Philosophy chapter
QMRThe Corpus Juris (or Iuris) Civilis ("Body of Civil Law") is the modern name[1] for a collection of fundamental works in jurisprudence, issued from 529 to 534 by order of Justinian I, Eastern Roman Emperor. It is also sometimes referred to as the Code of Justinian, although this name belongs more properly to the part titled Codex Justinianus.
The work as planned had three parts: the Code (Codex) is a compilation, by selection and extraction, of imperial enactments to date; the Digest or Pandects (the Latin title contains both Digesta and Pandectae) is an encyclopedia composed of mostly brief extracts from the writings of Roman jurists; and the Institutes (Institutiones) is a student textbook, mainly introducing the Code, although it has important conceptual elements that are less developed in the Code or the Digest. All three parts, even the textbook, were given force of law. They were intended to be, together, the sole source of law; reference to any other source, including the original texts from which the Code and the Digest had been taken, was forbidden. Nonetheless, Justinian found himself having to enact further laws and today these are counted as a fourth part of the Corpus, the Novellae Constitutiones (Novels, literally New Laws).
The work was directed by Tribonian, an official in Justinian's court. His team was authorized to edit what they included. How far they made amendments is not recorded and, in the main, cannot be known because most of the originals have not survived. The text was composed and distributed almost entirely in Latin, which was still the official language of the government of the Empire in 529–534, whereas the prevalent language of merchants, farmers, seamen, and other citizens was Greek. By the early 7th century, the official government language had become Greek during the lengthy reign of Heraclius (610–641).
How far the Corpus Iuris Civilis or any of its parts was effective, whether in the east or (with reconquest) in the west, is unknown. However, it was not in general use during the Early Middle Ages. After the Early Middle Ages, interest in it revived. It was "received" or imitated as private law and its public-law content was quarried for arguments by both secular and ecclesiastical authorities. This revived Roman law, in turn, became the foundation of law in all civil law jurisdictions. The provisions of the Corpus Juris Civilis also influenced the Canon Law of the church: it was said that ecclesia vivit lege romana — the church lives by Roman law.[2] Influence on the common-law systems has been much smaller, although some basic concepts from the Corpus have survived through Norman law - such as the contrast, especially in the Institutes, between "law and custom (lex et consuetudo)". The Corpus continues to have a major influence on public international law. Its four parts thus constitute the foundation documents of the Western legal tradition.
The four parts[edit]
Codex[edit]
Main article: Codex Justinianus
The "Codex" was the first part to be finished, on 7 April 529. It contained in Latin most of the existing imperial constitutiones (imperial pronouncements having force of law), back to the time of Hadrian. It used both the Codex Theodosianus and the fourth-century collections embodied in the Codex Gregorianus and Codex Hermogenianus, which provided the model for division into books that were themselves divided into titles. These works had developed authoritative standing.[3] This first edition is now lost; a second edition was issued in 534 and is the text that has survived. At least the second edition contained some of Justinian's own legislation, including some legislation in Greek. It is not known whether he intended there to be further editions, although he did envisage translation of Latin enactments into Greek.
Legislation about religion[edit]
Numerous provisions served to secure the status of Christianity as the state religion of the empire, uniting Church and state, and making anyone who was not connected to the Christian church a non-citizen.
Laws against heresy
The very first law in the Codex requires all persons under the jurisdiction of the Empire to hold the Christian faith. This was primarily aimed against heresies such as Nestorianism. This text later became the springboard for discussions of international law, especially the question of just what persons are under the jurisdiction of a given state or legal system.
Laws against paganism
Other laws, while not aimed at pagan belief as such, forbid particular pagan practices. For example, it is provided that all persons present at a pagan sacrifice may be indicted as if for murder.
Digesta[edit]
Main article: Digest (Roman law)
The Digesta or Pandectae, completed in 533, is a collection of juristic writings, mostly dating back to the second and third centuries. Fragments were taken out of various legal treatises and opinions and inserted in the Digest. In their original context, the statements of the law contained in these fragments were just private opinions of legal scholars - although some juristic writings had been privileged by Theodosius II's Law of Citations in 426. The Digest, however, was given complete force of law.
Institutiones[edit]
Main article: Institutes of Justinian
As the Digest neared completion, Tribonian and two professors, Theophilus and Dorotheus, made a student textbook, called the Institutions or Elements. As there were four elements, the manual consists of four books. The Institutiones are largely based on the Institutiones of Gaius. Two thirds of the Institutiones of Justinian consists of literal quotes from Gaius. The new Institutiones were used as a manual for jurists in training from 21 November 533 and were given the authority of law on 30 December 533 along with the Digest.
Novellae[edit]
Main article: Novellae Constitutiones
The Novellae consisted of new laws that were passed after 534. They were later re-worked into the Syntagma, a practical lawyer's edition, by Athanasios of Emesa during the years 572–77.
First Empire[edit]
See also: Nobility of the First French Empire
As Napoleon I, the founder of the Bonaparte dynasty and only head of the First French Empire, owed his success – both his personal rise and the growth of his empire – above all to his military excellence, it is hardly surprising that he bestowed most elaborate honours on his generals, especially those raised to the supreme army rank of maréchal (marshal).
The revival of the original victory title, created for a specific victory, was an ideal form, and many incumbents were victorious marshals (or posthumously, in chief of the widow).
The highest of these titles were four nominal principalities, in most cases awarded as a 'promotion' to holders of ducal victory titles:
Marshal Davout, Prince d'Eckmühl – 1809 (extinct 1853) – also duc d'Auerstaedt (see below)
Marshal Masséna, Prince d'Essling – 1810 – also duc de Rivoli
Marshal Ney, Prince de la Moskowa – 1813 (extinct 1969) – also duc d'Elchingen – Bataille de la Moskowa is the French name for the Battle of Borodino
Marshal Berthier, Prince de Wagram – 1809 (extinct 1918) – also duc de Valengin, and Prince de Neuchâtel (a sovereign title granted in 1806), neither of which were victory titles.
