Derde Wereldbeeld te introduceren (een By-Pass) of door een extra dimensie (een “bewustzijn of observator”) te introduceren waardoor ze boven (of onder) elkaar kunnen bewegen.

De vier wereldbeelden zijn inzichtelijk gemaakt in het Book of Kells

De wereldbeelden worden door Will McWhinney Unity, Sensory, Social en Mythic genoemd en zijn te vergelijken met de vier Archetypen van Jung die je kunt terugvinden in de persoonlijkheidstest MBTI. In deze test worden ze T(hinking, Unity), S(ensing, Sensory), F(eeling, Social) en I(ntuiting, Mythic) genoemd.

In MBTI worden er naast de 2-combinaties van STN & F ook nog Introvert & Extravert (I/E) en Perceiving/Judging (P/J) onderscheiden.

Introvert & Extravert slaan in het model van Will op de draairichting van de combinatie. Introvert is Naar-Binnen-Gericht (Van Sensory -> Unity -> Mythic -> Social -> Sensory) en Extravert is Naar-Buiten-Gericht (Sensory->Social->Mythic->Unity->Sensory).

P betekent Boven-het-Model (= de Observator/Bewustzijn/Abstractie/Monitor) en J is In-het-Model. Dit betekent dat er eigenlijk nog een Vijfde Wereldbeeld is maar het beeld bestaat buiten het 2-D-vlak van de vier anderen in de 3De dimensie.

Als je het projecteert in het 2D-vlak komt het in het midden uit op het Kruis-punt van de twee lijnen die de vier verbindt. In die zin staat het Kruis voor Centrum, Balans, Evenwicht en Bewustzijn.

Het grote verschil met de andere beelden is dat het net als het Oog van de Storm stil staat terwijl de rest van de paden ronddraaien. Mensen die problemen hebben met dit Wereldbeeld zijn onevenwichtig.

De Vijf Organen van de Acupunctuur passen perfect op de Vier Wereldbeelden. Het vijfde orgaan staat voor de relatie Geheel/Deel (Earth).

De wereldbeelden zijn ook te verbinden met Het Denken in Modellen (Unity, Waar-maken), het Sensory-Motor Systeem (Handelen en Waar-nemen, Sensory), de Emoties (Social, Waar-deren) en de Verbeelding (Mythic, Waar-om?).

Daarnaast kun je de wereldbeelden ook afbeelden naar IT-technologie (Smart Computing). In dat geval heeft Sensory te maken met Sensors & Proces-management, Unity met Analytics en natuurlijk Big Data, Mythic met User-Inter-Face & Action waarbij nu bijv. Augmented Reality en natuurlijk Games een grote rol spelen en Social met zoals de naam het al zegt Social Networks.

Die Sociale Netwerken kun je weer verdelen in vier onderdelen n.l. de Sociale Sociale netwerken (Friends & Family), de sociale netwerken die de interesse bevredigen (Mytisch Sociale Netwerken), de sociale netwerken waar je ervaring deelt (Sensory Sociale Netwerken, Community of Practice) en de Kenniscentra (Unity Sociale Networken). Hier zie je de “fractale” kracht van POC.

The map is not the territory.

Het is van groot belang om te beseffen dat het Model, de Waar-heid van POC  thuis hoort in de Unity-Mode, POC in de Praktijk van de Sensory-Mode kan worden toegepast, gewaardeerd wordt in de Social-Mode en In-zicht geeft in de Mythic-mode.

De ver-woording (= Unity) van POC die je nu leest is een voorbeeld van de Unity-Mode en niet van de andere Modes. Die andere Modes zul je zelf vorm moeten geven omdat je nu eenmaal een uniek (Mythic), bewegend (Social), waarnemend (Sensory) en naar autonomie (Unity) strevend mens bent.

Je bent geen wandelend verhaal maar een fysiek lichaam, je emoties zijn geen woorden maar die voel je en wat je ziet wordt door je verbeelding in beelden omgezet. De buitenwereld is geen plaatje dat je bekijkt maar iets waar je met je fysieke lichaam aan deelneemt.

Vindt je eigen beperkingen:

Door een MBTI test te doen (druk hier) kun je een indruk krijgen van je eigen perceptie van de  wereldbeelden die je hanteert (Let op: “die perceptie kan niet kloppen!”) en wat veel belangrijker is welke wereldbeelden je niet kunt zien (voelen, meten, vaststellen). Die vormen je zwakke plek of bias. Geloof je niet in een Bias dan maak je in ieder geval niet gebruik van het Mythische wereldbeeld omdat je daar “gelooft” (en het dus niet zeker weet). Zeker weten doe je als je Unity bent.

Als je dit verhaal tot op heden niet practisch vindt en voorbeelden mist dan ben je in ieder geval Sensory. Als je plaatjes mist en diagrammen en snel overzicht wilt hebben ben je Mythic en als je graag wilt weten wie POC ook gebruikt en aanbeveelt ben je Social.

OMDAT MENSEN VERSCHILLEN HEBBEN ZE ANDEREN NODIG OM HET GEHEEL TE KENNEN.

Als je de wereld als een geheel wilt zien, ervaren, waarnemen of waarderen zul je andere mensen moeten zoeken die beschikken over een complementaire kijk  en via de gedeelde wereldbeelden moeten gaan communiceren. Hierbij moet je beseffen dat je die anderen volledig zult moeten vertrouwen in de kijk die jij niet hebt.

De meeste mensen kunnen twee wereldbeelden hanteren en eenvoudig tussen die wereldbeelden switchen zonder dat ze dat merken.

Als je maar 1 wereldbeeld aankunt ben je volgens de Psychiatrie geestelijk in de war. Mensen die uitsluitend het Wereldbeeld Unity gebruiken zijn Paranoide en een unieke orientatie op Mythic wordt Histrionisch genoemd. In dat laatste geval speel je permanent een (toneel)spel en geloof je je eigen leugens omdat je volledig in je eigen fantasie leeft.

