In this blog you will learn that we are very close to a big Technical but also PhiloSophical, Social and Medical transformation caused by a major breakthrough in physics because of the Fusion of Quantum Mechanics, Gravitation, Electromagnetism, the Weak Interaction, and the Strong Interaction.
The new insights are explained by the Octonions that are extensions of the complex numbers. The octonions represent rotations of rotations of rotations (Sprials) in 8D space. Spiraling spirals have always been seen as the sources of our universe. See Chapter 0 Introduction.
The Big Transformation (Chapter 1) is the move from the Age of Pisces to the Age of Aquarius being the change of Dualistic Science to Non-Dualistic Science (Advaita) finding a shared Unity (1-ness), between what we See and what we Are.
The Shared Unity of Reality and the Self could be the Zero (0), of the nothingness of the Nilpotency (chapter 0) of the Heart of the Universe where 0=0 or the 1 of the Unity of the Point of the Singularity of the Bindu (the Zero-Point Field)or the 2 of the Line of the Observer of Projective Geometry,(Chapter 2)
In this Blog I Combine (Part 3), Change/ Transformation (Part 1 ) and Geometry (Part 2).
In Chapter 0 You will see that Physics can be explained by the Octonions being a Combination of the Combination (Quaternions) of the combination (Complex Numbers) of the Real Numbers being Rotations of Rotations of Rotations (= Spirals)of Space.
0 Introduction: The Nilpotent Universe
The Big Bang is an interpolation of the Expanding Universe to a theoretical Beginning. In Part 2 you will learn that there is a lot of doubt about this concept.
The main reason is that the foundational measurements of the “speed of Light” prove to be wrong destroying the theory of Albert Einstein.
The big problem is that a Big Bang needs a lot of Energy but also generates the same question again and again until we believe in an always returning, Cyclic Universe.
If you are willing and able to read this chapter you will see that the solution to our biggest and most expensive scientific problem is very simple and applicable to all the other exact sciences including Biology:
Our Universe is a self-replicating Turing Machine and
This 0th chapter contains links and texts that prove that our Universe is Nilpotent meaning that all the Values of the Parts Sum to Zero.
This makes it possible to bring a lot of the most complex formula’s back to simple formula that show very simple connections that can be explained by Symmetry Breaking.
Our Universe can be explained by simple building blocks that unite and disconnect in a very simple way that can be described by a simple machine just as the old Magus Leibniz imagined. He called this the principle of sufficient reason:
““Dieu a choisi celuy qui est… le plus simple en hypotheses et le plus riche en phenomenes” (God has chosen that which is the most simple in hypotheses and the most rich in phenomena)”.
The most useful Production rules” of the grammar of the Universe are the so called Octonions a generalization of the complex numbers in 8 (2**3) dimensions where i, j en k are √-1. are the foundation of the Quaternions. The most important point here is that he Complex numbers, the Quaternions and the Octionions represent Rotations in N-dimensional Space.
Our Universe rotates and its rotations rotate also generating changes that are unchanged. We always move back to the beginning that is Empty (“zero”). History Repeats Itself and patterns repeat themselves in so many different the same ways that most people don’t see that we are repeating the repetitions on every level of scale until the smallest Planck level and the biggest universe. The patterns are Scale-Free.
This is the Chinese Sheng Cycle (SC) which is result of the Lo Shu Magic Quadrant projected on Paths of Xhange.
Observe that the Model of Peter Rowlands looks a lot like the model I use (PoC) with the big difference that PoC is a Dynamic Model. In the Sheng Cycle you see the combination of Duality (<->) and Trinity by making a connection to the other Dualities. The Paths of Cange moves With (Producing) and against the Clock (Consuming).
Paths of Change (PoC) is based on a Dual model that contains two variables (1): Agency(Compression) & (2): Communion (Expansion) which are the same as Yin & Yang. 2×2= 4 = 2**2. 4 points have 12 + 1 (center) = 13 connections. Because of the 12 connections PoC contains many Triangels.
PoC contains 4 Points of View (PoV) called Unity (Blue, Rules, Thinking), Sensory (Sensory Meter System, Real Red), Social (Emotions, Green) and Mythic( Creation, View, Imagination), Yellow).
Time and Charge are Imaginary unless we use a Clock like the Earth rotating the Sun or the Polestar rotating with the Precession cycle.
