Quadrant Model of Reality Book 5 Philosophy

Philosophy Chapter

The four transformations of Chu space are

Identify when the function is not injective.

Adjoin when the function is not surjective.

Copy when the converse is not injective.

Delete when the converse is not surjective

Jesuit and theologian Bernard Lonergan had a worthy goal: to generalize the successful methods of science to all facets of human inquiry. Most particularly, he sought to consider not only exterior data from sensation but interior data from consciousness. He presented four epistemological precepts of ‘being’ that transcended cultural norms, to inform all domains of human knowing and knowledge: Being Attentive in Experience Being Intelligent in Understanding Being Reasonable in Judgment Being Responsible in Deciding In addition, his Generalized Empirical Method (GEM) had four facets, and four methodological questions: Cognitional What do I do when I know? Epistemological Why is doing that knowing? Metaphysical What do I know when I do it? Methodological What therefore should we do?

For a transcendental syntax Girard divides all of logical activity into four blocks that weave together: the Constat, the Performance (please forgive my shortening on the diagram above), L’usine (factory), and L’usage (use). These four blocks are partitioned by Kant’s analytic-synthetic and a priori-a posteriori distinctions. The analytic is said to have “no meaning”, that is, “locative”. The synthetic is said to have “meaning”, that is, “spiritual”. The a priori is said to be “implicit”, and the a posteriori is said to be “explicit”.

Schopenhauer is considered one of the greatest philosophers in history. Einstein claimed that reading Schopenhauer was what inspired his philosophy and his theories on the nature of reality

Schopenhauer graduated, in 1813, on a thesis called ‘On the Fourfold Root of the Principle of Sufficient Reason‘ (‘Die Vierfache Wurzel des Satzes vom Zureichenden Grunde‘). Sufficient reasons fall, according to Schopenhauer, into four logical categories:

—————— Category —————————————————————— Causation ————

1. physical world science

2. ongoing history time/space mathematical determination

3. organic physical objects moving through space and time logical entailment

4. medium (to animate physical objects) motivated action

This division, which covers every ‘necessary connection’, was an effort to construct a communication-model between the innate natural world and the human interference (intentions) therein. This presentation is, at scrutiny, an example of tetradic thinking, because it showed a fourfold subdivision in which the original quadrant-sequence is given (in a reverse order): ———————- First Quadrant (I) : motivated action ———————- Second Quadrant (II) : logical entailment ———————- Third Quadrant (III) : mathematical determination ———————- Fourth Quadrant (IV) : science His main work was called ‘The World as Will and Representation‘ (‘Die Welt als Wille und Vorstellung‘), which was published in 1818. The book consisted of four parts: epistemology, ontology, aesthetics and metaphysics of the person (ethics), and a critique of Kant as an appendix.

Spengler (fig. 191) tried to create a ‘Logik des Raumes’ (Logic of Place) and a ‘Logik der Zeit’ (Logic of Time), with the intention to explain the position of the human being in this incomprehensible world. He accepted the principle that the morphology of world-history could be read as a universal symbol. History is like man it-self: it is an organic unity, with all the characteristics of life.

The position of the observer in place and time was of all-embracing importance: ‘Truth is only applicable to a distinct cultural unit. My philosophy is, subsequently, an expression and mirror-image of the Western European soul, distinct from the Antique or Indian, and can only exist in its present, civilized appearance, which limits the world view in its practical influence and relevance’.

Spengler stretched the importance of the analogy within this given context: ‘Alles Vergängliche ist nur ein Gleichnis‘ (all transitoriness is only an analogy). And the comparison is sought in an organic environment: cultures are regarded as living things, passing through four phases: to sprout, flower, wither and die (TAINTER, 1988). The maturity of a culture (Zivilisation) leads eventually to its downfall.

Spengler dismissed the triple scheme of Antiquity – Middle Ages and New Era and voted for a four-fold model (following Goethe in his essay ‘Geistesepochen‘). The historical development (of a culture) is a passage through four seasons (‘Der Untergang des Abend-landes’, Band I: Gestalt und Wirklichkeit. p. 70: I. Tafel ‘Gleichzeitiger Geistesepochen‘): SPRING: Environmental – intuitive (Landschaftlich – intuitive) 1. The birth of a myth. A new feeling of holiness; Fear of the world; ‘Weltsehnsucht‘. 2. Development of mystical-metaphysical features. SUMMER: Growing consciousness (Reifende Bewussheit) 3. Reformation 4. Philosophical formation (idealist versus realist) 5. Mathematical development 6. Puritine revival AUTUMN: Metropolian Intelligence (Grosstädtische Intelligenz) 7. Aufklärung 8. Culmination of mathematical thinking 9. Large (finalizing) philosophical systems WINTER: Beginning of a civilisation of worldcities (Anbruch der weltstädtischen Zivilisation) 10. Materialism/cult of science 11. Ethical-social problems/sceptisism 12. Final understanding in a mathematical world of forms 13. Lecturers-philosophy/compendia 14. End-of-the-world mood Spengler elaborated on the division in short notes in later years (1924 -1936; ‘Früh-geschichte der Menschheit‘). He spoke of four ‘Kulturstufen‘ (SPENGLER, 1966; pp. 44 – 81), simply called a, b, c and d. They comprise: a. Old-Palaeoloticum (before 20.000 BC); b. Young-Palaeolicum (20.000 – 6/7000 BC); c. Neolithicum (6/5000 – 3000 BC) and d. ‘World-history’ (‘Weltgeschichte‘), divided in periods of 1000 years.

Cantor is considered one of the greatest mathematicians in history. 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. The nature of Cantor dust reflects the quadrant model image. This set would have been considered abstract at the time when Cantor devised it. Cantor himself was led to it by practical concerns about the set of points where a trigonometric series might fail to converge. The discovery did much to set him on the course for developing an abstract, general theory of infinite sets, considered one of the greatest discoveries in Math. It was a reaction to his success to map a surface onto a line in such a way that each point of the surface corresponded to one point of the line (and reciprocally that to each point of the line one point of the surface could be related). He arrived at a correlation, which uniquely mapped the x-variables onto y in terms of four equations (DAUBEN, 1979; p. 55). The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is one generalization of the Cantor set to two dimensions; another is the Cantor dust. In mathematics, the Menger sponge (also known as the Menger universal curve) is a fractal curve. It is a three-dimensional generalization of the Cantor set and Sierpinski carpet

The Sierpinski tetrahedron or tetrix is the three-dimensional analogue of the Sierpinski triangle, formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process.

The Sierpinski triangle is very famous in mathematics. The Sierpinski square is a fractal that reflects the quadrant model image.

The Sierpinski triangle was seen as a holy image to the ancient Pythagoreans. They saw it like the tetracyst as representing God. The reason it is so holy is unknown to people but I understand why. THe quadrant model of reality has revealed the mystery.

The Sierpinski triangle is a triangle that has a triangle within it that divides the original triangle into four triangles. The triangle within the triangle is surrounded by three triangles.

In other words the Sierpinski triangle in its first iteration is three triangles, and a triangle within them (the fourth is always different, yet encompasses the previous three, the nature of the quadrant model.)

A Sierpinski triangle is really just a triangle made into four triangles.

Sierpinski triangle in logic ahs the first 16 conjunctions of lexicographically ordered arguments. It reflects the quadrant model image.

The Sierpinski triangle is a fractal if the bisections into more and more triangles continues.

If you manipulate a Sierpinski triangle into a three dimensional manner you will get the icosphere which itself can be manipulated into the icosahedron which is one of Plato's platonic solids which he connected to the element water.

The triquetra is another famous ancient symbol that has four parts to it, explaining its holiness.

Topologically, any Cantor cube is: homogeneous; compact; zero-dimensional; AE(0), an absolute extensor for compact zero-dimensional spaces. (Every map from a closed subset of such a space into a Cantor cube extends to the whole space.) By a theorem of Schepin, these four properties characterize Cantor cubes; any space satisfying the properties is homeomorphic to a Cantor cube.

Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry. It improves on the Hartree–Fock method by adding electron correlation effects by means of Rayleigh–Schrödinger perturbation theory (RS-PT), usually to second (MP2), third (MP3) or fourth (MP4) order. The fourth is always different. The fifth is always questionable.

Fowers book recites Aristotle’s four kinds of character. The four character types emerge from the combination of the two dimensions of moral duty and one’s personal inclinations. Moral duty refers to acting toward what is good, whereas the latter refers to the emotional inclination to act on one’s desires. The four kinds of character that emerge are as follows: 1. The Continent Character is one who has selfish, amoral, or immoral desires, but exhibits control over them in the service of acting morally. For example, a man in a committed relationship who lusts after another woman but inhibits acting on those feelings because the betrayal of his wife goes against the good would be acting as a continent character. Interestingly, Kant believed that the moral and the personal inclinations were inevitably in conflict and the times when an individual suppressed his desires and acted morally were examples of the highest good. 2. The Incontinent Character knows what the right or virtuous thing is to do, but does not have the self-control to live by his morals. Continuing with the example above, this would be an individual who would know that it was wrong to betray his wife and have a casual affair, but would give into his desires, perhaps feeling guilty afterwards. 3. The Vicious Character, in contrast, feels no conflict between inclinations and moral duty because he has no moral sense of the good. Such individuals simply act on their own selfish inclinations, as these are seen as what is valuable. Continuing with the above example, a vicious character would cheat on his wife with no guilt and simply work to solve the problem of her finding out about it so that it would not inconvenience him. 4. The Virtuous Character also feels no conflict between emotional inclinations and moral duty. Why? Because the virtuous character has trained his emotional system to be aligned with his moral inclinations. In short, at a deep emotional level, the virtuous character wants to do the good. While such a character might indeed have sexual feelings for another, he would feel pride and connection in acting in a loyal, trustworthy manner and the very thought of cheating or acting immorally is deeply aversive for the virtuous character. In contrast to Kant, Aristotle believed that the virtuous character represented the highest ideal.

Aristotle presents four kinds of tragedy:

a) complex - depending entirely on reversal and recognition at the climax

b) pathetic - motivated by passion

c) ethical - motivated by moral purpose

d) simple - without reversal or recognition

Aristotle distinguishes among four types of agents on the basis of their character: The wicked, who doesn't even know what the right action is and, even worse, confuses virtue (moral/character excellence) with vice. He may think, for example, that prodigality is a virtue. The weak willed, who knows what the human excellencies are, but fails to perform the right action either because his moral perception fails him, or because he is moved by contrary passions. It's fair to say that all of us have experienced this state. The strong willed, who knows what to do and what kind of person to be and acts correctly without, however, feeling any pleasure in it. He brings himself to do it, as it were, like Kant’s misanthrope who, however, conscientiously performs his duty towards humanity. The virtuous, who knows what to do, what kind person to be, and being that kind of person feels pleasure in acting virtuously.

The ASTC or CAST or unit circle method for finding two angles having a given sin, cos or tan is called the CAST diagram/quadrant. In this method you draw a set of axes and label the quadrants 1, 2, 3 and 4 with the letters A, S, T and C respectively as shown in the diagrams below. The letters mean: A: all three functions, sin, cos and tan are positive in this quadrant S: only the sin function is positive in this quadrant T: only the tan function is positive in this quadrant C: only the cos function is positive in this quadrant This is known as the CAST or quadrant rule of trigonometry. This is the foundation of trigonometry. No coincidence it's foundation is the quadrant, the Form of Being. Notice how the CAST unit circle resembles the quadrant model pattern, with the fourth square A representing an amalgamation of the previous three. That is the quadrant model pattern. Using the Cartesian Plane to define the CAST diagram in order to define which trigonometric ratios will give us a positive value for the angle theta depending on the quadrant of the CAST diagram the angle is in. In a CAST diagram When we include negative values, the x and y axes divide the space up into 4 pieces: Quadrants I, II, III and IV (They are numbered in a counter-clockwise direction) In Quadrant I both x and y are positive, in Quadrant II x is negative (y is still positive), in Quadrant III both x and y are negative, and in Quadrant IV x is positive again, and y is negative.

A Jones diagram is a type of Cartesian graph developed by Loyd A. Jones in the 1940s, where each axis represents a different variable. In a Jones diagram opposite directions of an axis represent different quantities, unlike in a Cartesian graph where they represent positive or negative signs of the same quantity. The Jones diagram therefore represents four variables. Each quadrant shares the vertical axis with its horizontal neighbor, and the horizontal axis with the vertical neighbor. For example, the top left quadrant shares its vertical axis with the top right quadrant, and the horizontal axis with the bottom left quadrant. The overall system response is in quadrant I; the variables that contribute to it are in quadrants II through IV. A common application of Jones diagrams is in photography, specifically in displaying sensitivity to light with what are also called "tone reproduction diagrams". These diagrams are used in the design of photographic systems (film, paper, etc.) to determine the relationship between the light a viewer would see at the time a photo was taken to the light that a viewer would see looking at the finished photograph. The Jones diagram concept can be used for variables that depend successively on each other. Jones's original diagram used eleven quadrants[how?] to show all the elements of his photographic system.

The political compass is a multi-axis political model, used by the website of the same name, to label or organise political thought on two dimensions. In its selection and representation of these two dimensions, it is similar to the Nolan Chart and Pournelle Chart. The term "Political Compass" is claimed as a trademark by the British website Pace News Limited, which uses responses to a set of 61 propositions to rate political ideology on two axes: Economic (Left–Right) and Social (Authoritarian–Libertarian).The site also includes an explanation of the two-axis system they use, a few charts which place various past and present political figures according to their estimation, and reading lists for each of the main political orientations. Four results are yielded square 1:Authoritarian left Square 2: Libertarian left Square 3: Authoritarian right Square 4: Libertarian right

Brian Patrick Mitchell identifies four main political traditions in Anglo-American history. Mitchell analyzed modern American political perspectives according to their regard for kratos (defined as the use of force) and archē or “archy” (defined as the recognition of rank), grounding this distinction of archy and kratos in the West's historical experience of church and state and crediting the collapse of the Christian consensus on church and state with the appearance of four main divergent traditions in Western political thought: republican constitutionalism = pro archy, anti kratos libertarian individualism = anti archy, anti kratos democratic progressivism = anti archy, pro kratos plutocratic nationalism = pro archy, pro kratos

Milton Rokeach and his colleagues used content analysis on works exemplifying nazism (written by Adolf Hitler), communism (written by V.I. Lenin), capitalism (by Barry Goldwater) and socialism (written by various socialist authors). He found Socialists (socialism) — Freedom ranked 1st, Equality ranked 2nd Hitler (Nazism) – Freedom ranked 16th, Equality ranked 17th Goldwater (capitalism) — Freedom ranked 1st, Equality ranked 16th Lenin (communism) — Freedom ranked 17th, Equality ranked 1st

