literature chapter
QMRQMRAnother important metre in English is the ballad metre, also called the "common metre", which is a four-line stanza, with two pairs of a line of iambic tetrameter followed by a line of iambic trimeter; the rhymes usually fall on the lines of trimeter, although in many instances the tetrameter also rhymes. This is the metre of most of the Border and Scots or English ballads. In hymnody it is called the "common metre", as it is the most common of the named hymn metres used to pair many hymn lyrics with melodies, such as Amazing Grace:[11]
Amazing Grace! how sweet the sound
That saved a wretch like me;
I once was lost, but now am found;
Was blind, but now I see.
Emily Dickinson is famous for her frequent use of ballad metre:
Great streets of silence led away
To neighborhoods of pause —
Here was no notice — no dissent —
No universe — no laws.
QMRThe four tragedies of Prometheus attributed to Aeschylus, most of which are sadly lost to the passages of time into antiquity, are Prometheus Bound (Desmotes), Prometheus Delivered (Lyomens), Prometheus the Fire Bringer (Pyrphoros), and Prometheus the Fire Kindler (Pyrkaeus).
Ancient myths and legends relate at least four versions of the narratives describing Prometheus, his exploits with Zeus, and his eternal punishment as also inflicted by Zeus.
QMRThe Metamorphoses is comprehensive in its chronology, recounting the creation of the world to the death of Julius Caesar, which had occurred only a year before Ovid's birth;[12] it has been compared to works of universal history, which became important in the first century BC.[16] In spite of its apparently unbroken chronology, scholar Brooks Otis has identified four divisions in the narrative:[18]
Section I Book I–Book II (end, line 875): The Divine Comedy
Section II Book III–Book VI, 400: The Avenging Gods
Section III Book VI, 401–Book XI (end, line 795): The Pathos of Love
Section IV Book XII–Book XV (end, line 879): Rome and the Deified Ruler
QMRIn a major article published in 1954, Bascom argued that folklore can serve four primary functions in a culture:
Folklore lets people escape from repressions imposed upon them by society ex: tall tales
Folklore validates culture, justifying its rituals and institutions to those who perform and observe them.
Folklore is a pedagogic device which reinforces morals and values and builds wit. ex: scary stores/moral lessons
Folklore is a means of applying social pressure and exercising social control. ex: the boy who cried wolf
QMREvery Man in His Humour is a 1598 play by the English playwright Ben Jonson. The play belongs to the subgenre of the "humours comedy," in which each major character is dominated by an over-riding humour or obsession.
The play is based off of the four humors and is a four part play
The Four Horsemen of Four Horsemen studios are Jim Preziosi, Eric Treadway, H. Eric Mayse and Christopher Dahlberg. The four partners met while employed as figure sculptors at McFarlane Toys. In September 1999, the four left McFarlane to found Four Horsemen Studios, where, in a partnership with Mattel, they created hundreds of figures for Mattel's Masters of the Universe, The Dark Knight, Harry Potter, DC Universe Classics and Man of Steel toy lines, among others.
In 2005, Four Horsemen Studios began creating their own properties and designing and manufacturing the toys to support them. The studio has developed several in house properties including: Seventh Kingdom, Gothitropolis, Magma Corps, and Symbiotech.
In early 2010, the Horsemen made the leap into licensed action figures. The studio signed a deal to produce figures based on the 1960s sci-fi toy line The Outer Space Men. A second license, 1980′s brand The Power Lords, has been purchased in 2013.
thor four waves action figures
Fourth World is a storyline told through a metaseries of interconnecting comic book titles written and drawn by Jack Kirby, and published by DC Comics from 1970 to 1973. Although not marketed under this title until the August-September, 1971 issues of New Gods and Forever People, the term Fourth World or Jack Kirby's Fourth World has gained usage in the years since.
v=In December 2007, DC Executive Editor Dan DiDio was discussing the aftermath of Death of the New Gods and said, "It’s the advent of the Fifth World... I think we’ve telegraphed so much that the New Gods are coming upon a rebirth, and the story that we’re telling with them now is a continuation of the story that was established when Kirby first conceived the concept. Talk about death — Kirby blew up worlds at the start of the series. The story started with, 'The Old Gods Died!' which made room for the New Gods — we’re picking up that thread and launching the DCU into the future."[51]
That series led into Final Crisis and DiDio clarified things further, saying "the Fourth World is over. The battle between the forces of Darkseid and those of Highfather is over, and a new direction is in place for the characters in what will be deemed the Fifth World."[52] The series' writer, Grant Morrison, added, "In Jack Kirby’s Fourth World books... it’s pretty clear that the New Gods have known about Earth for a long time and in JLA ten years ago, I suggested that part of their interest in us was rooted in the fact that Earth was destined to become the cradle of a new race of 'Fifth World' super-divinities — an eventuality Darkseid is eager to prevent from occurring."[53] It was during that run on JLA that Morrison had Metron deliver a speech outlining the general principles:
“ How like little children you appear to me. How small is your comprehension and yet... there is a seed in you... The Old Gods died and gave birth to the New. These New Gods, even such as I, must also pass, in our turn. Our search was long and our war continues, but we found the planetary cradle of the Gods to Come. ... you are only forerunners.[54] ”
Later, in the JLA storyline "World War III," Metron's dialog is more specific: "As New Genesis is to the Fourth World, Earth shall be to the Fifth that is to come."[55]
The fifth is always ultra transcendent
Fourth world was a tetralogy
QMRThe Legion of Super-Heroes is a fictional superhero team in the 30th and 31st centuries of the DC Comics Universe. The team first appears in Adventure Comics #247 (April 1958), and was created by Otto Binder and Al Plastino.
Initially, the team was closely associated with the original Superboy (Superman when he was a teenager), and was first portrayed as a group of time travelers who frequently visited him. In later years, the Legion's origin and back story were fleshed out, and the group was given prominence on par with Superboy's in a monthly comic. Eventually, Superboy was removed from the team altogether, and appeared afterwards as an occasional guest star.
The team has undergone two major reboots during its publication. The original version was replaced with a new rebooted version following the events of "Zero Hour" in 1994 and another rebooted team was introduced in 2004. A fourth version of the team, nearly identical to the original version, was introduced in 2007.