Space is Real when we move on Earth using a Reference System that also could be the Stars and the Planets we can see with our personal Sensors. Mass is Real because we experience Mass as an Attraction of a bigger Mass (Earth) and sense the influence of the Moon in the rise of the Sea. Mass & Charge are Attractors and Not Attractors and are therefore related to the Emotions.
Mass & Charge are “Conserved” Physical quantities that remain constant with time are called conserved quantities. Example, for a body under external force, the kinetic and potential energy change over time but the total mechanical energy (kinetic + potential) remains constant. The appearance of a given amount of positive charge in one part of a system is always accompanied by the appearance of an equal amount of negative charge somewhere else in the system;
Mass & Charge contain a “negative” and a “positive” value we could define as “zero”. According to Peter the Universe is Nilpotent meaning that its sum is always zero. This implies that the (Sum of the) Beginning of the Universe was Zero too (Empty).
The mathematician Emily Noeter proved that every conservation can be translated in a special type of Symmetry (see Chapter 2).
A Big Transformation is Predicted by The Precession Cycle
There are many Cycles with different Periodicities. The longest Cycle known by the ancient Astrologers is the Precession Cycle with a cycle-time of 25800 years. The cycle runs retrograde, in de opposite direction as the Seasonal cycle and covers the twelf Constellations of the Zodiac. An age takes 25800/12= 2150 years.
A much shorter cycle is the Kondratiev with a periodicity of about 50 years. Currently we are moving from the Kondratiev Winter to the Kondratiev Spring a period in which many disruptions take place. After the Spring we will move into the Golden Age (Summer).
An Age takes (2150/50=43 Kondratiev-cycles.
43=3×13+4 = is called the Bronze Mean X(n+2) = 3*X(n+1) + X(n), and is a generalization of the Golden Mean.
13=1+3×4 (Zodiac=Sun in Center, Jesus + 12 Disciples)), (Square) 4= 1+3×1, which means that x0=1 (Point,Zero Emptiness, ).
43 is the number of the Sri Yantra
We are allegedly in the Age of Aquarius.
According to astrologic we are leaving the Age of Pisces (started around 0BC. In Luke 22:10, when jesus (the Fisherman) is asked by his 12 apostles where he will go to settle
his new kingdom, he responds, “Behold, when ye are entered into the city, there
shall a man meet you bearing a pitcher of water, follow him into the house where
he entereth in.” This is the “House of Aquarius”.
Perception involves the more central regions making predictions, which propagate toward the peripheral (sensory) regions. The peripheral regions compare the prediction with incoming sensory information and send back prediction error signals. This happens across numerous layers.
We see what we expect to see, with the incoming information forcing corrections.
Solms notes that a self evidencing system receiving information that violates its expectations can react in one of three ways.
- It can act to change conditions to bring the signals more in line with its expectations.
- It can change which representation(s) it’s currently using to make better predictions. This is perception.
- It can adjust the precision of the predictions to more optimally match the incoming signal.
Solms identifies the last as Consciousness.
“Imagination is more important than knowledge For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand” (Albert Einstein)
In a Conformal Geometry you look at the world with the (cognitive) Instrument of a fisheye-lens.
In a conformal geometry Big and Small are comparable. This means that our Universe is Fractal or as was stated by the ancient Magi as As Above so Below: Our mind is a simulation of the universe.
“The feedback-loops in the cell-like structures of self-propelling space can be seen as a giant mind (a neural network) that is split in many (in)dependent minds. One of these minds is the mind of the Human but cells, the body, the brain, earth, our galaxy and the universe are also mindful” (Reginald Cahill)
According to Conformal Field Theory (CFT) we live on the almost Flat Boundary (“a Frame“) of a “sliced” (“layered”) (hyperbolic) Anti-de-Sitter Space.Observe the “fisheye-structure”on top and below of the 3D-“tube”.
Above you see 3 types of space in which space is curved at a special way in which the sum of the angles is equal smaller or bigger than 180 degrees. Observe that the all the types have their own way to define a RIGHT angle which is a way to define a new dimension.
Christi Belcourt (Métis) – The Wisdom of the Universe, 2014
Julian Barbour (Physicist, writer of the book “The end of Time“): The only thing that Exists in our Universe are Changing Shapes. “There is no invisible river of time. But there are Shapes that you could call Instants of Time, or ‘Nows‘. As we live, we seem to move through a succession of Nows, and the question is, what are they? They are arrangements of everything in the universe Relative to each other in any moment, for example, now“.
