https://en.wikipedia.org/wiki/Tetrabiblos

Tetrabiblos (Τετράβιβλος) 'four books', also known in Greek as Apotelesmatiká (Ἀποτελεσματικά) "Effects", and in Latin as Quadripartitum "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by the Alexandrian scholar Claudius Ptolemy (c. AD 90–c. AD 168).
Ptolemy is referred to as "the most famous of Greek astrologers"[2] and "a pro-astrological authority of the highest magnitude".[3] As a source of reference his Tetrabiblos is described as having "enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more"
The four books reflect the quadrant model pattern
Compiled in Alexandria in the 2nd century, the work gathered commentaries about it from its first publication.[2] It was translated into Arabic in the 9th century, and is described as "by far the most influential source of medieval Islamic astrology".[5]
Square 1:Book I: principles and techniques. The first square is gibing rules. The first square is homeostatic like the second. It is mental and gibes his philosophy. The first square is mental
Square 2:Book II: Mundane astrology
Book II presents Ptolemy's treatise on mundane astrology. This offers a comprehensive review of ethnic stereotypes, eclipses, significations of comets and seasonal lunations, as used in the prediction of national economics, wars, epidemics, natural disasters and weather patterns. The second square is always normal
And homeostasis. He describes gentiv stereotypes of people
In different climates. The second quadrant is belonging and belonging and belief is related to genetics and your group
Square 3:Book III: Individual horoscopes (genetic influences and predispositions). Recall the third quadrant is thinking and related to the individual
Square 4:Book IV: Individual horoscopes (external accidentals). The fourth square is the individual as well but is always transcendent
https://en.wikipedia.org/wiki/Tetrabiblos

Newton believed that scientific theory should be coupled with rigorous experimentation, and he published four rules of scientific reasoning in Principia Mathematica (1686) that form part of modern approaches to science:

admit no more causes of natural things than are both true and sufficient to explain their appearances,

to the same natural effect, assign the same causes,

qualities of bodies, which are found to belong to all bodies within experiments, are to be esteemed universal, and

propositions collected from observation of phenomena should be viewed as accurate or very nearly true until contradicted by other phenomena.

Cantor dust is a multi-dimensional version of the Cantor set. It can be formed by taking a finite Cartesian product of the Cantor set with itself, making it a Cantor space. Like the Cantor set, Cantor dust has zero measure.[20]

https://en.wikipedia.org/wiki/File:Cantors_cube.jpg

https://en.wikipedia.org/wiki/Cantor_set#Cantor_dust

makes a cross

In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1874 by Henry John Stephen Smith[1][2][3][4] and introduced by German mathematician Georg Cantor in 1883.[5][6]

Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment. Cantor himself mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense.

This is also from the website quadriformisratio

Order in nature was also sought in the classification of the rocks. Robert Jameson (1774 – 1854), geologist and professor of natural history at the University of Edinburgh, gave in his book ‘Elements of Geognosy’ (1808; SWEET, 1976) four main groups:

————– 1. Primitive

————– 2. Transition/Floetz

————– 3. Alluvial

————– 4. Volcanic

The then-known (23) minerals were grouped according to age:

1. the oldest primitieve formations (molybdena, menachine, tin, scheele, cerium, tantalium, uran, chrome, bismuth);

2. old, primitive formations and newer mountains (arsenic, cobalt, nickel, silver, copper);

3. middle period (newer primitive, transition and old floetz (sedimentairy) rocks (gold, sylvan, antimony, manganese);

4. later period (lead, zinc, mercury). Iron is finally found in every rock (and therefore very young).

The name ‘geology’ was – just like ‘biology’ – invented in the first years of the nineteenth century, and won supremacy over the simultaneously introduced word ‘geognosy‘.

http://cimss.ssec.wisc.edu/wxwise/class/frntmass.html

Classification: 4 general air mass classifications categorized according to the source region.

polar latitudes P - located poleward of 60 degrees north and south
tropical latitudes T - located within about 25 degrees of the equator
continental c - located over large land masses--dry
marine m - located over the oceans----moist
We can then make combinations of the above to describe various types of air masses.

cP continental polar cold, dry, stable

cT continental tropical hot, dry, stable air aloft--unstable surface air

mP maritime polar cool, moist, and unstable

mT maritime tropical warm, moist, usually unstable

The four basic domains of physics are

Square 1: Quantum mechanics- classical mechanics less than the size of an atom and far from the speed of light. This type of physics is weird. The first square is always weird. This was mapped out by Bohr and others.

Square 2: Classical mechanics. Larger than the size of an atom and far from speed of light. This is normal classical physics like Newtons physics. The second square is always normal.

Square 3: Relativistic mechanics. Close to the speed of light and close to the size of an atom. This deal a lot with movement. The third square is doing. This is Einsteins special relativity.

Square 4: Quantum field theory. Close to the size of an atom and Close to the speed of light. This one is weird and transcendent. It is different from the other three in that it has not been mapped out or discovered completely where the other three are understood. The fourth is always transcendent. The fourth square also encompasses the previous squares. It is said that quantum field theory would bring together quantum mechanics classical and relativistic mechanics. The nature of the fourth square is it encompasses the previous three. Paul Dirac and Einstein tried to discover Quantum field theory but they were unsuccessful. Some say that M theory is it's solution. I discussed M theory reflects the quadrant model pattern.

Four papers

https://en.wikipedia.org/wiki/Annus_Mirabilis_papers

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.

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?"),[einstein 4] in which Einstein developed an argument for arguably the most famous equation in the field of physics: E = mc2.

Four dimensions. The fourth is different (three space, one time)

Minkowski is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein's special theory of relativity (1905), could be understood geometrically as a theory of four-dimensional space–time, since known as the "Minkowski spacetime".

By 1907 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 1908) is now famous

Four dimensions. The fourth is different (three space, one time)
https://en.wikipedia.org/wiki/Hermann_Minkowski
Minkowski is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein's special theory of relativity (1905), could be understood geometrically as a theory of four-dimensional space–time, since known as the "Minkowski spacetime".

By 1907 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 1908) is now famous

The dirac equation is based on a four by four quadrant model matrix.

The wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation which described wave functions of only one complex value.

The Dirac equation is considered one of the greatest breakthroughs in physics and quantum mechanics history. In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-½ massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics.

It accounted for the fine details of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved and which was experimentally confirmed several years later. It also provided a theoretical justification for the introduction of several-component wave functions in Pauli's phenomenological theory of spin.

The wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation which described wave functions of only one complex value. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation.

The new elements in this equation are the 4 × 4 matrices αk and β, and the four-component wave function ψ. There are four components in ψ because evaluation of it at any given point in configuration space is a bispinor. It is interpreted as a superposition of a spin-up electron, a spin-down electron, a spin-up positron, and a spin-down positron (see below for further discussion).

The 4 × 4 matrices αk and β are all Hermitian and have squares equal to the identity matrix: (four by four matrices are the quadrant model)

\alpha_i^2=\beta^2=I_4

and they all mutually anticommute (if i and j are distinct):

\alpha_i\alpha_j + \alpha_j\alpha_i = 0

\alpha_i\beta + \beta\alpha_i = 0

These equations were the basis for the discovery of antimatter reflected the quadrant model pattern. A big part of quantum mechanics is the 4-vector.

https://en.wikipedia.org/wiki/Pauli_exclusion_principle
Four quantum numbers.

The Pauli exclusion principle is the quantum mechanical principle that states that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously. In the case of electrons, it can be stated as follows: it is impossible for two electrons of a poly-electron atom to have the same values of the four quantum numbers: n, the principal quantum number, ℓ , the angular momentum quantum number, mℓ, the magnetic quantum number, and ms, the spin quantum number. The Pauli exclusion principle is one of the most revolutionary discoveries in physics and quantum mechanics.
The Pauli exclusion principle is the basis and reason why there are quantum jumps in quantum mechanics and why there are different orbitals of the atom. I described that there are the four orbitals, s, p, d, and the different one f.
Therefore the Pauli Exclusion principle is the basis for all of chemistry and physics. It is no coincidence it fits the quadrant model pattern.
Quantum physicists did not know why the Pauli Exclusion Principle was the basis for atoms. They just said it was. This made Einstein say that quantum mechanics was weird and probably not the ultimate explanation for reality, because he felt it was based off of random weird rules that had no basis to them, and he felt that there was a higher order in physics. I would tell Einstein that the Pauli Exclusion principle was not random but based on the quadrant model pattern, the form of existence, which would rectify Einstein's view of reality.

The fourth quantum number is different from the previous three. Wolfgang Pauli, who discovered the quantum numbers, knew about the work of Carl Jung, and consciously recognized that the four quantum numbers fit Jung's concept of the quaternity, with the fourth being different.

Spatial and angular momentum numbers

Four quantum numbers can describe an electron in an atom completely. As per the following model, these nearly-compatible quantum numbers are:

Principal quantum number (n)

Azimuthal quantum number (ℓ)

Magnetic quantum number (m)

Spin quantum number (s)

The spin-orbital interaction, however, relates these numbers. Thus, a complete description of the system can be given with fewer quantum numbers, if orthogonal choices are made for these basis vectors.

Hund-Mulliken molecular orbital theory

Many different models have been proposed throughout the history of quantum mechanics, but the most prominent system of nomenclature spawned from the Hund-Mulliken molecular orbital theory of Friedrich Hund, Robert S. Mulliken, and contributions from Schrödinger, Slater and John Lennard-Jones. This system of nomenclature incorporated Bohr energy levels, Hund-Mulliken orbital theory, and observations on electron spin based on spectroscopy and Hund's rules.[1]

This model describes electrons using four quantum numbers, n, ℓ, mℓ, ms, given below. It is also the common nomenclature in the classical description of nuclear particle states (e.g. protons and neutrons). A quantum description of molecular orbitals require different quantum numbers, because the Hamiltonian and its symmetries are quite different.

The principal quantum number (n) describes the electron shell, or energy level, of an electron. The value of n ranges from 1 to the shell containing the outermost electron of that atom, i.e.[2]

n = 1, 2, ... .

For example, in caesium (Cs), the outermost valence electron is in the shell with energy level 6, so an electron in caesium can have an n value from 1 to 6.

For particles in a time-independent potential (see Schrödinger equation), it also labels the nth eigenvalue of Hamiltonian (H), i.e. the energy, E with the contribution due to angular momentum (the term involving J2) left out. This number therefore has a dependence only on the distance between the electron and the nucleus (i.e., the radial coordinate, r). The average distance increases with n, and hence quantum states with different principal quantum numbers are said to belong to different shells.

The azimuthal quantum number (ℓ) (also known as the angular quantum number or orbital quantum number) describes the subshell, and gives the magnitude of the orbital angular momentum through the relation

L2 = ħ2 ℓ (ℓ + 1).

In chemistry and spectroscopy, "ℓ = 0" is called an s orbital, "ℓ = 1" a p orbital, "ℓ = 2" a d orbital, and "ℓ = 3" an f orbital.

The value of ℓ ranges from 0 to n − 1, because the first p orbital (ℓ = 1) appears in the second electron shell (n = 2), the first d orbital (ℓ = 2) appears in the third shell (n = 3), and so on:[3]

ℓ = 0, 1, 2,..., n − 1.

A quantum number beginning in 3, 0, … describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles.

The magnetic quantum number (mℓ) describes the specific orbital (or "cloud") within that subshell, and yields the projection of the orbital angular momentum along a specified axis:

Lz = mℓ ħ.

The values of mℓ range from −ℓ to ℓ, with integer steps between them:[4]

The s subshell (ℓ = 0) contains only one orbital, and therefore the mℓ of an electron in an s orbital will always be 0. The p subshell (ℓ = 1) contains three orbitals (in some systems, depicted as three "dumbbell-shaped" clouds), so the mℓ of an electron in a p orbital will be −1, 0, or 1. The d subshell (ℓ = 2) contains five orbitals, with mℓ values of −2, −1, 0, 1, and 2.

The spin projection quantum number (ms) describes the spin (intrinsic angular momentum) of the electron within that orbital, and gives the projection of the spin angular momentum S along the specified axis:

Sz = ms ħ.

In general, the values of ms range from −s to s, where s is the spin quantum number, an intrinsic property of particles:[5]

ms = −s, −s + 1, −s + 2,...,s − 2, s − 1, s.

An electron has spin number s = ½, consequently ms will be ±½, referring to "spin up" and "spin down" states. Each electron in any individual orbital must have different quantum numbers because of the Pauli exclusion principle, therefore an orbital never contains more than two electrons.

https://en.wikipedia.org/wiki/Quantum_number

There are four quantum numbers. The fourth is different

Results from spectroscopy indicated that up to two electrons can occupy a single orbital. However two electrons can never have the same exact quantum state nor the same set of quantum numbers according to Hund's rules, which addresses the Pauli exclusion principle. A fourth quantum number with two possible values was added as an ad hoc assumption to resolve the conflict; this supposition could later be explained in detail by relativistic quantum mechanics and from the results of the renowned Stern–Gerlach experiment.

https://en.wikipedia.org/wiki/Quantum_number

Bohr studied the spectral lines of the hydrogen atom. These four spectral lines of the hydrogen atom were examined by Neils Bohr, and from them he deduced the modern theory of atoms and electron shells.

https://en.wikipedia.org/wiki/File:Emission_spectrum-H.svg
https://en.wikipedia.org/wiki/Hydrogen_spectral_series
Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen.[8] Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.

This is the famous X Ray that Rosalind Franklin obtained in an attempt to understand the structure of DNA. It was taken by Watson and Crick, and they used it to infer that DNA was a double helix of four nucleobases. The X ray image was a quadrant/X.

from the website quadriformisratio by Kullimer

The emblematic ‘Four Sources of Knowledge’ were later used by Athanasius Kircher in his optical publication ‘Ars Magna Lucis et Umbrae’ (Rome, 1646). Kircher compared the action of light to that of a magnet.

The dualistic element is enhanced by the opposition between the profane knowledge – associated with a garden – and the senses depicted as a cave, the symbol of darkness. In the garden stands a sundial, but the beam of light goes astray in the darkness of the cave. The tetradic notion was represented in the corners of the picture as the ‘Four Sources of Knowledge’: the Sacral Authority with the Scriptures), the Ratio (symbolized as a writing hand with an unlighted eye), the Worldly Authority, and the Senses, depicted with a telescope and a pointing hand.

On the title page of Galileo's work Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) would appear the four sources of knowledge according to people of that time. These sources fit the quadrant model pattern. The four-fold symbolism sometimes emerged in the engraved title-pages as the ‘Four Sources of Knowledge’: Divine Authority (or Scripture), Reason, Profane Authority (pagan philosophers like Aristotle) and Senses.
Square 1: senses- the first quadrant is sensation and perception
Square 2: Profane authority- the second quadrant is belief and faith which is trust in authority
Square 3: Reason- the third quadrant is thinking and emotion which I described in the first chapter of this book is rational consciousness.
Square 4: Divine authority- The fourth square is always transcendent.
Cristoph Scheiner introduced this emblematic element in the frontispiece of his ‘Rosa Ursina sive Sol‘ (The Rose of the Orsini, or the Sun), printed in Bracciano between 1626 and 1630. The book was dedicated to Paolo Orisini, the Duke of Bracciano (fig. 167). This early scientific study of the sun was a follow-up of his optical work called ‘Oculus‘, published in Innsbruck in 1611. He placed the four types of knowledge in a quadrant pattern.
It is key to note that Galileo was not questioning God. He was questioning what he viewed as profane authority, or beliefs that were incorrect. Ironically Galileos views of the solar system themeselves were not entirely correct because he still believed in circular orbits. It took until Kepler to fix Galileos errors, so the pope was not entirely wrong in saying that Galileo was incorrect.

The Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) was a 1632 Italian-language book by Galileo Galilei comparing the Copernican system with the traditional Ptolemaic system. It is one of the most famous works in science history, because it was the work that questioned the geocentric Ptolemaic view of the Universe and proposes a heliocentric Copernican view. This is the work that got Galileo in trouble and tried and put in prison. Galileo was not persecuted because he proposed a heliocentric universe, but because in this work he tried to make the Pope look dumb, giving him the title Simplicio, or simple. The work employs the quadrant model pattern.

The text of ‘A Dialogue of the Two Chief World Systems’ was divided in four parts (days), reflecting the quadrant model pattern. The first day was about dimensions and perfection, new stars, sunspots and observation of the moon. The second day dealt with movement, the pendulum, air and wind. The third day treated the measurement of the stars and the retrograde movement of sunspots and finally the fourth day was concerned with the tides and the impetus (each day builds on the next and interestingly the fourth day Galileo's ideas were wrong. The fourth is always different, and each square builds on the next, the nature of the quadrant model pattern). So the first and third days were ‘static’, about measurements and the second and fourth days were ‘dynamic’, concerned with the processes which lead to the argument of a sun-centered cosmos.

This presentation coincided with the four phases (unity – separation – unity – separation) in the Greek interpretation of being as proposed by the philosopher Empedocles. This characterization of the four phases is also is familiar in the (quadralectic) interpretation of the quadrants. There is no proof that Galileo deliberately employed the four-division in this way.

The dialogue signifies to scientists the triumph of science and one of the greatest achievements in science history, and they see it as the symbol of Galileo as the martyr for science, like Jesus was the Martyr for the Christians. It is no coincidence that it reflects the quadrant model pattern, the form of existence.

Notice how the fragment of the Antikythera mechanism (the first computer, which is ancient), is a quadrant

The Antikythera mechanism (/ˌæntɨkɨˈθɪərə/ ant-i-ki-theer-ə or /ˌæntɨˈkɪθərə/ ant-i-kith-ə-rə) is an ancient analog computer[1][2][3][4] designed to predict astronomical positions and eclipses for calendrical and astrological purposes,[5][6][7] as well as the Olympiads, the cycles of the ancient Olympic Games

After the knowledge of this technology was lost at some point in Antiquity, technological artifacts approaching its complexity and workmanship did not appear again until the development of mechanical astronomical clocks in Europe in the fourteenth century

It's shape reflects the quadrant image.

The Antikythera mechanism was discovered in 45 metres (148 ft) of water in the Antikythera shipwreck off Point Glyphadia on the Greek island of Antikythera.

The Metonic Dial is the main upper dial on the rear of the mechanism. The Metonic cycle, defined in several physical units, is 235 synodic months, which is very close (to within less than 13 one-millionths) to 19 tropical years. It is therefore a convenient interval over which to convert between lunar and solar calendars. The Metonic dial covers 235 months in 5 rotations of the dial, following a spiral track with a follower on the pointer that keeps track of the layer of the spiral. The pointer points to the synodic month, counted from new moon to new moon, and the cell contains the Corinthian month names:[citation needed]

ΦΟΙΝΙΚΑΙΟΣ (Phoinikaios)

ΚΡΑΝΕΙΟΣ (Kraneios)

ΛΑΝΟΤΡΟΠΙΟΣ (Lanotropios)

ΜΑΧΑΝΕΥΣ (Machaneus)

ΔΩΔΕΚΑΤΕΥΣ (Dodekateus)

ΕΥΚΛΕΙΟΣ (Eukleios)

ΑΡΤΕΜΙΣΙΟΣ (Artemisios)

ΨΥΔΡΕΥΣ (Psydreus)

ΓΑΜΕΙΛΙΟΣ (Gameilios)

ΑΓΡΙΑΝΙΟΣ (Agrianios)

ΠΑΝΑΜΟΣ (Panamos)

ΑΠΕΛΛΑΙΟΣ (Apellaios)

Thus, setting the correct solar time (in days) on the front panel indicates the current lunar month on the back panel, with resolution to within a week or so.

The Callippic dial is the left secondary upper dial, which follows a 76-year cycle. The Callippic cycle is four Metonic cycles, and this dial indicates which of the four Metonic cycles is the current one in the Callippic cycle.[citation needed]

The Olympiad dial is the right secondary upper dial; it is the only pointer on the instrument that travels in a counter-clockwise direction as time advances. The dial is divided into four sectors, each of which is inscribed with a year indicator and the name of two Panhellenic Games: the "crown" games of Isthmia, Olympia, Nemea, and Pythia; and two lesser games: Naa (held at Dodona) and another Olympiad location that to date, has not been deciphered.[36] The inscriptions on each one of the four divisions are:[5][28]

Olympic dial

Year of the cycle Inside the dial inscription Outside the dial inscription

1 LA ΙΣΘΜΙΑ (Isthmia)

ΟΛΥΜΠΙΑ (Olympia)

2 LB NEMEA (Nemea)

NAA (Naa)

3 LΓ ΙΣΘΜΙΑ (Isthmia)

ΠΥΘΙΑ (Pythia)

4 L∆ ΝΕΜΕΑ (Nemea)

[undeciphered]

The Saros dial is the main lower spiral dial on the rear of the mechanism.[5] The Saros cycle is 18 years and 11-1/3 days long (6585.333... days), which is very close to 223 synodic months (6585.3211 days). It is defined as the cycle of repetition of the positions required to cause solar and lunar eclipses, and therefore, it could be used to predict them — not only the month, but the day and time of day. Note that the cycle is approximately 8 hours longer than an integer number of days. Translated into global spin, that means an eclipse occurs not only eight hours later, but 1/3 of a rotation farther to the west. Glyphs in 51 of the 223 synodic month cells of the dial specify the occurrence of 38 lunar and 27 solar eclipses. Some of the abbreviations in the glyphs read:

Σ = ΣΕΛΗΝΗ (Moon)

Η = ΗΛΙΟΣ (Sun)

H\M = ΗΜΕΡΑΣ (of the day)

ω\ρ = ωρα (hour)

N\Y = ΝΥΚΤΟΣ (of the night)

The glyphs show whether the designated eclipse is solar or lunar, and give the day of the month and hour; obviously, solar eclipses may not be visible at any given point, and lunar eclipses are visible only if the moon is above the horizon at the appointed hour.[30]

The Exeligmos Dial is the secondary lower dial on the rear of the mechanism. The Exeligmos cycle is a 54-year triple Saros cycle, that is 19,756 days long. Since the length of the Saros cycle is to a third of a day (eight hours), so a full Exeligmos cycle returns counting to integer days, hence the inscriptions. The labels on its three divisions are:[5]

Blank (representing the number zero)

H (number 8)

Iϛ (number 16)

Thus the dial pointer indicates how many hours must be added to the glyph times of the Saros dial in order to calculate the exact eclipse times.

Merk Diezle

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https://en.wikipedia.org/wiki/Global_Positioning_System

The Global Positioning System (GPS) is a space-based navigation system that provides location and time information in all weather conditions, anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. At least four are needed, three for spacial dimensions and one for time.

At a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and clock deviation from satellite time).

https://en.wikipedia.org/wiki/Global_Positioning_System

https://en.wikipedia.org/wiki/Crux

Crux /ˈkrʌks/ is a constellation located in the southern sky in a bright portion of the Milky Way, and is the smallest but one of the most distinctive of the 88 modern constellations. Its name is Latin for cross, and it is dominated by a cross-shaped or kite-like asterism that is commonly known as the Southern Cross.
Predominating the asterism is the most southerly and brightest star, the blue-white Alpha Crucis or Acrux, followed by four other stars, descending in clockwise order by magnitude: Beta, Gamma (one of the closest red giants to Earth), Delta and Epsilon Crucis.

The typical elemental semiconductors are silicon and germanium, each atom of which has four valence electrons. The properties of semiconductors are best explained using band theory, as a consequence of a small energy gap between a valence band (which contains the valence electrons at absolute zero) and a conduction band (to which valence electrons are excited by thermal energy).Semiconductors have revolutionized technology and are one of the most important discoveries in technological history. It is no coincidence they are made up of silicon and germanium, both of which have four valence electrons, thus reflecting the quadrant image.

https://en.wikipedia.org/wiki/Amplifier
Amplifiers are also said to be one of the greatest technological inventions. Amplifiers were responsible for being able to send long distance signals anywhere in the world and were thus a huge invention. There are four types of amplifiers The four basic types of amplifiers are as follows:
Voltage amplifier – This is the most common type of amplifier. An input voltage is amplified to a larger output voltage. The amplifier's input impedance is high and the output impedance is low.
Current amplifier – This amplifier changes an input current to a larger output current. The amplifier's input impedance is low and the output impedance is high.
Transconductance amplifier – This amplifier responds to a changing input voltage by delivering a related changing output current.
Transresistance amplifier – This amplifier responds to a changing input current by delivering a related changing output voltage. Other names for the device are transimpedance amplifier and current-to-voltage converter.
Electronic amplifiers use one variable presented as either a current and voltage. Either current or voltage can be used as input and either as output, leading to four types of amplifiers. In idealized form they are represented by each of the four types of dependent source used in linear analysis, as shown in the figure, namely:
Input Output Dependent source Amplifier type
I I Current controlled current source CCCS Current amplifier
I V Current controlled voltage source CCVS Transresistance amplifier
V I Voltage controlled current source VCCS Transconductance amplifier
V V Voltage controlled voltage source VCVS Voltage amplifier
Each type of amplifier in its ideal form has an ideal input and output resistance that is the same as that of the corresponding dependent source:[8]
Amplifier type Dependent source Input impedance Output impedance
Current CCCS 0 ∞
Transresistance CCVS 0 0
Transconductance VCCS ∞ ∞
Voltage VCVS ∞ 0
Power amplifier circuits (output stages) are classified as A, B, AB and C for analog designs—and class D and E for switching designs based on the proportion of each input cycle (conduction angle), during which an amplifying device passes current. The image of the conduction angle derives from amplifying a sinusoidal signal. If the device is always on, the conducting angle is 360°. If it is on for only half of each cycle, the angle is 180°. The angle of flow is closely related to the amplifier power efficiency. The various classes are introduced below, followed by a more detailed discussion under their individual headings further down.
In the illustrations below, a bipolar junction transistor is shown as the amplifying device. However the same attributes are found with MOSFETs or vacuum tubes.
Conduction angle classes
Class A
100% of the input signal is used (conduction angle Θ = 360°). The active element remains conducting[11] all of the time.
Class B
50% of the input signal is used (Θ = 180°); the active element carries current half of each cycle, and is turned off for the other half.
Class AB
Class AB is intermediate between class A and B, the two active elements conduct more than half of the time
Class C
Less than 50% of the input signal is used (conduction angle Θ < 180°).
A "Class D" amplifier uses some form of pulse-width modulation to control the output devices; the conduction angle of each device is no longer related directly to the input signal but instead varies in pulse width. These are sometimes called "digital" amplifiers because the output device is switched fully on or off, and not carrying current proportional to the signal amplitude.
Other types are just variations on these four.
Like

https://en.wikipedia.org/wiki/File:Dependent_Sources.PNG

https://en.wikipedia.org/wiki/Amplifier
The four types of dependent source—control variable on left, output variable on right

Professionals use the 4 quadrant model as a diagnostic tool to help determine correct treatment recommendations.

As the name would indicate, the tool is based on a 4 box model, and every person with a co-occurring disorder will fall into one of the 4 quadrants.

Once you identify your quadrant you can narrow your focus onto treatment options that make the most sense for you.

Quadrant 1 – Less severe substance use disorder and less severe mental health disorder

Quadrant 2 – More serious mental health disorder and less severe substance use disorder

Quadrant 3 – More serious substance use disorder and less severe mental health disorder

Quadrant 4 – Severe mental health disorder and severe substance use disorder

Notice how the diagrams have four parts
http://astro.unl.edu/naap/hr/graphics/hr_basic.png

Hertzsprung-Russell Diagrams are the most important models in astronomy and anybody taking an introductory astronomy class will learn them. The diagram can be divided into four parts
1: hot and bright
2: hot and dim
3: cold and dim
4: hot and bright
The majority of stars, including our Sun, are found along a region called the Main Sequence. Main Sequence stars vary widely in effective temperature but the hotter they are, the more luminous they are, hence the main sequence tends to follow a band going from the bottom right of the diagram to the top left. These stars are fusing hydrogen to helium in their cores. Stars spend the bulk of their existence as main sequence stars. Other major groups of stars found on the H-R diagram are the giants and supergiants; luminous stars that have evolved off the main sequence, and the white dwarfs. Whilst each of these types is discussed in detail in later pages we can use their positions on the H-R diagram to infer some of their properties.
The diagram is always presented as divided into four parts, main sequence dwarfs, giants, supergiants, and white dwarfs. The white dwarfs are different form the other three. The fourth is always different. The fourth is death. White dwarfs are dead stars made out of pure carbon. Recall carbon is the quadrant image.

http://astro.unl.edu/naap/hr/graphics/hr_basic.png

The Einstein Cross or Q2237+030 or QSO 2237+0305 is a gravitationally lensed quasar that sits directly behind ZW 2237+030, Huchra's Lens. It is a famous cosmic mirage. Four images of the same distant quasar appear around a foreground galaxy due to strong gravitational lensing.

The quasar's redshift indicated that it is located about 8 billion light years from Earth, while the lensing galaxy is at a distance of 400 million light years.[2] The apparent dimension of the galaxy are 0.87x0.34 arcminutes[citation needed], while the apparent dimension of the cross in its centre accounts for only 1.6x1.6 arc seconds.

The Einstein cross looks like four stars but it is actually one. That is the nature of the quadrant model. The four seem separate but they are actually one.

The host galaxy of SN Refsdal is at a redshift of 1.49, corresponding to a comoving distance of 14.4 billion light-years and a lookback time of 9.34 billion years.[5] The multiple images are arranged around the elliptical galaxy at z = 0.54 in a cross-shaped pattern, also known as an "Einstein cross".[1]

When the four images fade away, astronomers predict they will have the rare opportunity to see the supernova again. This is because the current four-image pattern is only one component of the lensing display. The supernova may have appeared as a single image some 40–50 years ago elsewhere in the cluster field, and it is expected to reappear once more in about one year. The magnifications and staggered arrivals of the supernova images will help astronomers probe the cosmic expansion rate, as well as the distribution of matter and dark matter in the galaxy and cluster lenses.[1]https://en.wikipedia.org/wiki/SN_Refsdal

https://en.wikipedia.org/wiki/Diesel_fuel

The LZ 129 Hindenburg rigid airship was powered by four Daimler-Benz DB 602 16-cylinder diesel engines, each with 1,200 hp (890 kW) available in bursts and 850 horsepower (630 kW) available for cruising. This airship is arguably the most famous airship in the world. four is the number of the quadrant and 16 is the number of the whole quadrant. It went up in flames, one of the most famous catastrophes ever. It fit the quadrant pattern.

Northern Cross

https://en.wikipedia.org/wiki/Cygnus_(constellation)
Cygnus /ˈsɪɡnəs/ is a northern constellation lying on the plane of the Milky Way, deriving its name from the Latinized Greek word for swan. The swan is one of the most recognizable constellations of the northern summer and autumn, it features a prominent asterism known as the Northern Cross (in contrast to the Southern Cross). Cygnus was among the 48 constellations listed by the 2nd century astronomer Ptolemy,
Cygnus contains Deneb, one of the brightest stars in the night sky and one corner of the Summer Triangle, as well as some notable X-ray sources and the giant stellar association of Cygnus OB2. One of the stars of this association, NML Cygni, is one of the largest stars currently known. The constellation is also home to Cygnus X-1, a distant X-ray binary containing a supergiant and unseen massive companion that was the first object widely held to be a black hole.
Backbone of Milky Way. The Northern Cross serves to point out the Milky Way – the luminescent river of stars passing through the Northern Cross and stretching all across the sky.
You need a clear, dark sky to see this hazy swath of sky, whose “haze” is really myriad stars. But it’s a sight well worth pursuing. The Milky Way band we see stretched across our sky is an edgewise view into the disk of our galaxy, the flat part of the galaxy where nearly all the visible stars are.
Keep in mind, though, that all the stars outside this band visible to your unaided eye still belong to our home galaxy, the Milky Way.
When you look at the Northern Cross, you’re looking directly into the Milky Way disk, where the soft glow of millions of stars glazes over the heavens. In fact, the galactic plane (equator) runs right through the Northern Cross, encircling the sky above and below the horizon.

https://en.wikipedia.org/wiki/CMYK_color_model

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.[1][2] Some sources claim this explanation, although useful as a mnemonic, is incorrect, that K comes only from "Key" because black is often used as outline and printed first.[3]

https://en.wikipedia.org/wiki/CMYK_color_model

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.[1][2] Some sources claim this explanation, although useful as a mnemonic, is incorrect, that K comes only from "Key" because black is often used as outline and printed first.[3]

https://en.wikipedia.org/wiki/CMYK_color_model

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.[1][2] Some sources claim this explanation, although useful as a mnemonic, is incorrect, that K comes only from "Key" because black is often used as outline and printed first.[3]

https://en.wikipedia.org/wiki/Primary_color

Recent developments in primary colors
Some recent TV and computer displays are starting to add a fourth "primary" of yellow, often in a four-point square pixel area, to get brighter pure yellows and larger color gamut.[14] Even the four-primary technology does not yet reach the range of colors the human eye is theoretically capable of perceiving (as defined by the sample-based estimate called the Pointer Gamut[15]), with 4-primary LED prototypes providing typically about 87% and 5-primary prototypes about 95%. Several firms, including Samsung and Mitsubishi, have demonstrated LED displays with five or six "primaries", or color LED point light sources per pixel.[16] A recent academic literature review claims a gamut of 99% can be achieved with 5-primary LED technology.[17] While technology for achieving a wider gamut appears to be within reach, other issues remain; for example, affordability, dynamic range, and brilliance. In addition, there exists hardly any source material recorded in this wider gamut, nor is it currently possible to recover this information from existing visual media. Regardless, industry is still exploring a wide variety of "primary" active light sources (per pixel) with the goal of matching the capability of human color perception within a broadly affordable price. One example of a potentially affordable but yet unproven active light hybrid places a LED screen over a plasma light screen, each with different "primaries". Because both LED and plasma technologies are many decades old (plasma pixels going back to the 1960s), both have become so affordable that they could be combined.

In kinematics, cognate linkages are linkages that ensure the same input-output relationship or coupler curve geometry, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyschev Theorem, after Samuel Roberts and Pafnuty Chebyshev, states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram (named after Arthur Cayley).

Theres a popular video on youtube in which the video indicates, he divides the Global Warming debate into two dichotomies:

Global Climate Change (GCC) is “False” (Top Row) or “True” (Bottom Row), and

We take Action “Yes” (Column A) or “No” (Column B)

Here are the results he gives for his four boxes:

GCC is False but we unnecessarily take Action. The result is a high “Cost” that results in a “Global Depression”.

GCC is False and we take No Action. The result is a happy face.

GCC is True and we take Action that stops GCC dead in its tracks. The result is a happy face.

GCC is True and we take No Action. The result is “CATASTROPHES [in the] ECONOMIC, POLITICAL, SOCIETAL, ENVIRONMENTAL, [and] and HEALTH” areas.

He ends with the inevitable: “The only choice is Column A” – we must take Action!

“All or nothing”, “Camelot or Catastrophe” arguments have great emotional power in political discourse, where the (usually hidden) assumption is that some things are perfectly TRUE and others are perfectly FALSE. But the real world is mostly in shades of grey. He studiously avoids that complication, because, when shades of grey are considered, his argument, IMHO, falls apart.

Let us take a closer, more realistic look at his four boxes:

GLOBAL DEPRESSION: This box is included to make it appear he is being “fair” to Skeptics. He assumes that taking Action to stop GCC will be so costly that, if it turns out to have been unnecessary, the result will be a “Global Depression”. Certainly, maximum environmental spending will damage the world-wide economy, but I doubt that type of spending, alone, will trigger a “Global Depression”. When we get to box #3 we will see that he doesn’t really think so either!

HAPPY FACE: GCC is “False”, we take No Action, so all is well! But, is it? Does his “GCC” include NATURAL PROCESSES and CYCLES that have caused Global Warming (and Cooling), Floods (and Droughts), and Violent Storms (and Blessed Rain) prior to the advent of Humans on Earth, and before we Humans had the capability to affect the climate? Apparently not, else “GCC” could not be totally “False”. Therefore, by “GCC” he is referring ONLY to the HUMAN-CAUSED variety, totally ignoring the evidence from the geological, ice-core, and historical records of NATURAL Global Climate Change and some Catastrophes.

HAPPY FACE: This box is totally inconsistent with box #1! If Action to stop Human-Caused Global Warming is so costly as to cause a Global Depression in the first box, would it not also cause such a Global Depression in this box? So, why the Happy Face? Realistically, even if we in the US and other nations in the Developed World take maximum Action to reduce our CO2 emissions, it is totally unrealistic to expect those in the Developing World to do the same. Indeed, China, India, and other countries will continue to build power plants, nearly all of them coal-fired. CO2 levels are bound to continue their rapid increase for at least the coming several decades, no matter what we do.

TOTAL CATASTROPHE: This box is filled with terrible consequences and is intended to scare us into taking maximum Action. He assumes the worst-case Global Warming of several degrees predicted by Climate Models despite the failure of those Climate Models to predict the past 17 years of absolutely no net Global Warming. (The most realistic prediction is continued moderate change in Global Temperatures, mostly NATURAL but some small part HUMAN-CAUSED. As standards of living continue to improve world-wide, populations will stabilize which will allow reasonable action to be taken to moderate CO2 emissions, and Human Civilization will ADAPT to inevitable Natural and Human-Caused Climate Change as we have throughout history.)

http://www.basic-mathematics.com/lattice-method-for-multipl…

Although the lattice method for multiplication is no longer being used right now in school, it is easy understand
I will illustrate with two good examples. Study them carefully and follow the steps exactly as shown
Example #1:
Multiply 42 and 35
Arrange 42 and 35 around a 2 × 2 grid as shown below:
Draw the diagonals of the small squares as shown below:
Multiply 3 by 4 to get 12 and put 12 in intersection of the first row and the first column as show below.
Notice that 3 is located in the first row and 4 in the first column. That is why the answer goes in the intersection.
By the same token, multiply 5 and 2 and put the answer in the intersection of second row and the second column
And so forth...
Then, going from right to left, add the numbers down the diagonals as indicated with the arrows.
The first diagonal has only 0. Bring zero down.
The second diagonal has 6, 1, 0. Add these numbers to get 7 and bring it down.
And so forth...
After the grid is completed, what you see in red is the answer that is 1470
Example #2:
Multiply 658 and 47
Arrange 657 and 47 around a 3 × 2 grid as shown below:
Draw the diagonals of the small squares, find products, and put the answers in intersecting rows and columns as already demonstrated:
Then, going from right to left, add the numbers down the diagonals as shown before.
The first diagonal has only 6. Bring 6 down.
The second diagonal has 2, 5, and 5. Add these numbers to get 12. Bring 2 down and carry the 1 over to the next diagonal.
The third diagonal has 3, 0, 3, and 2. Add these numbers to get 8 and add 1 (your carry) to 8 to get 9.
and so forth...
After the grid is completed, what you see in red is the answer to the multiplication that is 30926
I understand that this may be your first encounter with the lattice method for multiplication. It may seem that it is tough. Just practice with other examples and you will be fine.
Any questions about the lattice method for multiplication? Just contact me
The lattice method employs quadrants and many math teachers think it is the ideal way to solve mathematical problems

I mentioned and posted that hertzberg russel diagrams of stars shows four groupings of stars the main sequence one of them and the fourth is off to its side different- the quadrant pattern

The fourth is different. Galileo discovered the fourth later

The Galilean moons are the four largest moons of Jupiter—Io, Europa, Ganymede, and Callisto.

The tiger stripes of Enceladus consist of four sub-parallel, linear depressions in the south polar region of the Saturnian moon . Near the center of this terrain are four fractures bounded on either side by ridges, unofficially called "tiger stripes". This is where scientists think they can find life in the solar system outside of Planet Earth. It is one of the biggest finds in science. No coincidence that there are the four tiger stripes, reminiscing the quadrant four.

The Solar System has four terrestrial planets: Mercury, Venus, Earth, and Mars. Only one terrestrial planet, Earth, is known to have an active hydrosphere.

During the formation of the Solar System, there were probably many more terrestrial planetesimals, but most merged with or were ejected by the four terrestrial planets.

They are divided from the four gaseous planets by the asteroid belt (the quadrant division of the fours)

http://www.space.com/30372-gas-giants.html

A gas giant is a large planet composed mostly of gases, such as hydrogen and helium, with a relatively small rocky core. The gas giants of our solar system are Jupiter, Saturn, Uranus and Neptune. These four large planets, also called jovian planets after Jupiter, reside in the outer part of the solar system past the orbits of Mars and the asteroid belt. Jupiter and Saturn are substantially larger than Uranus and Neptune, revealing that the pairs of planets have a somewhat different composition.

Although there are only four large planets in our own solar system, astronomers have discovered thousands outside of it, particularly using NASA's Kepler space telescope. These exoplanets (as they are called) are being examined to learn more about how our solar system came to be.

The moons of Jupiter fit the quadrant pattern. Four are Galilean moons. The other four are smaller moons. 16 is the squares of the quadrant model. There are 16 irregular satellites around Jupiter
https://en.wikipedia.org/wiki/Moons_of_Jupiter

Of Jupiter's moons, eight are regular satellites with prograde and nearly circular orbits that are not greatly inclined with respect to Jupiter's equatorial plane. The Galilean satellites are nearly spherical in shape due to their planetary mass, and so would be considered planets if they were in direct orbit around the Sun. The other four regular satellites are much smaller and closer to Jupiter; these serve as sources of the dust that makes up Jupiter's rings. The remainder of Jupiter's moons are irregular satellites whose prograde and retrograde orbits are much farther from Jupiter and have high inclinations and eccentricities. These moons were probably captured by Jupiter from solar orbits. Sixteen irregular satellites have been discovered since 2003 and have not yet been named.

æ_Naturalis_Principia_Mathematica

Rules of Reasoning in Philosophy

Perhaps to reduce the risk of public misunderstanding, Newton included at the beginning of Book 3 (in the second (1713) and third (1726) editions) a section entitled "Rules of Reasoning in Philosophy." In the four rules, as they came finally to stand in the 1726 edition, Newton effectively offers a methodology for handling unknown phenomena in nature and reaching towards explanations for them. The four Rules of the 1726 edition run as follows (omitting some explanatory comments that follow each):

Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes.

Rule 3: The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

Isaac Newton’s statement of the four rules revolutionised the investigation of phenomena. With these rules, Newton could in principle begin to address all of the world’s present unsolved mysteries. He was able to use his new analytical method to replace that of Aristotle, and he was able to use his method to tweak and update Galileo’s experimental method. The re-creation of Galileo's method has never been significantly changed and in its substance, scientists use it today.[citation needed]

The division of nature according to Honorius Augustodunensis in the ‘Clavis physicae’ (The Key of Nature). The manuscript is preserved in the Michelsberg Cloister near Bamberg, but probably written in the area of the Meuse, mid-twelfth century (Paris, Bibl. Nat. lat. 6734). The definition of the four phases in nature differs from the original interpretation of Scotus Eriugena, in particular with regard to the First and Fourth Quadrant, which are ‘reversed’.

The illustration in the ‘Clavis physicae‘ (fig. 137) showed four sections:

Section 1 (upper): eight ‘causae primordiales‘

———————————————– central : bonitas ——————————

left (4): iustitia right (3): essentia

virtus vita

ratio sapientia

veritas

Section 2 : three ‘effectus causarum‘ : tempus

materia informis

locus

Section 3 : four elements : fire

air

water

earth

(natura creata non creans)

Section 4 (lower): God/Christ finis

In computing, a nibble (often nybble or even nyble to match the vowels of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte[2] or tetrade. In a networking or telecommunication context, the nibble is often called a semi-octet, quadbit, or quartet. A nibble has sixteen (24) possible values. A nibble can be represented by a single hexadecimal digit and called a hex digit.

A full byte (octet) is represented by two hexadecimal digits; therefore, it is common to display a byte of information as two nibbles. Sometimes the set of all 256 byte values is represented as a table 16×16, which gives easily readable hexadecimal codes for each value.