Cosmic Boy is a founding member of the Legion of Super-Heroes, along with Lightning Lad and Saturn Girl, and he has the superhuman ability to generate magnetic fields. Cosmic Boy's brother, Pol, eventually joined the Legion as Magnetic Kid, but died during the "Magic Wars". Cosmic Boy is one of the few Legionnaires ever to have his own miniseries, which ran for four issues in the mid-1980s as a spin-off of the Legends cross-over.
Cosmic Boy was featured in a four-part limited series, cover dated December 1986 through March 1987. A tie-in to the Legends limited series, it was written by Paul Levitz, with art by Keith Giffen, Ernie Colón, and Bob Smith.
Cosmic Boy's original costume was pink with black at the sides, with four white circles, the code-name "Cosmic Boy" written on the chest, and a plastic bubble space helmet. After his first appearance, the helmet and the codename were replaced with white epaulets. For a period in the late 1970s, he was portrayed in a costume designed by Mike Grell which was essentially a black bustier[4] with black gloves and boots, with bare arms, shoulders, chest, and legs. Cosmic Boy returned to a close variation on the original costume a few years later. As Polestar, he wore a black and purple bodysuit with a stripe up the side and a black cowl. In the post-Zero Hour Legion, he wore a version of his original costume with lavender as the primary color instead of pink. On this version of the costume, the four circles on the chest were actually discs that he could magnetically manipulate and use as weapons. The "Threeboot" version is a similar pattern, with blue as the primary color and black circles instead of white.
Four Horsemen Studios is a collectible figure design studio and manufacturer, specializing in creating sculptures of toys and action figures. The company was founded in the late 1990s as a contractor to Mattel, and have since grown to an independent studio creating their own line of figures as well as manufacturing third party designs under license.
According to Aristotle, there are four species of tragedy:
1. Complex, which involves Peripety and Discovery
2. Suffering, tragedies of such nature can be seen in the Greek mythological stories of Ajaxes and Ixions
3. Character, a tragedy of moral or ethical character. Tragedies of this nature can be found in Phthiotides and Peleus
4. Spectacle, that of a horror-like theme. Examples of this nature are Phorcides and Prometheus
Athenian tragedies were performed in late March/early April at an annual state religious festival in honor of Dionysus. The presentations took the form of a contest between three playwrights, who presented their works on three successive days. Each playwright offered a tetralogy consisting of three tragedies and a concluding comic piece called a satyr play.[33] The four plays sometimes featured linked stories. Only one complete trilogy of tragedies has survived, the Oresteia of Aeschylus. The Greek theatre was in the open air, on the side of a hill, and performances of a trilogy and satyr play probably lasted most of the day. Performances were apparently open to all citizens, including women, but evidence is scant.[citation needed] The theatre of Dionysus at Athens probably held around 12,000 people.[34
Cicero as an author wrote during the Gallic wars four tragedies in Greek style. Three of them were titled Troas, Erigones, and Electra, but all are lost. He also wrote several poems on the second expedition of Caesar to Britannia, three epistles to Tiro (extant) and a fourth one to his brother. The long letter Commentariolum Petitionis (Little handbook on electioneering) has also survived, although its validity has been much questioned. It is in any case a valuable guide to political behaviour in Cicero’s time.
The Generic Universal RolePlaying System, or GURPS, is a tabletop role-playing game system designed to allow for play in any game setting. It was created by Steve Jackson Games and first published in 1986 at a time when most such systems were story- or genre-specific.
Characters in GURPS have four basic attributes:
Strength (ST): A measure of the character's physical power and bulk, ability to lift, carry, and do damage
Dexterity (DX): A measure of the character's physical agility, coordination, and manual dexterity
Intelligence (IQ): A measure of the character's mental capacity, acuity and sense of the world
Health (HT): A measure of the character's physical stamina, recovery speed, energy and vitality, ability to resist disease
Each attribute has a number rating assigned to it. Normally they begin at 10, representing typical human ability, but can go as low as 1 for nearly useless, to 20 (or higher) for superhuman power. Anything in the 8 to 12 range is considered to be in the normal or average area for humans. Basic attribute scores of 6 or less are considered crippling—they are so far below the human norm that they are only used for severely handicapped characters. Scores of 15 or more are described as amazing—they are immediately apparent and draw constant comment.
Players assign these ratings spending character points. The higher the rating the more points it will cost the player, however, assigning a score below the average 10 gives the player points back to assign elsewhere. Since almost all skills are based on Dexterity or Intelligence, those attributes are twice as expensive (or yield twice the points, if purchased below 10). In earlier editions (pre–4th Edition) all attributes followed the same cost-progression, where higher attributes cost more per increase than attributes close to the average of 10.
Attribute scores also determine several secondary characteristics. The four major ones are each directly based on a single attribute:
Hit Points (HP): how much damage and injury can be sustained, based on ST
Will (Will): mental focus and strength, withstanding stress, based on IQ
Perception (Per): general sensory alertness, based on IQ
Fatigue Points (FP): a measure of exertion, tiredness, and hunger, based on HT
In earlier GURPS editions (that is, prior to the 4th Edition) Hit Points were based on HT and Fatigue Points were based on ST.
The other secondary characteristics (Damage, Basic Lift, Basic Speed, Dodge, Move) are calculated from one or more attribute values using individual tables or formulae.
Fig. 756 – The Nakagin Capsule Tower by the Japanese architect Kisho Kurokawa is a cellular building in the Shimbashi district of Tokyo (Japan). The building consists of two interconnected concrete towers, with prefabricated modules stacked along them. Four high-tension bolts connect the individual capsules to the main shafts for easy replacement. This idea did not materialize.
nagakin
Nakagin Capsule Tower in Tokyo – Drawing by Marten Kuilman.
De Cauter’s ‘capsular society’ is proposed as the ultimate protection against fear. It offers a bleak scenario for the near future in which ‘daily life is becoming a kaleidoscope of incidents and accidents, catastrophes and cataclysms’ (VIRILIO, 2003). Other philosophers, like the Italian Giorgio Agamben (Rome, 1942), derive their symbolism from the idea of a (prisoners) camp, in which people are brought together in an undemocratic way and have lost all their human rights.
