Philosophy Chapter
QMRPythagorean proof
The Pythagorean proof (click to view animation)
The Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it.[2] In any event, the proof attributed to him is very simple, and is called a proof by rearrangement.
The two large squares shown in the figure each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem, Q.E.D.[8]
That Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus.[9] Several other proofs of this theorem are described below, but this is known as the Pythagorean one.
QMRThe Four Doctors of Bologna (Latin: Quatuor Doctores) were Italian jurists and glossators of the 12th century, based in the University of Bologna: Bulgarus, Martinus Gosia, Jacobus de Boragine and Hugo de Porta Ravennate.[1]
Their teachings in the law school of Bologna were based on glosses and commentaries on the rediscovered Corpus juris civilis of Justinian. Martinus may have studied with the founder of legal scholarship in Bologna, Irnerius.[2] The revived importance of Roman law, in the form of medieval Roman law, embodied by the Quattuor Doctores made its first impact in the political arena in 1158, when they gave their support to Frederick Barbarossa in his conflict with the Italian communes over imperial rights in Lombardy.[2]
Of the four the strongest contrast in interpretations of the revived Roman law were Bulgarus and Martinus. Bulgarus took the law at face value and applied the narrowest interpretation, the ius strictum; Martinus, on the other hand, applied the legal principle of aequitas, "equity" or "equivalence", which permitted broad latitude in extending Roman principles to modern situations. The followers of Bulgarus, the Bulgari, held sway in Bologna in the following generation, as nostri doctores ("our doctors"), while the followers of Martinus, the Gosiani, taught particularly in southern France.[2] The form of Questiones, questions and answers on the principles of law, rather than glosses on specific texts, was the particular contribution of Hugo.[3]
In the 13th century the combined tradition of the doctores bononienses were summarized in the form of a glossa ordinaria of Roman law, compiled by Accursius.
QMRBulgarus was a twelfth-century Italian jurist, born in Bologna. He is often confused with Bulgarinus, another 15th-century jurist.
Bulgarus was the most celebrated of the famous Four Doctors of the law school of the University of Bologna, probably because his school promoted Roman emperors, such as Justinian I, as the highest authority. Bulgarus was regarded as the Chrysostom of the Glossators, being frequently designated by the title of the "Golden Mouth" (os aureum). He died in 1166 at a very advanced age.[vague] According to popular tradition, all four of the famous Four Doctors (Bulgarus, Martinus Gosia, Hugo de Porta Ravennate and Jacobus de Boragine) were pupils of Irnerius; however, while there is currently no insuperable difficulty in substantiating this claim with regard to Bulgarus, Friedrich Karl von Savigny considers the evidence to be insufficient to support this claim. Martinus Gosia and Bulgarus were the chiefs of two opposite schools at Bologna, corresponding in many respects to the Proculians and Sabinians of Imperial Rome, Martinus being at the head of a school that accommodated the law in a manner that his opponents referred to as the "equity of the purse" (aequitas bursalis), whilst Bulgarus adhered more closely to the letter of the law. Martinus' school was also generally more flexible in its interpretation of the law, whereas Bulgarus' school was much more orthodox and adhered more closely to the tradition of the "Corpus Iuris Civilis". Bulgarus' school ultimately prevailed. Joannes Bassianus, Azo and Accursius all numbered amongst its notable adherents, each of whom, in turn, went on to exercise a commanding influence over the course of legal studies in Bologna.
Decretals with Glossa ordinaria
At the Diet of Roncaglia in 1158, Bulgarus assumed the leading role amongst the Four Doctors, and was one of the most trusted advisors to the emperor Frederick I.[1] His most celebrated work is a notable commentary, De Regulis Juris, which was at one time printed amongst the writings of Placentinus. However, this commentary has since been properly credited to its true author, Cujacius, based on internal evidence contained in the additions annexed to it, which were undoubtedly penned by Placentinus himself. This commentary is the earliest extant work of its kind emanating from the school of the Glossators. According to Savigny, it is a model specimen of the excellence of the method introduced by Irnerius, and a striking example of the brilliant results obtained in a short period of time by virtue of a constant, exclusive study of the sources of law.[2]
While the teaching of Bulgarus, became dominant in Bologna, the followers of Martinus, taught in southern France where they became known as the commentators.[3] Bulgarus teaching in turn influenced Joannes Bassianus, Azo and Accursius.
