Deze blog bevat een presentatie over de Community of Practice (CoP). Een CoP is een verzameling mensen die ervaring delen.
Opvallend is dat de zuivere Community of Practice niet voorkomt. Dat komt omdat men Kennis (Theorie) en Ervaring (Praktijk) door elkaar haalt.
De verwarring ontstaat omdat men de theorie als “dwingende” ervaring ziet. De theorie is foutloos. De gebruikers van de theorie maken fouten die worden veroorzaakt door tekortkomingen bij de gebruiker en niet in de theorie.
Doordat de gebruiker volgens de regels werkt en het mislukken van de regels door de gebruiker komt en niet door de regels wordt de theorie niet aangepast en worden de mislukkingen geaccepteerd totdat het systeem zich volledig volgens de regels gedraagt.
Het idee dat de praktijk ondergeschikt is aan de theorie is ontstaan in de Verlichting, een periode die samenvalt met de 18de eeuw.
In die tijd werd de verbeelding (het creatieve) teruggebracht tot de fantasie en werden de emoties (die waarderen) gezien als een geestelijk probleem (“hysterie“). Het enige wat telde was de ratio die werd vertaald in logisch redeneren.
In de verlichting ontstond de conduit-metafoor, een model waarbij communicatie een proces is waarbij conduits (objecten, containers) worden uitgewisseld die door iedereen te begrijpen kennis bevatten.
(2) De waarheid van een theorie is gebaseerd op de waarneming van dat wat gebeurt (een feit is een gebeurtenis (een geboorte)).
(3) De waarheid van een theorie is een mening, een waardering: “If we have Analyzed Judgment, we have solved the problem of Truth” (F.P. Ramsey, Fact and Propositions, 1927). Wat (belangrijke) mensen vinden (zoals de Paus of een Hoogleraar) is waar.
(4) De waarheid van een theorie is het gevolg van een persoonlijk inzicht. Vaak het resultaat van een waarom-vraag. Wat ik geloof is waar.
De vier kijken op de waarheid kunnen worden ondergebracht in een vierluik wat door Jung een Quaternio werd genoemd. Een Quaternio bestaat uit twee tegendelen en twee complementen.
Een Inzicht is het gevolg van een uitzicht, een waarneming die in een waargeving resulteert (Waar -> Weer, Beeld, Idee).
De waarheid is objectief (context-vrij) en subjectief (wat anderen er van vinden, context-afhankelijk).
Ervaring is wat de mens al doende in de werkelijkheid als afwijking van zijn eigen theorie, zijn Verwachting (Overtuiging), meemaakt. Ervaring is een persoonlijke reflectie op het persoonlijk handelen.
Een Community of Practice (CoP) lijkt erg veel op het Middeleeuwse Gilde met als groot verschil dat lokatie geen rol meer speelt zodat een Gilde niet meer bij een Stad hoeft te horen maar in theorie wereldwijd kan opereren.
Door de enorme schaal die nu optreedt is het vrijwel onmogelijk om een eenduidig definitie voor een gilde te formuleren waardoor er veel communities zijn die min of meer hetzelfde gebied betreffen.
Dit is voor een deel opgelost door de gildes om te zetten in Internationale Standaard/Beroeps Organisaties die zich bezig houden met het ontwikkelen van Normen. Normen zijn theorieen die door een groep mensen worden geaccepteerd.
De belangrijkste factor in een Gilde is het Delen van Fouten waardoor de Theorie van de Gezellen kan worden verbeterd. In de huidige tijd hebben mensen erg veel moeite met het delen van Fouten omdat Fouten maken wordt gezien als Falen.
De werkwijze om een eerste versie van een CoP op te zetten lijkt erg veel op het ontwikkelen van een Expert-Systeem, waarbij de Meesters en Gezellen de Experts zijn en de Fouten (Failures) door de leerlingen worden geleverd.
Aangezien iedereen een leerling is geweest kan iedereen een relatie leggen tussen een veelgemaakte fout en een oplossing van de fout.
In het algemeen maken mensen steeds weer dezelfde fouten als ze met een beroep beginnen behalve als de fout structureel in het ontwerp- en bouwproces is geadresseerd.
Op dit moment bestaan er miljoenen communities die kunnen worden getypeerd door de Menselijke Persoonlijkheid die een combinatie is van Kennis (Wikipedia), Ervaring (Praktijk), Relaties (Sociaal, Facebook) en Creatief (Inzicht, Interesse, Linkedin).
Een Gilde is een productie-systeem. In een product-systeem loopt de Cyclus rechtsom. Linksom gaat het om een consumptie-systeem. Beiden systemen houden elkaar in evenwicht bij het Hart (Communion/Wij).
Wat nu volgt zijn de sheets van de presentatie met toelichting in presentatievorm.
Het laatste plaatje voor de samenvatting laat zien dat er twee manieren zijn om de cyclus te doorlopen n.l. met de klok en tegen de klok. De eerste is de productie-cyclus en de tweede is de consumptie-cyclus.
Many people believe that the theor]]><![CDATA[y of Evolution is based on the concept of competition. They believe that every gene, every cell, and every organism is designed to promote its own evolutionary success at the expense of others.
The big problem with this concept is that it does not explain the enormous amount of cooperation that is visible in Nature.
Atoms cooperate in Molecules. Molecules cooperate in Genes. Genes cooperate in Chromosomes. Chromosomes cooperate in eukaryoticcells. Cells cooperate in Multicellular Organisms. Multi Cellular Organisms cooperate in Humans. Humans cooperate in Families and Tribes and Families and Tribes cooperate in Organizations and Nations.
The question of how natural selectioncan lead to cooperative behavior or reciprocal altruism has fascinated evolutionarybiologists for several decades.
When Charles Darwin was writing his famous book the Descent of Man (1871) he was already highly puzzled by the social structures of the ants. Their cooperative behavior was “one special difficulty, which at first appeared to me insuperable, and actually fatal to my theory”.
To solve his problem Darwin proposed that in the case of ant societies natural selection applies not to the individual, but to the family or group. The ants were part of a “Super-Organism”, that consists of genetically similar individuals.
Although many individuals showed altruistic behavior in the group the “genetic code” was replicated because the individuals in the group were all “look alikes”. The Ants were “the Same” (Similar) and therefore every Ant that survived promoted the Genes of the Community.
To explain his theory Darwin wrote ‘sympathy is directed solely towards members of the same community, and therefore towards known, and more or less loved members, but not all the individuals of the same species’.
