Archive for the ‘Completed’ Category

About the Next Wave of the Kondratiev Cycle

Thursday, April 17th, 2014

The Future Center Smart Systems will be launched, 23-4-2014 in the Hague.

To prepare for the interactive part of the meeting this document has been written to provide some Food for Thought.

What is a Future Center?

A Future Center is a place to connect and innovate. We want to create an environment that facilitates interaction and stimulates collaborative action. We want to support cross-innovation and make it possible to make new combinations. Last but not least we want you to challenge Science to produce valuable insights at the right time and the right place.

What is a Smart System?

A Smart System looks like a human being. It is equipped with a Sensory-Motor-System, a Mind, Imagination and Emotions.

Smart Systems senses the outside (and his inside) world with much more sensors-types than the five sensors of his human look-a-like.

A Smart System is able to react very fast with its predefined processes on a event that is detected by its sensors.

A Smart System is an adaptable system. It is able to analyze and improve its behavior, communicate with a human being and other Smart Systems in an understandable way.

Smart Systems are there to compensate the human biases. Smart Systems are able to transform and optimize everything that contains some kind of structure.

Smart Systems  can optimize software, data and content using software/data/text-mining, analyze patterns, predict the short and sometimes the long term.

Smart Systems are perfectly suited to provide the knowledge needed and answer the questions humans ask. They are able to train humans in an almost real situation using simulators.

Smart Systems can be fun to play with.

About Cycles

In 1931 the US Department of Commerce assigned Edward Dewey the task of discovering the cause and underlying dynamics of the Great Depression. Dewey created a special institute called the Foundation for the Study of Cycles that is still in existence.

The most interesting observation of Dewey is that Cycles restore themselves all the time and are connected by a Harmonic (“Musical”) Pattern. Dewey discovered that we cannot control the Cycles.  Ups and downs are a fact of life.

The most researched Cycle in history by far is the Kondratiev-Cycle named after the Soviet economist Nikolai Kondratiev. The Kondratiev Cycle has a periodicity of 52 years.

The Kondratiev arises from the combination of basic innovations that launch technological revolutions that in turn create leading industrial or commercial sectors.

In the year 2000 the Kondratiev was at his top and is now in a decline that will take 26 years.

Currently we are in  the Kondratiev Spring Phase. It is the time of what Schumpeter, a big fan of Kondratiev, called Creative Destruction.

The old structures are dying and the new structures that will start the new upward wave are created.  It is a time of tremendous disruptions.

About the Software Factory

The last wave that started around 1950 was dominated by the rise of the centralized computer.

This computer was based on the factory-model of Henry Ford and Frederick Winslow Taylor of the previous wave.

Between 1950-2000 isolated creative programmers united in big software factories that are controlled by unified standardized methods and processes. Between 1950-2000 the programmers automated their own processes.

The methods are now transformed into standardized (BPML-)process-models that are abstracted into standardized (VDML-) business models that are filled with Industry-Models. An example is the ARTS-model that covers Retail.

Creative programmers are now replaced by creative business-modelers.

About the Next Wave, The Network of the Human Mind

On Christmas 1990 Tim Berners-Lee working at CERN published the first version of The World Wide Web. He launched the theme for the next wave, The Network.

From 1950 until 2000 the causal linear manual processes were automated but now the next level, the network of the human mind is at stake.

At the end of this wave around 2040 or much earlier as some people predict, the machines will imitate and surpass the human because they will unite in a global brain that can be connected to our Brains if we want that to happen.

At this moment we are creating the memory-banks of the Global Brain by producing billions of connected parts that contain complete human life’s, theories, music, movies, measurements and much more that we are now unable to imagine.

A Short Scenario for the Next Forty Years

It is clear that the Business-Domain-Models will speed up the process of value-chain-integration and value-chain-reversal.

This means that the customer will be in control of the value-chain en there will be direct contact between customer and producer. Value-chain-integration will in the end remove all the intermediaries in the value chain.

Value chains will finally converge into one standardized value chain. Best-practices of separate value-chains will become leaders in the new value-chain. Cross-innovation, combining the best of all worlds, is the way to move on.