Martinus Gosia was one of the glossators and a 12th-century Italian jurist, counted among the Four Doctors of Bologna, the others being Bulgarus, Hugo de Porta Ravennate and Jacobus de Boragine.
Martinus Gosia and Bulgarus were the chiefs of two opposite schools at the University of Bologna, corresponding in many respects to the Proculians and Sabinians of the Roman Empire. Martinus was at the head of a school which accommodated the law to what his opponents styled the equity of the purse (aequitas bursalis), whilst Bulgarus adhered more closely to the letter of the law. The school of Bulgarus ultimately prevailed.
While the teaching of Bulgarus, became dominant in Bologna, among the nostri doctores, the followers of Martinus, taught in southern France where they became known as the commentators.[1]
Jacobus de Boragine was one of the Glossators, and Four Doctors of Bologna[1][2]
Also known as Jacobus, he was born in the early 12th century and was an Italian lawyer, one of four students of Irnerius called the Quattuor Doctores, although Savigny disputes the general tradition of his inclusion in this list.[3] The other doctors were Bulgarus, Martinus and Hugo. The legal philosophy of Bulgarus adhered closely to the letter of the law while their fellow, Martinus took a more natural law and Equity approach. His time at Bologna was therefore one of the formative times in legal theory.
Students of the German nation at Bologna university.
He was an author of many parts of the Gloss of the Corpus juris civilis.
The legal commentary De Regulis Juris, which Savigny called "a striking example of the brilliant results which had been obtained in a short space of time by a constant and exclusive study of the sources of law".[4]
He died 1178.[5]
Hugo de Porta Ravennate was an Italian jurist, and member of the Glossators of Bologna.
He came from a noble family who had residence in the city of Bologna, but whose family name meant "the gate of Ravenna".
Study and teaching at the University of Bologna, Hugo was one of the "four doctors", a group of disciples of Irnerius who were formitive in the development of European law. Their authority was such that the four lawyers were called by Frederick Barbarossa as directors imperial in the diet of Roncaglia in 1158. This royal patronage allowed them to secure privillages for the newly developing institution of the university, at Bologna.[1]
It is not known when he died but it was after 1166AD, when a document is attested to him, but no later than 1171AD, when a document mentions his widow.
He wrote the glosses to the recovered Roman law, the distinctiones and Summula de pugna.[2][3][4] His students established a third and latter fourth generation of legal scholars at bologna and also included many leaders of Europe including William of Tyre.
825–1025[edit]
The Tusi-couple is a mathematical device invented by Nasir al-Din al-Tusi in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle.
This period of vigorous investigation, in which the superiority of the Ptolemaic system of astronomy was accepted and significant contributions made to it. However, Dallal notes that the use of parameters, sources and calculation methods from different scientific traditions made the Ptolemaic tradition "receptive right from the beginning to the possibility of observational refinement and mathematical restructuring".[15] Astronomical research was greatly supported by the Abbasid caliph al-Mamun through The House of Wisdom. Baghdad and Damascus became the centers of such activity. The caliphs not only supported this work financially, but endowed the work with formal prestige.
The first major Muslim work of astronomy was Zij al-Sindh by al-Khwarizmi in 830. The work contains tables for the movements of the sun, the moon and the five planets known at the time. The work is significant as it introduced Ptolemaic concepts into Islamic sciences. This work also marks the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi's work marked the beginning of nontraditional methods of study and calculations.[16]
In 850, al-Farghani wrote Kitab fi Jawani (meaning "A compendium of the science of stars"). The book primarily gave a summary of Ptolemic cosmography. However, it also corrected Ptolemy based on findings of earlier Arab astronomers. Al-Farghani gave revised values for the obliquity of the ecliptic, the precessional movement of the apogees of the sun and the moon, and the circumference of the earth. The book was widely circulated through the Muslim world, and even translated into Latin.[17]
1025–1450[edit]
An illustration from al-Biruni's astronomical works, explains the different phases of the moon.