4-bit computer architectures use groups of four bits as their fundamental unit. Such architectures were used in early microprocessors and pocket calculators and continue to be used in some micro controllers

There are 16 nibbles representing the 16 squares of the quadrant model

A tetrad is an area 2 km x 2 km square. The term has a particular use in connection with the British Ordnance Survey national grid, and then refers to any of the 25 such squares which make up a standard hectad.[1]

Tetrads are sometimes used by biologists for reporting the distribution of species to maintain a degree of confidentiality about their data,[2] though the system is not in universal use.[1]

The tetrads are labelled from A to Z (omitting O) according to the "DINTY" system as shown in the grid below, which takes its name from the letters of the second line

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.

In astronomy, a tetrad is a set of four total lunar eclipses within two years.

https://en.wikipedia.org/wiki/Lunar_eclipse

Blood moon
Due to its reddish color, a totally eclipsed moon is sometimes referred to as a "blood moon".[14] In addition, in the 2010s the media started to associate the term with the four full moons of a lunar tetrad, especially the 2014–15 tetrad coinciding with the feasts of Passover and Tabernacles. A lunar tetrad is a series of four consecutive total lunar eclipses, spaced six months apart.[15][16]

Blood Moon is not a scientific term but has come to be used due to the reddish color seen on a Super Moon during the lunar eclipse. When sunlight passes through the earth's atmosphere, it filters and refracts in such a way that the green to violet lights on the spectrum scatters more strongly than the red light. This results the moon to get more red light[17]

In kinematics, cognate linkages are linkages that ensure the same input-output relationship or coupler curve geometry, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyschev Theorem, after Samuel Roberts and Pafnuty Chebyshev, states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram (named after Arthur Cayley).

The Hoeckens linkage is a four-bar mechanism that converts rotational motion to approximate straight-line motion. It is named after Karl Hoecken (1874−1962).

The example to the right spends over half of the cycle in the near straight portion.

The linkage was first published in 1926.[2][3]

Problems with pedal bob and brake jack began to be controlled in the early 1990s. One of the first successful full suspension bikes was designed by Mert Lawwill, a former motorcycle champion.[9] His bike, the Gary Fisher RS-1, was released in 1992. Its rear suspension adapted the A-arm suspension design from sports car racing, and was the first four-bar linkage in mountain biking.[9] This design reduced the twin problems of unwanted braking and pedaling input to the rear wheel, but the design wasn't flawless. Problems remained with suspension action under acceleration, and the RS-1 couldn't use traditional cantilever brakes since the rear axle, and thus rim, moved in relation to the chainstays and seatstays. A lightweight, powerful disc brake wasn't developed until the mid-1990s, and the disc brake used on the RS-1 was its downfall.

Horst Leitner began working on the problem of chain torque and its effect on suspension in the mid-1970s with motorcycles. In 1985 Leitner built a prototype mountain bike incorporating what became known later as the "Horst link". The Horst Link is a type of four-bar suspension. Leitner formed a mountain bike and research company, AMP research, that began building full-suspension mountain bikes. In 1990, AMP introduced the Horst link as a feature of a "fully independent linkage" rear suspension for mountain bikes. The AMP B-3 and B-4 XC full-suspension bikes featured optional disc brakes and Horst link rear suspension very similar to the Macpherson strut. Note that the sliding piston in the shock absorber represents the fourth "bar" in this case. A later model, the B-5, was equipped with a revolutionary four-bar front suspension fork, as well as the Horst link in the rear. It featured up to 125 mm (5 inches) of travel on a bicycle weighing around 10.5 kg (23 pounds). For 10 years AMP Research manufactured their full-suspension bikes in small quantities in Laguna Beach, California, including the manufacture of their own hubs, rear shocks, front suspension forks and cable-actuated-hydraulic disc brakes which they pioneered.[10]

Independent Drivetrain

The "Independent Drivetrain" (or "IDrive"[citation needed]) is a four-bar suspension system for bicycle crank assemblies,[23][24] the rear wheel itself is suspended as single pivot suspension. It was developed by mountain bike suspension designer Jim Busby Jr. and was a direct result of the limitations encountered with the GT LTS (GT Bicycles' "Links Tuned Suspension) four-bar linkage design used by GT Bicycles from 1993 to 1998. The IDrive attempts to maximize the efficiency of the transmission of energy from the rider to the rear wheel. The bottom bracket is placed eccentric in a bearing within the swingarm, the distance between the center of the bearing and the bottom bracket effectively creating a very short link, and the swingarm itself creating another. A link between bearing shell and frame then completes the four-bar linkage with the bottom bracket on the floating link and the linkage as a whole actuated by movement of the swingarm.

The "Monolink" made by Maverick Bikes and designed by RockShox founder Paul Turner, is a variant of the Independent Drivetrain suspension, and is a variation of the MacPherson strut. It uses three pivot points and the sliding action of the shock to provide the fourth degree of freedom. This design places the bottom bracket on the link (the Monolink) connecting the frame and rear triangle. Any load on the cranks is partly unsprung since it is also a load on one of the suspension's parts itself, and actively works against the suspension. However, because of this there is less bob during out-of-the-saddle sprints. Once again it is an attempt at maximizing drivetrain efficiency, compromising other areas. Notable bikes using this design are the Maverick ML7, Durance, ML8 and the Klein Palomino.

Pendbox

The "Pendbox" is found on several of Lapierre's linkage driven single pivot bikes in which the crank assembly is hung from the frame using a 'mini-swingarm'; the Pendbox. A link connects the swingarm and Pendbox such that they form a four-bar linkage.[25]

Watt's linkage (also known as the parallel linkage) is a type of mechanical linkage invented by James Watt (19 January 1736 – 25 August 1819) in which the central moving point of the linkage is constrained to travel on an approximation to a straight line. It was described in Watt's patent specification of 1784 for the Watt steam engine. It is also used in automobile suspensions, allowing the axle of a vehicle to travel vertically while preventing sideways motion.

Watt's linkage consists of a chain of three rods, two longer and equal length ones on the outside ends of the chain, connected by a short rod in the middle. The outer endpoints of the long rods are fixed in place relative to each other, and otherwise the three rods are free to pivot around the joints where they meet. Thus, counting the fixed-length connection between the outer endpoints as another bar, Watt's linkage is an example of a four-bar linkage.

Watt's linkage is used in the rear axle of some car suspensions as an improvement over the Panhard rod, which was designed in the early twentieth century. Both methods intend to prevent relative sideways motion between the axle and body of the car. Watt’s linkage approximates a vertical straight line motion more closely, and does so while locating the centre of the axle rather than toward one side of the vehicle, as more commonly used when fitting a long Panhard rod.[7]

It consists of two horizontal rods of equal length mounted at each side of the chassis. In between these two rods, a short vertical bar is connected. The center of this short vertical rod – the point which is constrained in a straight line motion - is mounted to the center of the axle. All pivoting points are free to rotate in a vertical plane.

In a way, Watt’s linkage can be seen as two Panhard rods mounted opposite each other. In Watt’s arrangement, however, the opposing curved movements introduced by the pivoting Panhard rods largely balance each other in the short vertical rotating bar.

The linkage can be inverted, in which case the centre P is attached to the body, and L1 and L3 mount to the axle. This reduces the unsprung mass and changes the kinematics slightly. This is used on Australian V8 Supercars.

Watt's linkage can also be used to prevent axle movement in the longitudinal direction of the car. This application involves two Watt's linkages on each side of the axle, mounted parallel to the driving direction, but just a single 4-bar linkage is more common in racing suspension systems

A four-bar linkage, also called a four-bar, is the simplest movable closed chain linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage.

If the linkage has four hinged joints with axes angled to intersect in a single point, then the links move on concentric spheres and the assembly is called a spherical four-bar linkage. Bennett's linkage is a spatial four-bar linkage with hinged joints that have their axes angled in a particular way that makes the system movable.

http://drmorgan.info/blog/four-bar-mechanism-knee/

To many clinicians, it may appear that the function of the anterior cruciate and posterior cruciate ligaments (ALL and PLL) is to limit anterior and posterior shear of the knee, as well as prevent rotation of the tibia in relation to the femur. This is what we were taught in orthopedics as we learned to perform the drawer and Lachman's tests of the knee.
In reality, the function of these ligaments is more than merely their contribution to knee stability. These ligaments are vital in transferring power from the muscles of the hip and pelvis (particularly the gluteus maximus and medius) to the leg. This transfer of power is done through the four-bar mechanism created by the degree of tension of these ligaments, and the stiffness of the tibia and femur.1-4
A four-bar mechanism is a simple closed-chain linkage composed of four bars (also referred to as links) and joined by four pivoting connections.5 This mechanism provides efficiency of motion, strength and stability.
Examples of four-bar mechanisms in engineering include vise-grips, lever-armed water pumps, car jacks, oil well pumps, folding chair mechanisms, and umbrellas. This mechanism is so efficient that many of the more modern prosthetic knees (for above-the-knee amputations) are now made with four-bar linkages. Researchers are trying to emulate this naturally occurring mechanism in knee-replacement prostheses.
The four-bar mechanism of the knee is a relatively simple apparatus that transfers power while maximizing leverage and minimizing energy loss. It is part of a broader biotensegrity system, which combines contractile and non-contractile tissues to efficiently transfer power and motion through the musculoskeletal system with minimal energy expenditure.
The four links transfer power and motion from relatively distant sources of power through a driver. In the knee, the femur, which is the longest lever in the body, acts as the driver as it transfers power from the gluteal muscles through its stiffness and strength to create tension on the ALL and PLL. This tension moves the femur relative to the plane(s) of the tibial plateau.
(It should be noted that the four-bar mechanism of the knee does not exactly mirror man-made mechanical models of four-bar machines. The ACL and PCL are relatively stiff only while under load, and even when under load, they maintain some elasticity.)
Certainly the ALL and PLL do not work autonomously in transferring power. The lower extremity is a complex aggregate of structures that includes ligaments, muscles, joint capsules and fascia. There is a concert of activity between these structures during knee motion.
While each of these components is important, the gluteal muscles have a prominent role in both power transfer and protection of the knee.6-10 This knee-gluteal muscle relationship is particularly interesting since the gluteal muscles do not directly attach to or even reside near the knee.

Tharsis Montes is the largest volcanic region on Mars. It is approximately 4,000 km across,10 km high, and contains 12 large volcanoes. The largest volcanoes in the Tharsis region are 4 shield volcanoes named Ascraeus Mons, Pavonis Mons, Arsia Mons, and Olympus Mons. The Tharsis Montes (Ascraeus, Pavonis, and Arsia) are located on the crest of the crustal bulge and their summits are about the same elevation as the summit of Olympus Mons, the largest of the Tharsis volcanoes. While not the largest of the Tharsis volcanoes, Arsia Mons has the largest caldera on Mars, having a diameter of120 km (75 mi)! The main difference between the volcanoes on Mars and Earth is their size; volcanoes in the Tharsis region are up to 100 times larger than those anywhere on Earth.
The pattern fits the quadrant model pattern. With Olympus Mons being off to the side and the other three together.

https://mars.jpl.nasa.gov/galle…/atlas/images/tharsislbl.jpg

https://mars.jpl.nasa.gov/gallery/atlas/tharsis-montes.html

generally group volcanoes into four main kinds--cinder cones, composite volcanoes, shield volcanoes, and lava domes.
Shield volcanoes are distinguished from the three other major volcanic archetypes—stratovolcanoes, lava domes, and cinder cones—by their structural form, a consequence of their unique magmatic composition. Of these four forms shield volcanoes erupt the least viscous lavas

Shield volcanoes are distinguished from the three other major volcanic archetypes—stratovolcanoes, lava domes, and cinder cones—by their structural form, a consequence of their unique magmatic composition. Of these four forms shield volcanoes erupt the least viscous lavas: where stratovolcanoes and especially lava domes are the product of highly immotile flows and cinder cones are constructed by explosively eruptive tephra, shield volcanoes are the product of gentle effusive eruptions of highly fluid lavas that produce, over time, a broad, gently sloped eponymous "shield".

Referring to the accompanying chart, drive applications can be categorized as single-quadrant, two-quadrant, or four-quadrant; the chart's four quadrants are defined as follows. This is called four quadrant control

Quadrant I -- Driving or motoring, forward accelerating quadrant with positive speed and torque

Quadrant II -- Generating or braking, forward braking-decelerating quadrant with positive speed and negative torque

Quadrant III - Driving or motoring, reverse accelerating quadrant with negative speed and torque

Quadrant IV - Generating or braking, reverse braking-decelerating quadrant with negative speed and positive torque.

Here in the order and quality of the planets, the quadrant model pattern is revealed. Scientists often try to explain this as saying that it is due to random and rational processes that the planets are the way they are. I say that the planets, and everything is the way it is, because it is to reveal the quadrant model pattern, which is the expression of Being.
In mathematics, conic sections are curves obtained as the intersection of a cone. There are four conic sections. These curves are the curves through which terrestrial bodies, like planets and asteroids travel. They are
square 1: hyperbola. If the plane intersects both halves of the double cone but does not pass through the apex of the cones then the conic is a hyperbola.
square 2: parabola. If the plane is not closed and t does not pass through the apex of the cones then it is a parabola.
square 3: ellipse. If the plane is a closed curve then it is an ellipse. The ellipse fits the qualities of the third square because the ellipse is a closed curve and thus it is an individual. It is solid and physical.
square 4: circle: If the plane is closed and the radius is the same throughout then it is a circle. Again, the fourth does not seem to belong. Sometimes there is only considered three conic sections, but the fourth is often considered a fourth conic section..
Chemistry and biology are very connected. Chemistry is the second square science and biology is the third square science. The second square is always connected to the thrid square. The second square is always intricately connected to the thrid square. Chemistry joins together and it manifests life.
There are two elements that are called the miracle elements. These are carbon and silicon. All living organisms are made up of carbon, and they are made up of mostly carbon. The reason carbon is so special is it has four valence electrons. In other words, carbon looks like a quadrant. Organic chemistry is the study of carbon chemistry. Silicon is also called the miracle element. Computers are made of silicon. Diamonds are made of silicon. Most of the Earth is made of carbon. Sand is made of silicon. Glass is made of silicon. What makes silicon so special is that it has four valence electrons. In other words, silicon looks like quadrants.
DNA is the instruction manual for life. Biologists describe DNA as the blueprint that contains the information for creating living organisms. DNA is made up of four nucleobases. These are
square 2 Guanine
square 3 Cytosine
square 4 Thymine
RNA has an additinal nucleobase Urine. There is always a sort of possible fifth. But the point is the instruction manual for all life is the quadrant model pattern.
There are four types of macromolecules.
square 1 carbohydrates. Carbohydrates are made up of carbon hydrogen and oxygen. Carbohydrates have less potential energy per gram than fats.
square 2 fats. Lipids like carbohydrates are made up of a lot of carbon and hydrogen. Lipids provide structure and support and protection. Tht is why lipids are the second square. The second square is structure.
Square 3 proteins. Proteins are the doers. Proteins perform actions in the cells and build things.
Square 4 nucleic acid. DNA and RNA are nucleic acids. DNA stands for Deoxyribonucleic acid. DNA gives instructions to proteins and tells them what to do. Without DNA ther would be no carbohydrates or fats or proteins. So DNA is separate from the previous three types of macromolecules, but it also encompasses them. That is the nature of the fourth square. The fourth square is a lot different from the previous three, yet it encompasses them.
Merkle I discussed the four domains of life. They are
1. Archaea. Archae is weird. Archaea are strange. They live in extreme environments. But they don't really do much. The first square is not a doer. The first square is the mind. The first square is more conservative.
2. Bacteria. Bacteria are the second square. Bacteria break down trash. They are homestasis. They break down food in you gut.
3. Eukaryotes. Eukayotes are the doers. Animals and plants are Eukaryotes.
4. Virus. The virus is alive and dead. It has to live within a host cell. Host cells that the virus live in are archaea, bacteria, and Eukaryotes. So the virus is separate, yet encompasses the previous three domains. There are very large viruses and there are scientists who say that they are another domain of life. The fourth always seems like it doesn't belong with the other three. The fourth is always a lot different.
Let's discuss the eukaryotes, and how they fit the quadrant model pattern. There are four kingdoms of Eukaryotes. Eukaryotes are important because humans are Eukaryotes. These are

The four seasons fit the quadrant model Square 1: Spring. The first square is birth Square2:Summer. Summer is associated with being very nice. It is the most social time when people play together. The second quadrant is about relationships and it is life. It is the normal square. Square 3:Fall. Fall is destruction. The leaves fall during fall. The third square is destruction and often seen as bad. Square 4:Winter. Winter is death. The fourth square is death
The planets fit the quadrant model pattern. A big point that I am making now is that scientists have always tried to explain things through naturalisitc phenomena. Scientists try to explain why the planets are the way they are, but they don't really know why. One example of this is scientists say that there is an asteroid belt after mars because this is probably leftover debris from two planets that collided and were destroyed. I however, say that scientists are wrong in all of their attempts to say why things are the way they are. The ultimate answer to why things are the way they are is that it reveals the quadrant model pattern, which is the Form of Existence. The reason the planets are organized the way they are is to reveal the quadrant model pattern.
Let me explain.
The first four planets are called terrestrial planets.
These planets are the first quadrant planets
square 1: Mercury. Mercury is tiny. Mercury is the sensor. Mercury goes very close to the sun. It is full of craters. It is weird. The first square is always weird. Mercury is the first square of the first quadrant. It is the senser. Mercury is very weird.
square 2:Venus. Venus is the perceiver. Venus is the second square. The second square is homeostasis. The second square is always pretty. Venus is pretty. Upon closer inspection though its atmosphere is made up of sulfuric acid which is deadly to humans. So it looks pretty but it is not that wonderful of a place. But nonethelesss it has a superficial quality of being pretty, and that is the nature of the second square.
square 3:Earth. Earth is the responder. The third square is the doing square. The third square is action. The third square is also bad. Earth is kind of a bad place. It is full of wars and destruction. Earth is where a lot of action goes on. It is the only known planet with life on it.
square 4: Mars. Mars is the aware square. The fourth has a quality of not belonging, and also of seeming like there is nothing there. For instance, Rationals only make up 5 percent of the population and they are a lot different from the other three tempearments. Mars is the an interesting planet. Scientists think that life used to be on it and that it used to be full with water. Some scientists even propose that life from Earth came from asteroids from Mars. But now Mars is vacant. Although there is always a kind of suspicion that there is life on the planet. The fourth is always kind of mysterious.
After mars there is the asteroid belt. I do not think that this is a coincidence. The asteroid belt demarcates the boundary between one quadrant and another. There has already been four squares. Now there needs to be another four squares. The asteroid belt demarcates the boundary between the first qudrant and the second quadrant. The first four planets are terrestrial planets, which are planets made of rock. The next four planets are gaseous planets. It is important to note that these next four planets are the second quadrant. The second quadrant is always the prettiest. The second quadrant is belief, faith, behavior and belonging. The second quadrant is also protection. These planets are very large, and it is true that they do protect Earth from asteroids because most asteroids are sucked into their gravitational fields.
This is quadrant 2. I am not gong to write it as square one of quadrant 2 but I am just going to say for the first square, square 5, since it is the fifth square in total.
square 5: Jupiter. Jupiter is a gaseous planet. It is the believer planet. It is the fifth planet. It is pretty large. The second quadrant is always structure. It is large but it is not very solid. It is made up of gas. It is the first square of the second quadrant, so it makes sense that it won't be very solid. Some scientists think that Jupiter may have been a failed star itself. Jupiter has a ring. Jupiter is pretty. The second quadrant is always pretty. Belief gives you comfort.
square 6: Saturn. Saturn is the second square of the second quadrant. It has to be the prettiest of them all. It is not solid. It is gaseous. That makes sense because this is the second square of the second quadrant. The second square is always the most pretty, so Saturn is extremely pretty. Saturn has very nice rings.
square 7: Uranus. Uranus is the third square of the second quadrant. Uranus is the behaver planet. It is interesting that Uranus is a gaseous planet, but it has a solid core. Because it is the third square, it is becoming more solid. Uranus is still in the second quadrant so it is still pretty. It has a ring.
square 8: Neptune: Neptune is the belonger planet. Neptune is still in the second quadrant so it still has a ring. It is pretty. Neptune also has a sort of solid core.
So that is quadrant 2. Now their is the comet belt. There needs to be a demarcation between the second quadrant and the third quadrant. That is the comet belt. Pluto is not a planet but a planetesimal. Pulto is the first square of the third quadrant.
Square 9: Pluto is the ninth square. Pluto is the thinker. Recall that thinking is wild. It is difficult to control your thoughts. This is interesting. The first 8 planets have cocentric orbits. But the orbit of Pluto is different. Pluto does its own thing. It is an individual. The third quadrant is the ego oriented selfish quadrant. Pluto is an individual and it doesn't follow the rules the other planets follow.

http://telecom.hellodirect.com/…/TelWiringBasics.1.040401.a…

Wires, plugs, and the network interface
The basics of the wiring is pretty easy to understand. Most telephone wires are one or more twisted pairs of copper wire. The most common type is the 4-strand (2 twisted pair). This consists of red and green wires, which make a pair, and yellow and black wires, which make the other pair. One telephone line needs only 2 wires. Therefore it follows that a 4-strand wire can carry 2 separate phone lines. The twisting keeps the lines from interfering with each other. If you need to run more lines than just 2, you may want to use a 6-strand, or higher. Telephone wire comes in 2 gauges, 22 gauge and 24 gauge, 24 gauge being today's standard.
There are 2 types of common modular plugs, the RJ-11 and the RJ-14. The most common is the RJ-11 which uses only 2 of the wires in a 4 (or more) strand wire. This is the same kind of plug that you use to plug your telephone into the wall. This is a 1-line plug. The RJ-14 uses 4 wires and is used to handle 2 lines, or 2-line phones.

The fourth is different/transcendent.

Most audio cables and headphones have three or four wires running through them: a red one, a green/blue one, and a bare/copper one. If there’s four, odds are there are two bare/copper ones. The red one is the right channel, the green or blue is the left channel, and the bare wire is the ground. These colors can be different, but the right channel will almost always be red, and the ground is usually a copper-colored one if it’s not bare.

NOTICE HOW THE FOURTH IS DIFFERENT

At 4:20 he talks about how most homes have four wires

At 2 minutes he talks about the four lines

There are four spiral arms of the Milky Way Galaxy, the Galaxy in which Earth resides.

Outside the gravitational influence of the Galactic bars, astronomers generally organize the structure of the interstellar medium and stars in the disk of the Milky Way into four spiral arms. Spiral arms typically contain a higher density of interstellar gas and dust than the Galactic average as well as a greater concentration of star formation, as traced by H II regions[105][106] and molecular clouds.

The Milky Way's spiral structure is uncertain and there is currently no consensus on the nature of the Galaxy's spiral arms. Perfect logarithmic spiral patterns only crudely describe features near the Sun, because galaxies commonly have arms that branch, merge, twist unexpectedly, and feature a degree of irregularity.[88][108][109] The possible scenario of the Sun within a spur / Local arm[106] emphasizes that point and indicates that such features are probably not unique, and exist elsewhere in the Milky Way.

As in most spiral galaxies, each spiral arm can be described as a logarithmic spiral. Estimates of the pitch angle of the arms range from about 7° to 25°. There are thought to be four spiral arms that all start near the Milky Way's center. These are named as follows, with the positions of the arms shown in the image at right:

Observed (normal lines) and extrapolated (dotted lines) structure of the spiral arms. The gray lines radiating from the Sun's position (upper center) list the three-letter abbreviations of the corresponding constellations.

Color Arm(s)

cyan 3-kpc Arm (Near 3 kpc Arm and Far 3 kpc Arm) and Perseus Arm

purple Norma and Outer arm (Along with extension discovered in 2004[111])

green Scutum–Centaurus Arm

pink Carina–Sagittarius Arm

In December 2013, astronomers found that the distribution of young stars and star-forming regions matches the four-arm spiral description of the Milky Way. Thus, the Milky Way appears to have two spiral arms as traced by old stars and four spiral arms as traced by gas and young stars

A galactic quadrant, or quadrant of the Milky Way, refers to one of four circular sectors in the division of the Milky Way. In actual astronomical practice, the delineation of the galactic quadrants is based upon the galactic coordinate system, which places the Sun as the origin of the mapping system.[84]

Quadrants are described using ordinals—for example, "1st galactic quadrant",[85] "second galactic quadrant",[86] or "third quadrant of the Milky Way".[87] Viewing from the north galactic pole with 0 degrees (°) as the ray that runs starting from the Sun and through the Galactic Center, the quadrants are as follows:

1st galactic quadrant – 0° ≤ longitude (ℓ) ≤ 90°[88]

2nd galactic quadrant – 90° ≤ ℓ ≤ 180°[86]

3rd galactic quadrant – 180° ≤ ℓ ≤ 270°[87]

4th galactic quadrant – 270° ≤ ℓ ≤ 360° (0°)[85]

Carl Sagan in his book Comet (1985) reproduces Han period Chinese manuscript (the Book of Silk, 2nd century BC) that shows comet tail varieties: most are variations on simple comet tails, but the last shows the comet nucleus with four bent arms extending from it, recalling a swastika. Sagan suggests that in antiquity a comet could have approached so close to Earth that the jets of gas streaming from it, bent by the comet's rotation, became visible, leading to the adoption of the swastika as a symbol across the world.[18] Bob Kobres in his 1992 paper Comets and the Bronze Age Collapse contends that the swastika like comet on the Han Dynasty silk comet atlas was labeled a "long tailed pheasant star" (Di-Xing) because of its resemblance to a bird's foot or footprint,[19] the latter comparison also being drawn by J.F.K. Hewitt's observation on page 145 of Primitive Traditional History: vol. 1.[20] as well as an article concerning carpet decoration in Good Housekeeping.[21] Kobres goes on to suggest an association of mythological birds and comets also outside China.[19]

Swastika Plate 5000 BC is a Model of the Milky Way

kachina2012.wordpress.com

…/swastika-plate-5000-bc…/

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.

The maltese cross was the first image on television

The leading pioneer in the creation of television, John Logie Baird, was a Scotsman, born in 1888, the son of a Presbyterian minister, and educated in Glasgow. An electrical engineer and an eccentric genius, he was no businessman, his health was precarious and after a time spent marketing socks, jam and soap he suffered a nervous breakdown.

In 1923 he retreated to Hastings in Sussex, where he was described as so thin ‘as to be almost transparent’. It was there that he invented a glass safety razor, with which he cut himself badly, and pneumatic soles for shoes, which burst after a hundred yards. At last he produced something that worked, the embryo of today’s television sets, a primitive apparatus that sat on a washstand in his attic and involved bicycle lamps, scanning discs cut out of cardboard, a biscuit tin, darning needles and string. It transmitted an unsteady, flickering image of a Maltese cross over a distance of a few feet.

https://en.wikipedia.org/wiki/Memristor
https://en.wikipedia.org/…/File:Two-terminal_non-linear_cir…
According to the original 1971 definition, the memristor was the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage.

A tetrad is an area 2 km x 2 km square. The term has a particular use in connection with the British Ordnance Survey national grid, and then refers to any of the 25 such squares which make up a standard hectad.[1]

Tetrads are sometimes used by biologists for reporting the distribution of species to maintain a degree of confidentiality about their data,[2] though the system is not in universal use.[1]

The tetrads are labelled from A to Z (omitting O) according to the "DINTY" system as shown in the grid below, which takes its name from the letters of the second line.[1]

The vierbein or tetrad theory much used in theoretical physics is a special case of the application of Cartan connection in four-dimensional manifolds. It applies to metrics of any signature. (See metric tensor.) This section is an approach to tetrads, but written in general terms.

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

In mathematics, four-dimensional space ("4D") is a geometric space with four dimensions. It typically is more specifically four-dimensional Euclidean space, generalizing the rules of three-dimensional Euclidean space. It has been studied by mathematicians and philosophers for over two centuries, both for its own interest and for the insights it offered into mathematics and related fields.

Algebraically, it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.

In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions (see below for the definition of the Minkowski metric/pairing). Spacetime is not a Euclidean space.

In meteorology, Buys Ballot's law (Dutch pronunciation: [ˌbœy̯s bɑˈlɔt]) may be expressed as follows: In the Northern Hemisphere, if a person stands with his back to the wind, the atmospheric pressure is low to the left, high to the right.[1] This is because wind travels counterclockwise around low pressure zones in the Northern Hemisphere. It is approximately true in the higher latitudes of the Northern Hemisphere, and is reversed in the Southern Hemisphere, but the angle between the pressure gradient force and wind is not a right angle in low latitudes.

The law outlines general rules of conduct for masters of both sail and steam vessels, to assist them in steering the vessels away from the center and right front (in the Northern Hemisphere and left front in the Southern Hemisphere) quadrants of hurricanes or any other rotating disturbances at sea. Prior to radio, satellite observation and the ability to transmit timely weather information over long distances, the only method a ship's master had to forecast the weather was observation of meteorological conditions (visible cloud formations, wind direction and atmospheric pressure) at his location.

Included in the Sailing Directions for the World are Buys Ballot's techniques for avoiding the worst part of any rotating storm system at sea using only the locally observable phenomena of cloud formations, wind speed and barometric pressure tendencies over a number of hours. These observations and application of the principles of Buys Ballot's Law help to establish the probability of the existence of a storm and the best course to steer to try avoid the worst of it—with the best chance of survival.

The underlying principles of Buys Ballot's law state that for anyone ashore in the Northern Hemisphere and in the path of a hurricane, the most dangerous place to be is in the right front quadrant of the storm. There, the observed wind speed of the storm is the sum of the speed of wind in the storm circulation plus the velocity of the storms forward movement. Buys Ballot's Law calls this the "Dangerous Quadrant". Likewise, in the left front quadrant of the storm the observed wind is the difference between the storm's wind velocity and its forward speed. This is called the "Safe Quadrant" due to the lower observed wind speeds.

To look at it another way, in the Northern Hemisphere if a person is to the right of where a hurricane or tropical storm makes landfall, that is considered the dangerous quadrant. If they are to the left of the point of landfall, that is the safe quadrant. In the dangerous quadrant an observer will experience higher wind speeds and generally a much higher storm surge due to the onshore wind direction. In the Safe quadrant, the observer will experience somewhat lower wind speeds and the possibility of lower than normal water levels due to the direction of the wind being offshore.

These are very general rules that are subject to many other factors, including shapes of the coastline, and topography in any location. Although the principles apply to a very limited extent to a coastal observer during the approach and passage of a storm in any location, Buys Ballot's law was primarily formulated from empirical data to assist ships at sea.

e

μ
plane: A new frontier in optics
Fig. 2.
Fig. 2.
Omitting the
Im
e
and
m
μ
Ι
, the
e

μ
plane is separated in four quadrants. The third one
(
0
μ
<

>0
e
), even if it is realized, leads to decay, and henc
e, it presents no intere
st form the point of
view of optics. The fourth quadrant (
0
μ
<

<0
e
), for which
0
μ
>
e
, allows propagation
Square 1: metal decay
Square 2: unusual propagation
Square 3:dialectic propoagation
Square 4: new propogation
Like

A four quadrant photo detector for measuring laser pointing stability

Quadrant- Optical phase diagram of a coherent state's distribution across phase space.

In quantum optics, an optical phase space is a phase space in which all quantum states of an optical system are described. Each point in the optical phase space corresponds to a unique state of an optical system. For any such system, a plot of the quadratures against each other, possibly as functions of time, is called a phase diagram. If the quadratures are functions of time then the optical phase diagram can show the evolution of a quantum optical system with time.

Operators given by

and

are called the quadratures and they represent the real and imaginary parts of the complex amplitude represented by .[1] The commutation relation between the two quadratures can easily be calculated:

This looks very similar to the commutation relation of the position and momentum operator. Thus, it can be useful to think of and treat the quadratures as the position and momentum of the oscillator although in fact they are the "in-phase and out-of-phase components of the electric field amplitude of the spatial-temporal mode", or u, and have nothing really to do with the position or momentum of the electromagnetic oscillator (as it is hard to define what is meant by position and momentum for an electromagnetic oscillator).[1]

The eigenstates of the quadrature operators and are called the quadrature states. They satisfy the relations:

and

and

and

as these form complete basis sets.

The following is an important relation that can be derived from the above which justifies our interpretation that the quadratures are the real and imaginary parts of a complex (i.e. the in-phase and out-of-phase components of the electromagnetic oscillator)

The following is a relationship that can be used to help evaluate the above and is given by:

[1]

This gives us that:

by a similar method as above.

Thus, is just a composition of the quadratures.

Another very important property of the coherent states becomes very apparent in this formalism. A coherent state is not a point in the optical phase space but rather a distribution on it. This can be seen via

and

.

These are only the expectation values of and for the state .

It can be shown that the quadratures obey Heisenberg's Uncertainty Principle given by:

[1] (where and are the variances of the distributions of q and p, respectively)

This inequality does not necessarily have to be saturated and a common example of such states are squeezed coherent states. The coherent states are Gaussian probability distributions over the phase space localized around .

Constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by one bit.

Sometimes this is known as quadriphase PSK, 4-PSK, or 4-QAM. (Although the root concepts of QPSK and 4-QAM are different, the resulting modulated radio waves are exactly the same.) QPSK uses four points on the constellation diagram, equispaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the bit error rate (BER) — sometimes misperceived as twice the BER of BPSK.

The mathematical analysis shows that QPSK can be used either to double the data rate compared with a BPSK system while maintaining the same bandwidth of the signal, or to maintain the data-rate of BPSK but halving the bandwidth needed. In this latter case, the BER of QPSK is exactly the same as the BER of BPSK - and deciding differently is a common confusion when considering or describing QPSK. The transmitted carrier can undergo numbers of phase changes.

Given that radio communication channels are allocated by agencies such as the Federal Communication Commission giving a prescribed (maximum) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice the data rate in a given bandwidth compared to BPSK - at the same BER. The engineering penalty that is paid is that QPSK transmitters and receivers are more complicated than the ones for BPSK. However, with modern electronics technology, the penalty in cost is very moderate.

As with BPSK, there are phase ambiguity problems at the receiving end, and differentially encoded QPSK is often used in practice.

The implementation of QPSK is more general than that of BPSK and also indicates the implementation of higher-order PSK. Writing the symbols in the constellation diagram in terms of the sine and cosine waves used to transmit them:

This yields the four phases π/4, 3π/4, 5π/4 and 7π/4 as needed.

This results in a two-dimensional signal space with unit basis functions

The first basis function is used as the in-phase component of the signal and the second as the quadrature component of the signal.

Hence, the signal constellation consists of the signal-space 4 points

The factors of 1/2 indicate that the total power is split equally between the two carriers.

Comparing these basis functions with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals. Note that the signal-space points for BPSK do not need to split the symbol (bit) energy over the two carriers in the scheme shown in the BPSK constellation diagram.

QPSK systems can be implemented in a number of ways. An illustration of the major components of the transmitter and receiver structure are shown below.

Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. With this interpretation, the even (or odd) bits are used to modulate the in-phase component of the carrier, while the odd (or even) bits are used to modulate the quadrature-phase component of the carrier. BPSK is used on both carriers and they can be independently demodulated.

As a result, the probability of bit-error for QPSK is the same as for BPSK:

However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the power (since two bits are transmitted simultaneously).

The symbol error rate is given by:

.

If the signal-to-noise ratio is high (as is necessary for practical QPSK systems) the probability of symbol error may be approximated:

The modulated signal is shown below for a short segment of a random binary data-stream. The two carrier waves are a cosine wave and a sine wave, as indicated by the signal-space analysis above. Here, the odd-numbered bits have been assigned to the in-phase component and the even-numbered bits to the quadrature component (taking the first bit as number 1). The total signal — the sum of the two components — is shown at the bottom. Jumps in phase can be seen as the PSK changes the phase on each component at the start of each bit-period. The topmost waveform alone matches the description given for BPSK above.

Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown at the top, and the total combined signal at the bottom. Note the abrupt changes in phase at some of the bit-period boundaries.

The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.

The odd bits, highlighted here, contribute to the in-phase component: 1 1 0 0 0 1 1 0

The even bits, highlighted here, contribute to the quadrature-phase component: 1 1 0 0 0 1 1 0

Offset QPSK (OQPSK)

Signal doesn't cross zero, because only one bit of the symbol is changed at a time

Offset quadrature phase-shift keying (OQPSK) is a variant of phase-shift keying modulation using 4 different values of the phase to transmit. It is sometimes called Staggered quadrature phase-shift keying (SQPSK).

Difference of the phase between QPSK and OQPSK

Taking four values of the phase (two bits) at a time to construct a QPSK symbol can allow the phase of the signal to jump by as much as 180° at a time. When the signal is low-pass filtered (as is typical in a transmitter), these phase-shifts result in large amplitude fluctuations, an undesirable quality in communication systems. By offsetting the timing of the odd and even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time. In the constellation diagram shown on the right, it can be seen that this will limit the phase-shift to no more than 90° at a time. This yields much lower amplitude fluctuations than non-offset QPSK and is sometimes preferred in practice.

The picture on the right shows the difference in the behavior of the phase between ordinary QPSK and OQPSK. It can be seen that in the first plot the phase can change by 180° at once, while in OQPSK the changes are never greater than 90°.

The modulated signal is shown below for a short segment of a random binary data-stream. Note the half symbol-period offset between the two component waves. The sudden phase-shifts occur about twice as often as for QPSK (since the signals no longer change together), but they are less severe. In other words, the magnitude of jumps is smaller in OQPSK when compared to QPSK.

π /4–QPSK

Dual constellation diagram for π/4-QPSK. This shows the two separate constellations with identical Gray coding but rotated by 45° with respect to each other.

This variant of QPSK uses two identical constellations which are rotated by 45° ( radians, hence the name) with respect to one another. Usually, either the even or odd symbols are used to select points from one of the constellations and the other symbols select points from the other constellation. This also reduces the phase-shifts from a maximum of 180°, but only to a maximum of 135° and so the amplitude fluctuations of –QPSK are between OQPSK and non-offset QPSK.

One property this modulation scheme possesses is that if the modulated signal is represented in the complex domain, it does not have any paths through the origin. In other words, the signal does not pass through the origin. This lowers the dynamical range of fluctuations in the signal which is desirable when engineering communications signals.

On the other hand, –QPSK lends itself to easy demodulation and has been adopted for use in, for example, TDMA cellular telephone systems.

The modulated signal is shown below for a short segment of a random binary data-stream. The construction is the same as above for ordinary QPSK. Successive symbols are taken from the two constellations shown in the diagram. Thus, the first symbol (1 1) is taken from the 'blue' constellation and the second symbol (0 0) is taken from the 'green' constellation. Note that magnitudes of the two component waves change as they switch between constellations, but the total signal's magnitude remains constant (constant envelope). The phase-shifts are between those of the two previous timing-diagrams.

SOQPSK

The license-free shaped-offset QPSK (SOQPSK) is interoperable with Feher-patented QPSK (FQPSK), in the sense that an integrate-and-dump offset QPSK detector produces the same output no matter which kind of transmitter is used.[9]

These modulations carefully shape the I and Q waveforms such that they change very smoothly, and the signal stays constant-amplitude even during signal transitions. (Rather than traveling instantly from one symbol to another, or even linearly, it travels smoothly around the constant-amplitude circle from one symbol to the next.)

The standard description of SOQPSK-TG involves ternary symbols.

DPQPSK

Dual-polarization quadrature phase shift keying (DPQPSK) or dual-polarization QPSK - involves the polarization multiplexing of two different QPSK signals, thus improving the spectral efficiency by a factor of 2. This is a cost-effective alternative, to utilizing 16-PSK instead of QPSK to double the spectral efficiency.

Any number of phases may be used to construct a PSK constellation but 8-PSK is usually the highest order PSK constellation deployed. With more than 8 phases, the error-rate becomes too high and there are better, though more complex, modulations available such as quadrature amplitude modulation (QAM). Although any number of phases may be used, the fact that the constellation must usually deal with binary data means that the number of symbols is usually a power of 2 to allow an integer number of bits per symbol

In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the complex numbers they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are "binary phase-shift keying" (BPSK) which uses two phases, and "quadrature phase-shift keying" (QPSK) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a power of 2.

In computing, quadruple precision (also commonly shortened to quad precision) is a binary floating-point-based computer number format that occupies 16 bytes (128 bits) in computer memory and whose precision is about twice the 53-bit double precision.

This 128 bit quadruple precision is designed not only for applications requiring results in higher than double precision,[1] but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables: as William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Point Arithmetic was framed." [2]

In IEEE 754-2008 the 128-bit base-2 format is officially referred to as binary128.

A 4-cylinder engine, often nicknamed "four bangers" do have several advantages. An inline four is small, compact and lightweight resulting in great nimbleness. An inline 4 has less frictional losses than a V6 or V8 as it has fewer moving parts, resulting in better efficiency, and therefore superior fuel consumption as well as being capable of revving to higher rpm compared to an engine with more rotating mass, such as a cross plane v8 which uses heavy counterweights. Higher rpm capability results in higher power per unit displacement, which straight fours are well known for. A notable inline 4 engine would be the BMW Megatron M12 1.5 litre Formula 1 straight 4 engine which won the 1983 World Drivers Championship installed in the Brabham BT52 chassis driven by Nelson Piquet. In the second half of the 1983 Formula 1 season, the BMW was capable of over 800 BHP in qualifying, while in race trim usually had an output of between 640 BHP to 700 BHP depending on how much boost the drivers used.

Automobile use

The Quadrajet is a four barrel carburetor, made by the Rochester Products Division of General Motors. Its first application was the new-for-1965 Chevy 396ci engine. Its last application was on the 1990 Oldsmobile 307 V8 engine, which was last used in the Cadillac Brougham and full size station wagons made by Chevrolet, Pontiac, Oldsmobile, and Buick.

A flat-four or horizontally opposed-four is a type of four-cylinder engine, a flat engine with four cylinders arranged horizontally in two banks of two cylinders on each side of a central crankcase.

The pistons are usually mounted on the crankshaft so that opposing pistons move back and forth in opposite directions at the same time, somewhat like boxing competitors punching their gloves together before a fight, which has led to it being referred to as a "boxer" engine. The design is rarely seen with shared crank throws (See Coventry Climax FWMW for such a non-boxer flat engine), so "flat-four" and "boxer-four" are usually used synonymously.

The configuration results in inherently good balance of the reciprocating parts, a low centre of gravity, and a very short engine length. The layout also lends itself to efficient air cooling with excellent thermal balance. However, it is an expensive design to manufacture, and somewhat too wide for compact automobile engine compartments, which makes it more suitable for cruising motorcycles and aircraft than ordinary passenger cars.[1]

This is no longer a common configuration, but some brands of automobiles use such engines and it is a common configuration for smaller aircraft engines such as those made by Lycoming, Continental and Rotax. Although they are superior to straight fours in terms of secondary vibration, they have largely fallen out of favour for overhead cam design engines, for which an opposed-four cylinder layout would require twice as many camshafts as a straight-four while the crankshaft is as complex to manufacture. The low centre of gravity of the engine is an advantage. The shape of the engine suits it better for mid engine or rear engine designs. With a rear engine layout, it allows a low-tail body while in front engine designs the width of the engine often interferes with the maximum front wheel steering angle. The latter problem has not stopped Subaru from using it in its all-wheel drive cars, where the difficulty of fitting the wide engine between the front wheels ahead of the front axle is compensated for by the ease of locating the transmission and four-wheel drive mechanisms behind the short length, between the front and rear axles.

The open and exposed design of the engine allows air cooling as well as water cooling, and in air-cooled applications fins are often cast into the external cylinder block walls to improve the engine cooling.

Balance and smoothness Edit

A four-stroke engine (also known as four cycle) is an internal combustion (IC) engine in which the piston completes four separate strokes while turning a crankshaft. A stroke refers to the full travel of the piston along the cylinder, in either direction. The four separate strokes are termed:

Intake: This stroke of the piston begins at top dead center (T.D.C.) and ends at bottom dead center (B.D.C.). In this stroke the intake valve must be in the open position while the piston pulls an air-fuel mixture into the cylinder by producing vacuum pressure into the cylinder through its downward motion.

Compression: This stroke begins at B.D.C, or just at the end of the suction stroke, and ends at T.D.C. In this stroke the piston compresses the air-fuel mixture in preparation for ignition during the power stroke (below). Both the intake and exhaust valves are closed during this stage.