To give customers control of the value-chain producers have to simplify their products and make it possible for the customers to create their own version of the product they want.

Products have to become configurations of simple building blocks that can be split into variable parts and infrastructure.  Product-configurators will connect to other configurators. This makes it possible to create completely new combinations.

In the next step the data that is produced by the systems will be analyzed and processes will not be controlled by human made models but by models that are created by statistical pattern recognition tools. The systems will understand humans and predict human behavior and adapt themselves to the human needs.

In the last stage the software will produce an image that reduces the complexity of its whole. It will create a virtual human world that gives us the illusion that we are still in control.

At that time most people will play and not work.

Challenges

The most important question you have to ask yourself is if your company is part of the “old world” that will finally be destructed by creativity or is already part of the new wave.

The big problem is change management,  how to move from the current state to a for most companies and institutions unknown future. Companies and people have to transform their collaboration patterns,  their software and data and their expertise.

The change process is accelerating. A lot of companies are stuck in their installed base of software and their organization structure that is not created to respond fast to the challenges that come from the outside word.

LINKS

About Smart Systems

Launch Future Center Smart Systems

Thursday, February 27th, 2014

Wednesday the 23th of April 2014 13:00 – 17:00 we want to launch the Future Center Smart Systems.

The meeting will take place in the Living Lab of the The Hague Centre for Innovation, 2nd floor Campus Den Haag, Schouwburgstraat 2, 2511 VA Den Haag.

The Future Center is an initiative of LIACS, Leiden Institute of Advanced Computer Science and Constable Research BV.

A Future Center is a place of dialogue and innovation.

Scientific research needs complicated real-life problems to solve to improve their theories. R&D wants to use proven solutions to improve or innovate their products or services.

R&D and Science can easily work together if the long-term strategy of Science matches with the short-term needs of Industry and Government. That is why we need to have a permanent dialogue.

We want to start a dialogue about Smart Systems between Scientific Research and the R&D of big and small companies and government agencies.

Smart Systems are and will be everywhere. Smart Systems control the car you (still) drive and the planes you fly. Smart Systems trade on the stock market, diagnose your illness and design sustainable buildings.

Smart Systems will manage courts & lawyers, cities, logistics and food safety. Smart Systems will entertain you and will stimulate your imagination. Smart Systems will even help you to innovate.

They are a combination of Analytics (Big Data), Artificial Intelligence, Expert Systems, Process/Case-Managers, Robots, Sensors (The Internet of Things), Simulators, Games, Intelligent User-Interaction (Augmented & Virtual Reality) and Social Networks.

The Smart Systems Future Center aims to help you find out what is happening with new technologies and its applications, what is already possible and what will be possible in the future.

We also want to discuss the big impact Smart Systems will have on our society. Many experts believe Smart Systems will lead to a huge increase of unemployment not only on the level of the not educated people but also on the level of the highly educated.

Others believe that the Smart Systems (“the machines, the robots”) will take over the World. They believe that this moment called the Singularity is near.  It is certain that Smart Systems will disrupt almost every company in the world. 

To prepare you for the future we want to connect people, companies and government agencies. We want to participate in projects and start the development of new research, new services or companies. We can also help with the funding of these projects.

In the first meeting representatives of other Future Centers in the Netherlands (ABN AMRO, Tax Office, Ministry of Infrastucture) will share their experiences, we want to tell you about the state of the art in Big Data and have an interactive discussion about our future plans and priorities and how you want to be part of this dialogue.

The amount of people of the first meeting is limited. After the first meeting we will organize many other meetings in which we will discuss a specialized subject. We will announce these meetings in the Linkedin group Smart Technology Network. If you join this closed network you will be always up-to-date.

If you are interested to come to the meeting or want to be informed by email about what we are doing please send an email to hans.konstapel@gmail.com. If you know people who could be interested to join our Future Center please forward this link to them.

About Autarky

Thursday, October 11th, 2012

The amount of local cooperative energy-companies in the Netherlands is increasing. It all has to do with the decrease of the price of solar-sells but there is more at stake.

