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

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).

 

 

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Explaining the Placebo Effect by Counting Stories

The unconscious is a new territory for mathematicians and physicists. Jung one of the inventors of the term unconsciousness was convinced mathematics was the key to understand the Unknown.

 

At the end of his life he asked one of his female pupils Marie-Louise Von Franz to look for the link between mathematics and the unconsciousness.

 

She wrote the book “Number and Time”. Later I found an article of the mathematician and physicist William A Tiller about the same issue. It is called “Human Psychophysiology, Macroscopic Information Entanglement and the Placebo Effect”. In the article he explains the so called placebo-effect.

The placebo-effect is a funny thing. A pharmacist is a person who wants to treat a disease with a chemical (mostly toxic) substance (a pill). When something that is not toxic (a placebo) heals the same disease he is sad.

He is sad because he is not able to make a profit and he is sad because he has spent a lot of time doing research for nothing. When the placebo-effect occurs people imagine that they are cured and their imagination cures them.

A citation: “In 1999, Enserink wrote a short but very interesting article concerning how greatly the magnitude of the placebo effect in double-blind pharmacological studies had grown in the previous 15 years. He pointed out that “when companies started testing drugs for obsessive-compulsive disorder back in the mid-1980’s, the placebo responserate was almost zero. As time went on, this response rate began to creep upward, up to a point where one could reasonably conclude that some clinical trials failed because of high placebo response rates. A very recent meta-analysis of 19 antidepressant drug trials revealed that the “placebo effect” on average accounted for 75% of the effect of real drugs”.

What Tiller is saying is that a “depression” was cured by believing it would be cured. This happened when people started to believe there was something (a pill) that could cure them.

Again a citation: “The information bandwidth (in bits per second) of the human unconscious is about 1 million times that of the conscious”. The so called unconscious is capable of finding patterns and its capacity to do this is enormous. The unconscious is more conscious than the conscious. Our “problem” is that our conscious is not able to “understand” the other conscious that is part of us. It uses another “language”.

Another citation: “If one counts the entire duplex space as a 4-space, then the entire multidimensional representation is a 7-space. If instead, we count the duplex space as a unique member of the general 8-space, then our reference frame is eleven-dimensional”.

What Tiller is explaining in his language (mathematics) is that besides our own space there exists an unseen space. It is a space we cannot SEE WITH OUR EYES because the capacity to see patterns with our eyes is incapable of seeing the other world. We use the “third eye” to have a look.

In this space you are able to travel with speed >C (the speed of Light). Perhaps you are getting confused now. You know this is impossible. You have learned this at school.

The mathematical reason behind this statement is that it is “impossible” to take the square root of a negative number.

If you define the square-root of the negative number -1 as the letter “i” (imaginary) your problem is gone. The IMAGINARY, “unseen” world, can be combined with the REAL world we SEE. 2 +4i is an example of a combined number.

Another mathematical problem is “division by zero”. You know again this is impossible. You have learned this also at school. This problem is created when you are moving with the speed of light.

The problem can be avoided if you use another concept of space. Division by zero is called a hole and you just navigate trough space avoiding THE HOLE.

Current physics assumes the space we live in consists of billons of billons of holes.

A funny thing is that 5000 years ago Indian science told the same story. They called the holes the bindu’s. The bindu’s where the holes to another world and out of this world something was transported called PRANA. PRANA is called QI (CHI) in China. QI means the force of life.

You have to believe that many (very expensive) experiments have shown that we are living in a very different space you have learned at school. Perhaps your teacher knew he was he was telling the wrong story. He learned when he was learning to become a teacher that young children are unable to understand the new concept of space.

Funny enough young children experience this space when they are sleeping or day-dreaming. When they are at school they believe the teacher and the teacher is believing his teacher and ….

What the experiments also show is something called ENTANGLEMENT. When something is created out of a WHOLE the parts of the whole stay CONNECTED and the connection travels with a speed >C (the speed of Light).

To explain entanglement physicists have accepted there are MANY UNIVERSES and every time a (UN?)CONSCIOUSNESS OBSERVES (becomes AWARE) a new PARALEL UNIVERSE is created.

In our REALITY we SEE one of the possible universes. In our IMAGINARY state we are able to move to all the others. We are even able to travel time because physicists accept the reality that the PAST and THE FUTURE are created in the NOW. They change with every act of consciousness.

Tiller explains that the 4-dimensional unseen space is created by the EMOTIONS.

Now I want to get back to the book “Time and Number”.

A huge part of the book is about China. Jung studied the I TJING with William Reich and was fascinated by the CYCLE (a rotating CIRCLE) of Lo CHI. Remember CHI means “Force of Life”.

The Lo Chi cycle (5000 years old) is described by a magic 3×3 square where all the numbers add up to 15. It has a 5 in the centre.

The magic Lo Chi magic square and related magic squares play an important role in modern physics. They are related to symmetry and symmetry is related to HARMONY and FIELDS.

Funny. The LO-CHI-cycle is exactly the cycle that is explaining the same thing Tiller is explaining.

The book NUMBER and TIME contains a very interesting observation about story-TELLING. When you count (telling = counting) the major persons in an “old” story (myth, fairy tale) and combine the counting with the flow of the story the Lo CHI CYCLE shows itself.

For some reason story-TELLERS were TELLING the same story all over again and again.

They wanted to make sure the concept of the Cycle was handed over and over and over again generation after generation.

The cycle explains one thing Tiller is proving “Your Imagination is the Creator of Your own Reality”.

The most interesting insight I got is that what Jung calls our unconsciousness is more aware than our consciousness. The Unknown is connected to our Emotions. So if you want to create trust them. Trust your gut-feeling and your imagination because they are doing “IT”. You are the Creator of every Situation and Person you encounter in Your Life. They are the Mirror of Your Self.