Modern ‘castles’ of the nineteenth and twentieth century (in Europe) often used the mixture of ancient lore and romanticism as an architectural tool to reach a visual impression (fig. 757). Some of them – as could be seen in chapter 3.9.4 – were outright follies, while others just used certain features of the ‘old’ defense structures (like towers) to create a historic setting.
The capsules in the building look like quadrants
The Larkin Soap Company was a successful soap manufacturer, which started business at the borders of Lake Erie and reached their zenith in the first decennia of the twentieth century. The company was a pioneering, national mail-order house with branch stores in Buffalo, New York City and Chicago. The architect Frank Lloyd Wright became involved (in 1904) in the design of the new office building in Buffalo, NY (fig. 759). The five story, dark red premises at 680 Seneca Street became the largest commercial building at the time and was designed as a model of efficiency.
larkin
Fig. 759 – The Larkin Building in Buffalo, NY was the first big commission for the American architect Frank Lloyd Wright. The building was demolished after a fire in 1949 to make way for a parking area.
.
The Larkin Building in Buffalo (New York State) and the S.C. Johnson Company’s Administration Building at Racine (Wisconsin) were the only two large office building design by Frank Lloyd Wright. His career has been largely in the field of domestic architecture and was inspired by the spirit of Puritanism. The concept of a vocation and of work as a ‘calling’ was central to Wright’s life (WESLEY (1988). Work-spirit was, in his view, a potential salvation for collective life. He wrote in his autobiography (1943, p. 151): ‘Rebellious and protestant as I was myself when the Larkin Building came to me, I was conscious also that the only way to succeed, either as rebel or protestant, was to make architecture a genuine and constructive affirmation of the new Order of this Machine Age’.
It is remarkable, but not surprising, that the structural concept of the four-fold helped to order his communication with the world. Ideality of form, great mass, permanence of material and memorability of plan were the hallmarks of Wright’s architecture.
He designed a house for himself and his bride Catherine Tobin in 1889 near Chicago (Oakland Park, Illinois) with references to the Garden of Eden (Paradise). The House and Studio underwent alterations in 1895 when two major rooms were added to the House, a dining room and a playroom (Wright had six children). The latter had a cross-axial base beneath a barrel fault. The skylight featured a foursquare design. The concept of a ‘citta ideale’ was reflected in the geometrical ideality of the forms. The playroom became, according to Wesley, a ‘theatrum mundi’’.
cinema chapter
QMR1981 film Raiders of the Lost Ark
1984 prequel film Indiana Jones and the Temple of Doom
1989 film Indiana Jones and the Last Crusade
2008 film Indiana Jones and the Kingdom of the Crystal Skull. Indiana Jones was a tetralogy with four movies
Philosophy chapter
QMRWhat is Deming's Theory of Profound Knowledge?
Are You Familiar with Deming's Theory of Profound Knowledge?
William Deming (1900-1993) is credited for his significant contributions to the theory of quality improvement. Deming is best known for his Fourteen Points for Quality Improvement and for his System of Profound Knowledge. Deming's Theory of Profound Knowledge consists of four parts:
Appreciation for a system,
Knowledge about variation,
Theory of knowledge, and
Knowledge of psychology
The four parts of Deming's theory tie into his fourteen points. The reason that Deming believed his theory of profound knowledge was so important was that it would help individuals to transform within their organizations, which would, in turn, improve the outcomes in quality improvement efforts. Understanding and applying the four parts of Deming's theory, he believes, will create a better leadership culture.
Each part of Deming's Theory of Profound Knowledge corresponds to several of his fourteen points. What do each of the above four parts consist of and how does each contribute to quality improvement efforts?
QMRTechnocover Innovations – New Registered Design Four-Part (Quadrant) Fall Protection System
Technocover Sentinel Louvre Vent in Building - External View
Fall protection safety grids continue to be one of the most important safety features protecting against the risk of injury from falls into access chambers.
Since 1993 Technocover have been providing safe access solutions to meet duty of care and site safety operational needs. Our access covers are manual handling compliant and depending upon the function and size of each chamber an appropriate integral fall protection safety grid system can be provided for the safe protection of operatives.
Technocover were “Finalists” in the inaugural 2004 Health & Safety Awards, with our integral G4W 2-part split hinged, gate system, pump-through safety grid, under the best safety product category for safeguarding operators over Wet Well chambers.
Through collaborative design with our customers we have over the years illustrated our ability to provide cost effective fall protection solutions to enable safe inspection and removal of submersible pumps without the need for restrictive vertical barrier systems.
Technocovers 4-part (Quadrant) G1Q and G4Q Fall Protection systems are the latest in our range of full protection safety solutions for wet wells, safeguarding operatives from accidental falls into chambers. Four individual grids hinge up around the pump on its removal enhancing operative protection.
G1Q Four-Part (Quadrant) Wet Well Protection System G4Q Four-Part (Quadrant) Open Mesh Wet Well Protection System
G1Q (Shown in upstand access cover)
G4Q (Shown in flush fitting access cover)
Illustrations show typical Technocover UltraSecure twin leaf, end hinged, access covers. These would be installed over wet well chambers having two submersible pumps each on twin guiderails to enable correct withdraw of the individual pumps up and out of the chamber for de-ragging or general pump maintenance purposes.
Benefits in Design
Improvements in existing “safe method of working in wet wells” and reduction of inspection/maintenance time. 4-part fall protection is designed so as not to expose operatives to the risk of injury/falling down into chamber.
Makes the task safe and achievable by a single operative with increased access efficiency.
Knowledge that operations personnel are safe and protected during maintenance and inspection operations at all time and in all weather conditions.
In addition, use of the four-part quadrant fall protection system can lead to reductions in operational costs by replacing the need for traditional site maintenance procedures involving the setup of protective guardrails together with davits which require mandatory routine inspection under Lifting Operations and Lifting Equipment Regulations (LOLER), 1998.
How the New 4-Part Fall Protection Works Over a Typical Wet Well Chamber
The hinged 4-part (Quadrant) G4Q unit stays in a closed position but allows a PCLA “Snatch” device to drop through the letterbox slot and the submersible pump to be withdrawn and setback safely during routine maintenance or inspection.
On withdrawal, as the pump nears the top it breaks through the two larger hinged grid segments and these instantly close shut once the pump is through.
On reinstalling the pump the segments are lifted up by hand to allow entry of the pump.