Local energy-companies are part of a movement aimed at Autarky. Autarky is the quality of being self-sufficient.

The word Autarky comes from Greek αὐτάρκεια (autárkeia), itself from αὐτός (autós) = self and ἀρκέω (arkéo) which in its passive form means be satisfied, content or “Out of my own Power“.

Fractal Human Distribution Network

Fractal Human Energy Distribution Network

The need to become self-sufficient has certainly to do with the current economic-, ecological- and energy crisis. People are afraid that the supply of vital energy and food will suddenly stop or become priceless. This is not the only reason.

Some people think we are wasting our money, food and energy by producing nondurable throw-away goods in which the packaging is sometimes more important than the content. They want to create durable products and services. This is not the only reason.

Some people don’t trust the suppliers of their food and energy, their politicians and/or the caretakers of their savings, the banks, anymore. They believe that their food is intentionally manipulated, their savings are wasted, their country is sold out to the rich and their environment is polluted for just one simple reason, Greed, the opposite of “Being Satisfied”.

The people of the autarkic movement want to recreate the necessary functions (bank, energy, food, work, healthcare, government) themselves in a cooperative way in their own living context.

Atmospheric Energy Diagram

Atmospheric Energy Diagram

The local cooperatives  are now joining on a higher (mostly country) level and are  in need of a shared (real-time)infrastructure. The current infrastructure does not support flows that move between many participants (so called peer-to-peer-networks).

The current system is a Hierarchic Top Down System containing Huge Highways that are connected to Big Production-facilities. This makes it impossible to consolidate, share and distribute resources peer-to-peer on a local level.

The Electric Highway

The Top Down System has created Global Markets where the local production is sold  to the highest bidder.

The Global Markets are the playing field for advanced speculators that make a lot of money. After the deal is made the local production is transported to a far away destination. That is the reason why the Top Down Systems are integrated in world-wide Logistic Systems.

If we want to coordinate all the local initiatives we need advanced systems that Up- and download, control, predict, connect, share, balance and distribute vital local resources on the short and long term.

The Panarchy Cycle of an Ecology

The Panarchy Cycle of an Ecology

Examples of these systems can be found in “crowd funding“, “virtual power plants”  and “treasury management” (balancing many small amounts of Money at the short and long term).

In Nature we find comparable (Fractal) Distribution-Systems in the Lungs, the Arteries, Riverdelta, the Weather Cycle and Ecologies.

All of these fysical Flow Systems, that map 1 Resource-> on Many Resources or Many Resources->on 1 Resource,  are based on the third Law of Thermodynamics called Constructal Law.

Virtual Power Plant

Virtual Power Plant

In the philosophy of the Stoics and Cynics of Ancient Greece the perfect human was not only arete (“all-around excellent”) but also independent of every need. Arete was associated with a full life as a citizen of a city.

Later Spinoza (“On Human Freedom“), Rousseau and David Thoureau (Walden) have developed their own autarkic philosophy.

Autarky was the ideal of a complete man who needed no one and no organization. This ideal can also be found in Zen Buddhism, Taoist practise, Early Christians (Nazarites), the Catholic Order of the Franciscans and the Protestant Quakers.

In reality it is almost impossible to be completely self-sufficient as a lonely human being. We need others when we are young, sick and old and we need others because we are specialized (“Talented”). Autarky is a possible aim for a small community.

Resource Balancing in Nature (Lungs, RiverDelta)

Resource Balancing in Nature (Lungs, RiverDelta)

The religious, cultural and political movements at the left and the right aimed at living the “good life” (“Living Slow“) are converging in  the movement of the Cultural Creatives. The Cultural Creatives are the new Elite that is moving to the AND-state (Left AND Right).

They don’t believe in the old Competitive Ideologies (Socialist, Capitalist, Religious, Liberal, Nationalist, Conservative, Globalist, etc..) but want  to focus on the Shared Collaborative Values between all Humans. We all need Love, Food and Shelter.

