Chapter 11.5: The Pattern of Four in Physics. The Four Forces
I discussed in the second chapter of the book how the four fundamental forces of physics fit the quadrant model pattern in that each force builds upon the last, and the final force, gravity, encompasses the previous three, in that without the previous three forces, gravity could not exist. The structure of the four forces fits the quadrant model pattern as such. There are two dichotomies. One dichotomy is nuclear forces in the microcosm v space forces in the macrocosm. The other dichotomy is unifying forces and separating forces. The four fundamental interactions in physics, thereby, are
Square 1: the strong nuclear force. This force is a unifying force, bringing hydrogen atoms to a helium atom. It is also a nuclear force, existing within the microcosm.
Square 2: the weak nuclear force. This force is a separating force, causing nuclear decay, such as in uranium and thorium. It is also a nuclear force.
Square 3: Electromagnetism. This force is a departing force, causing things to separate. It is a space force, existing in the macrocosm.
Square 4: Gravity. This force is a unifying force, bringing bodies together. It also works in the macrocosm.
CHAPTER 12: The Pattern of Four in Physics- Aristotle’s Four Elements
Aristotle, one of the first physicists, believed that four elements containing four qualities comprised everything. He identified the qualities as hot, cold, wet and dry. Relating these qualities to the personality model, hot corresponds to abstract. Hot things rise, hot things are weird, Abstract people are weird. Cold corresponds to concrete: cold things sink, and are normal, as are concrete people. Wet corresponds with cooperative: wet things fill their containers; cooperative people try to conform, and in a manner fill their containers/environments. Dry corresponds with utilitarian. Dry things are individuals, are solid, and “do their own thing”. Utilitarian people are individuals who do what they want, and are not influenced by others over what they think is best.
These four qualities yield four elements.
*Square one: Wind. Wind is hot and wet, and corresponds to the Idealist who is abstract and cooperative. Wind is hot in that it is weird, and rises. Hot corresponds with abstract. It is wet in that it fills all parts of its container, making it cooperative. Cooperative people fill their containers- they don’t do their own thing but mold to their environments.
*Square two: Water. Water is cold and wet, corresponding to the Guardian who is concrete and cooperative. Water is cold in that it is normal, and sinks. Cold corresponds with concrete. It is wet in that it fills its container. The second square is concerned with homeostasis. Water is healing and cleansing. The second square is homeostasis and thus is healing.
*Square three: Earth. Earth is cold and dry, and corresponds to the Artisan who is concrete and utilitarian. Earth is cold in that it is normal and sinks. It is dry in that it is an individual. It does its own thing, and is solid. The third square is always the most solid--Earth is solid and hard.
*Square four: Fire. Fire is hot and dry, corresponding to the Rational who is abstract and utilitarian. Fire is hot in that it is weird, and rises. Fire is utilitarian in that it is an individual, and seems solid, wanting to “do its own thing”, as opposed to filling its container. Square four is separate from the previous three, consistently evidencing differences. The fourth square has a quality of being like pure energy. Fire is like wind, water, and earth because it is ephemeral. Like the wind it rises, it flows like water, yet it seems solid like Earth.
*Square five: Aether. Aristotle postulated a possible fifth element, which he called the aether, relating it to the divine. The fifth is always related to the transcendent and the divine.. The fifth is God. Aristotle said that nothing exists without the aether, and the aether was located in the stars. While the fourth square hints at the transcendent, the fifth is always ultra transcendent.
Aristotle theorized that everything is composed of varying amounts of these five elements. Various cultures throughout the world also had a four/five element system. Some identified the fifth element as life, or the void. Interestingly the word, “one” sounds like wind; the word “two”, sounds somewhat like water, and has the “t” and “w” in it like water; the word “three” sounds like earth, having letters “erth” in it; the word “four” sounds like
fire. Five clearly sounds like life, which is considered in some cultures to be the fifth element.
Aristotle’s elements
Wind- hot and wet
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Earth- cold and dry
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Water- cold and wet
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Fire- hot and dry
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It is important to note that the four distinct squares of the quadrant model are often divided by two dichotomies which yield four results.
Chapter 13: Physics- The Four Phases of Matter
These four elements relate to the four phases of matter.
*Square one is gas. This corresponds to wind.
*Square two is liquid. This corresponds to water
*Square three is solid. This corresponds to earth.
*Square four is plasma. This corresponds to fire.
Plasmas are electrically conductive, create magnetic fields and electric currents, and react readily to electromagnetic forces. Positively charged nuclei swim in a "sea" of freely-moving disassociated electrons, and is similar to how such charges exist in conductive metal, and an electron "sea" that allows matter in the plasma state to conduct electricity. In fact, fire is a plasma; stars are plasma. The fourth, plasma, seems very different from the previous three states of matter, seeming not to belong. But the fourth is always essential.
It is important to note that movement between these phases always includes a distinct phase transition. Each stage is connected to the other, but they are all distinct. The squares of the quadrant model are simultaneously continuous and divided. Matter is either a gas, liquid, solid, or plasma. They are distinct yet unified. There is a possible fifth state of matter called the “Einstein Bose condensate”. Sometimes this is called the fifth state of matter. Again, this state is transcendent, like God; the fifth is always like God. It is sometimes called solid light. Light is often associated with God.
The States of Matter
gas
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solid
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liquid
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plasma
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Bose Einstein condensate
Chapter 14: Physics- The Four Kinematic Equations
There are also four kinematic equations describing the motion of all objects. The fourth one is different from the previous three in that it is a quadratic equation. There is a possible fifth kinematic that is also a quadratic equation. The fourth always points to the fifth, which is not necessary; the fifth always seem unnecessary. There only four essential kinematic equations, while allowing for a possible fifth. They are as follows:
*Square one: vf=vi+at
*Square two: x=.5(vf+vit)
*Square three: vfsquared=visquared+2ax
*Square four: x=vit+.5atsquared
*Square five: x=vft-.5atsquared.
Kinematic equations
vf=vi+at
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vfsquared=visquared+2ax
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x=.5(vf+vit)
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x=vit+.5atsquared
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x=vft-.5atsquared.
Chapter 15: Physics- The Four Maxwells’ Equations.
Four equations describe the nature of light. A lot of people walk around with these equations on their shirts. They are the famous Maxwell's equations. Maxwell's equations inspired Einstein because they combined electricity and magnetism. Maxwell's big discovery was that light was an electromagnetic phenomenon, and that all light travels at the same speed. This helped lead Einstein to the general theory of relativity. These equations are basically the equations for light. These equations define all electromagnetism, including television light rays, radio waves, and x rays. They are
*Square one: Gauss' law
*Square two: Gauss' law for magnetism
*Square three: Maxwell-Farraday equation
*Square four: Ampere's circuital law.
Chapter 16: Physics- Maxwell’s Equations
Gauss' law
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Maxwell-Farraday equation
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Gauss' law for magnetism
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Ampere's circuital law
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Crookes tubes were used in dozens of historic experiments to try to find out what cathode rays were.[12] There were two theories: British scientists Crookes and Cromwell Varley believed they were 'corpuscles' or 'radiant matter', that is, electrically charged atoms. German researchers E. Wiedemann, Heinrich Hertz, and Eugen Goldstein believed they were 'aether vibrations', some new form of electromagnetic waves, and were separate from what carried the current through the tube.[13][14] The debate continued until J.J. Thomson measured their mass, proving they were a previously unknown negatively charged particle, which he called a 'corpuscle' but was later renamed as 'electron'.