QMRBeing and Nothingness: An Essay on Phenomenological Ontology (French: L'Être et le néant : Essai d'ontologie phénoménologique), sometimes subtitled A Phenomenological Essay on Ontology, is a 1943 book by philosopher Jean-Paul Sartre.[1] Sartre's main purpose is to assert the individual's existence as prior to the individual's essence ("existence precedes essence"). His overriding concern in writing the book was to demonstrate that free will exists.[2] While a prisoner of war in 1940 and 1941, Sartre read Martin Heidegger's Being and Time, an ontological investigation through the lens and method of Husserlian phenomenology (Edmund Husserl was Heidegger's teacher). Reading Being and Time initiated Sartre's own philosophical enquiry.
Being is the 17th square of the quadrant model non being is the 18th
QMRBeing-in-itself for Sartre[edit]
In Sartrean existentialism, being-in-itself (être-en-soi) is also contrasted with the being of persons, which he describes as a combination of, or vacillation or tension between, being-for-itself (être-pour-soi) and being-for-others (I'être-pour-autrui).[citation needed]
Being-in-itself refers to objects in the external world — a mode of existence that simply is. It is not conscious so it is neither active nor passive and harbors no potentiality for transcendence. This mode of being is relevant to inanimate objects, but not to humans, who Sartre says must always make a choice.[1]
One of the problems of human existence for Sartre is the desire to attain being-in-itself, which he describes as the desire to be God — this is a longing for full control over one's destiny and for absolute identity, only attainable by achieving full control over the destiny of all existence. The desire to be God is one of the ways people fall into bad faith.[citation needed] Sartre's famous depiction of a man in a café who has applied himself to a portrayal of his role as a waiter illustrates this. The waiter thinks of himself as being a waiter (as in being-in-itself), which Sartre says is impossible since he cannot be a waiter in the sense that an inkwell is an inkwell. He is primarily a man (being-for-itself), just one who happens to be functioning as a waiter – with no fixed nature or essence, who is constantly recreating himself. He is guilty of focusing on himself as being-in-itself and not being-for-itself. Sartre would say that as a human, a being-for-itself by nature, the waiter is "a being that is not what it is and it is what it is not." Therefore, the waiter who acts as if he is at his very core a waiter "is not what [he] is"- which is to say, he is not solely a waiter- and "is what [he] is not"- meaning that he is many things other than a waiter. In simply playing the part of a waiter, the man in this example is reducing himself to a "being-in-itself" and is therefore in bad faith.
QMRQuadrants[edit]
Each holon can be seen from within (subjective, interior perspective) and from the outside (objective, exterior perspective), and from an individual or a collective perspective.[26]
Each of the four approaches has a valid perspective to offer. The subjective emotional pain of a person who suffers a tragedy is one perspective; the social statistics about such tragedies are different perspectives on the same matter. According to Wilber all are needed for real appreciation of a matter.
Wilber uses this grid to categorize the perspectives of various theories and scholars, for example:
Interior individual accounts (upper-left quadrant) include Freudian psychoanalysis, which interprets people's interior experiences and focuses on "I"
Interior plural accounts (lower-left) include Gadamer's philosophical hermeneutics which seeks to interpret the collective consciousness of a society, or plurality of people and focuses on "We"
Exterior individual accounts (upper-right) include B. F. Skinner's behaviorism, which limits itself to the observation of the behavior of organisms and treats the internal experience, decision making or volition of the subject as a black box, and which with the fourth perspective emphasizes the subject as a specimen to examine, or "It".
Exterior plural accounts (lower-right) include Marxist economic theory which focuses upon the behavior of a society (i.e. a plurality of people) as functional entities seen from outside.
According to Wilber, all four perspectives offer complementary, rather than contradictory, perspectives. It is possible for all to be correct, and all are necessary for a complete account of human existence. According to Wilber, each by itself offers only a partial view of reality.
According to Wilber modern western society has a pathological focus on the exterior or objective perspective. Such perspectives value that which can be externally measured and tested in a laboratory, but tend to deny or marginalize the left sides (subjectivity, individual experience, feelings, values) as unproven or having no meaning. Wilber identifies this as a fundamental cause of society's malaise, and names the situation resulting from such perspectives, "flatland".
QMRPublished in 1995, SES (as it is sometimes abbreviated) is a work in which Wilber grapples with modern philosophical naturalism, attempting to show its insufficiency as an explanation of being, evolution, and the meaning of life. He also describes an approach, called vision-logic, which he finds qualified to succeed modernism.
Wilber's project in this book requires nothing less than a complete re-visioning of the history of Eastern and Western thought. There are four philosophers that Wilber finds to be of the highest importance:
Plotinus, Neo-Platonic philosopher, who introduced the first nondual philosophy to the West
Nagarjuna, Buddhist philosopher, who did the same in the East
Friedrich Wilhelm Joseph von Schelling, German Idealist who created the first evolutionary nondual philosophy in the West and
Sri Aurobindo, Hindu yogi and philosopher who did the same in the East
Wilber argues that the account of existence presented by the Enlightenment is incomplete—it ignores the spiritual and noetic components of existence. He accordingly avoids the term cosmos, which is associated with merely physical existence. He prefers the term kosmos to refer to the sum of manifest existence, which harks back to the usage of the term by the Pythagoreans and other ancient mystics. Wilber conceives of the Kosmos as consisting of several concentric spheres: matter (the physical universe) plus life (the vital realm) plus mind (the mental realm) plus soul (the psychic realm) plus Spirit (the spiritual realm).
QMRIn the eighth chapter, "The Depths Of The Divine", Wilber uses the accounts of four mystics to describe the possibilities for further individual spiritual development: the Transcendentalist Ralph Waldo Emerson on nature mysticism, the Christian saint Teresa of Avila on deity mysticism, Meister Eckhart on formless mysticism, and the Hindu guru Ramana Maharshi on nondual mysticism.
In mathematics, Euler's identity[n 1] (also known as Euler's equation) is the equality
e^{i \pi} + 1 = 0
where
e is Euler's number, the base of natural logarithms,
i is the imaginary unit, which satisfies i2 = −1, and
π is pi, the ratio of the circumference of a circle to its diameter.
Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered an example of mathematical beauty.
It is also e to the pi i equals -1. Having four parts
It is ocnisdered one of the most beautiful equations ever
QMRThe hypocycloid is a special kind of hypotrochoid, which are a particular kind of roulette.
A hypocycloid with three cusps is known as a deltoid.