De trickster gelooft in zijn eigen leugens

De trickster gelooft in zijn eigen leugens

in POC worden de vier wereldbeelden gecombineerd in 6 2-combinaties, 4 3-combinaties en 1 vier-combinatie die allemaal ook nog een keer met de klok of tegen de klok kunnen ronddraaien. In dit opzicht kunnen ze allemaal worden gezien als een cyclus.

De zes 2-combinaties kun je Ontwerpen/Inspireren, Analyseren/Toetsen, Evalueren/Alloceren, Brainstormen/Faciliteren, Beinvloeden/Meningvormen en Uitvinden/Ondernemen noemen. Will McWhinney noemt ze Spellen (“Games”). De combinatie Social/Sensory noemt hij bijvoorbeeld het Spel van de Markt.

Het bijzondere van POC is dat de vier wereldbeelden met het bewustzijn in het midden afzonderlijk weer kunnen worden verdeeld in vier delen met behulp van dezelfde wereldbeelden waardoor er in eerste instantie 16 mogelijkheden ontstaan waarvan er 12 verschillend zijn en vier weer gelijk zijn aan de oorspronkelijke wereldbeelden. UnityXUnity is nu eenmaal gelijk aan Unity.

PATH OF CHANGE KAN OP ZICHZELF WORDEN TOEGEPAST

Het toepassen van POC op zichzelf laat zien dat POC fractaal (zelf-referend) is. De zelf-referentie kan eindeloos worden voortgezet met als enige kanttekening dat het bepaald ogenblik erg moeilijk wordt om de combinaties te benoemen.

De expansie naar 2**8=64 is een heel bijzondere en wordt toegepast in de I Tjing. Daarnaast zie je hem ook terug in spellen zoals het Schaakspel.

Na de 64 herhaalt alles zich en die herhaling kun je zien in het getal 8 dat een eigenlijk een Moebius-ring voorstelt. 8 = 2×4 en door het koppelen van twee ronddraaiende 4-hoeken op 1 punt (het Hart) komen we op de bekende 3-1-3 (=7) structuur die zich toont in de Zeven Chakra’s.

De Moebius Ring, het getal 8, toont zich in de Panarchy Theorie.

In wiskundig oogpunt heeft POC erg veel verband met de z.g. Driehoek van Pascal, die heel lang geleden de berg Meru werd genoemd.

De basis-fractal van POC is niet 2×2 maar tweevoudig of beter gezegd drie-voudig omdat het onmogelijk is om een verdeling te maken zonder de deling (“het onderscheid”) zelf ook mee te nemen ook al is het eerste onderscheid  ”geen onderscheid”.

DE ESSENTIE VAN PATH OF CHANGE IS MEER-DIMENSIONAAL ADEMEN.

De eerste Trinity  (Yin/Yang + Midden) kan op vele manieren worden weergegeven. Ik prefereer de Uitgaande (“Expansie”, Extravert) en de Ingaande (“compressie”, Introvert) Beweging die in combinatie het “ademen” van de werkelijkheid simuleert. De derde (“het Midden”, Rust, de Leegte) is het moment waarop de uitgaande beweging weer omdraait in een ingaande beweging.

In zijn wezen is ieder mens een unieke fractale expansie van Path of Change dus van het Ademende Heelal.

Er zijn aanwijzingen dat we op dit moment in de 42e expansie zitten. De expansies vinden ook weer volgens een regelmaat plaats. Die regelmaat wordt  beschreven door de Bronze Mean.

De Bronze Mean komt voort uit een abstractie van de Gulden Snede ook wel de reeks van Fibonacci genoemd. Het bijzondere is dat de generator van de Bronze Mean wordt gestuurd door de Trinity.

De berg Meru

HET LEVEN IS EEN SPEL

Volgens Will McWhinney spelen mensen met elkaar een spel waarbij ze soms gevangen zitten in een gezamenlijke cyclus zoals de “drama triangle“.

Het meest intigrerende spel is een combinatie van Mythic & Social (“Het waarderen van ideeen”) (Brainstorm, Explosie), (“het collectieve onderbewustzijn activeren”) (Scheppen, Implosie)). Dit is het spel dat spellen maakt, het spel dat kinderen spelen, het spel van de magier en de  trickster en het oneindige spel (“the infinite game“) omdat het niet wordt gespeeld om te winnen maar omdat het voortgaan van het spelen op zich het mooiste is wat de mens, als mede-schepper kan doen.

Een hele bekende 2-cyclus is de wetenschapscyclus waarbij theorien (Unity) worden getoetst aan de werkelijkheid (Sensory) en andersom.

Door de enorme waarde (= Social) die er in onze tijd aan wetenschap (=objectief) wordt toegekend lopen we het risico dat de weg terug (het aanpassen van de theorie aan de praktijk) niet plaatsvindt waardoor onze werkelijkheid een theoretische constructie wordt (een norm, regel) waar we ons aan te houden hebben.

Een veranderingspad werkt als er geen sprake is van een conflict van de wereldbeelden. Een conflict ontstaat als twee paden verschillende kanten oplopen en daardoor botsen.

Een voorbeeld is het boven beschreven conflict tussen praktijk en theorie maar het kan nog vervelender worden als de andere wereldbeelden (Social = Emoties en Mythic = Verbeelding) ook worden gedomineerd door het Unity-wereldbeeld.

Hierdoor worden Emoties vervormd tot Emotionele Intelligentie en wordt de Verbeelding gediskwalificeerd als een Illusie of Fantasie.

TOEPASSING

In de presentatie toon ik een klein aantal van de enorme hoeveelheid toepassingen van POC.

Het eerste deel, de Logica van de Schepping, laat zien dat de vier wereldbeelden eigenlijk bestaan uit een combinatie van slechts twee beelden (Expansie & Compressie) die de lege verzameling gemeen hebben.

Het ene beeld is een negatie (ont-kenning) van het andere beeld. Ze worden in de praktijk aangeduid met bijv. Yang en Yin, mannelijk en niet-mannelijk (=vrouwelijk), orde en niet-orde (chaos), licht en niet-licht (donker), koud en niet-koud (warm) etc etc.