Power: This is the start of the second revolution of the four stroke cycle. At this point the crankshaft has completed a full 360 degree revolution. While the piston is at T.D.C. (the end of the compression stroke) the compressed air-fuel mixture is ignited by a spark plug (in a gasoline engine) or by heat generated by high compression (diesel engines), forcefully returning the piston to B.D.C. This stroke produces mechanical work from the engine to turn the crankshaft.

Exhaust: During the exhaust stroke, the piston once again returns from B.D.C. to T.D.C. while the exhaust valve is open. This action expels the spent air-fuel mixture through the exhaust valve.

The RivalScape 2x2 WCI Matrix

Each of the four quadrants shown in the 2x2 matrix below lends itself to a productive discussion about corporate Workforce Competitive Intelligence™ (WCI) issues.

You Know You Don’t Know

You Know Facts, assumptions, beliefs… and blind spots Known intelligence gaps

You Don’t Know Hidden internal knowledge Unknown but not always unknowable

This matrix is a variation of the famous “Johari Window” created by psychologists Joseph Luft and Harry Ingham as an interpersonal communication tool.

Credit for the original intelligence adaptation is due to Liam Fahey of Babson College, author of “Learning From the Future.” Fahey first exposed us to his version of the Johari Window matrix at the Society of Competitive Intelligence Professionals annual conference in Anaheim, CA in 2003.

It is fair to say that each knowledge, insight and intelligence issue in your business would fit into one of these four quadrants. Let’s examine the quadrants and what the WCI implications are in each.

Quadrant One: “You Know You Know.”

Corporate certitude is dangerous because it causes blind spots. Ben Gilad, the author of “Business Blind spots.,” says an unexplored and unchallenged sense of certainty can lead to “corporate sclerosis.”

A WCI program will insure that you are constantly scanning the competitive landscape, exposing blind spots. and sharpening your vision.

Quadrant Two: “You Know You Don’t Know.”

A good executive recognizes the limits of his or her knowledge and then develops an action plan to gain the desired information and insight to solve the problem at hand.

RivalScape explores important competitive issues with the client as part of a workforce intelligence requirements planning exercise. If done properly, intelligence requirements planning leads to precise, well-defined and manageable issues called “key intelligence topics” (KITs).

The creation of KITS in a WCI program leads to a focused effort to gain exactly the intelligence you really need.

Quadrant Three: “You Don’t Know You Know.”

The tacit knowledge in your organization resides in this quadrant. Certain parts of this largely hidden knowledge pool can make important contributions to your bottom line, hence an effort should be made to make that silent knowledge explicit. Only then can it be used effectively to maximize competitive advantage.

For example: Are a significant number of key employees projected to retire in the next year or two? If so, think of the wealth of insight that will walk out the door, valuable knowledge “you didn’t know you knew.” (See our Pre-Retirement Insight Management Exchange program.)

Quadrant Four: “You Don’t Know You Don’t Know”

This is the worst “danger zone” for corporate decision making. It is often from this quadrant that the nastiest surprises emanate.

Competitors could be about to change the rules of the game in your market, or you might be about to have new labor market competitors – maybe even a new direct competitor that hasn’t made it to your radar screen yet. Or perhaps you have serious information security leakages from inside your workforce about which you are completely unaware and not even thinking about.

WCI provides a number of antidotes for such unwelcome surprises. The most obvious one is having access to a well-developed and motivated corporate intelligence network that is encouraged to “think outside the dots.” Another WCI tool is to cultivate and maintain a large internal and external source network that informs you of new and still-weak signals from the marketplace. (See our Competitor Alumni Program™, for example).

If you are concerned about possible information leakages from your workforce, a Workforce Information Security Program™ can help find you find and plug any leaks.

Like

Before beginning our discussion on how a DC motor works in 4 quadrants, we will look at the four quadrant operation of a motor driving a hoist load as shown in figure below.

This hoist consists of a cage with or without any load. A rope, generally made up of a steel wire is wounded on a drum to raise the cage and a balance weight.

This balance weight or counterweight magnitude is greater than that of empty cage, but less than the loaded cage.

For each quadrant of operation, direction of rotation, w, load torque, TL, and motor torque Tm are shown in figure. Consider that the load torque is constant and independent of motor speed.

The four operating modes of a hoist are described below.

This is the first quadrant operation of the hoist in which the loaded cage is moving upwards. Due to the upward movement, the direction of rotation of motor, w will be in anticlockwise direction, i.e., positive speed. Here the load torque acts in opposite direction to the direction of motor rotation.

Therefore, to raise the hoist to upwards, the motor torque, Tm must act in the same direction of motor speed, w. So both motor speed and motor torque will be positive.

To make these as positive, the power taken from the supply should be positive. This is called forward motoring.

four quadrant operations of a hoist

Empty cage moving up

This is the quadrant-2 operation of the hoist in which unloaded cage is moving upwards. As said above, the counterweight is heavier than the unloaded cage and hence hoist can move upwards at a dangerous speed.

To prevent this, motor must produce a torque in the opposite direction of motor speed, w in order to produce brake to the motor.

Therefore, the motor torque, Tm will be negative and motor speed, w will be positive. Since the speed of the hoist is positive, it receives the power from the supply and hence the power is positive. This quadrant operation is called forward braking.

Empty cage moving down

This is the quadrant-3 operation where empty cage is hoisting down as shown in figure. The downward journey of empty cage is prevented by the torque exerted by the counterweight. So the direction of motor torque, Tm should be in the same direction of motor rotation w.

Due to the downward movement of the cage, the direction of rotation is reversed, i.e., w is negative and hence Tm is also negative.

Since the machine acting as motor in reverse direction, it receives the power from the supply and hence power is positive. This quadrant operation is called reverse motoring.

In this quadrant, loaded cage is moving downwards. Since the loaded cage is moving downward (of which weight is more than counterweight), the motion takes place without use of any motor.

But there will be a chance to go downward at a dangerous speed because of loaded cage. To limit the speed of the cage within a safe range, the electrical machine must act as a brake.

In this the direction of the motor, w is negative and hence the motor torque Tm is positive to decrease the speed of the motor. Thus the power is negative that means the electrical machine delivering power to the supply.

This phenomenon is called as regenerative action. This quadrant operation is called reverse braking.

It is to be noted that the electrical machine acts as a motor in 1st and 2nd quadrants and acts as a generator in 3rd and 4th quadrants.

But the motor should be separately excited DC motor or three-phase AC induction motor to operate in these four different modes.

Four Quadrant Operation of a DC Motor

In a separately excited DC motor, the steady state speed is controlled at any desired speed by applying the appropriate magnitude of voltage, also in either direction simply by giving appropriate polarity of the voltage.

The torque of the motor is directly proportional to the armature current, which in turn depends on the difference between the applied voltage V and back emf, E, i.e.,

I = (V – E) / R

Therefore, it is possible to develop positive or negative torque by controlling voltage, which is less than or more than the back emf. Hence the separately excited DC motor inherently exhibit four quadrant operation.

The below figure shows four quadrant operation of a separately excited DC motor in which a dot symbol on one of motor terminals indicates the sign of the torque.

The machine produces a positive torque, if current flows into the dot. Similarly the torque is negative, if current flows out of the dot. Also, the relative magnitudes of voltage and back emf are shown in figure. These four quadrants are explained below.

four quadrant operations of a DC motor

Forward Motoring

In this mode of operation, the applied voltage is positive and greater than the back emf of the motor and therefore a positive current flow into the motor.

Since both current and voltage are positive, the power becomes positive. And also the speed and torque are also positive in this quadrant. Therefore the motor rotates in forward direction.

In this mode of operation, the motor runs in forward direction and the induced emf continues to be positive. But the supplied voltage is suddenly reduced to a value which is less than the back emf.

Hence the current (there by torque) will reverse direction. This negative torque reverses the direction of energy flow.

Since the load torque and motor torque are in opposite direction, the combined effect will cause to reduce the speed of the motor and hence back emf (motor emf is directly proportional to the speed) falls again below the applied voltage value.

Hence, both current and voltage become positive and the motor settle down to first quadrant again. The process by which the mechanical energy of the motor is returned to the supply is called as regenerative braking.

This quadrant operation is the example of regenerative braking.

Reverse Motoring

This is the third quadrant operation of the motor in which both motor voltage and current are negative. Thus the power is positive, i.e., the power is supplied from source to load.

Due to the reverse polarity of the supply, the motor starts rotating in a counterclockwise direction (or reverse to normal operation).

The operation of this quadrant is similar to the first quadrant, but only difference is the direction of rotation. The magnitude of voltage to the motor decides the appropriate speed in reverse direction.

Reverse Regenerative Braking

This is the quadrant-4 mode of operation in which motor voltage is still negative and its armature current is positive.

This mode of operation is similar to the second quadrant operation and once again the regeneration occurs whenever the back emf is more than the negative supply voltage.

Hence the torque will be positive which opposes the load torque, thus the speed of the motor will be reduced during reverse operation of the motor.

This mode of operation is mostly used for plugging in order to stop the motor rapidly. During plugging, the armature terminals are suddenly reversed, which causes the back emf to force an armature current to flow in reverse direction.

Now the effective voltage across the motor becomes 2V (as V+ Eb). A braking resistor in series with the motor has to be connected to limit this current.

Braking by plugging gives greater torque and more rapid stop, but the current drawn from the supply and energy stored in mechanical parts must be dissipated in resistance.

Vehicles conforming to US Government standards[12] must have the modes ordered P-R-N-D-L (left to right, top to bottom, or clockwise). Previously, quadrant-selected automatic transmissions often used a P-N-D-L-R layout, or similar. Such a pattern led to a number of deaths and injuries owing to driver error causing unintentional gear selection, as well as the danger of having a selector (when worn) jump into Reverse from Low gear during engine braking maneuvers.

FOUR FORCES AFFECT THINGS THAT FLY (like airplanes)

Weight is the force of gravity. It acts in a downward direction—toward the center of the Earth.

Lift is the force that acts at a right angle to the direction of motion through the air. Lift is created by differences in air pressure.

Thrust is the force that propels a flying machine in the direction of motion. Engines produce thrust.

Drag is the force that acts opposite

Merk Diezle

A quadrant is an instrument that is used to measure angles up to 90°. It was originally proposed by Ptolemy as a better kind of astrolabe.[1] Several different variations of the instrument were later produced by medieval Muslim astronomers.

There are several types of quadrants:

Mural quadrants used for measuring the altitudes of astronomical objects.

Large frame-based instruments used for measuring angular distances between astronomical objects.

Geometric quadrant used by surveyors and navigators.

Davis quadrant a compact, framed instrument used by navigators for measuring the altitude of an astronomical object.

"Galactic quadrants" within Star Trek are based around a meridian that runs from the center of the Galaxy through Earth's solar system,[7] which is not unlike the system used by astronomers. However, rather than have the perpendicular axis run through the Sun, as is done in astronomy, the Star Trek version runs the axis through the galactic center. In that sense, the Star Trek quadrant system is less-geocentric as a cartographical system than the standard. Also, rather than use ordinals, Star Trek designates them by the Greek letters Alpha, Beta, Gamma, and Delta.

A galactic quadrant, or quadrant of the Galaxy, refers to one of four circular sectors in the division of the Milky Way Galaxy.

Quadrants are described using ordinals—for example, "1st galactic quadrant"[1] "second galactic quadrant,"[2] or "third quadrant of the Galaxy."[3] Viewing from the north galactic pole with 0 degrees (°) as the ray that runs starting from the Sun and through the galactic center, the quadrants are as follow:

1st galactic quadrant – 0° ≤ longitude (ℓ) ≤ 90°[4]

Due to the orientation of the Earth with respect to the rest of the Galaxy, the 2nd galactic quadrant is primarily only visible from the northern hemisphere while the 4th galactic quadrant is mostly only visible from the southern hemisphere. Thus, it is usually more practical for amateur stargazers to use the celestial quadrants. Nonetheless, cooperating or international astronomical organizations are not so bound by the Earth's horizon.

Based on a view from Earth, one may look towards major constellations for a rough sense of where the borders of the quadrants are:[5] (Note: by drawing a line through the following, one can also approximate the galactic equator.)

For 0°, look towards the Sagittarius constellation. (The galactic center)

For 90°, look towards the Cygnus constellation.

For 180°, look towards the Auriga constellation. (The galactic anticenter)

For 270°, look towards the Vela constellation.

2nd galactic quadrant – 90° ≤ ℓ ≤ 180°[2]

3rd galactic quadrant – 180° ≤ ℓ ≤ 270°[3]

4th galactic quadrant – 270° ≤ ℓ ≤ 360° (0°)[1]

A long tradition of dividing the visible skies into four precedes the modern definitions of four galactic quadrants. Ancient Mesopotamian formulae spoke of "the four corners of the universe" and of "the heaven's four corners",[6] and the Biblical Book of Jeremiah echoes this phraseology: "And upon Elam will I bring the four winds from the four quarters of heaven" (Jeremiah, 49:36). Astrology too uses quadrant systems to divide up its stars of interest. And the astronomy of the location of constellations sees each of the Northern and Southern celestial hemispheres divided into four quadrants.

QUATERNION- IS FOUR

Hoagland has also proposed a form of physics he calls "hyperdimensional physics",[24][25] which he claims represents a more complete implementation of James Clerk Maxwell's original 20 quaternion equations,[26] instead of the original Maxwell's equations as amended by Oliver Heaviside commonly taught today.[27] These ideas are rejected by the mainstream physics community as unfounded.[28][29][30][31][32]

QUATERNION IS FOUR

James Clerk MAXWELL

20 Quaternion Equations

James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field" ( Royal Society Transactions, Vol. CLV, 1865, p 459 ); Orally read Dec. 8, 1864. [ MS-Word.doc ]

Andre Waser : On the Notation of Maxwell's Field Equations [ PDF ]

The 1873 edition of A Treatise on Electricity & Magnetism contains the 20 Quaternion Equations that later were rewritten --- censored --- by Oliver Heaviside, et al.. These equations reconcile relativity with modern quantum physics and help to explain "free energy" and anti-gravity.

Volume 1: 1 ~ 2 ~ 3 ~ 4 ~ 5 ~ 6 ~ 7 ~ 8 ~9 ~ 10 ~ 11 ~ 12 ~ 13

Volume 2: 1 ~ 2 ~ 3 ~ 4 ~ 5 ~ 6 ~ 7 ~ 8 ~ 9 ~ 10 ~ 11 ~ 12 ~ 13 ~ 14 ~ 15 ~ 16 ~ 17 ~ 18 ~ 19

Links to the complete copies in the Posner Collection at Carnegie Mellon University:

The complete copies also are included on Rex Research website CD.

Maxwell's Quaternion Equations

QUATERNION IS FOUR

Physical Space as a Quaternion Structure, I: Maxwell Equations. A Brief Note

Peter Michael Jack

(Submitted on 18 Jul 2003)

This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component is then revealed, which reduces part of the degree of freedom found in the gauge, but which can then be used to explain thermoelectricity, suggesting that the theory of heat has just as fundamental a connection to electromagnetism as the magnetic field has to the electric field, for the new theory now links thermal, electric, and magnetic phenomena altogether in one set of elementary equations. This result is based on an initial hypothesis, named The Quaternion Axiom,'' that postulates physical space is a quaternion structure.

THE FOURTH IS DIFFERENT- THE FOURTH i

People in the late 1800s figured out how to write the Maxwell equations using complex-valued quaternions, also known as biquaternions. Complex-valued quaternions are not a division algebra. To me, that is an enormous loss. The most important numbers in all of physics are division algebras: the real and complex numbers. It seams obvious to me to use a 4D division algebra for 4D problems in spacetime. I looked into a good number of papers where someone claimed to have written the Maxwell equations using quaternions, but that was someone else's summary. The author invariably needed the fourth i (quaternions already have i, j, and k). The magic fourth i commutes with all, unlike the other 3. Biquaternions to this day strike me as bogus.

QUATERNION IS FOUR

the 200 missing quaternion equations from maxwell's treatis on electromagnetism, edition 106 nov 2009

erstellt von doug

Hello:

A significant driver of traffic to my web site quaternions.com comes from a persistent story about the 200 quaternion equations that appeared in Maxwell's "Treatise on Electromagnetism", the first edition. By the third edition, there were no quaternion equations. In this post, I will report what I found.

After enough emails about the missing 200 equations, I thought I would look on the web for them (this was the late 1990's). Someone had scanned and put them up on the web. As I remembered it, the quaternion expressions where all "pure quaternions", or what I would call the 3-vector part of a quaternion. At the time, I thought that was an empty way to use quaternions. The main point of special relativity is that what is a pure quaternion in one inertial reference frame is not a pure quaternion in a different inertial reference frame. EM is inherently a relativistic theory, so one had best not start with non-relativistic terms. We cannot fault Maxwell on this point since relativity was build by Einstein's analysis of EM 40 years later.

Here it is a decade later. I get similar questions. And I was able to find the original source again. I can see that pure quaternions are used exclusively. What this indicates to me is that it is impossible to learn anything different by writing things in pure quaternions from the far more common vector notation. A fellow named Col. Tom Bearden claims that the deletion of this section - all of 3 pages - is one grand scientific conspiracy. It looks like Bearden thinks 20 equations were "lost", while the number I here cited more is 200. No matter, any information written in a pure quaternion form can 100% faithfully be represented using vectors.

Clicking around, I was able to confirm that Maxwell did keep his scalars separate from his 3-vectors. If you are into this old stuff - and I am not - read André Waser's paper, On the Notation of Maxwell’s Field Equations.

People in the late 1800s figured out how to write the Maxwell equations using complex-valued quaternions, also known as biquaternions. Complex-valued quaternions are not a division algebra. To me, that is an enormous loss. The most important numbers in all of physics are division algebras: the real and complex numbers. It seams obvious to me to use a 4D division algebra for 4D problems in spacetime. I looked into a good number of papers where someone claimed to have written the Maxwell equations using quaternions, but that was someone else's summary. The author invariably needed the fourth i (quaternions already have i, j, and k). The magic fourth i commutes with all, unlike the other 3. Biquaternions to this day strike me as bogus.

In the late 1990s, I felt compelled to represent the Maxwell equations using only real valued quaternions. I have an inch and a half stack of papers of failed efforts: there was always a sign wrong somewhere. I eventually found the combination of even ((a+b)/2) and odd ((a-b)/2) operators to do the trick:

The homogeneous equations are a combination of even and odd operators, while the source sequations need to double up on the odds and double up on the evens. Nice.

Maxwell had nothing like this in his amazing Treatise (and it is amazing, since Jackson's modern work looks like a variation on Maxwell). For a few years, I thought I was the first person to have done this, yet a fellow amateur named Peter Jack was the first, beating me by 1 year. I was preparing to go to the second and last meeting on quaternions in physics in Rome in 1999. The slide with this equation looked too complicated. I was wondering why I had to throw so many things away. What was the stuff I was throwing away? I guessed it might be gravity! That was an inspired leap, caused by the complexity of the expression for the Maxwell equations shown above.

Here is a summary of the next decade of work. Professional physicists are trained on tensors, not quaternions. I observed that writing equations using quaternions meant professionals didn't listen. Therefore I learned how to write everything I had done with quaternions using tensors. The last few years I was struggling with the current coupling equation. That drove me back to quaternions and on to hypercomplex numbers.

One important realization in my training is that one needs to work with an action, all the ways energy can be exchanged within a unit of volume. From the action, one can derive the field equations using the Euler-Lagrange equations. One can also calculate the stress-energy tensor, and head out into quantum field theory. All amateurs I have looked at work with field equations. That is not good enough, one needs to work with actions and derive the field equations from the action.

A message from the standard model of physics is that EM is not enough: one needs both the weak and the strong force. Folks who worry about the great scientific conspiracy ignore the standard model, staying focused on EM. That is understandable: the standard model is not easy to understand or do calculations with. The group sitting in the middle of the standard model, SU(2), is known as the unit quaternions! That name alone suggests writing equations with quaternions will lead to a way to represent the unit quaternion symmetry of the standard model. My latest work does exactly that. Maxwell naturally did not deal with these issues that physicists developed almost a century later.

Maxwell was a smarter cat than I will ever be. I live in a later time, with a vast accumulation of new knowledge. On a technical level, I don't think anything was lost by writing pure quaternions as 3-vectors in the transition from the first edition of Maxwell's Treatise to the third. My research suggests adapting quaternions to an action with all the symmetries of the standard model may be productive.

QUATERNION IS FOUR- THIS PERSON CLAIMS THAT MAXWELL ORIGINALLY HAD 20 QUATERNION EQUATIONS THAT WERE REDUCED TO FOUR

In truth the four equations traditionally included in the teaching of physics are more aptly named the “Maxwell-Heaviside Equations” inasmuch as Oliver Heaviside reformulated Maxwell's original equations from a quaternion format into a simple vector format. Maxwell's original paper [4] consisted of 20 equations with 20 unknowns. According to Tom Bearden [5], Maxwell's 1865 paper had its quaternion equations reduced to vector notation -- after a comparatively limited debate among some 30 scientists – a notation advocated by Heaviside, Gibbs, et al – after Maxwell was already dead.

“After publication of the first edition of his Treatise, Maxwell of course also caught strong pressure from his own publisher to get rid of the quaternions (which few persons understood). Maxwell thus rewrote and simplified about 80% of his own 1873 Treatise before he died of stomach cancer in 1879. The second edition of that treatise was later published with that 80% revision done by Maxwell himself under strong pressure, and with a guest editor. But the 1865 Maxwell paper shows the real Maxwell theory, with 20 equations in 20 unknowns (they are explicitly listed in the paper). The equations taught today in universities as ‘Maxwell's equations' are actually Heaviside's equations, with a further truncation via the symmetrical regauging performed by Lorentz.” [5]

Bearden [6] goes on to point out that:

“A higher group symmetry algebra such as quaternions will contain and allow many more operations than a lower algebra such as tensors, which itself contains more than an even lower algebra such as vectors.” [6]

In effect, the reduction of Maxwell's original theory from 20 equations to 4 – purely in order to make the mathematics a bit easier for the poor physicists – severely limits the capabilities of the original theory. This shows up dramatically in the Second Law of Thermodynamics, where the original equations were effectively “regauged” in order to force the theory to obey the law of conservation of energy. In all respects a return to the quaternion format in Maxwell's original equations seems likely to yield astounding results. Quaternions cannot simply be ignored any longer.

FOURTH IS ALWAYS DIFFERENT

The great flaw in mainstream physics today is that no one seems willing to look at the effects of accelerating fields. Adding a fourth term to the electromagnetic equations in fact yields such a condition, and lo and behold, conservation laws are redefined in a wholly connected and virtually unlimited universe. It's just the kind of thing Maxwell's Demon (and/or Tom Bearden [8]) could appreciate.

QUATERNION IS FOUR- REDUCING MAXWELLS 20 QUATERNIONS TO 4 VECTOR EQUATIONS THAT APPLY TO ALL ELECTROMAGNETISM

In 1880, Heaviside researched the skin effect in telegraph transmission lines. That same year he patented, in England, the coaxial cable. In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations. The four re-formulated Maxwell's equations describe the nature of electric charges (both static and moving), magnetic fields, and the relationship between the two, namely electromagnetic fields.

Heaviside did much to develop and advocate vector methods and the vector calculus.[22] Maxwell's formulation of electromagnetism consisted of 20 equations in 20 variables. Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (B, E, J, and ρ), the form by which they have been known ever since (see Maxwell's equations). Less well known is that Heaviside's equations and Maxwell's are not exactly the same, and in fact it is easier to modify the latter to make them compatible with quantum physics.[23] The possibility of gravitational waves was also discussed by Heaviside using the analogy between the inverse-square law in gravitation and electricity [24]

FOUR POINTS CROSS RATIO

In geometry, the cross-ratio, also called double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points A, B, C and D on a line, their cross ratio is defined as

(

A

,

B

;

C

,

D

)

=

A

C

B

D

B

C

A

D

where an orientation of the line determines the sign of each distance and the distance is measured as projected into Euclidean space. (If one of the four points is the line's point at infinity, then the two distances involving that point are dropped from the formula.)

The point D is the projective harmonic conjugate of C with respect to A and B precisely if the cross-ratio of the quadruple is −1, called the harmonic ratio. The cross-ratio can therefore be regarded as measuring the quadruple's deviation from this ratio; hence the name anharmonic ratio.

The cross-ratio is preserved by the fractional linear transformations and it is essentially the only projective invariant of a quadruple of collinear points, which underlies its importance for projective geometry. In the Cayley–Klein model of hyperbolic geometry, the distance between points is expressed in terms of a certain cross-ratio.

Cross-ratio had been defined in deep antiquity, possibly already by Euclid, and was considered by Pappus, who noted its key invariance property. It was extensively studied in the 19th century.[1] Variants of this concept exist for a quadruple of concurrent lines on the projective plane and a quadruple of points on the Riemann sphere.

Contents [hide]

1 Definition

2 Terminology and history

3 Properties

4 Projective geometry

5 Definition in homogeneous coordinates

6 Role in non-Euclidean geometry

7 Six cross-ratios and the anharmonic group

7.1 Role of Klein four-group

7.2 Exceptional orbits

8 Transformational approach

8.1 Co-ordinate Description

9 Quaternionic Cross Ratio

10 Differential-geometric point of view

11 Higher-dimensional generalizations

13 Notes and references

Definition

The cross-ratio of a 4-tuple of distinct points on the real line with coordinates z1, z2, z3, z4 is given by

(

z

1

,

z

2

;

z

3

,

z

4

)

=

(

z

1

z

3

)

(

z

2

z

4

)

(

z

2

z

3

)

(

z

1

z

4

)

.

(z_{1},z_{2};z_{3},z_{4})={\frac {(z_{1}-z_{3})(z_{2}-z_{4})}{(z_{2}-z_{3})(z_{1}-z_{4})}}.

It can also be written as a "double ratio" of two division ratios of triples of points:

(

z

1

,

z

2

;

z

3

,

z

4

)

=

z

1

z

3

z

2

z

3

:

z

1

z

4

z

2

z

4

.

(z_{1},z_{2};z_{3},z_{4})={\frac {z_{1}-z_{3}}{z_{2}-z_{3}}}:{\frac {z_{1}-z_{4}}{z_{2}-z_{4}}}.

The same formulas can be applied to four different complex numbers or, more generally, to elements of any field and can also be extended to the case when one of them is the symbol ∞, by removing the corresponding two differences from the formula. The formula shows that cross-ratio is a function of four points, generally four numbers

z

1

,

z

2

,

z

3

,

z

4

z_{1},\ z_{2},\ z_{3},\ z_{4} taken from a field.

In geometry, if A, B, C and D are collinear points, then the cross ratio is defined similarly as

(

A

,

B

;

C

,

D

)

=

A

C

B

D

B

C

A

D

,

where each of the distances is signed according to a consistent orientation of the line.

Terminology and history

Pappus of Alexandria made implicit use of concepts equivalent to the cross-ratio in his Collection: Book VII. Early users of Pappus included Isaac Newton, Michel Chasles, and Robert Simson. In 1986 Alexander Jones made a translation of the original by Pappus, then wrote a commentary on how the lemmas of Pappus relate to modern terminology.

Modern use of the cross ratio in projective geometry began with Lazare Carnot in 1803 with his book Géométrie de Position. The term used was le rapport anharmonique (Fr: anharmonic ratio). German geometers call it das Doppelverhältnis (Ger: double ratio). However, in 1847 Karl von Staudt introduced the term Throw (Wurf) to avoid the metrical implication of a ratio. His construction of the Algebra of Throws provides an approach to numerical propositions, usually taken as axioms, but proven in projective geometry.[2]

The English term "cross-ratio" was introduced in 1878 by William Kingdon Clifford.[3]

Properties

The cross ratio of the four collinear points A, B, C, D can be written as

(

A

,

B

;

C

,

D

)

=

A

C

C

B

:

A

D

D

B

where

A

C

C

B

{\frac {AC}{CB}} describes the ratio with which the point C divides the line segment AB, and

A

D

D

B

{\frac {AD}{DB}} describes the ratio with which the point D divides that same line segment. The cross ratio then appears as a ratio of ratios, describing how the two points C, D are situated with respect to the line segment AB. As long as the points A, B, C and D are distinct, the cross ratio (A, B; C, D) will be a non-zero real number. We can easily deduce that

(A, B; C, D) < 0 if and only if one of the points C, D lies between the points A, B and the other does not

(A, B; C, D) = 1 / (A, B; D, C)

(A, B; C, D) = (C, D; A, B)

Projective geometry

D is the harmonic conjugate of C with respect to A and B, so that the cross-ratio (A, B; C, D) equals −1.

Cross-ratio is a projective invariant in the sense that it is preserved by the projective transformations of a projective line. In particular, if four points lie on a straight line L in R2 then their cross-ratio is a well-defined quantity, because any choice of the origin and even of the scale on the line will yield the same value of the cross-ratio. Furthermore, let {Li, 1 ≤ i ≤ 4}, be four distinct lines in the plane passing through the same point Q. Then any line L not passing through Q intersects these lines in four distinct points Pi (if L is parallel to Li then the corresponding intersection point is "at infinity"). It turns out that the cross-ratio of these points (taken in a fixed order) does not depend on the choice of a line L, and hence it is an invariant of the 4-tuple of lines {Li}. This can be understood as follows: if L and L′ are two lines not passing through Q then the perspective transformation from L to L′ with the center Q is a projective transformation that takes the quadruple {Pi} of points on L into the quadruple {Pi′} of points on L′. Therefore, the invariance of the cross-ratio under projective automorphisms of the line implies (in fact, is equivalent to) the independence of the cross-ratio of the four collinear points {Pi} on the lines {Li} from the choice of the line that contains them.

Definition in homogeneous coordinates

If four collinear points are represented in homogeneous coordinates by vectors a, b, c, d such that c = a + b and d = ka + b, then their cross-ratio is k.[4]

Role in non-Euclidean geometry

Arthur Cayley and Felix Klein found an application of the cross-ratio to non-Euclidean geometry. Given a nonsingular conic C in the real projective plane, its stabilizer GC in the projective group G = PGL(3, R) acts transitively on the points in the interior of C. However, there is an invariant for the action of GC on pairs of points. In fact, every such invariant is expressible as a function of the appropriate cross ratio.[citation needed]

Explicitly, let the conic be the unit circle. For any two points in the unit disk, p, q, the line connecting them intersects the circle in two points, a and b. The points are, in order, a, p, q, b. Then the distance between p and q in the Cayley–Klein model of the plane hyperbolic geometry can be expressed as

d

(

p

,

q

)

=

1

2

log

|

q

a

|

|

b

p

|

|

p

a

|

|

b

q

|

d(p,q)={\frac {1}{2}}\log {\frac {|q-a||b-p|}{|p-a||b-q|}}

(the factor one half is needed to make the curvature −1). Since the cross-ratio is invariant under projective transformations, it follows that the hyperbolic distance is invariant under the projective transformations that preserve the conic C. Conversely, the group G acts transitively on the set of pairs of points (p, q) in the unit disk at a fixed hyperbolic distance.

Six cross-ratios and the anharmonic group

The cross-ratio may be defined by any of these four expressions:

(

A

,

B

;

C

,

D

)

=

(

B

,

A

;

D

,

C

)

=

(

C

,

D

;

A

,

B

)

=

(

D

,

C

;

B

,

A

)

.

{\displaystyle (A,B;C,D)=(B,A;D,C)=(C,D;A,B)=(D,C;B,A).\,}

These differ by the following permutations of the variables:

(A,B)(C,D) (A,C)(B,D) (A,D)(B,C){\displaystyle {\begin{aligned}(A,B)(C,D)\\[6pt](A,C)(B,D)\\[6pt](A,D)(B,C)\end{aligned}}}

These three and the identity permutation leave the cross ratio unaltered. They make up a realization of the Klein four-group, a group of order 4 in which the order of every non-identity element is 2.

Other permutations of the four variables alter the cross-ratio so that it may take any of the following six values.

(A,B;C,D) =λ (A,B;D,C) =

1

λ (A,C;D,B) =

1

1

λ (A,C;B,D) =1−λ (A,D;C,B) =

λ

λ

1

(A,D;B,C) =

λ

1

λ{\displaystyle {\begin{aligned}(A,B;C,D)&=\lambda &(A,B;D,C)&={\frac {1}{\lambda }}\\[6pt](A,C;D,B)&={\frac {1}{1-\lambda }}&(A,C;B,D)&=1-\lambda \\[6pt](A,D;C,B)&={\frac {\lambda }{\lambda -1}}&(A,D;B,C)&={\frac {\lambda -1}{\lambda }}\end{aligned}}}

As functions of λ, these form a non-abelian group of order 6 with the operation of composition of functions. This is the anharmonic group. It is a subgroup of the group of all Möbius transformations. The six cross-ratios listed above represent torsion elements (geometrically, elliptic transforms) of PGL(2, Z). Namely,

1

λ\frac{1}{\lambda},

1

λ

1-\lambda \,, and

λ

λ

1

\frac{\lambda}{\lambda-1} are of order 2 in PGL(2, Z), with fixed points, respectively, −1, 1/2, and 2 (namely, the orbit of the harmonic cross-ratio). Meanwhile, elements

1

1

λ\frac{1}{1-\lambda} and

λ

1

λ\frac{\lambda-1}{\lambda} are of order 3 in PGL(2, Z) – in PSL(2, Z) (this corresponds to the subgroup A3 of even elements). Each of them fixes both values

e

±

i

π

/

3

e^{\pm i\pi/3} of the "most symmetric" cross-ratio.

The anharmonic group is generated by λ ↦ 1/λ and λ ↦ 1 − λ. Its action on {0, 1, ∞} gives an isomorphism with S3. It may also be realised as the six Möbius transformations mentioned,[5] which yields a projective representation of S3 over any field (since it is defined with integer entries), and is always faithful/injective (since no two terms differ only by 1/−1). Over the field with two elements, the projective line only has three points, so this representation is an isomorphism, and is the exceptional isomorphism

S

3

P

G

L

(

2

,

2

)

{\mathrm {S}}_{3}\approx {\mathrm {PGL}}(2,2). In characteristic 3, this stabilizes the point

1

=

[

1

:

1

]

-1=[-1:1], which corresponds to the orbit of the harmonic cross-ratio being only a single point, since

2

=

1

/

2

=

1

2=1/2=-1. Over the field with 3 elements, the projective line has only 4 points and

S

4

P

G

L

(

2

,

3

)

{\mathrm {S}}_{4}\approx {\mathrm {PGL}}(2,3), and thus the representation is exactly the stabilizer of the harmonic cross-ratio, yielding an embedding

S

3

S

4

{\mathrm {S}}_{3}\hookrightarrow {\mathrm {S}}_{4} equals the stabilizer of the point

1

-1.

Role of Klein four-group

In the language of group theory, the symmetric group S4 acts on the cross-ratio by permuting coordinates. The kernel of this action is isomorphic to the Klein four-group K. This group consists of 2-cycle permutations of type

(

A

B

)

(

C

D

)

{\displaystyle (AB)(CD)} (in addition to the identity), which preserve the cross-ratio. The effective symmetry group is then the quotient group

S

4

/

K

{\mathrm {S}}_{4}/{\mathrm {K}}, which is isomorphic to S3.

Exceptional orbits

For certain values of λ there will be greater symmetry and therefore fewer than six possible values for the cross-ratio. These values of λ correspond to fixed points of the action of S3 on the Riemann sphere (given by the above six functions); or, equivalently, those points with a non-trivial stabilizer in this permutation group.

The first set of fixed points is {0, 1, ∞}. However, the cross-ratio can never take on these values if the points A, B, C and D are all distinct. These values are limit values as one pair of coordinates approach each other:

(

Z

,

B

;

Z

,

D

)

=

(

A

,

Z

;

C

,

Z

)

=

0

{\displaystyle (Z,B;Z,D)=(A,Z;C,Z)=0}

(

Z

,

Z

;

C

,

D

)

=

(

A

,

B

;

Z

,

Z

)

=

1

{\displaystyle (Z,Z;C,D)=(A,B;Z,Z)=1}

(

Z

,

B

;

C

,

Z

)

=

(

A

,

Z

;

Z

,

D

)

=

.

{\displaystyle (Z,B;C,Z)=(A,Z;Z,D)=\infty .}

The second set of fixed points is {−1, 1/2, 2}. This situation is what is classically called the harmonic cross-ratio, and arises in projective harmonic conjugates. In the real case, there are no other exceptional orbits.

In the complex case, the most symmetric cross-ratio occurs when

λ

=

e

±

i

π

/

3

\lambda = e^{\pm i\pi/3}. These are then the only two values of the cross-ratio, and these are acted on according to the sign of the permutation.

Transformational approach

Main article: Möbius transformation

The cross-ratio is invariant under the projective transformations of the line. In the case of a complex projective line, or the Riemann sphere, these transformation are known as Möbius transformations. A general Möbius transformation has the form

f

(

z

)

=

a

z

+

b

c

z

+

d

,

where

a

,

b

,

c

,

d

C

and

a

d

b

c

0.

These transformations form a group acting on the Riemann sphere, the Möbius group.

The projective invariance of the cross-ratio means that

(

f

(

z

1

)

,

f

(

z

2

)

;

f

(

z

3

)

,

f

(

z

4

)

)

=

(

z

1

,

z

2

;

z

3

,

z

4

)

.

(f(z_{1}),f(z_{2});f(z_{3}),f(z_{4}))=(z_{1},z_{2};z_{3},z_{4}).\

The cross-ratio is real if and only if the four points are either collinear or concyclic, reflecting the fact that every Möbius transformation maps generalized circles to generalized circles.

The action of the Möbius group is simply transitive on the set of triples of distinct points of the Riemann sphere: given any ordered triple of distinct points, (z2, z3, z4), there is a unique Möbius transformation f(z) that maps it to the triple (1, 0, ∞). This transformation can be conveniently described using the cross-ratio: since (z, z2, z3, z4) must equal (f(z), 1; 0, ∞), which in turn equals f(z), we obtain

f

(

z

)

=

(

z

,

z

2

;

z

3

,

z

4

)

.

{\displaystyle f(z)=(z,z_{2};z_{3},z_{4}).}

An alternative explanation for the invariance of the cross-ratio is based on the fact that the group of projective transformations of a line is generated by the translations, the homotheties, and the multiplicative inversion. The differences zj − zk are invariant under the translations

z

z

+

a

z\mapsto z+a

where a is a constant in the ground field F. Furthermore, the division ratios are invariant under a homothety

z

b

z

z\mapsto bz

for a non-zero constant b in F. Therefore, the cross-ratio is invariant under the affine transformations.

In order to obtain a well-defined inversion mapping

T

:

z

z

1

,

T:z\mapsto z^{{-1}},

the affine line needs to be augmented by the point at infinity, denoted ∞, forming the projective line P1(F). Each affine mapping f : F → F can be uniquely extended to a mapping of P1(F) into itself that fixes the point at infinity. The map T swaps 0 and ∞. The projective group is generated by T and the affine mappings extended to P1(F). In the case F = C, the complex plane, this results in the Möbius group. Since the cross-ratio is also invariant under T, it is invariant under any projective mapping of P1(F) into itself.

Co-ordinate Description

If we write the complex points as vectors

x

n

=

[

(

z

n

)

,

(

z

n

)

]

T

{\displaystyle {\overrightarrow {x}}_{n}=[\Re (z_{n}),\Im (z_{n})]^{T}} and define

x

n

m

=

x

n

x

m

{\displaystyle x_{nm}=x_{n}-x_{m}}. Let

(

a

,

b

)

(a,b) be the dot product of

a

a with

b

b then the real part of the cross ratio is given by:

C

1

=

(

x

12

,

x

14

)

(

x

23

,

x

34

)

(

x

12

,

x

34

)

(

x

14

,

x

23

)

+

(

x

12

,

x

23

)

(

x

14

,

x

34

)

|

x

23

|

2

|

x

14

|

2

{\displaystyle C_{1}={\frac {(x_{12},x_{14})(x_{23},x_{34})-(x_{12},x_{34})(x_{14},x_{23})+(x_{12},x_{23})(x_{14},x_{34})}{|x_{23}|^{2}|x_{14}|^{2}}}}

This is an invariant of the 2D special conformal transformation such as inversion

x

μ

x

μ

|

x

|

2

{\displaystyle x^{\mu }\rightarrow {\frac {x^{\mu }}{|x|^{2}}}}.

The imaginary part must make use of the 2-dimensional cross product

a

×

b

=

[

a

,

b

]

=

a

2

b

1

a

1

b

2

{\displaystyle a\times b=[a,b]=a_{2}b_{1}-a_{1}b_{2}}

C

2

=

(

x

12

,

x

14

)

[

x

34

,

x

23

]

(

x

43

,

x

23

)

[

x

12

,

x

34

]

|

x

23

|

2

|

x

14

|

2

{\displaystyle C_{2}={\frac {(x_{12},x_{14})[x_{34},x_{23}]-(x_{43},x_{23})[x_{12},x_{34}]}{|x_{23}|^{2}|x_{14}|^{2}}}}

Quaternionic Cross Ratio

There is also a quaternionic version of the cross ratio which shares many similar properties.

Differential-geometric point of view

The theory takes on a differential calculus aspect as the four points are brought into proximity. This leads to the theory of the Schwarzian derivative, and more generally of projective connections.

Higher-dimensional generalizations

Further information: General position

The cross-ratio does not generalize in a simple manner to higher dimensions, due to other geometric properties of configurations of points, notably collinearity – configuration spaces are more complicated, and distinct k-tuples of points are not in general position.

While the projective linear group of the plane is 3-transitive (any three distinct points can be mapped to any other three points), and indeed simply 3-transitive (there is a unique projective map taking any triple to another triple), with the cross ratio thus being the unique projective invariant of a set of four points, there are basic geometric invariants in higher dimension. The projective linear group of n-space

P

n

=

P

(

K

n

+

1

)

{\mathbf {P}}^{n}={\mathbf {P}}(K^{{n+1}}) has (n + 1)2 − 1 dimensions (because it is

P

G

L

(

n

,

K

)

=

P

(

G

L

(

n

+

1

,

K

)

)

,

{\mathrm {PGL}}(n,K)={\mathbf {P}}({\mathrm {GL}}(n+1,K)), projectivization removing one dimension), but in other dimensions the projective linear group is only 2-transitive – because three collinear points must be mapped to three collinear points (which is not a restriction in the projective line) – and thus there is not a "generalized cross ratio" providing the unique invariant of n2 points.

Collinearity is not the only geometric property of configurations of points that must be maintained – for example, five points determine a conic, but six general points do not lie on a conic, so whether any 6-tuple of points lies on a conic is also a projective invariant. One can study orbits of points in general position – in the line "general position" is equivalent to being distinct, while in higher dimensions it requires geometric considerations, as discussed – but, as the above indicates, this is more complicated and less informative.

However, a generalization to Riemann surfaces of positive genus exists, using the Abel-Jacobi map and theta functions.

Representation of the central tenet of the Orion Correlation Theory: the outline of the Giza pyramids superimposed over a photograph of the stars in Orion's Belt. The validity of this match has been called into question by Hancock's critics.

STARGATE GEOMETRY AND TETRAHEDRON

In terms of Richard Hoagland's 'hyperdimensional physics' derived from the geometric 'message' of Cydonia (Mars), the conduit or 'stargate' between this world and the Otherworld (i.e. hyperspace) is prominently represented by the angle 19.5°. According to the theory, it is the tetrahedral geometry signified by this angle that enables inter-dimensional energy transfer between the two realms.

This 'stargate' geometry is expressed by a circumscribed tetrahedron (made up of four equilateral triangles). Interestingly enough, the hieroglyphic sign denoting Sirius was a triangle in ancient Egypt.

The connection is made evident by archaeo-astronomy. First, it is widely accepted these days that the 'air shafts' inside the Great Pyramid were designed to aligned with certain stars. One was specifically targeted toward Sirius in c. 2350 BC.