A hypocycloid curve with four cusps is known as an astroid.
The hypocycloid with two cusps is a degenerate but still very interesting case, known as the Tusi couple.
QMRAn astroid is a particular mathematical curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times the radius.[1] By double generation, it is also the locus of a point on a circle as it rolls inside a fixed circle with 4/3 times the radius. It can also be defined as the envelope of a line segment with an end point on each of the axes. It is therefore the envelope of the moving bar in the Trammel of Archimedes.
Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse.
The astroid has four cusp singularities in the real plane, the points on the star. It has two more complex cusp singularities at infinity, and four complex double points, for a total of ten singularities.
The dual curve to the astroid is the cruciform curve with equation \textstyle x^{2}y^{2}=x^{2}+y^{2}. The evolute of an astroid is an astroid twice as large.
Cardioid (epicycloid with one cusp)
Nephroid (epicycloid with two cusps)
Deltoid (hypocycloid with three cusps)
Stoner–Wohlfarth astroid a use of this curve in magnetics.
QMRA trammel of Archimedes is a mechanism that traces out an ellipse.[1] It consists of two shuttles which are confined ("trammelled") to perpendicular channels or rails, and a rod which is attached to the shuttles by pivots at fixed positions along the rod. As the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path. The semi-axes a and b of the ellipse are the distances between the end of the rod and the two pivots. An ellipsograph is a trammel of Archimedes intended to draw, cut, or machine ellipses, e.g. in wood or other sheet materials. An ellipsograph has the appropriate instrument (pencil, knife, router, etc.) attached to the rod. Usually the distances a and b are adjustable, so that the size and shape of the ellipse can be varied.
The history of such ellipsographs is not certain, but they are believed to date back to Proclus and perhaps even to the time of Archimedes.[2]
An animation of a Trammel of Archimedes in action.
Wooden versions of the trammel of Archimedes have been produced also as toys or novelty items, and sold under the name of Kentucky do-nothings, nothing grinders or do nothing machines. In these toys the drafting instrument is replaced by a crank handle, and the position of the sliding shuttles is usually fixed.
The way that the trammel works is through a mechanism that moves two orthogonal pieces in a quadrant
QMRThe four points where these axes cross the ellipse are the vertices and are marked as a, −a, b, and −b. In addition to being at the largest and smallest distance from the center, these points are where the curvature of the ellipse is maximum and minimum.[10]
these are the minor axis and major axis. This is a crossQMRIn mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes are not parallel to our coordinate system.
Conic sections have the form of a second-degree polynomial:
Q\ {\stackrel {\mathrm {def} }{=}}\ Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0.\,
This can be written as:
\mathbf {x} ^{T}A_{Q}\mathbf {x} =0,
where \mathbf {x} is the homogeneous coordinate vector
{\begin{pmatrix}x\\y\\1\end{pmatrix}}
and where A_{Q} is a matrix:
A_{Q}={\begin{pmatrix}A&B/2&D/2\\B/2&C&E/2\\D/2&E/2&F\end{pmatrix}}.
matrices are quadrant grids
QMRTraditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas. In the focus-directrix definition of a conic the circle is a limiting case with eccentricity 0. In modern geometry certain degenerate cases, such as the union of two lines, are included as conics as well.
The conic sections have been named and studied at least since 200 BC, when Apollonius of Perga undertook a systematic study of their properties
The fourth is always differentQMREuclid (fl. 300 BCE) is said to have written four books on conics but these were lost as well.[6] Archimedes (died c. 212 BCE) is known to have studied conics, having determined the area bounded by a parabola and a chord in Quadrature of the Parabola. His main interest was in terms of measuring areas and volumes of figures related to the conics and part of this work survives in his book on the solids of revolution of conics, On Conoids and Spheroids.[7]
Apollonius of Perga
Diagram from Apollonius' Conics, in a 9th century Arabic translation
The greatest progress in the study of conics by the ancient Greeks is due to Apollonius of Perga (died c. 190 BCE), whose eight-volume Conic Sections or Conics summarized and greatly extended existing knowledge. Apollonius's study of the properties of these curves made it possible to show that any plane cutting a fixed double cone (two napped), regardless of its angle, will produce a conic according to the earlier definition, leading to the definition commonly used today. Circles, not constructable by the earlier method, are also obtainable in this way. This may account for why Apollonius considered circles a fourth type of conic section, a distinction that is no longer made. Apollonius used the names ellipse, parabola and hyperbola for these curves, borrowing the terminology from earlier Pythagorean work on areas.[8]
Pappus of Alexandria (died c. 350 CE) is credited with expounding on the importance of the concept of a conic's focus, and detailing the related concept of a directrix, including the case of the parabola (which is lacking in Apollonius's known works).[9]
QMRThe concept of four "generations" in the history of modern warfare was created by a team of United States analysts, including William S. Lind,[1] for the purpose of an argument for "the changing face of war" entering into a "fourth generation".
First-generation warfare refers to battles fought with massed manpower, using line and column tactics with uniformed soldiers governed by the state.
Second-generation warfare is the tactics used after the invention of the rifled musket and breech-loading weapons and continuing through the development of the machine gun and indirect fire. The term second generation warfare was created by the U.S. military in 1989.
Third-generation warfare focuses on using speed and surprise to bypass the enemy's lines and collapse their forces from the rear. Essentially, this was the end of linear warfare on a tactical level, with units seeking not simply to meet each other face to face but to outmaneuver each other to gain the greatest advantage.
The concept of fourth-generation warfare as presented by Lind et al. is characterized by a return to decentralized forms of warfare, blurring of the lines between war and politics, combatants and civilians due to nation states' loss of their near-monopoly on combat forces, returning to modes of conflict common in pre-modern times.