Currently we measure Time with an artificial constructed (atom-)Clock. Before the invention of the clock time was related to the cyclical processes in the year that were related to the movement of the (Male)Sun and the (Female)Moon.
The big patterns were related to the movement of the Stars that are related to the Precession Cycle. At that time the Map of the Sky and the Map of the Earth were aligned.This means that the maps of the Earth are projections of star maps but also that the locations on earth where looking like the patterns in the sky. A good example is the Seven Cities of Paul in the Apocalypse that were aligned to the Pleiades.
The Geometry of Shapes (“Similarity Geometry“) is the most important geometry because it contains the Potential of creation. This Geometry corresponds with Mythic in paths of Change (the Creative Personality) and Equality Matching in the theory about Social Relationships of Alan Fiske. It can also be found as the Hero in the Myths of all Cultures researched by Joseph Campbell., the Fool (o) in the Tarot, Zero in the Numbersystem and Λ or ∅ in Set Theory.
he most used geometry is Euclidian Geometry. We measure everything. Even our relationships are measured in terms of values like money and possession. We have forgotten to value social contributions.
In the Beginning
The blog begins after a few Video’s about the current insight about the Geometry of the Universe. It looks like our Universe is without a beginning and an end but also without Time and Space. It is filled with Infinite Possibilities.
The Tao-Te Ching:
The Tao is like a well:
used but never used up.
It is like the eternal void:
filled with infinite possibilities.
It is hidden but always present.
I don’t know who gave birth to it.
It is older than God.
In Hinduism, a Kalpa. , a Cycle of a Universe, is equal to 4.32 billion years, called a day of Brahma . In Hinduism, Brahmā (Sanskrit: meaning “swelling” or “expansion”) is God in his manifestation as Creator of the universe. Brahmā is part of the Trimurti (the Hindu Trinity) alongside Vishnu and Shiva. Brahma lives on top of Mount Meru (look at the triangle on the head of Brahma) also called Pascal’s Triangle (see Chapter 9).
When we push all the shapes together they will become a Black wHole. What is able to create such a Force? What lies behind the Black Hole? The Nothing, Empty Space? Is Empty space Possible? Is the Sum of Things Zero or Infinite (8)?
About the Conformal Booststrap : Geoffrey Chew, “Nature is as it is because this is the only possible nature consistent with itself,”
It is possible to unite all the different theories of the universe by playing with the the Dimensions and geometry of space which could be flat or curved in a positive or negative way.
List of Chapters
- The Pragmatism of Charles Sander Peirce, an Introduction into Semiotics plus an advanced application of Semiotics to determinate the beginning of our Universe by moving to Zeroness
- Thinking about Thinking: About the Implicate Order of David Bohm and Jiddu Krishnamurti
- About Hyperspace: Predicting the Future by Observing the Observer, The Mathematics of Hyperspace, about the Soul, Moving out of the Body, Healing and the Big Bang that never was
- The Geometry of Finite and Infinite Games, The role of the Trickster
- Science: Filosophy The future of Artificial Intelligence
- Foundations: Symmetry, Contradiction,Duality & Polarity
- Geometry: Spiritual, Indian, Curved Space, Topology,
- Theory of Measurement
- Mount Meru: About the Triangel of Pascal in Indian Music, Achitecture and Mathematics
- This blog is a fusion of blogs about Projective- and Algebraic Geometry with a blogs about Panarchy, Resilience and Anti-Fragility , the Future of the State and Complexity Theory
- Projective Geometry and the shared viewpoint Constructing by Connecting
- Introduction to Change Management
- Change Management and Affine Geometry
- Euclidian Geometry and Change Management, about the Horizon, MindScapes and Meta-systems
- Projective Geometry, about lines points and the shared view
- Similarity Geometry and Being Different, Creativity and the Holy Ghost
- Mappings between Geometries Moving back to Panarchy, what is a Geocology?
Chapters 1-12 are about Geometry, Mathematics and Physics.
In chapter 3 I will show you how a new concept of Space is able to produce a Theory of Everything that explains the Para-Normal.
From chapter 10 on I describe the relationship between geometry and change. I will show that our Embodied language already contains everything we have to know about geometry.
As an example, reflect on what we are projecting on What when we design(“ont-werp“) and what Scape we See when we are projecting.