The Stoic Zeno shows the Doors to Truth and False

The Stoic Zeno shows the Doors to Truth and False

Autarky has always been a major political aim of countries. Autarky is about the possibility to control your own future and to become independent of other powers that could use your dependency to tell you what to do to get what you desperately want.

At this moment the shortage of fossil fuels, especially oil and gaz, is used to influence the policy of other countries and is the cause of local conflicts in the Middle East.

China is buying all kinds of vital materials to make sure their economy will not become dependent on others. If they will succeed and nobody doubts about that, they will become the economic controlling power of the world.

Reaching a state of local autarky, being satisfied with what your environment provides you, has become the aim of the wordwide sustainability movement.

Total autarky is possible when you want to live as a stoic or a survivalist. Most people accept a more simple living, move off-the-grid and build autonomous buildings that make use of  renewable energy.

Allotment Garden

Allotment Garden

Others start to farm in their own backyard, join an allotment garden or move back-to-the-land and practice sustainable agriculture.  To handle their surpluses and shortages independent  local markets are created that make use of  alternative currencies.

A strive for (regional) Autarky pushes the need to innovate to a higher level because not all regions contain the right materials, knowledge or experience to realize everything everybody needs. To become fully Autarkic the Production and Consumption Systems in the Region have to be based on simple concepts and parts that are available everywhere. Simple concepts are concepts that are easely copied.

The only way to combine Simple and Complex concepts is to use the Concept of Self-Reference (Fractals). The only way to make use of parts that are available everywhere is to make use of the Simple Building Blocks of Nature. A good example is the use of algea in food processing.

The concept of Autonomy not only plays an important role on the many levels of human (personal, organization, country) and animal society (Competitive vs Collaborative (Ants)). It is also a major subject in the research of (Second-OrderCybernetics (Control Theory).

Self Reproducing Systems

Self Reproducing Fractal Systems

Second Order Cybernetics is concerned with the Control of the System of Systems (the Meta-System). Hierarchy is not the solution to this problem because it leads to the logical problem of Infinite Regress (“Turtles on turtles on … all the way down”).

The Meta-System is controlling, reproducing and balancing itself by a Fractal Feedback-Cycle that moves Backwards (Consumption) and Forwards (Production).

The concept of Self-Reproduction is called Autopoiesis or Autocatalysis. The Design Philosophy of Cradle to Cradle is a good example of Autopoiesis.

A System is an Autarky if all its Levels are capable of Self-Reproduction.

If a human wants to become self-sufficient he has to accept and develop his own talent and find complementary people so he is able to create a Self-Reproducing Unit.

The smallest Self-Reproducing Unit in Human Society is the Family living in one House. This House has to produce more than enough Energy and the Garden has to produce more than enough food to support the Family.

Garden City (Culemborg, the Netherlands)

Garden City (Culemborg, the Netherlands)

If we cluster all these Self-Reproducing Families/Houses & Gardens in a small City the chances are high that the combined talents of the families will be able to supply every profession needed if the people of the city want to Live a Simple Life.

It is also possible that the surplusses and shortages of the families can be compensated by creating a Market on the level of the small City or one level higher, the Region.

An Autarkic Movement becomes an Aggressive Competitive Nationalistic Movement when the Citizens of the Country feel that their Country is plundered by outsiders and their Leaders promise to get it all back by expanding the Space to Live (“Lebensraum“) to facilitate everything that is needed.

This happened when Germany was preparing for War after the enormous reparation payments of 132 billion gold marks to the Winners of World War I.

The Autarkic Movement could also become a Peaceful Cooperative Social Movement like the Movement of Gandhi in India when the people accept the Good Life they already live and want to share the surpluses with others who are in a worse state.

If you want to create an autarky or think you can help other to do so join this group on linkedin.