First generation[edit]
Prussian infantry advancing in line and column formation at the Battle of Hohenfriedberg in 1745
In 1648, at the end of the Thirty Years' War, the Treaty of Westphalia gave a practical sovereignty to the German states, which until then were semi-independent components of the Holy Roman Empire. This more firmly established the sovereignty of the nation-state, which meant, among other things, that governments would have exclusive rights to organize and maintain their own militaries. Before this time, many armies and nations were controlled by religious orders and many wars were fought in mêlée combat, or subversively through bribery and assassination. The first generation of modern warfare was intended to create a straightforward and orderly means of waging war.[2]
Alternatively, it has been argued that the Peace of Westphalia did not solidify the power of the nation-state, but that the Thirty Years' War itself ushered in an era of large-scale combat that was simply too costly for smaller mercenary groups to carry out on their own. According to this theory, smaller groups chose to leave mass combat—and the expenses associated with it—in the domain of the nation-state.[3]
The increased accuracy and speed of the rifled musket and the breech-loader marks the end of first generation warfare; the concept of vast lines of soldiers meeting face to face became impractical due to the heavy casualties that could be sustained. Because these technologies were adopted gradually throughout the Americas and Europe, the exact end of the first generation of modern warfare depends on the region, but all world powers had moved on by the latter half of the 19th century.[2]
In order to create a more controlled environment for warfare a military culture was developed that, in many ways, is still visible in the armed forces of today. Specially crafted uniforms set soldiers apart from the general populace.
An elaborate structure of rank was developed to better organize men into units. Rules for military drill were perfected, allowing line and column maneuvers to be executed with more precision, and to increase the rate of fire in battle.
Control of media information release during the war and production of counterfeit money in order to devaluate enemy's economy were used for the first time during Napoleonic wars.
Examples:
English Civil War
Anglo-Spanish War
Seven Years' War
American Revolutionary War
Napoleonic Wars
War of 1812
Mexican War of Independence
American Civil War
Second generation[edit]
Technological developments such as the Maxim gun gave smaller units the ability to operate more independently
In the 1800s, the invention of the breech-loading rifled musket meant longer range, greater accuracy, and faster rate of fire. Marching ranks of men straight into a barrage of fire from such weapons would cause tremendous rates of casualties, so a new strategy was developed.
Second generation warfare still maintained lines of battle but focused more on the use of technology to allow smaller units of men to maneuver separately. These smaller units allowed for faster advances, less concentrated casualties, and the ability to use cover and concealment to advantage.[2] To some degree, these concepts have remained in use even as the next generations have arisen, so the end of the second generation is not as clearly defined as that of the first. The development of the blitzkrieg highlighted some of the flaws of static firing positions and slow-moving infantry, so this can be considered the beginning of the end for the second generation, at least as the dominant force in military strategy.
The contributions of the second generation were responses to technological development. The second generation saw the rise of trench warfare, artillery support, more advanced reconnaissance techniques, extensive use of camouflage uniforms, radio communications, and fireteam maneuvers.
Examples:
American Civil War
Boer War
World War I
Spanish Civil War
World War II
Iran–Iraq War
Third generation[edit]
Fast advances and maneuvering allowed Allied cavalry forces to quickly penetrate deep into Iraq during the Gulf War
The use of blitzkrieg during the German invasion of France first demonstrated the power of speed and maneuverability over static artillery positions and trench defenses. Through the use of tanks, mechanized infantry, and close air support, the Germans were able to quickly break through linear defenses and capture the rear.
The emphasis on maneuvering and speed to bypass enemy engagement remains a common strategy throughout the world, and collapsing an enemy's defenses by striking at deeper targets is—in a somewhat different way—a major strategy in fourth generation warfare.[2]
The contributions of the third generation were based on the concept of overcoming technological disadvantage through the use of clever strategy. As linear fighting came to an end, new ways of moving faster began to appear.
The emphasis on cavalry moved from heavy armor to greater speed, the development of the helicopter allowed insertions in hostile territory, and advanced missile technology allowed forces to bypass enemy defenses and strike at targets from great distances. The speed inherent in these methods necessitated a greater degree of independence allowed to the units on the front lines.
Greater trust needed to be placed in junior officers commanding sub-units by higher-ranking officers—a belief that they could adequately achieve their objectives without micromanagement from higher ranking commanders in command headquarters.
Smaller units were allowed greater decision flexibility to deal with changing situations on the ground, rather than have decisions made for them by commanders who were distant from the front. This began to break down the regimented culture of order that was so important in previous theoretical eras of military command and control.
Examples:
World War II
Korean War
Vietnam War
Six-Day War
Gulf War
2003 invasion of Iraq
Fourth generation[edit]
Main article: Fourth-generation warfare
Fourth-generation warfare is characterized by a blurring of the lines between war and politics, combatants and civilians. The term was first used in 1989 by a team of United States analysts, including William S. Lind, to describe warfare's return to a decentralized form. In terms of generational modern warfare, the fourth generation signifies the nation states' loss of their near-monopoly on combat forces, returning to modes of conflict common in pre-modern times.
The simplest definition includes any war in which one of the major participants is not a state but rather a violent non-state actor. Classical examples, such as the slave uprising under Spartacus or the mercenary uprising that occurred in Carthage after the first Punic War, predate the modern concept of warfare and are examples of this type of conflict.
Guerillas in Maguindanao, 1999
Fourth generation warfare is defined as conflicts which involve the following elements:
Are complex and long term
Terrorism (tactic)
A non-national or transnational base – highly decentralized
A direct attack on the enemy's core ideals
Highly sophisticated psychological warfare, especially through media manipulation and lawfare
All available pressures are used – political, economic, social and military
Occurs in low intensity conflict, involving actors from all networks
Non-combatants are tactical dilemmas
Lack of hierarchy
Small in size, spread out network of communication and financial support
Use of insurgency and guerrilla tactics
QMRFukushima Daiichi nuclear disaster
Fukushima I by Digital Globe.jpg
Image on 16 March 2011 of the four damaged reactor buildings. From right to left: Unit 1, 2, 3 and 4. Hydrogen-air explosions occurred in Unit 1, 3 and 4, causing structural damage. A vent in Unit 2's wall, with water vapor/"steam" clearly visible, prevented a similar large explosion. Drone overflights on 20 March captured clearer images.[1]
QMR
The Terracotta Army was comprised of four main pits and the fourth was empty. In the quadrant model the fourth is always different. It is considered the greatest archeological find in Asia and one of the most astounding in history.
The Terracotta Army or the "Terracotta Warriors and Horses" is a collection of terracotta sculptures depicting the armies of Qin Shi Huang, the first Emperor of China. It is a form of funerary art buried with the emperor in 210–209 BCE and whose purpose was to protect the emperor in his afterlife.