De twee andere wereldbeelden zijn combinaties van de Yin en de Yang via EN (Mythic, Yin EN Yang) en OF (Social, Yin OF Yang).

Met behulp van  de twee-heid “Naar buiten gaan” (Extravert, Expansie) en “Naar binnen gaan” (Introvert, Compressie) en de logische operatoren EN en OF kun je eindeloos veel 2-combinaties maken waarvan het aantal een macht van twee is.

Een mooi voorbeeld van een betekenisvolle binaire combinatiereeks is de I Tjing die 64 (2**8) combinatie bevat. Het getal 64 is een heel bijzonder getal omdat na de 64 de cyclus zich weer herhaalt. Het symbool van het getal 8 is niet voor niets de Moebius Ring.

De Cyclus van 2-machten ook wel de Bron genoemd.

In de I Tjing zijn alle combinaties voorzien van een symbool en een kort verhaaltje dat de betekenis van dit symbool uitlegt. Duidelijk zal zijn dat men hierbij gebruik heeft gemaakt van de uitingen van het combinatie-spel in de Natuur en de Mens.

In het Mythic wereldbeeld dat wordt verbonden met Ideeen, Scheppen en het Verbeelden worden twee tegenstellingen (Appel en Niet-Appel, Goed en niet-Goed = Kwaad)  opgeheven door naar een hoger niveau van abstractie (Fruit, Ethiek) te springen. Die fusie geeft erg veel energie net als de combinatie van materie en anti-materie.

Mensen met een Social Wereldbeeld moeten steeds een keuze maken tussen de twee tegenstellingen omdat ze anderen te-vreden willen houden. Ze durven het conflict niet aan dat voortvloeit uit de contraverse tussen de twee tegendelen (bv Orde & Chaos).

Een waarde is een karakteristieke manier waarop mensen een keuze maken. Omdat POC fractaal (zelf-refererend) is bestaan er weer vier verschillende manieren om een keuze te maken, waarbij de vierde manier een combinatie van hetzelfde (hier Social/Social) is.  In dat laatste geval kiezen mensen door weer nieuwe keuzes te gaan formuleren.

Doordat mensen een keuze maken (en hun opties niet open houden) wordt de wereld die ze beschouwen steeds kleiner (gefragmenteerd, gespecialiseerd). Als de twee-deling overlapt (wat meestal het geval is) wordt de wereld ook steeds vager en conflicteuzer omdat mensen een claim gaan leggen op elkaars gebied. Ze zijn niet instaat om het conflict op te lossen omdat alles met alles lijkt samen te hangen. Er zijn geen duidelijke grenzen meer.

Het tweede deel gaat over de vier wereldbeelden in samenhang met het weer-systeem. Hier wordt ook de vier-combinatie-cyclus zichtbaar. Hier zie je dat Social en Mythic nodig zijn om de voortgaande expansie en/of  compressie een halt toe te roepen zodat het geheel niet weer opgaat in de Leegte die het Niet-Al is. Hierdoor ontstaat de Levensgolf (de Svara).

gravity waves

gravity waves

Het derde deel “Het Rad van Avontuur” genoemd, behandelt oude vormen van Path of Change (Indianen (Medicine Wheel), China(Sheng-Cyclus, Lo Shu) en het Buddhisme). Die staan allemaal uitgebreid beschreven in dit document.

Deel vier gaat over Interpersonal Theory, waarna wordt getoond dat de twee gekoppelde vier-combinatie-cycli overeenstemmen met het aloude concept van de chakra en dat het symbool van het Hart-Chakra (twee gekoppelde driehoeken) hetzelfde toont.

Het laatste plaatje in dit onderdeel gaat over de Egyptische Godin (= concept) Ma’at, die ook de bestuurder was van de toegang tot het dodenrijk (het pad van reincarnatie, het rad van avontuur). Het Egyptische concept Ma’at laat zien dat je uit het Rad van Avontuur kunt stappen als je de twee driehoeken van de Geest en het Lichaam in evenwicht brengt in het Hart dat dan zo licht weegt als de Veer van Ma’at. Ma’at werd door de Grieken Sophia (Wijsheid) genoemd.

In deel vijf worden een aantal toepassingen van POC getoond in het bedrijfsleven en het laatste deel gaat over de relatie tussen POC en tijd. Dit laatste deel staat ook hier beschreven.

In het deel over het bedrijfsleven toont POC dat de bedrijfskundigen vergeten zijn om het pad rond te laten lopen in een bedrijf waardoor er geen sprake is van feed-back. De beroemde waardeketen van Porter is eigenlijk een waardencyclus en ketenomkering is niets anders dan consumeren en consumeren is niets anders dan de omgekeerde rotatie van produceren.

Produceren is een vorm van Compressie (Versimpelen van de Praktijk) en Consumeren een vorm van Expansie die elkaar eigenlijk zouden moeten opheffen.

In dit laatste geval zijn we vergeten om de rechtsdraaiende cyclus van de productie te koppelen met de linksdraaiende cyclus van de consumptie waardoor het opheffen van de productie door de consumptie niet meer evenwichtig plaatsvindt. Productie en consumptie zijn een prachtig voorbeeld van boven beschreven complementaire wereldbeelden die samen de Leegte vormen.

LINKS

Over de wiskunde van het bewustzijn

Over de theorie van de Cycli

Over de vier wereldbeelden

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.

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.

.

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).

The Projective Plane is a Projection of a Sphere

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.

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 Darwin’s Superorganism

Saturday, May 8th, 2010
Charles Darwin

Charles Darwin

Many people believe that the theory of Evolution is based on the concept of competition. They believe that every gene, every cell, and every organism is designed to promote its own evolutionary success at the expense of others.

The big problem with this concept is that it does not explain the enormous amount of cooperation that is visible in Nature.

