The Chemical Origin of Semantic Intelligence

This blog is a Result of the Research I did for my blog about Heuristics.

Heuristics shows that Complex problems are never solved by complex solutions.

The best Explaining model is the Worst predictor and the Best predictors are Fourfold.

New Research: What do all the Organisms Share?

My re-search became a search for the relationship between the Human Cognitive system, its Evolutionary Development as an Organism and the State of Artificial Intelligence ending in an Insight that our Semantic intelligence has a Chemical origin.

For a Quick Start and a Summary push this link or start with the Introduction .

This blog starts with Physics moves over to Chemistry and Ends with (Evolutionary)Biology.

In between I discover many other Fusions with Biology like Bio-Physics and even Bio-mathematics.

Where Stuff is Made Off

Stuff (Matter) is made of Light (Photons) that moves in Spiralling Spiral motion just as Peter Rowlands explains.

What is Light?

Light is two Inteacting Fields Electric and Magnetic moving through Space.

When we look with our Multi-dimensional Worlview we see every dimension (Magnitude, Point, Line, Square, Volume, .. shows Another type of Particle.

John Williamsson Explains the PDF of Martin van der Mark who died recently.
Photon spiraling in a Tube.
How to compute with light.

Thermodynamics, the Sience of Heat

Natural processes are irriversible just as we are always moving into the future until we realize that natural laws are not laws at all but Context dependent Observations that can be changed when we change the context.

The Earth

The Russian scientist Wladimir Vernadsky divided the earth in 3 spheres called the (1) the Abiotic sphere – all the non-living energy and material processes (2) the Biosphere – the life processes that live within the abiotic sphere and the Noosphere – the sphere of the human cognitive processes.

The Earth as a Water Cycle

A simulation of the Creation of Life in an atmosphere like early Earth.

Our Chemical Origin

Chemical Bodily Communicators: Hormones

Our Emotions and our Personal Chemistry is controlled by our Hormones.

The endocrine system works in large part by acting on neurons in the brain, which controls the Pituitary Gland. This system is very important for the activation and control of basic behavioral activities.

Hormones are specialized Chemical Messengers that operate with different (Minutes, Days, even Years) Frequencies on a general Bodily level using the Blood flow controlled by the Heart but also on a Cell-to-Cell and an Internal Cell level.

They show an Ancient Fractal Pattern of Uni-ellular Integration.

This pattern repeats in human-to-human Social Structures and is visible in and between our our Cities and States.

Want to know more about Uni-ellular Integration? Push this link.

A City is an Organism

A Path of Change (PoC) model of self-Actualizing City that is an Ecology that grows out of the combined effort of Four different expanding and compressing Forces (look at the four Colors) that act as a 4D Wave. The Set point constitutes the base-line of well-being.

Change Management (Paths of Change)

Paths of Change uses four independent WorldViews with a fifth center.
The model behind PoC can be found in many theories including the Learning theory of Kolb. On this picture you see two cycles that move with-and against the clock.

The Endocrine System

Picture
The body is a system that is almost in balance (Homeostasis) controlled by chemical messengers that start and inhibit other messengers that do the same with the others.

Artificial Intelligence

Artificial Intelligence is is not able to React to unknown Situations. It has to be programmed by Intelligent Humans.

The most advanced AI-tool AlphaGo-Zero needs data gathered by humans to Analyze and supposes a Game to win.

AI-systems need Humans to adapt.

Human Heuristics are much smarter than AI-systems.

Wisdom is and Heuristics are an Accumulated Reflection on Experience.

0. Introduction

In this blog I analyze the human Cognitive Architecture and its relationship with the architecture of our fellow-Organisms including the bacteria and viruses.

bacterium
Bacterium
Nerve Net vs Bilateral Brain
The Hydra has a Distributed brain, the Salamander a Centralized brain.
The marine worm Platynereis has a muscle (red) which develops in the same place and has the same genetic signature as the notochord (blue) that develops into our spinal discs. Credit: Kalliopi Monoyios
The spine is developed out of the notocord that came out of he axocord that was used to Swim.

The marine worm Platynereis has a muscle (red) which develops in the same place and has the same genetic signature as the notochord (blue) that develops into our spinal discs. 

The small worm has eyes and other sensors that makes it possible to move in a 4D-frame.

Just as the bacteria the rotators are a integral part of the total cycle.
Trichoplax adhaerens is a species of placozoa, the simplest animals at the base of the tree of life.

Unbounded vs Bounded vs Ecological Rationality

I also relate the human Cognitive architecture to the architecture of Artificial Inteligence, a result of  Bounded Rationality theory of Herbert Simon that recently was taken over by the Human Bias of Daniel Kahneman and more recently by  Ecological Rationality of Gerd Gigenrenzer also called Heuristics.

The term Ecological means Context-Dependent.

Heuristics

Heuristics are the “positive” part of the Human Bias, a problem we encounter when we are put under Stress or don’t have enough Time to Reflect.

Gerd Gigerenzer and Nassim Taleb about why Complex systems Fail and Experts are not always Experts. About Taking Risk with Insight.

Organisms

Small Systems are just as Smart as Big Systems

The Law of Kleiber shows a relationship between the Metabolism (“Chemical Energy“) of an Organism and its Mass. The law holds for the Smallest (UniCellular) and the Biggest organisms and is even applicable to much bigger Organisations like Cities. Intelligence is independent from the Size of an Organism or
Big Systems are not more Intelligent than Small Systems.

Organisms are Chemical Factories

After cooling The Earth became a “giant Chemical reactor” that was able to Catch life that was part of Colliding Meteorites.

The Way Electrons Rotate around anti-electrons (protons, Kernel) in more Complex Elements looks a lot like Organisms just as very Big Far away structures look a lot like very small Close by structures .

Our Universe is a highly Self-referencing (Fractal) structure.

Fig. 2

Life is an Autocatalytic Chemical Reaction

Life is an Autocatalytic Chemical Reaction, a Loop in which an Activator produces its own inhibitor.

Example of an Activator/Inhibitor System.
An Activator/Inhibitor-System in Practice with the Slime Mold.Interesting is (1) Reuse of just one chemical AMP Adinine Mono Phosphate) as a Trigger to start clustering , (2) Synchronization and Repeating an old Pattern (“Growing into a Plant“). AMP is the simple form of ATP part of the Krebs-cycle.

Organisms are Moving Memories

Organisms are Moving Memories exploring their environment to satisfy their need for the Energy (chemicals) they need to Survive.

An Organism is its Emotion

To stay in de right place they move to the place their E-mover (“flagellum”) sends them to.

The Bodyplan of the Bacterium with the Memory in the middle and the Brain, A receptor at the Front. The place of the Memory is also the place of the Heart of the Human.

The Heart contains the Memory of the Body

In Ancient Religion the Heart was the Seat of the Soul.

The Brain in the Head is a Sensor. Its Memory is Distributed all over the Body in the Spindles of the Muscles and the Heart.

The Bodyplan of the bacterium can be seen in all the organisms including Humans.

In between a Sensor and Mover a short term Memory is created out of the molecules we take in at the Front.

Memory is a Repeating Pattern.

We are auto-poietic auto-catalytic systems Born in the Sea.

A Human is a Higher Order Embedding of a Bacterium

The difference between the bacterium and us is called Higher Order Embedding meaning the same principle is applied to Itself, creating a Hierarchy.

Creating a Hiearchy is a proces Without an End. That’s why our Living Context was transformed into a Infinite space Above us with an infinite Power that controls it. This resulted in many Stories that turned into Myths.

If you want to start now with the blog push here or first read about Scientific Narratives.

Scientific Narratives and the Meta-Myth

This hierarchy is really a very complicated Dynamic Network that contains many sub-structures {“Semantic” “Chemical“, “Ecological“, “Social“,and other types of Networks) we have Named (Categorized) using a Principle that was in Tune with the Spirit of the Time.

This resulted in a lot of Scientific Narratives that turned into Scientific Myths that are summarized by Joseph Campbell (a follower of Carl Jung) in the Hero Quest that starts with a Call to Adventure (a Vocation).

The Quest of Mankind

Scientific Narratives claim to be based on a Truth not realising that this truth is also a Belief.

Currenty especially Physics (“Big Bang“) and Biology (Evolution) is discovering that the Myth of Creation blocks us to see how Simple Life and the Universe really is.

My first Mentor was a director of ABN (Harry Haenen). My last mentor was Will McWhinney.

My Gift of the Goddess was the Discovery of the Coming of The Golden Age.

The Age of Aquarius

The hero’s Quest is an old Cyclic model that was projected on the Zodiac.

We are now moving from Pisces to Aquarius meaning from Dualism to Holism.