It is considered one of the greatest archaeological finds in history.
The figures, dating from approximately the late third century BCE,[1] were discovered in 1974 by local farmers in Lintong District, Xi'an, Shaanxi province. The figures vary in height according to their roles, with the tallest being the generals. The figures include warriors, chariots and horses. Estimates from 2007 were that the three pits containing the Terracotta Army held more than 8,000 soldiers, 130 chariots with 520 horses and 150 cavalry horses, the majority of which remained buried in the pits nearby Qin Shi Huang's mausoleum.[2] Other terracotta non-military figures were found in other pits, including officials, acrobats, strongmen and musicians.
Pits
View of Pit 1, the largest excavation pit of the Terracotta Army
Four main pits approximately 7 metres (23 ft) deep have been excavated.[22][23] These are located approximately 1.5 kilometres (0.93 mi) east of the burial mound. The soldiers within were laid out as if to protect the tomb from the east, where all the Qin Emperor's conquered states lay.
Pit one
Pit one, which is 230 metres (750 ft) long and 62 metres (203 ft) wide,[24] contains the main army of more than 6,000 figures.[25] Pit one has 11 corridors, most of which are more than 3 metres (9.8 ft) wide and paved with small bricks with a wooden ceiling supported by large beams and posts. This design was also used for the tombs of nobles and would have resembled palace hallways when built. The wooden ceilings were covered with reed mats and layers of clay for waterproofing, and then mounded with more soil raising them about 2 to 3 metres (6 ft 7 in to 9 ft 10 in) above the surrounding ground level when completed.[26]
Others
Pit two has cavalry and infantry units as well as war chariots and is thought to represent a military guard. Pit three is the command post, with high-ranking officers and a war chariot. Pit four is empty, perhaps left unfinished by its builders.
Some of the figures in pit one and two show fire damage, while remains of burnt ceiling rafters have also been found.[27] These, together with the missing weapons, have been taken as evidence of the reported looting by Xiang Yu and the subsequent burning of the site, which is thought to have caused the roof to collapse and crush the army figures below. The terracotta figures currently on display have been restored from the fragments.
Other pits that formed the necropolis also have been excavated.[28] These pits lie within and outside the walls surrounding the tomb mound. They variously contain bronze carriages, terracotta figures of entertainers such as acrobats and strongmen, officials, stone armour suits, burials sites of horses, rare animals and labourers, as well as bronze cranes and ducks set in an underground park.[29]
The fourth pit is empty. The fourth is always different from the previous three. Like with 9/11 three planes crashed into buildings the third didn't crash into anything
QMRIn abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers and the elements of {1, i, j, k} multiply as in the quaternion group. As there are three types of complex number, so there are three types of biquaternion:
(Ordinary) biquaternions when the coefficients are (ordinary) complex numbers
Split-biquaternions when w, x, y, and z are split-complex numbers
Dual quaternions when w, x, y, and z are dual numbers.
This article is about the ordinary biquaternions named by William Rowan Hamilton in 1844 (see Proceedings of Royal Irish Academy 1844 & 1850 page 388). Some of the more prominent proponents of these biquaternions include Alexander Macfarlane, Arthur W. Conway, Ludwik Silberstein, and Cornelius Lanczos. As developed below, the unit quasi-sphere of the biquaternions provides a presentation of the Lorentz group, which is the foundation of special relativity.
The algebra of biquaternions can be considered as a tensor product C ⊗ H (taken over the reals) where C is the field of complex numbers and H is the algebra of (real) quaternions. In other words, the biquaternions are just the complexification of the (real) quaternions. Viewed as a complex algebra, the biquaternions are isomorphic to the algebra of 2×2 complex matrices M2(C). They can be classified as the Clifford algebra Cℓ2(C) = Cℓ03(C). This is also isomorphic to the Pauli algebra Cℓ3,0(R), and the even part of the spacetime algebra Cℓ01,3(R).
QMRThe Jerusalem cross, also known as Crusaders' cross or the "Five-fold Cross", is a heraldic cross or Christian symbol consisting of a large cross potent surrounded by four smaller plain crosses, one in each quadrant. It is not to be confused with the Lorraine cross, which has also been called the "Jerusalem cross".[2]
There are variants to the design, also known as "Jerusalem cross", with either the four crosslets also in the form of Crosses potent, or conversely with the central cross also in the form of a plain cross.[3]
It is pretty amazing that the Jerusalem cross is actually 16 squares. It is the quadrant model.
Origins and classical heraldry[edit]
The design originates with the coat of arms worn by Godfrey of Bouillon during the First Crusade, and it remained in use as the arms of the King of Jerusalem throughout their duration (1099–1291).[1]
The symbolism of the five-fold cross is variously given as the Five Wounds of Christ, Christ and the four quarters of the world, or Christ and the four evangelists. The arms of the King of Jerusalem featured gold on silver, a metal on a metal, and thus broke the heraldic Rule of Tincture; this was justified by the fact that Jerusalem was so holy, it was above ordinary rules. The gold and silver were also connected to Psalms 68:13, which mentions a "dove covered in silver, and her feathers with yellow gold".[1] The symbolism of five crosses representing the Five Wounds is first recorded earlier in the 11th century, with the consecration of the St Brelade's Church under the patronage of Robert of Normandy (before 1035); the crosses are incised in the church's altar stone.
The Latin Empire of 1204–1261 used an extended variant of the Jerusalem cross, where each of the four crosslets was itself surrounded by four smaller crosslets (a "Jerusalem cross of Jerusalem crosses").
In late medieval heraldry, after the failure of the Crusades, the Crusader's cross was used for various Crusader states. The 14th-century Book of All Kingdoms uses it as the flag of Sebasteia. At about the same time, the Pizzigano chart uses it as the flag of Tbilisi (based on the latter example, the Crusader's cross was adopted as the flag of Georgia in 2004).
Carlo Maggi, a Venetian nobleman who had visited Jerusalem and was made a knight of the Order of the Holy Sepulchre in the early 1570s, included the Jerusalem cross in his coat of arms.
There is a historiographical tradition that Peter the Great flew a flag with a variant of the Jerusalem cross in his campaign in the White Sea in 1693.[4]
Modern use[edit]
Red Jerusalem cross (Crusader flag) is an official national flag of the republic of Georgia.