Atoms cooperate in Molecules. Molecules cooperate in Genes. Genes cooperate in Chromosomes. Chromosomes cooperate in eukaryoticcells. Cells cooperate in Multicellular Organisms. Multi Cellular Organisms cooperate in Humans. Humans cooperate in Families and Tribes and Families and Tribes cooperate in Organizations and Nations.

The question of how natural selectioncan lead to cooperative behavior or reciprocal altruism has fascinated evolutionarybiologists for several decades.

When Charles Darwin was writing his famous book the Descent of Man (1871) he was already highly puzzled by the social structures of the ants. Their cooperative behavior was “one special difficulty, which at first appeared to me insuperable, and actually fatal to my theory”.

To solve his problem Darwin proposed that in the case of ant societies natural selection applies not to the individual, but to the family or group. The ants were part of a “Super-Organism”, that consists of genetically similar individuals.

Although many individuals showed altruistic behavior in the group the “genetic code” was replicated because the individuals in the group were all “look alikes”. The Ants were “the Same” (Similar) and therefore every Ant that survived promoted the Genes of the Community.

To explain his theory Darwin wrote ‘sympathy is directed solely towards members of the same community, and therefore towards known, and more or less loved members, but not all the individuals of the same species’.

Darwin’s Theory of Group Selection was  later transformed into the theories of Genetic Kin Selection, Group Selection and the Genetic Similarity Theory. There is dramatic evidence that plants, animals and humans detect and act on genetic similarity.

For humans, both Spouses and best Friends are most similar on attributes with higher heritability.  People join clubs and societies that contain similar people and adopt ideologies that work in their genetic selfinterest. Genetic similarity also explains voting behaviour.

The Human Detection Center of Genetic Similarity is situated  in  the amygdala a part of the Limbic Brain System that is involved in Fear and Arousal.  The Amygdala activates the Sympathetic Nervous System responsible for the fight/flight-response of the Body. It prepares the body to get into action.

The recognition of another person depends on a long series of fast electrophysiological and slow biochemical reactions to the stimuli particular to that person or situation. These stimuli include seeing the other person’s face, hearing his voice, feeling his touch, and smelling his personal odors.

The reaction patterns of Humans to a fearfull situation are different. Some people, the Hawks, re-act very fast. They Fight and Compete. Some people, the Doves, re-act very slow. They Freeze, Flight or  Cooperate.

To find the appropriate reaction-pattern every one of our senses works hard to identify “the other” or “the others“. The detection of “dangerous others” has to happen very fast. This is the task of the electrophysiological pathways.

A fast detection is unreliable therefore a second “slow” cognitive pathway is started. In the cortex the frightening stimulus is analyzed in detail, using stored information from many parts of the brain, and a message is sent back down to the amygdala.

To detect stimuli that are really dangerous the amygdala uses a memory. This memory contains learned and inherited, imprinted, situations. The imprinted situations are highly related to the detection of genetic similarity.

If an animal or a human is frequently attacked the memory contains many Painfull Situations and the amygdala reacts more specific to a situation. The older a person gets the more difficult it becomes to erase this memory.

If people or animals are unable to make a distinction between their Own Whole and the Whole of the Others it will result in a Blurring of the Identity. The Whole of the Observer Merges or Overlaps with the Whole of the Observed. If this happens people act in a “friendly“, Emphatic,  mode and experience others as more “the same” than others do.

A Cooperative Strategy is highly related to the possibility of the Cognitive Part of the Human Detection-System to Move into the Other and Imagine what will Happen. The Hawks lack the ability to Imagine.

The most interesting concept that came out of Darwins Group Selection Theory is the Idea of the Super-Organism.

This Super Organism shows itself in many ways. Examples are the Family, the Tribe, Society and the Earth.

There is a similarity between the roles played by different organizations in Society and the functions of organs, systems and circuits in the body.

Industrial plants extract energy and building blocks from raw materials, just like the digestive system. Roads, railways and waterways transport these products from one part of the system to another one, just like the arteries and veins. Garbage dumps and sewage systems collect waste products, just like the colon and the bladder. The army and police protect the society against invaders and rogue elements, just like the immune system.

If we take the concept of the Super Organism a little bit further we could imagine the Super-Super-Super-Organism that contains all the other Organisms.  In some way every Organism is Genetically Similar (“the Same“) to this Organism.

If this is true and the Theory of Group Selection is Right every Organism is an enfolding of the “Architecture of the Whole“, the Tree of Life,  and a Majority of the Organisms (the Doves) will have an Altruistic Tendency to this Super-Organism.

The Doves Love, want to Unite With,  the Whole and the Hawks dislike the Whole because they want to be a Whole themselves.

Some Scientists call the Super Organism, Gaia,  Mother Earth, but there is no reason why we should not include the Bigger Structures in the Universe until we have reached the Boundary.

On every Level the Same Pattern appears.

On every level the Whole is splitted into Individual Parts. The parts  live a Life of their own (Agency). When we Move UP the Parts are United (Communion)  into a Bigger Structure.

When we look DOWN we interpret the proces of Splitting as a Competition. When we look UP we see a different pattern we Name “Cooperation“.

If we look at the history of the splitting process it looks like the wholes were splitted without any reason. It just happened. If we believe this Evolution is based on pure chance. Life is just a coincedence.

When we analyze the process of Evolution a Pattern emerges. This pattern is Cyclic, Leveled and Self-Referential. The process is almost invisible because with every Name we Utter we carve out a portion of the world and create a Boundary.

Every Time we Divide the World with Words the World becomes more complicated. Every New Concept that is not created without a View on the Pattern of the Whole generates a higher level of Confusion and increases the Complexity of Something that is really very Simple.

We create distinctions between Animals and Humans, Humans and Plants because the Hawkish Genes Want Us to Believe We Are Something Special.

Because of their Special Status the Hawks treat their fellow organisms in a very brutal way. They Exploit (Desire) them because of their Need to Control their Environment. They want to Control their Environment  because they are Afraid to lose Control. They are Afraid that their Identity (Their Ego, Their Agency, Their Whole) will disappear when they Commune with the Whole.