The period when a distinctive Islamic system of astronomy flourished. The period began as the Muslim astronomers began questioning the framework of the Ptolemaic system of astronomy. These criticisms, however, remained within the geocentric framework and followed Ptolemy's astronomical paradigm; one historian described their work as "a reformist project intended to consolidate Ptolemaic astronomy by bringing it into line with its own principles."[18]
Between 1025 and 1028, Ibn al-Haytham wrote his Al-Shukuk ala Batlamyus (meaning "Doubts on Ptolemy"). While maintaining the physical reality of the geocentric model, he criticized elements of the Ptolemic models. Many astronomers took up the challenge posed in this work, namely to develop alternate models that resolved these difficulties. In 1070, Abu Ubayd al-Juzjani published the Tarik al-Aflak. In his work, he indicated the so-called "equant" problem of the Ptolemic model. Al-Juzjani even proposed a solution for the problem. In Al-Andalus, the anonymous work al-Istidrak ala Batlamyus (meaning "Recapitulation regarding Ptolemy"), included a list of objections to the Ptolemic astronomy.
Other critical astronomers include: Mu'ayyad al-Din al-'Urdi (c. 1266), Nasir al-Din al-Tusi (1201–74), Qutb al-Din al Shirazi (c. 1311), Sadr al-Sharia al-Bukhari (c. 1347), Ibn al-Shatir (c. 1375), and Ali al-Qushji (c. 1474).[19]
1450–1900[edit]
The period of stagnation, when the traditional system of astronomy continued to be practised with enthusiasm, but with rapidly decreasing innovation of any major significance.
A large corpus of literature from Islamic astronomy remains today, numbering around some 10,000 manuscript volumes scattered throughout the world. Much of this has not even been catalogued. Even so, a reasonably accurate picture of Islamic activity in the field of astronomy can be reconstructed
Quadratic equations are based on the quadrant.Muḥammad ibn Mūsā al-Khwārizmī[note 1] (Arabic: محمد بن موسى الخوارزمی; c. 780 – c. 850), formerly Latinized as Algoritmi,[note 2] was a Persian[3] mathematician, astronomer and geographer during the Abbasid Caliphate, a scholar in the House of Wisdom in Baghdad.
In the 12th century, Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world.[4] Al-Khwārizmī's The Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources.[5] He revised Ptolemy's Geography and wrote on astronomy and astrology.
Some words reflect the importance of al-Khwārizmī's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name.[6] His name is also the origin of (Spanish) guarismo[7] and of (Portuguese) algarismo, both meaning digit.
Quadratic equations are based on the quadrant.Muḥammad ibn Mūsā al-Khwārizmī[note 1] (Arabic: محمد بن موسى الخوارزمی; c. 780 – c. 850), formerly Latinized as Algoritmi,[note 2] was a Persian[3] mathematician, astronomer and geographer during the Abbasid Caliphate, a scholar in the House of Wisdom in Baghdad.
In the 12th century, Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world.[4] Al-Khwārizmī's The Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources.[5] He revised Ptolemy's Geography and wrote on astronomy and astrology.
Some words reflect the importance of al-Khwārizmī's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name.[6] His name is also the origin of (Spanish) guarismo[7] and of (Portuguese) algarismo, both meaning digit.
Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing".
Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)
squares equal roots (ax2 = bx)
squares equal number (ax2 = c)
roots equal number (bx = c)
squares and roots equal number (ax2 + bx = c)
squares and number equal roots (ax2 + c = bx)
roots and number equal squares (bx + c = ax2)
QMRQuadrants[edit]
Ibn al-Shatir's model for the appearances of Mercury, showing the multiplication of epicycles using the Tusi-couple, thus eliminating the Ptolemaic eccentrics and equant.