A banner with a variation of the Jerusalem cross was used at the proclamation of the Revolution on Mount Pelion Anthimos Gazis in May 1821 in the Greek War of Independence.[5]
The papal Order of the Holy Sepulchre uses the Jerusalem cross as its emblem. It is also used by the Custodian of the Holy Land, head of the Franciscan friars who serve at the holy Christian sites in Jerusalem.
When Albert, Prince of Wales (later King Edward VII) visited Jerusalem in 1862, he had a Jerusalem cross tattooed on his arm.[6]
In the early 20th century, the Jerusalem cross also came to be used as a symbol of world evangelisation in Protestantism. A derived design known as the "Episcopal Church Service Cross" was first used during World War I by the Anglican Episcopal Church in the United States.[7] The Jerusalem cross was chosen as the emblem of the Deutscher Evangelischer Kirchentag (German Evangelical Church Congress) in the 1950s, since the 1960s shown in a simplified form where the central Cross potent is replaced by a simple Greek cross.[8]
The Jerusalem Cross has also been accepted to be an unofficial symbol of Christian Deism. It contains memory helps that point to twenty words that paraphrase the statements that Jesus used to describe the essence of his message. The 20 words are: "There is one God. I will love God with all my heart and love all others as I love myself." See Mark 12:28-31 and Luke 10:25-28 for two versions of Jesus' original statements. [9]
The Unicode character set has a character ☩, U+2629 CROSS OF JERUSALEM in the Miscellaneous Symbols table. However, the glyph associated with that character according to the official Unicode character sheet is shown as a simple cross potent, and not a Jerusalem cross.
QMRFour—Kentucky, Massachusetts, Pennsylvania, and Virginia—use the term commonwealth rather than state in their full official names.
QMRA 2007 study by Bauchet, which utilised about 10,000 autosomal DNA SNPs arrived at similar results. Principal component analysis clearly identified four widely dispersed groupings, corresponding to Africa, Europe, Central Asia and South Asia. PC1 separated Africans from the other populations, PC2 divided Asians from Europeans and Africans, whilst PC3 split Central Asians apart from South Asians.[45]
QMRThe Cross of Tau, named after the Greek letter it resembles, is a form of the Christian cross symbol.[1] It is also variously St. Anthony's Cross, Old Testament Cross, Anticipatory Cross, Cross Commissee, Egyptian Cross, Advent Cross, Croce taumata, Saint Francis's Cross, Crux Commissa.[citation needed]
The shape of the letter tau or T was interpreted as representing a crucifix from antiquity. The staurogram, from Greek ΣTAΥPOΣ "cross", was a tau-rho ligature used to abbreviate the Greek word for cross in very early New Testament manuscripts such as P66, P45 and P75.[2] The tau was also considered a symbol of salvation due to the identification of the tau with the sign which in Ezechiel 9:4 was marked on the forehead of the saved ones (וְהִתְוִיתָ תָּו עַל־מִצְחֹות הָאֲנָשִׁים "set a mark (tav; after the Phoenician cross-shape 𐤕) on the forehead of the men"), or due to the tau-shaped outstretched hands of Moses in Exodus 17:11.[2]
St. Anthony of Egypt bore a cross in the form of a tau on his cloak.[1] The Tau Cross is most commonly used in reference to the Franciscan Order and Saint Francis of Assisi, who adopted it as his personal coat of arms after hearing Pope Innocent III talk about the Tau symbol.[3] It is now used as a symbol of the Franciscan Order.
QMRThe Bolnisi cross (Georgian: ბოლნისის ჯვარი bolnisis ǰvari) is a cross symbol, taken from a 5th-century ornament at the Bolnisi Sioni church, which came to be used as a national symbol of Georgia.
It is a variant of the Cross pattée popular in Christian symbolism of late antiquity and the early medieval period. The same symbol gave rise to cross variants used during the Crusades, the Maltese cross of the Knights Hospitaller and (via the Jerusalem cross and the Black cross of the Teutonic Order) the Iron cross used by the German military.
The four small crosses used in the Georgian Flag are officially described as bolnur-kac'xuri (bolnur-katskhuri, ბოლნურ-კაცხური)[clarification needed] even though they are only slightly pattée.
QMRPeter Heylin's 1652 book Cosmographie (enlarged from his Microcosmos of 1621) was one of the earliest attempts to describe the entire world in English, and being the first known description of Australia and among the first of California. The book has 4 sections, examining the geography, politics, and cultures of Europe, Asia, Africa, and America, with an addendum on Terra Incognita, including Australia, and extending to Utopia, Fairyland, and the "Land of Chivalrie".
QMR Celestial cartography,[1] uranography[2][3] or star cartography[citation needed] is the fringe of astronomy and branch of cartography concerned with mapping stars, galaxies, and other astronomical objects on the celestial sphere. Measuring the position and light of charted objects requires a variety of instruments and techniques. These techniques have developed from angle measurements with quadrants and the unaided eye
QMR
America was named after Amerigo Vespucci. Vespucci is known for his four journeys like Columbus was known for his four journeys. The journeys fit the quadrant model pattern.
In 1508 the position of chief of navigation of Spain (piloto mayor de Indias) was created for Vespucci, with the responsibility of planning navigation for voyages to the Indies.
Vespucci's first encounter with Native Americans in Honduras, 1497 (De Bry's illustration, c.1592)
Two letters attributed to Vespucci were published during his lifetime. Mundus Novus (New World) was a Latin translation of a lost Italian letter sent from Lisbon to Lorenzo di Pierfrancesco de' Medici. It describes a voyage to South America in 1501–1502. Mundus Novus was published in late 1502 or early 1503 and soon reprinted and distributed in numerous European countries.[4] Lettera di Amerigo Vespucci delle isole nuovamente trovate in quattro suoi viaggi (Letter of Amerigo Vespucci concerning the isles newly discovered on his four voyages), known as Lettera al Soderini or just Lettera, was a letter in Italian addressed to Piero Soderini. Printed in 1504 or 1505, it claimed to be an account of four voyages to the Americas made by Vespucci between 1497 and 1504. A Latin translation was published by the German Martin Waldseemüller in 1507 in Cosmographiae Introductio, a book on cosmography and geography, as Quattuor Americi Vespucij navigationes (Four Voyages of Amerigo Vespucci).[4]
On March 22, 1508, King Ferdinand made Vespucci chief navigator of Spain at a huge salary[5] and commissioned him to found a school of navigation, in order to standardize and modernize navigation techniques used by Iberian sea captains then exploring the world. Vespucci even developed a rudimentary, but fairly accurate method of determining longitude (which only more accurate chronometers would later improve upon).
