Quadrant Model of Reality Book 7 Art and Philosophy Last

The fragrance wheel is shaped as a quadrant

Perfume is a billion dollar industry and has been very important throughout human history. Perfume oils usually contain tens to hundreds of ingredients and these are typically organized in a perfume for the specific role they will play. These ingredients can be roughly grouped into four groups: Primary scents (Heart): Can consist of one or a few main ingredients for a certain concept, such as "rose". Alternatively, multiple ingredients can be used together to create an "abstract" primary scent that does not bear a resemblance to a natural ingredient. For instance, jasmine and rose scents are commonly blends for abstract floral fragrances. Cola flavourant is a good example of an abstract primary scent. Modifiers: These ingredients alter the primary scent to give the perfume a certain desired character: for instance, fruit esters may be included in a floral primary to create a fruity floral; calone and citrus scents can be added to create a "fresher" floral. The cherry scent in cherry cola can be considered a modifier. Blenders: A large group of ingredients that smooth out the transitions of a perfume between different "layers" or bases. These themselves can be used as a major component of the primary scent. Common blending ingredients include linalool and hydroxycitronellal. Fixatives: Used to support the primary scent by bolstering it. Many resins, wood scents, and amber bases are used as fixatives. The top, middle, and base notes of a fragrance may have separate primary scents and supporting ingredients. The perfume's fragrance oils are then blended with ethyl alcohol and water, aged in tanks for several weeks and filtered through processing equipment to, respectively, allow the perfume ingredients in the mixture to stabilize and to remove any sediment and particles before the solution can be filled into the perfume bottles

Modern chypre perfumes have various connotations such as floral, fruity, green, woody-aromatic, leathery, and animalic notes, but can easily be recognized by their "warm" and "mossy-woody" base which contrasts the fresh citrus top, and a certain bitterness in the dry-down from the oak moss and patchouli. The accord consists of: Citrus: singular or blends of Bergamot, Orange, Lemon or Neroli Oak moss: mossy and woody Patchouli: camphoraceous and woody Musk: sweet, powdery, and animalic. Usually synthetic in modern times

The Fragrance wheel is a relatively new classification method that is widely used in retail and in the fragrance industry. The method was created in 1983 by Michael Edwards, a consultant in the perfume industry, who designed his own scheme of fragrance classification. The new scheme was created in order to simplify fragrance classification and naming scheme, as well as to show the relationships between each of the individual classes.[24] The five standard families consist of Floral, Oriental, Woody, Aromatic Fougère, and Fresh, with the first four families borrowing from the classic terminology and the last consisting of newer bright and clean smelling citrus and oceanic fragrances that have arrived in the past generation due to improvements in fragrance technology. Each of the families are in turn divided into subgroups and arranged around a wheel. In this classification scheme, Chanel No.5, which is traditionally classified as an aldehydic floral, would be located under the Soft Floral sub-group, and amber scents would be placed within the Oriental group. As a class, chypre perfumes are more difficult to place since they would be located under parts of the Oriental and Woody families. For instance, Guerlain's Mitsouko is placed under Mossy Woods, but Hermès Rouge, a chypre with more floral character, would be placed under Floral Oriental.

The Fragrance wheel is a relatively new classification method that is widely used in retail and in the fragrance industry. The method was created in 1983 by Michael Edwards, a consultant in the perfume industry, who designed his own scheme of fragrance classification after being inspired by a fragrance seminar by Firmenich. The new scheme was created in order to simplify fragrance classification and naming, as well as to show the relationships between each individual classes. The five standard families consist of Floral, Oriental, Woody, Fougère, and Fresh, with the former four families being more "classic" while the latter consists of newer, bright and clean smelling citrus and oceanic fragrances that have arrived due to improvements in fragrance technology. With the exception of the Fougère family, each of the families are in turn divided into three sub-groups and arranged around a wheel: 1. Floral Floral Soft Floral Floral Oriental 2. Oriental Soft Oriental Oriental Woody Oriental 3. Woody Wood Mossy Woods Dry Woods 4. Fresh Citrus Green Water 5. Fougère The Fougère family is placed at the center of this wheel since they are large family of scents that usually contain fragrance elements from each of the other four families. In this classification scheme, Chanel No.5, which is traditionally classified as a "Floral Aldehyde" would be located under Soft Floral sub-group, and "Amber" scents would be placed within the Oriental group. As a class, Chypres is more difficult to place since they would located under parts of the Oriental and Woody families. For instance, Guerlain Mitsouko, which is classically identified as a chypre will be placed under Mossy Woods, but Hermès Rouge, a chypre with more floral character, would be placed under Floral Oriental. According to Osmoz, there are eight major families: Chypre, Citrus, Floral and Oriental (feminine), and Aromatic, Citrus, Oriental and Woody (masculine). Each one of those olfactive families is then split into several subfamilies.

cross multiplication In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. Given an equation like: {\frac {a}{b}}={\frac {c}{d}} (where b and d are not zero), one can cross-multiply to get: ad=bc\qquad \mathrm {or} \qquad a={\frac {bc}{d}}. In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.

Matrix multiplication is the foundation of advanced math and physics. It involves multiplying quadrants of numbers.

In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. Numbers such as the real or complex numbers can be multiplied according to elementary arithmetic. On the other hand, matrices are arrays of numbers, so there is no unique way to define "the" multiplication of matrices. As such, in general the term "matrix multiplication" refers to a number of different ways to multiply matrices. The key features of any matrix multiplication include: the number of rows and columns the original matrices have (called the "size", "order" or "dimension"), and specifying how the entries of the matrices generate the new matrix.

Like vectors, matrices of any size can be multiplied by scalars, which amounts to multiplying every entry of the matrix by the same number. Similar to the entrywise definition of adding or subtracting matrices, multiplication of two matrices of the same size can be defined by multiplying the corresponding entries, and this is known as the Hadamard product. Another definition is the Kronecker product of two matrices, to obtain a block matrix.

One can form many other definitions. However, the most useful definition can be motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering. This definition is often called the matrix product.[1][2] In words, if A is an n × m matrix and B is an m × p matrix, their matrix product AB is an n × p matrix, in which the m entries across the rows of A are multiplied with the m entries down the columns of B (the precise definition is below).

This definition is not commutative, although it still retains the associative property and is distributive over entrywise addition of matrices. The identity element of the matrix product is the identity matrix (analogous to multiplying numbers by 1), and a square matrix may have an inverse matrix (analogous to the multiplicative inverse of a number). A consequence of the matrix product is determinant multiplicativity. The matrix product is an important operation in linear transformations, matrix groups, and the theory of group representations and irreps.

Computing matrix products is both a central operation in many numerical algorithms and potentially time consuming, making it one of the most well-studied problems in numerical computing. Various algorithms have been devised for computing C = AB, especially for large matrices.

This article will use the following notational conventions: matrices are represented by capital letters in bold, e.g. A, vectors in lowercase bold, e.g. a, and entries of vectors and matrices are italic (since they are scalars), e.g. A and a. Index notation is often the clearest way to express definitions, and is used as standard in the literature. The i, j entry of matrix A is indicated by (A)ij or Aij, whereas a numerical label (not matrix entries) on a collection of matrices is subscripted only, e.g. A1, A2, etc

The cross product In mathematics and vector calculus, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R3) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The cross product is anticommutative (i.e. a × b = −b × a) and is distributive over addition (i.e. a × (b + c) = a × b + a × c). The space R3 together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket. Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation or "handedness". The product can be generalized in various ways; it can be made independent of orientation by changing the result to pseudovector, or in arbitrary dimensions the exterior product of vectors can be used with a bivector or two-form result. Also, using the orientation and metric structure just as for the traditional 3-dimensional cross product, one can in n dimensions take the product of n − 1 vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions.[1] If one adds the further requirement that the product be uniquely defined, then only the 3-dimensional cross product qualifies. (See § Generalizations, below, for other dimensions.)