The Effect of the Behavior of the Hawks is the Destruction of the Environment that they Fear so Much. They are destroying their own Mother Earth who is certainly one of the Super Organisms that gave birth to the many wholes that are just there to Enjoy her Care.

The big problem we have is Naming. What we don’t see or don’t want to see is that every Split is a Split in two Opposite Complementary Parts (Yin/not-Yin= Yang, Male/not-Male = Female, Cooperate/not-Cooperate = Compete) that Share  the Void, the Empty Set, the State the Universe was in before it was created.

On every level the Nothing, the State of Infinite Potential and Love,  is still there but it is hidden because we started to use Words, to describe what meant to be an Experience.

This brings us to the final conclusion.

The big problem that is treatening Mother Earth is Hawkish Behavior. In the long term this kind of behavior is not helping the Human Gene at all. It not only destroys  the Human Gene. It destroys  the complete group of genetic “Look-a-Likes” of the Human Gene.

Darwin was Right.

Altruistic Behavior, Cooperation,  is the Only Way for the (Human) Genes to Survive.

Let us Help the Hawks to Erase their Fearfull Memories.

LINKS

About Genetic Similarity Theory and the Cyclic Universe

About Ethics and Genetic Similarity Theory

Edward O. Wilson: A video about the Super Organism

About the role of the Amygdala

A discussion about Morality and the Superorganism

A Mathematical Model that Explains the Evolution of Cooperation

Why Non-Cooperative Humans (Hawks) always Win and Cooperative Humans (Doves) always Lose

An Article in American Scientist about the Superorganism

How Multicellar Organisms cooperate in Humans

How the Void is able to cure Addiction

The Social Effects of Genetic Similarity

Genetic Similarity in Mate Choice and Friendship in Twins

Wittgenstein about Families and Language

An Article in Wired About the Super Organism

About the Super Organism and Systems Theory

About the problem of Naming and Dividing

About the Void

About the Triple Goddess

Tuesday, October 14th, 2008

lilith_michelangeThe Ancient Greek in the person of the famous philosopher Aristotle viewed Women as Imperfect Men. Women were inferior in Strength and the Powers of the Mind. Last but not least women were Without Soul.

Therefore Women had to submit to the Rule of the Male Sex. The views of Aristotle became the basis of Western Science and were codified in the teachings of the Catholic Church.

To stop the destructive effect of female dominance the old myths were rewritten. The Positive qualities of Female Deities were simply transformed into a Negative quality.

The Female Goddess became a wicked, old female, a Witch or a Whore. She became a stealer of children and a seductress of men. She was so frightful that humans turned into Stone when they saw here.

The Wicked Witch and the Whore has many names. Examples are Lilith, Istahar, Isis, Hekate, Astarte, Medusa, Morgan Le Fay and of course the White Virgin Mary and Mary Magdelena, the Black Madonna also known as Isis or Ishtar (the Planet Venus).

One of the Oldest Version of the Destructive Wicked Whore is Lilith. Lilith first appears around 3000 B.C.E. as a class of spirits, the Lilitu or the Ardat Lili. The lilitu are associated with the owl, the eagle, the lion, water, violent sand storms (the South Wind), disease and the destructive powers of nature. The Ardat Lili, winged night spirits, female vampires, seduce men at night and steal their sperm to create demonic children.

enlil_ninlilThe destructive South Wind was known as Ninlil (Nin Lil = Lady Wind) she was the wife of Enlil (En Lil= Lord Wind). Enlil is the sun of An(u) and Ki and holds possession of the Tablets of Destiny which gives him the power over the entire cosmos and the affairs of man.

He is sometimes friendly towards mankind, but can also be a stern and even cruel god who punishes man and sends forth disasters, such as the great Flood which wiped out humanity with the exception of Atrahasis (Noah). Enlil is portrayed wearing a Crown with Horns (the Devil), symbol of his power. When Enlil rapes Ninlil he has to leave Heaven and is send by Anu to the Underworld (Earth). Ninlil follows him to take revenge.

Enlil and Ninlil are the Babylonian origin of Adam and Eve and their banishment out of Heaven is comparative to Adam and Eve’s banishment from the Garden of Eden.

Eve is very different from Lilith. Lilith is a magically beautiful woman. She shares paradise with Adam. She is a female made by God in a manner similar to how the Lord made the first male.

After leaving both the first male and paradise she is replaced by a less independent and less equal Eve, a woman not made from the Earth but from a rib of the man Adam. Lilith is mentioned in the Death Sea Rolls, the Zohar and the Talmud.

If we look at the “original” story of Adam and Eve we can see that Eve (Lilith) had a good reason to leave the “first male”, Enlil. He raped her. Later we will see that Enlil (with different names) is playing the same game all the time.

Ishtar is the goddess of fertility, love, war and the planet Venus. Ishtar is like Lilith (and Isis) associated with sexuality and sexual mystic rituals (Invoking the Kundalini).The Kundalini (“The Serpent Power”) is a spiral pattern in the body. It connects the main energy-points (chakra’s).

When the energy points are connected to Mother Earth (Gaya, Sophia), spiritual awakening starts. The Kundalini is normally symbolized as a serpent coiled into three and a half circles, with its tail in its mouth, and spiraling around the central axis at the base of the spine.

In the Gnostic version of the Fall from Paradise, there is no sin on the part of our ancestral parents. The Serpent in Eden is Kundalini, a sublime ally to humanity, not a tempter.

Kundalini2In these texts, the Serpent Power is called “the instructor.” Eve (Lilith), the ancestral representative of the human species, acquires from the Serpent all the secret knowledge of the Mysteries.

One of the most famous myths about Ishtar describes her descent to the underworld. After Ishtar descends to the underworld, all sexual activity ceases on earth. She is begged to come back. She can only return from the underworld if she sends someone back in her place.

Each time when she runs into someone, she finds him to be a friend and lets him go free. When she finally reaches her home, she finds her husband (Enlil, Adam) seated on his throne, not mourning her at all. In anger, Ishtar has the demons take her husband back to the underworld as her replacement. When this happens sexual activity starts again.