The design of the two smaller quadrant sections allows them to be hinged open for the pump unit to be easily married back up its guiderails.
To see the four-part Quadrant fall protection system in action click here to view a demonstration video. Alternatively for further details or to request a 20 minute presentation, please contact our Business Development Department.
QMRIn The Question Concerning Technology, Martin Heidegger explains the four causes as follows:
causa materialis is the material or matter
causa formalis is the form or shape the material or matter enters
causa finalis is the end
causa efficiens is the effect that is finished.[20]
Upon explaining them in this formal state as well as with the example of a silver chalice, Heidegger raises the questions of why just these four causes, how was it determined that they exclusively go together, what exactly unifies them and what makes causa finalis and causa efficiens different. These are important questions to analyze and attempt to answer or else the definition of technology will remain obscure. He holds that the four causes are necessary to allow, for the material or matter which is not present, a path to become present. Heidegger argues that the ability to create a final product using these four steps is what unifies them as an exclusive group.
This group of causes brings Heidegger to poiesis: the bringing forth of something out of itself.[21] He states that poiesis is the highest form of physis. Heidegger states that the four causes are at play in the bringing forth process of bursting open to the next artisan or creator. This process of bringing forth is revealing truth or aletheia, a key function of technology.[22] Heidegger explains it as thus:
"Whoever builds a house or a ship or forges a sacrificial chalice reveals what is to be brought forth, according to the terms of the four modes of occasioning.[23]"
The word "reveals", instead of manufacturing, is important. Heidegger argues that manufacturing is not what brings forth a material but the actual revealing. Technology is the mode of revealing which gives truth, aletheia.
Highlighted is the issue of social and technological progress along with society with the four causes. One of his examples is the words through translation from the language of the Greeks, Romans and to today have created some issues with the definitions of these words. Most notably he emphasizes the need to clarify the difference between words that now have different meaning through these translations. In particular he uses the words responsible and indebted as they relate to the four causes and the creation process. Also used is the term techne which means technology now but it also was the word used for the “revealing which brings forth truth into the splendor of radiant appearance.[24]” Within Greece, techne also meant art as it required the revealing and presenting the appearance of the work of art. The word aletheia was replaced by the Romans with veritas.[25] Another issue arising with progress of technology and society is the techniques. Heidegger presents the argument that even though these Greek ideas work with techniques of handicraftsmen, they are essentially outdated with modern machine powered technology as they are based on modern physics. The problem is the modern physical theory of nature prepares for simple and modern technology. Heidegger uses examples like this to draw readers back to the four causes, proving that they remain relevant in today's world either directly with the newest products or their origination.
In number theory, a Woodall number (Wn) is any natural number of the form
W_n = n \cdot 2^n - 1
for some natural number n. The first few Woodall numbers are:
1, 7, 23, 63, 159, 383, 895, … Again the first three are more similar. The fourth is different. The fifth is a lot different
Four quadrant perspective of Ken Wilber: Considerable atterntion has been focused on the achievements of Ken Wilber (A Theory of Everything: An Integral Vision for Business, Politics, Science, and Spirituality, 2000) in ordering the range of insights into understanding individual integration and personal development in a social context. He notably groups a comprehensive list of twelve "schools" of consciousness (ranging from cognitive science to psychosomatic medicine and bioenergy) as subsets of four quadrants of existence (An Integral Theory Of Consciousness). Central to this perspective is a model based on two axes, giving rise to those four quadrants:
Axes:
Individual -- Collective:
Individual:
Collective
Interior view (subjective) -- Exterior view (objective)
Subjective: On the Left are positioned the "interior", unobservable things -- what individuals/groups think (and feel).
Objective: On the Right are positioned the "exterior", observable phenomena -- what an individual/society does (associated with nature and science).
Quadrants: The interaction of these two axes gives four personality types, to which codes are commonly attributed:.
Upper Left (UL): Intentional (individual subjective), notably associated with sincerity, integrity and trustworthiness (and the arts, beauty and the self).
Upper Right (UR): Behavioural / Neurological (individual objective), notably associated with correspondance, representation and propositional communication.
Lower Right (LR): Socio-economic (collective interobjective), notably associated with systems theory web, structural-functionalism and social systems mesh.(and morals)
Lower Left (LL): Cultural (collective intersubjective), notably associated with cultural fit, mutual understanding and a sense of rightness (and the good).
The quadrant model is enriched by concentric circles centred on the origin and indicative of successive stages of evolution or development. Thus in each quadrant there are ten or more developmental levels, such as from atoms to brains and from prehension to vision-logic. Complementing the attention that the quadrant model has attracted, a variety of reservations and criticisms have been expressed [more | more | more | more]
The question here is whether the understanding of Wilber can be meaningfully associated with the organization of the M-set, as graphically represented. Once again, the assumption of this exploration is that there should at least be a geometrical transform between the mappings they respectively constitute -- especially since the polarities identified by Wilber are fundamental to the dynamic of society.
In the case of the axes of the M-set, the distinction made (in mapping its emergence in the complex plane) is between "real" and "imaginary" -- with a concept of "positive" and "negative" in each case. It could be argued that "interior" can be understood as "imaginary", and "exterior" as "real". The problem with this is that Wilber places them on the same axis, rather than on orthogonal axes. With respect to "individual" and "collective", these might variously be understood as associated with "positive" (for those stressing individualism) or "negative" (for those stressing collectivism and community) as illustrated in the following table.
. "Negative" "Positive"
Individual Individualism perceived as selfish (as typical of Asian cultures, socialism, etc) Individualism perceived as the focus and justification of social developmenti (as typical of western cultures)
Collective Collectivism as perceived as a constraint on personal freedom and development (as typical of western cultures) Community as perceived as the key to well-being (as typical of many non-westerncultures)
The argument above suggests the possibility of providing a form of tentative dynamic integration, through creative play, of the elements of climate as they figure in the external and inner environments. The suggestion is that computer-mediated play can provide templates through which to explore variants and possibilities, whether these are meaningful and acceptable or not. There is also the possibility that this process would highlight isomorphism -- and a form of resonance -- between pathways of changing climate and those characteristic of the shifting moods of individuals and groups that characterize the dynamics of public opinion.