The very longterm Precession cycle is moving Against the Clock of the yearly Sun Cycle meaning the we are now at the Start of New long term cycle meaning a new Call to Adventure for Mankind.

FRom Dualism to Holism

An Astronomical Age takes 26000 years.

We are ending the Age of the Fish (Pisces) and are moving into the Age of Aquarius.

Pisces is the time of Duality, the battle about Good and Bad.

the Age of Aquarius heralds the arrival of a new stage of the kondratiev cycle, the Golden Age.

Drawing of man holding large water jar with water pouring out, with scattered stars.
Aquarius opens a Vessel with Water that brings the Fish to the Milkey Way.
Left you can see the Arrows of Sagittarius that precedes Aquarius. Water is the symbol of the Aether. (and other Flow Systems).
1192px-Zodiac_(PSF).png
The cycle of the Zodiac.

What are Heuristics?

When I was re-searching for ny blog about Heuristics I found the thesis of Sheldon J. Chow, called “Heuristics, Concepts, and Cognitive Architecture: Toward Understanding How The Mind Works”

Heuristics are cognitive procedures that satisfice, and that require little cognitive resources for their recruitment and execution; they operate by exploiting informational structures, called  Perceptual Symbol Systems (PSS).

Exploiting Perceptual Symbol Systems

Concepts are highly organized collections of linguistically coded perceptual information.

Our Cognition looks lke a Video-recorder connected to our real Emotions and Bodily-processes that are retrieved when certain concepts (Anchors) or Situations are recalled.

Concepts are Simulators that embody Perceptual symbols that are collections of neurons that are activated in the perceptual centres of the Brain.

What we can Imagine Exists

Brouwer: Mathematics is a product of the Imagination. What we can Imagine exists. See also Where mathematics comes from by George Lakoff who discovered the foundation of language being embodied methaphors who are 1-1 (Isomophic) Mappings from the Outside sensed world to the Inside bodily awareness.

Mathematical Language is a “Normal” language

An Assertion (If Condition (Boolean) =True do Action A or Action B) is called a Judgement that is Witnessed by a Fact (Evaluate Condition) that turns the Assertion into an Action. When we move to Space assertions become Points.

Martin Lof Type Theory describes Mathematical Language

Martin Lof Type theory is the definition of a programming language that makes it possible to program mathematical reasoning to support mathematical Proof checking.

About Type theory, the foundation of Mathematics.
Intuitional Mathenatics became the foundation of Homotopy Type theory that became the Foundation of Mathematics by the work of Martin Lof who started a discussion about what Judgementreally is. This i a very long Video about the research of Martin Lof into the history of the term Judgement.

Perceptual states arise in the Sensory-Motor system

Perceptual states arise in the Sensory-Motor system.A subset of the state is extracted by selective Attention and stored in long-term memory.

This perceptual memory can function as a symbol entering into symbol manipulation.Collections of the perceptual symbols comprise our conceptual representations.

The structure of a perceptual symbol corresponds (at least somewhat) to the perceptual state that produced it.
A Conceptual Model of a Perceptual Symbol System being a part of the PDF below.
Figure 3. (A) An example of establishing an initial frame for car after processing a first instance. (B) The frame’s evolution after processing a second instance. (C) Constructing a simulation of the second instance from the frame in panel B. In Panels A and B, lines with arrows represent excitatory connections, and lines with circles represent inhibitory connections.
An example of establishing an initial frame for car after processing a first instance. (B) The frame’s evolution after processing a second instance. (C) Constructing a simulation of the second instance…

Relevance Theory And the Frame Problem

The Thesis contains a reference to two for me interesting and highly interrelated Philosophical Questions called the Frame and the Relevance problem which is about determining what is and is not relevant in our cognitive processing or What do we Know when we Sense a Situation.

Relevance and Wisdom

Another result of my search into heuristics was a very impressive You Tube Playlist “John Vervaeke on Wisdom and the Meaning Crisis” that contains the link between Relevance and Wisdom being the result of Insight.

The egyptian goddess of Wisdom was called Maat . She represents the Concept of Harmony.

The Feather of Maat is a Measure that has a value of almost Nothing.

Ma’at aresponsible for Harmony and Thot, the Magician change the Ished Tree. This tree contains the Past and the Future. A Tree is a Symbol of the Path between the Point (Seed) of Creation and the Now.
The Heart is the Pump of the Up (Brain) and the Down Circulation of the Body.

Both parts are in Balance when their Sum is Zero.

The Ape represents the Human.
Two four-fold cycles connected at the Connection point (green) of both Cycles.

Left a comparable model where the parts (now called tatva’s) are called chakra’s (meaning “wheels“).

Every part of this model is able to turn into a new cycle until a new “emergent” level is reached.

Table of Content

Short description of the content of the Chapters:

Reason: This blog is the result of the Reserch i did for my blog about Heuristics.

During this research I found a Thesis that contained a lot of Interesting links.

Thermodynamics One of these links was a presentatation about Thermodynamics (the science of Heat) I was looking for that proved that the laws of physics are not “Eternal” laws but Context Dependent Observations. The same Vision as the American Pragmatists (Charles Sanders Peirce, William James, and John Dewey)  around 1840 had.

0. Introduction An old blog about bacteria brought me back on the path of Paths of Change but with the re-introduction of the Quaternio of Carl Jung.

A Video with Gerd Gigenrenzer and Nassim Taleb about Heuristics and Risk Taking.

In this blog I compare the human Cognitive Architecture with the Architecture of Organisms.

You will see that Bacteria are Controlled by an(1) Chemical Autocatalytic Cycle that contains a (2):Head that is used as a Sensor, 3):a Heart in the Middle that operates as a Memory and (4): a Tail that functions as a Motor.

In the Middle you can find the Heart, the Seat of the Soul.

Our chemical architecture is controlled by Hormones

What are Heuristics?

This blog started as a follow-up on my blog about Heuristics.

I found a thesis explaining Heuristics with the concept of Perceptual Symbol Systems being hierarchical Semantic Models linked into a Semantic Network, (SM) being a Meta SM.

The personal Semantic network not only contains Perceptual symbols but also Emotions, Patterns, and Intuitions, being Wisdom Gathered in many generations and transmitted by the epi-genes of the mother and the father.

Is mathematics a normal language?

In the thesis I also found the Frame -Problem and Relevance theory.

Both are a result of the big problem AI-systems have to look like humans being the same problem humans face when they want to do something Relevant.

The frame problem is the problem that we not really understand what is happening in a situation.

We are highly biased by What we know (including our Inate knowledge) and the Time our “brain” needs to come into Action.

This started an inquiry in the State of the Art of AI as a competitor of Heuristics.

I found that Relevance Theory(RT) looks like Interpersonal Theory (IT).

IT explains Mental Ilness and is a model of the Human Cognitive Architecture that is fully compatible with Paths of Change (PoC).

RT is also fully compatible with the theories of Mikhael Bahktin (MB).

Wisdom is the result of Reflection on Experience.

Chapter 1: Interpersonal Theory : Humans are Dialogical beings.

They comunicate internally and externally with many voices .

We not only communicate with sounds (words) but ook with movements (Eye), chemicals and EM-fields (“Bodyfield“). .

We are many personalities that react in a diffrent way and start an Internal dialogue.

Our personalities expect that the sender is providing meaning compressed in their Points of View.

People that have only one Point of View are disconnected because every View is Independent (Making an angle of 90 degrees) from all the others.

Normal communication takes two Complemenatary views into account.

Because of this RT, IP, MB,PoC are a Quaternion(Fourfold), a concept invented by Carl Jung who found the concept in ancient Mystics and ancient Egyptian, Indian and Chinese Theory including Alchemy.

Chapter 2: What is the Architecture of the Human Mind,

What is the link between AI and the Brain.

what is Innate and what is learned ?

Experiments show that the factor Nature is much bigger than Nurture.

It looks like a lot of what we know has been learned a very Long time ago by our ancestors.

What architecture do we share with the organisms?

Chapter 3: Relevance Theory:

What is important in a conversation? It has to have just enough information, with the right quality in the right manner,

We communicate much more than we think with our body and our Tone of Voice.

Our argumentation is primary used to Convice ourselves

Chapter 4: The Frame Problem

What do humans really know when they Observe a situation.

We see what we want to see.

What is Intelligence and therefore Artificial Intelligence?

Chapter 5: General Semantics and other AI Architectures.

: How to prevent that you are manipulated by language?

Alfred Korzibski deloped a theory called General Semantics that can be used to create an AI that is able to Adapt.

A description of many Other AI-Architectures shows that they are all based on Bounded Rationality.

This means that the AI expiriences the same Bias as a human and is therefore only applicable on a defined fixed Problem-domain.