In 1911, at Jacques' home in Puteaux, the brothers hosted a regular discussion group with Cubist artists including Picabia, Robert Delaunay, Fernand Léger, Roger de La Fresnaye, Albert Gleizes, Jean Metzinger, Juan Gris, and Alexander Archipenko. Poets and writers also participated. The group came to be known as the Puteaux Group, or the Section d'Or. Uninterested in the Cubists' seriousness or in their focus on visual matters, Duchamp did not join in discussions of Cubist theory, and gained a reputation of being shy. However, that same year he painted in a Cubist style, and added an impression of motion by using repetitive imagery. During this period Duchamp's fascination with transition, change, movement and distance became manifest, and like many artists of the time, he was intrigued with the concept of depicting the fourth dimension in art.[13] His painting Sad Young Man on a Train embodies this concern: First, there's the idea of the movement of the train, and then that of the sad young man who is in a corridor and who is moving about; thus there are two parallel movements corresponding to each other. Then, there is the distortion of the young man—I had called this elementary parallelism. It was a formal decomposition; that is, linear elements following each other like parallels and distorting the object. The object is completely stretched out, as if elastic. The lines follow each other in parallels, while changing subtly to form the movement, or the form of the young man in question. I also used this procedure in the Nude Descending a Staircase.

The most prominent example of Duchamp's association with Dada was his submission of Fountain, a urinal, to the Society of Independent Artists exhibit in 1917. Artworks in the Independent Artists shows were not selected by jury, and all pieces submitted were displayed. However, the show committee insisted that Fountain was not art, and rejected it from the show. This caused an uproar amongst the Dadaists, and led Duchamp to resign from the board of the Independent Artists. Duchamps urinal called has four holes in a line in it where the urine drains. A lot of people question if Duchamp was poking fun at art and asking the question, what is art, and irreverently making a urinal artwork subverting art. The urinal artwork is one of the most famous artworks in history. It is a very taboo item, usually held in private, but here it is on display as a work of art. But it does have the four holes. Art is the third quadrant field of inquiry and thus is supposed to make people think and question. The third quadrant is destructive. Duchamp white urinal is kind of a play on the continuity of White throughout White history, where the urinal has elegant contours and White features like ancient White sculptures from Greece (in reality they were not White but were painted but became White after the paint eroded)

Originally the rubiks cube was a two by two cube (the quadrant) Rubik's Cube is a 3-D combination puzzle invented in 1974[1][2] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube,[3] the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980[4] via businessman Tibor Laczi and Seven Towns founder Tom Kremer,[5] and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide[6][7] making it the world's top-selling puzzle game.[8][9] It is widely considered to be the world's best-selling toy.[10] In a classic Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement.[11] On early cubes, the position of the colours varied from cube to cube.[12] An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour. Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik. In March 1970, Larry Nichols invented a 2×2×2 "Puzzle with Pieces Rotatable in Groups" and filed a Canadian patent application for it. Nichols's cube was held together with magnets. Nichols was granted U.S. Patent 3,655,201 on April 11, 1972, two years before Rubik invented his Cube. On April 9, 1970, Frank Fox applied to patent his "Spherical 3×3×3". He received his UK patent (1344259) on January 16, 1974.[13]