LINKS

Dutch Report about Local Energy Companies (in Dutch)

About the house that produces his own energy (Passive House)

The Complete Book of Self Sufficiency

About Close-Loops Systems

About Smart Grids

About Fractal Distribution Systems

Jerry Rifkin: About the Distributed Economy

The John Seymour School for Self Sufficiency

About Entrainment

About the EU Policy of Smart Specialization of Regions

About Darwin and Collaboration 

About Artificial Life

About Smart Technology

About the Thermodynamics of Living Systems

About Worldviews (How to find Complementary People)

A City is an Organism

About the Viable Systems Model of Stafford Beer

About Garden City

Gandhi’s view on Capitalism

The Autarkic Dreams of Germany

 

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 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 Intelligent Design

Tuesday, April 17th, 2012

Thermodynamics, the Science of Heat, became an important science in the 19th century when physicists started to improve the Steam-Machine. This blog is about a recently discovered law of Thermodynamics called the Constructal Law.

The Constructal Law describes How Intelligent Systems emerge out of the Laws of Thermodynamics.

Heat is Random Motion

According to Thermodynamics our Universe moves from a highly improbable extreme hot state called the Big Bang to a highly probable extreme cold state called the Big Freeze.

The Big Bang was caused by a conflict between expanding and compressing (inflating) space in the Ocean of the Nothing (the Zero Point-Field) that contains infinite possibilities.

Our Universe is one of the many bubbles that drift in the Sea. At a certain moment the Bubble will dissolve and space will become evenly distributed.

To reach the Big Freeze in finite time every new state of our Universe has to be more probable than the old state. The Probability of a System is called Entropy in Thermodynamics.

Energy always moves from High (Chaos) to Low (Order) Temperature. This is the main reason why most of the energy of Earth comes from our Sun.

With help of the Electro-Magnetic radiation of the Sun we call Light, plants, algae and bacteria transform simple molecules into complex organic structures (Biomass = Potential Chemical Energy) and store the energy of the Sun. Bacteria and Fungi brake up these structures, produce heat, reduce the complexity, and close the Cycle.

The Input of the Heat of the Sun has to be compensated by a comparable Output of Radiation otherwise Earth would be burned instantly. The difference between the Input and Output of Energy is transformed into Movements on Earth.

The Earth’s climate is a huge flow system. It circulates air and water from the tropics to the poles and back. These flows develop as air and water move from hot to cold regions, a result of variation in the heating of the Earth’s surface by the sun.

The Earth is not only heated by the Sun. The hot kernel of the Earth is surrounded by a small crust. At certain places on Earth and the Sea the rotating pool of the magma-ocean produces a lot of energy.

The Earth with its solar heat input, heat rejection, and wheels of atmospheric and oceanic circulation, is a heat engine without shaft. Its maximized mechanical power cannot be delivered, but is instead destined to dissipate through air and water friction and other forms of heat loss. It produces maximum power, which it then dissipates at a maximum rate.

The earth is wasting a lot of energy because the transmission of  most of its energy is not contained in a Tube-like-system.

The system maximizes the sum of the work done driving the planetary circulation, and the heat rejected back to space at the cold end of the heat engine.

When the speed of the planetary circulation is low, so are the turbulent losses. As speed increases, up to a certain point the sum of work done (circulation speed) and heat rejected also increasing until the turbulence starts to interfere with the circulation and  actually decrease the total of work done and heat rejected. That is the point, “the edge of turbulence”,  at which the system will naturally run.

Every flow system tries to find the perfect balance between movement and friction.

The interesting point is that friction is movement in opposition to itself.

Clouds on the Edge of Turbulence

The biomass on Earth is direct or later (Oil, Gaz, Coal) consumed by all kinds of organisms. In Food-Webs Organisms are consumed by other organisms.

We, the Humans, describe the interaction of the organisms in the Food-Webs as a Struggle for Live, a Survival of the Fittest, but the flow of energy in the food webs could also be seen as an adaptive chain of chemical reactions that are performed in self-moving, self-reproducing chemical factories.

Energy is Potential Movement. The potential energy stored in the biomass on Earth is transformed into circular movement (kinetic energy). During this transformation Heat is produced. Heat is the waste produced by a restrained non-effective movement.

The energy of the Sun produces all kinds of movements on Earth. Examples are river-delta’s, our respiratory system and the weather-system.