Chapter 6: From Hierarchy to Network:,

Concepts are Simulators that part of a Hierchy of Semantic Networks that looks like a Network.

This is the most Important chapter.

What is this Hierarchy of hierarchies? It contains many levels called Scales.

On every scale a The same Pattern repeats itself.

What is the principle behind life itself?

The priciple of life is Self-Replication and EnergeticStability.

We Exist because there is Change.

About Autocatalytic and Autopoietic systems.

About Chemical-Intelligence.

What are Anticipatory Systems? , To be an anticipatory system it has to contain a model of the outside world.

Life is an expanding system in which all te possibilties of a very basic simple model are created until the basic model innovates itself.

This chapter is really the end of this blog because it shows that the basic model of life is Activation and Inhibition being a Duality. The duality is compatible with Movement being Distance divided by Time.

Rodney Cotterill was 20 years ago far ahead of his Colleaques.

The last part of this blog contains many highly abstract (Bounded?) subjects that show what’s wrong with current (bio-)Science.

Gategory Theory: Is it possible to define theories as Functions?

About the Gategory Theory of Networks.

A Petri-net was a Chemical Ttheory about Reaction-networks and was reused as a tool to define Software-programs and second order Differential Equations.

Is it possible to Map more “Knowledge fields”into other Knowledge-fields?

What are Meta-Meta-systems?

Is it possible to expand a Meta System in all Directions and not only Up?

Schema theory has a lot in common with Paths of Change but moves beyond a Point of View into higher dimensions and chaotic fields of Philosophy.

Schema theory is an alternative for Category Theory where different views are compared to find out where they are different.

Is a Meta Difference a real difference?

What are concepts and where do they come from.

Chapter 7. Meta-heuristics The Thesis of Seldon J. Show is about Reasoning about Heuristics.

Meta-heuristics.has become a new field of science,

It looks a lot like a Merger of Psychology with Operations Research (Mathematics).

Chapter 8. From Biophysics to Quantum Biology and Bio Mathematics

Erwin Schrödinger one of the Inventors of Quantum Mechanics (QM) wrote a book called What is Life.

QM can be applied at the very small level of the Cell. Ik can be shown that Photo-Sysynthesis in the Plant but also the detection of chemicals by the Nose can be explained with the same principle.

This part contains many interesting video’s and PDF’s.

Chapter 9. Conclusion: How to design a modern Expert System: AI is based on Neural Networks. It looks like Neural Networks are not needed for the funtioning of Brain. So what will be the next step?

This chapter has to be written.

It is impossible to See the Eye that Sees. Is it possible to analyse Intelligence with Intelligence? or we just What we are? Organisms are Selfreplicating Autocatalyc Chemical Processes (ACCP) that are part of higher level ACCP’s until their Sum is Zero.

1. Interpersonal Theory is an example of a Quaternio

This image has an empty alt attribute; its file name is ls_005.jpg
Two levels of Expansion and Compression linked to 7 essential Questions of an Individual in the Center.
Paths of Change (PoC) is a Scale Free (fractal) theory of Change developed by Will McWhinney. PoC is an example of what Carl Jung called a Quaternio (a Fourfold).

Every Combination of two Points of View generates a Question (6).

Every Dual combination of points-of-view is a Game

A Quaternio contains four concepts that all have a complementary relation.

So are the senses, looking outside connected with the imagination, looking inside connected by the process Invent or Explore.

You can also play with dualism (2), the distinction )1) Zero 0) or nothing (∅).

Relevance theory is devoped to explain the Evolution of the human Cognitive system and human intelligence. It is also used to create artificial intelligence.

Relevance theory has a lot in common with Interpersonal theory and the theories of Bahktin about the Utterance or the internal and external Dialogue we take part in.

Interpersonal theory assumes that humans expect meaningful information from other humans and from the humans that are inside. We are always in a dialogue.

It also assumes that a mental illness can be explained by a connection-problem. It is all about the Tension between Agency and Communion.
Interpersonal Circumplex. The interpersonal circumplex is defined by two orthogonal axes. In recent years, it has become conventional to identify the vertical and horizontal axes with the broad constructs of agency and communion.
Human interaction can be modelled with two orthogonal (90 degree angles)variables that were also called yin (communion) and yang Agency) or o en 1 or just yin and not yin. The four 90 degree angles support a 4 dimensional Universe of Discourse that contains rotating rotations being Spirals.
Humans learn when an Expectation is violated. This happens when an External or Internal Event takes place.

The event is evaluated by the Emotions and (when there is enough time (and interest and energy) Reflected upon by the Imagination and Abstracted (moved Up) into a Model (frame, scape)that is again Instructed and or Tested.

The Learning cycle moves with and against the Clock and also moves through the diagonal between Belief and and the Prove of Belief and Dependence and in-dependence.
This picture describes the model of Nico Frijda about the Emotions: the readiness (or unreadiness) to enter into contact or interaction with some object, and the mode of that contact or interaction. [ … ] Different motivational states or states of action readiness exist … Emotions are tendencies to establish, maintain, or disrupt a relationship with the environment.
Reflect: Finding a pattern in the many actions the senses detect.

2. Our Cognitive Architecture is shared with the Organisms

This part is about the architecture we share with all of the Organisms.

It is mainly based on earlier work of Rodney Cotterill and Will McWhinney, both diseased.

Peter Carruthers: Innate Human Cognition. What is the Architecture of the Mind?
Modular architecture of Peter Carruthers

The Self-Assembling Brain

“our genome contains the information required to create our brain. That information, however, is not a blueprint that describes the brain, but an algorithm that develops it with time and energy. In the biological brain, growth, organization, and learning happen in tandem. At each new stage of development, our brain gains new learning capabilities (common sense, logic, language, problem-solving, planning, math). And as we grow older, our capacity to learn changes”

Every Organism is a step in a very long term process we call evolution in which the outside-world is internalized and externalized in a new outside-world. The genome reproduces a body that is able to reproduce a body but also a system that is able to reproduce and adapt itself.

The Basic Architecture: We are Moving Memories

The picture shows the most simple structure of an organism being a Motor and a Receptor connected with a Short term Memory.

The bacterium is Exploring its environment by changing the rotation of its flagellum with and against the clock.

The short term memory is an autocatalytic, chemical reaction that determinates not only the Rythm of the rotation but also the Direction of the rotation of the rotor.

Rodney Cotterill’s neuro-physiological work supports the motor-environment-mind schema of complex feedback loops. The complex of feedback loops enables one to “Know what one knows.”:

The ability to know that one knows is referred to by psychologists as first-order embedding.

Higher embedding, such as that exemplified by knowing that one knows that one knows, merely depends on the ability to hold things in separate patches of neuronal activity in working memory.

This manifests itself in the creature’s intelligence, which also dictates its ability to consolidate existing schemata into new schema.” is a unique feature of mammalian brains.

Intelligence and reflection are explained as due to functioning of the web of feedback loops, both internal and external, that evolved in higher animals“.

3. Relevance Theory

The word Relevant comes from Latin relevare “to lessen, lighten, levis: light.

Relevance theory is a framework for understanding the interpretation of utterances.

It aims to explain the well recognised fact that communicators usually convey much more information with their  utterances and their Body than what is contained in their literal sense. 

Our Cognitive Architecture Supports Collaboration:

Daniel Kahneman and Amos Tversky used “cognitive biases,” to show that humans make irrational choices.

One of these biasses is called the conformation bias. Humans love to hear a confirmation of what they believe.

Lately a new “science” called Evolutionary Psychology” is trying to find out what “functions” helped the human to survive.

Historically, evolutionary pressure has resulted in cognitive systems that recognise potentially relevant stimuli and try to draw relevant conclusions.

Dan sperber and Hugo mercier argued that this type of bias, being a part of communication, is supporting collaboration.

To Attract the Attention the “uttering” has to be Relevant, making things easy, simple, light.

They also looked at the amount of Energy it takes to communicate.

Relevance theory started with the research of Robert Grice. The Gricean maximsQuantity (Just Enough), Quality (True), Relation (Relevant)), and Manner (the Right Way) describe the principles observed by people in pursuit of effective communication.

Argumentation Theory tries to show the evolutionary benifit of many cognitive biasses.

The Perceptual Symbol Systems are so rich in the type of connections that they generate free Associations that keep a group in the right direction making it possible to Nudge a group by giving them only one choice into the desired direction. This is comparable with a vector-field.

Conclusions Precede Arguments:

Argumentation theory and Rhetorics. We use arguments to convince others but also to convince ourselves.

We are able to use many different cognitive tools (modules) at the same time without knowing we do that.

We use generalizations and are not aware of the differences between the generalisations.

We love Dopamine and therefore love to act in situations were dopomine is produced (“gambling).