Maltese cross
Julius Plücker in 1869 built an anode shaped like a Maltese Cross in the tube. It was hinged, so it could fold down against the floor of the tube. When the tube was turned on, it cast a sharp cross-shaped shadow on the fluorescence on the back face of the tube, showing that the rays moved in straight lines. After a while the fluorescence would get 'tired' and decrease. If the cross was folded down out of the path of the rays, it no longer cast a shadow, and the previously shadowed area would fluoresce stronger than the area around it.
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Chapter 16: Physics- The Four Thermodynamic Equations
There are also the four laws of thermodynamics.
Law 1: helps define the notion of temperature
Law 2: energy is conserved--the second square is always about homeostasis
Law 3: entropy- the third square is always construction
Law 4: entropy of a system reaches a constant value at absolute zero.
Laws of Thermodynamics
Law 1
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Law 3
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Law 2
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Zeroeth Law
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Chapter 17: Physics- The Standard Model of Particle Physics
The standard model of particle physics is perhaps the most comprehensive and popular model that describes the nature of particles in physics. This model is essentially the quadrant model pattern. In it there are three generations of fermions, each with four particles. There are also four bosons. Fermions are particles that obey different laws than bosons; this is the quadrant model pattern. The first three quadrants are the three generations of fermions. The fourth quadrant is the four bosons. Physicists know that this is the way particle physics is structured, but they do not know why. The Quadrant Model of Reality states that the standard model of particle physics is structured in this form because the purpose of reality is to express the quadrant model pattern, which is what the standard model of particle physics does.
Quadrant 1: The first generation is fermions. The first two squares form the duality;
the first two squares are always a duality. The duality is the up and the down quark. The third square is the electron. The electron is the doer; the third square is always the doer. The electron is constantly moving and changing position, whereas the up quarks and the down quarks make up the protons and neutrons in the nucleus. Therefore they represent homeostasis which is characteristic of the first and second squares. The electron neutrino is the fourth. The fourth never seems to belong with the previous three. Scientists experienced great difficulty in discovering neutrinos. They eventually discovered that electron neutrinos can become electrons and down and up quarks. Electron neutrinos are essentially different from the previous three, yet they encompass them. That is the nature of the forth square being simultaneously different yet the same and encompassing the previous three.
*Square one: up quark
*Square two: down quark
*Square three: electron
*Square four: electron neutrino.
Quadrant 2: The second generation of fermions. Here a similar pattern emerges; there is the charm quark and the strange quark, which form the duality. The muon is the doer. the muon neutrino is the fourth, and different, yet it can become the previous three. The fourth is separate yet encompasses the previous three.
*Square one: charm quark
*Square two: strange quark
*Square three: muon
*Square four: muon neutrino.
Quadrant 3: In this quadrant the same pattern is formed. There is the duality between the first and second. The third is the doer, and the different fourth engages the previous three.
*Square one: top quark
*Square two: bottom quark
*Square three: tau
*Square four: tau neutrino.
Quadrant 4. The first three squares and quadrants are always very connected, whereas the fourth is always different. In the thinking, emotion, doing and dreaming quadrant thinking, emoting, and doing, seem interconnected, and dreaming seems different. But while dreaming seems different, it is clearly interconnected with the previous three. The same pattern holds true here; the first three generations of matter are fermions, and fermions are all very similar. There are four bosons:
*Square one: gluon
*Square two: photon
*Square three: z boson
*Square four: w boson. The four bosons are the fourth quadrant.
There is a 17th particle called the God particle. The 17th square transcends the first four quadrants; it is outside the quadrant model, establishing the first square of the fifth quadrant. The 17th is God. That which transcends the quadrant has a quality of being like God/Being. It is no coincidence that the 17th particle, the Higgs Boson, is viewed as the God particle; it was the last to be found. Without the Higgs Boson none of the other particles can exist, because the Higgs boson creates matter. The Higgs Boson is Being. The 17th square is Being. The 17th square is God. There is also a possible 18th and 18th particle which would fit the 19 squares of the quadrant model.
The Standard Model of Particle Physics
up quark
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electron
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top quark
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tau
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down quark
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electron neutrino
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bottom quark
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tau neutrino
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charm quark
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muon
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gluon
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z boson
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strange quark
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muon neutrino
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photon
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w boson
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Higgs Boson
The Annus mirabilis papers (from Latin annus mīrābilis, "extraordinary year") are the papers of Albert Einstein published in the Annalen der Physik scientific journal in 1905. These four articles contributed substantially to the foundation of modern physics and changed views on space, time, mass, and energy. The annus mirabilis is often called the "miracle year" in English or Wunderjahr in German.
These four papers of Einstein's miracle year reveal the quadrant model image.
Through these papers, Einstein tackles some of the era's most important physics questions and problems. In 1900, a lecture titled "Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light",[5] by Lord Kelvin, suggested that physics had no satisfactory explanations for the results of the Michelson-Morley experiment and for black body radiation. As introduced, special relativity provided an account for the results of the Michelson-Morley experiments. Einstein's theories for the photoelectric effect extended the quantum theory which Max Planck had developed in his successful explanation of black body radiation.
Square 1:The photoelectric effect. The article "On a Heuristic Viewpoint Concerning the Production and Transformation of Light"[einstein 1] received March 18 and published June 9, proposed the idea of energy quanta. This idea, motivated by Max Planck's earlier derivation of the law of black body radiation, assumes that luminous energy can be absorbed or emitted only in discrete amounts, called quanta.
Square 2: Brownian motion. The article "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen" ("On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat"), received May 11 and published July 18, delineated a stochastic model of Brownian motion.
In this paper it will be shown that, according to the molecular kinetic theory of heat, bodies of a microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitudes that they can be easily observed with a microscope. It is possible that the motions to be discussed here are identical with so-called Brownian molecular motion; however, the data available to me on the latter are so imprecise that I could not form a judgment on the question...
Square 3: Special relativity. Einstein's "Zur Elektrodynamik bewegter Körper" ("On the Electrodynamics of Moving Bodies"),[einstein 3] his third paper that year, was received on June 30 and published September 26. It reconciles Maxwell's equations for electricity and magnetism with the laws of mechanics by introducing major changes to mechanics close to the speed of light. This later became known as Einstein's special theory of relativity.
The paper mentions the names of only five other scientists, Isaac Newton, James Clerk Maxwell, Heinrich Hertz, Christian Doppler, and Hendrik Lorentz. It does not have any references to any other publications. Many of the ideas had already been published by others, as detailed in history of special relativity and relativity priority dispute. However, Einstein's paper introduces a theory of time, distance, mass, and energy that was consistent with electromagnetism, but omitted the force of gravity.
Square 4: On November 21 Annalen der Physik published a fourth paper (received September 27) "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" ("Does the Inertia of a Body Depend Upon Its Energy Content?"), in which Einstein developed an argument for arguably the most famous equation in the field of physics: E = mc2.
Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies. The paper is based on James Clerk Maxwell's and Heinrich Rudolf Hertz's investigations and, in addition, the axioms of relativity. The fourth square is the different square and transcendent square yet it encompasses the previous three. That is the nature of Einstein's fourth paper in his miracle year
These four papers created a paradigm shift in physics and changed physics from Newtonian physics to general relativity. It is no coincidence such a profound shift will reflect the quadrant model pattern, the form of existence
In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics, economics and physics.