Flow Systems that move from one  to many always look like a leaf or a tree

Flow Systems that move from One to Many always look like a Leaf or a Tree

According to Constructal Theory the generation of design (configuration, patterns, geometry, shape, structure, rhythm) in nature is a physical phenomenon that unites all animate and inanimate systems. Design in Nature always shows itself as systems that flow and improve themselves.  Systems improve themselves because the movement from chaos to order takes many discrete steps.

Biological organisms are flow systems. River basins are flow systems. A Tree is a flow system. The Traffic System is a flow system. The City of Paris is a flow system. The Financial Market is a flow system. The Internet is a flow system. A Proces-Manager is a flow system.

Flow Systems

All these flow systems must be structured (architecturally designed) in such a way that the currents that flow (Life Energy, Water, Air, Electricity, Gaz, People, Cars, Trains, Airplanes, Content, Money) increasingly get to where they need to go. This gives shape and structure to everything that evolves over time.

Flow Systems always remove the Resistance to the Flow themselves.

Constructal Law is formulated as follows: “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.”.

Nature always provides Resistance to Change (Heat, Erosion, Friction) and this resistance is provided by the Systems of the Past. The current Order resists the potential Chaos of Free Moving Energy.

The Paths of Change of our Universe always move in the same way. The pattern looks like a Moebius Ring, the number 8, because this is the only way to cope with the polarity of the movements. In a Moebius Ring two Opposite Cyclic Movements are perfectly United.

A Moebius Ring is a 2D-structure that operates in 3D because it needs a Twist to operate.

According to Constructal Theory the Energy of the Sun creates two types of Systems called Engines and Brakes.

Engines are the most effective and efficient states in the evolution of our Universe. They have found the best way to cope with the resistance that is provided by the Brakes. Brakes are the old systems like trees, forests and natural or constructed dams that slow down the movement so the potential energy can be stored.

If the Energy of the Sun is not stored,  the Self-Reproducing Systems are unable to evolve to a higher level of organization.  If every Resistance would be gone the Flow-Systems would Flow in a Radial Pattern to every Direction possible.

If we remove the Natural Brakes (Forests, River-delta’s) the Expansive Flow-systems will take over control and the Smart Highly Improbable Next Generation Brake Systems, the Organisms would die.

We, the Humans, are here to Resist the Engines that give the Flow-Systems the opportunity to make Everything the Same. Every Thing has to become the Same because the Universe does not discriminate. Every configuration has the same chance to be alive.

Dependent on the type of flow there are standard solutions to the dualities that are provided by the eternal battle between engine (movement) and brake (not-movement).

Paris is a Flow System

The standard solution can be calculated using the Laws of Thermodynamics. Tree (or Leaf)-shaped fractal systems are for example the best solution for a One-to-Many (or Many-to-One) Flow. The Flow Systems always converge to these Shapes.

Our Earth is rotating, spinning and moving around our moving Sun. The influx of Energy on every area on Earth is changing all the time. This means that every Flow-System on Earth has to adapt to the short term and long term changing Energy Input of the Sun.

The stability of a Flow-System, the Resistance to Change, is highly dependent on the Resilience of the System.

According to the theory of Panarchy the Resilience of a System is dependent on the Potential and the Connectedness of a System.

In  the Exploitation/Conservation phase of the Adaptive Panarchy-Cycle the Constructal Engines become more efficient (producing more Potential) and Connected. This means that the amount of possible paths in the River-delta of the System is reduced. This amount determinates the resilience of the system.

At the state of maximum production and maximum connection (conservation) the system is spending all its potential at self-reproduction and is highly vulnerable to external disturbances. At a certain moment when a disturbance destroys the majority of the paths the system collapses (release).

Revolt: A small Wildfire can destroy a complete Ecology

The bits and pieces, the components, of the scattered ecology are reassembled sometimes in a different way (reorganization) and the system starts again most of the time on a higher level of organization.