There are two systems active the Controlled (Dopamine) and the Control system (Observer).

Conclusions come first, arguments later.

We always pick the last we hear and find the arguments to justify our decision.

Falsification avoids bias.

We are social animals and our brain has to support cooperation.

We could benefit from deceiving but we have to keep our Status.

Gossip supports our status.

We have to Sell ourselves.

Conformation Bias helps to do that.

Humans are Curious Toolmakers .

Coding vs Decoding. Humans are Curious. We are tool makers improving our tools. the older the more knowledge and problems to retrieve out of memory. Attention is given to something that fits what we want know and is relevant. Time and Energy are always Limited.

Our Communication is mainly Implicit

Maximilisation of relevance.Balance between Energy and Cognitive-Contextual effects. Assesment is looking for relevance.

The difference between the foreground and the background of comunication or the difference between Explicit and Implicit, figurative language such as hyperbolemetaphor and irony.

4. The Frame Problem:

The frame problem is about What a “system” is able to see in a Situation and what changes what (“an Event“) and what is Changed and is Not Changed.

The frame problem was created when IT-technology moved into the area of Artificial Intelligence.

At that time every “problem” was solved by designing a new Language like LISP and PROLOG.

Logic (“rules“) put into a program was leading the way and logic was guided by Set-theory.

Although Chomsky’s Language theory was already there nobody realized that human Language is very diferent from a Progamming Language that is Context-indepentedent.

The Artifical Intelligence of the Computer does not understand what was out there and tried to catagorize the outside by also define the not-categories not realizing that they were not bounded (infinite).

Until now the AI-computer looks like a savant a highly specialized human that is in an expert in one area but incapable in the Infinite area’s outside its speciality.

It is not able to define what is relevant and does not see the difference between implicit and the explicit conversations. It is also not able to interpret the many illogical signs we send with our Body, Facial Expressions and Manner until Geroge Lakoff and his group of scientitst detected that we the human communication is embodied.

5. General Semantics and other AI-architectures

This chapter contains many AI-architectures even a model based on General Semantics at the end.

As you will see all the models are different from the model that is explaining heuristics in the Introduction.

The main reason is that the models are based on the theories of bounded rationality that existed before the time of Herbert Simon and Daniel Kahneman, both winners of the Nobel Prize in Economics , described in my blog about Heuristics.

According to Marcus Hutter Intelligence is Compression just as you can find in my blog about Heuristics. If you want to know more move directly to the Conclusion.

5.1 General Semantics

Alfred Korzibski was forced to fight in the first world war. He did not understand why humans act like cruel animals. After moving to the Us and marying he started to research human Communication and developed the theory of General Semantics.

General semantics is concerned with how events translate to perceptions, how they are further modified by the names and labels we apply to them, and how we might gain a measure of control over our own responses, cognitive, emotional, and behavioral.

General semantics had a lot of influence on cognitive-therapy including NLP.

The model of Korzybski looks a lot like the model of Interpersonal theory hat describes Mental Illness.
The model of Interpersonal based on the model of Paths of Change. Return to the Start of this blog.
General semantics explained by Korzibski himself.
Korzibski designed a model of Model of the Nervous-System

5.2 Artifical Intelligence Architectures:

When you press the link above you will find an impressive website about everything you want to know about AI-architectures. Below you find a few examples I have taken out of this website.

5.3 The LIDA Cognitive Cycle Architecture 

5.4 CYC : understanding common Sense:

CYC

5.5 AIXI Optimizing Reward:

AIXI is a AI-theory developed by Marcus Hutter. IXI is a reinforcement learning agent. It maximizes the expected total rewards received from the environment. Intuitively, it simultaneously considers every computable hypothesis (or environment). In each time step, it looks at every possible program and evaluates how many rewards that program generates depending on the next action taken.

5.6 CALO The Perfect PAL:

the DArpa CALO-project ( Cognitive Assistant that Learns and Organizes ).

5.7 ACT-R A new AI Program Language:

ACT-R is a cognitive architecture: a theory for simulating and understanding human cognition. Researchers working on ACT-R strive to understand how people organize.

5.8 AI Architecture based on General Semantics:

6. From Hierarchy to a Network of Hierarchies

6.1 Organisms are not Machines

In the Evolution of the the Organisms two things happened:

(1) the processes of life became auto-catalytic meaning that a chemical process became a repeating cycle (auto) that was sustained and became independent of other processes.

(2) the cycles got connected and created bigger cycles without breaking the katalytic mode until one of the cyclic cycles was able to look like an independent entity.

A cycle that reproduces itself is called an Autopoiesis, a Self-reproduction.

Below you can watch 4 video’s that give examples of autopoietic auto-catalytic systems and the big change in thinking they accomplished.

One of the major Scientists was Robert Rosen: See chapter 6.2.

He tried to explain Anticipatory Systems and found out that it is impossible to explain them with our current modelling language that supposes that Nature is a Machine made by a (Divine) Architect (Pthah) that got the Specifications from Ma,at (responsible for Balance, Harmony) and gave them to Khnum, the divine potter, to Make the animals (including the Humans) out of Clay.

Autopoietic Systems are Self-Reproducing.
Auto catalytic systems explain the Origin of life

We Exist because there is Change

A brilliant lecture of Mihai Nadin, the last living collaborator of Robert Rosen.

How do we account for change while being part of it? How do we account for anticipation as an expression of preparing and adapting to change?

There are Reactive and Anticipatory systems. The last category has to predict the Future.

To predict the future a system has to Contain the Future. we call an Expectation .

A good example of an anticipatory system is a Pregnant woman.

Humans learn from an Expectation Failure sometimes called a Mistake.

Collaborative Learning

Collaboration and learning are active in their own space (the physical context and the social context) and join in mental space (the internal state of a person).

The Evolution of Life

The origin of life lies deep in the Universe were stars like our Sun are created.

Life was ecreated in the labatory by simulating the situation of an early Earth. After that early life was also detected in Meteorites.

Later a lot of Suns where detected that look like our Sun so Life could be Abundant in the Universe.

The Pattern of Creation is repeating at every level of Scale.

Chemistry

Life is the result of Combining the combinations until infinity of Simple Molecules made out of Four basic molecules.
Again the many combinations of a Fourfold, Hydrogen, Oxygen, Nitrogen and Carbon (+1,-2,-3,+4) determinate the Origins of life.

The interesting point is that the Sum of theValences of the Elements of the fourfold cycle = Zero.

Because the four elements are Rotating structures the Chemistry of the Beginning of Life on Earth fits perfectly with the theory of Peter Rowlands about the Nilpotent Universe (See below).

The chemical elements are ordered by the Periodic Table of of  Dmitri Mendeleev . The document below describes how the elements facitated the birth of Life.

Prochlorococcus is thought to be the most abundant photosynthetic organism on Earth

The sea contains a Huge and very Divers amount of Small Foto-Synthetic cells. Inside the cell they look like Plants.

Video’s of an Impressive playlist.about the Origin of Life

Life was started at places where a boundary could be created.
The first step in the Evolition of Life is the creation of the multi-cellular organisms that were combinations of single cells.

This and the scond video are about choanoflagellates being a long flagellum (mover) connected to a Cell.

The cells Unite and disunite at will.
Cells”eat” bacteria but also work together(symbiosis) with bacteria to form clusters (Rosseta).

The geometry of the clusters is determinated by the type of bacteria in the symbioses.
How cells communicate.

Introduction: Anticipatory Systems

6.2 Robert Rosen: Anticipatory Sytems

Robert Rosen made a distinction between Simple and Complex Systems.

In Complex Systems the Whole is more than the Sum of its Parts meaning that there are many Relations between the Parts that are not only Causal but have another Meaning.

In Simple systems the nodes are Nouns and the links are Verbs creating a Narrative that explains its Behavior.

Simple systems are Mechanical systems.

They can be explained by the Four Causes of Aristototle that always begin with asking How (Processs, Verb) an Agent (in general a Human Craftsman (Agent, I, he, ) has assembled Material parts (Noun) ending with the Why being its Purpose.

Living System have no purpose because they are not made by an mechanical process controlled by a craftsman although many people believe this happened when the autocatalytic proces took place.

Systems that can anticipate, con­tain internal predictive models of themselves and/or their environments,

They are part of the class of Third Order Cybernetic Models.

Robert Rosen, Natural systems are explained by mapping them on a Machine-Model mapping (Encoding, Decoding) them on a Formal Model where the Causal relation turns into an Inference.
Pattern formation in Nature.Te model contains two processes called aan Activator and and an Inhibitor.
Gierer-Meinhardt-model is one of the important types of pattern formation and morphogenesis observed in development.