The Rosicrucian Cosmo-Conception Chapter X The Earth Period The Globes of the Earth Period are located in the four densest states of matter--the Region of Concrete Thought, the Desire World, the Etheric, and the Chemical Regions (See Diagram 8). The densest Globe (Globe D) is our present Earth. When we speak of "the densest Worlds" or "the densest states of matter," the term must be taken in a relative sense. Otherwise it would imply a limitation in the absolute, and that is absurd. Dense and attenuated, up and down, east and west, are applicable only relatively to our own status and position. As there are higher, finer Worlds than those touched by our life wave, so there are also denser states of matter which are the field of evolution for other classes of beings. Nor must it be thought that these denser worlds are elsewhere in space; they are interpenetrated by our worlds in a manner similar to that in which the higher Worlds interpenetrate this Earth. The fancied solidity of the Earth and the forms we see are no bar to the passage of a denser body any more than our solid dense walls bar the passage of a human being clothed in his desire body. Neither is solidity synonymous with density, as may be illustrated by aluminum, a solid which is less dense than the fluidic mercury; nevertheless the latter, in spite of its density, will evaporate or exude through many solids. This being the fourth Period, we have at present four elements. In the Saturn Period there was but one element, Fire--i.e., there was warmth, or heat, which is incipient fire. In the second, or Sun Period, there were to elements, Fire and Air. In the third, or Moon Period, there were three elements, Water being added; and in the fourth, or Earth Period, was added the fourth element, Earth. Thus it will be seen that a new element was added for each Period. In the Jupiter Period an element of a spiritual nature will be added, which will unite with the speech so that words will invariable carry with them understanding--not misunderstanding, as is frequently the case now. For instance, when one says "house," he may mean a cottage, while the hearer may get the idea of a tenement flat building. To this environment of the four elements, as specified above, the different classes mentioned in diagram 10 were brought over by the Hierarchies in charge of them. We remember that in the Moon Period these classes formed three kingdoms--animal, animal-plant and plant-mineral. Here on Earth, however, the conditions are such that there can be no large half-way classes. There must be four distinctly different kingdoms. In this crystallized phase of existence the lines between them must be more sharply drawn than was the case in former Periods, where one kingdom gradually merged into the next. Therefore some of the classes mentioned in diagram 10 advanced one-half step, while others went back a half a step. Some of the mineral-plants advanced completely into the plant kingdom and became the verdure of the fields. Others went down and became the purely mineral soil in which the plants grew. Of the plant-animals some advanced into the animal kingdom, ahead of time, and those species have yet the colorless plant-blood and some, like star-fishes, have even the five points like the petals of flowers. All of class 2 whose desire bodies could be divided into two parts (as was the case with all of class 1) were fitted to become human vehicles and were therefore advanced into the human group. We must carefully remember that in the above paragraphs we are dealing with Form, not with the Life which dwells in the Form. The instrument is graded to suit the life that is to dwell in it. Those of class 2, in whose vehicles the above mentioned division could be made were raised to the human kingdom, but were given the indwelling spirit at a point in time later than class 1. Hence, they are not now so far evolved as class 1, and are therefore the lower races of mankind. Those whose desire bodies were incapable of division were put into the same division as classes 3a and 3b. They are our present anthropoids. They may yet overtake our evolution if they reach a sufficient degree of advancement before the critical point already mentioned, which will come in the middle of the fifth Revolution. If they do not overtake us by that time, they will have lost touch with our evolution. It was said that man had built his threefold body by the help of others higher than he, but in the previous Period there was no coordinating power; the threefold spirit, the Ego, was separate and apart from its vehicles. Now the time had come to unit the spirit and the body. Where the desire body separated, the higher part become somewhat master over the lower part and over the dense and vital bodies. It formed a sort of animal-soul with which the spirit could unite by means of the link of mind. Where there was no division of the desire body, the vehicle was given over to desires and passions without any check, and could therefore not be used as a vehicle within which the spirit could dwell. So it was put under the control of a group-spirit which ruled if from without. It became an animal body, and that kind has now degenerated into the body of the anthropoid. Where there was a division of the desire body, the dense body gradually assumed a vertical position, thus taking the spine out of the horizontal currents of the Desire World in which the group-spirit acts upon the animal through the horizontal spine. The Ego could then enter, work in and express itself through the vertical spine and build the vertical larynx and brain for its adequate expression in the dense body. A horizontal larynx is also under the domination of the group-spirit. While it is true that some animals, as the starling, raven, parrot, etc., previously mentioned, are able, because of the possession of a vertical larynx, to utter words, they cannot use them understandingly. The use of words to express thought is the highest human privilege and can be exercised only by a reasoning, thinking entity like man. If the student will keep this in mind, it will be easier to follow the different steps which lead up to this result. The Saturn Revolution of the Earth Period This is the Revolution during which, in each Period. the dense body is reconstructed. This time it was given the ability to form a brain and become a vehicle for the germ of mind which was to be added later. This addition constituted the final reconstruction of the dense body, rendering it capable of attaining the highest degree of efficiency possible to such a vehicle. Unspeakable Wisdom has been employed in its construction. It is a marvel. It can never be sufficiently impressed upon the mind of the student what immeasurable facilities for the gaining of knowledge are contained in this instrument, and what a great boon it is to man; how much he should prize it and how thankful he should be to have it. Some examples of the perfection of construction and intelligent adaptability displayed in this instrument have previously been given, but in order to further impress this great truth upon the mind of the student, it might not be out of place to illustrate more fully this Wisdom, also the work of the Ego in the blood. It is generally know, in a vague kind of way, that the gastric juice acts upon the food to promote assimilation; but only a very few people, outside of the medical profession, are aware that there are many different gastric juices, each appropriate to the treatment of a certain kind of food. The researches of Pavlov, however, have established the fact beyond doubt, that there is one kind of juice for the digestion of meat, another for milk, another for acid fruit, etc. That fact, by the way, is the reason why all foods do not mix well. Milk, for instance, requires a gastric juice that is widely different from almost any other kind except that required for the digestion of starchy foods, and is not readily digested with any food other than cereals. This alone would show marvelous wisdom; that the Ego working subconsciously is able to select the different juices which are appropriate to the different kinds of food taken into the stomach, making each of just the right strength and quantity to digest the food. What makes the matter still more wonderful, however, is the fact that the gastric juice is poured into the stomach in advance of the food. We do not consciously direct the process of mixing this fluid. The great majority of people know nothing of metabolism or any other phrase of chemistry. So it is not enough to say that, as we taste what is coming, we direct the process by means of signals through the nervous system. When this fact of the selection of juices was first proven, scientists were sorely puzzled trying to learn how the right kind of juice was selected and caused to enter the stomach before the food. They thought the signal was given along the nervous system. But it was demonstrated beyond doubt that the proper juice was poured into to the stomach even though the nervous system was blocked. At last Starling and Bayliss, in a series of experiments of brilliant ingenuity, proved that infinitesimal parts of the food are taken up by the blood as soon as the food enters the mouth, go in advance to the digestive glands and cause a flow of the proper juice. This again, is only the physical side of the phenomena. To understand the whole wonderful connection, we must turn to occult science. That alone explains why the signal is carried by the blood. The blood is one of the highest expressions of the vital body. The Ego guides and controls its dense instrument by means of the blood, therefore the blood is also the means used to act on the nervous system. During some of the time that digestion is going on, it acts partially through the nervous system, but (especially at the commencement of the digestive process) it acts directly upon the stomach. When, during scientific experiments, the nerves were blocked, the direct way through the blood was still open and the Ego derived the necessary information in that way. It will also be seen that the blood is driven to wherever the Ego unfolds the greatest activity at any time. If a situation requires sudden though and action, the blood is promptly driven to the head. If a heavy meal is to be digested the greater portion of the blood leaves the head, centering around the digestive organs. The Ego concentrates its efforts on ridding the body of the useless food. Therefore a man cannot think well after a heavy meal. He is sleepy because so much blood has left the brain that the residue is insufficient to carry on the functions necessary to full waking consciousness, besides, nearly all the vital fluid or solar energy specialized by the spleen is absorbed by the blood rushing through that organ after a meal in greater volume than between meals. Thus the rest of the system is also deprived of the vital fluid in a large measure during digestion. It is the Ego that drives the blood into the brain. Whenever the body goes to sleep, the table will invariably tip towards the feet, raising the head. During coition the blood is centered in the sex organs, etc. All these examples tend to prove that during the waking hours, the Ego works in and controls the dense body by means of the blood. The larger portion of the total amount goes to that part of the body where at any given time, the Ego unfolds any particular activity. The reconstruction of the dense body in the Saturn Revolution of the Earth Period was for the purpose of rendering it capable of inter-penetration by the mind. It gave the first impulse to the building of the frontal part of the brain; also the incipient division in the nervous system which has since become apparent in its subdivisions--the voluntary and the sympathetic. The latter was the only one provided for in the Moon Period. The voluntary nervous system (which has transformed the dense body from a mere automaton acting under stimuli from without, to an extraordinary adaptable instrument capable of being guided and controlled by an Ego from within) was not added until the present Earth Period. The principal art of the reconstructive work was done by the Lords of Form. They are the Creative Hierarchy which is most active in the Earth Period, as were the Lords of Flame in the Saturn Period, the Lords of Wisdom in the Sun Period, and the Lords of Individuality in the Moon Period. The Earth Period is pre-eminently the Period of Form, for there the form or matter side of evolution reaches its greatest and most pronounced state. Here spirit is more helpless and suppressed and Form is the most dominant factor--hence the prominence of the Lords of Form. The Sun Revolution of the Earth Period During this Revolution the vital body was reconstructed to accommodate the germinal mind. The vital body was fashioned more in the likeness of the dense body, so that it could become fitted for use as the densest vehicle during the Jupiter Period, when the dense body will have become spiritualized. The Angels, the humanity of the Moon Period, were aided by the Lords of Form in reconstruction. The organization of the vital body is now next in efficiency to the dense body. Some writers on this subject call the former a link, and contend that it is simply a mold of the dense body, and not a separate vehicle. While not desiring to criticize, and admitting that this contention is justified by the fact that man, at his present stage of evolution, cannot ordinarily use the vital body as a separate vehicle--because it always remains with the dense body and to extract it in toto would cause death of the dense body--yet there was a time when it was not so firmly incorporated with the latter, as we shall presently see. During those epochs of our Earth's history which have already been mentioned as the Lemurian and the Atlantean, man was involuntarily clairvoyant, and it was precisely this looseness of connection between the dense and the vital bodies that made him so. (The Initiators of that time helped the candidate to loosen the connection still further, as in the voluntary clairvoyant.) Since then the vital body has become much more firmly interwoven with the dense body in the majority of people, but in all sensitives it is loose. It is that looseness which constitutes the difference between the psychic and the ordinary person who is unconscious of all but the vibrations contacted by means of the five senses. All human beings have to pass through this period of close connection of the vehicles and experience the consequent limitation of consciousness. There are, therefore, two classes of sensitives, those who have not become firmly enmeshed in matter, such as the majority of the Hindus, the Indians, etc., who possess a certain low grade of clairvoyance, or are sensitive to the sounds of nature, and those who are in the vanguard of evolution. The latter are emerging from the acme of materiality, and are again divisible into two kinds, one of which develops in a passive, weak-willed manner. By the help of others they re-awaken the solar plexus or other organs in connection with the involuntary nervous system. These are therefore involuntary clairvoyants, mediums who have no control of their faculty. They have retrograded. The other kind is made up of those who by their own wills unfold the vibratory powers of the organs now connected with the voluntary nervous system and thus become trained occultists, controlling their own bodies and exercising the clairvoyant faculty as they will to do. They are called voluntary or trained clairvoyants. In the Jupiter Period man will function in his vital body as he now does in his dense body; and as no development in nature is sudden, the process of separating the two bodies has already commenced. The vital body will then attain a much higher degree of efficiency than the dense body of today. As it is a much more pliable vehicle, the spirit will then be able to use it in a manner impossible of realization in the case of the present dense vehicle. The Moon Revolution of the Earth Period Here the Moon Period was recapitulated, and much the same conditions prevailed (on an advanced scale) as obtained on Globe D of that Period. There was the same kind of fire-fog atmosphere; the same fiery core; the same division of the Globe into two parts, in order to allow the more highly evolved beings a chance to progress at the proper rate and pace, which it would be impossible for beings such as our humanity to equal. In that Revolution the Archangels (humanity of the Sun Period) and the Lords of Form took charge of the reconstruction of the desire body, but they were not alone in that work. When the separation of the Globe into two parts occurred, there was a similar division in the desire bodies of some of the evolving beings. We have already noted that where this division took place, the form was ready to become the vehicle of an indwelling spirit, and in order to further this purpose the Lords of Mind (humanity of the Saturn Period) took possession of the higher part of the desire body and implanted in it the separate selfhood, without which the present man with all his glorious possibilities, could never have existed. Thus in the latter part of the Moon Revolution the first germ of separate personality was implanted in the higher part of the desire body by the Lords of Mind. The Archangels were active in the lower part of the desire body, giving it the purely animal desires. They also worked in the desire bodies where there was no division. Some of these were to become the vehicles of the animal group-spirits, which work on them from without, but do not enter wholly into the animal forms, as the individual spirit does into the human body. The desire body was reconstructed to render it capable of being interpenetrated by the germinal mind which, during the Earth Period, will be implanted in all those desire bodies in which it was possible to make the before-mentioned division. As has been previously explained, the desire body is an unorganized ovoid, holding the dense body as a dark spot within its center, as the white of an egg surrounds the yolk. There are a number of sense centers in the ovoid, which have appeared since the beginning of the Earth Period. In the average human being these centers appear merely as eddies in a current and are not now awake, hence his desire body is of no use to him as a separate vehicle of consciousness; but when the sense centers are awakened they look like whirling vortices. Rest Periods Between Revolutions Hitherto we have noted only the Cosmic Nights between Periods. We saw that there was an interval of rest and assimilation between the Saturn and the Sun Periods; another Cosmic Night between the Sun and the Moon Periods, etc. But in addition to these, there are also rests between the Revolutions. We might liken the Periods to the different incarnations of man; the Cosmic Nights between them to the intervals between deaths and new births; and the rest between Revolutions would then be analogous to the rest of sleep between two days. When a Cosmic Night sets in, all manifested things are resolved into a homogenous mass--the Cosmos again becomes Chaos. This periodical return of matter to primordial substance is what makes it possible for the spirit to evolve. Were the crystallizing process of active manifestation to continue indefinitely it would offer an insurmountable barrier to the progress of Spirit. Every time matter has crystallized to such a degree that it becomes too hard for the spirit to work in, the latter withdraws to recuperate its exhausted energy, on the same principle that a power-drill which has stopped when boring in hard metals, is withdrawn to regain its momentum. It is then able to bore its way further into the metal. Freed from the crystallizing energy of the evolving spirits, the chemical forces in matter turn Cosmos to Chaos by restoring matter to its primordial state, that a new start may be made by the regenerated virgin spirits at the dawn of a new Day of Manifestation. The experience gained in former Periods and Revolutions enables the Spirit to build up to the point last reached, with comparative celerity, also to facilitate further progress by making such alterations as its cumulative experience dictates. Thus at the end of the Moon Revolution of the Earth Period, all the Globes and all life returned to Chaos, re-emerging therefrom at the beginning of the fourth Revolution. The Fourth Revolution of the Earth Period In the exceeding complexity of the scheme of evolution, there are always spirals within spirals, ad infinitum. So it will not be surprising to learn that in every Revolution the work of recapitulation and rest is applied to the different Globes. When the life wave reappeared on Globe A in this Revolution, it went though the development of the Saturn Period; then after a rest which, however did not involve the complete destruction of the Globe; but only an alteration, it appeared on Globe B, where the work of the Sun Period was recapitulated. Then after a rest, the life wave passed on to Globe C, and the work of the Moon Period was repeated. Finally, the life wave arrived on Globe D, which is our Earth, and not until then did the proper work of the Earth Period begin. Even then, the spiral within the spiral precluded its beginning immediately on the arrival of the life wave from Globe C, for the bestowal of the germ of mind did not actually take place until the fourth Epoch, the first three Epochs being still further recapitulations of the Saturn, Sun and Moon Periods, but always on a higher scale. Notice how the fourth period is different from the previous three in this Rosicrucian model.

