Leonhard Euler | An Introduction

Leonhard Euler | An Introduction Born in Basel, Switzerland on 15th April 1707, Leonhard Euler was arguably the brightest mathematician of all time. The Swiss mathematician and physicist is considered a pioneer in many fields of mathematics. He introduced a lot of the mathematical terminology and notation used today and he is considered the father of mathematical analysis where, for instance, he introduced the notation of a mathematical function, f(x). His contributions to the field of mathematics are in analytic and differential geometry, calculus, the calculus of variation, differential equations, series and the theory of numbers. In physics, although really all his contributions to mathematics apply to physics, he introduced both rigid body mechanics and analytical mechanics (Kline, 401-402). Born to Paul Euler and Margarete Bruckner, Leonhard was the first of six children. He grew up in Riehen but attended school in Basel. Although mathematics was not taught in his school his father had kindled his interest in the subject (Paul Euler had been friends with another great mathematician at the time, Johann Bernoulli) by giving him lessons at home. Euler entered university at the age of 13 at the University of Basel. Although his official courses of study were philosophy and law, Euler met with Johann Bernoulli who advised Euler and gave him help with his mathematical studies on Saturday afternoons (Stillwell, 188). Euler lived and worked mainly in Russia and Germany. First he joined the faculty at St Petersburg Academy of Sciences were he worked at first in the medical department then he was quickly promoted to a senior position in the department of mathematics through the influence of his friend Daniel Bernoulli. He also helped the Russian government on many projects including serving in the Russian navy as a medical Lieutenant. After the death of Catherine I in1740 and because of the tough conditions that ensued, Euler moved to Germany at the invitation of Prussian King, Frederick II to the Prussian Academy of Science were he stayed for the next 25 years of his life. Euler gave much service to the Academy which compensated him generously. He sent most of his works to be published there, served as a representative as well as advising the Academy on its many scientific activities. It is there that he reached the peak of his career writing about 225 memoirs on almost every topic in physics and m athematics (Varadarajan, 11). Euler returned to St. Petersburg in 1766 under the invitation of the then czarina Catherine the Great (Catherine II) to the St Petersburg Academy. During this period he lost almost all his eyesight through a series of illnesses becoming nearly totally blind by 1771. Nevertheless, his remarkable memory saw him writing about 400 memoirs during this time. It is said that he had a large slate board fixed to his desk where he wrote in large letters so that he could view dimly what was being written. He died on the 18th day of September 1783 due to cerebral hemorrhaging. It is also recorded that he was working even to his last breath; calculations of the height of flight of a hot air balloon were found on his board (Varadarajan 13). Eulers contribution to Mathematics and Physics was a lot. His ideas in analysis led to many advances in the field. Euler is famously known for the development of function expressions like the addition of terms, proving the power series expansion, the inverse tangent function and the number e: ∑ (xn/n!)= lim ((1/0!) + (x/1!) + (x2/2!) +†¦+ (xn/n!) ) =ex The power series equation in fact helped him solve the famous 1735 Basel problem: ∑ (1/n2) = lim ((1/12) + (1/22) + (1/32) + †¦+(1/n2)) = Ï€2/6 He introduced the exponential function, e, and used it plus logarithms in analytic proofs. He also defined the complex exponential function and a special case now known as the Eulers Identity: eiφ = cos φ + isin φ And eiÏ€ + 1= 0 (Eulers Identity) In fact, De Moivres formula for complex functions is derived from Eulers formula. Similarly, De Moivre is recognized for the development of calculus of variations, formulating the Euler-Lagrange equation. He was also the first to use solve problems of number theory using methods of analysis. Thus, he pioneered the theories of hyperbolic trigonometric functions, hyper geometric series, the analytic theory of continued fractions and the q-series. In fact, his work in this field led to the progress of the prime number theorem (Dunham 81). The most prominent notation introduced by Euler is f(x) to denote the function, f that maps the variable x. In fact he is the one who introduced the notion of a function to the field of mathematics. He introduced, amongst others, the letter ∑ to mean the sum, Ï€ for the proportion regarding the perimeter of a circle up to the span or the diameter, i for the imaginary unit, √(-1) and the e (2.142†¦) to represent the base of the natural logarithm. Euler also contributed to Applied Mathematics. Interestingly