The first known depiction of cannibalism in the New World. Engraving by Johann Froschauer for an edition of Amerigo Vespucci's Mundus Novus, published in Augsburg in 1505.
In the 18th century three unpublished familiar letters from Vespucci to Lorenzo de' Medici were rediscovered. One describes a voyage made in 1499–1500 which corresponds with the second of the "four voyages". Another was written from Cape Verde in 1501 in the early part of the third of the four voyages, before crossing the Atlantic. The third letter was sent from Lisbon after the completion of that voyage.[4]
Some have suggested that Vespucci, in the two letters published in his lifetime, was exaggerating his role and constructed deliberate fabrications. However, many scholars now believe that the two letters were not written by him but were fabrications by others based in part on genuine letters by Vespucci. It was the publication and widespread circulation of the letters that might have led Waldseemüller to name the new continent America on his world map of 1507 in Lorraine. Vespucci used a Latinised form of his name, Americus Vespucius, in his Latin writings, which Waldseemüller used as a base for the new name, taking the feminine form America, according to the prevalent view (for other hypotheses, see the footnote in the introduction). The book accompanying the map stated: "I do not see what right any one would have to object to calling this part, after Americus who discovered it and who is a man of intelligence, Amerige, that is, the Land of Americus, or America: since both Europa and Asia got their names from women". It is possible that Vespucci was not aware that Waldseemüller had named the continent after him.[6]
The two disputed letters claim that Vespucci made four voyages to America, while at most two can be verified from other sources. At the moment there is a dispute between historians on when Vespucci visited the mainland the first time. Some historians like Germán Arciniegas and Gabriel Camargo Pérez think that his first voyage was made in June 1497 with the Spanish Pilot Juan de la Cosa.
Vespucci's real historical importance may well rest more in his letters, whether he wrote them all or not, than in his discoveries. From these letters, the European public learned about the newly discovered continents of the Americas for the first time; its existence became generally known throughout Europe within a few years of the letters' publication.
First voyage
A letter published in 1504 purports to be an account by Vespucci, written to Soderini, of a lengthy visit to the New World, leaving Spain in May 1497 and returning in October 1498. However, modern scholars have doubted that this voyage took place, and consider this letter a forgery.[7] Whoever did write the letter makes several observations of native customs, including use of hammocks and sweat lodges.[8] The names of Amerigo Vespucci's ships were the San Antiago, Repertaga, Wegiz, and the Girmand.
Second voyage
About 1499–1500, Vespucci joined an expedition in the service of Spain, with Alonso de Ojeda (or Hojeda) as the fleet commander. The intention was to sail around the southern end of the African mainland into the Indian Ocean.[9] After hitting land at the coast of what is now Guyana, the two seem to have separated. Vespucci sailed southward, discovering the mouth of the Amazon River and reaching 6°S, before turning around and seeing Trinidad and the Orinoco River and returning to Spain by way of Hispaniola. The letter, to Lorenzo di Pierfrancesco de' Medici, claims that Vespucci determined his longitude celestially [10] on August 23, 1499, while on this voyage. However, that claim may be fraudulent,[10] which could cast doubt on the letter's credibility.
Third voyage
Portrait of Vespucci which titles him "discoverer and conqueror of Brazilian land".
The last certain voyage of Vespucci was led by Gonçalo Coelho in 1501–1502 in the service of Portugal. Departing from Lisbon, the fleet sailed first to Cape Verde where they met two of Pedro Álvares Cabral's ships returning from India. In a letter from Cape Verde, Vespucci says that he hopes to visit the same lands that Álvares Cabral had explored, suggesting that the intention is to sail west to Asia, as on the 1499–1500 voyage.[9] On reaching the coast of Brazil, they sailed south along the coast of South America to Rio de Janeiro's bay. If his own account is to be believed, he reached the latitude of Patagonia before turning back, although this also seems doubtful, since his account does not mention the broad estuary of the Río de la Plata, which he must have seen if he had gotten that far south. Portuguese maps of South America, created after the voyage of Coelho and Vespucci, do not show any land south of present-day Cananéia at 25° S, so this may represent the southernmost extent of their voyages.
After the first half of the expedition, Vespucci mapped Alpha and Beta Centauri, as well as the constellation Crux, the Southern Cross and the Coalsack Nebula.[11] Although these stars had been known to the ancient Greeks, gradual precession had lowered them below the European horizon so that they had been forgotten. On his return to Lisbon, Vespucci wrote in a letter to Medici that the land masses they explored were much larger than anticipated and different from the Asia described by Ptolemy or Marco Polo and therefore, must be a New World, that is, a previously unknown fourth continent, after Europe, Asia, and Africa.[citation needed]
Fourth voyage
Vespucci's fourth voyage was another expedition for the Portuguese crown down the eastern coast of Brazil, that set out in May 1503 and returned to Portugal in June 1504. Like his alleged first voyage, Vespucci's last voyage in 1503–1504 is also disputed to have taken place.[12] The only source of information for the last voyage is the Letter to Soderini,[13] but as several modern scholars dispute Vespucci's authorship of the letter to Soderini, it is also sometimes doubted whether Vespucci undertook this trip.[b] However, Portuguese documents do confirm a voyage to Brazil was undertaken in 1503–04 by the captain Gonçalo Coelho, very likely the same captain of the 1501 mapping expedition (Vespucci's third voyage), and so it is quite possible that Vespucci went on board this one as well.[14] However, it is not independently confirmed Vespucci was aboard and there are some difficulties in the reported dates and details.
The letters caused controversy after Vespucci's death, especially among the supporters of Columbus who believed Columbus' priority for the discovery of America was being undermined, and seriously damaged Vespucci's reputation.[
A lot of historians question if the fourth voyage occurred. The fourth square is always different. The first square is always different and transcendent. The first square is weird, the second normal and homeostasis. The third is bad and the most physical. The fourth is always different.
