Posts Tagged ‘chaos’

About Chaos

Saturday, December 13th, 2008

tornadoHumans are desperately trying to preserve their Identity. To do this they create Order.

Behind every Order is non-Order, Chaos, the creative, destructive, force.

If the Human Order is gone, psychologists, try to Unite the broken pieces of the chaotic Personality.

If the Banking System is extremely volatile Economists believe they are able to repair the System.

If the Ecology is chaotic Biologists are doing the same. All of them believe they found a way to transform Chaos into Order.

Creating Chaos is not very difficult. One act of a small group of terrorists almost destroys the System of Society and the only way to prevent chaos is to create a higher level of order. One Act of God, an earthquake, a tornado or the outbreak of a virus, accomplishes the same.

Chaos and Order are part of the same System and we really don’t know how to unite the two perspectives on Nature.

When we want to keep Internal Order we put Chaos outside the boundaries of our own System. We move out of the chaotic city to the countryside to experience the Harmony of Nature.

We stop reading newspapers and stop watching television because we don’t want to see what is really happening outside. We don’t want to face the reality that the outside reality is a frightful, destructive place to live in but what is most of all frightening us is our own destructive part, the Shadow.

earthquakeSpace has always been the metaphor in which we project our Identity.

Our personality, our house, our job, our relationship, our culture, our country are protective boundaries but at this moment many of these protective boundaries are at stake.

The current crisis forces us to leave our home and our job.

The clash of the many cultures threatens our own culture and even our own country is gone because politicians are creating abstract countries that have no history and still no future.

The concept of Space is changing and with this our idea about our own boundary is changing.

Space is not a static state in which we live. Space is a dynamic process and is created and destructed. Space moves and because space is moving we are moved also. Every time a new order appears but we are not able to understand this order because we are caught in our own order.

A static personality is not able to adapt to the moving outside world. A personality who is not able to move has to stay at the place where he lives. A personality who is not able to be moved by what is happening is without Emotions and the Emotions are Chaotic.

The Chaotic Emotions are in direct contact with Space. They feel what is going to happen. They know when it is time to move but the Order of our personality is telling fairy-tales based on its experience of the Past. The Chaos will certainly change into Order. The Up will always follow the Down but Up and Down are Space-Dependent.

Many people are on the move. They know for sure that their Space/Time is not the Place to be. The order of our personality tells us that we have to protect our secure environment and create a protective or imaginary Wall.

EtnaIf somebody or something attacks our Personal Boundary our re-action is sometimes highly destructive. Our Order is much more important than their Order.

When we are aware of our bad intentions our Order creates a new fairy-tale to silence our Empathic Emotions. We are always able to find a very convincing explanation why we are the good they are the bad.

What we don’t understand is that our Chaotic Component, the Creative Force, is able to find a solution that is out of the existing order.

Mathematicians know for a long time that Order and Chaos are not their opposites. They are different states of the same function. Order and Chaos rise out of recursive or fractal functions.

Order and Chaos are created by an Order but this order is invisible to many people because they don’t know how to look. They look at the world with a view that was abandoned about 2000 years ago. Before that time people knew about the fractal pattern. They used many metaphors out of Nature to explain the pattern.

What is happening?

TsunamiThe fractal pattern is in its chaotic state and is moving to a new enfolding. The new enfolding will be very different from the old enfolding when you look at it through the old lens of Linear Space/Time but it will be a very old-fashioned State when you understand the Fractal Pattern.

What to do?

When the Script of Nature is its chaotic state you can do nothing. The Future is unpredictable when you use the old tools of statistics. They cannot handle fractal systems. In a Chaotic state The Past has no relation with the Future.

When the Script of Nature is its chaotic state you have to believe that Destiny will take care of you. You just Wait and See. If you run to the left order will appear at the right. When you run to the right order will appear at the left. There is no Place to Go.

If you don’t believe in Destiny you have to use the knowledge of the chaotic part of your personality, Intuition. The Intuition moves with the enfolding of the Fractal Pattern and it knows what to do at the right moment. It knows when there is a little bit of order in the chaotic movement and it knows where to go and what to do.