This blog is still under Construction.
1 The Pragmatism of Charles Sanders Peirce
Writing chapter 12 has generated (as always) many issues I never thought about before. The major cause is Charles Sanders Peirce , (1839-1914) the “inventor” of Semiotics and the first Pragmatist in the Us. He believed that science is finished when the theories are working in Practice but also that the Laws and Constants of Nature are changing all the time.
In this blog you wil find out that current science has moved far away from he path of converging because it lost its foundation. This foundation lies behind the imagination in the nothing.
After my encounter with Peirce I stumbled upon The theory of J. W.Dunne who experimented with predicting the Future and discovered Hyperspace.
Looking for Hyperspace gave the link to ANPA, an organization of scientists who try to understand the Paranormal. After that I rediscovered (New) Thinking Allowed (NTA), a YouTube-channel of Jeffrey Mislowe, a wellknown para-psychologist.
I (re)discovered NTA because I have always been interested in the paranormal because I was ” paranormal” since I was a child. Ghosts visited me when I was young and when I was older I became “enlightened” (“a terrifying experience”).
Looking for an interesting issue on NTA I rediscovered Alien Abductions and the Grays (our descendants out of the Future), an issue I also encountered when I met the medium Judith Moore. by accident. She helped me to understand what was happening to me after my Jump of my Kundalini that caused many strange effects. Through Judith I discovered that I was of the lineage of the Persian Magi.
As you can see this Blog grows by accident because I Explore (a connection between the Imagination and Action) every Possible paths just as Nature is doing.
Introduction in Semiotics
“If we are to proceed in a logical and scientific manner; we must; in order to account for the whole universe; suppose an initial condition in which the wholeuniverse was non existent; and therefore a state of absolute nothing:…We start; then; with nothing; pure zero: But this is not the nothing of negation: For not means other than; and other is merely a synonym of the ordinal numeral second: As such it implies a first; while the present pure zero is prior to even first: The nothing of negation is the nothing of death; which comes second to; or after; everything: But this pure zero is the nothing of not having been born: There isno individual thing; no compulsion outward nor inward; no law: It is the germinal nothing; in which the whole universe is involved or foreshadowed: As such; it is absolutely undefined and unlimited possibility boundless possibility There is no compulsion and no law: It is boundless freedom:(Collected papers of S. Peirce, 1931)
When you look at he 2 pictures below who are taken out of the second link about Semiotics you can see that the Representamen is an intermediary beween the Duality of the Object (Event, Outside) and the Subject (Inside, Square, (Mind<-> Senses)<-> (Emotions<->Imagination).
In the third picture below you see that the Triangel is a Connection of 3 Dualities.
The metamyth is a model that contains all the myths in every culture. This myth is defined by Joseph Campbell in his book The Hero with a thousand Faces.
2 Thinking about Thinking
3 About HyperSpace
Predicting the Future by Observing the Observer in Hyperspace
The Mathematics of Hyperspace
4 Infinite Games
This is Version 2. In this version I have finished the Educational part of this blog (Chapter 1) and I have started to write about the Geometry of Change. in chapter 12.
In this part I advice you to spend some time on a video of George Lakoff one of the Leading Scientists in Embodied Cognition . This part of Cognition Theory is based on the Fusion of Complementary concepts (“Bisocation“).
Will McWhinney gave me a book of J.P. Carse called Infinite Games. Infinite games are the opposite of the Finite Game that ends when somebody has won. The Infinite Game is a Game that Creates Games. It is the game of the Trickster. The same Dichotomy can be found in the difference between a Vocation and a Career. In a career (a Racetrack) you Win or Lose.
In this blog you will find that the Finite Game of the Controllers is related to Affine Geometry (Order, Ranking, Being the Same) and the Infinite Game of the Trickster to the Similarity Geometry (Being Different). There are two more Geometries that are related to Measures (Euclidian) and Connections (Projective).
We are witnessing the birth of Artificial Intelligence (AI). AI has nothing to do with Intelligence. It is producing Artificial Humans that beat humans in many area’s (Chess, GO) but still not in Mathematics. Just like you’re calculator you have the choice to be dependent on a machine or to become an exception a human who is able to calculate by Head. Every new Technology makes us more dependent from this new technology (“the so called Automation Paradox)
This is one of the most interesting documents about the Foundations of Physics and Mathematics I have read for a very long time. It shows what I already wrote down a few years ago about Geometric Algebra that the Number system opens up new number systems when to want to Reverse what you did.