QMRPeighambarieh Shrine: Where four Jewish saints who foretold the coming of Christ, are buried.
QMRIf continents are defined strictly as discrete landmasses, embracing all the contiguous land of a body, then Asia, Europe and Africa form a single continent which may be referred to as Afro-Eurasia. This produces a four-continent model consisting of Afro-Eurasia, America, Antarctica and Australia.
QMRIn 1507 Martin Waldseemüller published a world map, Universalis Cosmographia, which was the first to show North and South America as separate from Asia and surrounded by water. A small inset map above the main map explicitly showed for the first time the Americas being east of Asia and separated from Asia by an ocean, as opposed to just placing the Americas on the left end of the map and Asia on the right end. In the accompanying book Cosmographiae Introductio, Waldseemüller noted that the earth is divided into four parts, Europe, Asia, Africa and the fourth part, which he named "America" after Amerigo Vespucci's first name.[57] On the map, the word "America" was placed on part of South America.
An explanatory text, the Cosmographiae Introductio, widely believed to have been written by Waldseemüller's colleague Matthias Ringmann, accompanied the map. It was said in Chapter IX of that text that the earth was now known to be divided into four parts, of which Europe, Asia and Africa, being contiguous with each other, were continents, while the fourth part, America, was “an island, inasmuch as it is found to be surrounded on all sides by the seas”.[7]
The name for the northern land mass, Parias, is derived from a passage in the Four Voyages of Amerigo Vespucci, in which, after several stops, the expedition arrives at a region that was “situated in the torrid zone directly under the parallel which describes the Tropic of Cancer. And this province is called by them [the inhabitants] Parias”.[10] Parias was described by Waldseemüller’s follower, Johannes Schöner as: “The island of Parias, which is not a part or portion of the foregoing [America] but a large, special part of the fourth part of the world”, indicating uncertainty as to its situation.
The map shows the cities of Catigara (Kattigara) and Mallaqua (Malacca) on the western coast of the great peninsula that projects from the southeastern part of Asia, or INDIA MERIDIONALIS (Southern India) as Waldseemüller called it. This peninsula forms the eastern side of the SINUS MAGNUS ("Great Gulf"), the Gulf of Thailand.[12] Amerigo Vespucci, writing of his 1499 voyage, said he had hoped to sail westward from Spain across the Western Ocean (the Atlantic) around the Cape of Cattigara mentioned by Ptolemy into the Sinus Magnus.[13] Ptolemy understood Cattigara, or Kattigara, to be the most eastern port reached by shipping trading from the Graeco-Roman world to the lands of the Far East. Vespucci failed to find the Cape of Cattigara on his 1499 voyage: he sailed along the coast of Venezuela but not far enough to resolve the question of whether there was a sea passage beyond leading to Ptolemy’s Sinus Magnus. The object of his voyage of 1503–1504 was to reach the fabulous spice emporium of “Melaccha in India” (that is, Malacca, or Melaka, on the Malay Peninsula).[14] He had learned of Malacca from one Guaspare (or Gaspard), a pilot with Pedro Álvares Cabral’s fleet on its voyage to India in 1500–1501, whom Vespucci had encountered in the Atlantic on his return from India in May 1501.[15] Christopher Columbus, in his fourth and last voyage of 1502–1503, planned to follow the coast of Champa southward around the Cape of Cattigara and sail through the strait separating Cattigara from the New World, into the Sinus Magnus to Malacca. This was the route he understood Marco Polo to have gone from China to India in 1292 (although Malacca had not yet been founded in Polo’s time).[16] Columbus anticipated that he would meet up with the expedition sent at the same time from Portugal to Malacca around the Cape of Good Hope under Vasco da Gama, and carried letters of credence from the Spanish monarchs to present to da Gama.[17] The map therefore shows the two cities that were the initial destinations of Amerigo Vespucci and Christopher Columbus in their voyages that led to the unexpected discovery of a New Official WorldStarHipHop
QMRCosmographiae Introductio (Saint-Dié, 1507) was a book published in 1507 to accompany Martin Waldseemüller's printed globe and wall-map (Universalis Cosmographia), which were the first appearance of the name 'America'. Waldseemüller’s maps and book, along with his 1513 edition of Ptolemy’s Geography, were very influential and widely copied at the time.
That part of the page of the 1507 (September) edition of the Cosmographiae Introductio in which the name of America is proposed for the New World. From Narrative and critical history of America, Volume 2 by Justin Winsor.
It is widely held to have been written by Matthias Ringmann although some historians attribute it to Waldseemüller himself. The book includes the reason for using the name America in the wall map and the globe, and contains a Latin translation of the four journeys of Amerigo Vespucci as an appendix.
The full title of the book is: "Cosmographiae introductio cum quibusdam geometriae ac astronomiae principiis ad eam rem necessariis. Insuper quatuor Americi Vespucii navigationes. Universalis Cosmographiae descriptio tam in solido quam plano, eis etiam insertis, quae Ptholomaeo ignota a nuperis reperta sunt."
(translation: Introduction to Cosmography With Certain Necessary Principles of Geometry and Astronomy To which are added The Four Voyages of Amerigo Vespucci A Representation of the Entire World, both in the Solid and Projected on the Plane, Including also lands which were Unknown to Ptolemy, and have been Recently Discovered)[1]
Universalis Cosmographia (map of 1507)
The map of the world in 1507, entitled "Universalis cosmographia secundum Ptholomaei traditionem et Americi Vespucii aliorumque lustrationes", was published in an edition of 1000 copies, of which it seems only a single copy survives. The surviving copy was found in the library of Prince von Waldburg-Wolfegg-Waldsee in the Castle of Wolfegg in Württemberg. It was bought by the Library of Congress in 2001. This preservation seems to be due the several sheets being bound into a single cover by the cartographer, Johannes Schöner.
The map consists of twelve sections printed from woodcuts combined with metal types, each measuring 18 x 24.5 inches (46 x 62 cm). Each section is one of four, that form one of three zones. The map uses a modified Ptolemaic coniform projection with curved meridians to depict the entire surface of the Earth.
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