And at that pinpointed time (c. 2350 BC), Sirius and Orion's Alnitak (representing the Great Pyramid as per the Orion Correlation Theory) together produced the angle 19.5° (when Sirius was rising on the Giza horizon).[10]

Next, it is natural - given the Sirius-Great Bend connection - to wonder about the possibility of the Nile's 'Winding Waterway' having some relevance to tetrahedral geometry. Indeed, we do find a clear connection!

Believe it or not, the northern peak of the Great Bend precisely pinpoints the tetrahedral/stargate latitude, 19.5°N.!

What's even more incredible is the fact that the same Bend peak also pinpoints 33°E longitude. As those familiar with Hoagland's work would surely know, '33' and '19.5' are considered the two key numbers in the 'hyperdimensional code'! (Hoagland is just not yet aware of this Nile connection.)

In 1997, the esoteric importance of those numbers was overtly demonstrated as NASA landed a tetrahedron-shaped Mars Pathfinder lander on the Red Planet at 19.5 N and 33 W.! (That's pretty in your face, isn't it?)

Not only that, at the moment of touchdown, Earth was positioned 19.5 degrees above the eastern Martian horizon as seen from Pathfinder's landing site.[11]

As Mike Bara, Hoagland's right-hand man at the Enterprise Mission, wrote:

Pathfinder's unique tetrahedral spacecraft design geometry, coupled with the totally "recursive" tetrahedral geometry of the landing site itself, was obviously intended by NASA "ritualists" behind the scenes to celebrate – on their first return to Mars in over twenty years – the two key Hyperdimensional numbers underlying all the NASA rituals – "19.5" and "33."

Indeed, NASA obsessively incorporates those two numbers again and again into its space missions.[12]

The implication is clear: the Great Bend, along with the entire Nile system, is a key part of the 'stargate game' - or 'Stargate Conspiracy' - and the Nile is likely an 'intelligently designed' river with a profound message concerning the Red Planet as well as reality itself.

In The Time Rivers, I further discuss how the above interpretation seems to interact harmoniously with certain ancient Egyptian art themes having to do with the Otherworld (or the 'Duat').

The drawing shown right, for instance, depicts a pyramidal 'mound' of the 'House of Sokar' (the 'Fifth Division of the Duat') - a form of Giza-Rostau - with a female head at the apex. While the first impression is that it is a stylized Giza pyramid, the general shape also evokes the Great Bend especially given the mutual 'stargate' connection.

This interpretation is strongly supported by the fact that the female head at the apex belongs to Isis (according to the accompanying text) - the goddess signified by Sirius.[13] As we have seen, the Great Bend's apex (19.5°) is similarly associated with Sirius.

The Sirian nature of the pyramid apex reinforces the 'stargate-ness' of the Giza/30°N latitude because Giza sits at the southern apex of the triangular, or 'pyramidal', Nile Delta.

Indeed, as Jim Alison has recently pointed out, the angles of the Great Pyramid almost perfectly match those made by the Delta using Giza, Alexandria, and Port Said. (click on image left.) This 'Delta pyramid' is even exactly 1000 times the size of the Great Pyramid!

Pyramid apexes were also associated with the resurrection of Osiris. As the embodiment of the phoenix, the pyramid capstone (the Benben stone) signified the god's death-rebirth cycle. And the annual Nile flood that Sirius heralded was viewed in ancient Egypt as the revitalization of Osiris.

This is very fitting, after all resurrection occurs through an inter-dimensional gateway - a stargate - separating this world and the Otherworld of the dead.

As for the strange bell-like object placed just above Isis' head in the drawing, it is usually thought to represent the Benben Stone (or the omphalos, the navel stone), which is a form of the shem ('fire-stone') associated with the Tower of Babel etc. as discussed earlier. We recall that the Tower - analogous to the Jacob's stone pillar - is a form of stargate.

Let's take another look at the Genesis passage describing the pillar-stargate of Jacob:

...How dreadful is this place! This is none other but the house of God, and this is the gate of heaven. And Jacob rose up early in the morning, and took the stone that he had put for his pillows, and set it up for a pillar, and... this stone, which I have set for a pillar, shall be God's house... [emphasis added]

Notice how the pillar-stargate is being described as the 'house of God'. This directly relates to the pyramidal 'House of Sokar' (i.e. the drawing above-right), because Sokar is an alter ego of Osiris - the most revered god of ancient Egypt.

The 'House of Sokar', in other words, is a 'House of God' and vice versa.

TETRAHEDRAL MOTIF

We have also begun to look into the Moon, and discovered the remnants of an equally vast and advanced civilization there, marked by this same tetrahedral motif.

This civilization left behind a calling card: a series of "tetrahedral" pyramids with "magical" properties -- like anti-gravity --discovered in the Asteroid Belt and on the Moon.

But it was Clarke who defined the mechanism by which the "Hyperdimensional" transition would be made, through the central symbol of the film, The Monolith. As we have shown previously, Clarke's original idea for the Monolith is that it would be a massive black tetrahedron. However, he eventually decided that such a form would be "too obvious" and instead settled on the rectangular shape. Yet, he was still careful to encode the basic concepts of the tetrahedron in the proportions of the Monolith -- 1 x 4 x 9, the squares of 1,2,3, the ratios of inscribed/circumscribed tetrahedra to their respective spheres (planets).

TETRAHEDRON

Found by a miner in the Asteroid Belt, this tetrahedral pyramid is inscribed with Egyptian style hieroglyphs and floats 2 inches above any surface upon which it is placed. Earth's best scientists are at a loss to explain how the pyramid is defying gravity. Captain Strong, (seated, with pipe) explains that Earth's scientists think that the asteroids are remnants of an exploded planet between Mars and Jupiter, and that this tetrahedral artifact is a piece of technology from an advanced civilization which flourished there millions of years ago. The Space Cadet team is assigned to investigate, and they decide to start on the Moon, where many years before a similar tetrahedral pyramid was found on the "dark side." So, off to the Moon they go in their rocket ship, the "Polaris."

Now, to those of you who have been paying attention, the name "Polaris" will ring a bell. Since Hyperdimensional Physics and tetrahedrons are intimately connected with rotation and the riddle of precession, the choice of naming the spaceship in the series after the Polar star would seem, well, interesting.

As it does so, the now reassembled tetrahedral pyramid turns transparent and reveals a globe of the planet Mars contained inside. There is a red mark on the globe, indicating a signpost of some type. This marker, curiously, is tangential to a key "tetrahedral lattitude" -- 19.5 degrees. Deciding they are supposed to follow the lead, the crew heads back to the ship to head to Mars to investigate.

Meanwhile, a rival group to the Solar Guard has discovered that the crew of the "Polaris" are looking for an ancient artifact that can give them (and Earth) advanced anti-gravity technology. So, spies are dispatched to assure that Interplanetary Crime gets "the Secret" first.

Upon arriving at the Martian colony of Marsport, Tom meets with Dr. Joan Dale, and explains that the globe they found indicates there are ruins on Mars at the junctions of canals 7 and 19 (two "tetrahedral numbers," by the way). Dr. Dale shows him a partial map that was discovered years before. She tells him it is of an archeological site near the canal junctions where there was once a pyramid over 1,000 feet high (shades of Cydonia, anyone!) -- but that is now in ruin. As they make plans to head there, an Interplanetary Crime spy decides to follow them.

Upon arriving at the site, amid Egyptian style obelisks and under a terraformed blue Martian sky, Tom and Dr. Dale discover yet another ancient artifact. This time it is a sculpted Face of a feline-like creature.

Perhaps this explains why we had yet another of those curious Egyptian/Tetrahedral alignments at Cydonia the moment that first image of the Face was captured by Viking 1. They had been planning the opportunity for decades.

DOUBLE TETRAHEDRON EVERY PLANET- TETRA IS FOUR

According to Hoagland's novel theory of physics, every planet in our solar system (and the Sun) may contain a hyper-dimensional flow of energy within itself, that takes the shape of a double tetrahedron when viewed from around the equator, or the shape of a hexagon when viewed from above the north pole. How closely do Hoagland's models match the two prism shapes shown at Secklendorf or Oliver's Castle in the summer of 2008? Almost perfectly, as evidenced by the detailed comparisons provided below:

The double tetrahedron is sometimes called a star tetrahedron or stella octangula (see Star Tetrahedron). Furthermore, the details of its geometry when inscribed within a sphere seem particularly interesting:

"If a tetrahedron is placed inside of a sphere, with one vertex located on the north or south pole, then the resulting latitude of its other three vertices will equal arcsin (1 / 3) or 19.47 degrees. Such tetrahedral geometry, when studied on a solar or planetary scale, seems to reveal an internal flow of energy at the centers of large astronomical objects, out of higher dimensions into our three-dimensional space" (see geometry or esp_marte_4 or planets).

An outward flow of energy at latitude 19.5 degrees

Now as an important corollary to Hoagland's model, every planet in our solar system (or the Sun) should show three foci of outward energy flow at latitudes of 19.5 degrees above or below the equator, or else at the north and south poles, where those two imaginary tetrahedra intercept a spherical surface.

That notable corollary seems to have been shown twice in crops last summer: first in partial form at Reinshof in Germany on June 23, 2008 (see Reinsdorf2008a, and then in complete form at All Cannings in England on June 30, 2008 (see allcannings2008a):

Reinshof of June 23 seems to be telling us that "energy is flowing outward from inside of planets or the Sun". Then All Cannings of June 30 seems to be telling us that such an outward flow of energy may lie at three particular foci on any planetary surface, separated in longitude by 120 degrees. The overall diameter of three expanded circles as shown at All Cannings was found on further analysis to match latitudes of plus or minus 20 degrees, thereby providing a reasonable match to arcsin (1 / 3) = 19.47 degrees from Hoagland's model.

No other plausible interpretations of those four new crop pictures: Secklendorf of June 23, Reinshof of June 23, All Cannings of June 30, or Oliver's Castle of August 16, come to mind at present. Are we perhaps being shown specialized topics in planetary physics, from an extra-terrestrial science textbook?

What do other Earth scientists think?

Apart from any considerations of crop pictures, what do other scientists on Earth today think of Hoagland's theories? The vast majority seem to be either not knowledgeable, or else overwhelmingly sceptical! Indeed, before studying those four new crop pictures, I had never heard of Hoagland's proposals either.

"Richard Hoagland and Thomas Bearden have proposed a new form of physics that they call hyper-dimensional. They believe that their new model represents the original form of Maxwell's equations for electromagnetism. They also argue that large amounts of energy, originating from unseen dimensions, may be emitted at latitudes 19.5° south or north of the equator, on the Sun or various planets in our solar system" (see Richard C Hoagland or Interplanetary Day After or halexandria).

"Hyper-dimensional physics is a hypothesis that energy may be stored in higher space time dimensions than the three which we seemingly inhabit. Richard Hoagland believes that such energy may be focussed on points located at the intersection between a sphere and a tetrahedron: namely at three points on any planet of latitude 19.5°, plus one point of latitude 90° (north pole). His hypothesis has not been published in any peer-reviewed journals, and remains unknown today to most mainstream physicists" ( Hyperdimensional Physics).

A central vortex at Oliver's Castle in 2008

Yet does anybody really care what modern academics think? Or whether some new theory may or may not be deemed acceptable for their stuffy, dust-bound, library journals? The last word surely belongs to those mysterious crop artists, who seem to be trying to teach us advanced extra-terrestrial physics in English fields, although few people on Earth are currently listening. Here for example is part of a field report on Oliver's Castle by Janet Ossebaard, one of the more experienced investigators:

"The centre of Oliver's Castle showed a stunning swirl where its three central tracks joined together. What struck me was the way the crop had been swirled around the centre. This was not necessary, since that crop could more simply have been pushed straight ahead, then twisted into a central bundle. Yet the outer right side of those tracks flowed left as they reached the central point, thereby creating a river-like flow of three streams, meeting and swirling into each other as for a clockwise vortex." (see

oliverscastle2008a).

What could such a stunning, unexpected detail of the fallen crop be meant to represent, other than one of Hoagland's energy vortexes? Or an outward flow of energy into our three-dimensional space from higher dimensions? So much for crop pictures and pure theorizing. Let us examine next how Hoagland's model might account for certain unexplained aspects of our solar system, on its largest bodies Jupiter, Saturn or the Sun.

A Great Red Spot on Jupiter plus two new ones

Planet Jupiter has shown a Great Red Spot in its southern hemisphere for hundreds of years, that remains almost entirely unexplained. Within the past few years, its single red spot has even been joined by two new ones:

The mean latitude of 22 degrees South for that Red Spot seems to provide a reasonable fit to Hoagland's theoretical latitude of 19.5 degrees for outward energy flow, especially if the oblateness of Jupiter (due to fast rotation) might change that latitude of intersection slightly. Its north or south equatorial belts lie likewise at latitudes of +18 or -18 degrees (see /Great_red_spot#Great_Red_Spot or 24778267).

A mysterious hexagon and aurora at the north pole of Saturn

Planet Saturn seems anomalous enough already with its rings. Yet in recent years it has been shown to possess two more amazing and almost incomprehensible features: (i) a stable "hexagon" of atmospheric features at its north pole, and (ii) a newly glowing "aurora" of outward energy flow surrounding that hexagon (see cassini or Mysterious-glowing-aurora-Saturn-confounds-scientistsl). The strange hexagonal shape at Saturn's north pole seems to match Hoagland's double tetrahedral model as seen from above:

Furthermore, the new aurora seen at Saturn's north pole matches one of the energy vertices from his predicted tetrahedron:

For a video interview with Richard Hoagland concerning these features, see "Saturn's Hexagon Explained" on saturn-hexagon-explained.

Some people have offered a more conventional explanation for such strange observations: not in terms of hyper-dimensional physics, but in terms of standard fluid dynamics. Thus water or ethylene glycol, when placed into a fast spinning bucket, may sometimes produce triangular, square, pentagonal or hexagonal shapes, depending the height of the fluid and its speed of rotation: see Physical Review Letters 96, 174502, 2006, "Polygons on a fluid rotating surface" by T.R. Jansson et al.

The major problem with any conventional explanation, when applied to the north pole of Saturn, would be the instable and transient nature of such fluid dynamic structures, in contrast to the apparent long-term stability of the Saturn hexagon as observed.

A tetrahedron of energy flow within our Sun?

So much for Jupiter and Saturn. How about our Sun? Seventeen years ago at Barbary Castle on July 17, 1991, one of the most remarkable early crop pictures appeared. It showed a "double ring" symbol for our Sun, superimposed onto a single triangle (or tetrahedron) with three small circles attached (see barbry91):

Barbary Castle appeared just six days after a total solar eclipse on July 11, 1991, consistent with its solar symbolism (see astropix.com). Furthermore, a similar double ring symbol for "Sun" appeared at Avebury Manor on July 22, 2008, to tell us about solar events in late 2012 (see aveburymanor2008b).

Could there be an outward flow of energy within our Sun, corresponding to the single tetrahedron shown at Barbary Castle in 1991, or to Hoagland's double tetrahedron? In fact, every new 11-year solar cycle begins with a burst of new sunspots or magnetic field variations at solar latitudes close to +20 or -20 degrees:

Those initial energy flows seem to match predicted latitudes of +19.5 or -19.5 degrees from the double tetrahedral model. In the later years of any cycle, they move closer to the equator (see Educational or science.nasa.gov).

Returning now briefly to the crop picture (see above), what might those other three small circles from Barbary Castle 1991 be meant to signify? Its "hexagonal swirl" could be just a double tetrahedron as seen from above. The symbolic meaning of its "ratchet spiral" seems less clear, but could mean perhaps that some internal energy is quantized as one approaches the vortex centre. For other examples of tetrahedral geometry in crops, see universe2. For another example of that ratchet spiral at Barbary Castle in 2008, see barbury.

Hyper-dimensional physics and quantum gravity

It seems easy to understand why most modern academics have taken no notice of Richard Hoagland's model (except to discredit it). His model was based originally on very questionable kinds of evidence, concerning putative archaeological features from a long-forgotten human civilization, once supposedly based on Mars (see youtube.com or au.youtube.com or au.youtube.com).

Regardless of where Hoagland derived his ideas, could they still have some merit perhaps, in relation to modern theories of quantum gravity? In some of those theories, the basic building block of space-time is assumed to be a four-dimensional tetrahedron or "pentachoron". Such a geometric shape will project into our normal three-dimensional space as a series of five single tetrahedra, or perhaps even as Hoagland's double tetrahedron (see Polytopes or

We saw the three-dimensional projection of a tesseract or four-dimensional cube in crops at North Down on August 19, 2007 (see northdown2007). Could those crop artists be showing us in 2008 the three-dimensional projection of a four-dimensional tetrahedron? Tetrahedral symmetry appears for quantum electricity in many kinds of atom, for example the carbon orbitals in methane CH4. Tetrahedral deformations are well known in some atomic nuclei (see tetrahedron).

With regard to quantum gravity, one leading theory states: "Quantum gravity divides space-time into tiny triangular sections known as simplexes. The 3-simplex is usually called a tetrahedron. The 4-simplex as a basic building block is usually called a pentachoron. Each individual simplex remains geometrically flat, yet many simplexes may be joined together in a variety of ways, so as to create a variety of curved space times (see /Causal-dynamical-triangulation or Causal_dynamical_triangulation).

In summary, if the underlying structure of space-time on a large planetary scale (as well as a small quantum scale) is really that of a pentachoron or 4-simplex, then the projection of that pentachoron into our three-dimensional space might well resemble Hoagland's double tetrahedron, and thereby explain the anomalous planetary or solar data as observed.

What do we see at latitude 19.5 degrees on Earth?

Many people have speculated about various geological features found close to latitudes of +19.5 or -19.5 on Earth (see planets). But more interesting perhaps are certain archeological features that lie close to latitude 19.5 degrees North on Earth, namely the great pyramid complexes of Teotihuacan and Edzna in ancient Mexico (see or www.dartmouth.edu):

Why should those archaeological features be of relevance here? Simply because Mayan calendars, Mayan binary codes, or symbols for the legendary Quetzalcoatl constitute an important part of modern crop pictures (see http://cropcirclemeanings.blogspot.com). Could the same race of people who once built Teotihuacan at a chosen latitude of 19.5 degrees, now be sending us messages in crops, about a latitude of 19.5 degrees from hyper-dimensional physics?

A change of energy flow as we approach the year 2012?

What will happen to Earth and our solar system in the year 2012, when the Mayan Long Count calendar ends on December 21 or 23? Nobody today really knows. Could it be related somehow to the four crop pictures that they just showed in 2008 at Secklendorf, Reinshof, All Cannings or Oliver's Castle, concerning hyper-dimensional physics?

As of 2008, we seem to be seeing slightly altered flows of energy all through our solar system: (a) fewer sunspots or less solar wind than normal (see solarwind or www.earthfiles.com), (b) two new red spots on Jupiter (see apod.nasa.gov), (c) a glowing hexagonal aurora on Saturn (see cosmiclog.msnbc.msn.com), or (d) increased levels of green nightglow on Venus (see query.nytimes.com). We may wish to keep a close eye on such phenomena are we approach the year 2012:

"Strange things will happen to the Sun, Moon and stars".(Luke 21, 25).

Indeed, might our current understanding of solar or planetary physics be as incomplete as that of early 20th-century scientists, who did not yet understand how stars can burn for billions of years using radioactive fusion? And might those mysterious crop artists---benevolent extra-terrestrials of some kind---be intent on helping us to understand? For sure, they are not far away! See a recent series of UFO reports on or www.earthfiles.com.

Harold Stryderight

PS We will need increased membership for Crop Circle Connector in the years 2009-2012, in order to meet greatly increased public demand for free and open access to those pictures, as they appear fifty times each summer in England or (mainly) Europe. If you would like to support this important effort, please see

PSS Many thanks to Andreas Muller for the line drawings as used here.

TETRAHEDRAL

Needless to say, such a “tetrahedral force field,” coupled with Elenin’s “tetrahedrally-defined” orbital parameters, removes ALL remaining scientific doubt that Elenin is NOT “natural” — but is, in fact, an Artificial Object (some kind of “ship”)–

As an unmistakable, 3-D TETRAHEDRON!

This precise geometric shape is total confirmation of, and entirely consistent with, all the “19.5’s” I’ve been analyzing over the past several months … re Elenin’s ~13,000-year orbital trajectory into the inner solar system!

The sudden visibility of this immense “geometric structure” (which is obviously NOT a “physical object,” but only a “geometric field of force … over 300,000 miles across (!) … seen strongly interacting with the highly charged solar wind”) is only possible because Elenin is VERY close to the Sun itself now, where the density of the solar wind is high enough to make this “structure” briefly visible, especially during the density enhancement of a CME ….

Needless to say, such a “tetrahedral force field,” coupled with Elenin’s “tetrahedrally-defined” orbital parameters, removes ALL remaining scientific doubt that Elenin is NOT “natural” — but is, in fact, an Artificial Object (some kind of “ship”)–

TETRAHEDRON WATER- ONCE IT ATTAINS TETRAHEDRAL FORM, WATER ACHIEVES CONSCIOUSNESS SAYS VOEGEL

How is water and consciousness tied together and related to humans and plants? One of the original pioneers in water consciousness studies, Dr. Marcel Vogel, determined that when bulk water was in the process of freezing, excess energy is extracted from the water.

At this point, the molecules start to spin and link together in the pattern of a tetrahedron.
http://in5d.com/the-consciousness-of-water-and-plants/

Dr. Vogel also noted that, at this juncture, water develops a consciousness, ‘a memory, a knowing of what they were designed to do (and) to be.’

DOUBLE TETRAHEDRON MERKABA HAWAII (TETRA IS FOUR)

Hawaii and the Star tetrahedron

In the early 1990s Richard Hoagland, a former NASA scientist, had become intrigued by what appeared, in NASA photographs, to be a number of Pyramids and a Sphinx clustered together in a region called Cydonia on the surface of Mars. As his research continued he recognized that Cydonia sits astride the 19.5-degree latitude on Mars, and that furthermore so does the ‘eye’ on Jupiter and the most active volcanoes on Earth which are on The Big Island of Hawaii. (Also on Earth the Mayan ruins in the Yucatan of Mexico sit on the 19.5 line). He was pondering these coincidences when another researcher, Drunvalo Melchizedek, who was primarily interested in sacred geometry, noticed that if you place a Star Tetrahedron (which is composed of 2 interlocking 4-sided tetrahedrons) so that it fits inside a sphere with its points touching the surface of the sphere, then if the two opposite points of the tetrahedrons are the ‘poles’ of this sphere, then the other points of the tetrahedrons touch the sphere at 19.5 degrees north and south of the ‘equator’.

The star-tetrahedron inside a sphere, showing coordinate points

(www.enterprisemission.com)

The Star Tetrahedron is significant because it is one of the shapes that energetic interdimensional vehicles, known as the ‘Merkaba’ or ‘Light-body’, manifest as. At Planet Earth’s 19.5-degree latitude we have the intersection between the light body of the planet with its surface, and since light-bodies have the ability to connect us to other dimensions, at this latitude we have an energetic predisposition for inter-dimensional experience. Hence the massive volcanoes on Mars, the eye and Moon of Jupiter, two volcanoes on Venus, a ‘dark spot’ on Neptune, dark cloud bands on Saturn and the Volcanoes of Hawaii.

“My spherical model of the Universe, is composed of tetrahedrons, in the shape of a 600-cell tetrahedron”,

https://en.wikipedia.org/wiki/Tetractys
The tetractys occurs in the following, the baryon decuplet, an archbishop's coat of arms, the arrangement of pins in ten-pin bowling, and a Chinese checkers board

THE FOURTH IS ALWAYS DIFFERENT

Tetraquark

Standard Model of particle physics

Standard Model of Elementary Particles.svg

Fundamental particles of the standard model

Background[show]

Constituents[show]

Limitations[show]

Scientists[show]

v t e

A tetraquark, in particle physics, is an exotic meson composed of four valence quarks. In principle, a tetraquark state may be allowed in quantum chromodynamics,[1] the modern theory of strong interactions. Any established tetraquark state would be an example of an exotic hadron which lies outside the quark model classification.[qualify evidence]

Contents [hide]

1 History

3 References

History

Colour flux tubes produced by four static quark and antiquark charges, computed in lattice QCD.[2] Confinement in Quantum Chromo Dynamics leads to the production of flux tubes connecting colour charges. The flux tubes act as attractive QCD string-like potentials.

In 2003 a particle temporarily called X(3872), by the Belle experiment in Japan, was proposed to be a tetraquark candidate,[3] as originally theorized.[4] The name X is a temporary name, indicating that there are still some questions about its properties to be tested. The number following is the mass of the particle in MeV/c2.

In 2004, the DsJ(2632) state seen in Fermilab's SELEX was suggested as a possible tetraquark candidate.[citation needed]

In 2007, Belle announced the observation of the Z(4430) state, a

c

c

d

u

tetraquark candidate. There are also indications that the Y(4660), also discovered by Belle in 2007, could be a tetraquark state.[5]

In 2009, Fermilab announced that they have discovered a particle temporarily called Y(4140), which may also be a tetraquark.[6]

In 2010, two physicists from DESY and a physicist from Quaid-i-Azam University re-analyzed former experimental data and announced that, in connection with the

ϒ

(5S) meson (a form of bottomonium), a well-defined tetraquark resonance exists.[7][8]

In June 2013, the BES III experiment in China and the Belle experiment in Japan independently reported on Zc(3900), the first confirmed four-quark state.[9]

In 2014, the Large Hadron Collider experiment LHCb confirmed the existence of the Z(4430) state with a significance of over 13.9 σ.[10][11]

In February 2016, the DØ experiment announced the observation of a narrow tetraquark candidate, named X(5568), decaying to Bsπ±.[12] However, preliminary results from LHCb, presented at the 51st Rencontres de Moriond Electroweak session, show no evidence for the state, despite a much larger sample of

B0

sπ± candidates.[13]

In June 2016, LHCb announced the discovery of three additional tetraquark candidates, called X(4274), X(4500) and X(4700).[14][15][16]

THE FOUR DELTA BARYONS

Delta baryon

The Delta baryons (or Δ baryons, also called Delta resonances) are a family of subatomic particle made of three up or down quarks (u or d quarks).

Four Δ baryons exist:

Δ++

(constituent quarks: uuu),

Δ+

(uud),

Δ0

(udd), and

Δ−

(ddd), which respectively carry an electric charge of +2 e, +1 e, 0 e, and −1 e.

The Δ baryons have a mass of about 1232 MeV/c2, a spin of

3

/

2

, and an isospin of

3

/

2

. In many ways, a Δ baryon is an 'excited' nucleon (symbol N). Nucleons are made of the same constituent quarks, but they are in a lower-energy spin configuration (spin

1

/

2

). The

Δ+

(uud) and

Δ0

(udd) particles are the higher-energy equivalent of the proton (

N+

, uud) and neutron (

N0

, udd), respectively. However, the

Δ++

and

Δ−

have no nucleon equivalent.

Contents [hide]

1 Composition

2 Decay

3 List

4 References

4.1 Bibliography

Composition

The four Δ baryons are distinguished by their electrical charges, which is the sum of the charges of the quarks from which they are composed. There are also four antiparticles with opposite charges, made up of the corresponding antiquarks. The existence of the

Δ++

, with its unusual +2 charge, was a crucial clue in the development of the quark model.

Decay

All varieties of Δ baryons quickly decay via the strong force into a nucleon (proton or neutron) and a pion of appropriate charge. The amplitudes of various final charge states given by their respective isospin couplings. More rarely and more slowly, the

Δ+

can decay into a proton and a photon and the

Δ0

can decay into a neutron and a photon.

List

Delta baryons

Particle name Symbol Quark

content Rest mass (MeV/c2) I3 JP Q (e) S C B′ T Mean lifetime (s) Commonly decays to

Delta[1]

Δ++

(1232)

u

u

u

1,232 ± 2 + 3⁄2  3⁄2+ +2 0 0 0 0 (5.63±0.14)×10−24[a]

p+

+

π+

Delta[1]

Δ+

(1232)

u

u

d

1,232 ± 2 + 1⁄2  3⁄2+ +1 0 0 0 0 (5.63±0.14)×10−24[a]

π+

+

n0

or

π0

+

p+

Delta[1]

Δ0

(1232)

u

d

d

1,232 ± 2 − 1⁄2  3⁄2+ 0 0 0 0 0 (5.63±0.14)×10−24[a]

π0

+

n0

or

π−

+

p+

Delta[1]

Δ−

(1232)

d

d

d

1,232 ± 2 − 3⁄2  3⁄2+ −1 0 0 0 0 (5.63±0.14)×10−24[a]

π−

+

n0

[a] ^ PDG reports the resonance width (Γ). Here the conversion τ =

/

Γ

FOUR COMPONENT SPINOR

Pauli's theory of spin was non-relativistic. However, in 1928, Paul Dirac published the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a "Dirac spinor") was used for the electron wave-function. In 1940, Pauli proved the spin-statistics theorem, which states that fermions have half-integer spin and bosons have integer spin.

FOUR SPINORs

Four-spinors

For particles

Particles are defined as having positive energy. The normalization for the four-spinor ω is chosen so that

ω

ω

=

2

E

\scriptstyle \omega ^{\dagger }\omega \;=\;2E\,[further explanation needed]. These spinors are denoted as u:

u

(

p

,

s

)

=

E

+

m

[

ϕ

(

s

)

σ

p

E

+

m

ϕ

(

s

)

]

u({\vec {p}},s)={\sqrt {E+m}}{\begin{bmatrix}\phi ^{(s)}\\{\frac {{\vec {\sigma }}\cdot {\vec {p}}}{E+m}}\phi ^{(s)}\end{bmatrix}}\,

where s = 1 or 2 (spin "up" or "down")

Explicitly,

u

(

p

,

1

)

=

E

+

m

[

1 0

p

3

E

+

m

p

1

+

i

p

2

E

+

m

]

a

n

d

u

(

p

,

2

)

=

E

+

m

[

0 1

p

1

i

p

2

E

+

m

p

3

E

+

m

]

u({\vec {p}},1)={\sqrt {E+m}}{\begin{bmatrix}1\\0\\{\frac {p_{3}}{E+m}}\\{\frac {p_{1}+ip_{2}}{E+m}}\end{bmatrix}}\quad \mathrm {and} \quad u({\vec {p}},2)={\sqrt {E+m}}{\begin{bmatrix}0\\1\\{\frac {p_{1}-ip_{2}}{E+m}}\\{\frac {-p_{3}}{E+m}}\end{bmatrix}}

For anti-particles

Anti-particles having positive energy

E

\scriptstyle E are defined as particles having negative energy and propagating backward in time. Hence changing the sign of

E

\scriptstyle E and

p

→\scriptstyle {\vec {p}} in the four-spinor for particles will give the four-spinor for anti-particles:

v

(

p

,

s

)

=

E

+

m

[

σ

p

E

+

m

χ

(

s

)

χ

(

s

)

]

v({\vec {p}},s)={\sqrt {E+m}}{\begin{bmatrix}{\frac {{\vec {\sigma }}\cdot {\vec {p}}}{E+m}}\chi ^{(s)}\\\chi ^{(s)}\end{bmatrix}}\,

Here we choose the

χ\scriptstyle \chi solutions. Explicitly,

v

(

p

,

1

)

=

E

+

m

[

p

1

i

p

2

E

+

m

p

3

E

+

m

0 1

]

a

n

d

v

(

p

,

2

)

=

E

+

m

[

p

3

E

+

m

p

1

+

i

p

2

E

+

m

1 0

]

v({\vec {p}},1)={\sqrt {E+m}}{\begin{bmatrix}{\frac {p_{1}-ip_{2}}{E+m}}\\{\frac {-p_{3}}{E+m}}\\0\\1\end{bmatrix}}\quad \mathrm {and} \quad v({\vec {p}},2)={\sqrt {E+m}}{\begin{bmatrix}{\frac {p_{3}}{E+m}}\\{\frac {p_{1}+ip_{2}}{E+m}}\\1\\0\\\end{bmatrix}}

Completeness relations

The completeness relations for the four-spinors u and v are

s

=

1

,

2

u

p

(

s

)

u

¯

p

(

s

)

=

p

/

+

m

\sum _{s=1,2}{u_{p}^{(s)}{\bar {u}}_{p}^{(s)}}=p\!\!\!/+m\,

s

=

1

,

2

v

p

(

s

)

v

¯

p

(

s

)

=

p

/

m

\sum _{s=1,2}{v_{p}^{(s)}{\bar {v}}_{p}^{(s)}}=p\!\!\!/-m\,

where

p

/

=

γ

μ

p

μ

p\!\!\!/=\gamma ^{\mu }p_{\mu }\, (see Feynman slash notation)

u

¯

=

u

γ

0

{\bar {u}}=u^{\dagger }\gamma ^{0}\,

4 by 4 is 16- THE DIRAC MATRICES SIXTEEN SQUARES WERE USED TO FIND ANTI PARTICLES

The Dirac matrices are a set of four 4×4 matrices that are used as spin and charge operators.

https://en.wikipedia.org/wiki/Dirac_spinor
4 by 4 is 16- THE DIRAC MATRICES SIXTEEN SQUARES WERE USED TO FIND ANTI PARTICLES

The Dirac matrices are a set of four 4×4 matrices that are used as spin and charge operators.

USED TO FIND ANTI MATTER - 4 QUADRANT MODEL 16s
https://en.wikipedia.org/wiki/Gamma_matrices
Gamma matrices
(Redirected from Dirac matrices)
In mathematical physics, the gamma matrices,
{
γ
0
,
γ
1
,
γ
2
,
γ
3
}
\{\gamma ^{0},\gamma ^{1},\gamma ^{2},\gamma ^{3}\}, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cℓ1,3(R). It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-½ particles.

In Dirac representation, the four contravariant gamma matrices are

γ
0
=
(
1 0 0 0 0 1 0 0 0 0 −1 0 0 0 0 −1
)

γ
1
=
(
0 0 0 1 0 0 1 0 0 −1 0 0 −1 0 0 0
)
γ
2
=
(
0 0 0 −i 0 0 i 0 0 i 0 0 −i 0 0 0
)

γ
3
=
(
0 0 1 0 0 0 0 −1 −1 0 0 0 0 1 0 0
)
γ
0
\gamma ^{0} is the time-like matrix and the other three are space-like matrices.

Analogous sets of gamma matrices can be defined in any dimension and signature of the metric. For example, the Pauli matrices are a set of "gamma" matrices in dimension 3 with metric of Euclidean signature (3,0). In 5 spacetime dimensions, the 4 gammas above together with the fifth gamma matrix to be presented below generate the Clifford algebra.

(quote from a differnet sight) FUSIION OF FOUR HYDROGEN NUCLEI (INTO A QUADRANT TO HELIUM) IS WHAT POWERS SUN

Hydrogen burning is the fusion of four hydrogen nuclei (protons) into a single helium nucleus (two protons and neutrons.) The process is a series of reactions. The type of reactions depend on the mass of a star and its core temperature and density. In our Sun, the process is a proton-proton chain. In more massive stars, the C-N-O cycle (Carbon-Nitrogen-Oxygen) serves to fuse hydrogen into helium." This process is central to star fusion. The four hydrogen nuclei represent the quadrant

Hydrogen Burning

Hydrogen burning is the fusion of 4 hydrogen nuclei (protons) into a single helium nucleus (2 protons + 2 neutrons). The fusion process takes place via a series of reactions. Exactly which reactions take place in a given star depends on its mass, and therefore its core temperature and density. In the Sun, this process is called the proton-proton chain. In stars somewhat more massive than the Sun, a different sequence of reactions, called the C-N-O cycle (Carbon-Nitrogen-Oxygen), serves to fuse hydrogen into helium.

Here's an excerpt from QMR

The memresistor was theorized to exist, and recently was realized, completing the four basic electronic components, along with the resistor, capacitor, and inductor. These components are created from four factors charge, current, voltage and flux.

Square 1: Resistor

Square 2: Capacitor

Square 3: Indictor

Square 4: Memresistor. The fourth is always transcendent and does not seem to belong.

According to the original 1971 definition, the memristor was the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage. In 2011 Chua argued for a broader definition that included all 2-terminal non-volatile memory devices based on resistance switching.[2] Williams argued that MRAM, phase change memory and RRAM were memristor technologies.[15] Some researchers argued that biological structures such as blood[16] and skin[17][18] fit the definition. Others argued that the memory device under development by HP Labs and other forms of RRAM were not memristors but rather part of a broader class of variable resistance systems[19] and that a broader definition of memristor is a scientifically unjustifiable land grab that favored HP's memristor patents.[20]

FOUR DISCOURSES

Four discourses

Four discourses is a concept developed by French psychoanalyst Jacques Lacan. He argued that there were four fundamental types of discourse. He defined four discourses, which he called Master, University, Hysteric and Analyst, and suggested that these relate dynamically to one another.

Discourse of the Master – Struggle for mastery / domination / penetration. Based on Hegel's master–slave dialectic.

Discourse of the University – Provision and worship of "objective" knowledge — usually in the unacknowledged service of some external master discourse.

Discourse of the Hysteric – Symptoms embodying and revealing resistance to the prevailing master discourse.

Discourse of the Analyst – Deliberate subversion of the prevailing master discourse.

Lacan's theory of the four discourses was initially developed in 1969, perhaps in response to the events of social unrest during May 1968 in France, but also through his discovery of what he believed were deficiencies in the orthodox reading of the Oedipus Complex. The Four Discourses theory is presented in his seminar L'envers de la psychanalyse and in Radiophonie, where he starts using "discourse" as a social bond founded in intersubjectivity. He uses the term discourse to stress the transindividual nature of language: speech always implies another subject.

Contents [hide]

1 Necessity of Formalising Psychoanalysis

2 Structure

3 Relevance for cultural studies

5 References

Necessity of Formalising Psychoanalysis

Prior to the development of the Four Discourses, the primary guideline for clinical psychoanalysis was the Oedipus Complex. In Lacan's Seminar of 1969-70, he argues that there was a major problem with the Oedipus complex, namely that the father is already castrated at the point of intervention, rendering the orthodox Freudian reading, where the father becomes a terrifying figure, a neurotic fantasy. Lacan's solution to the tendency of analysts to invoke their own imaginary readings and neurotic fantasies was to begin to formalise psychoanalytic theory, and express it in mathematical functions. This would ensure not only that a minimum of the teaching is lost when communicated, but also limit the associations of the analyst with the concepts employed.

Structure

Discourse, in the first place, refers to a point where speech and language intersect. The four discourses represent the four possible formulations of the symbolic network which social bonds can take and can be expressed as the permutations of a four-term configuration showing the relative positions — the agent, the other, the product and the truth — of four terms, the subject, the master signifier, knowledge and objet petit a.

The four positions in each discourse are :

Agent = Upper left. This is the speaker of the discourse

Other = Upper right. This is what the discourse is addressed to

Product = Lower right. This is what the discourse has created

Truth = Lower left. This is what the discourse attempted to express

The four variables which occupy these positions are :

S1 = the master signifier

S2 = knowledge (le savoir)

$= the subject (barred) a = the objet petit a or surplus-jouissance S1 refers to "the marked circle of the field of the Other," it is the Master-Signifier. S2 is the "battery of signifiers, already there" at the place where "one wants to determine the status of a discourse as status of statement," that is knowledge (savoir). S1 comes into play in a signifying battery conforming the network of knowledge.$ is the subject, marked by the unbroken line (trait unaire) which represents it and is different from the living individual who is not the locus of this subject. Add the objet petit a, the object-waste or the loss of the object that occurred when the originary division of the subject took place — the object that is the cause of desire: the plus-de-jouir.

Discourse of the Master:

It is the basic discourse from which the other three derive. The dominant position is occupied by the master signifier, S1, which represents the subject, S, for all other signifiers: S2. In this signifying operation there is a surplus: objet a. All attempts at totalisation are doomed to fail. This discourse masks the division of the subject, it illustrates the structure of the dialectic of the master and the slave. The master, S1, is the agent who puts the slave, S2, to work: the result is a surplus, objet a, that the master struggles to appropriate.

Discourse of the University:

It is caused by an anticlockwise quarter turn of the previous discourse. The dominant position is occupied by knowledge (savoir). An attempt to mastery can be traced behind the endeavors to impart neutral knowledge: domination of the other to whom knowledge is transmitted. This hegemony is visible in modernity with science.