The Wiener process Wt is characterised by four facts:
Square 1: W0 = 0
Square 2: Wt is almost surely continuous
Square 3: Wt has independent increments
Square 4: W_t-W_s\sim \mathcal{N}(0,t-s) (for 0 \leq s \le t).
Brownian motion was one of Einstein’s four miraculous papers from his miracle year. Brownian motion proved that things were made of atoms. It was his second paper, and the second square is about structure and homeostasis. Boltzmann proposed atoms before Einstein, but Boltzmann was ridiculed by scientists and he was treated so poorly he committed suicide. Einstein later came and redeemed Boltzmann.
Scale vector diagrams are quadrants
Representing Vectors
Vector quantities are often represented by scaled vector diagrams. Vector diagrams depict a vector by use of an arrow drawn to scale in a specific direction. Vector diagrams were introduced and used in earlier units to depict the forces acting upon an object. Such diagrams are commonly called as free-body diagrams. An example of a scaled vector diagram is shown in the diagram at the right. The vector diagram depicts a displacement vector. Observe that there are several characteristics of this diagram that make it an appropriately drawn vector diagram.
a scale is clearly listed
a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a head and a tail.
the magnitude and direction of the vector is clearly labeled. In this case, the diagram shows the magnitude is 20 m and the direction is (30 degrees West of North).
Conventions for Describing Directions of Vectors
Vectors can be directed due East, due West, due South, and due North. But some vectors are directed northeast (at a 45 degree angle); and some vectors are even directed northeast, yet more north than east. Thus, there is a clear need for some form of a convention for identifying the direction of a vector that is not due East, due West, due South, or due North. There are a variety of conventions for describing the direction of any vector. The two conventions that will be discussed and used in this unit are described below:
The direction of a vector is often expressed as an angle of rotation of the vector about its "tail" from east, west, north, or south. For example, a vector can be said to have a direction of 40 degrees North of West (meaning a vector pointing West has been rotated 40 degrees towards the northerly direction) of 65 degrees East of South (meaning a vector pointing South has been rotated 65 degrees towards the easterly direction).
The direction of a vector is often expressed as a counterclockwise angle of rotation of the vector about its "tail" from due East. Using this convention, a vector with a direction of 30 degrees is a vector that has been rotated 30 degrees in a counterclockwise direction relative to due east. A vector with a direction of 160 degrees is a vector that has been rotated 160 degrees in a counterclockwise direction relative to due east. A vector with a direction of 270 degrees is a vector that has been rotated 270 degrees in a counterclockwise direction relative to due east. This is one of the most common conventions for the direction of a vector and will be utilized throughout this unit.
Two illustrations of the second convention (discussed above) for identifying the direction of a vector are shown below.
Observe in the first example that the vector is said to have a direction of 40 degrees. You can think of this direction as follows: suppose a vector pointing East had its tail pinned down and then the vector was rotated an angle of 40 degrees in the counterclockwise direction. Observe in the second example that the vector is said to have a direction of 240 degrees. This means that the tail of the vector was pinned down and the vector was rotated an angle of 240 degrees in the counterclockwise direction beginning from due east. A rotation of 240 degrees is equivalent to rotating the vector through two quadrants (180 degrees) and then an additional 60 degrees into the third quadrant.
Representing the Magnitude of a Vector
The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow. The arrow is drawn a precise length in accordance with a chosen scale. For example, the diagram at the right shows a vector with a magnitude of 20 miles. Since the scale used for constructing the diagram is 1 cm = 5 miles, the vector arrow is drawn with a length of 4 cm. That is, 4 cm x (5 miles/1 cm) = 20 miles.
Using the same scale (1 cm = 5 miles), a displacement vector that is 15 miles will be represented by a vector arrow that is 3 cm in length. Similarly, a 25-mile displacement vector is represented by a 5-cm long vector arrow. And finally, an 18-mile displacement vector is represented by a 3.6-cm long arrow. See the examples shown below.
The cloud quadrant
hpc
enterprise
cloud
appliance
Thinking about cloud
Amid the hype and glitz on cloud storage and computing it can be difficult to separate the essential from the transitory. The word scale is abused; APIs are debated; business models are in flux: and new varieties of cloud infrastructure are being developed or marketed every month.
To get a handle on the concept I’ve developed a descriptive model that may help move the conversation forward.
The essential elements of cloud are scale and management. Everything else is negotiable – including cost.
Putting those on the axes of a graph gives a simple visual picture of the scale and management environment.
Scale is reasonably self-explanatory: single namespace; single management domain; reasonable upward performance increment per incremental dollar investment.
Management is perhaps more complex. Researchers at IBM have long championed the idea of autonomic — self managing — systems. At the highest level cloud systems require an autonomic management paradigm: there’s just too much gear and too many failures for people to fix. The infrastructure must be self healing, load balancing, and fault and disaster tolerant.
These are qualitative not quantitative metrics. However it is worth exploring why the other quadrants are named as they are.
Appliance. This quadrant shares many of the same self management capabilities of the cloud but on a smaller scale. Today we see these systems popular with large volume imaging applications in medical and media production.
Enterprise. Enterprises don’t have the luxury of a few primary application types. They need systems that adapt to a wide variety of legacy application requirements. In addition they face considerable regulatory and legal constraints that make tuning the storage infrastructure imperative.
High-Performance Computing. HPC systems need to be highly tunable to meet specialized application requirements. When an application takes days or weeks to run even on few extra percentage points of performance out of the system translates into hours or days saved.
There are four visible hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right. The Balmer series of hydrogen was what Bohr used to establish his theory of quantum mechanics, and it turned out his theory only really worked perfectly with hydrogen. Hydrogen is the simplest Balmer series with four lines. This solved the mystery of quantum leaps and revolutionized physics.
In general relativity, a frame field (also called a tetrad or vierbein) is a set of four orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime. The timelike unit vector field is often denoted by {\vec {e}}_{0} and the three spacelike unit vector fields by {\vec {e}}_{1},{\vec {e}}_{2},\,{\vec {e}}_{3}. All tensorial quantities defined on the manifold can be expressed using the frame field and its dual coframe field.
Frames were introduced into general relativity by Hermann Weyl in 1929
Baryons, along with mesons, are hadrons, meaning they are particles composed of quarks. Quarks have baryon numbers of B = 1⁄3 and antiquarks have baryon number of B = −1⁄3. The term "baryon" usually refers to triquarks—baryons made of three quarks (B = 1⁄3 + 1⁄3 + 1⁄3 = 1).
Other exotic baryons have been proposed, such as pentaquarks—baryons made of four quarks and one antiquark (B = 1⁄3 + 1⁄3 + 1⁄3 + 1⁄3 − 1⁄3 = 1), but their existence is not generally accepted. In theory, heptaquarks (5 quarks, 2 antiquarks), nonaquarks (6 quarks, 3 antiquarks), etc. could also exist. Until recently, it was believed that some experiments showed the existence of pentaquarks—baryons made of four quarks and one antiquark. The particle physics community as a whole did not view their existence as likely in 2006, and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks] However, in July 2015, the LHCb experiment observed two resonances consistent with pentaquark states in the Λ0
b → J/ψK−
p decay, with a combined statistical significance of 15σ.