A citation of chapter 1 shows that the same pattern of Acitivation and Inhibition is happening in the body : ” The peripheral reflexes can act independently of the brain, but they can also be coordinated and sequenced by it. The main point to be grasped here is that the brain’s primary purpose lies in the need for inhibiting peripheral reflexes, when particularly sophisticated sequences of muscular movements have to be executed“.

6.3 Dynamic Networks

Dynamic Modularity. ?How Life expanded from a Bacterium to a Human. This a part of an impressive series of video’s.
The Evolution of the Organism can be seen as an expanding structure in time that is controlled by a Linear Bodyplan that starts with the “Head” and ends with the “Tail” in which the genes act as Switches that start a deeper level of expansion.
Brain of a Fruitfly is divided in functional area’s.

6.4 The Human Brain is an Adaptive Dymamic Network:

More about the development of the brain push here.

Mapping

Mapping looks a lot like Category Theory and Schema-theory.

The idea is to map a problem-space to a domain where the problem is already solved, solve the problem and map the Solution back.

To do that the function has to be Isomorphic meaning that structure is preserved in two ways.

Below an Example.

The first picture is the result of making use of a mapping from the Rational Model of Alan Fiske using the function of Paths of Change (see the colors) to the Scales in Measurement Theory.

The four Geometries of Paths of Change
A MApping from Alan Fiske’s theory of Human Relations to Geometry and Panarchy (Ecology) and Anti-fragility.connected by Paths of Change.
The Relational models of Alan Fiske (see below) mapped to the scales of Measurement. It looks like we “measure” our relationship with four possibel scales.
The model of Alan Fiske mapped to Path of Change (PoC)
The Four Scales (with the color of PoC)explained.

6.5 Category Theory: Systems are Functions, Metaphors are Functions:

How to combine category theory and network theory.

6.6 Kent Palmer: Meta-Systems

I found Kent Palmer a long tine ago.

He is exploring the Many Meta-Levels above Reality like Will McWhinney was exploring the 2×2-level (the Quaternio).

I have also played with the Higher than Quaternio levels and tried to keep the Four “types” based on the Duality (Agency, Communion) in tact.

A Generator of a cycling cycle related to the Chinese Sheng Cycle being a (Magic) Square with the Xenter or the Whole (White) in the middle (cross) connected to the other 4 points.

As you can see the Pentragram is a Fractal model. The Points of View point into many Orthogonal “Independent“) Directions where Up (Yellow) is Abstracting and Green is Implementing and Red and Blue are SpaceTime.

The types relate with the four JungianOrgans” of the human being Mind (blue, Thinking), Sensory-Motor (Red, Action-Sensing), Social (Green, Emotions, Feeling), Imagination (Yellow, Intuitive).

When we look at the Bacterium the Sensor and the Motor (Flagellum) are put into a Container (Cell, Boundary) and are related with a Chemical AutoCatalytic Process that is a Memory that operates in a Context that contains “active” chemicals (with an E/M-valence) and other Organisms (F.i. viruses).

The bacterium according to Rodney Cotterill.

The difference with the Four types of Carl Jung is the whole (1, Boundary) put into the Pentagram, the Five (3+2).

This problem was alreaday “solved” in Chinese Philosophy where the five was the symbol of the whole also called the Quintessence. the essential part of Matter we call Energy and also called Aether.

The Sheng Cycle is the result of connecting a 3×3 Magic Square called the Lo Shu.

Chinese (fractal) Sheng Cycle constructed with the PoC-model where White is the Whole (Boundary, Protect).

Kent became incomprehensible when he left the first the Meta-level trying to find alternatives for the Duality “abstraction or implementation”.

Below a website that explores all the 2**N-levels .

About meta-systems

6.8 What are Concepts?

I found a a thesis called Peirce, Vygotsky and Concept Formation by Chris Barnham. I is also about the Semiotics and Pragmatism of Peirce. Watch out. This is complicated stuff just as the theory of Kent Palmer.

7. Meta-Heuristics

8. From Biophysics to Quantum-Biology and Bio Mathematics

9. Conclusion

This blog started with additional research on Heuristics that resulted in research about the History of the human Cognitive architecture that brought me back to Rodney Cotteril a friend of my mentor Will McWhinney who rediscovered the Paths of Change of Carl Jung he called a Quaternio based on the Quaternions invented by William Rowan Hamilton in 1841 and used by Maxwell to define his theory of Electro Magnetism.

Later I found the Quaternions of Peter Rowlands that unites Physics and is based on “recent” mathematics he called Biomathematics for the reason that it also explains Biology and the Human.

Charge
Quaternions Multivariate Vectors
The Quaternio of Peter Rowlands is based on Octonions being an abstraction of the Quaternions that are an abstraction of the Complex numbers rhat are Rotations of Real Numbers.

Peter proved that our Universe is a Turing Machine based on a special language that is constantly Rewritten by a nilpotent condition meaning its Sum is Zero.

The last weeks I have explored Type Theory as a foundation of Computer languages and Cohomogy theory, a foundation of the fusion of Topology and Algebra.

Again everything got together even in my dreams where I discovered CoQ without knowing it existed.

An Eye cannot See itself. About the theory of Logical Types of Bertrand Russell applied by George Bateson to Play and Learning.

The infinite levels of Learning explained by Will McWhinney, A Chapter of his never published book.

About Number and Magnitude

A DEltapulse

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that  Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

Geometric Algebra has a strange relationship with Pascals Triangle. This Triangle, also called the Binomial Expansion, contains all the Possible Combinations of two Independent Variables. Our Universe is a Combination of Combinations exploring Every Possibility.

The last and perhaps most important Discovery in Mathematics called Bott Periodicity shows itself in Pascals Triangle.

Bott Periodicity proves that we live in a Cyclic Fractal Universe, the Wheel of Fortune, that is Rotating around the Void, the Empty Set. The Empty Set contains Every Thing that is Impossible in our Universe.

This blog is not a Scientific Article. I have tried to connect the Old Sciences and the New Sciences in my own Way.

It contains many links to Scientific Articles and even Courses in Geometric Algebra.

So if you want to Dig Deeper Nothing will Stop You.

About the One and the Dirac Delta Function

Every Thing was created out of  No Thing, the Empty Set, ɸ, the Void, the Tao. The Empty Set contains 0 objects.

The Empty Set is not Empty. It contains Infinite (∞) Possibilities that are Impossible.

Every impossibility has a probability of 0 but the sum of all possibilities (1/∞=0) is always 1. In the beginning ∞/∞ =1  or ∞x0=1.

This relationship is represented by the Dirac Delta Function. It is used to simulate a Point Source of Energy (a Spike, an Explosion) in Physics.

The Delta is reprented by the Symbol Δ, a Triangle. The Delta is called Dalet in the Phoenican and Hebrew Alphabet. Daleth is the number 4 and means Door.

The original symbol of the Delta/Daleth contains two lines with a 90 Degree Angle. Two orthogonal lines create a Square or Plane.

The Dirac Delta Function is defined as a Square  with an Area of 1,  a Width of 1/n and a Height of n where n->∞.

The Dirac Delta Function is a Line with an Area of 1.

The Dirac Delta Function δ (x) has interesting properties: δ (x) = δ (-x), δ (x) = δ (1/x). It has two Symmetries related to the Negative Numbers and the Rational Numbers.

When we move from 2D to 1D, the Number Line, the Delta Function becomes the Set of the Numbers N/N =1.

The Monad (1) of the Tetraktys of Pythagoras, the Top of the Triangle, was created by Dividing the One (1) by Itself without Diminishing itself. The Monad (1/1=1)  is part of  the 1D Delta Function.

Creation is an Expansion of the 1/1 into the N/N, adding 1/1 all the time,  until ∞/∞ is reached. At that moment every Impossibility has been realized.

To move Back to the Void and restore the Eternal Balance of  the One,  Dividing (Compression) has to be compensated by Multiplication (Expansion).

At the End of Time N/M and M/N have to find Balance in the N/N,  move Back to  1/1, Unite in the 0 and become The Void (ɸ) again.

About the Strange Behavior of Numbers

The big problem of the Numbers is that they sometimes behave very differently from what we Expect them to do.

This Strange Behavior happens when we try to Reverse what we are doing.

It looks like the Expansion of the Universe of Numbers is Easy but the Contraction creates many Obstacles.

It all starts with the Natural Numbers (1,2,3,).

When we Reverse an Addition (Subtract) and move over the Line of the Void Negative Numbers appear. Together with the Natural Numbers they are called the Integers.

The same happens when we Reverse a Division and the Fractions (the Rational Numbers) (1/3, 7/9) suddenly pop up.

An Integer N is a Rational Number divided by 1 (N/1).