Discourse of the Hysteric:

It is effected by a clockwise quarter turn of the discourse of the master. It is not simply "that which is uttered by the hysteric," but a certain kind of articulation in which any subject may be inscribed. The divided subject, $, the symptom, is in the pole position. This discourse points toward knowledge. "The cure involves the structural introduction of the discourse of the hysteric by way of artificial conditions": the analyst hystericizes the analysand's discourse. Discourse of the Analyst: It is produced by a quarter turn of the discourse of the hysteric in the same way as Freud develops psychoanalysis by giving an interpretative turn to the discourse of his hysterical patients. The position of the agent — the analyst — is occupied by objet a: the analyst becomes the cause of the analysand's desire. This discourse being the reverse of the discourse of the master, does it make psychoanalysis an essentially subversive practice which undermines attempts at domination and mastery? Relevance for cultural studies Slavoj Žižek uses the theory to explain various cultural artefacts, including Don Giovanni and Parsifal. Discourse Don Giovanni Parsifal Characteristics Master Don Ottavio Amfortas inauthentic, inconsistent University Leporello Klingsor inauthentic, consistent Hysteric Donna Elvira Kundry authentic, inconsistent Analyst Donna Anna Parsifal authentic, consistent FOUR PROCESSES OF THE CARNOT CYCLE Introduction In the early 19th century, steam engines came to play an increasingly important role in industry and transportation. However, a systematic set of theories of the conversion of thermal energy to motive power by steam engines had not yet been developed. Nicolas Léonard Sadi Carnot (1796-1832), a French military engineer, published Reflections on the Motive Power of Fire in 1824. The book proposed a generalized theory of heat engines, as well as an idealized model of a thermodynamic system for a heat engine that is now known as thea Carnot cycle. Carnot developed the foundation of the second law of thermodynamics, and is often described as the "Father of thermodynamics." The Carnot Cycle The Carnot cycle consists of the following four processes: A reversible isothermal gas expansion process. In this process, the ideal gas in the system absorbs qin amount heat from a heat source at a high temperature Th, expands and does work on surroundings. A reversible adiabatic gas expansion process. In this process, the system is thermally insulated. The gas continues to expand and do work on surroundings, which causes the system to cool to a lower temperature, Tl. A reversible isothermal gas compression process. In this process, surroundings do work to the gas at Tl, and causes a loss of heat, qout. A reversible adiabatic gas compression process. In this process, the system is thermally insulated. Surroundings continue to do work to the gas, which causes the temperature to rise back to Th. FOUR F CORRELATOR Hardware implementation of the system transfer function: The 4F correlator  Main article: Optical correlator The theory on optical transfer functions presented in section 4 is somewhat abstract. However, there is one very well known device which implements the system transfer function H in hardware using only 2 identical lenses and a transparency plate - the 4F correlator. Although one important application of this device would certainly be to implement the mathematical operations of cross-correlation and convolution, this device - 4 focal lengths long - actually serves a wide variety of image processing operations that go well beyond what its name implies. A diagram of a typical 4F correlator is shown in the figure below (click to enlarge). This device may be readily understood by combining the plane wave spectrum representation of the electric field (section 2) with the Fourier transforming property of quadratic lenses (section 5.1) to yield the optical image processing operations described in section 4. 4F Correlator The 4F correlator is based on the convolution theorem from Fourier transform theory, which states that convolution in the spatial (x,y) domain is equivalent to direct multiplication in the spatial frequency (kx, ky) domain (aka: spectral domain). Once again, a plane wave is assumed incident from the left and a transparency containing one 2D function, f(x,y), is placed in the input plane of the correlator, located one focal length in front of the first lens. The transparency spatially modulates the incident plane wave in magnitude and phase, like on the left-hand side of eqn. (2.1), and in so doing, produces a spectrum of plane waves corresponding to the FT of the transmittance function, like on the right-hand side of eqn. (2.1). That spectrum is then formed as an "image" one focal length behind the first lens, as shown. A transmission mask containing the FT of the second function, g(x,y), is placed in this same plane, one focal length behind the first lens, causing the transmission through the mask to be equal to the product, F(kx,ky) x G(kx,ky). This product now lies in the "input plane" of the second lens (one focal length in front), so that the FT of this product (i.e., the convolution of f(x,y) and g(x,y)), is formed in the back focal plane of the second lens. If an ideal, mathematical point source of light is placed on-axis in the input plane of the first lens, then there will be a uniform, collimated field produced in the output plane of the first lens. When this uniform, collimated field is multiplied by the FT plane mask, and then Fourier transformed by the second lens, the output plane field (which in this case is the impulse response of the correlator) is just our correlating function, g(x,y). In practical applications, g(x,y) will be some type of feature which must be identified and located within the input plane field (see Scott [1998]). In military applications, this feature may be a tank, ship or airplane which must be quickly identified within some more complex scene. The 4F correlator is an excellent device for illustrating the "systems" aspects of optical instruments, alluded to in section 4 above. The FT plane mask function, G(kx,ky) is the system transfer function of the correlator, which we'd in general denote as H(kx,ky), and it is the FT of the impulse response function of the correlator, h(x,y) which is just our correlating function g(x,y). And, as mentioned above, the impulse response of the correlator is just a picture of the feature we're trying to find in the input image. In the 4F correlator, the system transfer function H(kx,ky) is directly multiplied against the spectrum F(kx,ky) of the input function, to produce the spectrum of the output function. This is how electrical signal processing systems operate on 1D temporal signals. Samsung Galaxy Note 4 Benchmarks (Antutu, Quadrant, GFXBench, Vellamo) youtube.com Samsung galaxy note four benchmarks Merk Diezle shared a link. Sep 03, 2016 11:11pm HarmonyAngels - Physical Science harmonyangels.com this model of the four types quantum mechanics classical mechanics quantum field theory and relativistic mechancics based on the duality of fast and slow and atomic and planetary is in one of my books If continents are defined strictly as discrete landmasses, embracing all the contiguous land of a body, then Asia, Europe and Africa form a single continent which may be referred to as Afro-Eurasia. This produces a four-continent model consisting of Afro-Eurasia, America, Antarctica and Australia. FOUR VARIABLES The combination of Ohm's law and Joule's law gives us 12 formulas where 2 of the 4 variables are known. The wheel below is a handy tool and memory jogger. To use it, simply choose the quadrant corresponding to the variable you want to calculate, then select the segment corresponding to the variables that you know the values of. Quadrant I'm a paragraph. Click here to add your own text and edit me. It's easy. ADDS A FOURTH DIFFERENT PIXEL- THE WHITE ONE- THE FOURTH IS ALWAYS DIFFERENT LG's unique 4 Colour Pixel: makes the world more lifelike By TechRadar December 14, 2014 Television SPONSORED Delivering truest lifelike colours to your living room Colour's important, isn't it? If you're watching your wedding video, you want to see your mum's hat in all its feather-festooned, fuschia glory. If you're watching sport, you want the grass to look green. Posses of cowboys should stampede past under the richest azure skies. The walls of the pubs in British soap operas should look kind of brown. Colour TV changed the way we saw the world, bringing visuals to life; making the moving image seem real. For decades, TV colour, from cathode ray tubes to the sub-pixels in flatscreens, has been delivered via three parts of the spectrum – red, green and blue (RGB). But now LG wants to heighten your perceptions again with 4 Colour Pixel. The technical facts 4 Colour Pixel adds a white sub-pixel to the usual red, green and blue array – the first time such a system has been used in a TV. The 4th colour pixel lets you see more sub-pixels onscreen, creating a more detailed and full picture. The colour range and accuracy are enhanced so images are more vivid and colour blends more subtle and consistent. Meanwhile, LG's Colour Refiner manages the accuracy and consistency of your onscreen hues, increasing the realism still further. Put 4 Colour Pixel OLED sets side by side with old-school LED RGB TVs and the difference should be clear. The emotional results Movies and TV are brought to vivid life. More than ever, you feel the emotional charge as your football/rugby/lacrosse/kabbadi team runs out in its sacred colours, on rich, green turf. Watching your favourite film, it's like you're seeing it for the first time, as the lifelike colours draw you in. Cartoons and FX-driven blockbusters become total sensory overload. The pub walls in British soap operas? They're still brown. But richer brown. It's worth noting that the colour achieved by OLED TVs is already more accurate than what you'll find on LED TVs. Add 4 Colour Pixel and onscreen worlds become even more lifelike and real. It's a game changer. Colour your life Colour is among the most essential features on a new telly. It's one of the first things you look for when auditioning a new set in the shop, and it keeps the experience enjoyable for years after you take it home. Sure, contrast, clarity, smooth motion and smart TV connected services are essential - and LG's OLED sets have them in spades - but it's rich, accurate colour that makes watching movies at home feel so much more cinematic, makes sport really pop and your favourite TV shows sparkle. So, are you ready for colour that's fresher and more lifelike than ever? 4 Colour Pixel is in LG's full-HD 55EC930V. LG has set out to tick every box with this TV; it's beautifully designed, curved, has OLED screen tech and, thanks to 4 Colour Pixel, delivers the truest lifelike colours to your living room. It's a proper tech-head's telly: future-proofed and available now. THE FOURTH IS ALWAYS DIFFERENT LG's unique 4 Colour Pixel: makes the world more lifelike By TechRadar December 14, 2014 Television SPONSORED Delivering truest lifelike colours to your living room Colour's important, isn't it? If you're watching your wedding video, you want to see your mum's hat in all its feather-festooned, fuschia glory. If you're watching sport, you want the grass to look green. Posses of cowboys should stampede past under the richest azure skies. The walls of the pubs in British soap operas should look kind of brown. Colour TV changed the way we saw the world, bringing visuals to life; making the moving image seem real. For decades, TV colour, from cathode ray tubes to the sub-pixels in flatscreens, has been delivered via three parts of the spectrum – red, green and blue (RGB). But now LG wants to heighten your perceptions again with 4 Colour Pixel. The technical facts 4 Colour Pixel adds a white sub-pixel to the usual red, green and blue array – the first time such a system has been used in a TV. The 4th colour pixel lets you see more sub-pixels onscreen, creating a more detailed and full picture. The colour range and accuracy are enhanced so images are more vivid and colour blends more subtle and consistent. Meanwhile, LG's Colour Refiner manages the accuracy and consistency of your onscreen hues, increasing the realism still further. Put 4 Colour Pixel OLED sets side by side with old-school LED RGB TVs and the difference should be clear. The emotional results Movies and TV are brought to vivid life. More than ever, you feel the emotional charge as your football/rugby/lacrosse/kabbadi team runs out in its sacred colours, on rich, green turf. Watching your favourite film, it's like you're seeing it for the first time, as the lifelike colours draw you in. Cartoons and FX-driven blockbusters become total sensory overload. The pub walls in British soap operas? They're still brown. But richer brown. It's worth noting that the colour achieved by OLED TVs is already more accurate than what you'll find on LED TVs. Add 4 Colour Pixel and onscreen worlds become even more lifelike and real. It's a game changer. Colour your life Colour is among the most essential features on a new telly. It's one of the first things you look for when auditioning a new set in the shop, and it keeps the experience enjoyable for years after you take it home. Sure, contrast, clarity, smooth motion and smart TV connected services are essential - and LG's OLED sets have them in spades - but it's rich, accurate colour that makes watching movies at home feel so much more cinematic, makes sport really pop and your favourite TV shows sparkle. So, are you ready for colour that's fresher and more lifelike than ever? 4 Colour Pixel is in LG's full-HD 55EC930V. LG has set out to tick every box with this TV; it's beautifully designed, curved, has OLED screen tech and, thanks to 4 Colour Pixel, delivers the truest lifelike colours to your living room. It's a proper tech-head's telly: future-proofed and available now. THIS ONE IS NOT RGBG BUT IT IS RGBW- THE FOURTH IS ALWAYS DIFFERENT PenTile RGBW Magnified image of the RGBW unit. PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through,[15] hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power.[16] The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision.[17] The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine.[18] When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high brightness mode that doubles the brightness of the desaturated color image areas, such as black&white text, for improved outdoor view-ability. Devices Motorola MC65[19] Motorola ES55[20] Motorola ES400[21] Motorola Atrix 4G[22] Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook Pro UX501JW A QUINCUNX IS A CROSS MADE OF FIVE PARTS "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s.[1] The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell PIXELS ARE REPRESENTED BY THREE OR FOUR INTENSITIES THE FOURTH IS ALWAYS DIFFERENT In digital imaging, a pixel, pel,[1] dots, or picture element[2] is a physical point in a raster image, or the smallest addressable element in an all points addressable display device; so it is the smallest controllable element of a picture represented on the screen. The address of a pixel corresponds to its physical coordinates. LCD pixels are manufactured in a two-dimensional grid, and are often represented using dots or squares, but CRT pixels correspond to their timing mechanisms and sweep rates. Each pixel is a sample of an original image; more samples typically provide more accurate representations of the original. The intensity of each pixel is variable. In color imaging systems, a color is typically represented by three or four component intensities such as red, green, and blue, or cyan, magenta, yellow, and black. 16 Squares of the quadrant model- 16 segment display highest A sixteen-segment display (SISD) is a type of display based on 16 segments that can be turned on or off according to the graphic pattern to be produced. It is an extension of the more common seven-segment display, adding four diagonal and two vertical segments and splitting the three horizontal segments in half. Other variants include the fourteen-segment display which does not split the top or bottom horizontal segments, and the twenty two-segment display[1] that allows lower-case characters with descenders. Often a character generator is used to translate 7-bit ASCII character codes to the 16 bits that indicate which of the 16 segments to turn on or off.[2] Contents [hide] 1 History 2 See also 3 References 4 External links History Sixteen-segment displays were originally designed to display alphanumeric characters (Latin letters and Arabic digits). Later they were used to display Thai numerals[3] and Persian characters.[4] Non-electronic displays using this pattern existed as early as 1902.[5] Before the advent of inexpensive dot-matrix displays, sixteen and fourteen-segment displays were some of the few options available for producing alphanumeric characters on calculators and other embedded systems. However, they are still sometimes used on VCRs, car stereos, microwave ovens, telephone Caller ID displays, and slot machine readouts. Sixteen-segment displays may be based on one of several technologies, the three most common optoelectronics types being LED, LCD and VFD. The LED variant is typically manufactured in single or dual character packages, to be combined as needed into text line displays of a suitable length for the application in question. As with seven and fourteen-segment displays, a decimal point and/or comma may be present as an additional segment, or pair of segments; the comma (used for triple-digit groupings or as a decimal separator in many regions) is commonly formed by combining the decimal point with a closely 'attached' leftwards-descending arc-shaped segment. This way, a point or comma may be displayed between character positions instead of occupying a whole position by itself, which would be the case if employing the bottom middle vertical segment as a point and the bottom left diagonal segment as a comma. Such displays were very common on pinball machines for displaying the score and other information, before the widespread use of dot-matrix display panels. THE FOURTH IS DIFFERENT Quattron is the brand name of an LCD color display technology produced by Sharp Electronics. In addition to the standard RGB (Red, Green and Blue) color subpixels, the technology utilizes a yellow fourth color subpixel (RGBY) which Sharp claims increases the range of displayable colors,[1][2] and which may mimic more closely the way the brain processes color information.[3][4] The screen is a form of multi-primary color display, other forms of which have been developed in parallel to Sharp's version.[5][6] http://www.physicsclassroom.com/…/Lesso…/Kinematic-Equations THERE IS A QUESTIONABLE FIFTH EQUATION BUT IT IS NOT NEEDED THE FOURTH IS ALWAYS TRANSCENDENT FIFTH ULTRA TRANSCENDENT AND QUESIONABLE. THE FOURTH IS A QUADRATIC EQUATION DIFFERENT FROM THE OTHER THREE The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. THE FOURTH IS ALWAYS DIFFERENT- THE FOURTH QUANTUM NUMBER Pauli is the man who came up with the idea that one and only one electron could occupy each zone around a nucleus. This is called the Pauli Exclusion Principle. He figured-out there were four (not three, as had been previously thought) components to describing each electron zone; the first three, already conjectured before Pauli were: 1) the radius of the zone, 2) the shape of the zone, 3) and the orientation of the zone [I’m going by memory here, but I’m pretty sure those were the three]. Pauli added a fourth. It was only later that other physicists labeled this fourth quantum number “spin” (which at first, Pauli resisted). Pauli’s Exclusion Principle states that no two electrons on the same atom can share the same four Quantum Numbers. THE FOUR QUANTUM NUMBERS-- THE FOURTH IS DIFFERENT Four quantum numbers can describe an electron in an atom completely. As per the following model, these nearly-compatible quantum numbers are: Principal quantum number (n) Azimuthal quantum number (ℓ) Magnetic quantum number (m) Spin quantum number (s) The spin-orbital interaction, however, relates these numbers. Thus, a complete description of the system can be given with fewer quantum numbers, if orthogonal choices are made for these basis vectors. This model describes electrons using four quantum numbers, n, ℓ, mℓ, ms, given below. It is also the common nomenclature in the classical description of nuclear particle states (e.g. protons and neutrons). A quantum description of molecular orbitals require different quantum numbers, because the Hamiltonian and its symmetries are quite different. The principal quantum number (n) describes the electron shell, or energy level, of an electron. The value of n ranges from 1 to the shell containing the outermost electron of that atom, i.e.[2] n = 1, 2, ... . For example, in caesium (Cs), the outermost valence electron is in the shell with energy level 6, so an electron in caesium can have an n value from 1 to 6. For particles in a time-independent potential (see Schrödinger equation), it also labels the nth eigenvalue of Hamiltonian (H), i.e. the energy, E with the contribution due to angular momentum (the term involving J2) left out. This number therefore has a dependence only on the distance between the electron and the nucleus (i.e., the radial coordinate, r). The average distance increases with n, and hence quantum states with different principal quantum numbers are said to belong to different shells. The azimuthal quantum number (ℓ) (also known as the angular quantum number or orbital quantum number) describes the subshell, and gives the magnitude of the orbital angular momentum through the relation L2 = ħ2 ℓ (ℓ + 1). In chemistry and spectroscopy, "ℓ = 0" is called an s orbital, "ℓ = 1" a p orbital, "ℓ = 2" a d orbital, and "ℓ = 3" an f orbital. The value of ℓ ranges from 0 to n − 1, because the first p orbital (ℓ = 1) appears in the second electron shell (n = 2), the first d orbital (ℓ = 2) appears in the third shell (n = 3), and so on:[3] ℓ = 0, 1, 2,..., n − 1. A quantum number beginning in 3, 0, … describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. The magnetic quantum number (mℓ) describes the specific orbital (or "cloud") within that subshell, and yields the projection of the orbital angular momentum along a specified axis: Lz = mℓ ħ. The values of mℓ range from −ℓ to ℓ, with integer steps between them:[4] The s subshell (ℓ = 0) contains only one orbital, and therefore the mℓ of an electron in an s orbital will always be 0. The p subshell (ℓ = 1) contains three orbitals (in some systems, depicted as three "dumbbell-shaped" clouds), so the mℓ of an electron in a p orbital will be −1, 0, or 1. The d subshell (ℓ = 2) contains five orbitals, with mℓ values of −2, −1, 0, 1, and 2. The spin projection quantum number (ms) describes the spin (intrinsic angular momentum) of the electron within that orbital, and gives the projection of the spin angular momentum S along the specified axis: Sz = ms ħ. In general, the values of ms range from −s to s, where s is the spin quantum number, an intrinsic property of particles:[5] ms = −s, −s + 1, −s + 2,...,s − 2, s − 1, s. An electron has spin number s = ½, consequently ms will be ±½, referring to "spin up" and "spin down" states. Each electron in any individual orbital must have different quantum numbers because of the Pauli exclusion principle, therefore an orbital never contains more than two electrons. Note that there is no universal fixed value for mℓ and ms values. Rather, the mℓ and ms values are random. The only requirement is that the naming schematic used within a particular set of calculations or descriptions must be consistent (e.g. the orbital occupied by the first electron in a p orbital could be described as mℓ = −1 or mℓ = 0 or mℓ = 1, but the mℓ value of the next unpaired electron in that orbital must be different; yet, the mℓ assigned to electrons in other orbitals again can be mℓ = −1 or mℓ = 0, or mℓ = 1 ). These rules are summarized as follows: Name Symbol Orbital meaning Range of values Value examples principal quantum number n shell 1 ≤ n n = 1, 2, 3, … azimuthal quantum number (angular momentum) ℓ subshell (s orbital is listed as 0, p orbital as 1 etc.) 0 ≤ ℓ ≤ n − 1 for n = 3: ℓ = 0, 1, 2 (s, p, d) magnetic quantum number, (projection of angular momentum) mℓ energy shift (orientation of the subshell's shape) −ℓ ≤ mℓ ≤ ℓ for ℓ = 2: mℓ = −2, −1, 0, 1, 2 spin projection quantum number ms spin of the electron (−½ = "spin down", ½ = "spin up") −s ≤ ms ≤ s for an electron s = ½, so ms = −½, ½ Example: The quantum numbers used to refer to the outermost valence electrons of the Carbon (C) atom, which are located in the 2p atomic orbital, are; n = 2 (2nd electron shell), ℓ = 1 (p orbital subshell), mℓ = 1, 0 or −1, ms = ½ (parallel spins). Results from spectroscopy indicated that up to two electrons can occupy a single orbital. However two electrons can never have the same exact quantum state nor the same set of quantum numbers according to Hund's rules, which addresses the Pauli exclusion principle. A fourth quantum number with two possible values was added as an ad hoc assumption to resolve the conflict; this supposition could later be explained in detail by relativistic quantum mechanics and from the results of the renowned Stern–Gerlach experiment. FOUR LAWS OF THERMODYNAMICS The four laws of thermodynamics define fundamental physical quantities (temperature, energy, and entropy) that characterize thermodynamic systems at thermal equilibrium. The laws describe how these quantities behave under various circumstances, and forbid certain phenomena (such as perpetual motion). The four laws of thermodynamics are:[1][2][3][4][5] Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law helps define the notion of temperature. First law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind are impossible. Second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind are impossible. Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero.[2] With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the logarithm of the product of the quantum ground states. There have been suggestions of additional laws, but none of them achieves the generality of the four accepted laws, and they are not mentioned in standard textbooks.[1][2][3][4][6][7] 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. They are *Square one: Gauss' law *Square two: Gauss' law for magnetism *Square three: Maxwell-Farraday equation *Square four: Ampere's circuital law. Maxwell's four equations describe the electric and magnetic fields arising from distributions of electric charges and currents, and how those fields change in time. They were the mathematical distillation of decades of experimental observations of the electric and magnetic effects of charges and currents, plus the profound intuition of Michael Faraday. Maxwell's own contribution to these equations is just the last term of the last equation -- but the addition of that term had dramatic consequences. It made evident for the first time that varying electric and magnetic fields could feed off each other -- these fields could propagate indefinitely through space, far from the varying charges and currents where they originated. Previously these fields had been envisioned as tethered to the charges and currents giving rise to them. Maxwell's new term (called the displacement current) freed them to move through space in a self-sustaining fashion, and even predicted their velocity -- it was the velocity of light! Here are the equations: Gauss' Law for electric fields: (The integral of the outgoing electric field over an area enclosing a volume equals the total charge inside, in appropriate units.) The corresponding formula for magnetic fields: (No magnetic charge exists: no "monopoles".) Faraday's Law of Magnetic Induction: The first term is integrated round a closed line, usually a wire, and gives the total voltage change around the circuit, which is generated by a varying magnetic field threading through the circuit. Ampere's Law plus Maxwell's displacement current: This gives the total magnetic force around a circuit in terms of the current through the circuit, plus any varying electric field through the circuit (that's the "displacement current"). THE FOURTH STATE OF MATTER IS DIFFERENT In physics, a state of matter is one of the distinct forms that matter takes on. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. The four fundamental states Solid A crystalline solid: atomic resolution image of strontium titanate. Brighter atoms are Sr and darker ones are Ti. Main article: Solid In a solid the particles (ions, atoms or molecules) are closely packed together. The forces between particles are strong so that the particles cannot move freely but can only vibrate. As a result, a solid has a stable, definite shape, and a definite volume. Solids can only change their shape by force, as when broken or cut. In crystalline solids, the particles (atoms, molecules, or ions) are packed in a regularly ordered, repeating pattern. There are various different crystal structures, and the same substance can have more than one structure (or solid phase). For example, iron has a body-centred cubic structure at temperatures below 912 °C, and a face-centred cubic structure between 912 and 1394 °C. Ice has fifteen known crystal structures, or fifteen solid phases, which exist at various temperatures and pressures.[2] Glasses and other non-crystalline, amorphous solids without long-range order are not thermal equilibrium ground states; therefore they are described below as nonclassical states of matter. Solids can be transformed into liquids by melting, and liquids can be transformed into solids by freezing. Solids can also change directly into gases through the process of sublimation, and gases can likewise change directly into solids through deposition. Liquid Structure of a classical monatomic liquid. Atoms have many nearest neighbors in contact, yet no long-range order is present. Main article: Liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. The volume is definite if the temperature and pressure are constant. When a solid is heated above its melting point, it becomes liquid, given that the pressure is higher than the triple point of the substance. Intermolecular (or interatomic or interionic) forces are still important, but the molecules have enough energy to move relative to each other and the structure is mobile. This means that the shape of a liquid is not definite but is determined by its container. The volume is usually greater than that of the corresponding solid, the best known exception being water, H2O. The highest temperature at which a given liquid can exist is its critical temperature.[3] Gas The spaces between gas molecules are very big. Gas molecules have very weak or no bonds at all. The molecules in "gas" can move freely and fast. Main article: Gas A gas is a compressible fluid. Not only will a gas conform to the shape of its container but it will also expand to fill the container. In a gas, the molecules have enough kinetic energy so that the effect of intermolecular forces is small (or zero for an ideal gas), and the typical distance between neighboring molecules is much greater than the molecular size. A gas has no definite shape or volume, but occupies the entire container in which it is confined. A liquid may be converted to a gas by heating at constant pressure to the boiling point, or else by reducing the pressure at constant temperature. At temperatures below its critical temperature, a gas is also called a vapor, and can be liquefied by compression alone without cooling. A vapor can exist in equilibrium with a liquid (or solid), in which case the gas pressure equals the vapor pressure of the liquid (or solid). A supercritical fluid (SCF) is a gas whose temperature and pressure are above the critical temperature and critical pressure respectively. In this state, the distinction between liquid and gas disappears. A supercritical fluid has the physical properties of a gas, but its high density confers solvent properties in some cases, which leads to useful applications. For example, supercritical carbon dioxide is used to extract caffeine in the manufacture of decaffeinated coffee.[4] Plasma In a plasma, electrons are ripped away from their nuclei, forming an electron "sea". This gives it the ability to conduct electricity. Main article: Plasma (physics) Like a gas, plasma does not have definite shape or volume. Unlike gases, plasmas are electrically conductive, produce magnetic fields and electric currents, and respond strongly to electromagnetic forces. Positively charged nuclei swim in a "sea" of freely-moving disassociated electrons, similar to the way such charges exist in conductive metal. In fact it is this electron "sea" that allows matter in the plasma state to conduct electricity. The plasma state is often misunderstood, but it is actually quite common on Earth, and the majority of people observe it on a regular basis without even realizing it. Lightning, electric sparks, fluorescent lights, neon lights, plasma televisions, some types of flame and the stars are all examples of illuminated matter in the plasma state. A gas is usually converted to a plasma in one of two ways, either from a huge voltage difference between two points, or by exposing it to extremely high temperatures. Heating matter to high temperatures causes electrons to leave the atoms, resulting in the presence of free electrons. At very high temperatures, such as those present in stars, it is assumed that essentially all electrons are "free", and that a very high-energy plasma is essentially bare nuclei swimming in a sea of electrons. In 1924, Albert Einstein and Satyendra Nath Bose predicted the "Bose–Einstein condensate" (BEC), sometimes referred to as the fifth state of matter. In a BEC, matter stops behaving as independent particles, and collapses into a single quantum state that can be described with a single, uniform wavefunction. THE FIFTH IS ALWAYS ULTRA TRANSCENDNET- FOURTH TRANSCENDENT AKG DMS Tetrad Wireless Microphone System Hardware > Microphone Published April 2015 By Mike Crofts AKG DMS Tetrad AKG’s new 2.4GHz wireless system is easy to use, affordable, and incorporates some crafty anti-dropout technology. When they first appeared, wireless mics operating in the 2.4GHz band caused lots of interest, offering licence-free operation anywhere in the world, thanks to a digital-based technology incorporating encryption, status and control-data transfer — and, of course, top-quality audio. The first such ‘affordable’ system from AKG was their innovative DMS70 Quattro, which I tried, very much liked, and subsequently purchased along with a set of four AKG D5-based handheld mics. The Quattro was one of the most convenient, high-quality wireless mic systems I’d encountered at such a reasonable price. I’ve been happy with it ever since and have used it many times on a variety of live-sound jobs. The original Quattro system was, however, potentially vulnerable to interference from other nearby devices operating on the same band (such as mobile phones and Bluetooth equipment), but the receiver incorporated technology which — in my experience — was effective in reducing such interference. The one issue which did cause problems under some circumstances was the occurrence of brief signal dropouts, although in my own experience most of these were not real dropouts resulting in a loss of audio. On a few occasions I had singers telling me — both during and after a live set — that their mic had briefly stopped working, which I always found puzzling as I hadn’t noticed anything amiss. On one occasion I remember a singer saying (live over the PA) that the mic wasn’t working but all the time I could see the signal on my meters and clearly hear it on the front-of-house speakers. After some hours testing and trying to replicate the problem I discovered that, from time to time, the green LED indicator on the mic body would go off but without interrupting transmission, leading the user to assume that the mic itself was off. Only once did I notice any significant dropout, and that was during a product launch in a retail environment with all sorts of nearby devices (phones, tills, etc) of exactly the sort warned about in the manual! Now AKG have introduced the Tetrad system, which has the same basic functionality as the previous version. It’s a four-channel, fully automatic 2.4GHz system with dynamic frequency selection (ie. it switches frequencies automatically as necessary), and it uses the excellent D5 or slightly lower-specification P5 capsules. There are some physical changes to the receiver, as well as the inclusion of an anti-dropout technology called ‘DroCon’, so-called for ‘dropout concealment’. This uses extrapolation and advanced filtering methods to rebuild sections of missing signal and effectively conceal clicks caused by dropouts. What’s really impressive is how quickly this complex processing is implemented, requiring only two milliseconds to process all four received channels. With all that technology working in conjunction with automatic live channel switching, automatic detection and re-sending of lost signal blocks, plus standard twin-antenna diversity, AKG appear to have left no avenue unexplored in pursuit of reliable transmission. Building Blocks The system components, which are available as preconfigured sets and also as individual items, are the stationary DSR Tetrad four-channel receiver, a beltpack-style transmitter for use with lapel/headworn mics or instruments, and two variants of a handheld microphone transmitter. The ‘Vocal’ sets each come boxed with a DSR four-channel receiver and a single transmitter (either the P5 or D5 handheld mics), while the Performer set dispenses with the handheld mic but includes a DPT pocket transmitter and a C111 ear-hook mic. The already reasonable price then looks even more attractive should you wish to add more mics, as you only need to purchase extra transmitter units to work with your existing multi-channel receiver, so you can grow the system as requirements dictate or finances allow. All of the component parts are readily available from AKG retailers. At the heart of any Tetrad system is the DSR four-channel diversity receiver; it is built into a very neat casing that can be used free-standing (in which case it is slightly under 12-inches wide) or rackmounted using the included cast rack ears and fixings. The simple black look is appealing and understated in what you might call classic AKG style, with an illuminated power switch and four sets of controls consisting only of an assignment button and rotary output level control for each channel, with associated RF status and overload LEDs. The detachable antennae mount on the rear of the receiver by threaded coaxial connectors that appear to be of good quality and which screw on easily. If the receiver is to be rackmounted, the rack ears are fixed to each side and also serve as mounting points for the included antenna extensions so that the antennae can be front-mounted. I think this is a significant improvement over the old Quattro design, which used non-detachable front-panel antennae. The DPT beltpack transmitter comes with an AKG C111 ear-hook vocal microphone. The DPT beltpack transmitter comes with an AKG C111 ear-hook vocal microphone. At the rear of the receiver are the balanced XLR outputs for each channel, and also a local combined output that carries a mono mix of all channels, as controlled by the front-panel level settings. The mix output could be particularly useful in a simple application where no other mixer is required and the mix output is fed straight to a powered speaker, or where the number of stage feeds or mixer inputs has to be limited. As previously mentioned, the 2.4GHz area is a pretty crowded place, and in anticipation of a less-than-ideal operating environment AKG have provided a three-stage anti-interference control that can minimise the effect of nearby devices. Although a very slight delay is involved it’s not enough to affect a live performance, and none of my users noticed when I switched this function in. There will always be a concern around overall system processing time, especially when a digital mixer is in the path, but the technology seems to be delivering acceptably small delay times that are perfectly manageable in all but the most critical applications. Taking The Mic The two DHT handheld microphone models are outwardly similar and share substantially the same transmitter electronics and user controls. They are both fitted with dynamic supercardioid capsules but the D5 has a higher-performance version taken straight from the popular and successful D5 stage mic; the P5 version is a lower-cost option, with a somewhat reduced frequency response of 70Hz to 16kHz (the D5’s is 70Hz — 20kHz), and a slightly smaller dynamic range. My review set was blessed with the D5 variant, which is the one I’d personally favour as I use a lot of wired D5 mics in my own rig; also my own DMS Quattro system includes four D5 radio mics, so all my standard go-to dynamics have exactly the same performance. The Tetrad DHT wireless mics feel nicely balanced and are comfortable to hold; weight-wise I think they seem lighter than they look and have a high-quality finish and feel. I’ve never had anything but positive comments from performers who’ve used them, and I even had one client specifically ask for D5 mics as his band were making a live video and their manager just thought they “looked really cool”! In operation the Tetrad mics are easy to set up; the lower half of the casing unscrews and slides off to reveal the battery compartment and an inner body cylinder which houses the transmitter and antenna sections. As channel setting involves pairing the mic with an available receiver channel there are no frequency selector controls on or inside the mic, there’s just a pairing button and a ‘Hi/Lo’ sensitivity switch that varies the maximum input SPL by 13dB with an absolute maximum (in the low position) of 142dB. The DHT transmitter uses two AA batteries, and either alkaline (six hours use) or NiMH (seven hours) are suitable. I didn’t have an opportunity to run a set of batteries right down but I did two full concerts — a total of around five hours — on one set of alkalines (the black and gold ones), and normally I’d use a fresh or recharged set for every performance, so no worries there. I found that removing the first one can be a bit fiddly as there’s nothing to get hold of — it’s a fingernail-on-one-end job — but the second one can be simply pushed out from the other side, and they stay firmly in place during normal use. Pocket To Me The Tetrad DPT pocket transmitter has exactly the same function as the handheld versions, but an external mic or other source must be connected via a mini-XLR input connector, which supplies 4V via pin 3 for devices that require a power source, such as the included C111 mic. If using non-AKG microphones it would be advisable to check their output wiring before connecting to this input. Inside the battery compartment is a rotary sensitivity control which requires a small screwdriver to be adjusted — happily there is one tucked away inside the lid, which is a nice touch. Pairing with the receiver is accomplished in exactly the same way as for the handheld mics, and the indications from the LED are also the same. Setting Up Although these days we expect ‘plug and play’ operation from most of our audio equipment, wireless mics (especially when used in multiples) can still be tricky unless they incorporate automatic channel-seeking and Tx/Rx pairing functions, which are generally only found on more upmarket models. The Tetrad system really is about as easy as it gets — the single supplied transmitter is preconfigured to operate on channel one of the receiver, so as soon as they are both switched on they will just work, right out of the box. If additional transmitters are involved, or if for some reason you wanted to use your single mic on a different receiver channel, then allocating channels is quick and straightforward. Each transmitter and each receiver channel has a ‘connect’ button, and a quick press of either will result in the current paired transmitter or receiver channel LED to flash for a few seconds so that you can quickly identify the Tx/Rx pairs. To assign, say, a handheld mic to a particular receiver channel, press and hold one of the receiver channel connect buttons for more than a second. When it flashes, simply press the connect button on a transmitter and the two are then assigned to each other, using an available clean RF channel. The neat thing about this process is that it can be initiated from either the receiver or the transmitter, as the digital information flow is two-way. In the interests of conserving battery life, the transmitters will also switch off (after about two minutes) if the receiver is switched off, so after the soundcheck you can just power off the receiver and the mics will turn off all by themselves — and will of course need to be locally switched on again, which is by far the safest option for live sound. Once all is set up, the system will fire up using all the same channel allocations every time, and will automatically switch frequencies to avoid interference. Us mere mortals don’t need to know about this, so there’s nothing to indicate that this or any of the other clever under-the-hood business is going on — we can just get on with the show. As with any radio equipment, establishing a direct line-of-sight path between transmitters and receiver is always the best option, as is putting the minimum distance between them; to this end an ideal position for the receiver is at the front or side of the live stage, where the diversity technology should cope with brief obstacles in the RF path. Going The Distance I used the DMS Tetrad on three live shows and let various people use it in the rehearsal studio. Everyone who tried it liked both the sound quality and the feel of the handheld mic itself; I used the sensitivity switch in the ‘high’ position all the time and didn’t encounter any situations where the mic struggled to handle strong vocals. I experimented with transmit distances, and achieved good stable results at 30m in the open air (the same length as my Cat 5 cable on that occasion, and the manual says that the AKG system is specified to 50m), and front-to-back in two large concert halls with line of sight. I had no problems with dropouts or signal loss when I used the mic and receiver either side of a solid wall, and at home I managed to get three rooms and part of a corridor away (approximately 20 metres) before I lost clear audio. I’d have more confidence in using the DMS Tetrad in a less-than-ideal environment than with my old Quattro system, simply because it incorporates the DroCon technology and the older system doesn’t, but having said that I still like my old setup and will continue to use it. The main limitation of the DMS Tetrad is probably the channel count — you can only use two sets (that’s eight channels) together, but if you’re already the lucky owner of a DMS70 Quattro set (or even two) then, because they’re not cross-compatible, I reckon you could run 16 digital channels using the two systems together, and have tremendous fun. Alternatives There are various systems and components available which make direct comparison difficult, but look at the 2.4GHz product lines from all major manufacturers, including but not limited to Audio-Technica, Line 6, Shure and Sony, as well as Sennheiser’s 1.8GHz options. THE DYNAMIC OF THREE AND FOUR- FOUR IS ALWAYS DIFFERENT GUIDING THE SWITCH FROM TRIANGLE TESTING TO TETRAD TESTING Authors JOHN M. ENNIS First published: 7 August 2012Full publication history DOI: 10.1111/j.1745-459X.2012.00386.xView/save citation Cited by: 24 articlesCitation tools TEL: 804-675-2980; FAX: 904-675-2983; EMAIL: Abstract ABSTRACT Tetrad testing is theoretically more powerful than Triangle testing, yet the addition of a fourth stimulus raises questions – it is possible that the addition of a fourth stimulus places such an additional demand on subjects that the theoretical advantage of the Tetrad test is lost. In this paper, we provide a guideline to compare results of Tetrad and Triangle. Specifically, it is roughly correct to say that as long as the effect sizes do not drop by more than one third for the same stimuli, then the Tetrad test remains more powerful than the Triangle test. We explain this guideline in terms of perceptual noise, illustrate its use in several examples and discuss the statistical considerations that accompany its use. To assist with statistical evaluation, we provide a table for finding the variance in the Tetrad-based measurement of the effect size. Finally, we show how the Thurstonian framework helps us to improve discrimination testing efficiency even when we do not seek additional power. PRACTICAL APPLICATIONS Discrimination testing programs based on Triangle testing might be made more sensitive or more efficient by the use of Tetrad testing. This paper develops a guideline to assist sensory scientists who are considering a switch from the Triangle test to the Tetrad test. The paper displays the use of this guideline in several examples, discusses the relevant statistical considerations, provides a helpful table and demonstrates how Thurstonian theory can be used to improve efficiency even in an already successful discrimination testing program. The Cosmology of Tetradic Theory of Gravitation H. A. Alhendi, E. I. Lashin, G. L. Nashed (Submitted on 26 Feb 2007) We consider a special class of the tetrad theory of gravitation which can be considered as a viable alternative gravitational theories. We investigate cosmological models based on those theories by examining the possibility of fitting the recent astronomical measurement of supernova Ia magnitude versus shift. Our investigations result in a reasonable fit for the supernova data without introducing a cosmological constant. Thus, cosmological models based on tetradic theory of gravitation can provide alternatives to dark energy models. HINDU ASTROLOGY IS LITERALLY BASED AROUND QUADRANTS HINDU ASTROLOGY In general houses are classified into four categories: Kendra: the angular houses, that is the first, fourth, seventh and tenth houses. (kendra, from Greek κἐντρα,[38] also describes the relationship between any houses or grahas which are about 90 degrees apart.) These are very strong houses for grahas to occupy. Trikona: the houses forming a triangle within the chart with the first house, about 120 degrees apart from one another, that is the first, fifth and ninth. These are the most auspicious houses. (From Greek τρἰγωνα.[38]) Dusthāna: the less fortunate houses which tend to rule unhappy areas. These houses make no clear geometric connection to the Lagna. Dusthanas include the sixth, eighth and twelfth houses. Upachaya: "growth" or "remedial" houses, where malefic planets tend to improve, include the third, sixth, tenth and eleventh houses. The triplicities of seasonal elements in ancient astrology were the following four: Spring - Aries - Taurus - Gemini Summer - Cancer - Leo - Virgo Autumn - Libra - Scorpio - Sagittarius Winter - Capricorn - Aquarius - Pisces Classical elements Four Classical Elements; this classic diagram has two squares on top of each other, with the corners of one being the classical elements, and the corners of the other being the properties In traditional Western astrology there are four triplicities based on the classical elements. Beginning with the first sign Aries which is a Fire sign, the next in line Taurus is Earth, then to Gemini which is Air, and finally to Cancer which is Water -- in Western astrology the sequence is always Fire, Earth, Air, & Water in that exact order. This cycle continues on twice more and ends with the twelfth and final astrological sign, Pisces. The elemental rulerships for the twelve astrological signs of the zodiac (according to Marcus Manilius) are summarized as follows: Fire — Aries, Leo, Sagittarius - hot, dry Earth — Taurus, Virgo, Capricorn - cold, dry Air — Gemini, Libra, Aquarius - hot, wet Water — Cancer, Scorpio, Pisces - cold, wet Triplicty rulerships (using the "Dorothean system"[2]) are as follows: Triplicity Day Ruler Night Ruler Participating Ruler Fire (Aries, Leo, Sagittarius): Sun Jupiter Saturn Earth (Taurus, Virgo, Capricorn): Venus Moon Mars Air (Gemini, Libra, Aquarius): Saturn Mercury Jupiter Water (Cancer, Scorpio, Pisces): Venus Mars TETRA IS FOUR Tetrabiblos (Τετράβιβλος) 'four books', also known in Greek as Apotelesmatiká (Ἀποτελεσματικά) "Effects", and in Latin as Quadripartitum "Four Parts", is a text on the philosophy and practice of astrology, written in the 2nd century AD by the Alexandrian scholar Claudius Ptolemy (c. AD 90–c. AD 168). Ptolemy is referred to as "the most famous of Greek astrologers"[2] and "a pro-astrological authority of the highest magnitude".[3] As a source of reference his Tetrabiblos is described as having "enjoyed almost the authority of a Bible among the astrological writers of a thousand years or more" The four books reflect the quadrant model pattern Compiled in Alexandria in the 2nd century, the work gathered commentaries about it from its first publication.[2] It was translated into Arabic in the 9th century, and is described as "by far the most influential source of medieval Islamic astrology".[5] Square 1:Book I: principles and techniques. The first square is gibing rules. The first square is homeostatic like the second. It is mental and gibes his philosophy. The first square is mental Square 2:Book II: Mundane astrology Book II presents Ptolemy's treatise on mundane astrology. This offers a comprehensive review of ethnic stereotypes, eclipses, significations of comets and seasonal lunations, as used in the prediction of national economics, wars, epidemics, natural disasters and weather patterns. The second square is always normal And homeostasis. He describes gentiv stereotypes of people In different climates. The second quadrant is belonging and belonging and belief is related to genetics and your group Square 3:Book III: Individual horoscopes (genetic influences and predispositions). Recall the third quadrant is thinking and related to the individual Square 4:Book IV: Individual horoscopes (external accidentals). The fourth square is the individual as well but is always transcendent THE FOURTH IS ALWAYS DIFFERENT “Codon” is now a four letter word By Iddo on February 17th, 2010 ResearchBlogging.org As part of the process of manufacturing a new car, the designers will take the blueprints to the factory floor. There they will set up an experimental assembly line, tinkering with the manufacturing process of the prototype until it is ready for mass-production. Can we do the same with the machinery of life — the assembly of proteins? Can we set up an alternative assembly line for a new protein prototype — and then actually set up a working assembly line for the whole new protein? A proof-of-concept has been published this week in Nature by Jason Chin’s group at the Medical Research Council Laboratory of Molecular Biology, Cambridge UK. If there is a single common denominator to all life, it is the genetic code. All life is built around DNA encoding information for proteins nucleotide triplets or codons. Since there are four types of nucleotides (A,T,G,C) that are read in words of thee, there are 43 = 64 possible codons: more than enough to encode for the 22 amino acids that make up proteins. There is nothing more basic and fundamental to life on Earth than the three-letter based genetic code. Until now. Chin’s group has created a four-nucleotide codon system. It is not that the DNA is different: it is the way the cellular machinery decoding RNA transcripts interprets the nucleotide sequence. Ribosomes –large RNA and protein complexes which are the platform upon which messenger RNA is read and decoded — are set to serve up messenger RNA three nucleotides at a time. (Messenger RNA or mRNA is a transcript of the DNA which is carried to the ribosome.) Transfer RNA or tRNA is a short RNA molecule that shuttles the proper amino acid to the ribosome, but will only attach if the proper codon is served up by the ribosome. The whole protein synthesis “assembly line” looks something like this: Protein synthesis. Credit: Wikimedia Commons. To change the interpretation of the genetic code from three lettered words to four, Chin and his colleagues had to make new ribosomes, and new tRNAs. To create these new ribosomes, they designed orthogonal ribosomes, or o-ribosomes. O-ribosomes are genes inserted to produce extra ribosomes that operate in the cell alongside the regular ribosomes. The cell functions because it has the regular ribosomes to maintain its viability. The ribosomal RNA in the o-ribosomes is free to be mutated to create new unnatural traits: in this case, the ability to serve as a platform read four-letter codons. They selected for Escherichia coli bacterial cells that expressed a o-ribosomes which translated a four-letter codon in a gene, which would otherwise go untranslated by the regular ribosome. The gene gives the bacterial cells resistance to the antibiotic chloramphenicol. So cells that survive a dosage of chloramphenicol are those which have functioning o-ribosomes, as they have the chloramphenicol resistance gene that is being translated by the o-ribosomes. They also needed to create new tRNAs that have an four-nucleotide anticodon (the part that complementarily binds to the messenger RNA — see figure above.) So the surviving E. coli cells have a population of working o-ribosomes, regular ribosomes, modified tRNA (with a four-letter anticodon) and regular tRNA. Then they took their work a step further. Each three-letter tRNA carries a specific amino-acid, depending on its anticodon. Thus tRNAAAG will always have a phenylalanine attached, because CTT (the complement of AAG on the messenger RNA) codes for phenylalanine. If you start messing with that, the translation machinery will produce non-functional proteins, which will probably kill the cells pretty quick. But with the orthogonal 4-letter code machinery, that is not really a problem: the orthogonal machinery operates alongside the normal one. Also, there are no amino acids naturally assigned to any four letter code, because this code does not appear in nature in the first place! So Chin’s lab assigned an unnatural amino acids to a four-letter code. The non-naturally occurring p-azido-l-phenylalanine amino acid was assigned to tRNAUCCU. They then showed that the whole alternative translational machinery worked by synthesizing a mutant of the protein calmodulin which used this amino-acid in its structure. Why do it? Well, personally I don’t see the need for justification: just being able to do it is so cool! But seriously: think of the ability to design proteins from up to 44=256 different amino acids other than the 22 we have now. The possibilities of tinkering with existing proteins using this orthogonal, four-letter based machinery are huge. The other benefit of this orthogonal synthesis setup is the ability to control this orthogonal translational machinery: because it does not use the three-letter vocabulary, this orthogonal machinery would be much easier to manipulate, tinker with and switch on and off without getting in the way of regular cellular translational machinery. The analogy to a car assembly line breaks here. It is as if two different models are being assembled on the same line just by using different robots. The better analogy is for a program source code to be read by two different compilers, each producing a different program. Awesome. SWASTIKA SHAPE BLADE STRUCTURE Device for processing molecular clusters of liquid to nano-scale US 20100202247 A1 ABSTRACT A device for processing molecular clusters of a liquid to nano-scale is provided and includes a stirring chamber having a hexagonal (or octagonal) column space; a plurality of first stirring modules, each of which has at least one first stirring blade having a left-handed swastika shape (or right-handed swastika shape) for pushing a liquid to flow; and a plurality of second stirring modules, each of which has at least one second stirring blade having a right-handed swastika shape (or left-handed swastika shape) for pushing the liquid to reversely flow. Thus, molecular clusters of the liquid are collided with each other under a condition with high temperature, high pressure and high stirring speed, until the particle diameter of the molecular clusters is reduced to a nano-scale. Energy from Swastika-Shaped Rotors Michael Edward McCulloch University of Plymouth, Plymouth, PL4 8AA, UK E-mail: It is suggested here that a swastika-shaped rotor exposed to waves will rotate in the di- rection its arms are pointing (towards the arm-tips) due to a sheltering effect. A formula is derived to predict the motion obtainable from swastika rotors of different sizes given the ocean wave height and phase speed and it is suggested that the rotor could provide a new, simpler method of wave energy generation. It is also proposed that the swastika rotor could generate energy on a smaller scale from sound waves and Brownian motion, and potentially the zero point field. 1 Introduction With the recent awareness of the environmental damage caused by fossil fuels, there is a need to find renewable sources of energy. There are many possible sources of energy: sunlight, the wind, ocean tides and also the energy stored in ocean surface waves, and other types of waves. Ocean waves are particularly relevent for the island of Great Britain. It has been estimated that between 7 and 10 GW of energy might be extractable from the waves in UK waters by Wave Energy Converters (WECs), compared with the UK peak demand es- timated at 65 GW, so that 15% of UK peak demand could be met by wave power [1]. One of the first viable techniques for the generation of ocean wave power was Salter’s Duck which rotated along a horizontal axis under the undulation of waves and generated energy using dynamos. The result was an 81% conversion of wave energy into power [2], but this method extracts energy from waves only in one direction. Another problem with Salter’s duck and other wave en- ergy converters is that they have many moving parts which can degrade with time. The new wave energy generation method proposed here is far simpler in structure and has only one moving part: the rotor. It can also be deployed far from the coast, and, as discussed later in the paper, is applicable to all kinds of waves or fluctuations and not just ocean waves, maybe also the zero point field. Part of the inspiration for this paper was the proposal of Boersma [3] that two ships at sea will produce a wave shadow zone between them, so that more waves will hit the ships from outside than from between them and so the ships will tend to move together. This is an analogy to the well-known Casimir effect in quantum physics [4] which involves the suppression of the zero point field between two parallel conducting plates which are then forced together. The Casimir force has been measured [5]. The effect due to ocean waves is predicted to be small, but has recently also been measured by [6]. 2 Method & results This proposal uses a swastika, or Greek letter Chi, see Fig- ure 1. The idea is that if waves arrive from all directions, Fig. 1: Schematic showing the swastika rotor, the surrounding wave field (dashed lines) and the resulting forces (arrows). more waves hit the outer sides of the swastika’s arms, then hit the sheltered inner-facing sides of the arms, producing a torque that rotates the swastika about its axis. To explain this more clearly and estimate the force that can be extracted from this shape we can consider three square areas that interact with the southeast arm: areas A, B and C as shown in Fig. 1. The assumption is that the areas A and B are sheltered zones rather like harbours and that only certain waves can exist between the walls, those with a wavelength that has nodes at the walls. If we then assume that the par- ticular wavelength in the ocean does not fit, then there will be fewer waves in areas A and B, but there will of course be waves in area C since there is no closed boundary, it is open to the ocean. The maximum force obtainable from this shape can be found by looking at the net force on the southeast arm of the swastika and multiplying it by four. For the inner half of the southeast arm, between areas A and B, there is no net force since there are either no waves, or more likely the same intensity of waves, on either side, but for the outer half of the arm between B and C there will be a force on the arm pushing it westward because there are waves on the open east side, but not on the enclosed west side. According to [7, 8] the impact pressure or slamming force (P) due to wave impacts is P= F =KρC2, (1) A M. E. McCulloch. Energy from Swastika-Shaped Rotors 139 Volume 11 (2015) PROGRESS IN PHYSICS Issue 2 (April) where A is the area of impact, K is an empirical constant be- tween 3 and 10, ρ is the water density and C is the wave phase speed. For the southeast arm of the swastika this is F = KAρC2 (2) and A is the area hit by the waves which is the half-length of the arm (D) times the wave height h F = KDhρC2. (3) The force and resulting rotation will be clockwise, to- wards the arm-tips. Since F = ma, then the acceleration of atoms or molecules. A sheltering process similar to that de- scribed in this paper, might explain their results since, due to sheltering, these boomerang particles would see fewer im- pacts from atoms in the concave gap between their arms and more impacts on their convex side, so they should move to- wards their concave side, or towards their arm-tips, just as observed. A light-driven swastika-shaped rotor on the nanoscale has already been demonstrated. It does not utilise the zero point field, but is driven by an applied beam of light and works in a different manner since the light photons interact with the electrons in the conducting shape [10]. 4 Conclusions It is predicted that a rotor in the shape of a swastika will rotate in the direction its arms are pointing, i.e.: towards the arm- tips, in the presence of isotropic waves, due to the sheltering effect of the arms. It is proposed that such a rotor can be used to convert wave energy to electricity by using its axle to drive a dynamo. Its advantage over existing wave energy generating devices is its simplicity, its response to isotropic waves and its (reversed) response to surface currents. It now needs to be tested exper- imentally. The swastika shape could also be used on smaller scales to generate energy from sound waves or Brownian motion: for example it may explain the observed motion of Boomerang- shaped particles. It may be possible to use nanoscale swastika rotors to extract energy from the hitherto untapped zero point field. Submitted on February 1, 2015 / Accepted on February 4, 2015 References the arm will be KDhρC2 a=m. (4) Equation 4 predicts the maximum acceleration obtainable from the swastika, neglecting friction, if its dimensions are such that it cancels the waves in areas A and B completely. The acceleration increases as a function of the wave height (h), length of the arms (D) and the phase speed (C). The acceleration, of course, decreases as the mass increases (m). The effect missing here is friction, which will slow the rota- tional acceleration as soon as it begins. 3 Discussion This rotor is only a proposal at this stage. It requires testing in a wave tank big enough so that interactions between the swastika and the wave tank’s walls are reduced and also so that the waves in area C are not damped. The waves should be a similar wavelength to the width of the arms of the swastika or shorter. Longer waves than this will not be able to resolve the shape of the arms so there will be no rotation. Eqs. 3 and 4 imply that to get the maximum rotation, the test should use a light rotor with arms projecting enough from the water to intercept the waves, subject to high waves with a large phase speed. Since the effect may be subtle, care will have to be taken to reduce the effects of residual rotational flows. The swastika rotor has advantages over current wave en- ergy devices in that it is simple and has only one moving part: the axle, it does not require wave impacts from any particu- lar direction and can work just as well with isotropic random waves, and it will also rotate if a surface ocean current exists, but the opposite way, since it is then similar in design to an anenometer. One intriguing possibility is that the rotation of the swas- tika shape in a wave field could also be applied at a much smaller scale. A smaller-scale swastika may be spun by sound waves, Brownian motion or even on the nanoscale by the zero-point field allowing perhaps that source of energy to be tapped for the first time. On the Brownian scale [9] have shown that boomerang- shaped colloidal particles move towards their concave sides when subjected to Brownian motion: random collisions with 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Drew B., Plummer A.R., Sahinkaya M.N. A review of wave energy converter technology. Proc. Inst. Mechanical Engineers, Part A: Jour- nal of Power and Energy, 2009, v. 223, no. 8, 887–902. FalnesJ.Areviewofwave-energyextraction.MarineStructures,2007, v. 20(4), 185–201. Boersma S.L. A maritime analogy of the Casimir effect. Am. J. Phys., 1996, v. 64(5). Casimir H.B.G. On the attraction between two perfectly conducting plates. Proc. Kon. Nederland Akad. Wetensch., 1948, v. B51, 793. Lamoreaux S.K. Demonstration of the Casimir force in the 0.6 to 6 μm range. Phys. Rev. Lett., 1997, v. 78, 5–8. Denardo B.C., Puda J.J. and Larazza A. A water wave analog of the Casimir effect. Am. J. Phys., 2009, v. 77(12). Bea R.G., Xu T., Stear J., Ramos R. Wave forces on decks of off- shore platforms. Journal of Waterway, Coastal and Ocean Engineering, May/June 1999, 136–144. Chen E.S and Melville W.K. Deep-water plunging wave pressure on a vertical plane wall. Proc. R. Soc. Lond., 1988, v. A417, 95–131. Chakrabarty A., Konya A., Wang F., Selinger J.V., Sun K., Wie Q.- H. Brownian motion of boomerang colloidal particles. Phys. Rev. Lett., 2013, v. 111, 160603. LiuM.,ZentgrafT.,LiuY.,BartalG.,ZhangX.Light-drivennanoscale plasmonic motors. Nature Nanotechnology, 2010, v. 5, 570–573. 140 M. E. McCulloch. Energy from Swastika-Shaped Rotors GAMMODIAN IS ANOTHER WAY TO SAY SWASTIKA- THEY MADE Gammadions of gold Malcolm Kadodwala and colleagues produced their super-twisted light by shining ordinary light through a specially designed metamaterial made up of chiral gold nanoparticles. The metamaterial comprises left- or right-handed gold gammadions 400 nm long and 100 nm thick deposited on a glass substrate and arranged in a square lattice with a periodicity of 800 nm. The light produced allowed the team to detect certain proteins at picogram levels, a sensitivity a million times greater than that possible with current chiroptical techniques. "We are very excited about the research," says Kadodwala. "This light, which does not occur naturally, allows us to detect biological molecules at unprecedented low concentrations." The light seems to be particularly effective at detecting amyloid proteins – insoluble molecules that stick together to form plaques. These plaques are thought be responsible for certain neurodegenerative diseases. "In fact, super-twisted light is highly sensitive to the secondary, or beta, structure of a protein," Kadodwala told physicsworld.com. "Beta structure is found in the coat proteins of certain viruses and in amyloid fibrils." It would be useful to provide a definition of "gammadion", since it's not a word in common use. The cartoon figure makes it look like a "swastika" shape formed from four 90-degree circular arcs. Wikipedia redirects to their article on swastika, which says that the latter Sanskrit term replaced "gammadion" in English around 1871. Was the archaic form used here because of the political connotations? It would be nice to have a more quantitative explanation in the article of "super-twisted" than just "twisted much tighter". Does it mean that there is more than one rotation of the electric field per frequency cycle? If so, is it integral? Is there a phase relationship between the chiral rotation and oscillations, or is it arbitrary? Merk Diezle shared a link. Sep 03, 2016 11:11pm HarmonyAngels - Physical Science harmonyangels.com http://www.harmonyangels.com/Physical-Science.html this model of the four types quantum mechanics classical mechanics quantum field theory and relativistic mechancics based on the duality of fast and slow and atomic and planetary is in one of my books I'm a paragraph. Click here to add your own text and edit me. It's easy. https://en.wikipedia.org/wiki/Kardashev_scale THE FOURTH IS ALWAYS DIFFERENT- THE FOURTH IS ALWAYS DIFFERENT/TRANSCENDENT The Kardashev scale is a method of measuring a civilization's level of technological advancement, based on the amount of energy a civilization is able to use for communication.[1] The scale has three designated categories: A Type I civilization – also called planetary civilization – can use and store energy which reaches its planet from the neighboring star. A Type II civilization can harness the total energy of its planet's parent star (the most popular hypothetical concept being the Dyson sphere—a device which would encompass the entire star and transfer its energy to the planet(s)). A Type III civilization can control energy on the scale of its entire host galaxy.[2] Extensions to the original scale Many extensions and modifications to the Kardashev scale have been proposed. Type 4 Kardashev Rating: The most straight forward extension of the scale to even more hypothetical Type IV beings who can control or use the entire universe or Type V who control collections of universes. The power output of the visible universe is within a few orders of magnitude of 1045 W. Such a civilization approaches or surpasses the limits of speculation based on current scientific understanding, and may not be possible. Zoltán Galántai has argued that such a civilization could not be detected, as its activities would be indistinguishable from the workings of nature (there being nothing to compare them to).[26] Type 4 Kardashev-Kaku Ratings (Michio Kaku): In his book Parallel Worlds, Michio Kaku has discussed a Type IV civilization that could harness "extragalactic" energy sources such as dark energy.[27] 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 universe is made up of bubbles and different cosmic constants due to string theory. A level 2 multiverse is generally accepted. 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. These universes have different mathematical structures. FOUR LEVELS OF MULTIVERSE Max Tegmark's four levels Cosmologist Max Tegmark has provided a taxonomy of universes beyond the familiar observable universe. The four levels of Tegmark's classification are arranged such that subsequent levels can be understood to encompass and expand upon previous levels. They are briefly described below.[48][49] Level I: An extension of our Universe A prediction of chaotic inflation is the existence of an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions. Accordingly, an infinite universe will contain an infinite number of Hubble volumes, all having the same physical laws and physical constants. In regard to configurations such as the distribution of matter, almost all will differ from our Hubble volume. However, because there are infinitely many, far beyond the cosmological horizon, there will eventually be Hubble volumes with similar, and even identical, configurations. Tegmark estimates that an identical volume to ours should be about 1010115 meters away from us.[19] Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.[50] This follows directly from the cosmological principle, wherein it is assumed that our Hubble volume is not special or unique. Level II: Universes with different physical constants Bubble universes – every disk represents a bubble universe. Our universe is represented by one of the disks. Universe 1 to Universe 6 represent bubble universes. Five of them have different physical constants than our universe has. In the chaotic inflation theory, a variant of the cosmic inflation theory, the multiverse or space as a whole is stretching and will continue doing so forever,[51] but some regions of space stop stretching and form distinct bubbles (like gas pockets in a loaf of rising bread). Such bubbles are embryonic level I multiverses. Different bubbles may experience different spontaneous symmetry breaking, which results in different properties, such as different physical constants.[50] Level II also includes John Archibald Wheeler's oscillatory universe theory and Lee Smolin's fecund universes theory. Level III: Many-worlds interpretation of quantum mechanics Hugh Everett III's many-worlds interpretation (MWI) is one of several mainstream interpretations of quantum mechanics. In brief, one aspect of quantum mechanics is that certain observations cannot be predicted absolutely. Instead, there is a range of possible observations, each with a different probability. According to the MWI, each of these possible observations corresponds to a different universe. Suppose a six-sided die is thrown and that the result of the throw corresponds to a quantum mechanics observable. All six possible ways the die can fall correspond to six different universes. Tegmark argues that a Level III multiverse does not contain more possibilities in the Hubble volume than a Level I or Level II multiverse. In effect, all the different "worlds" created by "splits" in a Level III multiverse with the same physical constants can be found in some Hubble volume in a Level I multiverse. Tegmark writes that, "The only difference between Level I and Level III is where your doppelgängers reside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space." Similarly, all Level II bubble universes with different physical constants can, in effect, be found as "worlds" created by "splits" at the moment of spontaneous symmetry breaking in a Level III multiverse.[50] According to Yasunori Nomura,[26] Raphael Bousso, and Leonard Susskind,[24] this is because global spacetime appearing in the (eternally) inflating multiverse is a redundant concept. This implies that the multiverses of Levels I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds". Related to the many-worlds idea are Richard Feynman's multiple histories interpretation and H. Dieter Zeh's many-minds interpretation. Level IV: Ultimate ensemble The ultimate mathematical universe hypothesis is Tegmark's own hypothesis.[52] This level considers all universes to be equally real which can be described by different mathematical structures. Tegmark writes that: Abstract mathematics is so general that any Theory Of Everything (TOE) which is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of. He argues that this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be, say, a Level V."[19] Jürgen Schmidhuber, however, says that the set of mathematical structures is not even well-defined and that it admits only universe representations describable by constructive mathematics—that is, computer programs. Schmidhuber explicitly includes universe representations describable by non-halting programs whose output bits converge after finite time, although the convergence time itself may not be predictable by a halting program, due to the undecidability of the halting problem.[53][54][55] He also explicitly discusses the more restricted ensemble of quickly computable universes.[56] 3+1 IS THE QUADRANT MODEL The DGP model is a model of gravity proposed by Gia Dvali, Gregory Gabadadze, and Massimo Porrati in 2000.[1] The model is popular among some model builders, but has resisted being embedded into string theory. The model assumes the existence of a 4+1 dimensional Minkowski space, within which ordinary 3+1 dimensional Minkowski space is embedded. The model assumes an action consisting of two terms: One term is the usual Einstein–Hilbert action, which involves only the 4-D spacetime dimensions. The other term is the equivalent of the Einstein–Hilbert action, as extended to all 5 dimensions. FOUR CHERNOBYL REACTORS- FOURTH DIFFERENT The V.I. Lenin Nuclear Power Station (Russian: Чернобыльская АЭС им. В.И.Ленина) as it was known during the Soviet times, consisted of four reactors of type RBMK-1000, each capable of producing 1,000 megawatts (MW) of electric power (3.2 GW of thermal power), and the four together produced about 10% of Ukraine's electricity at the time of the accident.[2] Reactor number 1 shutdown (1996) Reactor number 2 shutdown (1991) Reactor number 3 shutdown (2000) Reactor number 4 destroyed in Chernobyl Disaster (1986) After the explosion at Reactor No. 4, the remaining three reactors at the power plant continued to operate. The schedule for plant decommissioning is intimately wrapped with the dismantling of Reactor No. 4 and the decontamination of its environs. The Chernobyl New Safe Confinement will have equipment which will make decommissioning relatively incidental to, yet an integral part of, the cleanup of the exploded reactor. The isotope responsible for the majority of the external gamma radiation dose at the site is caesium-137, which has a half-life of about 30 years. As of 2016, the radiation exposure from that radionuclide has declined by half since the 1986 accident. Reactor No. 1 In November 1996, following pressure from international governments, Reactor No. 1 was shut down.[16] Removal of uncontaminated equipment has begun at Reactor No. 1 and this work could be complete by 2020–2022.[17] Reactor No. 2. In October 1991, Reactor No. 2 caught fire, and was subsequently shut down.[18] Ukraine's 1991 independence from the Soviet Union generated further discussion on the Chernobyl topic, because the Rada, Ukraine's new parliament, was composed largely of young reformers. Discussions about the future of nuclear energy in Ukraine ultimately moved the government toward decision to cancel the operation of Reactor No. 2. In the mid 1990s, there were plans to restart reactor No. 2.[19][20][21] but ultimately they were never carried out and the reactor remained shut down. Reactor No. 3. In December 2000, Reactor No. 3. was shut down, and the plant as a whole ceased producing electricity.[16] On April 9, 2015, units 1–3 entered the decommissioning phase.[22] Reactor No. 4. Sarcophagus replacement New Safe Confinement in August 2016 Main article: Chernobyl New Safe Confinement Originally announced in June 2003, a new steel containment structure named the New Safe Confinement would be built to replace the aging and hastily built sarcophagus that protected Reactor No. 4.[23] Though the project's development has been delayed several times, construction officially began in September 2010.[24] The New Safe Confinement was financed by an international fund[25] managed by the European Bank for Reconstruction and Development (EBRD) was designed and built by the French-led consortium Novarka.[25] Novarka is building a giant arch-shaped structure out of steel, 270 m (886 ft) wide, 100 m (328 ft) high and 150 m (492 ft) long to cover the old crumbling concrete dome that is currently in use.[16] This steel casing project is expected to cost$1.4 billion (£700 million, €1 billion), and expected to be completed by 2017.[26] A separate deal has been made with the American firm Holtec to build a storage facility within the exclusion zone for nuclear waste produced by Chernobyl.[27][28][29]