The pentaquark, with four quarks is transcendent and does not seem to belong. That is the nature of the fourth square.
In quantum field theory, fermions are described by anticommuting spinor fields. A four-fermion interaction describes a local interaction between four fermionic fields at a point. Local here means that it all happens at the same spacetime point. This might be an effective field theory or it might be fundamental.
Chapter 18: Physics- M Theory
M theory is an attempt by physicists to combine all of the forces of nature into one theory. The theory is that particles are in fact vibrating strings. This theory evolved into five main theories called string theories to explain the nature of reality as a symphony of vibrating strings. These string theories were combined by Edward Witten into one, known as M theory. M theory recognizes that the different string theories are different aspects of one ultimate theory. Witten combined the separate theories, noticing that they were all interrelated. Similarly the Quadrant Model of Reality recognizes that thinking, emotion, doing, and dreaming are all different aspects of the same thing. They are all interrelated. The M theory fits the quadrant model pattern.
*Square one: type I string theory
*Square two: type II A string theory
*Square three: type II B string theory
*Square four: Heterotic SO(32)
*Square five: Heterotic E8xE8.
The first three string theories are very related. Then the fourth is different. The fourth
is heterotic, and indicates the nature of the fifth. Heterotic E8xE8 apparently is extremely transcendent, and people associate it with divine. The fifth has a quality of transcendence,
like God. This fits the quadrant model pattern. M theory is called the theory of everything for physics. But it is merely a reitteration of the quadrant model pattern.
M Theory
Heterotic E8xE8
Gromov Witten theory is a theory to find the number of curves on a manifold. This is a classical problem in algebraic geometry that every algebraic geometer knows.
Square 1: For lines of degree one curves there is 2875. This is a classical result in the 1880s
Square 2: In the 1980s the number of lines for d=2 conics was 609,250.
Square 3: For the number of curves by a cubic equation there was 317,206,375. Mathematicians needed a computer to find this number. Originally they discovered there was a problem in the computer code. Physicists asked them to redo the equation and they discovered the number.
square 4: For a manifold of degree four even a more massive effort was undertaken than with degree three. It was one of the most difficult problems in mathematics and took a huge amount of effort to discover. The fourth square is always different.
Square 5: By the time that physicists were trying to find the number of curves for degree five computer technology got to the point that there was no longer any effort to find the numbers and after finding degree four all of the numbers after four were found. Square 5 is always transcendent. The nature of this problem mirrors the nature of a child learning numbers, how he can learn the first four numbers having a difficult time and does not understand numbers, but by number five he understands all numbers and no longer has trouble learning numbers. There was a huge amount of effort to find the first four degrees in Gromov Witten theory. It took a century of mathematicians working tirelessly. At the fifth degree and beyond there was no more effort because high tech computers did it all effortlessly by that point.
This is not a coincidence. The nature of reality is it reveals the quadrant model pattern throughout. Groom Witten theory is essential for string theory, which I also described ultimately reflects the quadrant model pattern.
Chapter 19: Physics- The Four Levels of the Multiverse Theory
Physicists have proposed the multiverse theory, saying that there are multiple universes in existence. Hindus already hypothesized multiple universes. According to Tegmark there are four levels of multiverses, and this classification system is accepted by physicists. They are
Square 1: A level 1 multiverse is beyond the cosmological horizon due to inflatons. The notion of this multiverse is not controversial.
Square 2: A level 2 multiverse is made up of bubbles and different cosmic constants due to string theory. A level 2 multiverse is generally accepted by physicists.
Square 3: A level 3 multiverse is the many worlds theory which arises due to quantum mechanics. In this model the universes are right on top of each other due to constant splits in time and space due to collapsing of the wave function, and it is probabilistic. A level 3 multiverse is more controversial than level 1 and 2. The third is always more bad. But it is generally accepted.
Square 4: A level 4 multiverse is very controversial and it is a mathematical universe, first introduced by Tegmark. The fourth is always different from the previous three and does not seem to belong.These universes have different mathematical structures.
Chapter 20: Physics- Kardashev’s Civilizations
Kardashev is a famous physicist who discussed types of civilizations, and Michio Kaku is known for popularizing this view of types of civilizations, and suggests that humans are moving into a type 1 civilization by 2030. The types of civilization fit the quadrant model pattern. The civilizations are ranked by energy. They are
Square 1: Type 0 civilization. Humans have lived up until the current point in history as a type 0 civilization.
Square 2: Type 1 civilization. Humans in this civilization have mastered planetary energy. In this civilization hurricanes and earthquakes are controlled.
Square 3: Type 2 civilization. Humans in this civilization can manipulate the energy of stars and star systems.
Square 4: Type 3 civilization. Humans in this civilization are galactic and can control hundreds and thousands of star systems.
Kruskal–Szekeres diagram reflect the quadrant model pattern and describe phenomena in space. The quadrants are the black hole interior (II), the white hole interior (IV) and the two exterior regions (I and III). The dotted 45° lines, which separate these four regions, are the event horizons. The darker hyperbolas which bound the top and bottom of the diagram are the physical singularities. The paler hyperbolas represent contours of the Schwarzschild r coordinate, and the straight lines through the origin represent contours of the Schwarzschild t coordinate.
In general relativity Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole.
The maximally extended Schwarzschild geometry can be divided into 4 regions each of which can be covered by a suitable set of Schwarzschild coordinates. The Kruskal–Szekeres coordinates, on the other hand, cover the entire spacetime manifold. The four regions are separated by event horizons.
Square 1: I exterior region -X < T < +X 2GM < r
Square 2: II interior black hole \vert X \vert < T < \sqrt{ 1 + X^2 } 0 < r < 2GM
Square 3: III parallel exterior region +X < T < -X 2GM < r
Square 4: IV interior white hole - \sqrt{ 1 + X^2 } < T < - \vert X \vert 0 < r < 2GM
Square 2 and square 4 are always opposites but connected in that manner.
In special relativity, a light cone (or null cone) is the surface describing the temporal evolution of a flash of light in Minkowski spacetime. This can be visualized in 3-space if the two horizontal axes are chosen to be spatial dimensions, while the vertical axis is time.
The light cone is constructed as follows. Taking as event p a flash of light (light pulse) at time t_0, all events that can be reached by this pulse from p form the future light cone of p, while those events that can send a light pulse to p form the past light cone of p.
Given an event E, the light cone classifies all events in space+time into 5 distinct categories:
Square 1: Events on the future light cone of E.
Square 2; Events on the past light cone of E. These two are the duality.
Square 3: Events inside the future light cone of E are those affected by a material particle emitted at E. The third square is the doing square. It is physical.
Square 4: Events inside the past light cone of E are those that can emit a material particle and affect what is happening at E. The fourth square always points to a larger context.