The possibility, and the challenge, can be highlighted through traditional static symbols of the "four elements" of both climate and of psychic integration (whether individual or collective) -- such as the four-fold lauburu (the Basque cross) or its many cross-like equivalents in other cultures. In the case of the lauburu, each head (or arm) is drawn with three sweeps of a compass (upon a scribed cross, employing in each head a common center but two settings, one the half of the other). Superimposing the two variants gives rise to another form of cross.
In the Basque culture, the heads on the vertical axis represent female expression (emotional and perceptual) or the elements of fire and water. Those on the horizontal axis represent male energy (mental and physical) or the elements air and earth. Imanol Mujica (The Lauburu and Its Symbolism) considers that the lauburu symbolizes mankind, made up of four elements: Form, Life, Sensibility and Conscience. The first head symbolizes form or density, the second head symbolizes life or vitality, the third head symbolizes sensibility and the fourth head is the conscience state. Together they are held to represent nature in action and can be associated with the movement of the Earth around the Sun.
QMRThe lauburu could be related to conventional four-quadrant representations by rotating the symbol 45 degrees. It then lends itself to mapping both the 4-fold "elements" and their corresponding 4-fold personality types of thinking, feeling, sensation and intuition (as extensively explored by depth psychology following C G Jung). Such explorations relate to the four-quadrant synthesis of Ken Wilber [more | more]. A valuable commentary, informed by mathematical insights comparing the perspective of Jung and Wilber, is provided by Peter Collins (Clarifying Perspectives 2: Perspectives, Personality Types and Strings). Collins relates the 4-fold mapping to 8-fold mappings, to the 16-fold mapping of the Myers-Briggs Type Indicator, and to a 24-fold mapping necessary to handle a further ("missing") 8 personality types.
Construction of the lauburu in its two forms can be understood in several ways:
based on:
8 circles (of the same diameter) set on the axes of a cross, two to each branch.
a further circle (of twice their diameter) is then drawn on each branch, centered on the the tangent point of the two smaller circles there -- making a total of 12 circles -- three per branch.
the whole may be set, in some variants, within a 13th.
superposition of four classic circular Tao symbols (unshaded):
two in one sense, with one of them rotated 90 degrees with respect to the other
two in the opposite sense, again with one of them rotated 90 degrees with respect to the other
within each of the four smaller circles so created, again two superpositioned Tao symbols (unshaded), of opposite sense
The Diamond 16 Puzzle
Change the pair of patterns at right to any of the pairs at left. (The original pair is at top left.)
To change the patterns, click on a row, then click on the row you want to move it to. Do the same for other rows, columns, or quadrants.
You can make 322,560 pairs of patterns. Each pair pictures a different symmetry of the underlying 16-point space.
QMRGeometry of the 4x4 Square
Notes by Steven H. Cullinane
A Structure-Endowed Entity
"A guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure-endowed entity S, try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed. You can expect to gain a deep insight into the constitution of S in this way."
-- Hermann Weyl in Symmetry
Let us apply Weyl's lesson to the following "structure-endowed entity."
4x4 array of dots
What is the order of the resulting group of automorphisms?
First, of course, we must determine exactly what "structural relations" we wish to leave undisturbed.
Trivially, the overall 4x4 structure is left undistubed by any permutation of the sixteen dots. But not all substructures are left undistubed by an arbitrary permutation. For example, the set of four rows and the set of four columns are left undisturbed by permutations of rows and/or columns, but not by permutations of the four 2x2 quadrants.
We may be interested in permutations that preserve the structural relation of adjacency. In this case, it turns out that the group of symmetries of the four-dimensional hypercube, or tesseract,
QMRis what we are looking for, since it is well-known that adjacency in the hypercube is equivalent to adjacency in a 4x4 array-- provided we regard the array as drawn on a torus, so that each element of the array is adjacent to four other elements. The hypercube's symmetry group is of order 384.
We may, however, be interested in structural relations other than adjacency. For instance, we may be interested in families of subsets of the sixteen dots.
One such family, the 6-sets of the (166, 166) Kummer configuration, was discussed (without naming it as such) by R.D. Carmichael in 1937. For that configuration, see this website's note on Configurations and Squares. Carmichael's 1937 classic, Introduction to the Theory of Groups of Finite Order, seems, however, to have overlooked an even more interesting family of subsets.
It turns out that if we regard the 4x4 array as a picture of the affine space of four dimensions over the two-element field, a very natural family of subsets is provided by the 35 partitions of the space into four parallel affine planes -- that is to say, into the 35 two-dimensional linear subspaces of a corresponding vector space and their cosets under translations. The illustration below shows these 35 structures.
For a description of how the 4x4 array can be coordinatized to yield this family of partitions and also a group of 322,560 permutations (rather than the measly 384 of the hypercube) that leave affine "structural relations" undisturbed, see Finite Relativity.
Coordinates for the 4x4 space
Strangely enough, this rather obvious geometric picture -- that of the linear four-space over the two-element field as a 4x4 array -- seems to have been completely overlooked in the refereed literature, except for its occurrence in the "miracle octad generator" (MOG) devised by R. T. Curtis* in his study of the Mathieu group M24. Even in that occurrence, the 4x4 parts of Curtis's 4x6 MOG arrays were neither supplied with coordinates nor, indeed, explicitly identified as possessing the structure of a finite geometry (although the appropriate group -- which provides a nice solution to Weyl's problem above -- was described, albeit in a non-geometric manner).
The Curtis MOG is a pairing of 35 partitions of a 4x4 array into four-sets (which turn out, once the array has been suitably coordinatized as a linear space, to be the cosets, under translation, of the 35 two-dimensional linear subspaces) with the 35 partitions of an eight-set (shown as an array of four rows and two columns) into two four-sets. This pairing is not arbitrary; it is preserved under the action of the 244,823,040 permutations of the large Mathieu group M24 acting on an array of four rows and six columns. See published descriptions* of the MOG for details.
Within one of the maximal subgroups (a "brick stabilizer") of M24, each of the 322,560 affine transformations of the 4x4 array is accompanied by a related M24 action (the identity, if the affine transformation is a translation) on an associated 4x2 array, or "brick," of the MOG. These group actions illustrate the well-known isomorphism (pdf) of the alternating group on eight elements, A8, with the general linear group, GL(4,2), on the four-space over the two-element field.