On 14 November 2016, the arch began its expected five day journey over the existing sarcophagus,[30] however, it ended up taking fifteen days and arrived at its final resting place on 29 November 2016.[31]

THE FOURTH WAS DIFFERENT THAN THE PREVIOUS THREE

The 7 July 2005 London bombings, sometimes referred to as 7/7, were a series of coordinated terrorist suicide bomb attacks in central London which targeted civilians using the public transport system during the rush hour.

On the morning of Thursday, 7 July 2005, four Islamist extremists separately detonated three bombs in quick succession aboard London Underground trains across the city, and later, a fourth on a double-decker bus in Tavistock Square. Fifty-two people were killed and over 700 more were injured in the attacks, making it Britain's worst terrorist incident since the 1988 bombing of Pan Am Flight 103 over Lockerbie, Scotland, as well as the country's first ever Islamist suicide attack.

THE FOUR DAMAGED REACTOR BUILDINGS OF FUKUSHIMA- THE FOURTH WAS DIFFERENT/ NOT OPERATING WHILE THE FIRST THREE WERE- THE QUADRANT PATTERN
https://en.wikipedia.org/…/Fukushima_Daiichi_nuclear_disast…
https://en.wikipedia.org/…/Fukushima_Daiichi_nuclear_disast…

Image on 16 March 2011 of the four damaged reactor buildings. From left to right: Unit 4, 3, 2 and 1. Hydrogen-air explosions occurred in Unit 1, 3 and 4, causing structural damage. A vent in Unit 2's wall, with water vapor/"steam" clearly visible, prevented a similar large explosion. Drone overflights on 20 March captured clearer images.[1]

The Fukushima Daiichi Nuclear Power Plant (福島第一原子力発電所 Fukushima Daiichi Genshiryoku Hatsudensho?) is a disabled nuclear power plant located on a 3.5-square-kilometre (860-acre) site[1] in the towns of Ōkuma and Futaba in the Futaba District of Fukushima Prefecture, Japan.

In April 2012, Units 1-4 were decommissioned. Units 2-4 were decommissioned on April 19, while Unit 1 was the last of these four units to be decommissioned on April 20 at midnight.[citation needed] In December 2013 TEPCO decided none of the undamaged units will reopen.

Dismantling of reactors

On August 1, 2013, the Japanese Industry Minister Toshimitsu Motegi approved the creation of a structure to develop the technologies and processes necessary to dismantle the four reactors damaged in the Fukushima accident.[55]

“The brain is a three dimensional object.” It would seem that this is one of the least controversial facts about the brain, something we can all agree on. But now, in a curious new paper, researchers Arturo Tozzi and James F. Peters suggest that the brain might have an extra dimension: Towards a fourth spatial dimension of brain activity

From topology, a strong concept comes into play in understanding brain functions, namely, the 4D space of a ‘‘hypersphere’s torus’’, undetectable by observers living in a 3D world… Here we hypothesize that brain functions are embedded in a imperceptible fourth spatial dimension and propose a method to empirically assess its presence.

I must admit that I’m not sure whether Tozzi and Peters literally mean that the brain is a four dimensional object. I don’t know if we are to read this paper as meaning that neural activity is in some way analagous to a hypersphere (a four-dimensional sphere), or whether we’re being asked to believe that the brain actually is or contains one.

For instance, the authors write:

How do thoughts flow in the brain? Current advances in neuroscience emphasize the role of energetic landscapes (Watanabe et al. 2014; Sengupta et al. 2013), a sort of functional linens equipped with peaks, valleys and basins made of free-energy, where thoughts move, following erratic and/or constrained trajectories… This review, based on recent findings, introduces the concept of a spatial fourth dimension, where brain functions might take place, as a general device underlying our thoughts’ dynamics.

This suggests that the fourth dimension is a metaphor, in the same way that energy “landscapes” are metaphorical, not actual places. But then on the other hand, we read the following, which seems to imply that the fourth dimension is a real thing (albeit something we can’t see):

Brains equipped with a hypersphere is a counter-intuitive hypothesis, since we live in a 3D world with no immediate perception that 4D space exists at all. We need thus to evaluate indirect clues of the undetectable fourth dimension…

So what’s the evidence for this mysterious dimension? Tozzi and Peters say that we need to look for 3D “shadows” or “echoes” of the 4D object, and we can do this using the Borsuk-Ulam Theorem (BUT) which, they say, predicts that ‘antipodal points’ on the 4D brain will be activated during activity of the 3D brain, as follows:

The activation of a single point on the 3D brain S2 surface leads to the activation of two antipodal points on the 4D brain S3 surface (Fig. 3b). In turn, the activation of two antipodal points on S3 leaves on the 3D brain S2 surface ‘‘hallmarks’’ which can be detected by currently available neuroimaging techniques.

tozzi_peters_4DEssentially, the claim is that if an fMRI study detects activity at two opposite points on the brain, this is evidence for an unseen 4D reality. They review various resting state fMRI studies and, they report, find that many of them have indeed detected antipodal activations. The illustrate this with a series of images, taken from recently published papers, in which black and white bars are used to depict the antipodal points:

tozzi_peters_antipodalHmm. I can see a few problems with this. For one thing, it’s cherry picking: every fMRI study is different so some of them will produce antipodal patterns by chance alone. But more fundamentally, this approach ignores the facts of neuroanatomy. The brain is bilaterally symmetrical: it has a left and a right hemisphere, and the corresponding points on each hemisphere are connected by the corpus callosum. For this reason, neural activity is generally symmetrical. We don’t need to posit a 4D brain to explain this, yet many of the Tozzi and Peters “antipodal bars” can be easily explained in this manner.

So I’m not convinced by this paper, but nonetheless, I suspect it might become a ‘cult classic’ of theoretical neuroscience, as the idea is rather gloriously weird.

FOUR EONS UNIVERSE HISTORY

Eon - A primary division of geologic time lasting over 500 million years, four of which have been defined: Hadean, Archean, Proterozoic, and Phanerozoic. Eons are divided into Eras, which are in turn divided into Periods, Epochs and Ages (FOUR DIVISIONS)

NASA's series of Great Observatories satellites are four large, powerful space-based astronomical telescopes. Each of the four missions was designed to examine a specific wavelength/energy region of the electromagnetic spectrum (gamma rays, X-rays, visible and ultraviolet light, infrared light) using very different technologies. Dr. Charles Pellerin, NASA's Director, Astrophysics invented and developed the program. The four Great Observatories were launched between 1990 and 2003, and three remain operational as of 2017.

Great Observatories

The Hubble Space Telescope (HST) primarily observes visible light and near-ultraviolet. It was launched in 1990 aboard Discovery during STS-31. A servicing mission in 1997 added capability in the near-infrared range and one last mission in 2009 was to fix and extend the life of Hubble which resulted in some of the best results to date.

The Compton Gamma Ray Observatory (CGRO) primarily observed gamma rays, though it extended into hard x-rays as well. It was launched in 1991 aboard Atlantis during STS-37 and was de-orbited in 2000 after failure of a gyroscope.

The Chandra X-ray Observatory (CXO) primarily observes soft x-rays. It was launched in 1999 aboard Columbia during STS-93 into an elliptical high-earth orbit, and was initially named the Advanced X-ray Astronomical Facility (AXAF).

The Spitzer Space Telescope (SST) observes the infrared spectrum. It was launched in 2003 aboard a Delta II rocket into an earth-trailing solar orbit; it was called the Space Infrared Telescope Facility (SIRTF) before launch. Depletion of its onboard liquid helium coolant in 2009 reduced its functionality significantly, leaving it with only two short-wavelength imaging modules.

Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers or quadrature components — hence the name of the scheme.

In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (π/2 radians). All three functions have the same frequency. The amplitude modulated sinusoids are known as in-phase and quadrature components.[1] Some authors find it more convenient to refer to only the amplitude modulation (baseband) itself by those terms.

when φ happens to be such that the in-phase component is zero, the current and voltage sinusoids are said to be in quadrature, which means they are orthogonal to each other. In that case, no electrical power is consumed. Rather it is temporarily stored by the device and given back, once every seconds. Note that the term in quadrature only implies that two sinusoids are orthogonal, not that they are components of another sinusoid.

Vector monitors were also used by some late-1970s to mid-1980s arcade games such as Star Wars and Asteroids.[1] Atari used the term Quadrascan to describe the technology when used in their video game arcades.

The QUADRASCAN converter modulates the elevation and azimuth error signals in phase quadrature and adds them to the sum channel.

Tesla experimented with impulse current and oscillating current. Our electricity is direct current and alternating current. The Four Quadrant Theory of Electricity is:

● Impulse Current

● Oscillating Current ● Direct Current

● Alternating Current

Based on the storage and processing technologies employed, it is possible to distinguish four distinct phases of IT development: pre-mechanical (3000 BC – 1450 AD), mechanical (1450–1840), electromechanical (1840–1940), electronic (1940–present).[6] This article focuses on the most recent period (electronic), which began in about 1940.

This evocative movie of four planets more massive than Jupiter orbiting the young star HR 8799 is a composite of sorts, including images taken over seven years at the W.M. Keck observatory in Hawaii.

The movie clearly doesn’t show full orbits, which will take many more years to collect. The closest-in planet circles the star in around 40 years; the furthest takes more than 400 years.

But as described by Jason Wang, an astronomy graduate student at the University of California, Berkeley, researchers think that the four planets may well be in resonance with each other.

In this case it’s a one-two-four-eight resonance, meaning that each planet has an orbital period in nearly precise ratio with the others in the system.

Four Sided Triangle is a 1953 British science-fiction film directed by Terence Fisher, adapted from a novel by William F. Temple.[3] It starred Stephen Murray, Barbara Payton and James Hayter.[4] It was produced by Hammer Film Productions at Bray Studios.[3]

The film dealt with the moral and scientific themes (not to mention "mad lab" scenes) that were soon to put Hammer Films on the map with the same director's The Curse of Frankenstein. Four Sided Triangle has most in common with Fisher's Frankenstein Created Woman (1967).

Thomas Hood invented this CROSS-staff in 1590.[4] It could be used for surveying, astronomy or other geometric problems.

It consists of two components, a transom and a yard. The transom is the vertical component and is graduated from 0° at the top to 45° at the bottom. At the top of the transom, a vane is mounted to cast a shadow. The yard is horizontal and is graduated from 45° to 90°. The transom and yard are joined by a special fitting (the double socket in Figure 6) that permits independent adjustments of the transom vertically and the yard horizontally.

It was possible to construct the instrument with the yard at the top of the transom rather than at the bottom.[7]

Initially, the transom and yard are set so that the two are joined at their respective 45° settings. The instrument is held so that the yard is horizontal (the navigator can view the horizon along the yard to assist in this). The socket is loosened so that the transom is moved vertically until the shadow of the vane is cast at the yard's 90° setting. If the movement of just the transom can accomplish this, the altitude is given by the transom's graduations. If the sun is too high for this, the yard horizontal opening in the socket is loosened and the yard is moved to allow the shadow to land on the 90° mark. The yard then yields the altitude.

It was a fairly accurate instrument, as the graduations were well spaced compared to a conventional cross-staff. However, it was a bit unwieldy and difficult to handle in wind.

Like

Aries is a relatively dim constellation, possessing only four bright stars: Hamal (Alpha Arietis, second magnitude), Sheratan (Beta Arietis, third magnitude), Mesarthim (Gamma Arietis, fourth magnitude), and 41 Arietis (also fourth magnitude)

THE FOURTH IS ALWYAS DIFFERENT- FIFTH ULTRA TRANSCENDENT

Most multiple star systems are triple stars. Systems with four or more components are less likely to occur

4 Centauri is a star in the constellation Centaurus. It is a blue-white B-type subgiant with an apparent magnitude of +4.75 and is approximately 640 light years from Earth.

4 Centauri is a hierarchical quadruple star system. The primary component of the system, 4 Centauri A, is a spectroscopic binary, meaning that its components cannot be resolved but periodic Doppler shifts in its spectrum show that it must be orbiting. 4 Centauri A has an orbital period of 6.927 days and an eccentricity of 0.23. Because light from only one of the stars can be detected (i.e. it is a single-lined spectroscopic binary), some parameters such as its inclination are unknown.[7] The secondary component, is also a single-lined spectroscopic binary. It has an orbital period of 4.839 days and an eccentricity of 0.05. The secondary component is a metallic-lined A-type star. The two pairs themselves are separated by 14 arcseconds; one orbit would take at least 55,000 years.[5]

Although it appears to be a single star to the naked eye, Capella is actually a system of four stars in two binary pairs.

A few degrees to the southwest of Capella lie three stars Epsilon, Zeta, and Eta Aurigae, the latter two of which are known as "The Kids", or Haedi. The four form a familiar pattern, or asterism, in the sky.

HD 98800 is a quadruple star system located in the TW Hydrae association.

Capella, a pair of giant stars orbited by a pair of red dwarfs, around 42 light years away from the Solar System. It has an apparent magnitude of around −0.47, making Capella one of the brightest stars in the night sky.

4 Centauri[46]

Mizar is often said to have been the first binary star discovered when it was observed in 1650 by Giovanni Battista Riccioli[47], p. 1[48] but it was probably observed earlier, by Benedetto Castelli and Galileo.[citation needed] Later, spectroscopy of its components Mizar A and B revealed that they are both binary stars themselves.[49]

The Kepler-64 system has the planet PH1 (discovered in 2012 by the Planet Hunters group, a part of the Zooniverse) orbiting two of the four stars, making it to be the first known planet to be in a quadruple star system.[50]

KOI-2626 is the first quadruple star system with an Earth-sized planet.[51]

Xi Tauri (ξ Tau, ξ Tauri), located about 222 light years away, is a spectroscopic and eclipsing quadruple star consisting of three blue-white B-type main-sequence stars, along with an F-type star. Two of the stars are in a close orbit and revolve around each other once every 7.15 days. These in turn orbit the third star once every 145 days. The fourth star orbits the other three stars roughly every fifty years.[52]

THE FOURTH IS DIFFERENT

Xi Tauri (ξ Tau, ξ Tauri) is a hierarchical quadruple system[4] in the constellation Taurus.

Xi Tauri is a spectroscopic and eclipsing quadruple star. It consists of three blue-white B-type main sequence dwarfs. Two of the stars form an eclipsing binary system and revolve around each other once every 7.15 days. These in turn orbit the third star once every 145 days. The fourth star is a F star that orbits the other three stars in a roughly fifty-year period.[5] The mean combined apparent magnitude of the system is +3.73, but because the stars eclipse one another during their orbits, it is classified as a variable star, and its brightness varies from magnitude +3.70 to +3.79. Xi Tauri is approximately 210 light years from Earth.[1]

The four central stars in Hercules, Epsilon (ε Her), Zeta (ζ Her), Eta (η Her), and Pi (π Her), form the well-known Keystone.[4]

Alpha, Beta, Gamma, and Delta Delphini form Job's Coffin (FOUR STARS)

The Terebellum is a small quadrilateral of four faint stars (Omega, 59, 60, 62) in Sagittarius' hindquarters.[13]

Four other stars (Beta — Miaplacidus, Upsilon, Theta, and Omega Carinae) form a well-shaped diamond — the Diamond Cross

The diamond-shaped False Cross is composed of the four stars Delta and Kappa Velorum (δ and κ Vel) and Epsilon and Iota Carinae (ε and ι Car).[14] Although its component stars are not quite as bright as those of the Southern Cross, it is somewhat larger and better shaped than the Southern Cross, for which it was often mistaken, causing errors in astronavigation. Like the Southern Cross, three of its main four stars are whitish and one orange.[17]

The Trapezium is most readily identifiable by the asterism of four relatively bright stars for which it is named. The four are often identified as A, B, C, and D in order of increasing right ascension. The brightest of the four stars is C, or Theta1 Orionis C, with an apparent magnitude of 5.13. Both A and B have been identified as eclipsing binaries.

The Terebellum, by Ptolemy called τετράπλευρον (/tetrápleuron/), is a quadrilateral of stars in the constellation Sagittarius. It is formed of four 4th magnitude stars, all within two degrees of each other:

Omega Sagittarii, at the northeast corner.

59 Sagittarii or b Sagittarii, at the southeast corner.

60 Sagittarii or A Sagittarii, at the northwest corner.

62 Sagittarii or c Sagittarii, at the southwest corner.

The Diamond Cross is an asterism in the southern constellation Carina. The Diamond Cross is composed of four bright stars: Beta, Theta, Upsilon and Omega Carinae. These four bright stars create an almost perfect diamond shape, hence the name "Diamond Cross". The entire asterism is visible to all observers south of 20°N latitude. It bears a striking resemblance to Crux (The Southern Cross) and the False Cross, and, like them, it lacks a central star in its cross pattern, creating a diamond-shaped or kite-like appearance. Both the Diamond Cross and the False Cross are sometimes mistaken for the true cross Crux, although the False Cross has always been a worse deceiver than the Diamond Cross, because most of its stars have approximately the same declinations as the stars of Crux.

Alpha and Beta Centauri are the Southern Pointers leading to the Southern Cross[16] and thus helping to distinguish Crux from the False Cross.

NOTICE HOW THE FOURTH STAR IS DIFFERENT COLOR

The diamond-shaped False Cross is composed of the four stars Delta and Kappa Velorum (δ and κ Vel) and Epsilon and Iota Carinae (ε and ι Car).[14] Although its component stars are not quite as bright as those of the Southern Cross, it is somewhat larger and better shaped than the Southern Cross, for which it was often mistaken, causing errors in astronavigation. Like the Southern Cross, three of its main four stars are whitish and one orange.[17]

FOUR METHODS ONE USES CRUX/CROSS

The south celestial pole is visible only from the southern hemisphere. It lies in the dim constellation Octans, the Octant. Sigma Octantis is identified as the south pole star, over a degree away from the pole, but with a magnitude of 5.5 it is barely visible on a clear night.

Method one: The Southern Cross

The south celestial pole can be located from the Southern Cross (Crux) and its two "pointer" stars α Centauri and β Centauri. Draw an imaginary line from γ Crucis to α Crucis—the two stars at the extreme ends of the long axis of the cross—and follow this line through the sky. Either go four and a half times the distance of the long axis in the direction the narrow end of the cross points, or join the two pointer stars with a line, divide this line in half, then at right angles draw another imaginary line through the sky until it meets the line from the Southern Cross. This point is 5 or 6 degrees from the south celestial pole. Very few bright stars of importance lie between Crux and the pole itself, although the constellation Musca is fairly easily recognised immediately beneath Crux.

Method two: Canopus and Achernar

The second method uses Canopus (the second brightest star in the sky) and Achernar. Make a large equilateral triangle using these stars for two of the corners. The third imaginary corner will be the south celestial pole. If Canopus has not yet risen, the second magnitude Alpha Pavonis can also be used to form the triangle with Achernar and the pole.

Method three: The Magellanic Clouds

The third method is best for a moonless and cloudless night as it uses two faint 'clouds' in the southern sky. These are marked in astronomy books as Large and Small Magellanic Clouds. These 'clouds' are actually galaxies close to our own Milky Way. Make an equilateral triangle, the third point of which is the south celestial pole.

Method four: Sirius and Canopus

A line from Sirius, the brightest star in the sky, through Canopus, the second brightest, continued for the same distance lands within a couple of degrees of the pole. In other words, Canopus is halfway between Sirius and the pole.

In the case of 30 Ari, the discovery brought the number of known stars in the system from three to four. The fourth star lies at a distance of 23 astronomical units from the planet. While this stellar companion and its planet are closer to each other than those in the HD 2638 system, the newfound star does not appear to have impacted the orbit of the planet. The exact reason for this is uncertain, so the team is planning further observations to better understand the orbit of the star and its complicated family dynamics.

One planet, four stars: the second known case of a planet in a quadruple star system

The discovery suggests that planets in quadruple systems might be less rare than once thought.

By University of Hawaii at Manoa's Institute for Astronomy, Honolulu | Published: Thursday, March 5, 2015

RELATED TOPICS: EXOPLANETS | STARS

Ari 30 star system

Artist's conception of the 30 Ari star system. The system is composed of four stars. The distant companion 30 Ari A is actually a pair of stars in a close orbit. The research team discovered the fourth star in the system (the left-most star in the image). That star is a small red dwarf. A massive planet orbits the star named 30 Ari B in a nearly year-long orbit.

Karen Teramura, UH IfA

Researchers wanting to know more about the influences of multiple stars on exoplanets have come up with a new case study: a planet in a four-star system.

The discovery was made at Palomar Observatory using two new adaptive optics technologies that compensate for the blurring effects of Earth's atmosphere: the robotic Robo-AO adaptive optics system developed under the leadership of Christoph Baranec of the University of Hawaii at Manoa's Institute for Astronomy and the PALM-3000 extreme adaptive optics system developed by a team at Caltech and NASA's Jet Propulsion Laboratory (JPL) that also included Baranec.

The newfound four-star planetary system, called 30 Ari, is located 136 light-years away in the constellation Aries. The system's gaseous planet is enormous, with 10 times the mass of Jupiter, and orbits its primary star every 335 days.

The new study brings the number of known stars in the 30 Ari system from three to four. This discovery suggests that planets in quadruple star systems might be less rare than once thought.

"About 4 percent of solar-type stars are in quadruple systems, which is up from previous estimates because observational techniques are steadily improving," said Andrei Tokovinin of the Cerro Tololo Inter-American Observatory in Chile.

The newly discovered fourth star, whose distance from the planet is 23 times the Sun-Earth distance, does not appear to have impacted the orbit of the planet. The exact reason for this is uncertain, so the team is planning further observations to better understand the orbit of the newly discovered star and its complicated family dynamics.

Were it possible to see the skies from this world, the four stars would look like one small Sun and two very bright stars that would be visible in daylight. If viewed with a large enough telescope, one would see that one of those bright stars is actually a binary system — two stars orbiting each other.

Almach looks single, but is really four stars. Look through the telescope to see Almach transform into two colorful suns. The larger sun appears golden, and the smaller one appears blue.

FOUR TYPES

Classical types

Objects named nebulae belong to four major groups. Before their nature was understood, galaxies ("spiral nebulae") and star clusters too distant to be resolved as stars were also classified as nebulae, but no longer are.

H II regions, large diffuse nebulae containing ionized hydrogen

Planetary nebulae

Supernova remnant (e.g., Crab Nebula)

Dark nebula

SWASTIKA PLATE 5000 BC IS A MODEL OF THE MILKY WAY (really its a model of existence)

MILKY WAY HAS FOUR ARMS

FOUR TYPES

There are four types of mattress coils:

Bonnell coils are the oldest and most common. First adapted from buggy seat springs of the 19th century, they are still prevalent in mid-priced mattresses. Bonnell springs are a knotted, round-top, hourglass-shaped steel wire coil. When laced together with cross wire helicals, these coils form the simplest innerspring unit, also referred to as a Bonnell unit.

Offset coils are an hourglass type coil on which portions of the top and bottom convolutions have been flattened. In assembling the innerspring unit, these flat segments of wire are hinged together with helical wires. The hinging effect of the unit is designed to conform to body shape. LFK coils are an unknotted offset coil with a cylindrical or columnar shape.

Continuous coils (the Leggett & Platt brand name is "Mira-coil") is an innerspring configuration in which the rows of coils are formed from a single piece of wire. They work in a hinging effect similar to that of offset coils.