According to Rosicrucianism Etheric Region: related to the etheric body; home of the Angels (seen as being one step beyond the human stage, as humans are a degree in advance of the animal evolution), astrologically associated to Aquarius; Akashic records in the reflecting ether (pictures at least several hundred years back or much more in some cases, almost as the pictures on a screen, scene shifts backward). The etheric region is subdivided in four regions according to the grades of density of the aether permeating our physical planet Earth; Reflecting Ether, Light Ether, Life Ether and Chemical Ether. Chemical Region; the physical Earth as perceived through the five senses enhanced by the current technological equipment, subdivided in three regions according to the four main states of matter: solid, liquid, gaseous, and plasma. It is the current home of the self-conscious humanity, astrologically associated to Pisces. The Chemical region of the physical world is home to four life waves, or kingdoms, at a different stage in the evolutionary path: mineral life is the first and lowest level of spiritual evolution on Earth; then comes plants, with actual life, then animals (cold-blooded animals, then warm-blooded), and finally the human being. The beings belonging to each life wave either evolve through the work of the individual Spirit (human being) or are yet evolving under a group spirit and have acquired more or less subtle bodies according to the development stage of each life wave.

The Rosy Cross (also called Rose Cross and Rose Croix) is a symbol largely associated with the semi-mythical Christian Rosenkreuz, Qabbalist and alchemist and founder of the Rosicrucian Order.[1][2] The Rose Cross is said to be a cross with a white rose at its centre[3] and symbolizes the teachings of a tradition formed within the Christian tenets

Els Quarte Gats is the name of a café in Barcelona, Spain that famously became a popular meeting place for famous artists throughout the modernist period in Cataluña. The café opened on June 12, 1897 in the famous Casa Martí, and served as a hostel, bar and cabaret until it eventually became a central meeting point for Barcelona’s most prominent modernist figures, such as Pablo Picasso and Ramon Casas I Carbó. The bar closed due to financial difficulties in June 1903, but was reopened and eventually restored to its original condition in 1989. List of Famous Patrons[edit] Ramon Casas (Artist) Santiago Rusiñol (Artist) Rubén Dario (Poet) Pablo Picasso (Artist) Isaac Albéniz (Pianist and composer) Enric Granados (Pianist and composer) Lluís Millet (Musician and composer) Antoní Gaudí (Architect) Ricard Opisso (Cartoonist, illustrator and painter) Miquel Utrillo (Artist) Julio González (Sculptor)[8]

The Four Little Girls (Les Quatre Petites Filles) is a play written in French by the painter Pablo Picasso. It is the second of two full-length plays written by Picasso, the first being Desire Caught by the Tail. Written between November 24, 1947, and August 13, 1948,[1] it was published in 1949. In 1952 Picasso wrote a second version of the play using the same title.[2] Both versions use a stream of consciousness narrative style, and many critics believe that Picasso never meant for the play to be staged, only read.

Blues lyrics of early traditional blues verses consisted of a single line repeated four times. It was only in the first decades of the 20th century that the most common current structure became standard: the so-called AAB pattern, consisting of a line sung over the four first bars, its repetition over the next four, and then a longer concluding line over the last bars. Early blues frequently took the form of a loose narrative, often relating troubles experienced within African American society. There are theories that the four-beats-per-measure structure of the blues might have its origins in the Native American tradition of pow wow drumming.

The I–V–vi–IV progression is a common chord progression popular across several genres of music. It involves the I, V, vi, and IV chords; for example, in the key of C major, this would be: C–G–Am–F.[1] The V is often replaced by iii ("Price Tag"), III ("If We Ever Meet Again" chorus), ii ("Halo"), I ("Doesn't Mean Anything"), II ("Try Too Hard" by P!nk), or IV ("I Gotta Feeling"). A 2009 song by the comedy group The Axis of Awesome, called "Four Chords", parodied the ubiquity of the progression in popular music. It was written in E major (thus using the chords E major, B major, C# minor, and A major) and was subsequently published on YouTube.[2] As of August 2015, the most popular version has been viewed over 35 million times.

Three-chord tunes are more common than simple progressions, since a melody may then dwell on any note of the scale. They are often presented as successions of four chords, in order to produce a binary harmonic rhythm, but two of the four chords are then the same. Often the chords may be selected to fit a pre-conceived melody, but just as often it is the progression itself that gives rise to the melody. I - IV - V - V. I - I - IV - V. I - IV - I - V. (Common in Elizabethan music (Scholes 1977), this also underpins the American college song "Goodnight Ladies",[citation needed] is the exclusive progression used in Kwela.[10] I - IV - V - IV.