For humans, both Spouses and best Friends are most similar on attributes with higher heritability. People join clubs and societies that contain similar people and adopt ideologies that work in their genetic selfinterest. Genetic similarity also explains voting behaviour.
The Human Detection Center of Genetic Similarity is situated in the amygdala a part of the Limbic Brain System that is involved in Fear and Arousal. The Amygdala activates the Sympathetic Nervous System responsible for the fight/flight-response of the Body. It prepares the body to get into action.
The recognition of another person depends on a long series of fast electrophysiological and slow biochemical reactions to the stimuli particular to that person or situation. These stimuli include seeing the other person’s face, hearing his voice, feeling his touch, and smelling his personal odors.
The reaction patterns of Humans to a fearfull situation are different. Some people, the Hawks, re-act very fast. They Fight and Compete. Some people, the Doves, re-act very slow. They Freeze, Flight or Cooperate.
To find the appropriate reaction-pattern every one of our senses works hard to identify “the other” or “the others“. The detection of “dangerous others” has to happen very fast. This is the task of the electrophysiological pathways.
A fast detection is unreliable therefore a second “slow” cognitive pathway is started. In the cortex the frightening stimulus is analyzed in detail, using stored information from many parts of the brain, and a message is sent back down to the amygdala.
To detect stimuli that are really dangerous the amygdala uses a memory. This memory contains learned and inherited, imprinted, situations. The imprinted situations are highly related to the detection of genetic similarity.
If an animal or a human is frequently attacked the memory contains many Painfull Situations and the amygdala reacts more specific to a situation. The older a person gets the more difficult it becomes to erase this memory.
If people or animals are unable to make a distinction between their Own Whole and the Whole of the Others it will result in a Blurring of the Identity. The Whole of the Observer Merges or Overlaps with the Whole of the Observed. If this happens people act in a “friendly“, Emphatic, mode and experience others as more “the same” than others do.
A Cooperative Strategy is highly related to the possibility of the Cognitive Part of the Human Detection-System to Move into the Other and Imagine what will Happen. The Hawks lack the ability to Imagine.
The most interesting concept that came out of Darwins Group Selection Theory is the Idea of the Super-Organism.
This Super Organism shows itself in many ways. Examples are the Family, the Tribe, Society and the Earth.
There is a similarity between the roles played by different organizations in Society and the functions of organs, systems and circuits in the body.
Industrial plants extract energy and building blocks from raw materials, just like the digestive system. Roads, railways and waterways transport these products from one part of the system to another one, just like the arteries and veins. Garbage dumps and sewage systems collect waste products, just like the colon and the bladder. The army and police protect the society against invaders and rogue elements, just like the immune system.
If we take the concept of the Super Organism a little bit further we could imagine the Super-Super-Super-Organism that contains all the other Organisms. In some way every Organism is Genetically Similar (“the Same“) to this Organism.
If this is true and the Theory of Group Selection is Right every Organism is an enfolding of the “Architecture of the Whole“, the Tree of Life, and a Majority of the Organisms (the Doves) will have an Altruistic Tendency to this Super-Organism.
The Doves Love, want to Unite With, the Whole and the Hawks dislike the Whole because they want to be a Whole themselves.
Some Scientists call the Super Organism, Gaia, Mother Earth, but there is no reason why we should not include the Bigger Structures in the Universe until we have reached the Boundary.
On every Level the Same Pattern appears.
On every level the Whole is splitted into Individual Parts. The parts live a Life of their own (Agency). When we Move UP the Parts are United (Communion) into a Bigger Structure.
When we look DOWN we interpret the proces of Splitting as a Competition. When we look UP we see a different pattern we Name “Cooperation“.
If we look at the history of the splitting process it looks like the wholes were splitted without any reason. It just happened. If we believe this Evolution is based on pure chance. Life is just a coincedence.
When we analyze the process of Evolution a Pattern emerges. This pattern is Cyclic, Leveled and Self-Referential. The process is almost invisible because with every Name we Utter we carve out a portion of the world and create a Boundary.
Every Time we Divide the World with Words the World becomes more complicated. Every New Concept that is not created without a View on the Pattern of the Whole generates a higher level of Confusion and increases the Complexity of Something that is really very Simple.
We create distinctions between Animals and Humans, Humans and Plants because the Hawkish Genes Want Us to Believe We Are Something Special.
Because of their Special Status the Hawks treat their fellow organisms in a very brutal way. They Exploit (Desire) them because of their Need to Control their Environment. They want to Control their Environment because they are Afraid to lose Control. They are Afraid that their Identity (Their Ego, Their Agency, Their Whole) will disappear when they Commune with the Whole.
The Effect of the Behavior of the Hawks is the Destruction of the Environment that they Fear so Much. They are destroying their own Mother Earth who is certainly one of the Super Organisms that gave birth to the many wholes that are just there to Enjoy her Care.
The big problem we have is Naming. What we don’t see or don’t want to see is that every Split is a Split in two Opposite Complementary Parts (Yin/not-Yin= Yang, Male/not-Male = Female, Cooperate/not-Cooperate = Compete) that Share the Void, the Empty Set, the State the Universe was in before it was created.
On every level the Nothing, the State of Infinite Potential and Love, is still there but it is hidden because we started to use Words, to describe what meant to be an Experience.
This brings us to the final conclusion.
The big problem that is treatening Mother Earth is Hawkish Behavior. In the long term this kind of behavior is not helping the Human Gene at all. It not only destroys the Human Gene. It destroys the complete group of genetic “Look-a-Likes” of the Human Gene.
Darwin was Right.
Altruistic Behavior, Cooperation, is the Only Way for the (Human) Genes to Survive.
Let us Help the Hawks to Erase their Fearfull Memories.
The Ancient Greeks believed that the images of waking life and dreams came from the same source, Morpheus (Μορφέας, Μορφεύς), “He who Shapes“.
The Science of the Shapes, Morphology, was created and named by Goethe in his botanical writings (“Zur Morphologie“, 1817).
Goethe used comparative anatomical methods, to discover a primal plant form that would contain all the others-the Urpflanze. Goethe being a Romantic Idealist hoped that Morphology would Unify Science and Art.
“The Primal Plant is going to be the strangest creature in the world, which Nature herself shall envy me. With this model and the key to it, it will be possible to go on forever inventing plants and know that their existence is logical”. “Nature always plays, and from which she produces her great variety. Had I the time in this brief span of life I am confident I could extend it to all the realms of Nature – the whole realm“.