Several forms of quadrants were invented by Muslims. Among them was the sine quadrant used for astronomical calculations and various forms of the horary quadrant, used to determine time (especially the times of prayer) by observations of the Sun or stars. A center of the development of quadrants was ninth-century Baghdad.[37]
QMRThe name and explanations given by Mercator to his world map (Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendata: "new and augmented description of Earth corrected for the use of sailors") show that it was expressly conceived for the use of marine navigation. Although the method of construction is not explained by the author, Mercator probably used a graphical method, transferring some rhumb lines previously plotted on a globe to a square graticule, and then adjusting the spacing between parallels so that those lines became straight, making the same angle with the meridians as in the globe.
The squares of the map are quadrants
QMRThe name and explanations given by Mercator to his world map (Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendata: "new and augmented description of Earth corrected for the use of sailors") show that it was expressly conceived for the use of marine navigation. Although the method of construction is not explained by the author, Mercator probably used a graphical method, transferring some rhumb lines previously plotted on a globe to a square graticule, and then adjusting the spacing between parallels so that those lines became straight, making the same angle with the meridians as in the globe.
The squares of the map are quadrants
QMRThe Cross of Lorraine (French: Croix de Lorraine) was originally a heraldic cross. The two-barred cross consists of a vertical line crossed by two shorter horizontal bars. In most renditions, the horizontal bars are "graded" with the upper bar being the shorter, though variations with the bars of equal length are also seen. The Lorraine name has come to signify several cross variations, including the patriarchal cross with its bars near the top.
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]
Phonological systems[edit]
Linguistic typology will also apply to the structure and spread of sound systems in languages world-wide in identifying patterns. Ultimately, the goal is to understand the patterns of relative frequency between sounds and their co-occurrences and why they are thus. An example of this relative spread can be seen in trying to explain why contrastive voicing commonly occurs with plosives, such as in English with “neat” and “need”, but much fewer have this occur in fricatives, such as the English “niece” and “knees”. According to a worldwide sample of 637 languages,[1] 62% have the voicing contrast in stops but only 35% have this in fricatives. In the vast majority of those cases, the absence of voicing contrast occurs because there is a lack of voiced fricatives and because all languages have some form of plosive, but there are languages with no fricatives. Below is a chart showing the breakdown of these languages, showing the numbers as shown in this sample and how they relate to each other.
Plosive Voicing Fricative Voicing
Yes No Total
Yes 117 218 395 (62%)
No 44 198 242 (38%)
Total 221 (35%) 416 (65%) 637
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.
QMRFrancis Bacon wrote in his Advancement of Learning (1605) that natural science "doth make inquiry, and take consideration of the same natures : but how? Only as to the material and efficient causes of them, and not as to the forms." According to the demands of Bacon, apart from the "laws of nature" themselves, the causes relevant to natural science are only efficient causes and material causes in terms of Aristotle's classification, or to use the formulation which became famous later, all nature visible to human science is matter and motion. Using the terminology of Aristotle, he divided knowledge into physics and metaphysics in The New Organon.
From the two kinds of axioms which have been spoken of arises a just division of philosophy and the sciences, taking the received terms (which come nearest to express the thing) in a sense agreeable to my own views. Thus, let the investigation of forms, which are (in the eye of reason at least, and in their essential law) eternal and immutable, constitute Metaphysics; and let the investigation of the efficient cause, and of matter, and of the latent process, and the latent configuration (all of which have reference to the common and ordinary course of nature, not to her eternal and fundamental laws) constitute Physics. And to these let there be subordinate two practical divisions: to Physics, Mechanics; to Metaphysics, what (in a purer sense of the word) I call Magic, on account of the broadness of the ways it moves in, and its greater command over nature. Francis Bacon The New Organon, Book II, Aphorism 9, 1620
Bacon's position became the standard one for modern science.
QMRResearchers implemented the Huta & Ryan Scale: Four Eudaimonic Measurement Questionnaire to analyze the participants eudaimonic motives, through motivation towards activities. The investigation was conducted on Canadian university undergraduates.