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

Between the interpretation of Honorius and Eriugena is a significant difference, which indicated a development within the four-fold way of thinking itself. Eriugena’s ninth-century tetradic manifest (Book I) opened with a ‘First Principle of Nature’, which was creating and not created (quae creat et non creatus). Dionysius the Areopagite described this principle as a ‘Divinity Who is above Being’. The realm of this Divinity is a Unity, a monad, and a place before division. This is understood (by Eriugena) to be the invisibility of God-self, who was not created, but is the origin of all creation. Creation is, in a quadralectic view, the state of a communication after a decision on division has been taken. The first section (I) is, in Eriugena’s opinion (following Aristotle in his four-fold way of thinking), typified by the ‘potency’ (possibility) of division. The division has not yet taken place. Honorius positioned the eight ‘primordial causes‘ in the ‘First Quadrant’. His ‘First Principle’ is not a unity, but a plurality (4 + 1 + 3), reflecting the ‘Seven Steps to Heaven’ (in which Bonitas is the representative of God). Honorius applied the ‘ratiocinationis quadrivium‘ and defined the first stage in a multitude of human-oriented causes. The second section (II) of Honorius’ illustration is a three-division of Time (Tempus) and Place (Locus) with the ‘Materia Informis‘ in the middle. Aristotle’s potentiality surfaces here in a material, human-directed form, with four faces and five eyes (fig. 138), anticipating the four visible elements of the ‘Natura creata, non creans‘ (and the ‘quitessentia’?). The ‘materia informis’, or potential matter, is placed by Honorius in the second stage of his division of nature. The third stage gives the four elements in the sequence (from left to right): fire (three holy men), air (birds), water (fish and a source) and earth (crop, three animals and a couple). This ‘evolutionary’ depiction differs from the quadralectic sequence based on visibility: fire, air, earth and water. Honorius’ last quadrant (IV) is solely attributed to God, closing the stage (‘finis’). Eriugena saw the last quadrant as a human affair, summing up all creation within himself. He even mentioned at this stage – following Maximus in the thirty-seventh Chapter of his ‘Ambigua’ – a five-fold division of all created nature: 1. God; 2. Sensible and intelligible nature; 3. Heaven and earth; 4. Paradise and the habitable globe and 5. The final division segregates mankind into male and female (Periph. V, 893B). The differences of interpretation between the ninth (Eriugena) and twelfth (Honorius) century indicate a shift within the four-fold division from a God-orientated to a man-orientated interpretation of being. Honorius Augustodunensis was instrumental in the simplification of division thinking. He noticed, in his book ‘Elucidarium’, that the universe was built from four elements and that Man, as micro cosmos, consisted of four elements: the flesh (earth), blood (water), breathing (air) and body heath (fire). He also spoke of three heavens: a material or visible heaven, a spiritual heaven, filled with spiritual substances like the angels, and an intellectual heaven with a confrontation of the mortal soul with the holy Trinity (LeGOFF, 1984/1987, p. 174, 191). The cultural move from a Celtic to a Gothic world in Europe, which took place in approximately six hundred years (from 600 to 1200), can be seen as the result of a change in division thinking. The Carolingian ideas, steeped in a Celtic heritage, were filled with conceptions based on four types of visibility. The emphasis was gradually changing from the invisible (invisibility, worship of God without questioning) to the visible (visibility, worship of the material/human, associated with a questioning of God). The European intellectuals moved from a God-centered universe (of the ninth century) to a man-centred world from the twelfth century onwards. In the latter interpretation God still pulls the cords, but only at the end of the story. The period of actual visible transition, around the year 1200, is of utmost important in the history of European division thinking. It is newly-coined as the ‘Tetractus‘-Age and will be discussed next.

There are three boat-shaped pits around the pyramid, of a size and shape to have held complete boats, though so shallow that any superstructure, if there ever was one, must have been removed or disassembled. In May 1954, the Egyptian archaeologist Kamal el-Mallakh discovered a fourth pit, a long, narrow rectangle, still covered with slabs of stone weighing up to 15 tons.

The Mausoleum at Halicarnassus or Tomb of Mausolus [a] (Persian: آرامگاه هالیکارناسوس; Modern Greek: Μαυσωλείο της Αλικαρνασσού) was a tomb built between 353 and 350 BC at Halicarnassus (present Bodrum, Turkey) for Mausolus, a satrap in the Persian Empire, and his sister-wife Artemisia II of Caria. The structure was designed by the Greek architects Satyros and Pythius of Priene. The Mausoleum was approximately 45 m (148 ft) in height, and the four sides were adorned with sculptural reliefs, each created by one of four Greek sculptors—Leochares, Bryaxis, Scopas of Paros and Timotheus. The finished structure of the mausoleum was considered to be such an aesthetic triumph that Antipater of Sidon identified it as one of his Seven Wonders of the Ancient World. It was destroyed by successive earthquakes from the 12th to the 15th century. Each sculpture did one of the four sides. Perched on the top was a quadriga: four massive horses pulling a chariot in which rode images of Mausolus and Artemisia.

KV 35 is one of the most remarkable period structures found in Egypt where Queen Nefertiti was thought to be found. It has four side chambers.

Four Heavenly Kings (四大天王) is a Chinese term created in June 1992 by Oriental Daily News to refer to the four biggest male superstars in Hong Kong at that time: Andy Lau, Jacky Cheung, Aaron Kwok and Leon Lai.[1] They dominated entertainment not only in Hong Kong but throughout the Chinese speaking world in the 1990s, having very successful singing careers (in both Cantopop and Mandopop) as well as acting careers well into the 2000s. The 1990s is sometimes called the "Four Heavenly Kings Era" in Hong Kong entertainment because their songs swept the awards of Top 10 Songs of the Year during a 6-year span, especially by Cheung and Lau.

The Kanto Elite Four act as the Elite Four in the original series of Pokémon games consisting of Pokémon Red, Blue, Green, and Yellow versions as well as in Pokémon FireRed and LeafGreen versions which act as remakes of the original games. Within the timeline of the game series they are eventually also given the status as the 'Johto Elite Four', as Johto shares its Pokémon league with Kanto. Specifically, this Elite Four is located on the Indigo Plateau, shared by both Kanto and Johto. Lorelei (Kanna (カンナ)): Lorelei is a specialist of Ice-type Pokémon. She is originally from the Sevii Islands and she collects Pokémon Dolls. She appears in the Orange Islands series of the anime, where she is known as Prima in the English version. She is a villain in Pokémon Adventures, who attempts to take over the world with the other Elite Four. She later allies with Red and Blue to save her home. Bruno (Shiba (シバ)): Bruno is an expert on Fighting-types, and a friend and training partner of Brawly. He constantly trains his own body along with his Pokémon, and he wishes to fight the best trainers in the world, which is why he is part of the group. He regularly trains on the Sevii Islands and utilizes the spa for his Pokémon. He appears in the first episode of the anime as a combatant on television, and he later meets Ash when he seeks out Bruno to learn of his "secret" to become a great trainer. Bruno is an unwilling villain in Pokémon Adventures, where he is forced by Agatha to fight for her. He later forms the Johto Elite Four with Will, Karen, and Koga. Bruno attaches his Poké Balls to the ends of a set of nunchaku, and unleashes his Pokémon at high speeds to give him an advantage. Agatha (Kikuko (キクコ)): Agatha is an elderly woman who specializes in Ghost-type Pokémon. In the anime, she appears in the episode "The Scheme Team" where she is acting Gym Leader for the Viridian City Gym, defeating Ash in a battle. She is the main antagonist of the Yellow chapter of Pokémon Adventures. She attempts to destroy most of humanity from their base on Cerise Island. She controls Bruno against his will by utilizing the mind-controlling powers of her ghost Pokémon, and she is a former rival of Professor Oak, though their relationship eventually grew very bitter when he decided to pursue his own research career rather than stick with their group, which according to Oak, was only interested in finding new ways to control Pokémon, which the professor found unethical. Lance (Wataru (ワタル)): Lance, known as one of the best Pokémon trainers in the world, specializes in dragon Pokémon. He is Clair's cousin, having previously trained with her in Blackthorn City. He helps the protagonist in the second generation games in the fight against Team Rocket. He appears in the anime, where he helps Ash's group defeat Team Rocket, catching a red Gyarados that is part of their experiments, and later helps to stop the battle between Groudon and Kyogre. He is an antagonist in Pokémon Adventures who wishes to destroy humanity due to all of the pollution and their hurting of Pokémon. He later becomes an ally of Silver, who he sends on various missions. He is promoted to a Pokémon League champion of the Indigo Plateau in the sequel games.

The Elite Four (四天王 Shitennō, lit. "Four Heavenly Kings") is an order of exceptionally skilled Pokémon trainers consisting of four member trainers of ascending rank. Like the Gym Leaders, they also specialize on a type of Pokémon but are far stronger. Most different regions possess their own organizations. The player must first defeat them all so that they may gain the right to challenge the 'Pokémon Champion'. The player must obtain all eight badges from each respective region's gym leaders. Pokemon was one of the most popular games of all time. It is no coincidence that the quadrant pattern was reflected in the game.