Goethe observed nature and reflected on similar structures. He believed that there was something behind this similarity, an archetypal plant.
According to Goethe the archetypal plant was the leaf (“While walking in the Public Gardens of Palermo it came to me in a flash that in the organ of the plant which we are accustomed to call the leaf lies the true Proteus who can hide or reveal himself in all vegetal forms. From first to last the plant is nothing but leaf“).
At this moment scientists know the reason why the leaf is the most important structure of the plant. It is a solar collector full of photosynthetic cells.
The energy of the sun provides the energy to transform water from the roots gathered by the leafs and carbon dioxide out of the air also gathered by the leafs, into sugar and oxygen. Plants are structures with many leaves. These leafs shield other leafs from collecting sunlight and water.
To solve this problem a plant has to optimize its structure to collect enough Sunlight and Water. The process of Optimization is not a Central Coordinated action. Every leaf tries to find the best place in the Sun on its own. This place determinates the growth of the next level of branches and leafs.
Goethe observed a pattern and deduced a structure, the leaf, the Uhrplanze. What Goethe really observed was not a Static Uhrplant but the DynamicProcess of the Branching of all kinds of leaves in all kinds of plants (Morpho-Genesis).
The leafs of the plants are not the main target of the morphogenesis of the plant. The visible External and the invisible Internal Forms or Organs are one of the many solutions of an equation with many variables and constraints. The optimal solution is reached by experimenting (“Nature always plays”).
Many solutions fail but some survive (Evolution of the Fittest). When a solution survives it is used as a Foundation to find new rules for more specific problems (Specialization). When the environment, the context, changes old rules have to be replaced by new rules (a Paradigm Shift).
In 1931, in a monograph entitled On Formally Undecidable Propositions of Principia Mathematica and Related SystemsGödel proved that it is impossible to define a theory that is both Self-Consistent and Complete. The paper of Gödel destroyed the ambitions of the Mathematicians at that time to define one theory that explains everything.
In 1936 Alan Turing produced a paper entitled On Computable Numbers. In this paper Alan Turing defined a Universal Machine now called a Turing Machine. A Turing machine contains an infinite tape that can move backwards and forwards and a reading/writing device that changes the tape. The Turing Machine represents every Theory we can Imagine.
Turing proved that the kinds of questions the machine can not solve are about its own Performance. The machine is Unable to Reflect about Itself. It needs another independent machine, anObserver or Monitor to do this.
It can be proved that Turing proved the so called Incompleteness Theorem and the Undecidability Theorem of Gödel in a very simple way.
In 1943 Turing helped to Crack the Codes of the Germans in the Second World War. At that time the first computers were build (Eniac, Collossus).
It was very difficult to Program a Computer. This problem was solved when Noam Chomsky defined the Theory of Formal Grammars in 1955 (TheLogical Structure of Linguistic Theory).
When you want to define a Language you need two things, an Alphabet of symbols and Rules. The symbols are the End-Nodes (Terminals) of the Network of Possibilities that is produced when the Rules (Non-Terminals) are Applied. The Alphabet and the (Production- or Rewriting) rules are called a Formal Grammar.
If the Alphabet contains an “a” and a “p” the rules S→AAP, A→”a” and P→”p” produce the result “aap”. Of course this system can be replaced by the simple rule S→”aap”. The output becomes an infinite string when one of the rules contains a Self-Reference. The rules A→a and S→AS produce an Infinity String of “a’-s (“aaaaaaaaaaaaaaaaaa….”).
The system becomes more complicated when we put terminals and rules (non-terminals) on the Left Side. The System S→aBSc, S→abc, Ba→aB and Bb→bb produces strings like, “abc”, “aabbcc” and “aaabbbccc”. In fact it produces all the strings a**n/b**n/c**n with n>0.
The inventor of the theory of Formal Grammar, Chomsky, defined a Hierarchy of Languages. The most complex languages in his hierarchy are called Context-Dependent and Unrestricted. They represent complex networks of nodes.
A language where the left-hand side of each production rule consists of only a single nonterminal symbol is called a Context Free language. Context Free Languages are used to define Computer Languages. Context Free Languages are defined by a hierarchical structure of nodes. Human Languages are dependent on the context of the words that are spoken.
It is therefore impossible to describe a Human Language, Organisms, Organisations and Life Itself with a Context Free Computer Language.
Context Free Systems with very simple rule-systems produce natural and mathematical structures. The System A → AB, B → A models the Growth of Algae and the Fibonacci Numbers.
A Recognizer or Parser determinates if the output of a formal grammar is produced by the grammar. Parsers are used to check and translate a Program written in a Formal (Context Free) Language to the level of the Operating System of the Computer.
Regular and Context Free Grammars are easily recognized because the process of parsing is linear (causal, step by step). The stucture of the language is a hierarchy.
The recognizer (now called a Push-Down Machine) needs a small memory to keep the books.
Context Dependent (L-systems) and Unrestricted Grammars are difficult to recognize or are not recognizable in practice because the parser needs a huge sometimes Infinite Memory or Infinite Time to complete its task.
To find the Context the Recognizer has to jump backwards and forwards through the infinite string to detect the pattern.
If the network loops the recognizer will Never Stop (“The Halting Problem“).
Turing proved that the Halting Problem is Undecidable. We will Never Know for Sure if an Unrestricted Grammar contains Loops.
The Rules and the Output of Unrestricted Grammars Change and never stop Changing. Our Reality is certainly Context Dependent and perhaps Unrestricted.
Parsing or Recognizing looks like (is similar with) the process of Scientific Discovery. A theory, a Grammar of a Context-Free Systems (“aaaaaaaaaaa…”) is recognizable (testable) in Finite Time with a Finite Memory. Theories that are Context Dependent or Unrestricted cannot be proved although the Output of the Theory generates Our Observation of Nature. In this case we have to trust Practice and not Theory.
In 2002 the Mathematician Stephen Wolfram wrote the book A New Kind of Science.
In this book he tells about his long term Experiments with his own Mathematical Program Mathematica. Wolfram defined a System to Generate and Experiment with Cellular Automata.
Wolfram believes that the Science of the Future will be based on Trial and Error using Theory Generators (Genetic Algorithms). The big problem with Genetic Algorithms is that they generate patterns we are unable to understand. We cannot find Metaphors and Words to describe the Patterns in our Language System.