If you don’t believe in Destiny you have to use the destructive part of your Personality, the Creative Force, but you have to balance this part with your Empathy (The Emotions). Both of them emanate from the same Source.

LINKS

About Dynamic Space

About Boundaries

About the Triple Goddess

About Alchemy

Wednesday, December 10th, 2008

alchemyWhen I studied Chemistry at the University of Leiden I wanted to learn more about “Ancient Chemistry“.

At that time I really did not understand the Symbolism behind Alchemy. This changed a few years later when I encountered Jung. Suddenly Alchemy moved to the Social Sciences.

At this moment I am convinced modern Mathematics and Physics are exploring the same issue Jung and many others Alchemists were exploring.

The Material World and the Spiritual World are both based on the same principles. They only operate on different Levels.

When you understand one level it is not so difficult to map this level to another level. The real big problem is to map the simplicity of the parts to the complexity of the Whole.

Human understanding is based on our Imagination. When you are not capable to visualize the Parts and the Whole you are lost. The old Alchemist understood this problem and they produced many visual metaphors to help the explorer of the Spiritual Domain.

ouroborosThe most important unifying concept in Alchemy is represented by the Snake Ouroboros. The Snake is “Eating Itself“.

When you try to imagine what is happening you will understand that the Snake will be spiraling inwards until it simply vanishes.

You also could imagine that the Snake appears again in another “space” where it starts to spiral outwards until it moves back to our reality.

By “eating itself” the Snake is “compressed” into what is now called a “singularity” (A Black Hole).

klein bottleIn the other (Imaginary) world the Snake expands and spirals through another hole (A White Hole) back into Our Reality.

The Imaginary Universe is the Twin Universe of Our Universe.

If the Imaginary Universe is represented by the Complex or Imaginary Numbers there is also an In-Between or Joint Universe.

This Universe existst in a higher dimension. We are able to experience the Real Part of the Numbers. Our Twins only see the Imaginary parts.

The aim of the process of Alchemy is to move through the singularity to another Space/Time. In this Space/Time you are “immortal”. This Space/Time is the Imaginary World of Mathematics, the Complex Plane.

holy weddingTo Reach the World of Immortality You have to Unite the Opposites. Alchemy uses many Metaphors to show how this is accomplished. One of them is the Holy Wedding. In the Holy Wedding the Male and the Female Unite.

It is very important to understand what the Alchemists meant with the Male and the Female. Of course the first interpretation is simply the Human Male and the Human Female.

In this case the Holy Wedding is a sexual metaphor. The Male and the Female Unite when they have Sexual Intercourse.

In Sacred Sexual Intercourse, Tantra, something called the Kundalini, the Serpent Power, is activated.

Awakening the Kundalini without a good Preperation (Psychological Cleaning) and a Good Guidance is very dangerous.

The Rising of the Kundalini will generate tremendous energies (Extreme Heating) and intense Psychological Disturbances, the Kundalini-Syndrome.

Although Sacred Sexual Intercourse is a very powerful tool for Enlightment it is still not the Right Metaphor.

The Male and the Female have to be seen as complementary functions. The Male represents Order/Control and the Female Chaos/Desire. The complementary functions are independent of the sexes. A Female Human is perfectly able to act with a (Dominant) Male Pattern.

Uniting Male and Female is accomplished when you Live on the Edge (in the Middle) of Control/Order and Chaos/Desire (Wu-Wei). When Chaos and Order are in Balance the Union of Both Forces, The Void (also called the Tao), takes over and Synchronicity starts to Happen. The Human Action is Guided by a Higher Force, the Holy Spirit.

pentagleThe Human can also be viewed as a FiveFold Being (The Pentagram). In this case the Human is a combination of Male/Male (Control), Female/Female (Desire) AND Male/Female and Female/Male.

At the Center (In the Middle, At the Cross) of the Four Combinations is always the One, The Void. Most of the time the “new” combinations are called Soul and Spirit.