The Positive numbers end by zero and move over to the negative numbers. When you standardize repeating adding and call it multiply dividing ends when you reach zero. Repeating multiplying generates the square roots that end with the negative numbers generating the Imaginary numbers (i=SqRT-1) but this is not the end. Generalizing the imaginary numbers (the Quaternions) created numbers nobody understood until it was found that they are Rotations in N-Dimensional Space.
Peter Rowland surprises by showing that the symmetries in the symmetries show the Implicate Order of David Bohm and more important that zero (“truly empty) is the Beginning (“alpha”) and the end (“omega”). Which means that the universe is always in balance.
Duality & Polarity
If a statement is true its Negation is also true. In geometry Points also called incidents are lines that Meet and Lines are unions of Points. A point is not-Space and is empty and Flat space is a union of lines. True Statements can be rephrased with different components that create new truths about existing components. The next step is Category Theory in which you can reason with theories (called Functors) as objects called Types.
The third video is about the emerging Global Brain. The first two video’s are about the Foundation of Mathematics which is based on Contradiction . The fourth video is about the Human Relationship theory of Alan Fiske.THis theory is a Bridge between Geometry and Change Management.
History of this Blog
The reason behind this blog is explained in the last chapter of my blog About the Ecology of the State.
I combined Panarchy with Paths of Change also a Theory about change and the theory of Alan Fiske about Human relationships. This combination gave me the insight that there is a shared Geometry behind many of the theories tabout Change.
This blog gives you an opportunity to combine the theories yourself. I also will show you that this geometry was known for a very long time ago mainly starting in India (See “Vedic Mathematics“). In the interpretation of the Theory of Alan Fiske the Scales of Measurement play an important role. I have created a special Chapter 8. for this subject.
In this blog I want to explore the Geometry of Change. To make it possible that others are also able to think about Geometries this blog contains many Educational Videos’.
As you can see in this Chapter Geometry is very old. It was the Foundation of Art, Architecture , the State and Religion. People have been fascinated by Patterns like the visible patterns Up in the Sky of the Sun, Moon Planets and the Zodiac but also the patterns in numbers. Out of Geometry many sciences have grown that were grouped in schools sometimes called a University. Behind he patterns music was found and music was also created using patterns. The most important Music was the Music of the Spheres . This chapter is Big. It contains many Video’s that contain simulations. The main reason is that you have to See (“insight”) the Theory to understand the Practice.
How Physics, Movement, Symbols and Sound are supported by Geometry
The geometry of our space has zero curvature. In spaces with positive or negative curvature other rules are valid. George Bernhard Riemann developed a new geometrical concept by imagining a 2-dimensional bookworm living on a 3D crumpled sheet of paper.
The surface of the paper would seem to be flat and undistorted. Because the worm can only perceive two dimensions it would not be able to detect that his own body crumples with the paper in the higher dimension. The “force” that would keep the bookworm from moving in a straight line was not a mysterious “action at a distance”, but a result of the unseen warping from the third dimension.
You can imagine a similar experience by walking a straight line on a rotating platform. To you the shortest connection is a straight line while you move with a curve when observed by someone outside the platform. The geometry changes the idea that the shortest distance between two points is a straight line.
It even changes the idea that we return on the same point when we move in a loop (“circle”). This happens when our space contains one or more holes (“singularities”, “dividing by zero”).
8 Theory of Measurement
Measurements can be made through the human Senses or through the use of a measurement Instruments.
Measurement is the assignment of Numerals to a system according to a set of rules. These rules are called a Theory.
Our senses or the instruments that are used to measure the system also represent a theory. This theory has a sometimes unknown impact on our measurement.
To avoid the Bias of the Theory behind our Measurement Systems a theory has to be a Structure Preserving mapping, a homomorphism. The Structure of the system has to stay the same when the rules are applied.
If the theory does not preserve structure the theory introduces its own theory and we are not measuring the original system.
Not only the primary theory has to be a homomorphism. The complete chain of theories we use has to preserve the structure (The Uniqueness Axioma) of the original system.
To avoid Bias a System of Measurement Scales is defined.
a Nominal Scale defines Sets. Sets contain the Same elements. When we want to preserve structure we have to satisfy the constraint If s1 = s2 ⇔ f(s1) = f(s2) (“the Same stays the Same”). This is called the Symmetric group, the group of all Permutations of the objects in the Set.