Leibniz believed that our Universe was based on Simple Understandable Rules that are capable of generating Highly Complex Systems.
It is now very clear that the Self-Referencial Structures, the Fractals, of Mandelbrot are the solution of this problem.
The Scientific Quest at this moment is to find the most simple Fractal Structure that is capable of explaining the Complexity of our Universe. It looks like this fractal has a lot to do with the Number 3.
It is sometimes impossible to define a structured process to recognize (to prove) a Grammar. Therefore it is impossible to detect the rules of Mother Nature by a Structured process. The rules of Mother Nature are detected by Chance just like Goethe discovered the Uhrplanze. Science looks a lot like (is similar with) Mother Nature Herself.
When a Grammar is detected it is possible to use this grammar as a Foundation to find new solutions for more specific problems (Specialization, Add More Rules) or when the system is not able to respond to its environment it has to Change the Rules (a Paradigm Shift). All the time the result of the System has to be compared with Mother Nature herself (Recognizing, Testing, Verification).
Turing proved that if Nature is equivalent to a Turing machine we, as parts of this machine, can not generate a complete description of its functioning.
In other words, a Turing machine, A Scientific Theory, can be a very useful tool to help humans design another, improved Turing Machine, A new Theory, but it is not capable of doing so on its own – A Scientific Theory, A System, can not answer Questions about Itself.
The solution to this problem is to Cooperate. Two or more (Human) Machines, A Group, are able to Reflect on the Other. When the new solution is found the members of the Group have to Adopt to the new solution to move on to a New Level of Understanding and drop their own Egoistic Theory.
Each of the individuals has to alter its Own Self and Adapt it to that of the Group. It is proved that Bacteria use this Strategy and are therefore unbeatable by our tactics to destroy them.
Turing proved that Intelligence requires Learning, which in turn requires the Human Machine to have sufficient Flexibility, including Self Alteration capabilities. It is further implied that the (Human) Machine should have the Freedom to make Mistakes.
Perfect Human Machines will never Detect the Patterns of Nature because they get Stuck in their Own Theory of Life.
The Only ONE who is able to Reflect on the Morphogenesis of Mother Nature is the Creator of the Creator of Mother Nature, The Void.
Gregory Chaitin used the theory of Chomsky and proved that we will never be able to understand The Void.
The Void is beyond our Limits of Reason. Therefore the first step in Creation will always be a Mystery.
At the end of his life (he commited suicide) Alan Turing started to investigate Morphology.
As you can see the Patterns of Alan Turing are created by combining many Triangels. The Triangel is called the Trinity in Ancient Sciences.
According to the Tao Tse King, “The Tao produced One; One produced Two; Two produced Three; Three produced All things”, which means that the Trinity is the Basic Fractal Pattern of the Universe.
In modern Science this pattern is called the Bronze Mean.
It generates so called Quasi Crystals and the Famous Penrose Tilings.
The Bronze Mean is represented by the Ancient Structure of the Sri Yantra (“Devine Machine”).
Goethe was not the real discoverer of Morphology. The knowledge was already there 8000 years ago.
One Cellar Creatures, Bacteria, have no need for a central Multi-Cellar Coordi]]><![CDATA[nation system, a Central Nervous System. Their only need is to find Food (Chemicals).
To find food they Move Around in the Chemical Soup with their Flagellum in a Chaotic Pattern (Creativity, Exploration) until they are Attracted by (Fall in Love with) a Source they Like.
When the Bacteria are Attracted by the Food, their Creative Behavior stops. The Chaotic Pattern changes into a Stable Cyclic Pattern.
The Movement of the Flagellum of the Bacterium is comparable with the Emotional System of the Human Being.
The Creative and the Emotional System are the Basic Systems of Nature. Conscioussness, the Feed Back Cycle, was there from the Beginning. Conscioussness, Creativity and Compassion are also the Basic Systems of the Human Being.
They are independent of Time and Place. In the first step of Evolution the Organisms where Connected and in the Now.
In the next step of Evolution two new Protective Systems came into existence, the Predictive System (Thinking) and the Sensory System.
They are related to the Multi-Cellar Organisms, the Organisms with a Brain and a Spine. The Protective Systems came into existence because the Organisms became Disconnected (Specialized) and started a Competition.
Although they may look plant-like, Sponges are the simplest and the oldest (635 million yrs) of the multi-cellular animals. Sponges evolved in shallow ocean basins, because the deeper seas did not yet contain oxygen, a necessity for almost all life.
At that time the Sponzes could live an Easy Life because there was no Competition from more complicated animals.
Sea sponges are not moving at all. They attach themselves to the sea bed and filter nutrients from the water that they force through their porous bodies with flagella.
Because of the Life-Style they lead sea sponges do not need, and therefore lack, nerve cells, muscle cells and internal organs of any kind.
The first step in the development of the Central Nervous System (CNS) is the Community. The Cells are coordinated by specialized interconnected nerve cells, the Nerve Net.
Although the Nerve Net allows the animal to respond to its environment, it has trouble alerting the animal from Where the Stimulus is Coming.
For this reason, simple animals with Nerve Nets always Respond in the Same way to Contact with an Object, regardless of where the contact occurs. The organisms coordinated by a Nerve Net are able to move in a Plane.
The next step is the development of organisms happened about 590 million years ago. At that moment the Central Coordinating System, the Brain, appeared.
Sea stars have a nerve net in each arm, connected by a Central Radial Nerve Ring at the center.
This is better suited to controlling more complex movements than a Diffuse Nerve Net.
The organisms with a CNS, the Bilateria, are able to Act and React to a Possible Harmful Stimulus.
They Move in the 3rd Dimension, endowing them with not only a top and a bottom, but a left and a right, and a front and a back. Therefore they are comparable to a Sphere.
The 3-Dimensional Bilateria make use of Five fluid filled Cavities (Spheres) to Protect the Organs and a Digestive Tube with a Mouth and an Anus.
The Bilateria (including the Humans) have Five Body Cavities: (1) the Brain; (2) the Spinal Cord; (3) the Heart and Lungs; (4) the Digestive Organs and Kidneys; (5) the Bladder and Reproductive organs.
The Five Spheres are incorporated in one Super Protective Sphere, the Coelum (Skin).
In the Human Embryo the First step of Division of the Cells is between the Coelum (the Multi-Cellar Body) and the Brain (CNS, Coordinating the Multi Cellar Body).