To Understand this process a little bit better we will change the Metaphor of the Sexes to the Metaphor of the Movements (Up & Down, Inside & Outside). The Opposite Movements are a Tension, that is Voided in the Middle.

Inside Outside
Up Up/Inside (Spirit) Up/Outside (Control)
Down Down/Inside (Soul) Down/Outside (Desire)

When there are Four Movements in Action, there are Six Ways to Integrate the Two Opposites and there are many more ways to combine the Six Ways into a Four Fold Integration. One of the most effectives ways to do this is to travel the Matrix in a Circular Motion(○) With or Against the Clock or by Circulating the Cross following the Pattern of the Moebius Ring (∞) also With or Against the Clock.

To move from the Mortal to the Immortal, Timeless, Domain we have to apply the Ouroboros-pattern. This is accomplished by connecting the Circulations of the Circle or the Moebius Ring at the Singularity, The Middle of the Cross. The circulations move against or with the Clock.

We are now moving from a 2-dimensional Matrix to a 3-dimensional Cube. To avoid confusion we have to define a third terminology for the two opposite Movements. In many cultures the directions of the Winds are used (East, West, North, South) combined with Up and Down but it is up to You to find other Terms.

It is still possible to visualize this structure in 3-dimensional space. This structure is called by the Topologists, The Klein Botlle. The Klein Bottle is a connection of two complementary Moebius Rings with the Void in the Middle.

There are of course other metaphors available to explain what is “happening”. The most interesting ia a Physical Metaphor. It is called the Holographic Universe.

In the Holographic Universe the Hologram is used as a methaphor. A Hologram is a 3-dimensional picture stored in a rotating 2-dimensional structure. A “grain of sand” could contain the complete image of the Universe.

In the Holographic Universe Time is not Linear or Cyclic. The Now expands into the Past and the Future. We are able to change the Past and the Future with our Imagination. Time Travel is possible if we are able to find the same point in the Multi-Universe we started our Travel. The Humans also exists in many Space/Times at the same Moment, The Now.

We are able to see with our (Higher) Conscioussnes the Complete Network of Time Loops that are enfolding in the weird structure that has no Inside and Outside.

Many people still live in the Hierarchical Word, where the Movements are always going Up. They believe in a beginning and an end and believe that every Cause has an Effect. Some people, The Holists (New Age), moved from the Outside to the Inside. To them everything is Energy and Reality is a Circle. They are the people of Soul and Spirit. The Holists believe in the Wheel of Karma or the Wheel of Destiny.

The new Age of Aquarius will be a completely different world. We, the Humans, are not moving around in the Merry Go Round that is created by the Gods. We will be the Co-Creators of the Creative Force that is in the Center of the Wheel.

We are the Whole AND the Part. We are the Cycle AND we are Not the Cycle. We will take part in a new enfolding of the Self-Reference, that is Whole and Empty.

Hierarchical Cyclic Holographic
Movements are always going Up Movements go Up and Down Self-Reference
Triangle/Pyramid/Cube/Tube Circle/Torus Moebius Ring/Klein Bottle
Causal/Linear Cyclic/Spiraling Closed in Itself
Creation Compression/Expansion Enfolding
Evolution Growth and Decay Continuous Creation
Outside Inside and Outside No Inside and Outside
Part/Whole Wave Fractal
Everything is Different Everything is the Same (Make a) Difference
Individual Collective Whole
Control/Desire Soul/ Spirit Center

 

LINKS

About the Kundalini Syndrome

About the Klein Bottle and Alchemy

About our Imaginary Twin Universe

About the Relationship between Alchemy, Tantra and The Gnostics

About the Holy Wedding

All You Want to Know About Alchemy

About Alchemy

The Gnostic Science of Alchemy

Dimension of Apeiron by Steven M. Rosen

About The Limits of Reason

Sunday, August 3rd, 2008

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.

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz

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.

Gregory Chaitin
Gregory Chaitin

Gregory Chaitin is the expert of the Limits of Reason and he is highly influenced by Leibniz.

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)”.