The twelve bar blues and its many variants use an elongated, three-line form of the I - IV - V progression that has also generated countless hit records, including the most significant output of rock and rollers such as Chuck Berry and Little Richard. In its most elementary form (there are many variants) the chords progress as follows: I - I - I - I IV - IV - I - I V - IV - I - I

Another common way of extending the I - IV - V sequence is by adding the chord of the sixth scale degree, giving the sequence I - vi - IV - V or I - vi - ii - V, sometimes called the 50s progression. 50s progression in C, ending with C About this sound Play (help·info) In fact this sequence had been in use from the earliest days of classical music (used often by Wolfgang Amadeus Mozart[citation needed]), but after generating popular hits such as Rodgers and Hart's "Blue Moon" (1934),[citation needed] Jerome Kern and Dorothy Fields' 1936 "The Way You Look Tonight",[citation needed] and Hoagy Carmichael's "Heart and Soul" (1938),[12] it became associated with the black American vocal groups of the 1940s, The Ink Spots and The Mills Brothers ("Till Then"),[citation needed] and thus later became the entire basis of the 1950s doo-wop genre, a typical example being The Monotones' "The Book of Love".[citation needed] Taken up into the pop mainstream, for example with Felice and Boudleaux Bryant's "All I Have to Do Is Dream",[citation needed] a hit for The Everly Brothers, in the 1960s it continued to generate records as otherwise disparate as The Paris Sisters' "I Love How You Love Me" (written by Mann and Kolber) and Boris Pickett's "Monster Mash".[citation needed] It continued to be used sectionally, as in the last part of The Beatles' "Happiness Is a Warm Gun",[13] and also to form the harmonic basis of further new songs for decades ("Every Breath You Take" by The Police).[citation needed]

Similar strategies to all the above work equally well in minor modes: there have been one-, two- and three-minor-chord songs, minor blues. A notable example of a descending minor chord progression is the four-chord Andalusian cadence, i - VII - VI - V.

Picassos cubist painting makes me think about quadrants with the lines intersecting. Picasso was known for his cubist paintings with. I discussed how science and art are connected in that science is the first square form of inquiry and art is the third square. Picasso paintings coincided with Einsteins theory of relativity. The question is which came first? It was Picasso's cubism, which distorted time and space. You would think it would be the other way around.

Robert Delaunay, Simultaneous Windows on the City, 1912, 46 x 40 cm, Hamburger Kunsthalle, an example of Abstract Cubism. It is a cubist work that kind of seems to have quadrants within it due to the lines of cubism.

The Three Dancers (French: Les Trois Danseuses[1]) is a painting by Spanish artist Pablo Picasso, painted in June 1925. It is an oil on canvas and measures 84.8 in x 56 in (215.3 cm x 142.2 cm).

It was suggested that one of the dancers was being crucified, and that was what Picasso was portraying

Picasso's Guernica has a mother carrying her dead trial. It is argued that this is a continuation of the Madonna motif in which Mary holds Jesus after his crucifixion. The cross never leaves art even in so called secular art. For instance, in Van Gohs secular paintings he purposefully places crosses, like in window, where in previous eras there would have been actual crosses. This was intentional according to art historians. Andy Warhol is a modern artist who would make pictures of celebrities as if they were iconic religious images. It is not a coincidence growing up he was a devout catholic, and his modern images the feel as though the celebrities were religious icons, while also their cartoonish character undermined it.

Salvador Dali's paintings reflected the nature of dreams with distorted time and space and surrealist content. Art is the third quadrant form of inquiry, the third quadrant itself in the quadrant model is the dreaming quadrant. And recall that Art, the third square field of inquiry, is connected to religion, the second. Dali did not stray completely from the religious motifs that dominated art history. The Temptation of St. Anthony shows St. Anthony naked holding up a cross, and he also has a picture of the Madonna with the baby Jesus, but unlike earlier periods of religious paintings, his were absurd. He even has a painting of Christ on a hovering cross from the perspective looking down from a birds eye view on the cross and a landscape in the background

Crucifixion (Corpus Hypercubus) is a 1954 oil-on-canvas painting by Salvador Dalí which depicts the Crucifixion of Jesus, though it deviates from traditional portrayals of the Crucifixion by depicting Christ on the polyhedron net of a hypercube and adding elements of Surrealism. It is one of his most well known paintings from the later period of his career. Dalí’s inspiration for Corpus Hypercubus came from his change in artistic style during the 1940s and 1950s. Around that time, his interest in surrealism diminished and he became fascinated with nuclear science, feeling that “thenceforth, the atom was [his] favorite food for thought.” His interest grew from the bombing of Hiroshima at the end of World War II which left a lasting impression on him. In his 1951 essay “Mystical Manifesto”, he introduced an art theory he called “nuclear mysticism” that combined Dalí’s interests in Catholicism, mathematics, science, and Catalan culture in an effort to reestablish Classical values and techniques, which he extensively utilizes in Corpus Hypercubus.[1] That same year, to promote nuclear mysticism and explain the “return to spiritual classicism movement” in modern art,[2] he traveled throughout the United States giving lectures. Before painting Corpus Hypercubus, Dalí announced his intention to portray an exploding Christ using both classical painting techniques along with the motif of the cube and he declared that “this painting will be the great metaphysical work of [his] summer.” Juan de Herrera’s Treatise on Cubic Forms was particularly influential to Dalí.[3] Dali was inspired by nuclear physics, and once again, art was influenced by science, and Dali began making paintings that he felt reflected the quantum world. In his painting of Christ on the hypercube, he sought to portray the fourth dimension time in the painting. Remember that time is an illusion. The fourth square is always different. The first three spatial dimensions are similar, but the fourth, time, is different.

In geometry, the tesseract is the four-dimensional analog of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells. The tesseract is one of the six convex regular 4-polytopes, along with the 16 cell. A net of a tesseract is what Dali portrayed as Jesus's cross.

The tetradic (double complementary) colors scheme is the richest of all the schemes because it uses four colors arranged into two complementary color pairs. This scheme is hard to harmonize and requires a color to be dominant or subdue the colors.; if all four colors are used in equal amounts, the scheme may look unbalanced. Rectangle The rectangle color scheme uses four colors arranged intotwo complementary pairs and offers plenty of possibilities for variation. Rectangle color schemes work best when one color is dominant. Square The square color scheme The fourth is always different.

Recent developments in primary colors[edit] 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 the printing industry, to produce the varying colors the subtractive primaries cyan, magenta, and yellow are applied together in varying amounts. Before the color names cyan and magenta were in common use, these primaries were often known as blue-green and purple, or in some circles as blue and red, respectively, and their exact color has changed over time with access to new pigments and technologies.[18] Subtractive color mixing – the magenta and cyan primaries are sometimes called purple and blue-green, or red and blue. Mixing yellow and cyan produces green colors; mixing yellow with magenta produces reds, and mixing magenta with cyan produces blues. In theory, mixing equal amounts of all three pigments should produce grey, resulting in black when all three are applied in sufficient density, but in practice they tend to produce muddy brown colors. For this reason, and to save ink and decrease drying times, a fourth pigment, black, is often used in addition to cyan, magenta, and yellow. The resulting model is the so-called CMYK color model. The abbreviation stands for cyan, magenta, yellow, and key—black is referred to as the key color, a shorthand for the key printing plate that impressed the artistic detail of an image, usually in black ink.[19] In practice, colorant mixtures in actual materials such as paint tend to be more complex. Brighter or more saturated colors can be created using natural pigments instead of mixing, and natural properties of pigments can interfere with the mixing. For example, mixing magenta and green in acrylic creates a dark cyan—something which would not happen if the mixing process were perfectly subtractive. In the subtractive model, adding white to a color, whether by using less colorant or by mixing in a reflective white pigment such as zinc oxide, does not change the color's hue but does reduce its saturation. Subtractive color printing works best when the surface or paper is white, or close to it. A system of subtractive color does not have a simple chromaticity gamut analogous to the RGB color triangle, but a gamut that must be described in three dimensions. There are many ways to visualize such models, using various 2D chromaticity spaces or in 3D color spaces.