Marshall coils, also known as wrapped or encased coils or pocket springs, are thin-gauge, barrel-shaped, knotless coils individually encased in fabric pockets—normally a fabric from man-made, nonwoven fiber. Some manufacturers precompress these coils, which makes the mattress firmer and allows for motion separation between the sides of the bed. As the springs are not wired together, they work more or less independently: the weight on one spring does not affect its neighbours. More than half the consumers who participated in a survey had chosen to buy pocket spring mattresses.[6]

FOUR STEPS PROCESS FEELING PAIN

There are four main steps in the process of feeling pain: transduction, transmission, perception, and modulation

THE MOST COMMON COLOR PALLETTES ARE 4 DISTINCT COLORS, 16, or 256----- 16 IS FOUR SQUARED. 256 IS FOUR TO THE FOURTH POWER- 256 IS A QUADRANT MODEL OF QUADRANT MODELS. 256 IS FOUR TO THE FOURTH POWER- 256 IS 16 TIMES FOUR-64 TIMES FOUR- 64 IS FOUR QUADRANT MODELS- 256 IS A QUADRANT MODEL OF QUADRANT MODELS

Palette size

Main article: Palette (computing)

The palette itself stores a limited number of distinct colors; 4, 16 or 256 are the most common cases. These limits are often imposed by the target architecture's display adapter hardware, so it is not a coincidence that those numbers are exact powers of two (the binary code): 22 = 4, 24 = 16 and 28 = 256. While 256 values can be fit into a single 8-bit byte (and then a single indexed color pixel also occupies a single byte), pixel indices with 16 (4-bit, a nibble) or fewer colors can be packed together into a single byte (two nibbles per byte, if 16 colors are employed, or four 2-bit pixels per byte if using 4 colors). Sometimes, 1-bit (2-color) values can be used, and then up to eight pixels can be packed into a single byte; such images are considered binary images (sometimes referred as a bitmap or bilevel image) and not an indexed color image.

Color depth

1-bit monochrome

8-bit grayscale

8-bit color

15- or 16-bit color (high color)

24-bit color (true color)

30-, 36-, or 48-bit color (deep color)

Related

Indexed color

Palette

RGB color model

Web-safe color

v t e

If simple video overlay is intended through a transparent color, one palette entry is specifically reserved for this purpose, and it is discounted as an available color. Some machines, such as the MSX series, had the transparent color reserved by hardware.[5]

Indexed color images with palette sizes beyond 256 entries are rare. The practical limit is around 12-bit per pixel, 4,096 different indices. To use indexed 16 bpp or more does not provide the benefits of the indexed color images' nature, due to the color palette size in bytes being greater than the raw image data itself. Also, useful direct RGB Highcolor modes can be used from 15 bpp and up.

If an image has many subtle color shades, it is necessary to select a limited repertoire of colors to approximate the image using color quantization. Such a palette is frequently insufficient to represent the image accurately; difficult-to-reproduce features such as gradients will appear blocky or as strips (color banding). In those cases, it is usual to employ dithering, which mixes different-colored pixels in patterns, exploiting the tendency of human vision to blur nearby pixels together, giving a result visually closer to the original one.

Here is a typical indexed 256-color image and its own palette (shown as a rectangle of swatches):

EARLY COLOR TECHNIQUES USED 16 COLORS- 16 SQUARES IN THE QUADRANT MODEL

Early color techniques

Many early personal and home computers had very limited hardware palettes that could produce a very small set of colors. In these cases, each pixel's value mapped directly onto one of these colors. Well-known examples include the Apple II, Commodore 64 and IBM PC CGA, all of which included hardware that could produce a fixed set of 16 colors. In these cases, an image can encode each pixel with 4-bits, directly selecting the color to use. In most cases, however, the display hardware supports additional modes where only a subset of those colors can be used in a single image, a useful technique to save memory. For instance, the CGA's 320×200 resolution mode could show only four of the 16 colors at one time. As the palettes were entirely proprietary, an image generated on one platform cannot be directly viewed properly on another.

Other machines of this era had the ability to generate a larger set of colors, but generally only allowed a subset of those to be used in any one image. Examples include the 256-color palette on Atari 8-bit machines or the 4,096 colors of the VT241 terminal in ReGIS graphics mode. In these cases it was common for the image to only allow a small subset of the total number of colors to be displayed at one time, up to 16 at once on the Atari and VT241. Generally, these systems worked identically to their less-colorful brethren, but a key difference was that there were too many colors in the palette to directly encode in the pixel data given the limited amount of video memory. Instead, they used a colour look-up table (CLUT) where each pixel's data pointed to an entire in the CLUT, and the CLUT was set up under program control. This meant that the image CLUT data had to be stored along with the raw image data in other to be able to re-produce the image correctly.

9 BIT RBG HAS 512 COMBINATIONS- THAT IS 256 (4 to the 4th power) TIMES 2- 12 BIT RBG HAS 4096 COMBINATIONS WHICH IS FOUR TO THE SIXTH POWER
https://en.wikipedia.org/wiki/Indexed_color
9-bit RGB provides 512 combinations, a 12-bit RGB provides 4,096

FOUR SQUARE CIPHER

The four-square cipher uses four 5 by 5 (5x5) matrices arranged in a square. Each of the 5 by 5 matrices contains the letters of the alphabet (usually omitting "Q" or putting both "I" and "J" in the same location to reduce the alphabet to fit). In general, the upper-left and lower-right matrices are the "plaintext squares" and each contain a standard alphabet. The upper-right and lower-left squares are the "ciphertext squares" and contain a mixed alphabetic sequence.

THERE ARE FOUR BRANCHES OF THE PP CHAIN

–proton_chain_reaction

The P-P I branch

3

2He

+ 3

2He

→ 4

2He

+ 2 1

1H

+ 12.86 MeV

The complete p-p I chain reaction releases a net energy of 26.732 MeV.[7] Two percent of this energy is lost to the neutrinos that are produced.[8] The p-p I branch is dominant at temperatures of 10 to 14 MK. Below 10 MK, the P-P chain does not produce much 4

He

.[citation needed]

The P-P II branch

Proton–proton II chain reaction

3

2He

+ 4

2He

→ 7

4Be

+

γ

7

4Be

+

e−

→ 7

3Li

+

ν

e + 0.861 MeV / 0.383 MeV

7

3Li

+ 1

1H

→ 2 4

2He

The P-P II branch is dominant at temperatures of 14 to 23 MK.

Note that the energies in the equation above are not the energy released by the reaction. Rather, they are the energies of the neutrinos that are produced by the reaction. 90 percent of the neutrinos produced in the reaction of 7

Be

to 7

Li

carry an energy of 0.861 MeV, while the remaining 10 percent carry 0.383 MeV. The difference is whether the lithium-7 produced is in the ground state or an excited (metastable) state, respectively.

The P-P III branch

Proton–proton III chain reaction

3

2He

+ 4

2He

→ 7

4Be

+

γ

7

4Be

+ 1

1H

→ 8

5B

+

γ

8

5B

→ 8

4Be

+

e+

+

ν

e

8

4Be

→ 2 4

2He

The P-P III chain is dominant if the temperature exceeds 23 MK.

The p-p III chain is not a major source of energy in the Sun (only 0.11 percent), but it was very important in the solar neutrino problem because it generates very high energy neutrinos (up to 14.06 MeV).

The P-P IV (Hep) branch

This reaction is predicted theoretically, but it has never been observed due to its rarity (about 0.3 ppm in the Sun). In this reaction, helium-3 captures a proton directly to give helium-4, with an even higher possible neutrino energy (up to 18.8 MeV).

3

2He

+ 1

1H

→ 4

2He

+

e+

+

ν

e + 18.8 MeV

NUCLEAR FUSION HAPPENS THROUGH FOUR PARTICLES- AND THERE ARE FOUR IMPORTANT REACTIONS
https://en.wikipedia.org/wiki/Nuclear_fusion
The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos (which changes two of the protons into neutrons), and energy.

Four-Phase Systems was a computer company, founded by Lee Boysel and others, which built one of the earliest computers using semiconductor main memory and LSI MOS logic. The company was incorporated in February 1969 and had moderate commercial success. It was acquired by Motorola in 1981.[1]

AL1 Microprocessor

History

The idea behind Four-Phase Systems began when Boysel was designing MOS components at Fairchild Semiconductor in 1967. Boysel wrote a manifesto explaining how a computer could be built from a small number of MOS chips. Fairchild made Boysel head of a MOS design group, which he used to design parts satisfying the requirements of his putative computer. After doing this, Boysel left to start Four-Phase in October 1968, initially with two other engineers from his Fairchild group as well as others. Boysel was not sued by Fairchild, perhaps because of chaos caused by a change in Fairchild management at that time.[2] When the company was incorporated in February 1969, he was joined by other engineers from the Fairchild group. Boysel arranged for chips to be fabricated by Cartesian, a wafer-processing company founded by another engineer from Fairchild.[3] Four-Phase showed its system at the Fall Joint Computer Conference in 1970. The system was in operation at four different customers by June 1971, and by March 1973, they had shipped 347 systems to 131 customers.[4] The company enjoyed a substantial level of success, having revenues of $178 million by 1979. In 1982, it was sold to Motorola for a$253 million stock exchange.[5] The former location of the original business is now Infinite Loop.

System

The Four-Phase CPU used a 24-bit word size. It fit on a single card and was composed of three AL1 chips, three read-only-memory (ROM) chips, and three random logic chips. A memory card used Four-Phase's 1K RAM chips.[6] The system also included a built-in video controller which could drive up to 32 terminals from a frame buffer in main memory.[7]

The AL1 was an 8-bit bit slice which contained eight registers and an arithmetic logic unit (ALU). It was implemented using four-phase logic and used over a thousand gates, with an area of 130 by 120 mils. The chip was described in an April 1970 article in Computer Design magazine.[8][9] Although the AL1 was not called a microprocessor, or used as one, at the time, it was later dubbed one in connection with litigation in the 1990s, when Texas Instruments claimed to have patented the microprocessor. In response, Lee Boysel assembled a system in which a single 8-bit AL1 was used as part of a courtroom demonstration computer system, together with ROM, RAM and an input-output device.[10][11]

IT IS THOUGHT THAT 16 DIMENSIONS WOULD BE THE MAXIMUM IN STRING THEORY- IT WOULDN'T GO BEYOND 16---- 16 SQUARES QMR--- ALSO THE FIVE STRING THEORIES FIT QUADRANT PATTERN FIRST THREE SIMILAR FOURTH DIFFERNET FIFTH ULTRA TRANSCENDENT

QMRIt is conceivable that the five superstring theories are approximated to a theory in higher dimensions possibly involving membranes. Because the action for this involves quartic terms and higher so is not Gaussian, the functional integrals are very difficult to solve and so this has confounded the top theoretical physicists. Edward Witten has popularised the concept of a theory in 11 dimensions M-theory involving membranes interpolating from the known symmetries of superstring theory. It may turn out that there exist membrane models or other non-membrane models in higher dimensions—which may become acceptable when we find new unknown symmetries of nature, such as noncommutative geometry. It is thought, however, that 16 is probably the maximum since O(16) is a maximal subgroup of E8 the largest exceptional lie group and also is more than large enough to contain the Standard Model. Quartic integrals of the non-functional kind are easier to solve so there is hope for the future. This is the series solution, which is always convergent when a is non-zero and negative:

THE FOUR BOSONIC STRING THEORIES BASED ON TWO DICHOTOMIES CREATING FOUR POSSIBLITIES LIKE THERE ARE FOUR TYPES OF BLACK HOLE

There are four possible bosonic string theories, depending on whether open strings are allowed and whether strings have a specified orientation. Recall that a theory of open strings also must include closed strings; open strings can be thought as having their endpoints fixed on a D25-brane that fills all of spacetime. A specific orientation of the string means that only interaction corresponding to an orientable worldsheet are allowed (e.g., two strings can only merge with equal orientation). A sketch of the spectra of the four possible theories is as follows:

Bosonic string theory Non-positive

M

2

M^{2} states

Open and closed, oriented tachyon, massless antisymmetric tensor, graviton, dilaton

Open and closed, unoriented tachyon, graviton, dilaton

Closed, oriented tachyon, U(1) vector boson, antisymmetric tensor, graviton, dilaton

Closed, unoriented tachyon, graviton, dilaton

Note that all four theories have a negative energy tachyon (

M

2

=

1

α

M^{2}=-{\frac {1}{\alpha '}}) and a massless graviton.

The rest of this article applies to the closed, oriented theory, corresponding to borderless, orientable worldsheets.

FIRST OFF THERE ARE 16 EINSTEIN FIELD EQUATIONS AND 16 SQUARES QMR- THERE ARE FOUR TYPES OF BLACK HOLE-- NASSIM HARAMEINS THEORIES ARE BASED AROUND THE SCHWARZSCHILD- BUT THERE ARE THREE MORE TYPES

There are four known, exact, black hole solutions to the Einstein field equations, which describe gravity in general relativity. Two of those rotate: the Kerr and Kerr–Newman black holes. It is generally believed that every black hole decays rapidly to a stable black hole; and, by the no-hair theorem, that (except for quantum fluctuations) stable black holes can be completely described at any moment in time by these eleven numbers:

mass-energy M,

linear momentum P (three components),

angular momentum J (three components),

position X (three components),

electric charge Q.

While an infalling observer falls into a rotating black hole in a finite proper time and with a very high rapidity (left), from the perspective of a coordinate observer at infinity he slows down freezing at the horizon approaching zero velocity relative to a stationary probe on site while being whirled around the horizon with the black hole's frame-dragging-rate infinitely often (right).

These numbers represent the conserved attributes of an object which can be determined from a distance by examining its electromagnetic and gravitational fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole. This is because anything happening inside the black hole horizon cannot affect events outside of it.

In terms of these properties, the four types of black holes can be defined as follows:

Non-rotating (J = 0) Rotating (J > 0)

Uncharged (Q = 0) Schwarzschild Kerr

Charged (Q ≠ 0) Reissner–Nordström Kerr–Newman

THE FOURTH IS DIFFERENT- THE NO HAIR THEOREM SAYS THAT ONLY THREE PARAMETERS ARE NEEDED- BUT MAGNETIC CHARGE MAY BE THE FOURTH PARAMETER

"Magnetic charge, if detected as predicted by some theories, would form the fourth parameter possessed by a classical black hole."

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum

Extensions

The no-hair theorem was originally formulated for black holes within the context of a four-dimensional spacetime, obeying the Einstein field equation of general relativity with zero cosmological constant, in the presence of electromagnetic fields, or optionally other fields such as scalar fields and massive vector fields (Proca fields, spinor fields, etc.).[citation needed]

It has since been extended to include the case where the cosmological constant is positive (which recent observations are tending to support).[6]

Magnetic charge, if detected as predicted by some theories, would form the FOURTH parameter possessed by a classical black hole.

I WATCHED A TEACHING COMPANY COURSE ON BLACK HOLES AND IT WAS ALL PENROSE DIAGRAMS WHICH ARE QUADRANTS

Penrose diagrams the basis of black hole studies are quadrants as well as kruskal szekeres diagrams are also quadrants with four aspects

THESE ARE KNOWN AS THE BIG FOUR ASTEROIDS-- I DESCRIBED THERE ARE FOUR TERRESTRIAL ROCK PLANETS- THEN THE ASTEROID BELT- THEN THERE ARE FOUR GAS GIANT PLANETS- THEN THE KUIPER BELT

About half the mass of the belt is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea.[

The four largest objects, Ceres, 4 Vesta, 2 Pallas, and 10 Hygiea, account for half of the belt's total mass, with almost one-third accounted for by Ceres alone.

THERE ARE FOUR MARS TROJANS

The Mars trojans are a group of objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars. The origin of the Mars trojans is not well understood. One theory suggests that they were captured in its Lagrangian points as the Solar System was forming. However, spectral studies of the Mars trojans indicate this may not be the case.[1][2] One explanation for this involves asteroids wandering into the Mars Lagrangian points later in the Solar System's formation. This is also questionable considering the very low mass of Mars.[3][4]

Presently, this group contains seven asteroids confirmed to be stable Mars trojans by long-term numerical simulations but only four of them are accepted by the Minor Planet Center (†)[5] and there is one candidate:[3][4][6][7]

THERE ARE FOUR TRANS NEPTUNIAN DWARF PLANETS ACCEPTED BY THE IAU

Brown currently identifies ten known trans-Neptunian objects—the four accepted by the IAU plus 2007 OR10, Quaoar, Sedna, Orcus, (307261) 2002 MS4 and Salacia—as "virtually certain", with another twenty highly likely.[13] Stern states that there are more than a dozen known dwarf planets.[12]

Under this arrangement, the twelve planets of the rejected proposal were to be preserved in a distinction between eight classical planets and four dwarf planets

THERE ARE FOUR GALILEAN MOONS NOTICE HOW HE ONLY FIRST NOTICED THREE- THEN LATER HE NOTICED THE FOURTH- THE FOURTH IS ALWAYS DIFFERENT

On January 7, 1610, Galileo wrote a letter containing the first mention of Jupiter's moons. At the time, he saw only three of them, and he believed them to be fixed stars near Jupiter. He continued to observe these celestial orbs from January 8 to March 2, 1610. In these observations, he discovered a fourth body, and also observed that the four were not fixed stars, but rather were orbiting Jupiter.[2]

THERE IS A QUASAR SYSTEM CALLED TRIPLE QUASAR BUT THERE IS ACTUALLY A FOURTH IT IS JUST DIM- THE FOURTH IS ALWAYS DIFFERENT

Triple Quasar From the fact that there are three bright images of the same gravitationally lensed quasar is produced. There are actually four images: the fourth is faint.

CLOVERLEAF QUASAR IS FOUR QUASARS

The Cloverleaf quasar (H1413+117, QSO J1415+1129) is a bright, gravitationally lensed quasar.

Contents [hide]

1 Quasar

1.1 Black hole

2 History

4 References

Quasar

Molecular gas (notably CO) detected in the host galaxy associated with the quasar is the oldest molecular material known and provides evidence of large-scale star formation in the early universe. Thanks to the strong magnification provided by the foreground lens, the Cloverleaf is the brightest known source of CO emission at high redshift[1] and was also the first source at a redshift z = 2.56 to be detected with HCN[2] or HCO+ emission.[3] The 4 quasar images were originally discovered in 1984; in 1988, they were determined to be a single quasar split into four images, instead of 4 separate quasars. The X-rays from iron atoms were also enhanced relative to X-rays at lower energies. Since the amount of brightening due to gravitational lensing doesn't vary with the wavelength, this means that an additional object has magnified the X-rays. The increased magnification of the X-ray light can be explained by gravitational microlensing, an effect which has been used to search for compact stars and planets in our galaxy. Microlensing occurs when a star or a multiple star system passes in front of light from a background object. If a single star or a multiple star system in one of the foreground galaxies passed in front of the light path for the brightest image, then that image would be selectively magnified.

RX J1131-1231's quasar4RX J1131-1231's elliptical galaxyRX J1131-1231 is the name of the complex, quasar, host galaxy and lensing galaxy, together. The quasar's host galaxy is also lensed into a Chwolson ring about the lensing galaxy. The four images of the quasar are embedded in the ring image.

FIRST QUASAR QUARTET DISCOVERED

quasars of SDSS J0841+3921 protocluster 4 First quasar quartet discovered.[15][16]

FAMOUS EINSTEIN CROSS

Picture shows a cosmic mirage known as the Einstein Cross. Four apparent images are actually from the same quasar.

THE EMISSION SPECTRUM OF HYDROGEN IS WHAT BOHR USED TO DISCOVER QUANTUM MECHANCIS-- IT HAS FOUR LINES

A second, related, puzzle was the emission spectrum of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by hydrogen consists of four different colours, as shown in the picture below. The intensity of the light at different frequencies is also different. By contrast, white light consists of a continuous emission across the whole range of visible frequencies. By the end of the nineteenth century, a simple rule known as Balmer's formula had been found which showed how the frequencies of the different lines were related to each other, though without explaining why this was, or making any prediction about the intensities. The formula also predicted some additional spectral lines in ultraviolet and infrared light which had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.

Emission spectrum of hydrogen. When excited, hydrogen gas gives off light in four distinct colours (spectral lines) in the visible spectrum, as well as a number of lines in the infrared and ultraviolet.

THE FOURTH QUANTUM NUMBER IS DIFFERENT AND PAULI UNDERSTOOD THIS AND EVEN MENTIONED JUNG AND THE QUATERNITY NOTICING THAT THE PATTERN WAS SIMILAR TO THE QUATERNITY PATTERN WHERE THE FOURTH IS DIFFERENT

Within Schrödinger's picture, each electron has four properties:

An "orbital" designation, indicating whether the particle wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy;

The "shape" of the orbital, spherical or otherwise;

The "inclination" of the orbital, determining the magnetic moment of the orbital around the z-axis.

The "spin" of the electron.

The collective name for these properties is the quantum state of the electron. The quantum state can be described by giving a number to each of these properties; these are known as the electron's quantum numbers. The quantum state of the electron is described by its wave function. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four numbers.

FOUR QUANTUM DOTS
https://en.wikipedia.org/wiki/File:CA02.jpg
https://en.wikipedia.org/wiki/Quantum_dot_cellular_automaton
Modern cells
Today, standard solid state QCA cell design considers the distance between quantum dots to be about 20 nm, and a distance between cells of about 60 nm. Just like any CA, Quantum (-dot) Cellular Automata are based on the simple interaction rules between cells placed on a grid. A QCA cell is constructed from four quantum dots arranged in a square pattern. These quantum dots are sites electrons can occupy by tunneling to them.

FOUR STAGES

A QCA clock induces four stages in the tunneling barriers of the cells above it. In the first stage, the tunneling barriers start to rise. The second stage is reached when the tunneling barriers are high enough to prevent electrons from tunneling. The third stage occurs when the high barrier starts to lower. And finally, in the fourth stage, the tunneling barriers allow electrons to freely tunnel again. In simple words, when the clock signal is high, electrons are free to tunnel. When the clock signal is low, the cell becomes latched.

Figure 7 shows a clock signal with its four stages and the effects on a cell at each clock stage. A typical QCA design requires four clocks, each of which is cyclically 90 degrees out of phase with the prior clock. If a horizontal wire consisted of say, 8 cells and each consecutive pair, starting from the left were to be connected to each consecutive clock, data would naturally flow from left to right. The first pair of cells will stay latched until the second pair of cells gets latched and so forth. In this way, data flow direction is controllable through clock zones

THE FOUR BELL STATES

The prerequisites for quantum teleportation are a qubit that is to be teleported, a conventional communication channel capable of transmitting two classical bits (i.e., one of four states), and means of generating an entangled EPR pair of qubits, transporting each of these to two different locations, A and B, performing a Bell measurement on one of the EPR pair qubits, and manipulating the quantum state of the other of the pair. The protocol is then as follows:

An EPR pair is generated, one qubit sent to location A, the other to B.

At location A, a Bell measurement of the EPR pair qubit and the qubit to be teleported (the quantum state

|

ϕ

⟩|\phi \rangle) is performed, yielding one of four measurement outcomes, which can be encoded in two classical bits of information. Both qubits at location A are then discarded.

Using the classical channel, the two bits are sent from A to B. (This is the only potentially time-consuming step after step 1, due to speed-of-light considerations.)

As a result of the measurement performed at location A, the EPR pair qubit at location B is in one of four possible states. Of these four possible states, one is identical to the original quantum state

|

ϕ

⟩|\phi \rangle, and the other three are closely related. Which of these four possibilities actually obtains is encoded in the two classical bits. Knowing this, the qubit at location B is modified in one of three ways, or not at all, to result in a qubit identical to

THE VERY FAMOUS FOUR BELL STATES
https://en.wikipedia.org/wiki/Bell_state
The Bell states are four specific maximally entangled quantum states of two qubits.

In 1968, Fuat Sezgin found four previously unknown books of Arithmetica at the shrine of Imam Rezā in the holy Islamic city of Mashhad in northeastern Iran.[3] The four books are thought to have been translated from Greek to Arabic by Qusta ibn Luqa (820–912).[2] Norbert Schappacher has written:

[The four missing books] resurfaced around 1971 in the Astan Quds Library in Meshed (Iran) in a copy from 1198 AD. It was not catalogued under the name of Diophantus (but under that of Qust¸a ibn Luqa) because the librarian was apparently not able to read the main line of the cover page where Diophantus’s name appears in geometric Kufi calligraphy.[4]

PRINTING IS WITH FOUR COLORS THE FOURTH K BLACK IS DIFFERENT

The widespread offset-printing process is composed of four spot colors: Cyan, Magenta, Yellow, and Key (black) commonly referred to as CMYK.

The Source Four PAR is a stage lighting instrument manufactured by Electronic Theatre Controls. The name of the fixture derives from the stylistic and construction features it shares with ETC's Source Four. The suffix identifies the Source Four PAR as a parabolic aluminized reflector (PAR). It is designed and marketed as a modern, energy efficient alternative to traditional PAR fixtures used in theatrical and broadcast lighting.

THE FIRST TIGER STRIPE PATTERN HAD 64 STRIPES THAT IS FOUR TIMES 16 FOUR QUADRANT MODELS
https://en.wikipedia.org/wiki/Tigerstripe
It is unclear who developed the first tigerstripe pattern, consisting of sixty-four (64) stripes.

PHYSICISTS ARE AMAZED BY THE FOUR TIGER STRIPES ON THE MOON SHOOTING OUT WATER AND THEY DO NOT KNOW HOW IT IS SO- I LEARNED ABOUT IT ON A ASTRONOMY PROGRAM- IT IS BECAUSE OF THE QUADRANT MODEL
The tiger stripes of Enceladus consist of four sub-parallel, linear depressions in the south polar region of the Saturnian moon.[1] First observed on May 20, 2005 by the Cassini spacecraft's Imaging Science Sub-system (ISS) camera (though seen obliquely

GALILEOS FAMOUS BOOK IS DIVIDED INTO FOUR DAYS AND FOUR CLASSES OF ARGUMENT- THE FOURTH DAY HE GIVES A THEORY OF TIDES WHICH TURNS OUT TO BE WRONG- THE FOURTH IS ALWAYS DIFFERENT- A FAMOUS COPY OF THE TEXT EVEN OMITS THE FOURTH DAY

The book is presented as a series of discussions, over a span of four days

Galileo attempted a fourth class of argument:

Direct physical argument for the Earth's motion, by means of an explanation of tides.

As an account of the causation of tides or a proof of the Earth's motion, it is a failure. The fundamental argument is internally inconsistent and actually leads to the conclusion that tides do not exist. But, Galileo was fond of the argument and devoted the "Fourth Day" of the discussion to it.

The degree of its failure is—like nearly anything having to do with Galileo—a matter of controversy. On the one hand, the whole thing has recently been described in print as "cockamamie."[12] On the other hand, Einstein used a rather different description:

It was Galileo's longing for a mechanical proof of the motion of the earth which misled him into formulating a wrong theory of the tides. The fascinating arguments in the last conversation would hardly have been accepted as proof by Galileo, had his temperament not got the better of him. [Emphasis added][13][14]

Nov 26, 2015 2:14pm

4 Types of Innovation (and how to approach them) | Digital Tonto

A periodic waveforms include these while

t

t is time,

λ\lambda is wavelength,

a

a is amplitude and

ϕ\phi is phase:

Sine wave

(

t

,

λ

,

a

,

ϕ

)

=

a

sin

2

π

t

ϕ

λ{\displaystyle (t,\lambda ,a,\phi )=a\sin {\frac {2\pi t-\phi }{\lambda }}}. The amplitude of the waveform follows a trigonometric sine function with respect to time.

Square wave

(

t

,

λ

,

a

,

ϕ

)

=

{

a, (t−ϕ)

mod

λ<

duty

−a,

otherwise

{\displaystyle (t,\lambda ,a,\phi )={\begin{cases}a,&(t-\phi ){\bmod {\lambda }}<{\text{duty}}\\-a,&{\text{otherwise}}\end{cases}}}. This waveform is commonly used to represent digital information. A square wave of constant period contains odd harmonics that decrease at −6 dB/octave.

Triangle wave

(

t

,

λ

,

a

,

ϕ

)

=

2

a

π

arcsin

sin

2

π

t

ϕ

λ{\displaystyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arcsin \sin {\frac {2\pi t-\phi }{\lambda }}}. It contains odd harmonics that decrease at −12 dB/octave.

Sawtooth wave

(

t

,

λ

,

a

,

ϕ

)

=

2

a

π

arctan

tan

2

π

t

ϕ

2

λ{\displaystyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arctan \tan {\frac {2\pi t-\phi }{2\lambda }}}. This looks like the teeth of a saw. Found often in time bases for display scanning. It is used as the starting point for subtractive synthesis, as a sawtooth wave of constant period contains odd and even harmonics that decrease at −6 dB/octave.

01/24/2006: The most important characteristic of sounds that have a definite pitch is that they have a repeating waveform. With audio oscillators we can generate what are considered to be the 4 most basic waveforms, the sine, triangle, square, and sawtooth (or "ramp") waves. These waveforms, in that order, represent a steadily increasing complexity of shape and of timbre as the number and strength of the harmonics for each wave form increases. (Some folks consider the 'pulse' wave to be among the basics but I consider it a more complex cousin of the square wave so I haven't included it here.)

Envelopes like the one pictured here are called ADSR envelopes, so named for their four stages: Attack, Decay, Sustain, and Release. When we put an ADSR envelope module in a synthesizer, we specify exactly what is to happen during each stage of the envelope after an "on" gate signal is received. For example, the envelope pictured above has an attack stage that lasts 250 milliseconds, where the level increases to 1. After that, it has a decay stage lasting 200 milliseconds where the level decreases to 0.7. During the sustain stage, the level stays at 0.7 for as long as the envelope generator is receiving an "on" gate signal. Sustain stages do not have a specified duration. When the gate signal changes to "off," we enter the release stage, where the level takes 200 milliseconds to drop to 0.

There’s a lot of truth in the book and I thought it would be fun to relate the four characters to the four PSIU forces of Organizational Physics. That way, the next time you’re managing a Hem, Haw, Sniff, or Scurry, you’ll have a better sense for how to handle it.

As a refresher, here’s a matrix that shows the traits of the four universal PSIU forces. If this concept is new to you, you can quickly get a sense of it using the world’s fastest personality test (it takes less than 15 seconds to get a good sense of someone’s style).

The four forces of Organizational Physics: PSIU.

The four forces of Organizational Physics: PSIU.

And here are the four Who Moved My Cheese characters mapped to each force:

The characters of Who Moved My Cheese mapped to the four PSIU forces of Organizational Physics.

The characters of Who Moved My Cheese mapped to the four PSIU forces of Organizational Physics.

In a nutshell:

Sniff is an Innovator style. He’s got the ability to sense and respond to changes happening in the environment much more quickly than the other styles. He gets excited about creating new things and likes you to get excited with him.

Scurry is a Producer style. He’s got the ability to run, run, run and do the work from early to late. He gets frustrated when there are obstacles in his path and seeks to run around them or punch through them.

Hem is a Stabilizer style. He’s got the ability to make things systematized and controllable. In the story, it is Hem who gets left behind because change can be seen as a really big threat to someone who excels at control and stability.

Haw is a Unifier style. He’s got the ability to empathize and connect well with others. In the story, it is Haw who follows Sniff and Scurry but all the while is concerned about where Hem is and how Hem is doing. Ultimately, Haw leaves the writing on the wall for others like Hem to follow.

Key Takeaways

The main thing I want you to take away is that the four PSIU forces of Organizational Physics are universal. That means they show up in good children’s books and the board room alike. When you learn to spot and understand them, you exponentially increase your own capabilities as a communicator and manager.

FOUR ELEMENTARY CATASTROPHES- FOUR WITH ONE VARIABLE

I created a table with each of these equations for the first four elementary catastrophes. I am still working on the last three, which have more complex partial derivatives than the previous.

I created in Mathematica family of functions for the first four catastrophes; the fold (A2), the cusp (A3), the swallowtail (A4), and the butterfly (A5). These are known as cuspoids and depend on only one state variable

Above you can see the family of functions for the first four catastrophes. A clear relationship can be seen among them. Notice how there are more functions in the higher order catastrophes because, unlike the fold catastrophe that only has the control parameter a, they have more than one control parameter. In the cusp the control parameters a and b are varied. In the swallowtail the control parameters a, b and c are varied. In the butterfly the control parameters a, b, c and d are varied. These plots are pretty awesome looking! The plot of the family of functions for butterfly catastrophe is pretty fitting ☺. I have also plotted the formation of the ray (critical point) and the formation of the catastrophe (the degenerate). My next step is to try and create the shapes of the umbilics, which as I mentioned previously depend on two state parameters.

THE GO BOARD IS QUADRANTS AND MAX WAS CORRECT THAT THERE IS AN ORDER AND INTERESTINGLY HE CALLED IT THE 216 NUMBER 16- AT THE BEGINNING OF THE MOVIE HE HAS FOUR AXIOMS

Unified Model, Keirsey-Bartle Diagram

Here are some brief descriptions of each combination, showing how Keirsey and Bartle ascribe the same basic motivations to each temperament/type.

Idealist/Socializer: Socializers are described by Bartle as "... interested in people, and what they have to say. ... Inter-player relationships are important ... seeing [people] grow as individuals, maturing over time. ... The only ultimately fulfilling thing is ... getting to know people, to understand them, and to form beautiful, lasting relationships."

This is closely related to the Keirseian description of Idealists, who are very aware of other people as part of their lifelong journey of self-discovery (Internal Change). In a way, the highly imaginative Idealists are always roleplaying; they are constantly creating images of themselves (or others) that they feel they should model through their own actions in order to produce the emotions in themselves that they want to feel.

Guardian/Achiever: For the Guardian, the world is an insecure place, so it's necessary to protect oneself by accumulating material possessions... just in case. Thus, Guardians focus on earning money, on competing with others for resources perceived as scarce, on buying nice things and maintaining them, on forming stable and hierarchical group relationships, and generally on working hard to make their place in the world secure by locking down their connections to the world as possessions (External Structure).

Compare that to Bartle's description of Achievers: "Achievers regard points-gathering and rising in levels as their main goal" and "Achievers are proud of their formal status in the game's built-in level hierarchy, and of how short a time they took to reach it." Leveling up, leaderboards, and the accumulation of vast quantities of looted items are all behaviors that are driven more by a security-seeking motivation than by other motivations such as powerful sensations, understanding or self-growth.

This explains why the Guardian/Achiever is willing to persist in long stretches of "grind" that other kinds of gamers don't perceive as fun at all. To this gamer, rewards should be proportional to the amount of effort invested. When a game is designed around simple, well-defined tasks that enable the competitive accumulation of status tokens, that game is virtually guaranteed to attract security-seeking Guardian/Achievers.

Rational/Explorer: Rationals play in the same way that they do everything else -- they find pleasure in discovering the organized structural patterns behind raw data (Internal Structure). These can be patterns in space (as in geography) or patterns in time (as in morphology). Or they can be cause-and-effect patterns (entailment) or relationship patterns (connections). Ultimately, it's all about achieving a strategic understanding of the system as a whole thing.

As Bartle describes Explorers: "The real fun comes only from discovery, and making the most complete set of maps in existence." Of the core motivations -- sensation-seeking, security-seeking, knowledge-seeking, and identity-seeking -- exploration as "discovery" is most closely aligned with the Rational's knowledge-seeking preference. For the Rational/Explorer, once the principle behind the data is revealed, that's enough -- understanding is its own reward. These gamers can enjoy imparting knowledge to others, but no extrinsic reward for doing so is needed or expected.

Artisan/Killer: Finally, there are the Killers (or, as I prefer to call them, Manipulators). These can be difficult to understand in a gameplay context because most virtual worlds have encoded rules that marginalize their play style as "griefing" (i.e., upsetting other players) and try to prevent it. As Bartle puts it, "Killers get their kicks from imposing themselves on others." He also points out that Killers "wish only to demonstrate their superiority over fellow humans."

This desire for power over everything in their world is most closely echoed in the Keirseian description of Artisans, who (as their temperament name suggests) delight in the skillfully artistic manipulation of their environment. The Artisan/Killers are the tool-users, the adrenaline junkies, the natural politicians, the combat pilots, the high-stakes gamblers, and the negotiators par excellence. They instinctively find and exploit advantages in any tactical situation, and they express this need for dominance of their world in order to retain the greatest amount of personal freedom possible (External Change).

I believe a very good example of this can be found in Ryan Creighton's "social engineering" of the coin-collecting game at the Social Game Developers Rant of the 2011 Game Developers Conference. A Guardian/Achiever would have played by the rules and raced around the room begging others for their coins to try to win the game; an Idealist/Socializer would have asked for coins as a way to meet new people or help others win; and a Rational/Explorer would have sat quietly watching the flow of coin exchanges to try to understand the nature of the game. But an Artisan/Killer would instantly see how to short-circuit the designed system, and, as a born negotiator, would find it easy to persuade the person holding one of the bags of coins to hand the whole thing over... which is exactly what happened.

If the attendees needed to hear a rant from anyone, it would be the Manipulator who is out there, just waiting to exploit any opportunity to bring a little chaos to the carefully designed order of a social game. (See Ryan's description of the event for a wonderful first-hand account of gameplay from what appears to me to be a classic Artisan/Killer perspective.)

A final note on the Keirsey/Bartle linkage: the Keirsey temperaments and Bartle Types may appear not to line up directly where attitudes toward other people are concerned. This is because the Bartle Types were developed within a multi-player environment, which selects for more extroverted, sociable gamers, while the temperaments include both extroverts and introverts.

So, for example, the "Socializer" term that makes sense within the Bartle Types for its emphasis on interacting with other people can seem not to apply to an introverted Idealist who prefers to play single-player games. These less-social Socializers are more likely to prefer individualized entertainment or abstract games, making it difficult to distinguish them from Rational/Explorer gamers. Closer study is usually required to see whether their primary reason for playing is to feel good (an Idealist preference) or to exercise their thinking skills (a Rational goal).

Four Craters Lava Field is a basaltic volcanic field located south east of Newberry Caldera in the U.S. state of Oregon.[1] The volcanic field covers about 30 square kilometers. Four Pleistocene cinder cones are the source of the flows in the field and are aligned along a fissure trending N 30° W. The cones rise 75 to 120 meters above the flows and the distance between the northern most and southern most cones is about 3.5 kilometers.[3]

In a pure (intrinsic) Si or Ge semiconductor, each nucleus uses its four valence electrons to form four covalent bonds with its neighbors (see figure below). Each ionic core, consisting of the nucleus and non-valent electrons, has a net charge of +4, and is surrounded by 4 valence electrons. Since there are no excess electrons or holes In this case, the number of electrons and holes present at any given time will always be equal.

Intrinsic semiconductor.jpg

An intrinsic semiconductor. Note each +4 ion is surrounded by four electrons.

Now, if one of the atoms in the semiconductor lattice is replaced by an element with three valence electrons, such as a Group 3 element like Boron (B) or Gallium (Ga), the electron-hole balance will be changed. This impurity will only be able to contribute three valence electrons to the lattice, therefore leaving one excess hole (see figure below). Since holes will "accept" free electrons, a Group 3 impurity is also called an acceptor.

SEMICONDUCTORS HAVE A "HOLE" AT THE FOURTH ELECTRON SPOT OF SILICON- SILICON IS A QUADRANT WITH FOUR VALENCE ELECTRONS

Semiconductors are most often made from silicon. Silicon is an element with four electrons in its outer shell. To make a p-type semiconductor extra materials like boron or aluminium are added to the silicon. These materials have only three electrons in their outer shell. When the extra material replaces some of the silicon it leaves a 'hole' where the fourth electron would have been if the semiconductor was pure silicon.

FOUR TERMINAL DEVICE

Although the MOSFET is a four-terminal device with source (S), gate (G), drain (D), and body (B) terminals,[1] the body (or substrate) of the MOSFET is often connected to the source terminal, making it a three-terminal device like other field-effect transistors. Because these two terminals are normally connected to each other (short-circuited) internally, only three terminals appear in electrical diagrams.

AGAIN THE HIGHEST LEVEL IS FOUR TERMINAL DEVICES- THE FOURTH IS ALWAYS TRANSCENDENT

Two-terminal devices:

DIAC

Diode (rectifier diode)

Gunn diode

IMPATT diode

Laser diode

Light-emitting diode (LED)

Photocell

Phototransistor

PIN diode

Schottky diode

Solar cell

Transient-voltage-suppression diode

Tunnel diode

VCSEL

Zener diode

Three-terminal devices:

Bipolar transistor

Darlington transistor

Field-effect transistor

Insulated-gate bipolar transistor (IGBT)

Silicon-controlled rectifier

Thyristor

TRIAC

Unijunction transistor

Four-terminal devices:

Hall effect sensor (magnetic field sensor)

Photocoupler (Optocoupler)

Four-phase logic is a type of, and design methodology for, dynamic logic. It enabled non-specialist engineers to design quite complex ICs, using either PMOS or NMOS processes. It uses a kind of 4-phase clock signal.

Contents [hide]

1 History

2 Structure

3 Usage

4 Evolution

5 References

History

R. K. "Bob" Booher, an engineer at Autonetics, invented four-phase logic, and communicated the idea to Frank Wanlass at Fairchild Semiconductor; Wanlass promoted this logic form at General Instrument Microelectronics Division.[1] Booher made the first working four-phase chip, the Autonetics DDA integrator, during February 1966; he later designed several chips for and built the Autonetics D200 airborne computer using this technique.[2]

In April 1967, Joel Karp and Elizabeth de Atley published an article "Use four-phase MOS IC logic" in Electronic Design magazine.[3] In the same year, Cohen, Rubenstein, and Wanlass published "MTOS four phase clock systems."[4] Wanlass had been director of research and engineering at General Instrument Microelectronics Division in New York since leaving Fairchild Semiconductor in 1964.

Lee Boysel, a disciple of Wanlass[5] and a designer at Fairchild Semiconductor, and later founder of Four-Phase Systems, gave a "late news" talk on a four-phase 8-bit adder device in October 1967 at the International Electron Devices meeting.[6] J. L. Seely, manager of MOS Operations at General Instrument Microelectronics Division, also wrote about four-phase logic in late 1967.[7]

In 1968 Boysel published an article "Adder On a Chip: LSI Helps Reduce Cost of Small Machine" in Electronics magazine;[8] Four-phase papers from Y. T. Yen also appear that year.[9][10] Other papers followed shortly.[11]

Boysel recalls that four-phase dynamic logic allowed him to achieve 10X the packing density, 10X the speed, and 1/10 the power, compared to other MOS techniques being used at the time (metal-gate saturated-load PMOS logic), using the first-generation MOS process at Fairchild.[12]

HIGHEST AGAIN IS THE FOUR PHASE- THE FOURTH IS ALWAYS TRANSCENDENT

4-phase clock

A "4-phase clock" has clock signals distributed on 4 wires (four-phase logic).[7]

In some early microprocessors such as the National Semiconductor IMP-16 family, a multi-phase clock was used. In the case of the IMP-16, the clock had four phases, each 90 degrees apart, in order to synchronize the operations of the processor core and its peripherals.

The DEC WRL MultiTitan microprocessor uses a four phase clocking scheme.[8]

Some ICs use four-phase logic.

Intrinsity's Fast14 technology uses a multi-phase clock.

Most modern microprocessors and microcontrollers use a single-phase clock, however.

AGAIN FOUR TERMINAL IS THE HIGHEST- FOURTH IS ALWAYS TRANSCENDENT

A power device may be classified as one of the following main categories (see figure 1):

A two-terminal device (e.g., a diode), whose state is completely dependent on the external power circuit to which it is connected.

A three-terminal device (e.g., a triode), whose state is dependent on not only its external power circuit, but also the signal on its driving terminal (this terminal is known as the gate or base).

A four terminal device (e.g. Silicon Controlled Switch -SCS). SCS is a type of thyristor having four layers and four terminals called anode, anode gate, cathode gate and cathode. the terminals are connected to the first, second, third and fourth layer respectively.[3]

I'm a paragraph. Click

LOOK AT THE FOUR TYPES BASED ON QUADRANT MODEL- "FOUR DISTINCT REGIONS OF OPERATION"

Regions of operation

Applied voltages B-E junction

bias (NPN) B-C junction

bias (NPN) Mode (NPN)

E < B < C Forward Reverse Forward-active

E < B > C Forward Forward Saturation

E > B < C Reverse Reverse Cut-off

E > B > C Reverse Forward Reverse-active

Applied voltages B-E junction

bias (PNP) B-C junction

bias (PNP) Mode (PNP)

E < B < C Reverse Forward Reverse-active

E < B > C Reverse Reverse Cut-off

E > B < C Forward Forward Saturation

E > B > C Forward Reverse Forward-active

Bipolar transistors have four distinct regions of operation, defined by BJT junction biases.