LINKS

George Chaitin about the Principle of Sufficient Reason

About  Geometry and Fractal Patterns

About Formal Languages and Mistakes 

About the Quest for the perfect language (A Talk of Chaitin about the book of Umberto Ecco)

Leibniz forgot to mention the role of the Artist

About Leibniz and Deleuze

About Turing Machines

The Relationship between Chaos Theory, Fractals, Lyapunov, Minkowski and the TAO

Thursday, November 1st, 2007

chaotic attractorChaos theory is the theory of Dynamic (Non-Linear) Systems. Dynamic systems converge to a state called an Attractor.

A fractal is a shape that can be subdivided in parts, each of which is a copy of the whole. This property is called Self-Reference.

Self-Referencial Dynamic Systems are represented by a Strange Attractor .

I want to start with a few citations of HUMAN DIMENSIONS OF CHAOS THEORY: Consciousness, Physiology, Perception, and Psychology by Iona Miller and Graywolf Swinney, ©1992.

Chaos underlies the ability of the brain to respond flexibly to the outside world and to generate novel activity patterns, including those that are experienced as fresh ideas (also fresh behavior, emotions, belief systems, mythologies, etc.).

Chaos results in meaning-laden perception, a gestalt, that is unique to each individual.

Chaos is implicated in human perception as a multi-sensory phenomenon. The controlled chaos of the brain is more than an accidental by-product, like “putting your brain in neutral.”

Indeed, it may be the chief property that makes the brain different from an artificial-intelligence machine. One profound advantage chaos may confer on the brain is that chaotic systems continually produce novel activity patterns“.

Research may reveal that assessments of personality or a personality trait over time generate data that leads to a fractal correlation dimension. Such evidence would confirm that personality or that a particular personality trait may be desribed as a strange attractor of associated behavior”.

In the article they apply Chaos Theory and Fractals to the Human. What they are showing is that Self-Reference (A Fractal) is the Result of a Chaotic Process.

Out of the Chaos of Creativity a Repeating Pattern Emerges.

Chaos is not total randomness, but implies an implicate, “hidden”, or occult order within the nature of reality“.

point attractorThe Repeating Patterns looks Chaotic but when we find the Right Fractal behind the Order in Chaos we can know where the Path is Moving to (the Attractor).

To dig deeper into Chaos we have to dig deep into mathematics. We have to dig so deep that the language becomes almost incomprehensible but let us have a try.

A citation out of More than Synchrony: Chaoticity may be necessary for conscious brain functioning (Juergen Fell ea): “Indeed, estimation of nonlinear EEG characteristicslike dimensions and Lyapunov exponents revealed a pronounced decrease not only of complexity, but also of chaoticity during unconscious states like deep sleep”

 ” Sufficient dynamical complexity of brain activity, seems to be one more necessary condition.

Without chaoticity our brains might be unable to switch immediately between different oscillatory patterns and thereby different modes of operation”. 

A citation out of Some Thoughts on Time, Quantum Mechanics, Geometry and Free Will (Linas VEPSTAS) : “The strange thing for us is, we live in this hyperbolic Minkowski space, but we don’t seem to notice much positive Lyapunov exponents in our lives.

 Other than that nature all around us seems to be fractal and self-similar … other than that, we don’t notice.

I sometimes wonder if the quantum-entanglement problems of quantum-mechanics are really some manifestation of life in Minkowski space, some deep connection we haven’t noticed just yet“.

The Lyapunov exponents determine the predictability of a dynamical (Chaotic) system. When we don’t seem to notice much positive Lyapunov exponents in our life we experience life as a “random” process. The main reason that we don’t notice the self-reference is that we are stuck with our own attractor. We are repeating our own patterns all the time and are unable to resonate with the pattern of the Universe.

When the exponents decrease Life become simple again. This happens when we dream. So dreaming is a way “to make things simple“, to “understand what is happening“.

Minkowski space is a four-dimensional space. It was used by Einstein to describe space/time (The Chronotope).

When Space/Time contains positive Lyaponov exponents Space/Time is highly predictable.