You have to understand that Enlil lived in Heaven (or Paradise) and the Underworld is the next level below Paradise. This level is called Earth. So Ishtar (Lilith) sends her “husband”, The Devil, back to Earth.

The little stories in this blog are part of a much bigger story called the Gilgamesh Epos. This story is used by many comtemporary scientists to prove that Earth was visited by members of an old Civilization (The Anunaki, The Archons, The Serpents) that was situated in the Constellation Sirius.

The Annunaki engineered the Humans (called the Lu-lu) to work for them. They also interbred with their own creation (Demi-Gods). If this story is true Paradise could be Sirius.

medusaMedusa means “sovereign female wisdom,” in Sanskrit Medha, Greek Metis, Egyptian Met or Ma’at . In Egypt she was the Goddess of Justice. Medusa/Ma’at destroys and purifies in order to recreate Balance.

In ancient history Medusa was symbolized by a female figure positioned in holy postures with the presence of animals, primarily birds and snakes whom she is intimately connected with. Medusas symbol of female wisdom is her ceremonial mask.

It has wide unblinking eyes that reflect her immense wisdom. The mask was used to guard and protect women and the secret knowledge of the Divine Feminine. It was erected in stone, corresponding to her look of stone, on caves and gateways at sacred sites dedicated to the Goddess.

The myths about the Female Goddesses are a very complicated mix of deliberated distortion by the “female haters” (Anunnaki, Archons), historical accounts, hermetic (secret, encryped) knowledge and fantasy. One thing is for sure, everybody wanted to hide the Power of and the Knowlegde about the Feminine Energy, the Kundalini.

If we look more closely we are able to detect Four Perspectives on the Female Goddess. Three of them are related to the Female Stages of Life, Maiden, Mother, and Crone (Grandmother). These stages are United in one Concept, the Triple Goddess, the Female Trinity.

trinityThe Triple Goddess, the Unity of the three stages of the Female is the Dark Goddess called Medusa or Kali. She is associated with Total Chaos and Rebirth, the Unconsciousness, Horror, Terror, Evil, the Dark Moon, Winter, Night, Darkness and Death itself. She is the Regent of the Underworld, seen in those times as a place where souls went to rest between incarnations, before coming back to the earthly plane.

The Ancient Underworld is now called Heaven. The Regent of the Underworld and Heaven is the Triple Goddess Itself, The Whole, the Creator, The One, The Goddess who has no Name, the Unknown. The three parts of the Triple Goddess Unite in Her. She is Three and One which makes Four.

The Maiden (The Fool, Seductress, Spring, Birth, Waxing Moon) represents enchantment, innocence, lack of worries, the joy of living, inception, youth, discovery and excitement.

The Mother (Warrior, The High Priestess, Dove, Dolphin, Summer, Life, Full Moon) represents ripeness, fertility, fulfilment, stability, and power.

The Grandmother (Autumn, Death (Old Age), Fate, Waning moon) represents wisdom, repose, and compassion.

The Concept of the Triple Goddess is probably of Celtic Origin. The Celts believed that all important things come in three phases. The Triple Goddess is represented by the triple spiral or triskele.

This symbol is found in the Newgrange site from the Bronze Age (3300 BC) in Ireland. The Triple Spiral has a lot in common with the triple spiral of the “Serpent Power”. With this Power the “Feminine Energy” (The Kundalini) is awakened.

danuThe Triple Goddess in Celtic Mythology is represented by the Morrigan (Death), Cerridwen (Grandmother), Dana/Danu/Anu (Mother) and Brigid (Maiden).

The Morrigan (“Great Queen”, “Phantom Queen,”) appears as a beautiful woman, a crow, a raven or a wolf. She is associated with fate, war, strife and death. In one of the many stories Morrigan appears to the hero Cu Chulainn and offers him her love.

When he fails to recognize her and rejects her, she tells him that she will hinder him when he is in battle. When Cu Chulainn is eventually killed, she transforms in a crow and sits on his shoulder. The Morrigan in the person of Morgan Le Fay plays an important role in the Legends of King Arthur.

magic chaldrounCerridwen is the keeper of the Magic Cauldron. She is the mother of very ugly son, Afagdu. To give her sun the ultimate insight she uses a magical formula, known as the “greal”.

For a year and a day, she keeps six herbs simmering in her magical cauldron, known as “Amen”, under the constant care of a boy named Gwion. One day a few drops of the bubbling liquid spatter on his hand.

Unthinkingly Gwion, sucks his burned hand, and, suddenly, he is able to hear everything in the world, and understands all the secrets of the past and future. He runs away, but Cerridwen pursues him.

After a long chase she eats him and, nine months later, gives birth to an infant son, whom she, in disgust, throws into the water of a rushing stream. He is rescued by a Prince, and becomes the great Celtic bard, Taliesin.

This is a special version of a very old story where a Child is Born without the intervention of a Male. The origins of this story go back to the time of Zoroaster and the Magi.

The Magi are called the Druids in the Celtic Mythology. The Magic Caudron is the symbol of Life (something is Cooking) and the Magical Formula is of course the Grale. The Grale stands for the Heart. If You live out of the Heart a New Child (“The Inner Child”) will be born. This Inner Child is highly creative (a Bard) which relates it to the Holy Spirit also the symbol of (Divine) Creativity. When the Inner Child is born you will understand the secrets of past and future. You will be able to read the Tablets of Destiny of Enlil.

The Mother Goddess is represented by Danu, Don or Anu. The Name Dana means Wisdom or Teacher. She is the mother of the Tuatha De Danann, the Faery-People. Anu was the Father of Isthar.

The original territory of the Celts is close to the sources of the Danube. The Greeks referred to Danube as Ister. The link between the river Danube and Celtic culture is particularly intimate and the sacredness of rivers and lakes as an expression of the sacredness of life and death was built into the whole structure of Celtic culture.

bridgetThe Maiden Goddess is named Brigid but has many other names like Bloudewedd, Blodewedd, Blodwin, and Blancheflor. Her name means flowerface or White Lily. The White Lily represents the Innocent White Soul. In the old story of Blancheflor and Flor, Flor, the Red Rose, symbolises  the Red Impulse of the Passions of the Ego to become Self-conscious.