Painters have long used more than three "primary" colors in their palettes—and at one point considered red, yellow, blue, and green to be the four primaries.[23] Red, yellow, blue, and green are still widely considered the four psychological primary colors,[24] though red, yellow, and blue are sometimes listed as the three psychological primaries,[25] with black and white occasionally added as a fourth and fifth.

Ewald Hering proposed opponent color theory in 1892.[6] He thought that the colors red, yellow, green, and blue are special in that any other color can be described as a mix of them, and that they exist in opposite pairs. That is, either red or green is perceived and never greenish-red; although yellow is a mixture of red and green in the RGB color theory, the eye does not perceive it as such. Most artists used yellow and blue highlights. Matisse changed painting by using green and red.

Matisse was known in his later life for spearheading art that was extremely simple. One of his later paintings was simply squares, like the squares of the quadrant model of reality. The quadrant model itself is extremely simple. Just think, 16 squares, four quadrants, but it can explain all of reality, and it is not just that it can explain all of reality, it does. The last olympic logo had four parts to it, inspired by Matisse's later cut out works. In some of Matisses' later works he merely cut out squares of different colors. At the end of Matisse's life he became religious. His whole life he was an atheist but he had surgery and at the end of his life he made a sort of cathedral where he tried to represent color in its purest form just through light, and he has an image of Jesus in the Cathedral and a cross.

Psychiatry is bull shit. I want to show you all an example of how bull shit psychiatry is. These are the symptoms for PTSD. Let's analyze them. One is reexperienceing symptoms where you relive trauma. I don't relive any trauma never have. The only trauma I might relive is the trauma of being injected in the psych ward with a drug that almost killed me. There is no such thing as an illness called PTSD. Reexperiencing a traumatic experience is called a symptom of PTSD. That is not an illness. That is just a regular consequence of experiencing something very traumatic. Just imagine if you were in Vietnam and you saw your friend explode next to you. If you did not relive that experience then you have something wrong with you. It's not an illness it's just what happens. People relive all types of experiences all the time, just the dude in Vietnam had experiences that were extraordinary. He doesn't have a disease called PTSD he just experienced something incredible and a normal consequence of that is remembering it like people remember things all the time. If it is an incredible memory it might make you sweat ok big deal. Bad dreams and frightening thoughts. Everybody has bad dreams and frightening thoughts. Staying away from places, events or objects that are reminders of the experience. That is just probably a normal consequence of a very tragic thing. Imagine you had your friend killed in Vietnam and he carried a teddy bear. You might not want to carry a teddy bear. That's normal. All of these symptoms are very vague. Psychiatrists stop trying to symptomize and encapsulate normal things into "diseases" it's really annoying and you have a whole populace of people who love it and are into it because they are dumb sheep who can't think deeply about things so they like to categorize people and create self fulfilling prophecies with their categorizations. "feeling emotionally numb". What does that even mean? Maybe if somebody saw his friend blow up he might sometimes feel emotionally sad when he thinks about it. That's a normal reaction to experiencing something sad its not a disorder. You act like this is a real thing like it is a real disorder. No PTSD is just fancy language for normal reactions to experiencing something very sad. PTSD can cause many symptoms. These symptoms can be grouped into three categories: 1. Re-experiencing symptoms Flashbacks—reliving the trauma over and over, including physical symptoms like a racing heart or sweating Bad dreams Frightening thoughts. Re-experiencing symptoms may cause problems in a person’s everyday routine. They can start from the person’s own thoughts and feelings. Words, objects, or situations that are reminders of the event can also trigger re-experiencing. 2. Avoidance symptoms Staying away from places, events, or objects that are reminders of the experience Feeling emotionally numb Feeling strong guilt, depression, or worry Losing interest in activities that were enjoyable in the past Having trouble remembering the dangerous event. Things that remind a person of the traumatic event can trigger avoidance symptoms. These symptoms may cause a person to change his or her personal routine. For example, after a bad car accident, a person who usually drives may avoid driving or riding in a car. 3. Hyperarousal symptoms Being easily startled Feeling tense or “on edge” Having difficulty sleeping, and/or having angry outbursts. Hyperarousal symptoms are usually constant, instead of being triggered by things that remind one of the traumatic event. They can make the person feel stressed and angry. These symptoms may make it hard to do daily tasks, such as sleeping, eating, or concentrating. It’s natural to have some of these symptoms after a dangerous event. Sometimes people have very serious symptoms that go away after a few weeks. This is called acute stress disorder, or ASD. When the symptoms last more than a few weeks and become an ongoing problem, they might be PTSD. Some people with PTSD don’t show any symptoms for weeks or months. Do children react differently than adults? Children and teens can have extreme reactions to trauma, but their symptoms may not be the same as adults. In very young children, these symptoms can include: Bedwetting, when they’d learned how to use the toilet before Forgetting how or being unable to talk Acting out the scary event during playtime Being unusually clingy with a parent or other adult. Older children and teens usually show symptoms more like those seen in adults. They may also develop disruptive, disrespectful, or destructive behaviors. Older children and teens may feel guilty for not preventing injury or deaths. They may also have thoughts of revenge. For more information, see the NIMH booklets on helping children cope with violence and disasters. (from Post-Traumatic Stress Disorder (PTSD) )

Being is the 17th square. Being represents God. According to Leo Kass the patriarch Jacob lived 17 years after his son Joseph went missing and presumed dead, and lived 17 years after their reunion in Egypt, and the lifespans of Abraham aged 175, Isaac aged 180, and Jacob aged 147 are not a coincidence. "(The sum of the factors in all three cases is 17; of what possible significance this is, I have no idea.)" Leon Kass, The beginning of wisdom: reading Genesis,(Simon and Schuster, 2003)

sudoku is made up of quadrants and is a very popular mind game

In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. It is quadrants

In the design of experiments, Latin squares are a special case of row-column designs for two blocking factors:[5] Many row-column designs are constructed by concatenating Latin squares.[6] In algebra, Latin squares are generalizations of groups; in fact, Latin squares are characterized as being the multiplication tables (Cayley tables) of quasigroups. A binary operation whose table of values forms a Latin square is said to obey the Latin square property.

The popular Sudoku puzzles are a special case of Latin squares; any solution to a Sudoku puzzle is a Latin square.

Latin squares have been used as the basis for several board games, notably the popular abstract strategy game Kamisado.

Sudoku imposes the additional restriction that nine particular 3×3 adjacent subsquares must also contain the digits 1–9 (in the standard version). The more recent KenKen puzzles are also examples of Latin squares

Euler diagram for P, NP, NP-complete, and NP-hard set of problems. The left side is valid under the assumption that P≠NP, while the right side is valid under the assumption that P=NP (except that the empty language and its complement are never NP-complete This is one of the biggest problems in math and is divided into p no np complete and np hard, those four choices. In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. The set of NP-complete problems is often denoted by NP-C or NPC. The abbreviation NP refers to "nondeterministic polynomial time". Although any given solution to an NP-complete problem can be verified quickly (in polynomial time), there is no known efficient way to locate a solution in the first place; indeed, the most notable characteristic of NP-complete problems is that no fast solution to them is known. That is, the time required to solve the problem using any currently known algorithm increases very quickly as the size of the problem grows. As a consequence, determining whether or not it is possible to solve these problems quickly, called the P versus NP problem, is one of the principal unsolved problems in computer science today.

A lot of people do crossword puzzles. I know my Dad did every morning A crossword is a word puzzle that normally takes the form of a square or a rectangular grid of white and black shaded squares. The goal is to fill the white squares with letters, forming words or phrases, by solving clues which lead to the answers. In languages that are written left-to-right, the answer words and phrases are placed in the grid from left to right and from top to bottom. The shaded squares are used to separate the words or phrases. Crossword puzzles are made of quadrants

One of the smallest crosswords in general distribution is a 4×4 crossword compiled daily by John Wilmes, distributed online by USA Today as "QuickCross" and by Universal Uclick as "PlayFour." A four by four grid is the quadrant model

A crossnumber (also known as a cross-figure) is the numerical analogy of a crossword, in which the solutions to the clues are numbers instead of words. Clues are usually arithmetical expressions, but can also be general knowledge clues to which the answer is a number or year. There are also numerical fill-in crosswords. The Daily Mail Weekend magazine used to feature crossnumbers under the misnomer Number Word. This kind of puzzle should not be confused with a different puzzle that the Daily Mail refers to as Cross Number.