This happens when Quantum Entanglement takes place.

cycle attractorQuantum Entanglement (QE) is the Union of seperate Parts into a Whole. QE makes it possible to be in Two or more States at the same moment.

It even makes it possible to Unite with Everything.

QE gives us the feeling that there is something that is connecting us to an Entity on a Higher Level.

When QE happens we are in the AND-state and experience a feeling of Harmony.

When we are not in the AND-state we are in the OR-state.

In this OR-state there are Four “Fractal Attractors” possible. They also give us a “feeling”.

We feel we are Stuck” (Point-Attractor) or

we feel we are “Going Round in Circles (Cycle-attractor)” or

Spirals (Torus-Attractor).

The most Attractive Fractal Attractor, the AND-attractor gives us the feeling that “We are in the Flow (Tao) or in The Now (Chaos)”.

Our Universe is “looking” for Quantum Entanglement. This state of Harmony cannot be perceived in our current 4D-Reality (The Minkowski-Space).

According to Tiller our Unconsciousness connects to another 4D-Reality that is highly related to what the Scientists call Dark Matter.

Out of this Reality The Force of Life (Chi, Prana) is moving into our Body.

If we look at the current state of our World it does not feel as a Strange Feeling that we have to connect to the Force of Life again.

Connecting to this Force is Difficult for us (and me).

Strange attractorThe knowlegde about it is hidden in old “Mysteries” and “Magical practices“.

Many people don’t believe in this or even don’t want to believe in it because it is connected to the Dark Forces.

Strangely enough the Force is also connected to Dark Matter.

It seems we need to enter the Dark to find the Light.

We have to fight and embrace our Dark Shadow (Jung).

About Chaos Theory, Pendulums, Emergence and the New Leaders

Tuesday, October 30th, 2007

Chaos theory describes the behavior of nonlinear dynamic system that may exhibit dynamics that are highly sensitive to initial conditions. As the result of this sensitivity, the behavior of these systems appears to be random. The cases of most interest arise when the chaotic behaviour takes place on an Attractor since then a large set of initial conditions will lead to orbits that converge to a region.

The Dutch Scientist Christiaan Huygens observed that clocks always synchronize. They converge to the same rhythm. How this was possible was resolved when Chaos Theory was developed.

The problem of Huygens is now reformulated as “Coupled Oscillators“. When the Parts of a System are more or less “the Same”, they Unite and start to behave as a Collective.

In recent years it has become more and more evident that well organized structures arise out of chaotic states. The functioning of these systems can be maintained only by a flux of energy (and matter) through them.In contrast to man to man-made machines, which are devised to exhibit special structures these structures develop spontaneously they are self-organizing”.

The appearance of Self-organization is called Emergence. Suddenly a new structure emerges out of the blue.

A few years ago I was asked to participate in an event where many people were drumming. We started with our own rhythms. Suddenly a Pattern Emerged. I felt this pattern and started to play the rhythm. Suddenly everybody Synchronized with my pattern. I was in the Lead and started to play Variations. Suddenly a new pattern appeared. This went on for hours.

When I was drumming I felt there was an new ATTRACTOR emerging. The state before the Pattern Emerged was an “In-Between-State”. Many people felt something was Moving but they did not know where the Pattern was going to.

The world is now in an “IN-BETWEEN-STATE”. Many ATTRACTORS are Possible. The ATTRACTOR is dependent on how many People will be “The Same”.

Some people are Sensitive. They feel the new pattern much earlier than others. They can take the Lead and show others where we are heading to.

In Dutch Politics the new Leaders are visible. They preach the War against Islam just like Pim Fortuyn. They use the Fear to Change as an Attractor. In the Media another type of Leader is visible, The Star. She is using Desire (Ego) to Attract.

We are waiting for other types that use Soul, Spirit and Harmony as an attractor. Some of them will come out of the New Religious Movement (The new Mystics) that is very visible in the Netherlands. Others, Artists, will create new Myths and Music. Others will stimulate People to Take Care of the Others (Charitas). Perhaps One of Them is able to Unite Everybody.