The Integers are the Multiples of 1, the Fractions are its Parts.

Numbers behave even stranger when we want to Reverse a Repeating Repeating Addition (Irrational Numbers) and want to calculate a Rational Power (2**1/2).

The Complex Numbers (or Imaginary Numbers), based on the Square Root of -1 called i, are a combination of the Negative Numbers and the Irrational Numbers.

Irrational Numbers ( the Pythagorean Theorem), Fractions (a Piece of the Cake) and Negative Numbers (a Debt) are part of our Reality but the Strange Number i represents something we cannot Imagine.

About the Duality and the Expansion of Space

In the beginning the only One who was in existence was the 1.

When the One divide itself again the number -1, the Complement of 1, came into existence.

1 and -1 are voided in the No Thing, the Empty Set, 0:  -1 + 1 = 0.

The Two, the Duality, both started to Expand in Two Opposite Directions (<– and +->) both meeting in the  ∞/∞. This expansion is what we call Space.

Space is a Combination of the Strings S(1,1,1,1,1,…) and -S = (-1,-,1,-,1,-1,…) where S+S=(0,0,0,0,0,0,…).

The Expansion pattern of Space is a Recursive Function S: S(N)=S(N-1)+1 in which + means concatenate (or add) the String “,1”.

An Addition X + Y is a concatenation of S(X) and S(Y). A Substraction X-Y is a concatenation of S(X) and -S(Y). In the last case all the corresponding combinations of 1 and -1 are voided. (1,1,1,1)-(1,1,1)=(0,0,0,1)=(1).

Multiplication XxY is Adding String S(Y) every time a “1” of S(X ) is encountered: 111 x 11 = 11  11  11. Dividing X/Y is Subtracting S(X) every time a “1” of S(Y) is encountered:.111  111  1/111=11 1/111. In the last example a Fraction 1/111 appears.

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

The Strange Behavior of Numbers is caused by the Limitations of our Memory System. We are unable to remember long strings that contain the same Number.

To make things easy for us we Divide Space into small Parts so we were able to Re-Member (Re-Combine the Parts).

When we want to Re-member, Move Back in Time, we have to Compress Expanding Space.

Compressed Space is Time.

Time and Space have a Reciprocal Relationship called Movement (Velocity = Space/Time).

There are  many ways ( (1,1,1), (1,1,1),..) or ((1,1),(1,1))) to Compress a String in Repeating Sub-Patterns.

In the blog About the Trinity I showed that the most Efficient Way to group the One’s is to make use of a Fractal Pattern (a Self Reference) and Groups of Three Ones.

The Trinity applied to the Trinity ( A Fractal) is a Rotating Binary Tree. Binary Trees represent the Choices we make in Life.

The rotating Expanding Binary Trees generate the Platonic Solids (see linked video!) when the (number)-parts of the Binary Tree Connect.

When we connect Three Ones (1,1,1) by Three Lines (1-1,1-1,1-1) a 2 Dimensional Triangle Δ is Created.

If we take the Δ as a new Unity we are able to rewrite the patterns of 1’s and -1’s into a much Shorter Pattern of Δ’s and 1’s: (1,1,1),(1,1,1),(1,1,1), 1,1 becomes Δ,Δ,Δ,1,1.

We can repeat this approach when there is still a Trinity left: Δ,Δ,Δ,1,1 becomes ΔxΔ,1,1.

This Number System is called the Ternary Number System.

About Ratio’s and Magnitudes

According to EuclidA Ratio is a sort of relation in respect of size between two magnitudes of the same kind“.

A Magnitude is a Size: a property by which it can be compared as Larger or Smaller than other objects of the Same Kind. A Line has a Length, a Plane has an Area (Length x Width), a Solid a Volume (Length xWitdth x Height).

For the Greeks, the Numbers (Arithmoi) were the Positive Integers. The objects of Geometry: Points, Lines, Planes , were referred to as “Magnitudes” (Forms). They were not numbers, and had no numbers attached.

Ratio, was a Relationship between Forms and a Proportion was a relationship between the Part and the Whole (the Monad) of a Form.

Newton turned the Greek conception of Number completely on its head: “By Number we understand, not so much a Multitude of Unities, as the abstracted Ratio of any Quantity, to another Quantity of the same Kind, which we take for Unity”.

We now think of a Ratio as a Number obtained from other numbers by Division. A Proportion, for us, is a statement of equality between two “Ratio‐Numbers”.

This was not the thought pattern of the ancient Greeks. When Euclid states that the ratio of A to B is the same as the ratio of C to D, the letters A, B, C and D do not refer to numbers at all, but to segments or polygonal regions or some such magnitudes.

The Ratio of two geometric structures  was determinated  by fitting the Unit Parts of the first geometric Stucture into the Other.

An Example:  The Tetraktys is a Triangle (A Monad) and contains 9 Triangles (a Monad). The 1x1x1-Triangle Δ, a Part of the Tetraktys,  is Proportional to the Whole of the Tetraktys (T) and has a Ratio T/Δ = 3= Δ -> T = Δ (3)  x Δ (3) = 9.

The Mathematics of Euclid is not a Mathematics of Numbers, but a Mathematics of Forms.

The symbols, relationships and manipulations have Physical or Geometric Objects as their referents.

You cannot work on this Mathematics without Knowing (and Seeing) the Objects that you are Working with.

About Hermann Grassman, David Hestenes and the Moving Line called Vector

Hermann Grasmann lived between 1809 and and 1877 in Stettin (Germany). Grassmann was a genius and invented Geometric Algebra a 100 years before it was invented.

In his time the most important mathematicians did not understand what he was talking about although many of them copied parts of his ideas and created their own restricted version. None of them saw the whole Grassmann was seeing.

When he was convinced nobody would believe him he became a linguist. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda were recognized among philologists.

Grassmann took over the heritage of Euclid and added, Motion, something Euclid was aware of but could not handle properly.

angle between vectors in 2 dimentions

Grassmann became aware of the fact your hand is moving when you draw a 2D Geometric Structure. He called the Moving Lines, that connect the Points, Displacements (“Strecke”).

screw theory 2

In our current terminology we would call the Displacements “Vectors”.

blades

Vector algebra is simpler, but specific to Euclidean 3-space, while Geometric Algebra works in all dimensions. In this case Vectors become Bi/Tri or Multi-Vectors (Blades).

The Trick of Grassmann was that he could transform every transformation on any geometrical structure into a very simple Algebra. Multi-Dimensional Geometric Structures could be Added, Multiplied and Divided.

The Greek Theory of Ratio and Proportion is now incorporated in the properties of Scalar and Vector multiplication.

add-bivectors

About a 100 years later David Hestenes improved the Theory of Grassmann by incorporating the Imaginary Numbers. In this way he united many until now highly disconnected fields of Mathematics that were created by the many mathematicians who copied parts of Grassmanns Heritage.

About Complex Numbers, Octions, Quaternions, Clifford Algebra and Rotations in Infinite Space

Grassmann did not pay much attention to the Complex Numbers until he heard of a young mathematician called William Kingdon Clifford (1845-1879).

Complex numbers are ,just like the Rationals (a/b), 2D-Numbers. A Complex number Z = a  + ib where  i**2=-1. Complex Numbers can be represented in Polar Coordinates: Z = R (cos(x) + i sin(x)) where R = SQRT(a**2 + b**2).  R is the Radius, the Distance to the Center (0,0).

When you have defined a 2D-complex Number it is easy to define a 4-D-Complex Number called a Quaternion:  Z = a + ib + jc + kd or a 8-D Complex Number called an Octonion.

William Rowan Hamilton, the inventor of the Quaternions, had big problems to find an interpretation of all the combinations i, j and k until he realized that i**2 =j**2 = k**2 = ijk=-1.

What Hamilton did not realize at that time was that he just like Grassmann had invented Vector Algebra and Geometric Algebra.

This all changed when William Kingdon Clifford united everything in his new Algebra.  Clifford’s algebra is composed of elements which are Combinations of Grassman’s Multivectors.

The Clifford Algebra that represents 3D Euclidean Geometry has 8 = 2**3 components instead of 3: 1 number (Point), 3 vectors (Length), 3 bivectors (Area) and 1 trivector (Volume).

It turns out if you use combinations of these elements to describe your geometric objects you can do the same things you did before (you still have 3 vector components).

In addition, you can have additional data in those other components that let you find distances and intersections (and a lot of other useful information) using simple and (computationally) cheap numerical operations.

The most important Insight of William Kingdom Clifford was that the Complex Numbers are not Numbers all.

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

The String 1,3,3,1 of Clifford’s 3D Geometry is related to the 4th Level of Pascal’s Triangle. Level N of Pascal’s Triangle represents N-1-Dimensional Geometries.