The Johto Elite Four act as the Elite Four in the original series of Pokémon games consisting of Pokémon Gold, Silver, and Crystal versions as well as in Pokémon HeartGold and SoulSilver versions which act as remakes of the original games. Within the timeline of the games series, they become the successors of the Kanto Elite Four. Some of the members from the previous games return while others are replaced by new ones. Will (Itsuki (イツキ)): Will is a Psychic-type specialist, who wears formal clothes and a mask. In the Pokémon Adventures manga, he was kidnapped by the Mask of Ice as a child and raised to be his servant. He is initially one of the leaders of Neo Team Rocket, but he eventually goes on to form the new Elite Four with Karen, Koga, and Bruno. He takes over Lorelei's place. Koga, Fuchsia City Gym Leader in the Kanto-based versions of the games, is promoted to the Elite Four in Johto-based versions. Bruno, member of the Elite Four in the Kanto-based games, retains his membership in the Elite Four in the Johto-based editions. Karen (Karin (カリン)): Karen is a Dark-type specialist; she likes Dark-types because she finds their wild and tough nature appealing. In the Pokémon Adventures manga, she was kidnapped as a child and raised by Mask of Ice to be his servant. Like Will, she is initially a leader of Neo Team Rocket until she joins the others to form the new Elite Four. She takes over Agatha's place.

The Hoenn Elite Four act as the Elite Four in the original series of Pokémon games consisting of Pokémon Ruby, Sapphire, Emerald, Omega Ruby, and Alpha Sapphire. Sidney (Kagetsu (カゲツ)): Dark-type specialist, who believes that the dark-side is beautiful, and that "might is right." He is always upbeat, and congratulates those who defeat him. Phoebe (Fuyō (フヨウ)): is a Ghost-type specialist, whose grandparents are responsible for guarding the Blue, Red, and Green Orbs at Mt. Pyre. She takes control of Regice, together with Glacia, in the Pokémon Adventures manga. Glacia (Prim (プリム Purimu)): Ice-type specialist, who came to Hoenn while looking for a warmer climate that, as she claims, help her Pokémon grow strong. Drake (Genji (ゲンジ)): Dragon-type specialist. He battles Ash in the anime, and he wins overwhelmingly due to Ash's overconfidence.

Sinnoh Elite Four[edit] Aaron (Ryō (リョウ)): Aaron uses Bug Pokémon, calling them beautiful and perfect. He appears in the anime preparing for a championship battle against Cynthia. When he meets Ash, who tells him about his experience with Cynthia, Aaron tells Ash about how he abandoned his Wurmple during his youth. He does his best to train and understand Bug-types out of regret for his mistake. He is later shown to have lost his match. Bertha (Kikuno (キクノ)): Bertha is an elderly Ground-type specialist. She appears in the anime along with Cynthia. Flint (Ōba (オーバ)): Flint is a Fire-type specialist, who meets the protagonist in Sunyshore City. He is a friend of Volkner and he has a younger brother named Buck. Flint's also seen on TV battling Cynthia in the final episode of Pokémon Diamond and Pearl. Lucian (Goyō (ゴヨウ)): Lucian is a Psychic-type trainer, who is an avid reader. He battles with Dawn in the anime, and he is shown on television battling Cynthia.

Unova Elite Four[edit]

Shauntal (Shikimi (シキミ)): Shauntal is a Ghost-Type Pokémon Trainer. Her hobby is writing books. She can also be seen at Cynthia's holiday home in Undella Town on occasion. According to one of her stories, she once battled Volkner.

Grimsley (Gīma (ギーマ)): Grimsley is a Dark-Type Pokémon Trainer. The son of a distinguished family that fell into ruin, he has since become an expert gambler.

Caitlin (Cattleya (カトレア Katorea)): Caitlin is a Psychic-Type Pokémon Trainer; she is described as having psychic powers which she had trouble controlling in the past due to her explosive temper. She travels to the region of Unova to learn how to control them and become a better trainer. She previously appeared in the Generation IV games' Battle Frontier and was in charge of running the Battle Castle but was unable to battle, with her valet taking that responsibility in her place.

Marshal (Renbu (レンブ)): Marshal is a Fighting-Type Pokémon Trainer. He is one of Alder's apprentices.

Kalos Elite Four[edit] Malva (Pachira (パキラ Pakira)): Malva is a Fire-Type Pokémon Trainer. A hot-headed news reporter and a self-proclaimed star of the Holo Caster, she is also a former member of Team Flare and expresses animosity towards the player for the team's defeat. Looker later blackmails her into helping the player stop Xerosic's plans. Siebold (Zumi (ズミ)): Siebold is a Water-Type Pokémon Trainer. He is a chef, whose customers notably include Valerie and Grant, and compares the art of cooking to the art of Pokémon battles. Wikstrom (Gampi (ガンピ Ganpi)): Wikstrom is a Steel-Type Pokémon Trainer. He wears a suit of armor and is eager to battle challengers. Drasna (Dracaena (ドラセナ Dorasena)): Drasna is a Dragon-Type Pokémon Trainer, inspired to train Dragon-types after her grandparents from Sinnoh told her about the region's mythology surrounding Dialga and Palkia. She is just happy to battle and enjoys it when trainers and their Pokémon like each other.

The Four Beauties or Four Great Beauties are four ancient Chinese women, renowned for their beauty. The Four Great Beauties lived in four different dynasties, each hundreds of years apart. In chronological order, they are: Xi Shi (c. 7th to 6th century BC, Spring and Autumn Period), said to be so entrancingly beautiful that fish would forget how to swim and sink away from the surface when seeing her reflection in water.[1] Wang Zhaojun (c. 1st century BC, Western Han Dynasty), said to be so beautiful that her appearance would entice birds in flight to fall from the sky.[2] Diaochan (c. 3rd century, Late Eastern Han/Three Kingdoms period), said to be so luminously lovely that the moon itself would shy away in embarrassment when compared to her face.[3] Yang Guifei (719-756, Tang Dynasty), said to have a face that puts all flowers to shame.[4] The talmud says that potiphars wife was one of the four most beautiful women in the world but still joseph did not sleep with her

The Carolingian age is, in the present survey, defined between 750 and 1000 AD. This is the period between the ‘first’ emergence of Europe as a geographical and political unity, established under Charlemagne, and the subsequent eventful continuation into the ‘Romanesque’ period, in which the Roman Catholic Church provided the intellectual bond towards a cultural consensus. A good example of symbolic meaning is the signature of Charlemagne, who could hardly read or write. He employed the quadripartite imagery of the eighth and nine century to affirm the generally known greatness of multiple division thinking Some autographs and signatures of the beginning of European visibility are given here, characterized by four-fold references. 1. King Henriquez of Portugal, 1159; 2. Charlemage (K-R-L-S; Karolus), around 800 A.D.; 3. Konrad I (C-N-R-D), Würzburg, 912; 4. Notker the Physician, St. Gallen, 925; 5. Cruciform emblems, drawn in the monastery of Lorsch under the authority of Folcwich, bishop of Worms. Second quarter of the nineth century A.D.; 6. Cruciform text. Ambros. B 80 Sup., 13r, 1071 – 1178 AD, Milan, Bibl. Ambrosiana. All of these huge rulers signatures were quadrants. The power of signatures and seals (signa) as a spiritual meaning (repraesentatio) of a world view reached a widespread visibility in the middle of the eleventh century and arrived at static and monumental proportions in the twelfth century. Axials, rota and ‘benevalete’ (BTE) had an institutionalized character. The ‘in hoc signo‘ (IHS, in this sign) became ‘Jesus hominum salvator‘ (JHS; KOCH, 1926/1984) and the believers knew in both cases exactly the precise meaning.

Charlemagne was engaged in almost constant battle throughout his reign,[39] often at the head of his elite scara bodyguard squadrons, with his legendary sword Joyeuse in hand. In the Saxon Wars, spanning thirty years and eighteen battles, he conquered Saxonia and proceeded to convert the conquered to Christianity. The Germanic Saxons were divided into four subgroups in four regions. Nearest to Austrasia was Westphalia and furthest away was Eastphalia. In between these two kingdoms was that of Engria and north of these three, at the base of the Jutland peninsula, was Nordalbingia.