The CNS shows the greatest development in Vertebrates. In the vertebrates the CNS is protected by the Skeletal System.
The CNS is connected to the rest of the body through a peripheral nervous system that includes the nerves connecting the brain and spinal cord with Receptors such as the Ears and Eyes and Effectors such as the Muscles in the Body.
In the evolution of Vertebrates from Fish to Mammals, the most significant changes have occurred in the Structure of the Brain.
Even in the earliest vertebrates, the brain had three divisions: the Hindbrain, Midbrain, and Forebrain.
The Hindbrain is concerned with Motor Reflexes, the Effectors, the Muscles (the 2nd Dimension).
The Midbrain coordinates the Receptors (Eyes, 3rd Dimension). In the progression from Fish to Mammals, the Forebrain becomes more prominent.
The Forebrain is used for Receiving and Integrating Information to create a 4-Dimensional Picture of the Space/Time. This System is used to Predict the Causal Path of the Future. The Predictive System is fed by the experiences of the Past and tries to avoid Pain and Destruction. Its Basic Emotion is the Fear to lose Control.
At this moment the most advanced creatures on Earth, the Humans are able to operate in the Fourth Dimension. The Blueprint of the Organisms, the DNA, contains enough Junk DNA to reach into higher Dimensions. The next step is the Fifth Dimension. In this Dimension Space & Time Travel are possible.
Scientists recently discovered that the DNA of one of the most primitive and ancient Multi-Cellular creatures on Earth, the Sea Sponge, contains almost the Same Blueprint as the Central Nervous System of the Human Being.
Many people still believe the Evolution Theory of Darwin is Right. This theory states that the evolution of the species is governed by Random Mutation and Natural Selection. The discovery of the DNA of the Sponge shows a completely different view, the view of the much despised Lamarck.
Behind the seemingly Random Pattern of Evolution a highly stable (geometric fractal) structure, The Trinity Pattern, emerges. The DNA is not adapting to Evolution. It is the other way around. Evolution is an Enfolding of a Highly Stable Self Referencial (Fractal) Multi Dimensional Blueprint. This Blueprint was already there when the Universe was created. The Trinity Pattern shows that the basic structure of the Universe is an enfolding of Trinities in Trinities.
The Sequence of the Enfolding is controlled by a pattern called the Bronze Mean (1,1,4,13,43). The pattern is visible in the ancient Sri Yantra.
We are now in the 42th step of enfolding. The 43th step will create a completely new Universe.
In this step the Seven Seperate Multi-Verses of our Universes will Merge into One Structure that is connected to the Rotating Primal Void, the Sekhem.
If this step will occur we will be able to move out of the 4th dimension into the 5th, Space/Time.
The good thing is that many scientists especially the Physicists and the Mathematicians believe the Eternal Blueprint is there and will be found.
Many of them also believe that this Blueprint was already discovered a long time ago. In the next part of this blog I will continue with my discovery of the Old Egyptian Physics. We will see that the Old Egyptian Scientists were aware of the Patterns behind the Patterns.
What is Happening?
In the Beginning, 3.8 billion years ago, the Self Reproducing Central Coordination Sphere called Earth, moving in 4-dimensional Space/Time, was a “chemical soup“. When the Earth cooled down the Soup transformed itself into Self-Reproducing Cells, the Bacteria.
The Cells clustered into Self Reproducing Central Coordination Systems called Humans. In every step of the Evolution from Chemical Soup to Human a new Dimension of Space/Time was discovered. The next step must be a step into the 5th Dimension.
The Klein Bottle is just like the Moebius Ring a structure without an Up and a Down. The Klein Bottle is also a structure without an Inside and an Outside.
It is Closed in Itself just like the first God of Egypt Atum and the Serpent, the Ouroburos.
The most interesting feature of the Klein Bottle is the Void, the Singularity.
In current Physics a Singularity is called a Black Hole or Wormhole. In the Old Egyptian Science the Void was called the Sekhem.
When you read the article you will see that The Klein Bottle also explains the Ancient theory of Alchemy.
This theory was developed in Egypt by a person (or a God) called Thoth (or DJ-huti). The Greek changed his name in Hermes.
The Old Egyptians explain their theory by the Myths of the Pesedjet. The Ancient Narrative describes the whereabouts of Nine Deities (or Concepts). Two of them are named Isis and Osiris. Osiris is the God of the Resurrection. Isis is the Mother Goddess.
In the next step of the story Isis and Osiris give birth to a child called Horus.
Horus is the Symbol of the Human Body. Isis is represented in Catholic Tradition by Mary, the Black Madonna. In most representations she is depicted with her Child (Horus, Jezus).
The Four Suns of Horus are the symbols of the Four Organs situated in the Four Cavities of the Human Body.
The last Fifth Cavity of the Human Body, The Brain and the Spinal Cord protected by the Backbone is represented by a symbol called the Djed Pillar. The Djed Pillar was one of the most Magical Symbols in Egypt.
The Five Cavaties correspond with the Five Organs in Acupuncture. Acupunture is an Ancient Chinese Medical Treatment to cure and stabilize the Electro Magnetic Body of the Human. The Cavities now called Cells also exist in the Universe. They are the Birth Places of Star Clusters.
Why is the Djed Pillar such an Important Concept?
The name Djed contains the term DJ meaning Serpent. Dj comes back in Dj-huti (Thoth/Hermes), Dj-inn (a Magical Serpent Ghost) and Djedi (An Egyptian Magician).
The name Djedi was used in the famous Movie Star Wars. The Djedi are called the Skywalkers because they are able use the Power of the Serpent to move in Space/Time, the Fifth Dimension.
In other cultures the Serpent Power is called the Kundalini.
The Serpent or the Kundalini is a Tremendous Power that rests in the Spinal Chord at the place of the Sacrum, the first part of the Spine.
At this place the first Chakra, the Muladhara is situated. The Muladhara Chakra is made of the Earth Element and represents the Beginning of Life (the Chemical Soup).
When awakened and nourished, this association with the Earth element manifests itself as a Electro Magnetic Force within that person.
One of the most important secret rituals in the Cult of Osiris was called the Raising of the Djed. When you Raise Your Backbone you are opening the Path of the Serpent to let the Electro Magnetic Field of Mother Earth move you to the Fifth Dimension.
What is the Physical Explanation of the Serpent Energy?