Square5: All other events are in the (absolute) elsewhere of E and are those that cannot affect or be affected by E. The fifth square is always ultra transcendent like God. Remember that the fifth element is the ether, which is hot cold dry and wet. The ether is supposed to be everywhere. Here these events are absolutely everywhere
When studying black hole physics the main subject that is taught is Penrose diagrams. Penrose diagrams reflect the quadrant model pattern
In theoretical physics, a Penrose diagram (named for mathematical physicist Roger Penrose) is a two-dimensional diagram that captures the causal relations between different points in spacetime. It is an extension of a Minkowski diagram where the vertical dimension represents time, and the horizontal dimension represents space, and slanted lines at an angle of 45° correspond to light rays. The biggest difference is that locally, the metric on a Penrose diagram is conformally equivalent to the actual metric in spacetime. The conformal factor is chosen such that the entire infinite spacetime is transformed into a Penrose diagram of finite size. For spherically symmetric spacetimes, every point in the diagram corresponds to a 2-sphere.
Penrose diagrams are often used to illustrate the hypothetical Einstein-Rosen bridge connecting two separate universes in the maximally extended Schwarzschild black hole solution. The precursors to the Penrose diagrams were Kruskal–Szekeres diagrams. The Penrose diagram for the maximally extended Schwarzschild spacetime i the Kruskal geometry. I already discussed the Kruskal-Szekeres diagrams and how they portray the quadrant model pattern.
The horizons divide the Kruskal geometry into four regions. The original Schwarzschild region with r>2m is the righthand asymptotic region (“us”). The upper quadrant with r<2m represents the black hole region, and the lower quadrant is a time-reversed copy, corresponding to a white hole. There is also a second asymptotic region on the left (“them”), which cannot communicate with the righthand region.
The Kruskal-Szekeres diagrams and Penrose diagrams are divided into four quadrants.
The Michelson–Morley experiment was performed over the spring and summer of 1887 by Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year. It compared the speed of light in perpendicular directions, in an attempt to detect the relative motion of matter through the stationary luminiferous aether ("aether wind"). The result was negative, in that the expected difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles, was found not to exist; this result is generally considered to be the first strong evidence against the then-prevalent aether theory, and initiated a line of research that eventually led to special relativity, which rules out a stationary aether.The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution".
The structure of the experiment fit the quadrant image in that the light was shot in perpendicular directions and formed a quadrant image. This is one of the most famous and revolutionary experiments in physics history and it reflects the quadrant image
The Double Tetrahedron is also known as a Star Tetrahedron or the MerKahba. The tetrahedron is platonic solid with 4 Vertices and 4 Faces.
Within it lies the energy that holds all life together. The bonds that hold atoms, particles and molecules together, all the way down to nanoparticles and all the way up to macroparticles, are tetrahedral.
"The tetrahedron occurs conceptually independent of events and independent of relative size. By tetrahedron, we mean the minimum thinkable set that would subdivide the Universe and have the interconnectedness where it comes back upon itself…The basic structural unit of physical Universe quantation, tetrahedron has the fundamental prime number oneness.” R. Buckminster Fuller
R. Buckminster Fuller from his book Synergetics I. R. Buckminster Fuller noted that the prime geometry of nature is the tetrahedron. Without this structure, our universe as we know it, wouldn’t exist.
Metatron’s cube is a wonderful picture of the geometry and energy that flows through Star Tetrahedra.
DNA is made of two spiraling strands that make many tetrahedra down the DNA helix.
“Tetrahedron as Vectorial Model of Quantum: The tetrahedron as a basic vectorial model is the fundamental structural system of the Universe. The open-ended triangular spiral as action, reaction, and resultant (proton, electron, and anti-neutrino; or neutron, positron, and neutrino) becomes half quantum. An association of positive and negative half-quantum units identifies the tetrahedron as one quantum.” R. Buckminster Fuller
Nassim Harramein has attempted to discover the Unified Field Theory. I actually coincidentally met him at a mall in Kauai. Harmon notes quantums strung together creating tetrahedra which creates everything. The unknown in unified field theory is the spin. Harmon declares that the structure of this energy is tetrahedral. According to Haramein the inherent vibration within tetrahedra creates spin. The faster or higher the vibration, the faster the spin. Quantum physicists have observed that everything in the universe is spinning faster.
The tetragrammaton YHV and H or YHW and H of the Hebrew’s put into 3-dimensional form makes a star tetrahedra. It is the Star of David.
Ancient art depicts the Creator as a circle of fire. Fire is the forge of creation. The circle pictures the energy of creation. ALL that exists is a pleurage of interconnected energy. At the heart is the star tetrahedra and its pleurality is the icosahedron. The hexagon is the strongest structure known to man. At its heart lies the star tetrahedra. Carbon, soft graphite, has been made to be stronger than steel by forming it into hexagonal sheets. This year, one of the Nobel Prizes went to the inventors of graphene.
According to this theory the star tetrahedron fingerprint geometry (reflecting the quadrant four pattern) is the SOURCE of ALL that IS.
In the center of the flower of life, a very famous pattern in mathematics, with the interconnected dots, a star tetrahedron is formed.
Algae is a superfood. Unless it is harvested from a clean source and processed properly, I do not recommend its use. One of the things that struck me at the time was that the nucleus of chlorophyll and the nucleus of hemoglobin are almost identical! The only difference is the center atom – in chlorophyll it is magnesium, in hemoglobin it is iron. But the most remarkable thing is that both are Star Tetrahedron. Another word for the star tetrahedron is the Merkabah. I wonder if it is a coincidence that Merkabah is the name of this fundamental structure of existence, and my rap name is Merk Diezle, given to me in high school.
A tetrahedron is a four-sided pyramid. A Star Tetrahedron is a double tetrahedron, an octahedron. In its plane form, you would recognize it as the “Star of David”; in its spherical form, you would recognize it as the universal symbol of the atom.
R. Buckminster Fuller had a unique perspective on the Universe. He believed that “the tetrahedron is a form of energy package,” that the Universe in all of its “definable structuring””is tetrahedrally coordinate in rational number increments of the tetrahedron.” In other words, our Universe is “defined” by the tetrahedron. Again, the tetrahedron’s four sides symbolize the quadrant image.
"Tetrahedron as Vectorial Model of Quantum: The tetrahedron as a basic vectorial model is the fundamental structural system of the Universe. The open-ended triangular spiral as action, reaction, and resultant (proton, electron, and anti-neutrino; or neutron, positron, and neutrino) becomes half quantum. An association of positive and negative half-quantum units identifies the tetrahedron as one quantum.” R. Buckminster Fuller
The principle of yin-yang, positive and negative half quantums together making a quantum, light-dark, the principle of opposites exists in the basic tetrahedral model.
"The tetrahedron is the first and simplest subdivision of Universe, because it could not have an insideness and an outsideness unless it had four vertexes and six edges…The vertexial set of four local-event foci coincides with the requirement of quantum mathematics for four unique quanta numbers for each uniquely considerable quantum.
The tetrahedron is a form of energy package. The tetrahedron is transformable…All of the definable structuring of Universe is tetrahedrally coordinate in rational number increments of the tetrahedron.” R. Buckminster Fuller
"Two Triangular Energy Events Make Tetrahedron: The open-ended triangular spiral can be considered one “energy event” (or quantum) consisting of an action, reaction and resultant. Two such events (one positive and one negative) combine to form the tetrahedron.” R. Buckminster Fuller
The Star Tetrahedra is marks hemoglobin in blood and chlorophyll in plants. It is in everything that exists because it is the power that holds atoms together and atoms into molecules. The tetragrammaton YHV and H or YHW and H of the Hebrew’s put into 3-dimensional form makes a star tetrahedra. It is the Star of David. It is the Merkabah.