After much negotiation, the following outcomes of the Yalta Conference emerged: Unconditional surrender of Nazi Germany, the division of Germany and Berlin into four occupational zones controlled by the United States, Great Britain, France and the Soviet Union. Germany was divided into four occupied zones: Great Britain in the northwest, France in the southwest, the United States in the south and the Soviet Union in the east. Berlin, the capital city situated in Soviet territory, was also divided into four occupied zones.

The Allies of World War II, called the United Nations from the 1 January 1942 declaration, were the countries that together opposed the Axis powers during the Second World War (1939–1945). The Allies promoted the alliance as seeking to stop German, Japanese and Italian aggression. The anti-German coalition at the start of the war (1 September 1939) consisted of France, Poland and Great Britain, soon to be joined by the British Commonwealth (Canada, Australia, New Zealand and South Africa).[1] Poland was a minor factor after its defeat in 1939; France was a minor factor after its defeat in 1940. After first having cooperated with Germany in partitioning Poland whilst remaining neutral in the Allied-Axis conflict, the Soviet Union perforce joined the Allies in June 1941 after being invaded by Germany. The United States provided war material and money all along, and officially joined in December 1941 after the Japanese attack on Pearl Harbor. As of 1942, the "Big Three" leaders of the United Kingdom, the Soviet Union, and the United States controlled Allied policy; relations between the United Kingdom and the United States were especially close. China had been already at war with Japan since 1937 but officially joined the Allies in 1941. The Big Three and China were referred as a "trusteeship of the powerful", then were recognized as the Allied "Big Four" in Declaration by United Nations[3] and later the "Four Policemen" of "United Nations" for the Allies. Other key Allies included British India, the Netherlands, and Yugoslavia as well as Free France; there were numerous others. Together they called themselves the "United Nations" and in 1945 created the modern UN.

The Four Policemen refers to a post-war council consisting of the Big Four that U.S. President Franklin D. Roosevelt proposed as a guarantor of world peace. The members of the Big Four, called the Four Powers during the war, were the four major Allies of World War II: the United States, the United Kingdom, the Soviet Union and the Republic of China. The United Nations envisioned by Roosevelt consisted of three branches: an executive branch comprising the Big Four, an enforcement branch composed of the same four great powers acting as the Four Policemen or Four Sheriffs, and an international assembly representing the member nations of the UN. The Four Policemen would be responsible for keeping order within their spheres of influence: Britain in its empire and in Western Europe; the Soviet Union in Eastern Europe and the central Eurasian landmass; China in East Asia and the Western Pacific; and the United States in the Western Hemisphere. As a preventive measure against new wars, countries other than the Four Policemen were to be disarmed. Only the Four Policemen would be allowed to possess any weapons more powerful than a rifle. The Four Policemen came into fruition as the permanent members of the United Nations Security Council, but its powers were significantly diminished as a compromise with internationalist critics. France was later added as the fifth member of the council due to the insistence of Churchill.

The idea that great powers should "police" the world had been discussed by President Roosevelt as early as August 1941, during his first meeting with Winston Churchill. Roosevelt made his first references to the Four Policemen proposal in early 1942.[9] He presented his postwar plans to Molotov,[10] who had arrived in Washington on May 29 to discuss the possibility of launching a second front in Europe. Roosevelt told Molotov that the Big Four must unite together after the war to police the world and disarm aggressor states.[9] When Molotov asked about the role of other countries, Roosevelt answered by opining that too many "policemen" could lead to infighting, but he was open to the idea of allowing other allied countries to participate.[9] A memorandum of the conference summarizes their conversation:

The President told Molotov that he visualized the enforced disarmament of our enemies and, indeed, some of our friends after the war; that he thought that the United States, England, Russia and perhaps China should police the world and enforce disarmament by inspection. The President said that he visualized Germany, Italy, Japan, France, Czechoslovakia, Rumania and other nations would not be permitted to have military forces. He stated that other nations might join the first four mentioned after experience proved they could be trusted.

Roosevelt and Molotov continued their discussion of the Four Policemen in a second meeting on June 1. Molotov informed the President that Stalin was willing to support Roosevelt's plans for maintaining postwar peace through the Four Policemen and enforced disarmament. Roosevelt also raised the issue of postwar decolonization. He suggested that former colonies should undergo a period of transition under the governance of an international trusteeship prior to their independence.

The Republic of China was brought in as a member of the Big Four and a future member of the Four Policemen. Roosevelt was in favor of recognizing China as a great power because he was certain that the Chinese would side with the Americans against the Soviets. He said to British Foreign Secretary Anthony Eden, "In any serious conflict of policy with Russia, [China] would undoubtedly line up on our side." The President believed that a pro-American China would be useful for the United States should the Americans, Soviets, and Chinese agree to jointly occupy Japan and Korea after the war.[13] When Molotov voiced concerns about the stability of China, Roosevelt responded by saying that the combined "population of our nations and friends was well over a billion people."

Churchill objected to Roosevelt's inclusion of China as one of the Big Four because he feared that the Americans were trying to undermine Britain's colonial holdings in Asia. In October 1942, Churchill told Eden that Republican China represented a "faggot vote on the side of the United States in any attempt to liquidate the British overseas empire." Eden shared this view with Churchill and expressed skepticism that China, which was then in the midst of a civil war, could ever return to a stable nation. Roosevelt responded to Churchill's criticism by telling Eden that "China might become a very useful power in the Far East to help police Japan" and that he was fully supportive of offering more aid to China. Roosevelt's Four Policemen proposal received criticism from the liberal internationalists, who wanted power to be more evenly distributed among the member nations of the UN. Internationalists were concerned that the Four Policemen could lead to a new Quadruple Alliance

In World War I the Big Four refers to the four top Allied powers and their leaders who met at the Paris Peace Conference in January 1919. The Big Four are also known as the Council of Four. It was composed of Woodrow Wilson of the United States, David Lloyd George of Britain, Vittorio Emanuele Orlando of Italy, and Georges Clemenceau of France.

"The Big Four" was the name popularly given to the famous and influential businessmen, philanthropists and railroad tycoons who built the Central Pacific Railroad, (C.P.R.R.), which formed the western portion through the Sierra Nevada and the Rocky Mountains of the First Transcontinental Railroad in the United States, built from the mid-continent at the Mississippi River to the Pacific Ocean during the middle and late 1860s.[1] Composed of Leland Stanford, (1824–1893), Collis Potter Huntington, (1821–1900), Mark Hopkins, (1813–1878), and Charles Crocker, (1822–1888), the four themselves however, personally preferred to be known as "The Associates."

Japanese Big Four, the four largest Japanese motorcycle manufacturers: Honda, Kawasaki, Suzuki, and Yamaha

Big Four in the United States wireless communications service providers, AT&T Mobility, Verizon Wireless, Sprint Corporation, and T-Mobile US

Big Four, the most influential international technology companies,Amazon, Apple, Facebook, and Google.

Big Four airlines, AA, EA, TW, and UA airlines, the four U.S. air carriers which dominated air travel prior to deregulation

The Big Four are the four largest international professional services networks, offering audit, assurance, tax, consulting, advisory, actuarial, corporate finance, and legal services. They handle the vast majority of audits for publicly traded companies as well as many private companies, creating an oligopoly in auditing large companies. It is reported that the Big Four audit 99% of the companies in the FTSE 100, and 96% of the companies in the FTSE 250 Index, an index of the leading mid-cap listing companies.[1] The Big Four firms are shown below, with their latest publicly available data. Firm Revenues Employees Revenue per employee Fiscal year Headquarters Source PwC $35.4 billion 208,100 $169,892 2015 United Kingdom [2] Deloitte $35.2 billion 225,400 $156,167 2015 United States [3] EY $28.7 billion 212,000 $135,517 2015 United Kingdom [4] KPMG $24.4 billion 173,965 $140,488 2015 Netherlands [5] This group was once known as the "Big Eight", and was reduced to the "Big Six" and then "Big Five" by a series of mergers. The Big Five became the Big Four after the demise of Arthur Andersen in 2002, following its involvement in the Enron scandal. BDO and Grant Thornton are the fifth and sixth largest firms, respectively.