Kleiber's law

Kleiber’s Law is an example of the Constructal Law. It shows the many levels of organization that have occured since the chemical factories of the bacteria started to work together. Kleiber’s Law can be extented to the level of the Community and the City.

The Panarchy Cycle is Self-Similar. It repeats itself on many Scales. The higher the scale the bigger the impact and the slower change takes place.

The Scales are interconnected. A huge disturbance on a lower scale (Revolt) can have an huge impact on a higher scale when both cycles are moving into the Release State.

A Slow moving High Level Cycle can help to restructure a fast moving cycle by providing the template of the way the components were originally assembled (its CommunityDNA) (Remember).

Constructal Law is a Law of Thermodynamics. Thermodynamics has evolved into a Statistical Theory called Statistical Mechanics. To calculate a probability you have to define the Space of all Possibilities of a System, the Phase Space.

When you don’t know what a system will look like it is impossible to calculate the Phase Space. To calculate the possibilities of Constructal Law you have to imagine the possible constructions of Mother Nature.

It is possible to play with Probability Theory without knowing the exact Phase Space. In this case you have to look at the probabilities of the probabilities. These probabilities are described by the Triangle of Pascal. Behind the Triangle of Pascal a new Triangular Structure shows itself. This pattern goes on and on until the primary Triangle of Creation, the Holy Trinity, is reached.

The Trinity is a combination of Desire (Mother, Female, Expansion, FLOW), Control (Father, Male, Compression, BRAKE) and the combination of both Expansion AND Compression also called the Void or the Tao. In Physics the Void is called the Vacuum or the Zero-Point-Field.

The Triangular Pattern behind the Triangle of Pascal

When we have moved back in time and have reached the state of the Trinity we are very close to the Big Bang. The Big Bang is a result of the Union of the Opposites (Yin/Yang, Male/Female, Matter/Anti-Matter, Expansion/Compression) that both came out of the Void.

The Vacuum is the Eternal Flow System of Creation. It contains everything that is possible even the impossible, the Empty Set.

The Tao is like a well: 

used but never used up.

It is like the eternal void:

filled with infinite possibilities.

It is hidden but always present.

I don’t know who gave birth to it.

It is older than God.

(Tao Te Ching 4)

According to Constructal Law every finite-size system must evolve in such a way that it provides easier access to the imposed currents that flow through it.

The Tao is the Channel of the Energy of Life. If Constructal Law is Right we have to give easier access to this Flow. We have to become the River to move to our final destination, the Sea of the Nothing.

LINKS 

A video about Constructal Theory

About the Higgs Field and the Big Bang

About Innovation and Thermodynamics 

About the Big Bang

About Friction

About the Constructal Theory of David Deutsch

The Website about Constructal Theory

An Introduction into Constructal Theory

About Morphology

About Panarchy

About Kleiber’s Law

About Genetic Similarity Theory

Why a City is an Organism

About the Triangle of Pascal and the Holy Trinity

About the Holy Trinity

About Constructal Law and the Trinity

Attraction + Obstacles = Excitement 

About the Law of three & Gurdjieff

 

 

Over Veerkracht (Resilience) (in Dutch)

Monday, April 2nd, 2012

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Bacteria wisselen DNA uit

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

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

Spons

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

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

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

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

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

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

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

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

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

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

Wetenschap en Godsdienst gaan uiteindelijk over hetzelfde.

LINKS

Over de Big Bang

Over Thermodynamica

Over Constructal Theory

Waarom een stad een organisme is

Waarom de genen bepalen wie we aardig vinden 

Over Pan en Anarchie

Over de Wet van Kleiber

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

Over de Uitgebreide Driehoek van Pascal

Over de drie-eenheid.

About Perspective

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

Medieval Perspective

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

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

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

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

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

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

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

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

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

The Future is Expanding Space with Infinite Potential.

Time moves behind Space and Scales Space.

About Perspective Drawing

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

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

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

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

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

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

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

Perspective Machine designed by Albrecht Durer

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

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

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

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

IMAGE: Leonardo's perspectograph

The Perspectograph of Leonardo Da Vinci

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

About Projective Geometry

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

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.

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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