The Sum of every level N of the Triangle is 2**N. This Number expresses the Number of Directions of the Geometric Structure of a Space with Dimension N.

A Point has 0 Direction, while a Line has 2 Directions, relative to its Center point, a Plane has 4 Directions, relative to its Center Point, and a Cube has 8 directions, relative to its Center point.

Pascal’s Triangle is also called the Binomial Expansion. This Expansion shows all the Combinations of two letters A and B in the function (A+B)**N. Level 1 of the Triangle is (A+B)**0 = 1  and level 2 is A x A + 2 A x B + B x B -> 1,2,1.

The Binomial Expansion converges to the Bell-Shaped Normal Distribution when N-> ∞.

The Diagonals of Pascal’s Triangle contain the Geometric Number Systems (Triangular Numbers, Pyramid Numbers, Pentatonal Numbers, ..) and the Golden Spiral of the Fibonacci Numbers.

Pascal’s Triangle is a Repository of all the Possible Magnitudes and their Components.

The Normal Distribution shows that the first level of the Triangle (the Tetraktys) is much more probable than the last levels.

The first four Levels of the Triangle of Pascal contain the Tetraktys of Pythagoras.

The Tetraktys  is an Ancient Vedic Mathematical Structure called the  Sri Yantra, Meru Prastara or Mount Meru.

About Numbers, Operations and the Klein Bottle

The Complex Numbers are not “Numbers” (Scalars) at all.

They are “Operations” (Movements) that can be applied to Magnitudes (Geometries) and Magnitudes are Combinations of the Simple Building Blocks of the Tetraktys, Points and Lines.

The Tao of Ancient China was not for nothing represented by a Flow of Water. According to the Ancient Chinese Mathematicians Every Thing Moves.  In the Beginning there was only Movement.

In the Beginning only the One was Moved but when the Duality was created the Two moved around each other never getting into contact to Avoid the Void.

When we look at the Numbers we now can see that they are the result of the Movements of  the first Diagonal of Pascals Triangle,  the 1’s (Points) or better the Powers of  the One: 1 **N (where N is a Dimension).

Even in the most simple Number System, the Unary Number System, Concatenation is an Operation, An Algorithm.

The Mathematician John Conway recently invented a new Number System called the Surreal Numbers that contains Every Number you can Imagine.

The Surreal Numbers are created out of the Void (ɸ)  by a simple Algorithm (Conway calls an Algorithm a Game) that describes Movements (Choices of Direction: Up, Down, Left, Right, ..)  that help you to Navigate in the N-Dimensional Number Space.

The Ancient Chinese Mathematicians played the same Game with the Numbers.

Algorithms were already known for a very long time by the Ancient Vedic Mathematicians. They called them Yantra’s.

Geometry is concerned with the Static Forms of Lines and Points but there are many other more “Curved” forms that are the result of  Rotating Expansion and Compression. These forms are researched by the modern version of Geometry called Topology.

The most interesting 4D Topological Structure is the Klein Bottle.  The Klein Bottle is  a combination of two Moebius Rings. It represents a Structure that is Closed in Itself.

It can be constructed by gluing both pairs of opposite edges of a Rectangle together giving one pair a Half-Twist. The Klein Bottle is highly related to the Ancient Art of Alchemy.

The movement of the Duality around the Void can be represented by a Moebius Ring the Symbol of Infinity ∞.

Later in this Blog we will see why the Number 8 is a Rotation of ∞ and the symbol of Number 8 is a combination of the symbol of the number 3 and its mirror.

First we will have a look at the Reciprocal Relation between Space and Time.

About Dewey B. Larson, Velocity and Time

Dewey B. Larson (1898 – 1990) was an American Engineer who developed the Reciprocal System of Physical Theory (RST).

Larson believed that the failure to recognize that Motion is the most basic physical constituent of the universe has handicapped the progress of the traditional study of physics, which focuses on Forces.

The definition of Motion stems from the Equation of Velocity, v = ds/dt.

Instead of depending upon the change of the location of an object to define an arbitrary “quantum” of space per “quantum” of time, such as miles per hour, or meters per second, the RST assumes that the observed universal passage, or progression, of time is one aspect of a universal motion that necessarily must be accompanied by a universal “passage,” or progression, of space.

The Units of Time fill up the Units of Space. Space and Time are Duals.

Space is not-Time and Time is not-Space. Time is Non-Local, Cyclic and represented by the Rotating Imaginary Numbers. Space is Local, Linear and Represented by the Scalar Numbers. Space is the Vacuum and the Nothing and Time is the non-vacuum, the Every Thing, the Solids represented by the Cube of Space.

The Cube of Space is the structure behind the Tetraktys but also behind the Book of Genesis.

Our Reality contains two Reciprocal 3D-structures related to Space and Time. Space and Time are related by the Simple Formula N/N=1/1=1, the Formula of Diracs Delta Function.

We are able to perceive the Real 3D-Structure of Space. The 3D-Structure of Time is Imaginary. It is situated in the Imaginary Number Space of i.

LarsonsScalarCube.jpg

Larson, a Self Thought Genius like Grassmann, developed Geometric Algebra without knowing anything about Geometric Algebra but he also invented String Theory long before String Theory was invented.  The Mathematics of Larson is also the Mathematics of the Tetraktys of Pythagoras without even knowing anything about it.

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Larson was able to Calculate all the important Physical Numbers without any problem and was also able to Calculate Chemical Structures and Reactions.

About the Bott Periodicity

The fourth line of Pascals Triangle and the Tetraktys contains 8 Directions in the Four Geometric Dimensions: 0, 1, 2, and 3.

Mathematicians are intrigued with this number 8, because they find it popping up unexpectedly in advanced mathematics.

In fact, expanding the Binomial Expansion to 8 dimensions just creates an inverse copy of these first Four Dimensions, and then the pattern just repeats itself with a half-twist and back from there, ad infinitum.

This is called Bott Periodicity discovered by the mathematician Raoul Bott (1923-2005).

The mathematician John Baez wrote an article in which he relates this 8-fold Periodicity to the Scalars (1), the Complex Numbers (2), the Quaternions (2×2), and the Octonions (2x2x2 = 2**3).

The Universe of Numbers and Magnitudes  is Cyclic and Fractal.

Our own Reality, symbolized by the Tetraktys,  repeats itself in Higher Dimensions until Infinity.

The Tetrad, represents Completion, because it contains all its Previous Numbers, the 1, 2, 3, and itself, 4, in One Number, 10 = (The One) +  9 (= 3 (Trinity)x 3 (Trinity) = Tetraktys).

As you can see in the Picture above the Fractal Pattern of 8 contains two kinds of Trinities/Triangles, an Upside and a Downside (Rotated by 180 Degrees) Triangle. When you Rotate by 180 Degrees the 1 becomes -1 and 1 + -1 =0 is the Void.

The Multi Dimensional Rotations of the Octonions always Come Back to Square 1/1=1, the One and keep Rotating around the Center, the Nothing,   Until Infinity.

LINKS

About the Tetraktys (2)

About Triangular Numbers and Pascal’s Triangle

About the Empty Set

About the Relationship Between Geometry and Music

About the Trinity

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

About Number and Magnitude

About Ratio and Proportion

About Ratio and Proportion by Euclid

A book of Augustus deMorgan about “The Connection between Number and Magnitude”

The text of the Fifth Book of Euclid

An Educational You Tube Channel called Insights in Mathematics

About the History of Geometric Algebra

About the Sri Yantra

About Geometric Algebra

Free Software to use Geometric Algebra

About Clifford Algebra

About Topology

About the Digital Root Patterns

About the Heart Chakra

A Video that shows how the Platonic Solids are created out of the Trinity Numbers

All you want to know about Geometric Patterns

The History of Western Medicine

At the end of the Middle Ages the Merchants of the Big Cities took over the Power of the Church of Rome. The income of the Church went down dramatically. The amount of poor (and sick) people moving to the Big Cities increased and the Costs of the Free of Charge Hospitals went up.

At the Council of Trent (1545) the Church of Rome decided that the Cities would take over the responsibility and the payment for the Hospitals. From that time on the Hospitals were run by the Merchants as a Commercial Company. The Seven Acts of Mercy lost their meaning. The only thing that counted was making Profit.

The managers of the Hospitals made a distinction between paying and poor non-paying patients. The patients with an income  had to pay for their food and everything else that was needed. The sick poor people were put into Almshouses who were paid out of the charity of the Rich.

At that time the Guilds became a very important power in the Cities. They regulated just like the Unions today almost everything to avoid competition and took care of the Healthcare and Education of their members.