Besides a Female Trinity Celtic Mythology also contains a Male Trinity (the Dagda (“The Good God”, Lugh (“Light”) and Herne (the handsome and playful young Satyr)).

It is now possible to map the much older Female Trinity back unto the Christian Male Trinity. If we do this it is easy to see that the Holy Spirit is the Feminine Energy, the Force of Creativity, Inspiration and Joy, the Maiden. The Father must be the Grandfather (“The Good God“). He (or She) restores the Balance and creates Harmony. This leaves us with the Sun as the Father (“The Light“).

The Druids believed in three worlds and in transmigration from one to the other: in a world above this one, in which happiness predominated; a world below, of misery; and this present state in which good and evil are so exactly balanced that man has the utmost freedom and is able to choose or reject either.

In This World we have to Unite into the Soul the Properties of All Beings, to Acquire a Knowledge of All Things, to get the Power to Conquer all Evil and to Face the Face behind the Mask of Death. To accomplish this we need the Open Mind of the Maiden, the Power of the Mother and the Wisdom of the Grandmother. In every step we take on Our Path from Birth to Death we will acquire more Light to See what is Wrong and what is Right until we Accept the Love of The Great Mother who is Three and One.

I end this blog with a poem of the Sufi mystic Ibn Arabi (1165-1240) about the Triple Goddess:

I follow the religion of Love,

Now I am sometimes called

A Shepherd of gazelles

And now a Christian monk,

And now a Persian sage.

My beloved is three-

Three yet only one;

Many things appear as three,

Which are no more than one.

Give Her no name,

As if to limit one

At sight of Whom

All limitation is confounded.

 

LINKS

 

About the Trinity in Mathematics

 

About the Life of Ibn Arabi

 

About the Gnostic Teachings and Kundalini

 

About the Annunaki

 

About the Divine Feminine in Sufism

 

About the Tablets of Destiny

 

About Harmony

 

 

About Virtue and Wisdom

Tuesday, July 8th, 2008

When you lend somebody something you assume he (or she) will give the item back in due time. To lend you have to Trust somebody. There are many ways to create a trusted relation. When a long term trusted relationship grows out of a long chain of interactions the Iterated Prisoners Dilemma is at stake. The Chinese are the Masters of Playing this Game.

In some situations it is very clear that a try-out is not necessary. If we look at the cultures of the Earth we can see that the concept of Family or Tribe more or less guaranties a trustful relationship. In a Family it is not needed to create very complicated arrangements like contracts, procedures, laws and judges. The Family uses it own rules.

The consequence of the Concept of the Family and the Tribe is a formalization of relationships based on a Place in a Hierarchy. Everybody has to know its place.

A King has to play the role of the King and a Father has to play the role of the Father. In a Family or an Extended Family (Tribe) you are trained to play the roles you have to play in your life.

Confucius (551-479 BC) saw the universe and all living things in it as a manifestation of a unifying force called the Doe (translated as the Truth, Unity, or the Way). Doe constitutes the very essence, basis, and unit of life that perpetuates order, goodness, and righteousness.

It manifests itself in the harmonious opposition of yin (“feminine, gentle“) and yang (“masculine, strong“), and in humans through duk (“virtue“). Virtue is a gift received from Heaven.

It is through Virtue that a person is able to know the Heavenly Truth and it is the “locus where Heaven and I meet“. Virtue can be realized through self-cultivation. It provides the fundamental source of insight and strength to rule peacefully and harmoniously within oneself, one’s family, one’s nation, and the world.

There are two inter-related aspects of virtue: in (“Human-hearted-ness“) and ui (“Rightness“).

The basis of individual and humanity is the Human-heartedness. Human-heartedness is essentially relational and it involves loving, sacrificing and taking care of others. Individuals are born with Human-heartedness and experience Human-heartedness through the sacrifice and devotion of their parents.

The second concept, ui (“rightness“), notes that an individual is born into a particular family with a particular status. Rightness articulates that individuals must perform and fulfil their duties as defined by their particular status and role.

Confucius considered family and society to be hierarchically ordered, necessitating that everyone fulfil their duties. Fulfilling one’s given role as a father, mother, child, elder, teacher, or politician is considered a moral imperative and not a matter of personal choice.

Confucius considered society to be socially ordered and that each person has beun (“portion or place“) in life. Each beun had attached roles and duties, and each person must fulfil these roles and duties. Duties and obligations of each beun are prescribed by yea (“propriety“).

Propriety articulates expectations, duties, and behavior of each individual according to his or her status and role. For example, chemyon (“social face“) need to be maintained by a person of social stature defined by his or status, regardless of his or her personal preference.

Social order and harmony are preserved when people observe their place in society and fulfil their required obligations and duties.

The fourth concept is ji (“knowledge“). Knowledge allows us to understand the virtues of Human-heartedness and Rightness and to follow these virtues through Propriety. It is the basis of the development of Wisdom.

By the applying the principles of Confucius Chinese Society became a Well Oiled Machine. Every action that was taken was pre-programmed by all levels of education. Every part in the machine knew its role. Life was highly predictable and everybody accepted its place in Society. There was Harmony and Peace in the world.

If there be righteousness in the heart, there will be beauty in character,

If there be beauty in character, there will be harmony in the home.

If there be harmony in the home, there will be order in the nation.

If there be order in the nation, there will be peace in the world.

The big changes of Chinese Society came Out of the West. The English Empire destroyed the Heavenly Order by selling large quantities of Opium. The huge underclass of China was a beautiful target for the people who followed the theories of Lenin.

The Upperclass was destroyed and a new Upperclass, The Communist Party, took over. The culture of China has not changed. People still know their place and the Doe (The Way It Is) is now proclaimed by the Party. The new upperclass knows it has to keep the underclass in harmony.