The Ordinal Scale is part of the nominal scale. The relational structure preserved during the measurement process preserves equality and order. The set of admissible transformations are relations that satisfy the constraint If s1 < or >s2 ⇔ f(s1) < or >f(s2). This is called the Order-Preserving Group and is the group of monotonic increasing functions.
The Interval Scale has to satisfy the constraint If s1−s2 = s3−s4 ⇔ f(s1)−f(s2)=f(s3)−f(s4).This is called the General Linear Group (or Affine Group). Differences can only be preserved when the transformation is a Linear transformation Ax + B where A is a Rotation and B is Translation (Displacement).
The Ratio Scale has to satisfy the constraint If s1/s2 = s3/s4 ⇔ f(s1)/f(s2) = f(s3)/f(s4). This is called the Linear Group.The only transformation that satisfies this constraint is the functions f(x) = Ax. This means that the only tranasformation that is left is muliplication and division (“not by zero!). which is transl;lated in Expansion and Compression the object of Topology.
New scale classification within the representational theory of measurementDownload
With Geometric Algebra you can Calculate with Shapes. Geometric algebra is a very convenient representational and computational system for geometry. It is going to be the way computer science deals with geometrical issues. It contains, in a fully integrated manner, linear algebra, vector calculus, differential geometry, complex numbers and quaternions as real geometric entities, and lots more.
Geometric Algebra brings us back to the Tetractys of Pythagoras which shows the Fourth triangular number which is part of the Triangle of Pascal.also called the Yang Hui in China and Mount Meru in Sanskrit. The Triangle of Pascal contains many Fractal structures that were used a very long time ago in Music (Rythms), Art & Architecture (Proportions) and Numerology (“The Art of interpreting Patterns in Numbers).
9 Mount Meru
the roots of all the geometries can be found in Ancient Indian Mathematics.
It all comes back to Breathing
Realize that the 3D version of Panarchy is also a 3D version of the Movement of the Relational Models of Alan Fiske and their related Geometries in Cognitive Space and the movement of many Concepts that share the same Worldviews of Path of Change.
Also Realize that Panarchy is a result of a theory (Cultural Theory) that is based on the same Worldviews of PoC and of Alan Fiske that can be explained by a 2×2 Matrix containing the variables Agency and Communion that are the same as Yin and Yang.
Yin and Yang are also represented by 0 and 1 and therefore the Triangle of Pascal represents the many combinations of possible personalities on earth but is also a result of a completely different System (Geometries) to calculate Combinations. Think about (X>Y)**n (Affine) or (X-Y)**n (Euclidian) as an example (X>Y)**n is a Program (“Protocol”) to n times create all the possible combinations of X>Y.
It is therefore also not strange to call the total process of the movement of Expansion (Yin) and Compression (Yang) in space the Cosmic Breath named the Svara in Sanskrit. Svara स्वर (svara and svāra): Voice, musical note, sound; note of the musical scale, tone in recitation, accent in grammar, symbolic expression.
11 About Perspectives and Projective Geometry
Projective Geometry PG)is a result of Perspective Drawing
As you can see in the picture above PG makes use of drawing Lines that connect the Point of the Eye (the Sensor) with the \Planes and Points of the Object of the Drawing. Observe that the object is a Sphere. and that the two lines connect with the sphere at the Horizon which is a line we often confuse with Infinity(“the point we will never reach”).. Also observe that the rear-end of the Sphere is invisible.
The pole of the Sphere can be connected to Parallel Lines that Never Cross. The lines connected to the eye of the artist and the Pole always have an Angle>0.
PG Connects many Points(“people”) by Lines (“Connectors“) and is there fore highly comparable with Communal Sharing of Fiske and Social of PoC.
about Meta Geometries
Moving one step Higher in Abstraction.
In this program Projective Geometry was emphasized as the Unifying Frame for all other Geometries.
Although lines in the Projective Plane meet in one point of Infinity Klein argued that there could be two points of Infinity if the Projective Plane was a Surface Closed in Itself.
When we look at the Origin of Projective Geometry, the Artist painting A Sphere, Earth, on a Flat Surface, it is not difficult to realize that this Closed Surface is a Sphere. This sphere is projected on a plane that contains the imaginary numbers that are solutions of the cross-ratio when the 4 points 𝐴𝐵𝐶𝐷 are not on a circle.