The quintuply transitive Mathieu group M24 is the automorphism group of the set of octads, or 8-sets, generated by the Curtis Miracle Octad Generator (MOG). (See Peter J. Cameron's Geometry of the Mathieu Groups (pdf).)
There are 759 such octads:
(7 * 2 * 2 * 3) + (28 * 2 * 4 * 3) + 3 = 759,
or, in symbols,
(A * B * C * D) + ( E * F * G * H) + I = 759.
Where the above numbers come from:
Each octad occurs within a 24-set: an array of 4 rows and 6 columns. This 4x6 array is made up of three 4x2 completely interchangeable "bricks."
Each brick, considered by itself, is an octad. Hence the "I" value of 3, for the 3 individual bricks.
A non-brick octad is formed by selecting 4 similarly marked locations (all black or all white) within one of the 35 4x2 MOG pictures, and 4 similarly marked locations (all black, all white, all circles, or all dots) in the corresponding 4x4 MOG picture, then applying a permutation (possibly the identity) of the three bricks of the resulting 4x6 array.
Apart from the octads that are themselves bricks, the 8 cells that define an octad may occur in a 4 + 4 + 0 (or 4 + 0 + 4 or 0 + 4 + 4) pattern within the three bricks. or they may occur in a 4 + 2 + 2 (or 2 + 4 + 2 or 2 + 2 + 4) pattern within the three bricks.
In the 4 + 4 + 0, etc., case, one of the two nonempty bricks in a 4x6 array contains 4 cells (either the four white or the four black cells) from one of the 7 bricks pictured in the leftmost column of the MOG picture, which can be chosen in 2 ways (hence "A" and "B"), and the other nonempty brick contains 4 cells (any 4 cells marked alike) from the corresponding picture in column 6 of the MOG; these 4 cells can fall within this nonempty brick in exactly 2 ways (hence "C"). Switching the two nonempty bricks adds no new octads. The third, empty, brick can fall in any of the three brick positions (hence "D").
In the 4 + 2 + 2, etc., case, one of the 3 bricks, the "heavy" brick, contains 4 elements of the octad. This can fall within any of the three brick positions (hence "H"). There are clearly 28 * 2 choices (from the MOG pictures in columns 2 through 5) for the 4 elements of the heavy brick (hence "E" and "F"). Paired with each of these choices are 4 ways of selecting the "2 + 2" elements in the other two bricks, based on the sets of 4 like elements in each of the MOG pictures in columns 7 through 10 (hence "G"). Switching the two "2 + 2" bricks adds no new octads.
The Curtis MOG plays a prominent role in the book Twelve Sporadic Groups, by Robert L. Griess, which discusses some of the groups involved in Griess's Monster.** A picture of a MOG action appears on the book's cover. For some other connections between the MOG and the Monster, see the October 2004 paper Cross Orbits (pdf), by Peter Rowley.
For a description of how the 4x4 array also provides a nice picture of the 35 lines in the finite projective space PG(3,2) (as well as the 35 planes through a point in the finite affine space AG(4,2)), see Orthogonal Latin Squares as Skew Lines.
In fact, the MOG has an ancestor in the literature of finite projective geometry. A pairing equivalent to that in the MOG was described (though without the rectangular arrays devised by Curtis) in a paper on the projective space PG(3,2) published in 1910. See page 72 of G. M. Conwell's "The 3-Space PG(3,2) and Its Group," Ann. of Math. 11 (1910), 60-76.
The relevant result is as follows:
"There exists a bijective correspondence between the 35 lines of PG(3,2) and the 35 unordered triples in a 7-set such that lines are concurrent if and only if the corresponding triples have exactly one element in common."
-- Elisabeth Kuijken, Thesis (ps), March 2003.
Kuijken cites Conwell as the source of this result. The result may be verified by examining the MOG illustration above in light of the note Orthogonal Latin Squares as Skew Lines.
For another approach to constructing the MOG that involves the symplectic generalized quadrangle known as W(2), see Picturing the Smallest Projective 3-space.
For a theorem illustrating a nice interplay between affine and projective substructures of the 4x4 array, see Map Systems.
It is conceivable that the decomposition strategy sketched in the "Map Systems" note might have some valuable generalizations.
The affine group in the 4x4 space can be generated by permuting rows, columns, and quadrants. For an illustration, see the Diamond 16 Puzzle. For a proof, see Binary Coordinate Systems. For some background, see Diamond Theory and Galois Geometry.
As noted above, the 4x4 square model
lets us visualize the projective space PG(3,2) as well as the affine space AG(4,2). For tetrahedral and pentagonal (pdf) models of PG(3,2), see the work of Burkard Polster. The following is from an advertisement of a talk by Polster on PG(3,2).
Apart from its use in studying the 759 octads of a Steiner system S(5,8,24) -- and hence the Mathieu group M24 -- the Curtis MOG nicely illustrates a natural correspondence C (Conwell [2], p. 72) between
(a) the 35 partitions of an 8-set H (such as GF(8) above, or Conwell's 8 "heptads") into two 4-sets, and
(b) the 35 partitions of L into four parallel affine planes.
Two of the H-partitions have a common refinement into 2-sets iff the same is true of the corresponding L-partitions. (Cameron [1], p. 60).
Note that C is particularly natural in row 1, and that partitions 2-5 in each row have similar structures.
Cameron, P. J., Parallelisms of Complete Designs, Camb. U. Pr. 1976.
Conwell, G. M., The 3-space PG(3,2) and its group, Ann. of Math. 11 (1910) 60-76.
Curtis, R. T., A new combinatorial approach to M24, Math. Proc. Camb. Phil. Soc. 79 (1976) 25-42
QMR Diocletian divided the empire into four regions, each ruled by a separate Emperor (the Tetrarchy).[21] Confident that he fixed the disorders that were plaguing Rome, he abdicated along with his co-emperor, and the Tetrarchy soon collapsed. Order was eventually restored by Constantine, who became the first emperor to convert to Christianity, and who established Constantinople as the new capital of the eastern empire. During the decades of the Constantinian and Valentinian dynasties, the Empire was divided along an east–west axis, with dual power centers in Constantinople and Rome. The reign of Julian, who attempted to restore Classical Roman and Hellenistic religion, only briefly interrupted the succession of Christian emperors. Theodosius I, the last emperor to rule over both East and West, died in 395 AD after making Christianity the official religion of the Empire.