The Hospitals even made money with the Sale of the Dead body of a poor person to an Anatomical Theatre. The Theatre was used for Entertainment and the Education of the Guild of Surgeons.

The Rich People were treated in their Own Houses by the Doctores Medicinae, educated at the University. The Doctores used a Medical Theory that was based on Analogy. This system looks a lot like the Ancient Practice of Chinese Medicin and The System of the Four Humors. At that time it was believed that the Mind, the Spirit, was more important than the Body.

The patients were mostly treated with herbs that carried the “signature” of the Disease (Homeopathy).  The “dirty” work was done by Barbers and Surgeons who were part of the Guild System. The Bloodletting Points have a lot in common with Chinese Medicine.

The System of the Four Humors was abondoned by the Medical Profession at the End of the 19th century but is still used in Psychology (Archetypes of Jung, Interpersonal Theory, Big Five).

In the 19th Century in the Middle of the Industrial Revolution the Quality of the Medical System was at its deepest point in History.

The Factories took over the work of the Guilds who until that time took care of the Healthcare of their members. In the Big Cities the Owners of the Factories took over control. Some of them started to create Healtcare Facilities for their own Factory Workers.

Many people moved to the big cities to find work and failed to do this. The hygiene in the Cities with its open sewers was very low.  Epidemic after epidemic hit the highly vulnarable poor population of the cities.

The innovation of the Health System began in France. In 1617 Vincent de Paul started the Confrerie de Charité. The Daugthers of Charity were rich unmarried women who devoted their lifes to the care of poor and sick people.

In 1633 the first nursing school was started by Louise Legas-de Marillac. In 1836 Theodor Fliedner in Germany together with Elisabeth Fry in England founded a comparable institute of young women of the Protestant Faith called the Deaconesses.

From that time on the Catholic and Protestant Nurses started to reorganize the Medical System. Hundreds of new Hospitals were created in Europe, Asia and the United States.

In the first half of the 20th century, medicine was completely revolutionized with the explosion of the use of medical technology.

Some of the medical technologies invented in this period were the thermometer, the stethoscope, the microscope, the ophthalmoscope, the laryngoscope, and the x-ray. With these medical devices, doctors were able to Sense parts of the patient’s body such as lungs, and hearts. In the beginning the specialists created their own diagnostic centres with their big tools in the center.

Physicians in early 19th century mostly practiced General Medicine including Mental Diseases. At that time the Church was still the most important factor in the Cure of Mental Diseases.

In England at the beginning of the nineteenth century there were, a few thousand ‘lunatics‘ housed in a variety of disparate institutions. After the Creation of the Psychiatric Specialism by 1900 that figure had grown to about 100,000.

When a Specialism is created it creates its own diseases and of course its own patients. The Health Care Industy generates its own Market.

Because of medical technology the  development of specialities occured at a very fast rate. In 1930s, 1 out of every 4 doctors was a medical specialist. By 1980, 4 out of 5 doctors were specialists. The extreme specialization of the Physicians created a highly fragmented view on the Human Body and the Human Mind.

At this moment every small part of the Human is analyzed and treated but the effects of the treatment on the other parts is often not known. This  generates Side-Effects which create knew diseases which create new diseases.

In the late 19th and early 20th centuries apothecaries started to produce their own drugs in small factories. Later these small factories where joined into one big Chemical Plant. One of the most powerful conglomerates in the Health Care Industry,  IG Farben ,was created in 1926 in Germany.

At this moment the Pharmaceutical Industry is the most important Power in the Medical Ecology. It influences governments, customers and physicians in their decisions to diagnose and cure a disease. To sell their drug the companies create and promote new diseases.

The main effect of this development is that a huge part of the treatment of patients is based on “chemical warfare” against sometimes artificial created enemies.

Until the end of the 19th Century Hospitals looked like Churches. The main function of the Hospitals was to Take Care of the Sick, the task of the Sisters of Charity, the Nurses. The Physicians did not play an important role. At the end of the 19th Century the Medical Profession was not highly valued.

When the Specialized Diagnostic Centres were created the Hospitals changed into a Pavillion. The Patients were moved from Center to Center. At that time the Medical Specialists took over the power in the Hospital. It was also the moment when the System of the Sisters of Charity started to dissolve. Taking Care became a Profession instead of a vocation although many Nurses are still “called” to their profession.

In the last step the Diagnostic, Operational and Care centres of the hospital were fused into one Big Highly Specialized Integrated Building.

What is Happening?

Many people are highly dissatisfied with the Current Medical System. They know that the Fragmented Technological  Approach will not solve the problems of their Whole Body and Mind. A huge amount of money is spend at so called Alternative Medicine. This field is just like the Current Medical System highly fragmented and the quality of the practioners is not clear.

What we need is a new approach in which the Reactive Fragmented World of Western Technology and the Preventive Eastern Word of Wholeness are United.

What is Going to Happen?

Medical Technology will  take over Medicine just like Technology will taken over every other Profession.

It will not take long until an Intelligent Diagnostic System will be much Smarter than every Specialist on Earth.

It will not take long until there are portable Sensors that are able to Measure everything that is happening in Your Body.

It will not take long until the Diagnostic System will send you the Medicine (or an Advise) you need long before you even think about going to the Doctor.

A complementary approach to the Western Reactive mostly “Chemical approach is the Eastern Preventive approach.

In this case the Electro Magnetic (Chi) Field of the Body will play an important role. The E/M Field of your Body is the most sensitive system. It can easily be used to balance all the other Systems.

Of course we have to integrate Body (Medicine) and Mind (Psychology) in our Preventive Approach.  The State of Mind of a Person is one of the most important causes of a disease.

It will not take a long time until the Sensors will be able to detect a fatal State of Stress in your Body caused by your Mind.

It will not take long until the People with an Intuitive Medical Talent, the Healers, will become more important than Highly Advanced Diagnostic Tools.

It will not take long before the Preventive Approach will completely take over the Reactive Approach.

If this happens we don’t need the Healthcare System anymore.

What will Happen with the Hospital?

At this moment big investments are made in huge Hospitals. If the Future develops the way it goes these Big Buildings will not be needed anymore.

Treatment and Care will take place in your own House just as happened with the Rich People in the Past.

The only question is.

Will there be enough Caretakers (Nurses?)  to Take Care of you or will the Robots take over their task?

Perhaps we have to revive the Daughters (and Sons?) of Charity!

LINKS

About the Calvinistic Work Ethic

About Vocation

About the Industrial Revolution

About the History of IG Farben

Catching the Light: About Steiner, Goethe and The Placebo Effect

When I was working at ABN-bank I was doing a project to reorganize the Archives of the bank. One of my colleagues was heavily inspired by the work of Rudolph Steiner. He was very busy to create a new type of bank based on his ideas (now The Triodos-Bank). 

 

At the same time I met people that were practicing his ideas in the process of automation and organizational change processes. I loved what they were doing so I started to read his Books. 

 

Steiner came back in my life when I wanted to know more about Colors. I bought the Color Theory of Goethe and I found out that Goethe was the person that inspired Steiner the most. 

 

Goethe and Steiner became a force of Inspiration for Me and my Wife. She started to do Art-courses and I saw that she loved it. She even considered to become an Art-Therapist. We visited the Goetheaneum in Dornach (Zwitserland). We found an Antroposophic general practitioner. She uses Homeopathic medicine. I practiced Eurhythmics and lately I got a treatment to strengthen my “boundaries” where they use the Essential Oil of Flowers.

 

Arthur Zajonc is a well known Professor of Physics. He is also inspired by Rudolph Steiner and Goethe. Many people think the ideas of Steiner are weird and non-scientific but as you see even a professor of Physics knows that what he is saying to the world is of tremendous value. 

 

Arthur Zajonc wrote a beautifull book called “Catching The Light”. The book tries to explain Light.  It uses two perspectives. The perspective of Physics and the perspective of Steiner.

 

Zajonc shows that Science and Spirituality are basically telling the same story. Mind, Spirit and Soul are seeing the same thing but use different words to describe the same phenomenon.

 

 The most interesting part of the book is about the Imagination. Experiments show that we don’t see with our eyes. We see the world through our Imagination. 

 

Experiments in Physics show also that our Imagination (Our Creative Power) is controlling the Material world. Matter (Photons) is doing what the Imagination wants them it to do. We Get what we See.

 

Many people don’t understand the impact of this. They Think we are controlled by an outside Force (Fate) and they don’t realize that everything they are encountering in Life is created by Themselves. They don’t want to see that the Outside World is reflecting their personal creative process. If things go wrong they don’t realize that they want them to go wrong.

 

How can we make things go right? It’s simple. Imagine they are going right. Think positive.

Do you know why Medicine is working? 

Because we Believe its Working. 

I Love the Placebo effect!