Nassim Haramein decoded the geometric information that is the I-Ching, an ancient set of oracular Chinese hexagrams. If you want to build the geometry of the structure of the space that is everywhere in the universe, which is an infinite tetrahedral array, you begin with the first octave of what becomes an infinite fractal division of the space in a perfectly balance state: a set of 64 tetrahedrons. At 64 tetrahedrons you have what Buckminster Fuller called the "vector equilibrium" also called the cube octahedron (8 tetrahedrons pointing inward) inside a second cube octahedron that is twice as large made of a total of 64 tetrahedrons: an octave.
To get to 64 tetrahedrons you bring together 8 star tetrahedrons. Each star tetrahedron is made from a tetrahedron pointing up and another polarized pointing downward creating what is also commonly known as a merkaba.
Nassim Haramein noticed the only "3D" geometry you can make with 6 solid lines is a tetrahedron and in order to make the second tetrahedron of a star tetrahedron you would need 6 broken lines to pass through the lines of the first tetrahedron. Nassim decoded the I Ching by showing how 6 solid lines and 6 broken lines are both the building blocks of the I Ching and that of a star tetrahedron.
Thus, the I Ching encodes the most fundamental geometric information you need to build the geometry of the universe!
The tetrahedron is the fourfold pattern expressing the quadrant four, the foundation of reality.
Within 64 perfectly stacked tetrahedrons, exist 2 octaves of a perfectly balanced geometry called the cube octahedron, or what Buckminster Fuller called the vector equilibrium. According to the physics of Nassim Haramein, the 64 tetrahedron grid is the seed geometry of what eventually becomes, with more and more octave growth, the infinite holofractographic vacuum structure of the entire universe.
As well:
• 64 codons in human DNA.
• 64 hexagrams in the I Ching.
• 64 sexual positions in the Kama sutra.
• 64 classical arts listed in many Indian scriptures.
• 64 "tantras" (books) of the "tantrism", which is a form of Hinduism.
• 64 is the maximum number of strokes in any Chinese character.
• 64 is the number of cells we have before our cells start to bifurcate (differentiate) shortly after conception.
• 64 is fundamental in computer memory bits and coding.
• 64 things are needed to be able to approach the Ark of the Covenant of the Lord according to the 2 copper scrolls that were found among the 300 Dead Sea Scrolls.
• 64 is encoded in the description of the Tetragrammaton in the Hebrew Bible, which is the 4-letter theonym YHW and H which means God in Hebrew.
• 64 is the number of generations from Adam until Jesus according to the Gospel of Luke.
• 64 forms or manifestations of the Lord Shiva in Hinduism
• 64 squares on chess and checker boards.
• 64 Braille characters in the old 6-dot system
• 64 demons in the Dictionnaire Infernal
• 64 is the smallest number with exactly seven divisors.
• Even The Beatles knew: "When I'm 64"
If you look at the number 64 it is the ultimate quadrant model, in that it is the epitome of the quadrant pattern. 64 is four quadrant models within four squares. In other words it is four squares of 16 within a quadrant.
The Flower of Life is a geometrical figure that is found all over the world. According to Nassim Haramein, the fundamental geometry of the fabric of space-time is an infinite tetrahedral array with spheres around each tetrahedron forming an infinite flower of life holofractographic lattice structure.
Ancient cultures from all over the world encoded the same geometric structure of the fabric of universe into their architecture, monuments and documents as was later deduced by a unified field theorist using the scientific method informed by observations made by using advanced modern technology in the late 20th century.
The Jains and the Vedics understood this pattern, as evidenced by the work of Bharati Krsna Tirthaji, for example, and so did the Kabalists, discussed extensively in the Sefer Yetzirah, in which it references “the cube of space.”
If so many ancient cultures understood the God pattern, then why is Haramein butting heads with mainstream physicists still? Even the Illuminati are said to have worshipped divine geometry. It shows up in crop-circles.
Even artists from recent history understood divine geometry. Leonardo Da Vinci was well versed in the phenomenon as evidenced in both his commentary and work. He studied the ‘flower of life’ extensively. The Mayans were aware of this divine archeological rhythm as well. It shows up in temples in Chichen Itza, and other sacred places.
Sacred Geom-2In more ancient history, the Temple of Osiris at Abydos, Egypt contains the oldest ‘Seed of Life’ to date. It is formed from seven circles in six-fold symmetry. It is unknown why the symbol was carved into granite, but some suggest it represents the ‘Eye of Ra,’ a pharaohic and religious authority of the time.
This flower of life and seed of life pattern appear all over the world. They were considered a part of the alchemists’ secrets, and the Metatron’s cube is based upon it
According to Haramein qycles of seed, egg & flower of life: Scalar geometric field patterning of the quantum vacuum fluctuations (based on the tetrahedron) that make up the very fabric of space itself. Metatron's Cube is a symbol derived from the Flower of Life which was used as a containment circle or creation circle. Leonardo da Vinci studied the Flower of Life's form and its mathematical properties. He drew the Flower of Life itself, as well as various components such as the Seed of Life. He drew geometric figures representing shapes such as the platonic solids, a sphere, a torus, etc., and also used the golden ratio of phi in his artwork; all of which may be derived from the Flower of Life design.
Nassim Haramein decoded the geometric figure that is know as "The Tree of Life". 10 "golden globes" connected by 22 channels, they say they come in pairs: 10 + 22 x 2 = 64, the same number as the number of tetrahedrons you need to create the first octivisation of the perfect vector equilibrium geometry of space-time.
The Tree of Life expresses the geometry of the fabric of the vacuum of space.
This short clip from the "Crossing the Event Horizon" 4 DVD set shows how Nassim Haramein decoded the Tree of Life, an ancient symbol from the Kabalistic tradition. If you consider the tree to be a 3D shape, not a flat symbol, and you consider them come in pairs at the tradition states, then you have all the geometric information you need to be able to build the foundational geometry of the fabric of space: a 64 tetrahedron grid. Nassim goes on to explain the geometry of space in great detail and how many ancient cultures encodes this information into their monuments, traditions and documents.
Leonardo da Vinci studied the Flower of Life's form and its mathematical properties. He drew the Flower of Life itself, as well as various components such as the Seed of Life. He drew geometric figures representing shapes such as the platonic solids, a sphere, a torus, etc., and also used the golden ratio of phi in his artwork; all of which may be derived from the Flower of Life design.
The 'Seed of Life' is formed from seven circles being placed with sixfold symmetry, forming a pattern of circles and lenses, which acts as a basic component of the Flower of Life's design. According to some, the seed of life depicts the 7 days of creation in which God created life.
The 'Egg of Life' is also a symbol composed of seven circles taken from the design of the Flower of Life.The shape of the Egg of Life is said to be the shape of a multi-cellular embryo in its first hours of creation.
The 'Fruit of Life' symbol is composed of 13 circles taken from the design of the Flower of Life. It is said to be the blueprint of the universe, containing the basis for the design of every atom, molecular structure, life form, and everything in existence. It contains the geometric basis for the delineation of Metatron's Cube, which brings forth the platonic solids.
Metatron's cube depicts the five platonic solids which may be derived form the flower of life. The five platonic solids are geometrical forms which are said to act as a template from which all life springs, according to spiritual belief. The Platonic solids are five structures that are crucial because they are the building blocks of organic life. These five structures are found in minerals, animated and organic life forms, sound, music, language, etc. Metatron's cube is also considered a holy glyph, used to ward off evil spirits. The Kabbalah's Tree of life is also thought to be derived from the flower of life.