The Party decided to create a higher standard of living by importing capitalistic principles from the West. It is now moving in high speed to the level of the Consumer Society. The West is paying for this move by buying Chinese products for a very low price.

In this way China has accumulated an enormous amount of money (mostly dollars). They are able to buy what they want. With the enormouss stock of dollars they are able to manipulate US Government. China is able to destroy the US Financial System in one fast move. They certainly will not do that.

The Chinese people are experts in strategy. They know how to acquire power without fighting. They keep a social face and play the game others want them to play. They are experts in applying the Iterated Prisoners Dilemma. They know Confucius and his predecessors were Wise man. They knew how to move with The Cycle, the Tao.

Western Society has lost its cultural foundation. The principles of Confucius don’t sound very strange to us. They are easily translated into Christianity.

When the West lost the basic principle of Christianity, Human-hearted-ness (in) one of the two pillars of Trust was lost. The West rationalized Empathy (Compassion, Emotion). I Think, therefore I Am (Descartes) became the basis of the Self.

When people started to do the “wrong thing” the second pillar of Trust, Integrity (ui, Rightness) dropped. Politicians were not Playing the Role of the Politician and Managers were not Playing the Role of Manager. They lost their Virtue.

Finally the Doe (Unity) of Western Society was gone. Families broke up. Everybody was Left on its Own and started to act on a Short-Term Perspective.

The Interated Prisoners Dilemma changed into a chain of disconnected attempts to leave the Prison. The best way to win such a Game is to defect. You always win but your victory is never a Win-Win. On the long term Everybody changes into a potential Enemy.

The West entered the State of Individualism and even Egoism. In this state it is almost impossible to act out of Unity. Everybody is going its Own Way or is Competing with the Other. This makes it even easier for the Chinese Masters to create a new Machine to support their Extended Family.

About the Renaissance

Wednesday, April 2nd, 2008

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

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

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

T704836_23The printing press, invented in 1450, made it possible to distribute all the new knowledge all over the known world.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

On a macro level we see an interesting pattern.

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

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

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

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

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

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

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

What does this say about Innovation?

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

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

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

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

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

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

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

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

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

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

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

Funny.

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

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

LINKS

About the Perspective

Lectures about the Renaissance part 1

Lectures about the Renaissance part 2

Lectures about the Renaissance part 3

About Subsidies

Thursday, March 6th, 2008
Around 1993 I became responsible for Subsidy Management at ABN AMRO. The whole thing started when the bank contracted a specialized company called PNO. I was asked to coordinate their activities in the Bank.
  • First you have to write a proposal (estimate time (including advisor).
  • When you get a subsidy you have to spend time reporting (estimate time).
  • The sum of both multiplied by the price per hour result in the costs.
  • Multiply the sum of subsidy by the chance you get the subsidy. A simple way to do that is to estimate the amount of contenders. This gives you a simple statistical expectation.
  • If the Estimated sum is lower than the costs don’t spend your time and try to get money in a different way. In general when you are a small company stay out of subsidies.

If you really want to become rich start a company like PNO (Pecunia Non Olet, Money Does Not Stink).

When I met them I soon found out that I was there when the company was created. They started their activities at the same place (Hengelo) and the same building as the company of a friend of mine. This company (Utopics) developed the expert-system they use to track subsidy opportunities.

Until 1993 I did not realize that it was possible to acquire a huge amount of money when you play the game the right way.

The Subsidy Game is played the right way when you combine two things. You have to align your strategy and related projects with the vision of government and you have to create the right level of contacts.

When the local or international government defines a policy they look for instruments to support this policy. One of the instruments they use is subsidies. They pay you to do what they want you to do.

When you want to get a lot of money you have to align your policy with the policy of the government.

It is very important to understand that aligning your policy is a virtual act. You have to show that the policy is written down on paper. If you are clever you don’t have to adjust your plans. In reality you play the same game government is playing. They also act very differently at the inside.

They play the Game of Politics. The game of politics is a combination between the Unity (Plan, Model) and the Social (Emotions, Network) World-View. The game is about persuading people to accept a model or plan or asking an opinion about a plan.

The simple trick is to relate all the projects you are doing to the policies of the Government and translate the project-plan into a proposal for subsidy.

The next step is much more important. You have to influence the network of decision makers. I hope you are not a naive person who believes in an objective government.

Everybody in government can be influenced to do what you want. The only thing that counts is the price you have to pay. Please understand that bribing is possible but this is a very stupid way to get influence because it only influences one person.

To get an optimal result you have become an “important person” in the network of decision makers itself.

To do this you have practice the art of Public Relations (PR). When you are practicing PR you have to know WHO is WHO, visit meetings and parties and give something to receive something.

When the Subsidy-project grew I became involved in PR at a large scale. PR is really fun. You talk a lot, travel a lot, you eat (and drink) a lot and sometimes you make a beautiful deal.

Soon I found out that the power of the Dutch Government was gone. The power was moved to Brussels. I made a proposal the create a special lobby-office in Brussels and to my surprise top-management agreed.

This started a new level of sophisticated manipulation. Getting things done in Brussels is much more difficult that getting things done in the Hague.

Brussels can be compared with Washington and the European Union acts the same as the USA. Many things are decided behind close doors and the most important influencers are the rich companies.

To get some instant experience I visited a few lobby offices and talked with the managers to find out how they were doing “it”.

My most spectacular experience was with IBM. IBM seemed to me the perfect lobby machine. The manager of the Lobby Office was the Minister of Foreign Affairs of IBM and he also had the power to act.

Influencing EG Policy was a very important issue at IBM. You have to understand that the EG is deciding about many standards and the standards have to be built in the products of IBM.

When I got acquainted with the practices of Brussels I discovered many “bribing patterns”. Later they were also detected and many scandals appeared. Yes, High Level Officials of the EG asked for money and they were also payed.

When you are not a high level player in the Subsidy Business I advice you to make use of an advisor. Even if you use an advisor the changes are low. Because of the low changes you are able to make a simple calculation to find out if subsidies are something you have pursue.