The four eudaimonic pursuits as described by Huta & Ryan are: 1. “Seeking to pursue excellence or a personal ideal” 2. “Seeking to use the best in yourself” 3. “Seeking to develop a skill, learn, or gain insight into something” 4. “Seeking to do what you believe in"
QMRThe Physics (from physis, Greek for "nature") is Aristotle's principal work on nature. In Physics II.1, Aristotle defines a nature as "a source or cause of being moved and of being at rest in that to which it belongs primarily".[1] In other words, a nature is the principle within a natural raw material that is the source of tendencies to change or rest in a particular way unless stopped. For example a rock would fall unless stopped. Natural things stand in contrast to artifacts, which are formed by human artifice, not because of an innate tendency. (The raw materials of a bed have no tendency to become a bed.) In terms of Aristotle's theory of four causes, the word natural is applied both to the innate potential of matter cause and the forms which the matter tends to become naturally.[2]
According to Leo Strauss,[3] the beginning of Western philosophy involved the "discovery or invention of nature" and the "pre-philosophical equivalent of nature" was supplied by "such notions as 'custom' or 'ways'". In ancient Greek philosophy on the other hand, Nature or natures are ways that are "really universal" "in all times and places". What makes nature different is that it presupposes not only that not all customs and ways are equal, but also that one can "find one's bearings in the cosmos" "on the basis of inquiry" (not for example on the basis of traditions or religion). To put this "discovery or invention" into the traditional terminology, what is "by nature" is contrasted to what is "by convention". The concept of nature taken this far remains a strong tradition in modern western thinking. Science, according to Strauss' commentary of Western history is the contemplation of nature, while technology was or is an attempt to imitate it.[4]
Going further, the philosophical concept of nature or natures as a special type of causation - for example that the way particular humans are is partly caused by something called "human nature" is an essential step towards Aristotle's teaching concerning causation, which became standard in all Western philosophy until the arrival of modern science.
Aristotle
Whether it was intended or not, Aristotle's inquiries into this subject were long felt to have resolved the discussion about nature in favor of one solution. In this account, there are four different types of cause:
The material cause is the "raw material" - the matter which undergoes change. One of the causes of a statue being what it is might be that it is bronze. All meanings of the word nature encompass this simple meaning.
The efficient cause is the motion of another thing, which makes a thing change, for example a chisel hitting a rock causes a chip to break off. This is the way which the matter is forming into a form so that it become substance like what Aristotle said that a substance must have a form and matter in order to call it substance. This is the motion of changing a single being into two. This is the most obvious way in which cause and effect works, as in the descriptions of modern science. But according to Aristotle, this does not yet explain that of which the motion is, and we must "apply ourselves to the question whether there is any other cause per se besides matter".[5]
The formal cause is the form or idea which serves as a template towards which things develop - for example following an approach based upon Aristotle we could say that a child develops in a way partly determined by a thing called "human nature". Here, nature is a cause.
The final cause is the aim towards which something is directed. For example a human aims at something perceived to be good, as Aristotle says in the opening lines of the Nicomachean Ethics.
The formal and final cause are an essential part of Aristotle's "Metaphysics" - his attempt to go beyond nature and explain nature itself. In practice they imply a human-like consciousness involved in the causation of all things, even things which are not man-made. Nature itself is attributed with having aims.[6]
The artificial, like the conventional therefore, is within this branch of Western thought, traditionally contrasted with the natural. Technology was contrasted with science, as mentioned above. And another essential aspect to this understanding of causation was the distinction between the accidental properties of a thing and the substance - another distinction which has lost favor in the modern era, after having long been widely accepted in medieval Europe.
To describe it another way, Aristotle treated organisms and other natural wholes as existing at a higher level than mere matter in motion. Aristotle's argument for formal and final causes is related to a doctrine about how it is possible that people know things: "If nothing exists apart from individual things, nothing will be intelligible; everything will be sensible, and there will be no knowledge of anything—unless it be maintained that sense-perception is knowledge".[7] Those philosophers who disagree with this reasoning therefore also see knowledge differently from Aristotle.
Aristotle then, described nature or natures as follows, in a way quite different from modern science...