The Temple of Osiris at Abydos, Egypt contains the oldest known examples of the Flower of Life. They are at least over 6,000 years old and may date back to as long ago as 10,500 B.C. or earlier. It appears that it had not been carved into the granite and instead may have been burned into the granite or somehow drawn on it with incredible precision. It is thought to possibly represent the Eye of Ra, a symbol of the authority of the pharaoh. Other examples can be found in Phoenician, Assyrian, Indian, Asian, Middle Eastern, and medieval art.
Nassim Haramein decoded the geometric figure that is know as "The Tree of Life". 10 "golden globes" connected by 22 channels, they say they come in pairs: 10 + 22 x 2 = 64, the same number as the number of tetrahedrons you need to create the first octivisation of the perfect vector equilibrium geometry of space-time.
The Tree of Life expresses the geometry of the fabric of the vacuum of space.
Nassim Haramein decoded the Tree of Life, an ancient symbol from the Kabalistic tradition. If you consider the tree to be a 3D shape, not a flat symbol, and you consider them come in pairs at the tradition states, then you have all the geometric information you need to be able to build the foundational geometry of the fabric of space: a 64 tetrahedron grid. Nassim goes on to explain the geometry of space in great detail and how many ancient cultures encodes this information into their monuments, traditions and documents.
Leonardo da Vinci studied the Flower of Life's form and its mathematical properties. He drew the Flower of Life itself, as well as various components such as the Seed of Life. He drew geometric figures representing shapes such as the platonic solids, a sphere, a torus, etc., and also used the golden ratio of phi in his artwork; all of which may be derived from the Flower of Life design.
The 'Seed of Life' is formed from seven circles being placed with sixfold symmetry, forming a pattern of circles and lenses, which acts as a basic component of the Flower of Life's design. According to some, the seed of life depicts the 7 days of creation in which God created life.
The 'Egg of Life' is also a symbol composed of seven circles taken from the design of the Flower of Life.The shape of the Egg of Life is said to be the shape of a multi-cellular embryo in its first hours of creation.
The 'Fruit of Life' symbol is composed of 13 circles taken from the design of the Flower of Life. It is said to be the blueprint of the universe, containing the basis for the design of every atom, molecular structure, life form, and everything in existence. It contains the geometric basis for the delineation of Metatron's Cube, which brings forth the platonic solids.
Metatron's cube depicts the five platonic solids which may be derived form the flower of life. The five platonic solids are geometrical forms which are said to act as a template from which all life springs, according to spiritual belief. The Platonic solids are five structures that are crucial because they are the building blocks of organic life. These five structures are found in minerals, animated and organic life forms, sound, music, language, etc. Metatron's cube is also considered a holy glyph, used to ward off evil spirits. The Kabbalah's Tree of life is also thought to be derived from the flower of life.
The Temple of Osiris at Abydos, Egypt contains the oldest known examples of the Flower of Life. They are at least over 6,000 years old and may date back to as long ago as 10,500 B.C. or earlier. It appears that it had not been carved into the granite and instead may have been burned into the granite or somehow drawn on it with incredible precision. It is thought to possibly represent the Eye of Ra, a symbol of the authority of the pharaoh. Other examples can be found in Phoenician, Assyrian, Indian, Asian, Middle Eastern, and medieval art.
At the entrance to the Forbidden City – an ancient imperial palace in Beijing that was built in the early 1400’s – you can see the same flower of life under the paw of the Fu Dog (more accurately called "Guardian Lions"). This palace was home to 24 emperors of the Ming and Qing Dynasties. Could the Fu Dogs not only be a symbol of protection to buildings and their inhabitants, but guardians of the knowledge of how universal energy works?
Female Fu Dog Could it be that the female Fu Dog, is guarding the life force itself – which is always in the form of a pup beneath her paw – while the partnered male is guarding the knowledge of how to access that life force for energy, sustainable design and the transformation of consciousness itself?
Since silicon is the most common semiconductor used in solid-state electronics, and silicon has a valence of four, the tetrahedral shape of the four chemical bonds in silicon is a strong influence on how crystals of silicon form and what shapes they assume.
The Royal Game of Ur, dating from 2600 BC, was played with a set of tetrahedral dice
Especially in roleplaying, this solid is known as a 4-sided die, one of the more common polyhedral dice, with the number rolled appearing around the bottom or on the top vertex. Some Rubik's Cube-like puzzles are tetrahedral, such as the Pyraminx and Pyramorphix.
The net of a tetrahedron also makes the famous Triforce from Nintendo's The Legend of Zelda franchise.
Tetrahedra are used in color space conversion algorithms specifically for cases in which the luminance axis diagonally segments the color space (e.g. RGB, CMY)
In numerical analysis, complicated three-dimensional shapes are commonly broken down into, or approximated by, a polygonal mesh of irregular tetrahedra in the process of setting up the equations for finite element analysis especially in the numerical solution of partial differential equations. These methods have wide applications in practical applications in computational fluid dynamics, aerodynamics, electromagnetic fields, civil engineering, chemical engineering, naval architecture and engineering, and related fields.
The tetrahedron shape is seen in nature in covalently bonded molecules. All sp3-hybridized atoms are surrounded by atoms (or lone electron pairs) at the four corners of a tetrahedron. For instance in a methane molecule (CH4) or an ammonium ion (NH4+), four hydrogen atoms surround a central carbon or nitrogen atom with tetrahedral symmetry. For this reason, one of the leading journals in organic chemistry is called Tetrahedron. The central angle between any two vertices of a perfect tetrahedron is \arccos{\left(-\tfrac{1}{3}\right)}, or approximately 109.47°.[20] [21]
Water, H2O, also has a tetrahedral structure, with two hydrogen atoms and two lone pairs of electrons around the central oxygen atoms. Its tetrahedral symmetry is not perfect, however, because the lone pairs repel more than the single O-H bonds.
Quaternary phase diagramsin chemistry are represented graphically as tetrahedra.
The Austrian artist Martina Schettina created a tetrahedron using fluorescent lamps. It was shown at the light art biennale Austria 2010.
It is used as album artwork, surrounded by black flames on The End of All Things to Come by Mudvayne.
Stanley Kubrick originally intended the monolith in 2001: A Space Odyssey to be a tetrahedron, according to Marvin Minsky, a cognitive scientist and expert on artificial intelligence who advised Kubrick on the HAL 9000 computer and other aspects of the movie. Kubrick scrapped the idea of using the tetrahedron as a visitor who saw footage of it did not recognize what it was and he did not want anything in the movie regular people did not understand.[26]
In Season 6, Episode 15 of Futurama, aptly named "Möbius Dick", the Planet Express crew pass through an area in space known as the Bermuda Tetrahedron. Many other ships passing through the area have mysteriously disappeared, including that of the first Planet Express crew.
In the 2013 film Oblivion the large structure in orbit above the Earth is of a tetrahedron design and referred to as the Tet.
The tetrahedral hypothesis, originally published by William Lowthian Green to explain the formation of the Earth, was popular through the early 20th century.
A tetrahedron having stiff edges is inherently rigid. For this reason it is often used to stiffen frame structures such as spaceframes.