The Four Motors for Europe are four highly industrialized regions in Europe. It is composed of the Rhône-Alpes region in France, centered in Lyon, the Lombardy region in Italy, centered in Milan, Catalonia region in Spain centered in Barcelona, and Baden-Württemberg in Germany, centered in Stuttgart. On September 9, 1988, in Stockholm, Sweden, the presidents of these four territories signed an agreement, called the "Memorandum", to increase economic and social cooperation between the realms. The agreement was to have the four regions cooperate in a long term relationship in the fields of science, research, education, environment, culture, and other sectors. The purpose of this relationship was to provide a unification force within Europe as well as increasing the potential for economic growth within the four regions. These regions focus on the exchange of information with each other to expand their technology and R&D. Wales and Flanders are also associated with this group.

Kenneth Pargament is noted for his book Psychology of Religion and Coping (1997; see article),[20] as well as for a 2007 book on religion and psychotherapy, and a sustained research program on religious coping. He is professor of psychology at Bowling Green State University (Ohio, USA), and has published more than 100 papers on the subject of religion and spirituality in psychology. Pargament led the design of a questionnaire called the "RCOPE" to measure Religious Coping strategies.[21] Pargament has distinguished between three types of styles for coping with stress:[22] 1) Collaborative, in which people co-operate with God to deal with stressful events; 2) Deferring, in which people leave everything to God; and 3) Self-directed, in which people do not rely on God and try exclusively to solve problems by their own efforts. He also describes four major stances toward religion that have been adopted by psychotherapists in their work with clients, which he calls the religiously rejectionist, exclusivist, constructivist, and pluralist stances.

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.

16 cell cayley quaternoon group

As Richard Dean showed in 1981, the quaternion group can be presented as the Galois group Gal(T/Q) where Q is the field of rational numbers and T is the splitting field, over Q, of the polynomial x^8 - 72 x^6 + 180 x^4 - 144 x^2 + 36. The development uses the fundamental theorem of Galois theory in specifying four intermediate fields between Q and T and their Galois groups, as well as two theorems on cyclic extension of degree four over a field.

In abstract algebra, one can construct a real four-dimensional vector space with basis {1, i, j, k} and turn it into an associative algebra by using the above multiplication table and distributivity. The result is a skew field called the quaternions.

In mathematics, the Klein four-group (or just Klein group or Vierergruppe (English: four-group), often symbolized by the letter V or as K4) is the group Z2 × Z2, the direct product of two copies of the cyclic group of order 2. It was named Vierergruppe by Felix Klein in 1884

In recreational mathematics, a Harshad number (or Niven number) in a given number base, is an integer that is divisible by the sum of its digits when written in that base. There are only four all-Harshad numbers: 1, 2, 4, and 6 (The number 12 is a Harshad number in all bases except octal).

In constructive cultures people are encouraged to be in communication with their co-workers, and work as teams, rather than only as individuals. In positions where people do a complex job, rather than something simple like a mechanic one, this culture is efficient.[22]

Achievement: completing a task successfully, typically by effort, courage, or skill (pursue a standard of excellence) (explore alternatives before acting) - Based on the need to attain high-quality results on challenging projects, the belief that outcomes are linked to one's effort rather than chance and the tendency to personally set challenging yet realistic goals. People high in this style think ahead and plan, explore alternatives before acting and learn from their mistakes.

Self-actualizing: realization or fulfillment of one's talents and potentialities - considered as a drive or need present in everyone (think in unique and independent ways) (do even simple tasks well) - Based on needs for personal growth, self-fulfillment and the realisation of one's potential. People with this style demonstrate a strong desire to learn and experience things, creative yet realistic thinking and a balanced concern for people and tasks.

Humanistic-encouraging: help others to grow and develop (resolve conflicts constructively) - Reflects an interest in the growth and development of people, a high positive regard for them and sensitivity to their needs. People high in this style devote energy to coaching and counselling others, are thoughtful and considerate and provide people with support and encouragement.

Affiliative: treat people as more valuable than things (cooperate with others) - Reflects an interest in developing and sustaining pleasant relationships. People high in this style share their thoughts and feelings, are friendly and cooperative and make others feel a part of things.

Organizations with constructive cultures encourage members to work to their full potential, resulting in high levels of motivation, satisfaction, teamwork, service quality, and sales growth. Constructive norms are evident in environments where quality is valued over quantity, creativity is valued over conformity, cooperation is believed to lead to better results than competition, and effectiveness is judged at the system level rather than the component level.

These types of cultural norms are consistent with (and supportive of) the objectives behind empowerment, total quality management, transformational leadership, continuous improvement, re-engineering, and learning organizations

Passive/defensive cultures[edit] Norms that reflect expectations for members to interact with people in ways that will not threaten their own security are in the Passive/Defensive Cluster. The four Passive/Defensive cultural norms are: Approval Conventional Dependent Avoidance In organizations with Passive/Defensive cultures, members feel pressured to think and behave in ways that are inconsistent with the way they believe they should in order to be effective. People are expected to please others (particularly superiors) and avoid interpersonal conflict. Rules, procedures, and orders are more important than personal beliefs, ideas, and judgment. Passive/Defensive cultures experience a lot of unresolved conflict and turnover, and organizational members report lower levels of motivation and satisfaction.

Aggressive/defensive cultures[edit] This style is characterized with more emphasis on task than people. Because of the very nature of this style, people tend to focus on their own individual needs at the expense of the success of the group. The aggressive/defensive style is very stressful, and people using this style tend to make decisions based on status as opposed to expertise.[25] Oppositional - This cultural norm is based on the idea that a need for security that takes the form of being very critical and cynical at times. People who use this style are more likely to question others work; however, asking those tough question often leads to a better product. Nonetheless, those who use this style may be overly-critical toward others, using irrelevant or trivial flaws to put others down. Power - This cultural norm is based on the idea that there is a need for prestige and influence. Those who use this style often equate their own self-worth with controlling others. Those who use this style have a tendency to dictate others opposing to guiding others’ actions. Competitive - This cultural norm is based on the idea of a need to protect one’s status. Those who use this style protect their own status by comparing themselves to other individuals and outperforming them. Those who use this style are seekers of appraisal and recognition from others. Perfectionistic - This cultural norm is based on the need to attain flawless results. Those who often use this style equate their self-worth with the attainment of extremely high standards. Those who often use this style are always focused on details and place excessive demands on themselves and others. Organizations with aggressive/defensive cultures encourage or require members to appear competent, controlled, and superior. Members who seek assistance, admit shortcomings, or concede their position are viewed as incompetent or weak. These organizations emphasize finding errors, weeding out "mistakes" and encouraging members to compete against each other rather than competitors. The short-term gains associated with these strategies are often at the expense of long-term growth.

A reticle, or reticule (from Latin reticulum, meaning "net"), also known as a graticule (from Latin craticula, meaning "gridiron"), is a net of fine lines or fibers in the eyepiece of a sighting device, such as a telescope, a telescopic sight, a microscope, or the screen of an oscilloscope. Today, engraved lines or embedded fibers may be replaced by a computer-generated image superimposed on a screen or eyepiece. Both terms may be used to describe any set of lines used for optical measurement, but in modern use reticle is most commonly used for gunsights and such, while graticule is more widely used for the covers of oscilloscopes and similar roles. There are many variations of reticles; this article concerns itself mainly with a simple reticle: crosshairs. Crosshairs are most commonly represented as intersecting lines in the shape of a cross, "+", though many variations exist, including dots, posts, circles, scales, chevrons, or a combination of these. Most commonly associated with telescopic sights for aiming firearms, crosshairs are also common in optical instruments used for astronomy and surveying, and are also popular in graphical user interfaces as a precision pointer. The reticle is said to have been invented by Robert Hooke, and dates to the 17th century.[1] Another candidate as inventor is the amateur astronomer William Gascoigne, who predated Hooke. Telescopic sights for firearms, generally just called scopes, are probably the device most often associated with crosshairs. Motion pictures and the media often use a view through crosshairs as a dramatic device, which has given crosshairs wide cultural exposure.

In music composition the four-group is the basic group of permutations in the twelve-tone technique. In that instance the Cayley table is written

The smallest non-cyclic group has four elements; it is the Klein four-group. Four is also the order of the smallest non-trivial groups that are not simple.