12 Using The Geometry of Change
Refresh and Surprise
First I present a few Slides to refresh your knowledge about the Background of the Blog or to surprise you.
In chapter 13 start to talk about the Geometries of Change.
The issue of this chapter is to help you to think about related issues like Machines, Cybernetics, the Anticipatory System of Rosen but also about Semiotics.
You don’t have to understand everything and you can also skip as many issues as you want.
I hope you become inspired to look at the geometry with another view (“I hope the Mythic“) and see the Magic (“have you looked at . the video about “Mystic Geometry in Chapter 1″?).
Mind, Machines and Anticipatory Systems
Autoiesis is about Self-Reproduction or Repair during Production. Neil Theise loops from makro-levels to micro-levels of what we call reality. He explains complexity, autopoiesis,positive &negative feedback-loops, cancer and how all that relates to us in the universe and the universe in us? Why ants move away from their territory to come back when they have found the food that is needed.
The presentation behind the link above explains the theory of Robert Rosen in combination of the theory of George Lakoff. For the last one move below. For the first one explore this blog about Meta-Engineering. As you will see is that the presentation tells a comparable story as Chapter 2 about measurement in the way that it explains that a model is a mapping from something we experience outside with our senses (A natural system) or with our instruments and we have to make a structure preserving mapping to avoid that we introduce a bias with our measurement instruments.
The first thing you have to realize is that you have been looking at pictures that describe the same subject with different names. All of them are about Change and Change looks like Breathing <-.-> (Contract/Expand). Below you see the Expansion Pattern of “nothing”/. This pattern is controlled by the Trinity, the number 3 and the Triangel. This pattern is called the Bronze Mean. It is a specialization of the Golden mean. The bronze mean contains a very important number 43.
The first picture of this paragraph contains a Cycle connected to another Cycle where both cycles move in opposite direction showing the well known Moebius Ring (8). The model contains a center that contains the model of the whole. This is called a fractal. When you compare this model with other models look at the colors. I have used the same colors of PoC all the time.
13 About Affine Geometry, Maps, Metaphors and Mappings
In the model of the Geometry of Change you see that Blue, named Unity in PoC and Knowledge in other models is called an Affine Geometry and is connected the concept Rank and the Constraint If s1 < or >s2 ⇔ f(s1) < or >f(s2) which is called the Order-Preserving Group. Knowledge is an Order but what order?
The solution to this puzzle can be found at the beginning of this blog where you read the sentence “The role of Higher Dimensions in Physics and Mathematics”. The concept Dimension is used to define a Ranking of Spaces.
14 About Euclidian Geometry, Distance and the Horizon
In the picture above you see the Horizon. Horizon is related to Horizontal, a line that is perpendicular to a line that moves from Up to Down or Back. the horizon is an Illusion because we live on a Globe. Behind the Horizon we see nothing but we know that there is something behind the Horizon. In our Perspective the Horizon is the place where parallel lines Cross. The word horizon derives from the Greek “ὁρίζων κύκλος” horizōn kyklos, “separating circle”, where “ὁρίζων” is from the verb ὁρίζω horizō, “to divide”, “to separate”, which in turn derives from “ὅρος” (oros), “boundary, landmark. The horizon is a symbol for infinity (“the place we never will reach” but also something we can find wen we keep on moving at the right direction.
About Deep Learning & Euclidian and Non-Euclidian Shapes.
This video explains Neural Networks using Graphs that are able to recognize Non-Euclidian Objects.
About Scapes and Meta-Systems.
Below you see a picture and a presentation of Kent Palmer. He found out that the term Scape (Schap in Dutch) we use in Landscape is used to imagine a “flat plane” . In dutch and english scape is also translated into ship (“Friendship, vriendschap) being a relationship that carries as a tray, something to hold something.
Perspectives are about seeing something but seeing is used as an insight. We look at our personal frame.
A Few years ago I gave a presentation about Context to Software-architects about Mikhail Bahktin: The Wordwide Carnival: A Short Introduction into the World of Mikhail Bakhtin. He was a Russian Philosopher that was put into a Goelag-camp by stalin. He was an expert in Dialog and what he called the Chronotope: “The place where the knots of narrative are tied” or “the intrinsic connectedness of temporal and spatial relationships”.