QMRUnder Claudius, the Empire invaded Britannia, its first major expansion since Augustus. After Claudius' successor, Nero, committed suicide in 68, the Empire suffered a period of brief civil wars, as well as a concurrent major rebellion in Judea, during which four different legionary generals were proclaimed Emperor. Vespasian emerged triumphant in 69, establishing the Flavian dynasty, before being succeeded by his son Titus, who opened the Colosseum shortly after the eruption of Mt. Vesuvius. His short reign was followed by the long reign of his brother Domitian, who was eventually assassinated. The Senate then appointed the first of the Five Good Emperors. The Empire reached its greatest extent under Trajan, the second in this line.
QMRThe case of R v. Dudley and Stephens (1884) 14 QBD 273 (QB) is an English case which dealt with four crew members of an English yacht, the Mignonette, who were cast away in a storm some 1,600 miles (2,600 km) from the Cape of Good Hope. After several days, one of the crew, a seventeen-year-old cabin boy, fell unconscious due to a combination of the famine and drinking seawater. The others (one possibly objecting) decided then to kill him and eat him. They were picked up four days later. Two of the three survivors were found guilty of murder. A significant outcome of this case was that necessity was determined to be no defence against a charge of murder.[83]
the fourth is always different
QMRThe Four State Area or Quad State Area, is the area where the states of Arkansas, Kansas, Missouri and Oklahoma touch.[1][2] The Tulsa, Oklahoma; Joplin, Missouri; and Fayetteville-Springdale-Rogers, Arkansas metropolitan areas are located within the region. Notable cities and towns in the area are Tulsa, Oklahoma; Pittsburg, Kansas; Joplin, Missouri; and Fayetteville, Springdale, Rogers and Bentonville, Arkansas.
QMRThe Four Corners is a region of the United States consisting of the southwestern corner of Colorado, southeastern corner of Utah, northeastern corner of Arizona, and northwestern corner of New Mexico. The Four Corners area is named after the quadripoint where the boundaries of the four states meet, where the Four Corners Monument is located. It is the only location in the United States where four states meet. Most of the Four Corners region belongs to semi-autonomous Native American nations, the largest of which is the Navajo Nation, followed by Hopi, Ute, and Zuni tribal reserves and nations. The Four Corners region is part of a larger region known as the Colorado Plateau and is mostly rural, rugged, and arid. In addition to the monument, commonly visited areas within Four Corners include Monument Valley, Mesa Verde National Park, Chaco Canyon, and Canyon de Chelly National Monument. The most populous city in the Four Corners region is Farmington, New Mexico, followed by Durango, Colorado.
QMRQMRUtilitarianism is often referred to as exchange theory or rational choice theory in the context of sociology. This tradition tends to privilege the agency of individual rational actors and assumes that within interactions individuals always seek to maximise their own self-interest. As argued by Josh Whitford, rational actors are assumed to have four basic elements, the individual has (1) "a knowledge of alternatives," (2) "a knowledge of, or beliefs about the consequences of the various alternatives," (3) "an ordering of preferences over outcomes," (4) "A decision rule, to select among the possible alternatives"[90] Exchange theory is specifically attributed to the work of George C. Homans, Peter Blau and Richard Emerson.[91] Organisational sociologists James G. March and Herbert A. Simon noted that an individual's rationality is bounded by the context or organisational setting. The utilitarian perspective in sociology was, most notably, revitalised in the late 20th century by the work of former ASA president James Coleman.
QMR The success of Augustus in establishing principles of dynastic succession was limited by his outliving a number of talented potential heirs: the Julio-Claudian dynasty lasted for four more emperors — Tiberius, Caligula, Claudius and Nero — before it yielded in 69 AD to the strife-torn Year of Four Emperors, from which Vespasian emerged as victor. Vespasian became the founder of the brief Flavian dynasty, to be followed by the Nerva–Antonine dynasty which produced the "Five Good Emperors": Nerva, Trajan, Hadrian, Antoninus Pius and the philosophically inclined Marcus Aurelius. In the view of the Greek historian Dio Cassius, a contemporary observer, the accession of the emperor Commodus in 180 AD marked the descent "from a kingdom of gold to one of rust and iron"[18]—a famous comment which has led some historians, notably Edward Gibbon, to take Commodus' reign as the beginning of the decline of the Roman Empire.
QMREarly solid-treed saddles were made of felt that covered a wooden frame. Asian designs appeared during the Han dynasty approximately 200 BC.[6] One of the earliest solid-treed saddles in the west was the "four horn" design, first used by the Romans as early as the 1st century BC.[10] Neither design had stirrups
QMRThe Sykes-Picot Treaty in 1916 divided the region that later became Palestine into four political units
QMRIsrael is divided into four physiographic regions: the Mediterranean coastal plain, the Central Hills, the Jordan Rift Valley and the Negev Desert.[1]
QMRBalfour wrote a memorandum from the 1919 Paris Peace Conference in which he noted that:
" ... the literal fulfilment of all our [the Allies] declarations is impossible, partly because they are incompatible with each other and partly because they areincompatible with facts ..." Although, in his view, the Allies had implicitly rejected the Sykes–Picot agreement by adopting the system of League of Nations mandates, which allowed for no annexations, trade preferences, or other advantages, Balfour declared that: "The four Great Powers are committed to Zionism. And Zionism, be it right or wrong, good or bad, is rooted in age-long traditions, in present needs, in future hopes, of far profounder import than the desires and prejudices of the 700,000 Arabs who now inhabit that ancient land".[25][26]
QMRBalfour wrote a memorandum from the 1919 Paris Peace Conference in which he noted that:
" ... the literal fulfilment of all our [the Allies] declarations is impossible, partly because they are incompatible with each other and partly because they areincompatible with facts ..." Although, in his view, the Allies had implicitly rejected the Sykes–Picot agreement by adopting the system of League of Nations mandates, which allowed for no annexations, trade preferences, or other advantages, Balfour declared that: "The four Great Powers are committed to Zionism. And Zionism, be it right or wrong, good or bad, is rooted in age-long traditions, in present needs, in future hopes, of far profounder import than the desires and prejudices of the 700,000 Arabs who now inhabit that ancient land".[25][26]
QMRThe Four Seasons (fr Les Quatre Saisons) was the last set of four oil paintings completed by the French painter Nicolas Poussin (1594–1665). The set was painted in Rome between 1660 and 1664 for the Duc de Richelieu, the nephew of Cardinal Richelieu. Each painting is an elegiac landscape with Old Testament figures conveying the different seasons and times of the day. Executed when the artist was in failing health suffering from a tremor in his hands, the Seasons are a philosophical reflection on order in the natural world. The iconography evokes not only the Christian themes of death and resurrection but also the pagan imagery of classical antiquity: the poetic worlds of Milton's Paradise Lost and Virgil's Georgics. The paintings currently hang in a room on their own in the Louvre in Paris.