The Earth is a huge magnetic sphere. The E/M field of the Earth varies in strength and consistency through the ages. Our bodies own magnetic frequencies and our bio-field patterns react to this variance of the Earth’s field.
The pineal gland, the Eye of Horus (or the Horn of the Unicorn), is the “clock” that controls biological cycles. The Eye of Horus stands for the sixth chakra.
The pineal gland is the principal structure in the brain that is directly sensitive to the Earth’s magnetic field.
The pineal gland produces a host of psychoactive chemicals (such as Melatonin, Dopamine, Serotonin, and others).
Its abnormal functioning may result in a variety of Physical (the Immune System), Neurological (Tremors) and Psychological (Psychosis) Problems including Mystical and Para-Normal Experiences.
Our bone structure Converts Vibrational Energy, such as sound or light, into Magnetic and Electric Energy. When the bone is bent it produces an E/M-field. This E/M-field interacts with the Pineal Gland and creates a Feed-Back Cycle.
The E/M-field of our Body, the Aura, is a combination of all kind of waves. A special type of wave-structure is called a Standing Wave.
When the E/M-field acts as a Standing Wave all the waves are in harmony and conserve structure. The Human body is in harmony when the total field of all the separate E/M-fields of the Body act as a Standing Wave.
The Standing Wave appears when the Spinal Wave of the Vertebrae of the Body is in a special Alignment. This alignment happens when the Djed is Raised.
If this happens the Standing Wave of the Spine Resonates with the Standing Wave of the Earth. At that moment the Kundalini Rises and the Pineal Gland reacts with a Huge Mystical Experience.
What was the Aim of the Djedi?
The E/M-field of the Earth is different at every place on Earth. It also changes every day because of the influence of the Moon, the Sun and other powerful fields in the Universe.
At a certain moment in Time, at a certain place on Earth and with the help of special instruments (The Pyramid of Giza, the BnBn Stone) the old Egyptian Magicians, the Djedi, imagined it would be possible to resonate with the Standing Wave of the Center of our Galaxy situated in the Pleiades.
If this happens it will generate a tremendous, almost deadly, Mystical Experience, a giant influx of the Serpent of the Galaxy (the Black Hole) also called the Phoenix (Greek) or the Bennu Bird (Egyptian).
To endure this experience the Mystical Body, the Sahu, the Resurrection Body of Osiris, the Barque of the Sekhem, has to be available. The Sahu, the Light Body, is activated when the Djedi has balanced his chakras in the middle, the Heart Chakra. To experience a mystical union with the One, the Djedi has to live from the Heart.
At that moment the Skywalker will become Immortal. He will Climb Jacobs Ladder, move through the Einstein-Rosen Bridge (Sekhem, Bindu, Wormhole) into our (Black Matter) Twin Universe, the Underworld, the Nagual, the Duat, the Daad, Heaven, the Place where the Souls Live.
This Special Alignment of the Stars, The Galactic Cross, the Return of the Galactic Serpent, is the Moment the Egyptian Djedi, the Pharaos in their Coffin, the Jews (The Coming of Christ), the Muslims (the Coming of Christ), the Christians (the Return of Christ, the Resurrection), the Mayas (the Return of Quetzalcoatl, the End of the Maya Calendar, 2012), the Hopis (the Fifth World) and many other cultures are waiting for for a very long time.
A Last Remark
The E/M-field of the Earth is at this moment heavily influenced by human activities. Especially the strong fields of the Mobile Infrastructure on Earth have a devastating impact on the harmony of the Human Body. Project yourself!
The belief in Rational Decision Making has been the focus of Economic Theory for a very long time.
Although everybody knew that Humans are Highly Impulsive and Emotional, Economists based their theoretical models of the Market on a Rational Human Being who is always able to Calculate the best Alternative possible. This Theory is wrong. The Economic Behavior is controlled by the Emotions.
The current economic crisis shows that the old Rational Theory is not applicable and the attention for alternative theories of Economic Behavior is rising. These theories are called Behavioral Economics.
An important paper in the development of behavioral economics was written by Kahneman and Tversky in 1979 (Prospect Theory, Analysis of Decision Under Risk). Kahneman was awarded the 2002 Nobel Prize in Economics for his research in Prospect Theory.
According to Prospect Theory, Humans attach much greater weight to future losses than to future gains related to their personal reference point. When you expect a certain gain in the future and this gain is lower than you expect the gain is experienced as a loss.
Kahmeman and Tversky became the experts on Cognitive Bias. A Bias is a “not-rational” mostly fast response to a stressful situation. In this case the Human System uses old structures (The Reptile Brain) that were created a very long time ago when the human lived in a completely different environment. The Reptile Brain uses many shortcuts to save time.
Social and cognitive psychologists have identified a number of predictable errors in the ways that humans judge situations and evaluate risks. Biases have been documented both in the laboratory and in the real world. For example, people are prone to exaggerating their strengths: About 80 percent of us believe that our driving skills are better than average.
In 2009 Kahneman and Renshon wrote a paper called Hawkish Biases. It is an attempt to unite the many Cognitive Biases into one Model. The model shows that Humans are highly Confused Predators (Hawks).
As a Predator they protect their Territory with every means possible. They are Confused because they are capable to Observe and Reason about their own behavior and the behavior of others.
Humans need the “Illusion of Control” to sustain their own Identity. Every time something happens they are looking for reasons to believe that they are the Primary Actor in their own context. They don’t want to believe that Other Human Beings are also Active Agents.
If they would believe this was the case their “Unrealistic Optimism” could change into “Realistic Pessimism”. Unrealistic Optimism makes managers, politicians and generals receptive to advisors who offer highly favorable estimates of the outcomes. Such a predisposition, often shared by leaders on both sides of a conflict, is likely to produce a disaster.
When a Human is Depressed by Realism he Loses his Face and moves down in the Picking Order of the Territory.
Humans believe that every other Human is always capable to see their Weaknesses (“the Illusion of Transparency“) just like they are convinced that the intentions of others are always clear to them (“the Fundamental Attribution Error“). To hide their Weaknesses they have to wear a Mask and Play the Strong Leader of the Pack. They have to Keep Up their Appearances.
Humans base their theory of the other on inferences about historical behavior and completely forget Situational aspects. When a context is hostile the other must be hostile too. When others behave differently from their expectations they suddenly introduce situational factors to sustain their believe system.