The quadrant count ratio (QCR) is a measure of the association between two quantitative variables. The QCR is not commonly used in the practice of statistics; rather, it is a useful tool in statistics education because it can be used as an intermediate step in the development of Pearson's correlation coefficient.

The Gartner Magic Quadrant (MQ) is the brand name for a series of market research reports published by Gartner Inc., a US-based research and advisory firm. According to Gartner, the Magic Quadrant aims to provide a qualitative analysis into a market and its direction, maturity and participants.[1] Their analyses are conducted for several specific technology industries and are updated every 1–2 years. Gartner rates vendors upon two criteria: completeness of vision and ability to execute.Using a methodology which Gartner does not disclose, these component scores lead to a vendor position in one of four quadrants: Leaders are said to score higher on both criteria: the ability to execute and completeness of vision. These are said to be typically larger, mature businesses. Challengers are said to score higher on the ability to execute and lower on the completeness of vision. Typically larger, settled businesses with what Gartner claims to be minimal future plans for that industry. Visionaries are said to score lower on the ability to execute and higher on the completeness of vision. Typically smaller companies. Niche players are said to score lower on both criteria: the ability to execute and completeness of vision. Typically new additions to the Magic Quadrant.

The Microsoft Scenarios is four “future of the world” scenarios that Microsoft uses to test its strategies, and is the basis of Listening to the Future by Dan Rasmus and Rob Salkowitz. The diagram is used for scenario planning, and the idea is that if a strategy seems robust to the four scenarios (the metaphor used is “wind tunnel testing”), then it is a good strategy. The quadrant diagram is Square 1: more regionalized, centralized and hierarchical- continental drift Square 2: more regionalized, distributed and networked- frontier fiction Square 3: centralized and hierarchical, more globalized- proud tower Square 4: more globalized, distributed and networked- freelance planet

Plato has been credited for the "justified true belief" theory of knowledge- knowledge is the 16th square philsoophers say no such thing.

In Plato's Hippias Major, Socrates gives four definitions of beauty

First definition: beauty is that which is appropriate[edit]

Tiring of the errors of Hippias, Socrates offers a definition in his turn, which he holds came from his famous harasser: the beautiful is simply that which is appropriate. This response pleases Hippias. But further examination is needed: first of all, is it the appropriateness which makes things beautiful, or does it simply make them appear to be beautiful? The second hypothesis is tempting: even a ridiculous man, dressed in nice clothing, will appear more beautiful. But inside he would still be ridiculous; thus appropriate and beautiful are not the same.

Hippias suggests that appropriateness provides at the same time the reality and the appearance of beauty. But then, nothing could be less sure; if everything was that simple, citizens and politicians would no longer have to quarrel to decide which action was the nicer.[2]

Second definition: beauty is that which is useful[edit]

Socrates proposes a second solution: if it is beautiful, is it useful? But here again problems surface: it is through power that men make things useful. Nevertheless, as is well known, power can as much serve evil as it serves good. And there is difficulty in qualifying actions as bad or good. Which in turn requires that the definition be refocused; beauty is only usefulness applied to good ends, or those that are "favourable".[2]

Third definition: beauty is that which is favourable[edit]

Identifying the beautiful and the favourable leads to a paradox: the favourable procreates the beautiful, as a father procreates a son. Since the favourable and the beautiful are thus considered to be one and the same, they arrive at the finding that beauty is the reason of goodness. In logic, a cause and an effect are two different things, as a father is different from the son. And thus they must conclude that Beauty is not good, and good is not beauty; an assertion which pleases neither Socrates nor Hippias.[2]

Fourth definition: beauty is the pleasure that comes from seeing and hearing[edit]

To conclude, Socrates brings out a final definition; at first glance quite amazing: "[what] if we were to say that that is beautiful which makes us feel joy ; I do not mean all pleasures, but that which makes us feel joy through hearing and sight?" This hypothesis, while appealing, contains according to Socrates himself a fundamental flaw; that it ignores the beauty of the more noble pleasures, drawn from the studious occupations or the study of laws.

On the other hand, it seems striking that only the senses of sight and hearing are taken into account. Is this a way to submit to common opinion, which is that touch, taste and smell are somehow more shameful and base than the other senses? Finally, it is not simply because pleasure comes from seeing or hearing that it is beautiful. Socrates throws himself into a series of considerations: taking into account pairs of objects, in the Majority of cases the term which they apply to both objects (A and B are beautiful, A and B are just) can apply also to an object taken separately (A is beautiful and B is beautiful). But in some rare cases it can happen that it this is not the case, notably when the sum of A and B forms an even number and A and B, taken in isolation, are two odd numbers.

In the case of beauty, it is the first category that is appropriate, because if a pair of two objects is beautiful, it stands to reason that each of them is. But a new paradox appears, since the beautiful, in discreet definition, must belong to both pleasures of sight and hearing, taken jointly, and cannot belong to only one of them. The definition as a result proves to be flawed. Exhausted by the many questions they have considered, Hippias berates Socrates and urges him instead of "with mere talk and nonsense" to seek beauty in "the ability to produce a discourse well and beautifully in a court of law or a council-house or before any other public body before which the discourse may be delivered."[2] Socrates, taking his leave, pretends to feel bad about the situation, cornered between the attacks of Hippias and those of his mysterious opponent. His only certainty, he concludes with a sense of humour, is that from now on he better understands the Greek proverb "beautiful things are difficult"

Xenophanes is credited with being one of the first philosophers to distinguish between true belief and knowledge, which he further developed into the prospect that you can know something but not really know it Belief is second quadrant knowing is fourth

Hu was well known as the primary advocate for the literary revolution of the era, a movement which aimed to replace scholarly classical Chinese in writing with the vernacular spoken language, and to cultivate and stimulate new forms of literature. In an article originally published in New Youth in January 1917 titled "A Preliminary Discussion of Literature Reform", Hu originally emphasized eight guidelines that all Chinese writers should take to heart in writing:

1. Write with substance. By this, Hu meant that literature should contain real feeling and human thought. This was intended to be a contrast to the recent poetry with rhymes and phrases that Hu saw as being empty.
2. Do not imitate the ancients. Literature should not be written in the styles of long ago, but rather in the modern style of the present era.
3. Respect grammar. Hu did not elaborate at length on this point, merely stating that some recent forms of poetry had neglected proper grammar.
4. Reject melancholy. Recent young authors often chose grave pen names, and wrote on such topics as death. Hu rejected this way of thinking as being unproductive in solving modern problems.
5. Eliminate old clichés. The Chinese language has always had numerous four-character sayings and phrases used to describe events. Hu implored writers to use their own words in descriptions, and deplored those who did not.
6. Do not use allusions. By this, Hu was referring to the practice of comparing present events with historical events even when there is no meaningful analogy.
7. Do not use couplets or parallelism. Though these forms had been pursued by earlier writers, Hu believed that modern writers first needed to learn the basics of substance and quality, before returning to these matters of subtlety and delicacy.
8. Do not avoid popular expressions or popular forms of characters. This rule, perhaps the most well-known, ties in directly with Hu's belief that modern literature should be written in the vernacular, rather than in Classical Chinese. He believed that this practice had historical precedents, and led to greater understanding of important texts.

In April of 1918, Hu published a second article in New Youth, this one titled "Constructive Literary Revolution - A Literature of National Speech". In it, he simplified the original eight points into just four:

1. Speak only when you have something to say. This is analogous to the first point above.
2. Speak what you want to say and say it in the way you want to say it. This combines points two through six above.
3. Speak what is your own and not that of someone else. This is a rewording of point seven.
4. Speak in the language of the time in which you live. This refers again to the replacement of Classical Chinese with the vernacular language.

The following excerpt is from a poem titled Dream and Poetry, written in vernacular Chinese by Hu. It illustrates how he applied those guidelines to his own work.