QMRIn philosophy, four-dimensionalism (also known as the doctrine of temporal parts and the theory that objects "perdure") is an ontological position that an object's persistence through time is like its extension through space and an object that exists in time has temporal parts in the various subregions of the total region of time it occupies.[1]
Eternalism is a philosophical approach to the ontological nature of time, according to which all points in time are equally "real", as opposed to the presentist idea that only the present is real.[2]
Perdurantism—or perdurance theory—is a philosophical theory of persistence and identity,[3] according to which an individual has distinct temporal parts throughout its existence. Thus eternalism is a theory of time, while perdurantism is a theory about the identity of objects over time. Sider (1997)[1] uses the term four-dimensionalism to refer to perdurantism. Michael Rea (Forthcoming in The Oxford Handbook for Metaphysics), however, uses the term "four-dimensionalism" to mean the view that presentism is false as opposed to "perdurantism", the view that objects last over time without being wholly present at every time at which they exist.[4]
Eternalism and perdurantism tend to be discussed together because many philosophers argue for a combination of eternalism and perdurantism, considering both as better theories than their counterparts, presentism and endurantism, respectively. It may be argued that the acceptance of perdurantism and rejection of eternalism would be incoherent.
Contemporary four-dimensionalists include, according to Sider (1997), Armstrong (1980), Hughes (1986), Heller (1984, 1990,1992,1993) and Lewis (1983, 1986)
Presentism vs. eternalism (and the growing block theory)[edit]
Presentism is an ontological viewpoint which attempts to account for how consciousness functions in relation to time. Presentism asserts that only the present exists. The past and the future, therefore, are seen as non-existent. To a presentist, the memory accounts for the collection of events that have already occurred. Similarly, the future is conceptualized as being a mental construct. Therefore, presentism is attempting to demonstrate that the total sum of the actual world occupies the present moment.
Consequently, eternalism is the ontological view which postulates that past, present and future all equally exist. While the presentist asserts that the past and future are only logical constructs, the eternalist believes that time exists as an objective manifestation. Eternalism is the basic construct behind four-dimensionalism, as it accounts for the reality of past and future rather than proposing that all events occupy the present.
Additionally there is the "growing block theory" which accepts present and past objects (and events) into its ontology but not future ones. This purportedly allows for an open future (and closed past), thus making room for libertarian free will. It also makes good on the intuition that there is a significant metaphysical distinction to be made between past and future.
A-series and B-series[edit]
Main article: A-series and B-series
J.M.E. McTaggart in The Unreality of Time, identified two descriptions of time, which he called the A-series and the B-series. The A-series identifies positions in time as past, present, or future, and thus assumes that the "present" has some objective reality, as in both presentism and the growing block universe.[5] The B-series defines a given event as earlier or later than another event, but does not assume an objective present, as in four-dimensionalism.
Comparisons to three-dimensionalism[edit]
Unlike the four dimensionalist, the three dimensionalist considers time to be a unique dimension that is not analogous to the three spatial dimensions: length, width and height. Whereas the four dimensionalist proposes that objects are extended across time, the three dimensionalist adheres to the belief that all objects are wholly present at any moment at which they exist. While the three dimensionalist agrees that the parts of an object can be differentiated based on their spatial dimensions, they do not believe an object can be differentiated into temporal parts across time. For example, in the three dimensionalist account, "Descartes in 1635" is the same object as "Descartes in 1620", and both are identical to Descartes, himself. However, the four dimensionalist considers these to be distinct temporal parts, neither of which are identical with the whole Descartes, the spacetime "worm" concatenating these temporal parts.[6]
QMRIn philosophy, the Rietdijk–Putnam argument, named after C. W. Rietdijk and Hilary Putnam, uses 20th-century findings in physics—specifically in special relativity—to support the philosophical position known as four-dimensionalism.
If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. If each three-dimensional universe exists, then the existence of multiple three-dimensional universes suggests that the universe is four-dimensional. The argument is named after the discussions by Rietdijk (1966)[1] and Putnam (1967).[2] It is sometimes called the Rietdijk–Putnam–Penrose argument.[3]
QMRAt least four distinct techniques have been used to estimate distances to the Andromeda Galaxy.
QMRNASA's series of Great Observatories satellites are four large, powerful space-based telescopes. The four missions were designed to examine a specific region of the electromagnetic spectrum using very different technologies. Dr. Charles Pellerin, NASA's Director, Astrophysics invented and developed the program.