Humans need to sustain their believe-system because this system is the foundation of their personality. Their view on the World has to stay constant because when it changes too fast they will get into big psychological problems. When people get older their believe-system becomes very rigid.
Humans value their own possessions much higher as the possessions of others (“TheEndowment Effect”). They even consider possible, imaginary, possessions as real possessions if they are convinced there is an easy way to get them.
If they lose a real or imaginary possession they take tremendous risks to get their possessions back (“Risk Seeking in Losses“). People in general don’t like cutting their losses. They’re willing to gamble on in the hope of recovering them.
Humans simply believe that a Hawk always wins the Game and a Dove always loses. What Humans (want to) forget is that they are living in a group and their In-Group and the many Out-Groups contains many Hawks. They need the confidence that they are “the best” to Survive.
The world of the Human Hawk is a world of Competition (Winner takes all) and therefore highly Stressful. The Sad Thing is that the many faces of Stress are the Major Cause of the Cognitive Bias. When Humans relax and reflect they are much more capable to solve a complicated conflict.
The competitive Hawks always fall in the trap of the Prisoners Dilemma and don’t realize that Cooperation, the Win-Win is the only Certain Way to Leave the Prison.
At this moment another Behavioral Economist, Robert Shiller, is getting a lot of attention. Together with the Economic Nobel Prize Winner George Akerlof he wrote the book “Animal Spirits“.
In the book they identify five distinct elements that blur the theory of the Rational Economy. These elements or “animal spirits” are called: confidence, fairness, corruption; money illusion and the reliance on “stories”of others.
The first three have a lot to do with the “hawk“-theory of Kahneman. The Hawks use the Rational System for their own benifit. They Play with the Rules and invent new exiting possibilities to win more than they ever could imagine.
Sometimes they Play Dirty Games to beat their Opponents. The Doves believe the Economic (Rational) Fairy Tales of the Hawks and are unable to understand the Real Value of their Money.
The Money Illusion is caused by Inflation. Inflation happens when prices Rise but the value of the objects that are priced stays the same. Inflation give people the feeling that they are making money but in reality they are losing money.
The Hawks use Inflation to keep the Doves Buying and Investing. They also use the weapon of Inflation to win the war with the other Hawks.
The Majority of the Human Beings are Doves. They believe the Hawks or are afraid of the Hawks. The Doves are the Workers in the Economy and they make it possible for the Hawks to Hunt.
The Hawks provide the Workers with many things to live an easy life until other Hawks start to Attack the Territory. In this case the Hawks need the Workers to fight and win the War.
Sometimes even the Hawks lose their Rational Capacity. They see a Big Win and become Greedy and Vulnerable. If this happens the Territory is open for other Hawks (The Chinese?) to enter and to take over without any problem.
What has Happened?
The Economic System is just like the Weather System a Cyclic System. When the Economic Cycles and the Weather Systems move UP the Hawks have an Easy Time. Their is enough food for all the Hawks. When the System is going Down Competition starts.
The Hawks forgot to look at the patterns. They did not see or believe that the downfall was approaching. They did not take enough stock to survive the Seven Bad Years. Suddenly the Autumn turned into Winter.
At this moment they are regrouping to create a Powerfull Alliance to take from the other Hawks what they need. They don’t care about the Doves. They always believe the Tales they Tell.
They are afraid of the Other Hawks that are outside their Huge Territory and are Prepared to Fight the Wars that are needed. The Doves will believe them as usual.
The Movie the Matrix states an ancient belief that we are living in a Dream World.
In the old Gnostic version the Matrix is created by the Demiurg, the Creator of our Material Universe.
In the new version the Dream World is created by a Computer Simulator.
At this moment Physicists and Mathematicians are exploring the Concept of the Matrix and are achieving remarkable results.
One of these scientists is Reginald Cahill. He has developed a challenging theory called Process Physics.
One of the most important experiments in Physics was the Michelson and Morley experiment in 1887. The aim of this experiment was to discover the speed of the Ether. At that time the physicists believed space (ether) was moving. The result of the experiment was spectacular.
Michelson and Morley found that the speed of Light was a constant (now called c) and the Ether (Space) was empty and static.
Cahill (and many others) analyzed the experiments and many other comparable experiments and detected a fatal error. The fatal error was a scientific “script”, the theory of Newton.
At that time Quantum Mechanics was not invented. Cahill found what they were looking for, the Absolute Motion of Space.
The result of the Michelson and Morley Experiment was used by Einstein in 1905 to create his Special Theory of Relativity.
This theory has been verified by many experiments so almost nobody started to question the theory of Einstein. Cahill proved that the absolute motion of space is not contradictory to the experiments that verified the theory of Einstein. Einstein was totally wrong!
Everything that is, is Space itself and Space is generating Space. This statement is a “self-reference” and can be formulated as an iterative function Space (i) = Function (Space (i-1)) + Randomness.
This Randomness is the result of Quantum Mechanics.
Every Self-Propelling Extension of Space has a Free Will to choose a “direction”. This “direction” can be organized as a causal system in which case Time appears. In general “space” is trying to create a Space-Time that is the most predictable to give the objects in Space-Time a change to survive and grow.
Cahill found the “Function” and suddenly many disjoint fields of physics were united. Like every other big “paradigm shift” the theory of Cahill is officially banned.
Attacking Einstein is “not-done” because when the foundation of Einstein falls the new (old) Physics falls apart
The paradigm shift of Cahill is not really a paradigm shift at all. It brings Physics back to a very ancient track that was abandoned a 100 years ago.
What is happening?
Space now called Quantum Foam is creating Space. In this process of continuous creation every possible form is created.
Space is Relational, a connector of forms, and the connectors have a lot in common with the cells in our body. The fabric of Space is self-referential which means that the creative pattern behind every form is basically the same.
Cahill shows that the creation of space, the creation of the Stars and the Planets, the creation of the body and the cells is based on the same iterative process.
This process can be seen as the calculation of a very fast quantum-computer that is creating itself. Cahill has discovered the software-design of the Matrix.
The interpretation of the output of the quantum-computer is done by a conscious mind but the conscious mind is also the output of the quantum computer.
The feedback-loops in the cell-like structures of self-propelling space can be seen as a giant mind (a neural network) that is split in many (in)dependent minds. One of these minds is the mind of the Human but cells, the body, the brain, earth, our galaxy and the universe are also mindful.
What we are able to see depends on what we are able to see. If we want to look through the lens of Special Relativity we are able to get a long way. At some point we get stuck.