Kakuro or Kakkuro (Japanese: カックロ) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword The canonical Kakuro puzzle is played in a grid of filled and barred cells, "black" and "white" respectively. Puzzles are usually 16×16 in size, although these dimensions can vary widely.

Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunamupure) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic; the hardest ones, however, can take hours to crack.

In sudoku although the 9×9 grid with 3×3 regions is by far the most common, many other variations exist. Sample puzzles can be 4×4 grids with 2×2 regions; 5×5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has featured a 6×6 grid with 2×3 regions and a 7×7 grid with six heptomino regions and a disjoint region. Larger grids are also possible. The Times offers a 12×12-grid "Dodeka Sudoku" with 12 regions of 4×3 squares. Dell Magazines regularly publishes 16×16 "Number Place Challenger" puzzles (using the numbers 1-16 or the letters A-P). Nikoli offers 25×25 Sudoku the Giant behemoths. A 100×100-grid puzzle dubbed Sudoku-zilla was published in 2010.[12]

Alphabetical variations have emerged, sometimes called Wordoku; there is no functional difference in the puzzle unless the letters spell something. Some variants, such as in the TV Guide, include a word reading along a main diagonal, row, or column once solved; determining the word in advance can be viewed as a solving aid. A Wordoku might contain words other than the main word.

"Quadratum latinum" is a Sudoku variation with Latin numbers (I, II, III, IV, ..., IX) proposed by Hebdomada aenigmatum, a monthly magazine of Latin puzzles and crosswords. Like the "Wordoku", the "Quadratum latinum" presents no functional difference with a normal Sudoku but adds the visual difficulty of using Latin numbers.

Hypersudoku is one of the most popular variants. It is published by newspapers and magazines around the world and is also known as "NRC Sudoku", "Windoku", "Hyper-Sudoku", and "4 Square Sudoku". The layout is identical to a normal Sudoku, but with additional interior squares defined in which the numbers 1 to 9 must appear. The solving algorithm is slightly different from the normal Sudoku puzzles because of the emphasis on the overlapping squares. This overlap gives the player more information to logically reduce the possibilities in the remaining squares. The approach to playing is similar to Sudoku but with possibly more emphasis on scanning the squares and overlap rather than columns and rows. Hypersudoku is so popular because there are four squares in the game and a quadrant is explicitly images in the game

If you unfold a cube you get the image of a cross

V-Cube also produces a 2×2×2, 3×3×3 and a 4x4x4 rubiks cubes.

Rubiks cube is another enormously popular game that reflects the image of quadrants

The unit circle for trigonometry is fundamental to trigonometry. It is a circle with a quadrant inside of it. The four angle of the unit circle are 0, pi over 2, pi, and 3pi over 2 in radian angles.

In quadrant 1 cosine and sin are positive. In quadrant 2 cosine is negative and sign is positive. In quadrant 3 of the cartesian coordinate system cosine is negative and sin is negative. In quadrant 4 of the unit circle cosine is positive and sin is negative.

Cosine is the x coordinate and sine is the y coordinate.

The unit circle is the basis for trigonometry and it reflects the quadrant model image.

graphs of sine, cosine and tangent are made from information in the unit circle.

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

In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together) Outer ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second) Inner ("inside" terms are multiplied—second term of the first binomial and first term of the second) Last ("last" terms of each binomial are multiplied) The general form is: (a+b)(c+d)=\underbrace {ac} _{\mathrm {first} }+\underbrace {ad} _{\mathrm {outside} }+\underbrace {bc} _{\mathrm {inside} }+\underbrace {bd} _{\mathrm {last} } Note that a is both a "first" term and an "outer" term; b is both a "last" and "inner" term, and so forth. The order of the four terms in the sum is not important, and need not match the order of the letters in the word FOIL. The Foil method is the basis for algebra and multiplying binomials. It has four components fitting the quadrant model image. Even if you represent the foil model pictorially, you get four squares/ the quadrant model image.

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side a + b can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side a + b can be cut into a cube of side a, a cube of side b, three a×a×b rectangular boxes, and three a×b×b rectangular boxes. In calculus, this picture also gives a geometric proof of the derivative (x^{n})'=nx^{n-1}:[9] if one sets a=x and b=\Delta x, interpreting b as an infinitesimal change in a, then this picture shows the infinitesimal change in the volume of an n-dimensional hypercube, (x+\Delta x)^{n}, where the coefficient of the linear term (in \Delta x) is nx^{n-1}, the area of the n faces, each of dimension (n-1): (x+\Delta x)^{n}=x^{n}+nx^{n-1}\Delta x+{\tbinom {n}{2}}x^{n-2}(\Delta x)^{2}+\cdots . Substituting this into the definition of the derivative via a difference quotient and taking limits means that the higher order terms – (\Delta x)^{2} and higher – become negligible, and yields the formula (x^{n})'=nx^{n-1}, interpreted as "the infinitesimal change in volume of an n-cube as side length varies is the area of n of its (n-1)-dimensional faces". If one integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral \textstyle {\int x^{n-1}\,dx={\tfrac {1}{n}}x^{n}} – see proof of Cavalieri's quadrature formula for details.[9] Notice how this geometric proof, fundamental to algebra and geometry, reflects the four squares of the quadrant model image.

Look at the geometric proof. That proof is the foundation of Calculus it is what Newton used to prove Calculus. The geometric proof involves four sections of a square. It is the quadrant model image.

In the 11th century, the Islamic mathematician Ibn al-Haytham (known as Alhazen in Europe) computed the integrals of cubics and quartics (degree three and four) via mathematical induction, in his Book of Optics

In algebra, a quartic function, is a function of the form f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e, where a is nonzero, which is defined by a polynomial of degree four, called quartic polynomial. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form f(x)=ax^{4}+cx^{2}+e. A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form ax^{4}+bx^{3}+cx^{2}+dx+e=0, where a ≠ 0. The derivative of a quartic function is a cubic function. Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If a is positive, then the function increases to positive infinity at both ends; and thus the function has a global minimum. Likewise, if a is negative, it decreases to negative infinity and has a global maximum. In both cases it may or may not have another local maximum and another local minimum. The degree four (quartic case) is the highest degree such that every polynomial equation can be solved by radicals. Notice how four degrees is the highest degree. And it took a ton of effort to discover the quartic equation. It has been proven that five degrees is impossible. Any higher than five it is assume it has been impossible but it has not been proven. Four is always different. Five is ultra transcendent.

Lagrange's four-square theorem is a special case of the Fermat polygonal number theorem and Waring's problem. Another possible generalisation is the following problem: Given natural numbers a,b,c,d, can we solve n=ax_{1}^{2}+bx_{2}^{2}+cx_{3}^{2}+dx_{4}^{2} for all positive integers n in integers x_{1},x_{2},x_{3},x_{4}? The case a=b=c=d=1 is answered in the positive by Lagrange's four-square theorem. The general solution was given by Ramanujan. He proved that if we assume, without loss of generality, that a\leq b\leq c\leq d then there are exactly 54 possible choices for a,b,c,d such that the problem is solvable in integers x_{1},x_{2},x_{3},x_{4} for all n. (Ramanujan listed a 55th possibility a=1,b=2,c=5,d=5, but in this case the problem is not solvable if n=15.[8])

In additive number theory, Pierre de Fermat's theorem on sums of two squares states that an odd prime p is expressible as p=x^{2}+y^{2},\, with x and y integers, if and only if p\equiv 1{\pmod {4}}. For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways: 5=1^{2}+2^{2},\quad 13=2^{2}+3^{2},\quad 17=1^{2}+4^{2},\quad 29=2^{2}+5^{2},\quad 37=1^{2}+6^{2},\quad 41=4^{2}+5^{2}. On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 or 1 modulo 4. Albert Girard was the first to make the observation, describing all positive integral numbers (not necessarily primes) expressible as the sum of two squares of positive integers; this was published posthumously in 1634.[1] Fermat was the first to claim a proof of it; he announced this theorem in a letter to Marin Mersenne dated December 25, 1640: for this reason this theorem is sometimes called Fermat's Christmas Theorem. Since the Brahmagupta–Fibonacci identity implies that the product of two integers each of which can be written as the sum of two squares is itself expressible as the sum of two squares, by applying Fermat's theorem to the prime factorization of any positive integer n, we see that if all the prime factors of n congruent to 3 modulo 4 occur to an even exponent, then n is expressible as a sum of two squares. The converse also holds.[2] This equivalence provides the characterization Girard guessed.