“ By his absolute humility, by his effacement of himself, by his refusal to use any tricks or overstate himself, Poussin has succeeded in identifying himself with nature, conceived as a manifestation of the divine reason. The Seasons are among the supreme examples of pantheistic landscape painting. ”
— Anthony Blunt, Nicolas Poussin[1]
QMR The Chimú were the residents of Chimor, with its capital at the city of Chan Chan, a large adobe city in the Moche Valley of present-day Trujillo city. The culture arose about 900 AD. The Inca ruler Tupac Inca Yupanqui led a campaign which conquered the Chimú around 1470 AD.[2] The Chimú society was a four-level hierarchical system,[8] with a powerful elite rule over administrative centers. The hierarchy was centered at the walled cities, called ciudadelas, at Chan Chan.[9] The political power at Chan Chan is demonstrated by the organization of labor to construct the Chimú's canals and irrigated fields.
Chan Chan was the top of the Chimu hierarchy, with Farfán in the Jequetepeque Valley as a subordinate.[8] This organization, which was quickly established during the conquest of the Jequetepeque Valley, suggests the Chimú established the hierarchy during the early stages of their expansion. The existing elite at peripheral locations, such as the Jequetepeque Valley and other centers of power, were incorporated into the Chimú government on lower levels of the hierarchy.[9] These lower-order centers managed land, water, and labor, while the higher-order centers either moved the resources to Chan Chan or carried out other administrative decisions.[9] Rural sites were used as engineering headquarters, while the canals were being built; later they operated as maintenance sites.[10] The numerous broken bowls found at Quebrada del Oso support this theory, as the bowls were probably used to feed the large workforce that built and maintained that section of canal. The workers were probably fed and housed at state expense.[10]
The state governed such social classes until imperial Sican conquered the kingdom of Lambayeque. The legends of war were said to have been told by the leaders Naylamp in the Sican language and Tacayanamo in Chimú. The people paid tribute to the rulers with products or labor. By 1470, the Incas from Cuzco defeated the Chimú. They moved Minchancaman to Cuzco, and redirected gold and silver there to adorn the Temple of the Sun.
The Chimú embellished their fabrics with brocades, embroidery, fabrics doubles, and painted fabrics. Sometimes textiles were adorned with feathers and gold or silver plates. Colored dyes were created from plants containing tannin, mole, or walnut; and minerals, such as clay, ferruginosa, or mordant aluminum; as well as animals, such as cochineal. The garments were made of the wool of four animals: the guanaco, llama, alpaca, and vicuna. The people also used varieties of cotton, that grows naturally in seven different colors. The clothing consisted of the Chimú loincloth, sleeveless shirts with or without fringes, small ponchos, and tunics.
QMRThe largest Pre-Columbian city in South America,[1] Chan Chan is an archaeological site in the northern Peruvian region of La Libertad, 5 km west of Trujillo.[2] Chan Chan is located in the mouth of the Moche Valley[3] and was the capital of the historical Chimor Empire from AD 900-1470[4] until they were defeated and incorporated into the Inka empire.[5] The Chimor empire, a conquest state,[3] developed from the Chimú culture which established itself along the Peruvian coast around 1400 AD.[6] In the Chimú tongue, Chan Chan means "Sun Sun;" it was named for its sunny climate which is cooled year round by a southerly breeze.[7]
They had four waqas
QMRSome early European-American settlers moved in and set up trading posts, often buying Navajo rugs by the pound and selling them back east by the bale. The traders encouraged the locals to weave blankets and rugs into distinct styles. These included "Two Gray Hills" (predominantly black and white, with traditional patterns); Teec Nos Pos (colorful, with very extensive patterns); "Ganado" (founded by Don Lorenzo Hubbell[35]), red-dominated patterns with black and white; "Crystal" (founded by J. B. Moore); oriental and Persian styles (almost always with natural dyes); "Wide Ruins", "Chinlee", banded geometric patterns; "Klagetoh", diamond-type patterns; "Red Mesa" and bold diamond patterns.[36] Many of these patterns exhibit a fourfold symmetry, which is thought to embody traditional ideas about harmony or hózhǫ́.
QMR four is the first non prime number
The Big 4 is a sculpture made of steel bars located outside the headquarters of the Channel Four Television Corporation in London. It is designed to represent the logo of Channel 4 while providing a basis for a number of art installations. As of November 2012 seven installations have been made on the statue's steel framework, including those to coincide with the 2012 Summer Paralympics, covered with both newsprint and umbrellas, and a design to simulate the statue breathing.
QMRMonument to Multiculturalism by Francesco Perilli in Toronto, Canada. Four identical sculptures are located in Buffalo City, South Africa; Changchun, China; Sarajevo, Bosnia and Sydney, Australia
QMRRhododendron (from Ancient Greek ῥόδον rhódon "rose" and δένδρον déndron "tree")[3][4] is a genus of 1,024 species of woody plants in the heath family (Ericaceae), either evergreen or deciduous, and found mainly in Asia, although it is also widespread throughout the Southern Highlands of the Appalachian Mountains of North America. It is the national flower of Nepal. Most species have showy flowers which bloom from late winter through to early summer.[5][full citation needed] Azaleas make up two subgenera of Rhododendron. They are distinguished from "true" rhododendrons by having only five anthers per flower.
The Species of Rhododendron (1930), referred to as the Balfourian system.[24] That system continued up to modern times in Davidian's four volume The Rhododendron Species (1982-1995)
four subgenera wiki