Contents [hide]
1 Great Observatories
2 History of the program
2.1 Hubble telescope program
2.2 Gamma ray program
2.3 Chandra X-ray history
2.4 Spitzer history
2.5 Great Observatory origin
3 Strengths
4 Impact
5 Synergies
6 Successors to GO instruments
7 Later programs
8 Gallery
9 See also
10 References
11 External links
Great Observatories[edit]
The Hubble Space Telescope (HST) primarily observes visible light and near-ultraviolet. It was launched in 1990 aboard Discovery during STS-31. A servicing mission in 1997 added capability in the near-infrared range and one last mission in 2009 was to fix and extend the life of Hubble which resulted in some of the best results to date.
The Compton Gamma Ray Observatory (CGRO) primarily observed gamma rays, though it extended into hard x-rays as well. It was launched in 1991 aboard Atlantis during STS-37 and was de-orbited in 2000 after failure of a gyroscope.
The Chandra X-ray Observatory (CXO) primarily observes soft x-rays. It was launched in 1999 aboard Columbia during STS-93 and was initially named the Advanced X-ray Astronomical Facility (AXAF).
The Spitzer Space Telescope (SST) observes the infrared spectrum. It was launched in 2003 aboard a Delta II rocket and was called the Space Infrared Telescope Facility (SIRTF) before launch.
Of these satellites, only the Compton Gamma Ray Observatory is not currently operating; one of its gyroscopes failed, and NASA ordered it to be de-orbited on June 4, 2000. Parts that survived reentry splashed into the Pacific Ocean. Hubble was originally intended to be retrieved and returned to Earth by the Space Shuttle, but the retrieval plan was later abandoned. On October 31, 2006 NASA Administrator Michael D. Griffin gave the go-ahead for a final refurbishment mission. The 11-day STS-125 mission by Atlantis, launched on 11 May 2009,[1] installed fresh batteries, replaced all gyroscopes, replaced a command computer, fixed several instruments and installed the Wide Field Camera 3 and the Cosmic Origins Spectrograph.[2]
Spitzer was the only one of the Great Observatories not launched by the Space Shuttle. It was originally intended to be so launched, but after the Challenger disaster, the Centaur LH2/LOX upper stage that would have been required to push it into a heliocentric orbit was banned from Shuttle use. Titan and Atlas rockets were canceled for cost reasons. After redesign and lightening, it was launched by a Delta II rocket instead.
QMRThe history of Native Hawaiians, like the history of Hawaii, is commonly classified into four major periods:
the pre-unification period (before c. 1800)
the unified monarchy and republic period (c. 1800 to 1898)
the US territorial period (1898 to 1959)
the US statehood period (1959 to present)
Κρήτης), one of the 13 regions of Greece which were established in the 1987 administrative reform.[19] With the 2010 Kallikratis plan, the powers and authority of the regions were redefined and extended. The region is based at Heraklion and is divided into four regional units (pre-Kallikratis prefectures). From west to east these are: Chania, Rethymno, Heraklion, and Lasithi. These are further subdivided into 24 municipalities.
The region's governor is, since 1 January 2011, Stavros Arnaoutakis, who was elected in the November 2010 local administration elections for the Panhellenic Socialist Movement.
QMRPerhaps the most striking extant structures to date are the ruins of Persepolis, a once opulent city established by the Achaemenid king, Darius the Great for governmental and ceremonial functions, and also acting as one of the empire's four capitals. Persepolis, would take 100 years to complete and would finally be ransacked and burnt by the troops of Alexander the Great in 330 B.C.E.[4] Similar architectural infrastructures were also erected at Susa and Ecbatana by Darius the Great, serving similar functions as Persepolis, such as reception of foreign dignitaries and delegates, performance of imperial ceremonies and duties, and also housing the kings.