Our interpretation system is desperately trying to fit our experiments with our theory. We measure what we want to see and we are able to get a long way. We develop instruments that contain our current theory and we prove the theory we want to prove.
Is there an end to our Interpretation System?
Our interpretation system fails if we don’t see a structure anymore. At that moment we think our interpretation system is seeing Chaos but Chaos is non-existent. Chaos is an interpretation of something we don’t understand.
The Limits of Chaos are just like Space extending every time we embrace a new form. Our Knowledge of our Reality expands just like the creator of forms, space, is expanding.
There is a Limit to our Understanding. This limit is the smallest self-referential pattern that is able to generate every form there is. Finding this pattern, the Essence, is the Quest of Mathematics.
One of the most briljant mathematicians, Stephen Wolfram, the founder of Mathematica, a software package to program mathematics has spend many years, playing with his own software, to find this pattern. He even created a complete new science, a New Kind of Science, to explore this issue.
The mathematician Chaitin has proved that we, the Humans, are unable to find this pattern, with the help of programming languages and computers. He proves that we are able to get a long way but at a certain moment Time is going to bother us. We will simply not be able to beat the speed of the creative wave of ever expanding Space.
Is there an end to the expansion of space?
In our current thinking space looks like a bubble and bubbles can be expanded into eternity. The new forms of space are different.
The interpretation of space is changing and space could be expanding until eternity in a closed system.
Space could be bounded by itself. It is not impossible that space could find another form to expand again and again.
If space is creative and mindful it could create every space that is possible but we the Humans have no idea what this could be because we are moving behind space itself.
If we could become space itself we could imagine everything we wanted.
How could we move out of the Matrix?
We are a part of the consciousness that contains the consciousness that..
If we merge the splits in our simulated consciousness and merge the splits between our consciousness and the conscioussness of the other simulated consciousnesses and ….we could move out of the Matrix.
What are we doing in the Simulator?
The ancient Gnostic Mystics believed that Our Universe was created by the Demiurg, the Great Architect. The Demiurg was a “high level’ Consciousness who was allowed by the Creator (The Light, The Void) to create a Universe that would speed up the awareness of many “splitted” consciousnesses, The Sparks of the Light.
The Earth Simulator is a Learning Device and every Soul is allowed to enter the Simulator to (re-)play a Game.
When the Soul enters the Matrix his memory of past lives, other games playd, is erased (the Veil). On Earth we are playing the Games we have chosen. When you are aware of the Game you are able to move out of the Simulator to move to another place to play different games of creation.
What are the possibilities when you leave the Simulator?
Create Your Own Universe. You don’t need to be a Game Designer to do this. The Simulator is already in place and Old Designs are never repeated in the Multi-Universe.
You can always find an infinite amount of equations that fits a finite set of points.
When the set of points changes the equation changes. This represents a major problem when you want to find a general pattern. The solution is to assume that the pattern behind the set of points has to be a Simple Equation (or a Simple Law).
A theory has to be simpler than the data it explains, otherwise it does not explain anything.
To define Simplicity we have to define a tool that measures the simplicity of an equation. Mathematicians have tried to solve this problem in many different ways. The problem seamed unsolvable until computers and software-languages were invented.
A law of nature is a piece of software, a computer algorithm, and instead of trying to measure the complexity of a law via the size of an equation, we now consider the size of programs, the number of bits in the software that implements a theory.
If every theory is represented by a string of bits we are able to analyze what a computer (our “thinking mind”) is able to represent. The problem is transformed to the problem of representation. Behind this problem lies the problem of Compression.
Our Reality is represented by the simplest equation (the shortest (most compressed) binary set) that when it is expanded represents the most complex binary set that represents our reality.
One of the conditions we have to add is the condition of “understand ability”. Perhaps the expression exists but we are unable to grasp the law. Leibniz calls this law the principle of sufficient reason.
Leibniz formulated this principle as follows: “Dieu a choisi celuy qui est… le plus simple en hypotheses et le plus riche en phenomenes” (God has chosen that which is the most simple in hypotheses and the most rich in phenomena)”. “Mais quand une regle est fort composée, ce qui luy est conforme, passe pour irrégulier” (But when a rule is extremely complex, that which conforms to it passes for random)”.
The interesting point in the statements of Leibniz is de term “irrégulier“. It is translated by the term “random“. This term can be interpreted in many ways. In the world of Statistics it means that a certain event is unpredictable. In algorithmic terms it means that we are unable to find a pattern behind the pattern we observe. A random pattern is an essential pattern. It cannot be compressed.
Science ends when we have found randomness and have reached the Limits of Reason.
Everybody has a Limit of Reason and this limit expands in time but for every mind that will be born there is an absolute limit of Reason. When we have reached this limit we will know there are still patterns to find but we will be unable to prove they are real patterns.
By running a program you can eventually discover that it halts, if it halts. When it halts you have found a theory. The problem is to decide when to give up on a program that does not halt.
A great many special cases can be solved, but Turing showed that a general solution is impossible. No algorithm, no mathematical theory, can ever tell us which programs will halt and which will not.
We are never certain that we have found a theory because when we wait a little longer (collect more facts) we find the final theory that explains what we want to explain (if we understand the theory).
We could use a computer to search for patterns (this happens already) but the computer presents an incomprehensible theory (this happens already) or it has to search a little longer. A computer could run “for ever” when there is enough energy but a human has a fixed lifetime. The halting problem shows that we will not know how long “for ever” is. We also will not have enough minds to analyze the output. The Halting problem is proved to be unsolvable.
Chaitin defined a constant Ω that shows our progress in reaching the Limit of Reason. It shows our progress to reach the Incomprehensible.
We still have a long way to go.
The Halting Problem cannot be solved because we (the Humans) are unable to define the Limits of Reason. Even the Brightest Minds will not be able to understand all the patterns that are available in Our Universe. Even Mechanical Devices programmed by the Brightest minds will not solve the Mystery. Somewhere we will make a Mistake.
The Mistake will start a new process of Inquiry and New Theories will be created that will always contain a Mistake. We will be Busy until Enternity to Create because we are not perfect. Only Perfect Solutions are Impossible.
I want to close this blog with a statement of Leibniz: ”Sans les mathématiques on ne pénètre point au fond de la philosophie. Sans la philosophie on ne pénètre point au fond des mathématiques. Sans les deux on ne pénètre au fond de rien”(Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything)”.