At some airfields, a large frame in the shape of a tetrahedron with two sides covered with a thin material is mounted on a rotating pivot and always points into the wind. It is built big enough to be seen from the air and is sometimes illuminated. Its purpose is to serve as a reference to pilots indicating wind direction
The flower of life also appears on the walkway around the Golden Temple, or Harmandir Sahib, one of the holiest shrines of the Sikh religion. It was built in the 16th Century and means the “Temple of God.”
This temple was intricately designed and has many symbolic aspects. For example, it has four entrances that signify the importance of acceptance and openness in the Sikh religion – all visitors are welcome.
Given the thought and care that went into the temples construction, it seems significant that the flower of life also appears here.
Stan Tenen illustrates how the hebrew alphabet lays out perfectly on the structure of the Vector Equilibrium, with the ‘Tagin crownlets” identifying orienting spin axes.
Kototama is the millennia old tradition in which Morihei Ueshiba, the founder, was trained is the founder of Aikido
Kototama seems to be a message from ancient cultures of how to tune ones consciousness to the energy of the universe. Kototama is an ancient Japanese tradition that means “spirit of language”, “sacred sound”, or “the knowledge of the vibration of the Universe.” It is the practice of generating ritual sounds and words, with the belief that they can influence your body, mind, and soul. The Kototama chant creates a resonant torus around the body as Jack Wada demonstrates in this video.
Ancient texts cite 49 “motive” sounds in Kototama and one toning, the 50th, which encompasses them all. This 50th toning is the secret – it’s the active dynamic of the torus and it’s what allows people to access higher levels of consciousness through the Kototama. This is a strategic and enduring way to pass along vital information across generations.
Could it be mere coincidence that the sequence of vowels is identical to the Hebrew name of God – “Yah and weh” – that people were told not to speak aloud?
The Cabalistic Tree of Life, one of the central icons of the Hebrew holy book, the Torah, reveals a 64 tetrahedron array when composited and seen in 3D as ancient texts suggest.
If we visualize in 3D, we can see that the “seed” at the bottom of the tree grows into a tetrahedron and then into an octahedron – in the same way that living geometry complexifies most efficiently – regardless of scale.
The same pattern has appeared in the mysterious patterns in fields called “crop circles.” The authentic ones of these seem to be messages from advanced cultures about how energy works in the Universe, so that humans can learn to align with nature – as the Kototama tradition suggests, before it is too late.
It also fits perfectly on the flower of life…which also appeared in numerous forms as crop circles.
The half-octahedral shape of the Cheops pyramids is a key part of the fundamental structure of space-time itself.
Isotropic Vector Matrix It alternates with tetrahedra in the make-up of the Vector Equilibrium – the mother of all geometric symmetries - and the Isotropic Vector Matrix – the invisible structure of space.
This meta-physical “skeleton” of the cosmos itself was confirmed by a 10-year study by Italian Astronomers to see if the arrangement of galactic clusters was random or had any intrinsic structure.
Octahedra It turned out to be based on what they called “The Egg Carton Universe” – Octahedra – point to point
Researcher Nassim Haramein suggests that the key to the energy capabilities of the Ark of the Covenant was the 64 tetrahedra crystal he believes was contained within – that it tapped the energy that was then contained by the “capacitor box” and discharged through the gold cherubim “electrodes.”t
The CMYK color model (process color, four color) is a subtractive color model, used in color printing, and is also used to describe the printing process itself. CMYK refers to the four inks used in some color printing: cyan, magenta, yellow, and key (black). Though it varies by print house, press operator, press manufacturer, and press run, ink is typically applied in the order of the abbreviation.
The "K" in CMYK stands for key because in four-color printing, cyan, magenta, and yellow printing plates are carefully keyed, or aligned, with the key of the black key plate. Some sources suggest that the "K" in CMYK comes from the last letter in "black" and was chosen because B already means blue. However, this explanation, although useful as a mnemonic, is incorrect. K is used as "Key", which was possibly chosen because black is often used as outline
The first three are the triad. The k is the transcendent fourth that encompasses the previous three.
Printing is done through this process, which reflects the quadrant model pattern.
A Turing machine is an abstract "machine" that manipulates symbols on a strip of tape according to a table of rules; to be more exact, it is a mathematical model that defines such a device. Despite the model's simplicity, given any computer algorithm, a Turing machine can be constructed that is capable of simulating that algorithm's logic.
The Turing machine mathematically models a machine that mechanically operates on a tape. On this tape are symbols, which the machine can read and write, one at a time, using a tape head. Operation is fully determined by a finite set of elementary instructions such as "in state 42, if the symbol seen is 0, write a 1; if the symbol seen is 1, change into state 17; in state 17, if the symbol seen is 0, write a 1 and change to state 6;" etc. In the original article ("On computable numbers, with an application to the Entscheidungsproblem", see also references below), Turing imagines not a mechanism, but a person whom he calls the "computer", who executes these deterministic mechanical rules slavishly (or as Turing puts it, "in a desultory manner").
The head is always over a particular square of the tape; only a finite stretch of squares is shown. The instruction to be performed is shown over the scanned square.
Here, the internal state is shown inside the head, and the illustration describes the tape as being infinite and pre-filled with "0", the symbol serving as blank. The system's full state (its complete configuration) consists of the internal state, any non-blank symbols on the tape (in this illustration "11B"), and the position of the head relative to those symbols including blanks, i.e. "011B".
More precisely, a Turing machine consists of:
Square 1: A tape divided into cells, one next to the other. Each cell contains a symbol from some finite alphabet. The alphabet contains a special blank symbol (here written as '0') and one or more other symbols. The tape is assumed to be arbitrarily extendable to the left and to the right, i.e., the Turing machine is always supplied with as much tape as it needs for its computation. Cells that have not been written before are assumed to be filled with the blank symbol. In some models the tape has a left end marked with a special symbol; the tape extends or is indefinitely extensible to the right.
Square 2: A head that can read and write symbols on the tape and move the tape left and right one (and only one) cell at a time. In some models the head moves and the tape is stationary.
Square 3: A state register that stores the state of the Turing machine, one of finitely many. Among these is the special start state with which the state register is initialized. These states, writes Turing, replace the "state of mind" a person performing computations would ordinarily be in.
Square 4: A finite table of instructions that, given the state(qi) the machine is currently in and the symbol it is reading on the tape (symbol currently under the head), tells the machine to do the following in sequence (for the 5-tuple models):
Either erase or write a symbol (replacing aj with aj1), and then
Move the head (which is described by dk and can have values: 'L' for one step left or 'R' for one step right or 'N' for staying in the same place), and then
Assume the same or a new state as prescribed (go to state qi1).
In the 4-tuple models, erasing or writing a symbol (aj1) and moving the head left or right (dk) are specified as separate instructions. Specifically, the table tells the machine to (ia) erase or write a symbol or (ib) move the head left or right, and then (ii) assume the same or a new state as prescribed, but not both actions (ia) and (ib) in the same instruction. In some models, if there is no entry in the table for the current combination of symbol and state then the machine will halt; other models require all entries to be filled.
Note that every part of the machine (i.e. its state, symbol-collections, and used tape at any given time) and its actions (such as printing, erasing and tape motion) is finite, discrete and distinguishable; it is the unlimited amount of tape and runtime that gives it an unbounded amount of storage space.
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