Persepolis is the Latinized version of the Old Persian name, "Parsa" literally meaning the "city of Persians." Another spectacular achievement of the Achaemenids, Persepolis became one of the four capitals of the empire. Initiated by Darius the Great around 518 B.C.E., it would grow to become a center for ceremonial and cultural festivities, a center for dignitaries and visitors to pay homage to the king, a private residence for the Persian kings, a place for satraps to bring gifts for the king in the Spring during the festival of Nowruz, as well as a place of governance and ordinance.[9] Persepolis's prestige and grand riches were well known in the ancient world, and it was best described by the Greek historian Diodorus Siculus as "the richest city under the sun".[5]
A recreation of the details of the four winged figure in Olympic Park, Sydney. Note the details of the two-horned crown
QMRNaqsh-e Rustam (Persian: Naqŝe Rostam Persian pronunciation: [næɣʃeɾosˈtæm]) is an ancient necropolis located about 12 km northwest of Persepolis, in Fars Province, Iran, with the best group of ancient rock reliefs in Iran cut into the cliff, from both the Achaemenid and Sassanid periods. It lies a few hundred meters from Naqsh-e Rajab, with a further group of Sassanid reliefs.
Four tombs belonging to Achaemenid kings are carved out of the rock face at a considerable height above the ground.
The tombs are known locally as the 'Persian crosses', after the shape of the facades of the tombs. The entrance to each tomb is at the center of each cross, which opens onto to a small chamber, where the king lay in a sarcophagus. The horizontal beam of each of the tomb's facades is believed to be a replica of the entrance of the palace at Persepolis. The order of the tombs in Naqshe-e Rustam, from left to right is: Darius II, Artaxerxes I, Darius I, Xerxes I
Panorama of Naqsh-e Rustam. The order of the tombs in Naqshe-e Rustam, from left to right is: Darius II, Artaxerxes I, Darius I, Xerxes I
The fourth tomb is farther away than the other three. The fourth is always different from the other three
Description[edit]
Badly damaged and with its once jewelled front missing, the Brussels Cross takes the form of a large piece of cross-shaped wood covered with a silver plate bearing medallions engraved with the evangelists' symbols at the end of the arms and an Agnus Dei at the center. Across the arms the artist has inscribed his name in large Latin letters: + Drahmal me worhte (‘Drahmal made me’). An inscription around the edges reads: + Rod is min nama; geo ic ricne Cyning bær byfigynde, blod bestemed (‘Rood is my name. Trembling once, I bore a powerful king, made wet with blood’). These lines bear a close relationship to ll. 44 and 48 in the Old English poem, 'The Dream of the Rood'. This is followed by a common form of dedication: þas rod het Æþmær wyrican and Aðelwold hys beroþo[r] Criste to lofe for Ælfrices saule hyra beroþor (‘Æthlmær and Athelwold, his brother, ordered this rood to be made so as to praise Christ for the soul of Ælfric, their brother’). The Anglo-Saxon inscription is contained on a silver strip which runs around the edges of the cross. It is written not in runes, but in Roman letters, in a curious mixture of Latin-style majuscules and minuscules. The letters 'NE' of ricne, 'NG' of cyning and 'ME' of bestemed are written as ligatures. Although it has not proved possible to identify with any certainty the persons named in the inscription, the text is in late West-Saxon which would ascribe it to the late tenth century or perhaps later.
Provenance[edit]
The Brussels Cross and its two-line inscription in Anglo-Saxon verse were first brought to public attention in modern times by H. Logeman in 1891. Traditionally reputed to contain the largest extant fragments of the True Cross, it has been preserved at the Cathedral of SS. Michel and Gudule since the middle of the seventeenth century. The cross is 46.5 by 28 cm. (18.3 by 11 inches) in size. The front was once covered by a jewelled gold plate, probably taken away by French soldiers under Dumouriez in 1793; the back is still covered with silver, with the symbols of the four evangelists at the ends of the four arms and the symbol of the Agnus Dei in the centre. The earlier Lothair Cross is a comparable work that is still intact. The name of the craftsman, Drahmal, is probably Norse and from the northern England, but nothing more can be deduced about him. Judging from the language of the inscription as well as from the epigraphy and the style of the images, the cross most likely dates from the beginning of the 11th century. The images are in a "stolid" version of the early "Winchester style".[1]
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.
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