The lauburu or Basque cross (Basque: lauburu, "four heads") is a traditional Basque swastika with four comma-shaped heads. Today, it is a symbol of the Basque Country and the unity of the Basque people. It is also associated with Celtic peoples, most notably Galicians and Asturians. It can be constructed with a compass and straightedge, beginning with the formation of a square template; each head can be drawn from a neighboring vertex of this template with two compass settings, with one radius half the length of the other.

Historians and authorities have attempted to apply allegorical meaning to the ancient symbol. Some say it signifies the "four heads or regions" of the Basque Country. The lauburu does not appear in any of the seven coats-of-arms that have been combined in the arms of the Basque Country: Higher and Lower Navarre, Gipuzkoa, Biscay, Álava, Labourd, and Soule. The Basque intellectual Imanol Mujica liked to say that the heads signify spirit, life, consciousness, and form, but it is generally used as a symbol of prosperity.

Lau buru means "four heads", "four ends" or "four summits" in Basque. Some[who?] argue this might be a folk etymology applied to the Latin labarum.[4]

the Sun cross (or "Bolgar cross") Also known as the Bolgar cross, Sunwheel, solar cross or Woden's cross. Used in Europe since the Neolithic era and by ancient and contemporary Native American culture to represent respectively Neopagan beliefs and the great Medicine Wheel of life. Was used by the Bulgarian Tzars (emperors) as a symbol of the Bulgarian Orthodox Church. The cross-in-a-circle was interpreted as a solar symbol derived from the interpretation of the disc of the Sun as the wheel of the chariot of the Sun god.[1] Wieseler (1881) postulated an (unattested) Gothic rune hvel ("wheel") representing the solar deity by the "wheel" symbol of a cross-in-a-circle, reflected by the Gothic letter hwair (𐍈).[2]

Swastika The swastika is an equilateral cross with its arms bent at right angles, in either right-facing (卐) form or its mirrored left-facing (卍) form. The fylfot is a similar version. Archaeological evidence of swastika-shaped ornaments dates from the Neolithic period. It occurs mainly in the modern day culture of India, sometimes as a geometrical motif and sometimes as a religious symbol. It remains widely used in Eastern and Dharmic religions such as Hinduism, Buddhism and Jainism. Though once commonly used all over much of the world without stigma, because of its right-facing variant's iconic usage in National Socialist Germany, the symbol has become stigmatized in the Western world.

Isometric illusion Crosses frame this cube that appears to be hollow or solid and projected either inward or outward. A similar design was photographed in a crop circle. This design can be made by repeating the central hexagon outward once on all 6 sides then erasing some inner line segments and filling in the voids.

Skull and crossbones Traditionally used to mark Spanish cemeteries; the symbol evolved to represent death/danger, poison, and pirates. Also the illuminati

The tallest cross, at 152.4 metres high, is part of Francisco Franco's monumental "Valley of the Fallen", the Monumento Nacional de Santa Cruz del Valle de los Caidos in Spain.

A cross at the junction of Interstates 57 and 70 in Effingham, Illinois, is purportedly the tallest in the United States, at 198 feet (60.3 m) tall.[7]

The tombs at Naqsh-e Rustam, Iran, made in the 5th century BC, are carved into the cliffside in the shape of a cross. They are known as the "Persian crosses".

Cross shapes are made by a variety of physical gestures. Crossing the fingers of one hand is a common invocation of the symbol. The sign of the cross associated with Christian genuflection is made with one hand: in Eastern Orthodox tradition the sequence is head-heart-right shoulder-left shoulder, while in Oriental Orthodox, Catholic and Anglican tradition the sequence is head-heart-left-right. Crossing the index fingers of both hands represents the number 10 in Chinese-speaking societies and a charm against evil in European folklore (hence its frequent appearance in vampire movies). Other gestures involving more than one hand include the "cross my heart" movement associated with making a promise and the Tau shape of the referee's "time out" hand signal.

1600 BC marble sacral cross from the Temple Repositories of Knossos. (Heraclion Archaeological Museum, Greece)

Dutch philosopher Frans Hemsterhuis (1721 – 1790) – who belongs together with Erasmus, Spinoza en Geulincx to the most important philosophers of the Low Countries – said the same thing in his recognition of the four fundamental powers of the soul (in: ‘Aristaios of over de Goddelijkheid’, 1779; PETRY, 1990): ———————— 1. imagination – unsorted collection of ideas; ———————— 2. reason – comparison of thoughts, their substance; ———————— 3. willpower – will and action; ——————– 4. moral principle – connection with other humans and the ability . to see the other as oneself.

The world of painting was not an isolated case. It was the crowning point of a continuous development of the soul, which became visible as early as the eighth century. Isaac Ben Solomon Israeli (850 – 932) wrote his ‘Book of Definitions‘ and distinguished four types of questioning (SIRAT, 1985): ———————– 1. existence – if something exists ———————– 2. quiddity – what something is, the essential ———————– 3. quality – how something is ———————– 4. quarity – why something is Israeli was considered the father of medieval Jewish Neoplatonism and was the foremost physician and philosopher of his time.

Han, Zhao, Wei and Zhi.This allowed other clans to gain fiefs and military authority, and decades of internecine struggle led to the establishment of four major families, the Han, Zhao, Wei and Zhi.

The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants, traders and clerks in Asia, Africa, and elsewhere. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal. Very complex mental mathematics can be done with abaci and they are sued in math competitions. Their significance is they are math devices that use peoples mental capacities optimally. Humans can perform mental mathematics very well with the number four and using four beads. Any higher number does not work. The key to the abacus is the number four. It is no coincidence because four is the number of the quadrant, the form of being.

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.

There is one theory that the cross is a time telling device and Jesus on the cross represented the freezing of time, or the flow.

QMRIn his early books, such as The System of Objects, For a Critique of the Political Economy of the Sign, and The Consumer Society, Baudrillard's main focus is upon consumerism, and how different objects are consumed in different ways. At this time Baudrillard's political outlook was loosely associated with Marxism (and situationism), but in these books he differed from Karl Marx in one significant way. For Baudrillard, as for the situationists, it was consumption rather than production that was the main driver of capitalist society. Baudrillard came to this conclusion by criticising Marx's concept of "use-value". Baudrillard thought that both Marx's and Adam Smith's economic thought accepted the idea of genuine needs relating to genuine uses too easily and too simply. Baudrillard argued, drawing from Georges Bataille, that needs are constructed, rather than innate. He stressed that all purchases, because they always signify something socially, have their fetishistic side. Objects always, drawing from Roland Barthes, "say something" about their users. And this was, for him, why consumption was and remains more important than production: because the "ideological genesis of needs" precedes the production of goods to meet those needs.[17] He wrote that there are four ways of an object obtaining value. The four value-making processes are:[18] The first is the functional value of an object; its instrumental purpose. A pen, for instance, writes; a refrigerator cools. The second is the exchange value of an object; its economic value. One pen may be worth three pencils; and one refrigerator may be worth the salary earned by three months of work. The third is the symbolic value of an object; a value that a subject assigns to an object in relation to another subject (i.e., between a giver and receiver). A pen might symbolize a student's school graduation gift or a commencement speaker's gift; or a diamond may be a symbol of publicly declared marital love. The last is the sign value of an object; its value within a system of objects. A particular pen may, while having no added functional benefit, signify prestige relative to another pen; a diamond ring may have no function at all, but may suggest particular social values, such as taste or class. Baudrillard's earlier books were attempts to argue that the first two of these values are not simply associated, but are disrupted by the third and, particularly, the fourth. Later, Baudrillard rejected Marxism totally (The Mirror of Production and Symbolic Exchange and Death). But the focus on the difference between sign value (which relates to commodity exchange) and symbolic value (which relates to Maussian gift exchange) remained in his work up until his death. Indeed, it came to play a more and more important role, particularly in his writings on world events.

As spatial interrelationships are key to this synoptic science, maps are a key tool. Classical cartography has been joined by a more modern approach to geographical analysis, computer-based geographic information systems (GIS). In their study, geographers use four interrelated approaches: Systematic — Groups geographical knowledge into categories that can be explored globally. Regional — Examines systematic relationships between categories for a specific region or location on the planet. Descriptive — Simply specifies the locations of features and populations. Analytical — Asks why we find features and populations in a specific geographic area.