The 2-torus double-covers the 2-sphere, with four ramification points. Every conformal structure on the 2-torus can be represented as a two-sheeted cover of the 2-sphere. The points on the torus corresponding to the ramification points are the Weierstrass points. In fact, the conformal type of the torus is determined by the cross-ratio of the four points.

The Procuress is a 1656 oil-on-canvas painting by the 24-year-old Jan Vermeer. It can be seen in the Gemäldegalerie Alte Meister in Dresden. It is his first genre painting and shows a scene of contemporary life, an image of mercenary love[1] perhaps in a brothel. It differs from his earlier biblical and mythological scenes. It is one of only three paintings Vermeer signed and dated (the other two are The Astronomer and The Geographer). It seems Vermeer was influenced by earlier works on the same subject by Gerard ter Borch, and The Procuress (c. 1622) by Dirck van Baburen, which was owned by Vermeer's mother-in-law Maria Thins and hung in her home.[2] The procuress is a painting by vermeer that reflects the quadrant model pattern. There are three figures very close. Two are interlocked, a man and a woman. That is the duality. There is a third the triad, very close to them. The fourth figure is close but a little bit farther.

Another painting by Vermeer in which one can perceive the quadrant model pattern is Diana and Her Companions. Again there are three girls very close to each other. There is a fourth a little bit farther away with her back turned. Finally in the back there is a fifth who is in the dark. The fifth is ultra transcendent (and sometimes leads to a new quadrant).

Of the many types of perspective drawings, the most common categorizations of artificial perspective are one-, two- and three-point. The names of these categories refer to the number of vanishing points in the perspective drawing. There is also four point perspective though, although this is a lot different from the previous three. The fourth is always different/ transcendent. The fifth is always ultra transcendent/questionable.

The way that one point perspective is pictorially represented is usually by drawing an X on the paper, with the midpoint of the X representing the horizon/ vanishing point. The X is the quadrant.

Perspective is very important in drawing and painting and revolutionized painting, especially during the Renaissance.

The Rosicrucian quadrant

The primary principle of the Prenatal Epoch has been stated by Max Heindel in The Message of the Stars, where he says that the body is the product of lunar forces and that the position of the Ascendant, or its opposite, at birth, is the Moon's position at conception. The keyword of the Moon is fecundation or fertility, and it is Jehovah and the lunar Angels that preside at the birth of a child. This is stated in the Cosmo-Conception and other works of the Rosicrucian Philosophy. We thus see that the Moon has primary influence over the formation of the physical body, and that the Ascendant represents merely the transference of the Moon's position from conception to birth.

This law was known to the ancients as the "Truitine of Hermes," from Hermes Trismegistus, who first correctly formulated and stated the law as follows: "The place of the Moon at conception becomes the birth ascendant or its opposite point."

"But this proved to be but one-half of a very important law, for while the Ascendant at birth was the place of the Moon at a certain Epoch, the Ascendant or its opposite point at this Epoch was the place of the Moon at birth -- a very remarkable interchange of factors." --E.H. Bailey.

According to the Ancient Wisdom, "The World-Breath has a definite and periodic pulsation, a systole and diastole action, whereby birth and death are controlled." This idea of periodicity, well established by modern science, furthers the idea that birth can take place only in respect to any single locality at intervals, that these intervals are in accord with lunar motion, and that only every seventh impulse of the World-Breath permits of human births.

The modern version of the Prenatal Epoch we first established by the English astrologer known to the astrological world as Sepharial, in the year 1886. It was published by him in 1890. In this he had the collaboration of a trained and veteran scientist, a doctor, who helped him to establish the primary laws of the Prenatal Epoch by years of painstaking research and actual experiments. This doctor was an expert obstetrician and proved the laws of the Prenatal Epoch by actual firsthand data.

These laws have been further verified, extended, and complemented by the painstaking researches of E.H. Bailey, to whom great credit is due for his many and exact proofs of the Prenatal Epoch. His book upon this subject is considered standard authority, and we are in the main following his very worthy contribution to the subject and are extending him full credit.

One of the primary uses of the Prenatal Epoch is the correction or rectification of the birth time when only the approximate time is given. Another is its utility in determining correctly the sex of the native. Finally, it gives sidelights on the character and inner nature of the individual as fundamental as those of the birth chart.

"As births are brought about in exact harmony with lunar laws, it is shown that intrauterine life is in direct relation with the sidereal world without, that the great fact of maternity is capable of purely astronomical measurement and rule .... The law is nothing less than a mathematical measurement of human life, a stupendous natural fact; nothing more exactly mathematical and matter of fact is to be found in the records of scientists than this record of intra- uterine life, for only through its study will the laws of generation be fully understood." -- Sepharial.

"In the measurement of the intra-uterine period we actually measure the whole future of the individual; alter this one fact -- the moment of conception (or its spiritual counterpart, the Epoch) -- and you change the whole course of the progeny's destiny. If we accept the occult theory that the Prenatal Epoch is the descent of the Ego to the Desire World, then it must show the inherent character of the Ego about to incarnate. It may be stated that the Epoch has a more intimate relationship with the individual than the horoscope at birth, the latter appearing to reject the personality and its heredity and environment. In other words, the Epoch represents the man about to manifest in the flesh, the horoscope denotes actual personal conditions and environments into which he is born. Every birth is directly connected with the Epoch, and every authentic natural birth will, within the limits of an error of observation, yield an Epoch in accordance with the rules to be given."-- Bailey.

For summary, let us restate the fundamental principle of the Prenatal Epoch known as the Truitine of Hermes: "The Ascendant at birth is the place of the Moon at a certain Epoch, ant the Ascendant or its opposite point at Epoch was the place of the Moon at birth."

This yields the:

Four Laws of the Epoch

1. When the Moon at birth increases in light, it will be on the ascending degree of Epoch, and the Moon at Epoch will be on the ascending degree at birth.

2. When the Moon at birth decrease in light, it will be on the decreasing degree at Epoch, and the Moon at Epoch will be on the descending degree at birth.

3. When the Moon at birth is (a) increasing in light and below the horizon, or (b) decreasing in light and above the horizon, the period of gestation is longer than the norm.

4. When the Moon at birth is (a) increasing in light and above the horizon or (b) decreasing in light and below the horizon, the period of gestation is shorter than the norm.

From these four laws we deduce the following:  

Four Orders of Epoch

1. Moon above horizon and increasing in light.......... 273 days minus x.

2. Moon above horizon and decreasing in light.......... 273 days plus x.

3. Moon below horizon and increasing in light.......... 273 days plus x.

4. Moon below horizon and decreasing in light.......... 273 days minus x.

It is to be understood that the 273 days referred to in the above table is the normal period of gestation, or nine solar or ten lunar months. This normal period is increased or decreased in accordance with the distance of the Moon from either the Ascendant or Descendant, and "x" is a certain number of days corresponding to this distance obtained by dividing the distance in degrees by thirteen degrees, the latter being the average daily motion of the Moon.

When making the count, count to the Ascendant (AC) when the Moon is increasing in light, and to the Descendant (DC) when the Moon is decreasing in light. Another more definite way of stating this would be: In orders Nos. 1 and 4 the distance in degrees of the Moon from the horizon last crossed (AC or DC), divided by thirteen, gives "x", or the number of days by which this period is decreased; and in orders Nos. 2 and 3 the distance of the Moon in degrees from the horizon which it is approaching, divided by thirteen, gives the number of days by which this period is increased. These rules are illustrated by the following examples