Forward-active (or simply active)

The base–emitter junction is forward biased and the base–collector junction is reverse biased. Most bipolar transistors are designed to afford the greatest common-emitter current gain, βF, in forward-active mode. If this is the case, the collector–emitter current is approximately proportional to the base current, but many times larger, for small base current variations.

Reverse-active (or inverse-active or inverted)

By reversing the biasing conditions of the forward-active region, a bipolar transistor goes into reverse-active mode. In this mode, the emitter and collector regions switch roles. Because most BJTs are designed to maximize current gain in forward-active mode, the βF in inverted mode is several times smaller (2–3 times for the ordinary germanium transistor). This transistor mode is seldom used, usually being considered only for failsafe conditions and some types of bipolar logic. The reverse bias breakdown voltage to the base may be an order of magnitude lower in this region.

Saturation

With both junctions forward-biased, a BJT is in saturation mode and facilitates high current conduction from the emitter to the collector (or the other direction in the case of NPN, with negatively charged carriers flowing from emitter to collector). This mode corresponds to a logical "on", or a closed switch.

Cut-off

In cut-off, biasing conditions opposite of saturation (both junctions reverse biased) are present. There is very little current, which corresponds to a logical "off", or an open switch.

IT IS FOUR LAYERS

A silicon controlled rectifier or semiconductor-controlled rectifier is a four-layer solid-state current-controlling device. The principle of four layer p-n-p-n switching was developed by Moll, Tanenbuam, Goldey and Holonyak of Bell Laboratories in 1956.[1] The practical demonstration of silicon controlled switching and detailed theoretical behavior of a device in agreement with the experimental results was presented by Dr Ian M. Mackintosh of Bell Laboratories in January 1958.[2][3] The name "silicon controlled rectifier" is General Electric's trade name for a type of thyristor. The SCR was developed by a team of power engineers led by Gordon Hall[4] and commercialized by Frank W. "Bill" Gutzwiller in 1957.

Some sources define silicon controlled rectifiers and thyristors as synonymous,[5] other sources define silicon controlled rectifiers as a proper subset of the set of thyristors, those being devices with at least four layers of alternating n- and p-type material.[6][7] According to Bill Gutzwiller, the terms "SCR" and "controlled rectifier" were earlier, and "thyristor" was applied later, as usage of the device spread internationally.[8]

The silicon control rectifier (SCR) consists of four layers of semiconductors, which form NPNP or PNPN structures have three P-N junctions labeled J1, J2 and J3, and three terminals. The anode terminal of an SCR is connected to the p-type material of a PNPN structure, and the cathode terminal is connected to the n-type layer, while the gate of the SCR is connected to the p-type material nearest to the cathode.[9]

An SCR consists of four layers of alternating p- and n-type semiconductor materials. Silicon is used as the intrinsic semiconductor, to which the proper dopants are added. The junctions are either diffused or alloyed (alloy is a mixed semiconductor or a mixed metal). The planar construction is used for low-power SCRs (and all the junctions are diffused). The mesa-type construction is used for high-power SCRs. In this case, junction J2 is obtained by the diffusion method, and then the outer two layers are alloyed to it, since the PNPN pellet is required to handle large currents. It is properly braced with tungsten or molybdenum plates to provide greater mechanical strength. One of these plates is hard-soldered to a copper stud, which is threaded for attachment of heat sink. The doping of PNPN depends on the application of SCR, since its characteristics are similar to those of the thyristor. Today, the term "thyristor" applies to the larger family of multilayer devices that exhibit bistable state-change behaviour, that is, switching either on or off.

FOUR LAYERS

A thyristor is a solid-state semiconductor device with four layers of alternating N and P-type materials. It acts exclusively as a bistable switch, conducting when the gate receives a current trigger, and continuing to conduct while the voltage across the device is not reversed (forward-biased).

Some sources define silicon-controlled rectifier (SCR) and thyristor as synonymous.[1] Other sources define thyristors as a larger set of devices with at least four layers of alternating N and P-type material.

The thyristor is a four-layered, with each layer consisting of alternately N-type or P-type material, for example P-N-P-N. The main terminals, labelled anode and cathode, are across all four layers. The control terminal, called the gate, is attached to p-type material near the cathode. (A variant called an SCS—Silicon Controlled Switch—brings all four layers out to terminals.)

SEMICONDUCTORS ARE MADE OF SILICON OR GERMANIUM BECAUSE THEY HAVE FOUR VALENCE ELECTRONS (ARE QUADRANTS)

Semiconductor materials like silicon and germanium have four electrons in their outer shell (valence shell). All the four electrons are used by the semiconductor atom in forming bonds with its neighbouring atoms, leaving a low number of electrons available for conduction. Pentavalent elements are those elements which have five electrons in their outer shell. When pentavalent impurities like Phosphorus or Arsenic are added into semiconductor, four electrons form bonds with the surrounding silicon atoms leaving one electron free. The resulting material has a large number of free electrons. Since electrons are negative charge carriers, the resultant material is called N-type (or negative type) semiconductor. The pentavalent impurity that is added is called 'Dopant' and the process of addition is called 'doping'.

FOUR TRANSISTORS SINGLE WAFER

Their first marketed transistor was the 2N697 (1958) (initially a mesa transistor),[5] and was a huge success. The first batch of 100 was sold to IBM for $150 a piece. The first planar silicon transistor was the 2N1613 developed by Jean Hoerni. Its introduction was a historic event in semiconductor history. Only two years later (1960) they had managed to build a circuit with four transistors on a single wafer of silicon, thereby creating the first silicon integrated circuit (Texas Instruments' Jack Kilby had developed an integrated circuit made of germanium on September 12, 1958, and was awarded a U.S. patent). The company grew from twelve to twelve thousand employees, and was soon making$130 million a year.

SEMICONDUCTORS ARE DUE TO THE FOUR VALENCE ELECTROSN OF SILICON

In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form a n-type region.

Phosphorus atom acting as a donor in the simplified 2D Silicon lattice.

For example, when silicon (Si), having four valence electrons, needs to be doped as a n-type semiconductor, elements from group V like phosphorus (P) or arsenic (As) can be used because they have five valence electrons. A dopant with five valence electrons is also called a pentavalent impurity. [1] Other pentavalent dopants are antimony (Sb) and bismuth (Bi).

When substituting a Si atom in the crystal lattice, four of the valence electrons of phosphorus form covalent bonds with the neighbouring Si atoms but the fifth one remains weakly bonded. At room temperature, all the fifth electrons are liberated, can move around the Si crystal and can carry a current and thus act as charge carriers. The initially electroneutral donor becomes positively charged (ionised).

FOUR LAYER DIODE INSTEAD OF THREE- THE FOURTH IS ALWAYS DIFFERENT

While work on the transistors continued, Shockley hit upon the idea of using a four-layer device (transistors are three) that would have the novel quality of locking into the "on" or "off" state with no further control inputs. Similar circuits required several transistors, typically three, so for large switching networks the new diodes would greatly reduce complexity.[3][4] The four-layer diode is now called the Shockley diode.

FOUR LAYERS

The Shockley diode (named after physicist William Shockley) is a four-layer semiconductor diode, which was one of the first semiconductor devices invented. It was a "pnpn" diode. It is equivalent to a thyristor with a disconnected gate.

Four point probe is used to measure resistive properties of semiconductor wafers and thin films. If the thickness of a thin film is known, the sheet resistance measured by four point probe can be used to calculate the resistivity of the material; conversely, if the material's resistivity is known, the thickness of the thin film can be calculated.

Contents [hide]

1 Method of operation

2 Applications

3 Equipment

3.1 Miller FPP-5000 4-Point Probe

5 References

Method of operation

A four point probe is typically used to measure the sheet resistance of a thin layer or substrate in units of ohms per square by forcing current through two outer probes and reading the voltage across the two inner probes. Using this four-terminal configuration avoids measurement error due to the contact resistance between the probe and sample.

THERE ARE FOUR TYPES OF AMPLIFIER IN A QUADRANT PATTERN

https://en.wikipedia.org/wiki/Amplifier

Electronic amplifiers use one variable presented as either a current and voltage. Either current or voltage can be used as input and either as output, leading to four types of amplifiers.[1] In idealized form they are represented by each of the four types of dependent source used in linear analysis, as shown in the figure, namely:

FOUR TERMINALS

The field-effect transistor, sometimes called a unipolar transistor, uses either electrons (in n-channel FET) or holes (in p-channel FET) for conduction. The four terminals of the FET are named source, gate, drain, and body (substrate). On most FETs, the body is connected to the source inside the package, and this will be assumed for the following description.

FETS HAVE THREE TERMINALS FOR SURE BUT THEY ALSO HAVE A FOURTH- THE FOURTH IS ALWAYS DIFFERENT

The FET's three terminals are:[3]

Source (S), through which the carriers enter the channel. Conventionally, current entering the channel at S is designated by IS.

Drain (D), through which the carriers leave the channel. Conventionally, current entering the channel at D is designated by ID. Drain-to-source voltage is VDS.

Gate (G), the terminal that modulates the channel conductivity. By applying voltage to G, one can control ID.

Cross section of an n-type MOSFET

All FETs have source, drain, and gate terminals that correspond roughly to the emitter, collector, and base of BJTs. Most FETs have a fourth terminal called the body, base, bulk, or substrate. This fourth terminal serves to bias the transistor into operation; it is rare to make non-trivial use of the body terminal in circuit designs, but its presence is important when setting up the physical layout of an integrated circuit. The size of the gate, length L in the diagram, is the distance between source and drain. The width is the extension of the transistor, in the direction perpendicular to the cross section in the diagram (i.e., into/out of the screen). Typically the width is much larger than the length of the gate. A gate length of 1 µm limits the upper frequency to about 5 GHz, 0.2 µm to about 30 GHz.

Grunge guitarist Kurt Cobain used four 800 watt PA amplifiers for his early guitar set-up.

To understand how TRIACs work, consider the triggering in each of the four quadrants. The four quadrants are illustrated in Figure 1, and depend on the gate and MT2 voltages with respect to MT1. Main Terminal 1 (MT1) and Main Terminal (MT2) are also referred to as Anode 1 (A1) and Anode 2 (A2) respectively.[1]

FOUR INPUTS
https://en.wikipedia.org/wiki/Guitar_amplifier
https://en.wikipedia.org/…/File:1968_Fender_Bandmaster_fron…
Even in the 2010s, the vintage Fender Bandmaster remains a sought-after amp by guitarists. Note the four inputs, two for regular sound and two which are run through the onboard vibrato effect unit. The amp pictured is a 1968 model.

FOUR LAYERS

The IGBT is a semiconductor device with four alternating layers (P-N-P-N) that are controlled by a metal-oxide-semiconductor (MOS) gate structure without regenerative action.

This mode of operation was first proposed by Yamagami in his Japanese patent S47-21739, which was filed in 1968. This mode of operation was first experimentally reported in the lateral four layer device (SCR) by B. W. Scharf and J. D. Plummer in 1978.[3] This mode of operation was also experimentally discovered in vertical device in 1979 by B. Jayant Baliga.[4] The device structure was referred to as a ‘V-groove MOSFET device with the drain region replaced by a p-type Anode Region’ in this paper and subsequently as 'the insulated-gate rectifier' (IGR),[5] the insulated-gate transistor (IGT),[6] the conductivity-modulated field-effect transistor (COMFET)[7] and "bipolar-mode MOSFET".[8]

Plummer filed a patent application for IGBT mode of operation in the four layer device (SCR) in 1978. USP No.4199774 was issued in 1980 and B1 Re33209[9] was reissued in 1995 for the IGBT mode operation in the four layer device (SCR).

FOUR P-N LAYERS

It is a close cousin to the thyristor and like the thyristor consists of four p-n layers

Transistrons were commercially manufactured for the French telephone company and military, and in 1953 a solid-state radio receiver with four transistrons was demonstrated at the Düsseldorf Radio Fair.

August 1953 at the Düsseldorf Radio Fair by the German firm Intermetall. It was built with four of Intermetall's hand-made transistors, based upon the 1948 invention of Herbert Mataré and Heinrich Welker.

The TR-1 used four Texas NPN transistors and had to be powered by a 22.5-volt battery, since the only way to get adequate radio frequency performance out of early transistors was to run them close to their collector-to-emitter breakdown voltage. This made the TR-1 very expensive to run, and it was far more popular for its novelty or status value than its actual performance, rather in the fashion of the first MP3 players.

FOUR STORAGE SLOTS FOUR BIT REGISTER

The data are stored after each flip-flop on the 'Q' output, so there are four storage 'slots' available in this arrangement, hence it is a 4-bit Register. To give an idea of the shifting pattern, imagine that the register holds 0000 (so all storage slots are empty). As 'Data In' presents 1,0,1,1,0,0,0,0 (in that order, with a pulse at 'Data Advance' each time—this is called clocking or strobing) to the register, this is the result. The left hand column corresponds to the left-most flip-flop's output pin, and so on.

Toshiba TC4015BP - Dual 4-Stage Static Shift Register (with serial input/parallel output)

This configuration has the data input on lines D1 through D4 in parallel format, D1 being the most significant bit. To write the data to the register, the Write/Shift control line must be held LOW. To shift the data, the W/S control line is brought HIGH and the registers are clocked. The arrangement now acts as a PISO shift register, with D1 as the Data Input. However, as long as the number of clock cycles is not more than the length of the data-string, the Data Output, Q, will be the parallel data read off in order.

4-Bit PISO Shift Register

So the serial output of the entire register is 10110000. It can be seen that if data were to be continued to input, it would get exactly what was put in, but offset by four 'Data Advance' cycles. This arrangement is the hardware equivalent of a queue. Also, at any time, the whole register can be set to zero by bringing the reset (R) pins high.

16 ROWS- 16 SQUARES QMR

In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits.[6] Eventually, vacuum tubes replaced relays for logic operations. Lee De Forest's modification, in 1907, of the Fleming valve can be used as an AND logic gate. Ludwig Wittgenstein introduced a version of the 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Walther Bothe, inventor of the coincidence circuit, got part of the 1954 Nobel Prize in physics, for the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 (from 1935–38).

OR Gates are basic logic gates, and as such they are available in TTL and CMOS ICs logic families. The standard 4000 series CMOS IC is the 4071, which includes four independent two-input OR gates. The ancestral TTL device is the 7432. There are many offshoots of the original 7432 OR gate, all having the same pinout but different internal architecture, allowing them to operate in different voltage ranges and/or at higher speeds. In addition to the standard 2-Input OR Gate, 3- and 4-Input OR Gates are also available. In the CMOS series, these are:

4075: Triple 3-Input OR Gate

4072: Dual 4-Input OR Gate

Variations include:

74LS32: Quad 2-input OR gate (low power Schottky version)

74HC32: Quad 2-input OR gate (high speed CMOS version) - has lower current consumption/wider voltage range

74AC32: Quad 2-input OR gate (advanced CMOS version) - similar to 74HC32, but with significantly faster switching speeds and stronger drive

74LVC32: Low voltage CMOS version of the same.

THERE ARE THREE FACTORS OF PRODUCTION BUT IT IS QUESTIONED IF THERE IS A FOURTH FACTOR- THE FOURTH IS ALWAYS DIFFERENT

In economics, factors of production, resources, or inputs are what is used in the production process to produce output—that is, finished goods and services. The utilized amounts of the various inputs determine the quantity of output according to a relationship is called the production function. There are three basic resources or factors of production: land, labor and capital. The factors are also frequently labeled "producer goods or services" to distinguish them from the goods or services purchased by consumers, which are frequently labeled "consumer goods". All three of these are required in combination at a time to produce a commodity.

A fourth factor?

As mentioned, recent authors have added to the classical list. For example, J.B. Clark saw the co-ordinating function in production and distribution as being served by entrepreneurs; Frank Knight introduced managers who co-ordinate using their own money (financial capital) and the financial capital of others. In contrast, many economists today consider "human capital" (skills and education) as the fourth factor of production, with entrepreneurship as a form of human capital. Yet others refer to intellectual capital. More recently, many have begun to see "social capital" as a factor, as contributing to production of goods and services.

HIGHEST IT GOES TO IS QUAD

NOR Gates are basic logic gates, and as such they are recognised in TTL and CMOS ICs. The standard, 4000 series, CMOS IC is the 4001, which includes four independent, two-input, NOR gates

CMOS

4025: Triple 3-input NOR gate

4002: Dual 4-input NOR gate

4078: Single 8-input NOR gate

TTL

7427: Triple 3-input NOR gate

7425: Dual 4-input NOR gate (with strobe, obsolete)

74260: Dual 5-Input NOR Gate

744078: Single 8-input NOR Gate

THE MOST COMMON 2 TO FOUR LINE- IT IS A QUADRANT MODEL

A 2-to-4 line decoder

16 SQUARES QMR

In the example above, the four input variables can be combined in 16 different ways, so the truth table has 16 rows, and the Karnaugh map has 16 positions. The Karnaugh map is therefore arranged in a 4 × 4 grid.

AND gates are available in IC packages. 7408 IC is a famous QUAD 2-Input AND GATES and contains four independent gates each of which performs the logic AND function.

https://en.wikipedia.org/wiki/AND_gate
AND gates are available in IC packages. 7408 IC is a famous QUAD 2-Input AND GATES and contains four independent gates each of which performs the logic AND function.

FOUR

Equipment such as Inverto’s Unicable Cascadable Switch can be connected to a conventional quattro LNB to provide a single SatCR output and a conventional LNB output. The four IF inputs from the Quattro LNB are looped through to outputs so the unit can be cascaded to further SatCR switches or to the existing multiswitches of the IRS, so an SatCR-enabled output is provided without replacing the existing LNB or affecting the provision for conventional receivers in other households served by the rest of the system.[7]

Versions of the Unicable Switch to provide for four and eight tuners within a household are available, and to combine a digital terrestrial signal onto the SCR-enabled output as well.

Global Invacom’s SatCR Adaptor unit performs a similar function but is connected to the existing multiswitch outputs, to provide SatCR compatibility for one connection (one household) of an existing IRS.

The SatCR Adaptor connects to four outputs of an IRS multiswitch and provides a single SatCR output that is typically connected to the existing single coaxial cable to the household to be converted. A further four conventional IF outputs are provided to recover usage of the existing multiswitch outputs for other households. Within the SatCR enabled household, a splitter and power injector provides power to the SatCR Adaptor and splits the signal to feed the separate tuners connected.

FOUR

Equipment such as Inverto’s Unicable Cascadable Switch can be connected to a conventional quattro LNB to provide a single SatCR output and a conventional LNB output. The four IF inputs from the Quattro LNB are looped through to outputs so the unit can be cascaded to further SatCR switches or to the existing multiswitches of the IRS, so an SatCR-enabled output is provided without replacing the existing LNB or affecting the provision for conventional receivers in other households served by the rest of the system.[7]

Versions of the Unicable Switch to provide for four and eight tuners within a household are available, and to combine a digital terrestrial signal onto the SCR-enabled output as well.

Global Invacom’s SatCR Adaptor unit performs a similar function but is connected to the existing multiswitch outputs, to provide SatCR compatibility for one connection (one household) of an existing IRS.

The SatCR Adaptor connects to four outputs of an IRS multiswitch and provides a single SatCR output that is typically connected to the existing single coaxial cable to the household to be converted. A further four conventional IF outputs are provided to recover usage of the existing multiswitch outputs for other households. Within the SatCR enabled household, a splitter and power injector provides power to the SatCR Adaptor and splits the signal to feed the separate tuners connected.

FOUR ASPECTS

Four aspects of CIPP evaluation

These aspects are context, inputs, process, and product. These four aspects of CIPP evaluation assist a decision-maker to answer four basic questions:

What should we do?

This involves collecting and analysing needs assessment data to determine goals, priorities and objectives. For example, a context evaluation of a literacy program might involve an analysis of the existing objectives of the literacy programme, literacy achievement test scores, staff concerns (general and particular), literacy policies and plans and community concerns, perceptions or attitudes and needs.[1]

How should we do it?

This involves the steps and resources needed to meet the new goals and objectives and might include identifying successful external programs and materials as well as gathering information.[1]

Are we doing it as planned?

This provides decision-makers with information about how well the programme is being implemented. By continuously monitoring the program, decision-makers learn such things as how well it is following the plans and guidelines, conflicts arising, staff support and morale, strengths and weaknesses of materials, delivery and budgeting problems.[1]

Did the programme work?

By measuring the actual outcomes and comparing them to the anticipated outcomes, decision-makers are better able to decide if the program should be continued, modified, or dropped altogether. This is the essence of product evaluation.[1]

Using CIPP in the different stages of the evaluation

The CIPP model is unique as an evaluation guide as it allows evaluators to evaluate the program at different stages, namely: before the program commences by helping evaluators to assess the need and at the end of the program to assess whether or not the program had an effect.

CIPP model allows you to ask formative questions at the beginning of the program, then later gives you a guide of how to evaluate the programs impact by allowing you to ask summative questions on all aspects of the program.

Context: What needs to be done? Vs. Were important needs addressed?

Input: How should it be done? Vs. Was a defensible design employed?

Process: Is it being done? Vs. Was the design well executed?

Product: Is it succeeding? Vs. Did the effort succeed?

LOOK AT THE DIAGRAM OF THE FOUR XNOR GATES

XNOR gates are represented in most TTL and CMOS IC families. The standard 4000 series CMOS IC is the 4077 and the TTL IC is the 74266. Both include four independent, two-input, XNOR gates

AGAIN THEY ARE FOUR NANDS IN A QUADRANT FORMATION- LOOK AT THE DIAGRAM

The TTL 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground

This schematic diagram shows the arrangement of NAND gates within a standard 4011 CMOS integrated circuit.

FOUR LAYERS

In the most popular techniques, the capacitive or resistive approach, there are typically four layers:

Top polyester coated with a transparent metallic conductive coating on the bottom.

Glass layer coated with a transparent metallic conductive coating on the top

Adhesive layer on the backside of the glass for mounting.

Users of handheld and portable touchscreen devices hold them in a variety of ways, and routinely change their method of holding and selection to suit the position and type of input. There are four basic types of handheld interaction:

Holding at least in part with both hands, tapping with a single thumb

Holding with one hand, tapping with the finger (or rarely, thumb) of another hand

Holding the device in one hand, and tapping with the thumb from that hand

Holding with two hands and tapping with both thumbs

FOUR LAYERS

In the most popular techniques, the capacitive or resistive approach, there are typically four layers:

Top polyester coated with a transparent metallic conductive coating on the bottom.

Glass layer coated with a transparent metallic conductive coating on the top

Adhesive layer on the backside of the glass for mounting.

Users of handheld and portable touchscreen devices hold them in a variety of ways, and routinely change their method of holding and selection to suit the position and type of input. There are four basic types of handheld interaction:

Holding at least in part with both hands, tapping with a single thumb

Holding with one hand, tapping with the finger (or rarely, thumb) of another hand

Holding the device in one hand, and tapping with the thumb from that hand

Holding with two hands and tapping with both thumbs

FOUR FACTORS

The Kaya identity is an identity stating that the total emission level of the greenhouse gas carbon dioxide can be expressed as the product of four factors: human population, GDP per capita, energy intensity (per unit of GDP), and carbon intensity (emissions per unit of energy consumed)

The Kaya identity plays a core role in the development of future emissions scenarios in the IPCC Special Report on Emissions Scenarios. The scenarios set out a range of assumed conditions for future development of each of the four inputs.

STANDARD IS FOUR

A diode bridge is an arrangement of four (or more) diodes in a bridge circuit configuration that provides the same polarity of output for either polarity of input.

Prior to the availability of integrated circuits, a bridge rectifier was constructed from "discrete components", i.e., separate diodes. Since about 1950, a single four-terminal component containing the four diodes connected in a bridge configuration became a standard commercial component and is now available with various voltage and current ratings.

FOUR OF THEM "DEFINITIVE ROCK AMP"

The Marshall Super Lead Model 1959 is a guitar amplifier head made by Marshall. One of the famous Marshall Plexis, it was introduced in 1965 and with its associated 4×12" cabinets gave rise to the "Marshall stack".

1968 Marshall Plexi, with angled 4×12" cabinet, for sale. (A "half stack.")

The 1959 had 100 watts of power, two channels, and four inputs. They were equipped with two KT66 tubes, but models made after 1967 had four EL34 tubes; it had three ECC83 tubes in the pre-amplification stage. A model with tremolo, the 1959T, was available until 1973.[1]

The amplifier had four inputs into two channels. The lead channel has a boosted bright tone, and the rhythm channel has a flat response. Each channel has a high and a low gain input; the low gain input is attenuated by 6 dB.[2] The channels can be linked with a jumper cable.[11]

Notable early users

Besides Pete Townshend of The Who, early users include Eric Clapton, who in 1966, when he founded Cream, traded in his famous Bluesbreaker combo for a 1959 Plexi,[12][13] and Jimi Hendrix, who used a 1959 with four 4×12" cabinets (his "couple of great refrigerators") at the 1969 Woodstock Festival[9] and established the Marshall as the "definitive rock amp".[14]

LOOK AT THE FOUR NANDS IN QUADRANT PATTERN

The 7400 chip, containing four NANDs. The second line of numbers (7645) is a date code; this chip was manufactured in the 45th week of 1976.[1] The N suffix on the part number is a vendor-specific code indicating PDIP packaging.

16 BOOLEAN FUNCTIONS 16 SQUARES QMR

In two-valued logic, there are sixteen possible truth functions, also called Boolean functions, of two inputs P and Q. Any of these functions corresponds to a truth table of a certain logical connective in classical logic, including several degenerate cases such as a function not depending on one or both of its arguments. Truth and falsehood is denoted as 1 and 0 in the following truth tables, respectively, for sake of brevity.

FOUR TELESCOPES

The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. The VLT consists of four individual telescopes, each with a primary mirror 8.2 m across, which are generally used separately but can be used together to achieve very high angular resolution.[1] The four separate optical telescopes are known as Antu, Kueyen, Melipal and Yepun, which are all words for astronomical objects in the Mapuche language. The telescopes form an array which is complemented by four movable Auxiliary Telescopes (ATs) of 1.8 m aperture.

Four-wave mixing (FWM) is an intermodulation phenomenon in non-linear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave mixing can be compared to the intermodulation distortion in standard electrical systems. It is a parametric nonlinear process, in that the energy of the incoming photons is conserved. FWM is a phase-sensitive process, in that the efficiency of the process is strongly affected by phase matching conditions.

Contents [hide]

1 Mechanism

2 Non-degenerate four-wave mixing[1]

3 Deleterious effects of FWM in fiber-optic communications

4 Applications of FWM

6 References

Mechanism

FWM energy level diagram

Energy level diagram for a non-degenerate four-wave mixing process. The top energy level could be a real atomic or molecular level (resonant four-wave mixing) or a virtual level, far detuned off-resoance. This diagram describes the four-wave mixing interaction between frequencies f1, f2, f3 and f4.

When three frequencies (f1, f2, and f3) interact in a nonlinear medium, they give rise to a fourth wavelength (f4) which is formed by the scattering of the incident photons, producing the fourth photon.

Given inputs f1, f2, and f3, the nonlinear system will produce

±

f

1

±

f

2

±

f

3

\pm f_{1} \pm f_{2} \pm f_{3}

with the most damaging signals to system performance calculated as

f

i

j

k

=

f

i

+

f

j

f

k

,

w

h

e

r

e

i

,

j

k

f_{ijk} = f_{i} + f_{j} - f_{k}, \mathrm{where}\, i, j \neq k

since these frequencies will lie close to one of the incoming frequencies.

From calculations with the three input signals, it is found that 12 interfering frequencies are produced, three of which lie on one of original incoming frequencies.

Non-degenerate four-wave mixing[1]

Four-wave mixing is also present if only two components interact. In this case the term

f

0

=

f

1

+

f

1

f

2

f_{0} = f_{1} + f_{1} - f_{2}

couples three components, thus generating so-called non-degenerate four-wave mixing, showing identical properties as in case of three interacting waves.

Deleterious effects of FWM in fiber-optic communications

FWM is a fiber-optic characteristic that affects wavelength-division multiplexing (WDM) systems, where multiple optical wavelengths are spaced at equal intervals or channel spacing. The effects of FWM are pronounced with decreased channel spacing of wavelengths (such as in dense WDM systems) and at high signal power levels. High chromatic dispersion decreases FWM effects, as the signals lose coherence, or in other words, increases the phase mismatch. The interference FWM caused in WDM systems is known as interchannel crosstalk. FWM can be mitigated by using uneven channel spacing or fiber that increases dispersion.

Applications of FWM

FWM finds applications in optical phase conjugation, parametric amplification, supercontinuum generation and in microresonator based frequency comb generation. Parametric amplifiers and oscillators based on four-wave mixing use the third order nonlinearity, as opposed to most typical parametric oscillators which use the second-order nonlinearity.

HIGH END HEADPHONES HAVE FOUR WIRES- LOW END HAVE THREE- FOURTH IS ALWAYS DIFFERENT

Sometimes only one channel of audio will get through the damaged wire and sometimes no audio at all. With high end headphones you will usually have 4 wires rather than 3 like more common headphones will have.

FOUR BY FOUR BLOCKS OF PIXELS- 16 SQUARES- THERE ARE FOUR MODES- ONE IS SINGLE COLOR MODE ONE IS FOUR COLOR MODE AND THE OTHER IS 16 COLOR MODE

The codec operates on 4×4 blocks of pixels in the RGB colorspace. Each frame is segmented into 4×4 blocks in raster-scan order. Each block is coded in one of four coding modes: skip, single color, four color, or 16 color.[3] Colors are represented by 16 bits with a bit-depth of 5 bit for each of the three components red, green, and blue, a format known as RGB555.[3] Because Apple Video operates in the image domain without motion compensation, decoding is much faster than MPEG-style codecs which use motion compensation and perform coding in a transform domain. As a tradeoff, the compression performance of Apple Video is lower.

Skip mode

The skip mode realizes conditional replenishment. If a block is coded in skip mode, the content of the block at same location in the previous frame is copied to the current frame.[3] Runs of skip blocks are coded in a run-length encoding scheme, enabling a high compression ratio in static areas of the picture.[3]

Single color mode

In single color mode, all pixels in a block are decoded in the same color.[3] This can be interpreted as a palette with a single color.

Four color mode

In four color mode, each pixel in a block is decoded as one of four colors which are specified in a palette.[3] To select one of the four entries, 2 bits per pixel are written to the bit-stream. The same palette is used for a run of length between one and 32 blocks.[3] Of the four colors, two are explicitly written to the bit-stream, while the other two are calculated at the decoder by linear interpolation in the RGB colorspace using the following equations:

{\mathrm {color2}}={\frac {11}{32}}*{\mathrm {color0}}+{\frac {21}{32}}*{\mathrm {color3}}\approx {\frac {1}{3}}*{\mathrm {color0}}+{\frac {2}{3}}*{\mathrm {color3}}

where color0 and color3 are the two colors which are written in the bit-stream.[3] The four colors can be interpreted as lying equidistantly spaced on a line segment in the three-dimensional vector space with the three components red, green, and blue. The end-points of this line are written in the bit-stream. A similar color-interpolation scheme is used in S3 Texture Compression.

Interpreted as vector quantization, a three-dimensional vector with the components red, green, and blue is quantized using a codebook with four entries.

16 color mode

In 16-color mode, the color of each pixel in a block is explicitly written in the bit-stream.[3] This mode is lossless and equivalent to raw PCM without any compression.

MOST COMMON ARE FOUR 16 AND 256- 256 IS FOUR TO THE FOURTH POWER

In the early days of PCs, it was common for video adapters to support only 2, 4, 16, or (eventually) 256 colors due to video memory limitations; they preferred to dedicate the video memory to having more pixels (higher resolution) rather than more colors. Color quantization helped to justify this tradeoff by making it possible to display many high color images in 16- and 256-color modes with limited visual degradation. Many operating systems automatically perform quantization and dithering when viewing high color images in a 256 color video mode, which was important when video devices limited to 256 color modes were dominant. Modern computers can now display millions of colors at once, far more than can be distinguished by the human eye, limiting this application primarily to mobile devices and legacy hardware.

PIXEL IMAGES ARE BLOCKS OF FOUR BY FOUR- FOUR BY FOUR IS 16 IT IS A QUADRANT MODEL

A pixel image is divided into blocks of typically 4×4 pixels. For each block the Mean and Standard Deviation of the pixel values are calculated; these statistics generally change from block to block. The pixel values selected for each reconstructed, or new, block are chosen so that each block of the BTC compressed image will have (approximately) the same mean and standard deviation as the corresponding block of the original image. A two level quantization on the block is where we gain the compression and is performed as follows:

Using sub-blocks of 4×4 pixels gives a compression ratio of 4:1 assuming 8-bit integer values are used during transmission or storage. Larger blocks allow greater compression ("a" and "b" values spread over more pixels) however quality also reduces with the increase in block size due to the nature of the algorithm.

This 16-bit block is stored or transmitted along with the values of Mean and Standard Deviation. Reconstruction is made with two values "a" and "b" which preserve the mean and the standard deviation. The values of "a" and "b" can be computed as follows:

FOUR PIXEL BY FOUR PIXEL BLOCKS- QUADRANT 16S

Decompression

Decompression is very easy and straightforward. To reconstruct each compressed 4-pixel by 4-pixel block, the 16-bit luminance bitmap is consulted for each block. Depending on whether an element of the bitmap is 1 or 0, one of the two 8-bit indices into the lookup table is selected and then dereferenced and the corresponding 24 bit per pixel color value is retrieved.[1][2][3]

EACH FRAME IS SPLIT INTO FOUR BY FOUR PIXEL BLOCKS- FOUR BY FOUR IS 16 A QUADRANT MODEL 16 SQUARES

Microsoft Video 1 operates either in a 8-bit palettized color space or in a 15-bit RGB color space.[2] Each frame is split into 4×4 pixel blocks.[2] Each 4×4 pixel block can be coded in one of three modes: skip, 2-color or 8-color.[2] In skip mode, the content from the previous frame is copied to the current frame in a conditional replenishment fashion.[2] In 2-color mode, two colors per 4×4 block are transmitted, and 1 bit per pixel is used to select between the two colors.[2] In 8-color mode, the same scheme applies with 2 colors per 2×2 block.[2] This can be interpreted as a 2-color palette which is locally adapted on either a 4×4 block basis or a 2×2 block basis. Interpreted as vector quantization, vectors with components red, green, and blue are quantized using a forward adaptive codebook with two entries.

256 COLORS- 4 TO THE 4TH POWER- FOUR BY FOUR BLOCKS- QUADRANT MODELS

The input video that the codec operates on is in an 8-bit palettized RGB colorspace. Compression is achieved by conditional replenishment and by reducing the palette from 256 colors to a per-4×4 block adaptive palette of 1-16 colors. Because Apple Video operates in the image domain without motion compensation, decoding is much faster than MPEG-style codecs which use motion compensation and perform coding in a transform domain. As a tradeoff, the compression performance of Apple Graphics is lower. The decoding complexity is approximately 50% that of the QuickTime Animation codec.[4]

Each frame is segmented into 4×4 blocks in raster-scan order. Each block can be coded in one of the following coding modes: skip mode, single color, 2-, 4-, and 8 color palette modes, two repeat modes, and PCM.

Skip mode

The skip mode realizes conditional replenishment. If a block is coded in skip mode, the content of the block at same location in the previous frame is copied to the current frame.[1] Runs of skip blocks are coded in a run-length encoding scheme, enabling a high compression ratio in static areas of the picture.[1]

Single color

In single color mode, the entire 4×4 block is painted with a single color.[1] This mode can also be considered as a 1-color palette mode.

Palette (2, 4, or 8-color) modes

In the palette modes, each 4×4 block is coded with a 2, 4, or 8-color palette.[1] To select one of the colors from the palette, 1, 2, or 3 bits per pixel are used, respectively. The palette can be written to the bitstream either explicitly or as a reference to an entry in the palette cache.[1] The palette cache is a set of three circular buffers which store the 256 most recently used palettes, one each for of the 2, 4, and 8-color modes.[1]

Interpreted as vector quantization, three-dimensional vectors with components red, green, and blue are quantized using a forward adaptive codebook with between 1 and 8 entries.

Repeat modes

There are two different repeat modes.[1] In the single block repeat mode, the previous block is repeated a specified number of times.[1] In the two block repeat mode, the previous two blocks are repeated a specified number of times.[1]

PCM (16 color) mode

In 16-color mode, the color of each pixel in a block is explicitly written to the bit-stream.[1] This mode is lossless and equivalent to raw PCM without any compression.

256 COLORS- 4 to the 4th power- FOUR BY FOUR BLOCKS- 16 SQUARES

Smacker video supports 256 colors, and includes transparency support.[2] While being a palette-based format, which is inherently limited to having not more than 256 colors in each frame, Smacker videos may still contain more colors in total due to "palette rotation", whereby the palette is updated on a per-frame basis.[2] This usually results in SMK files that look better if the source video has more than 256 colors. The compression rate of Smacker can reach 1:12, but at the loss of quality (pixelation).[citation needed]

In Smacker video, a frame is split into 4×4 blocks in raster-scan order.[2] Each block can be coded in one of six coding modes: skip, fill, mono, and three full modes. Each mode can be signaled for multiple blocks in a run-length encoding scheme. In skip mode, the current block is copied from the previous frame in a conditional replenishment fashion. In fill mode, the current block is filled with a single color. In mono mode, the palette is locally reduced from 256 colors to two colors. Both colors are written to the bitstream and one bit per pixel is used to indicate which of the two colors a pixel should be.[2] The mono mode can be interpreted as vector quantization, where a three-dimensional vector with the components red, green, and blue is quantized using an adaptive codebook with two entries. There are three full modes, one was specified in version 2 of the Smacker format, while the other two were added in version 4.[2] In the original full mode, 16 colors are transmitted, one for each pixel, equivalent to raw uncompressed PCM. The two full modes added in version 4 use 4 and 8 colors in a block, respectively.[2] In the 4-color mode, the 4×4 block is split into four 2×2 blocks, each of which is filled with a solid color. In the 8-color mode, the 4×4 block is split into eight 1×2 blocks, each of which is filled with a solid color.[2]

Further compression is achieved by entropy coding using Huffman coding of the various bitstream elements that result from the process above.[2] There are four separate Huffman tables, each with 16-bit entries: one for mode decision, run-length, and fill color in fill color mode, one for the color indices in mono mode, one for the bitmap in mono mode, and one for all data in the full mode. Each table is adaptive and transmitted once per file in the header. The Huffman tables in the header are themselves compressed: the 16 bit values in the leaves of the code tree are split into a high byte and a low byte. Each byte is compressed using a Huffman table that is also contained in the header.[2]

FOUR BY FOUR BLOCKS OF PIXELS/ QUADRANT MODELS

There are five variations of the S3TC algorithm (named DXT1 through DXT5, referring to the FourCC code assigned by Microsoft to each format), each designed for specific types of image data. All convert a 4×4 block of pixels to a 64-bit or 128-bit quantity, resulting in compression ratios of 6:1 with 24-bit RGB input data or 4:1 with 32-bit RGBA input data. S3TC is a lossy compression algorithm, resulting in image quality degradation, an effect which is minimized by the ability to increase texture resolutions while maintaining the same memory requirements. Hand-drawn cartoon-like images do not compress well, nor do normal map data, both of which usually generate artifacts. ATI's 3Dc compression algorithm is a modification of DXT5 designed to overcome S3TC's shortcomings with regard to normal maps. id Software worked around the normalmap compression issues in Doom 3 by moving the red component into the alpha channel before compression and moving it back during rendering in the pixel shader.[6]

THE 16 AND 256 NUMBERS FOUR SQUARED AND FOUR TO THE FOURTH POWER

LATER IT TALKS ABOUT 512 WHICH IS 256 TIMES TWO

The DP measurement of a printer often needs to be considerably higher than the pixels per inch (PPI) measurement of a video display in order to produce similar-quality output. This is due to the limited range of colors for each dot typically available on a printer. At each dot position, the simplest type of color printer can either print no dot, or print a dot consisting of a fixed volume of ink in each of four color channels (typically CMYK with cyan, magenta, yellow and black ink) or 24 = 16 colors on laser, wax and most inkjet printers, of which only 14 or 15 (or as few as 8 or 9) may be actually discernible depending on the strength of the black component, the strategy used for overlaying and combining it with the other colors, and whether it is in "color" mode.

Higher-end inkjet printers can offer 5, 6 or 7 ink colors giving 32, 64 or 128 possible tones per dot location (and again, it can be that not all combinations will produce a unique result). Contrast this to a standard sRGB monitor where each pixel produces 256 intensities of light in each of three channels (RGB).

256 IS FOUR TO THE FOURTH POWER- 16 BLOCKS

The Photron FASTCAM SE is a 256 x 256 High-speed camera. It is part of the Photron FASTCAM line of cameras, introduced in 1996. Photron FASTCAM SE was introduce in 2000. However, the camera was trade branded previously in 1992 as a KODAK MASD product. The Kodak HS4540 and the Photron SE are the same camera, just different trade names.

Contents [hide]

1 Overview and features

3 References

Overview and features

The FASTCAM SE native resolution is 256 x 256 pixels x 8 bits at 4,500 FPS. By reducing the resolution, the frame rate for recording can be increased. As an example, 40,500 FPS is achieved with a resolution of 64 x 64 pixels at 8 bits. The FASTCAM SE processor came with three memory configurations that allowed full frame storage of 8192 images (512 MB), 16,384 images (1GB) or 24,576 images (1.5 GB). At 4,500 fps and maximum memory, the recording time is 5.46 seconds. The SE image sensor reads images in blocks which is commonly called a Block Readout sensor. The image sensor is divided into 16 blocks where each block is 256 x 16 pixels. And within one block, one half to one fourth of the block can be partially read out. Digital image data could be read from the Processor through a SCSI interface. Live video images could be displayed on NTSC or PAL monitors. Ancillary information would be display as OSD (On-Screen-Data). The camera cable could be up to 15m from the Processor. The system could be controlled from a computer through an RS-232 interface sending simple ASCII commands.

64 TIMES 16 IS 1024- 256 FOUR TO THE FOURTH POWER 64 IS FOUR 16S- 16 TIMES 48 IS 768 (16 TIMES 3 IS 48)

XGA, the Extended Graphics Array, is an IBM display standard introduced in 1990. Later it became the most common appellation of the 1024×768 pixels display resolution, but the official definition is broader than that. It was not a new and improved replacement for Super VGA, but rather became one particular subset of the broad range of capabilities covered under the "Super VGA" umbrella.

The initial version of XGA (and its predecessor, the IBM 8514) expanded upon IBM's older VGA by adding support for four new screen modes (three, for the 8514), including one new resolution:[54]

640×480 pixels in direct 16 bits-per-pixel (65,536 color) RGB hi-color (XGA only, with 1 MB video memory option) and 8 bpp (256 color) palette-indexed mode.

1024×768 pixels with a 16- or 256-color (4 or 8 bpp) palette, using a low frequency interlaced refresh rate (again, the higher 8 bpp mode required 1 MB VRAM[55]).

THE FOUR NUMBERS

At the same time, in the introductory part of the Lecture he reported that the first impulse for his research work was given by Sommerfeld, who explained the struc- ture of atoms using Rydberg’s Formula and the numbers 2, 8, 18, and 32 (the natu- ral period lengths of chemical elements). However, Sommerfeld emphasized number 8 among the former, and used the geometry of the cube to demonstrate it. With Pauli’s own words:

In astrological parlance Thithi has great significance in the fact that each Thithi from 1 to 14 in both Pakshas has what are called Daghda rasis or Burnt Rasis – two rasis for each Thithi except Chaturdasiwhich has four Daghda rasis. But New Moon and Full Moon have no Dagdha Rasis.

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