enough, he developed some Mathematics applications into music by which he hoped to incorporate musical theory in mathematics. This was however, not successful. This notwithstanding, Euler did solve real-world problems by applying analytical techniques. For instance, Euler incorporated the Method of Fluxions which was developed by Newton together with Leibnizs differential calculus to develop tools that eased the application of calculus in physical problems. He is remembered for improving and furthering the numerical approximation of integrals, even coming up with the Euler approximations. More broadly, he helped to describe many applications of the constants Ï€ and e, Euler numbers, Bernoulli numbers and Venn diagrams. The Euler-Bernoulli beam equation (one of the most fundamental equations in engineering) is just one of the contributions of the mathematician to physics. He used his analytical skills in classical mechanics and used the same methods in solving celestial problems. He determined the orbits of celestial bodies and calculated the parallax of the sun. He differed with Newton (then the authority in physics) on his corpuscular theory of light. He supported the wave theory of light proposed by Hugens. Eulers contributions to graph theory are at the heart of the field of topology. He is famously known to have solved the Seven Bridges of Konigsberg problem, the solution of which is considered the first theorem of planar graph theory. He introduced the formula V-E+F=2 It is a mathematical formula relating vertices, edges and faces of a planar graph or polyhedron. The constant in the above formula in now called the Euler characteristic. Euler is also recognized for the use of closed curves in the provision of explanation concerning reasoning which is of syllogistic nature. Afterwards the illustration or diagrams were referred to as the Euler diagrams. The Number Theory is perhaps the most difficult branch of mathematics. Euler used ideas in analysis linking them with the nature of prime numbers to provide evidence that the total of all the reciprocals of prime numbers diverges. He also discovered the link between the primes Riemann zeta function, what is now called the Euler product formula for the Riemann zeta function. Euler made great strides in the Lagrange four-square theorem while proving Fermats theorem on the sum of two squares, Fermats Identities and Newtons identities. Number theory consists of several divisions which include the following: Algebraic Number Theory, Combinational Number theory, Analytic Number Theory, Transcendental number theory, Geometric number theory and lastly we have the Computational Number Theory. For his numerous contributions to academia, Euler won numerous awards. He won the Paris Academy Prize twelve times over the course of his career. He was elected as a foreign member, in 1755, of the Royal Swedish Academy of Sciences while his image has been featured on many Russian, Swiss and German postage stamps. Above all, he was respected greatly amongst his academic peers demonstrated by a statement made by the great French mathematician, Laplace to his students to read Euler since he was the master of them all (Dunham xiii). Though not all of the proofs of Euler are satisfactory in regard to the current standards or principles used in mathematics, the ideas created by him are of great importance. They have set a path to the current mathematical advancements. To conclude, we can therefore say that Euler is a very significant person in the development and advancement of Mathematics. His work has contributed a lot to mathematics up to the current period. References Dunham, William. Euler: The Master of Us All. Dolciani Mathemathical Expositions Vol. 22. MAAA, 1999. Kline, Morris. Mathematical Thoughts from Ancient to Modern Times, Vol 2. New York: Oxford University Press, 1972. Stillwell, John. Mathematics and its History. Undergraduate Texts in Mathematics. Springer, 2002. Varadarajan, V. S. Euler Through Time: A New Look at Old Themes. AMS Bookstore, 2006.

Literacy Essay -- Education Learning Papers

Literacy Why is literacy of such interest to postsecondary teachers of writing? If "literacy," as it might be defined by someone outside the field of English studies, is "the ability to read and write," then why are we interested in it when our own students presumably acquired this ability in the distant past, about the time they learned to tie bows in shoelaces? That we are interested in literacy, I take it, is obvious from the proliferation of books with the word in their titles, of conferences on topics in literacy (the Modern Language Association has now held two), and of review essays such as this one, commissioned by the editors of a journal that purports to deal in issues relevant to "composition theory" and "advanced composition" at the college level. Defining Literacy I might answer my opening question by redefining "literacy" from within English studies in such a way as to make it more complex and problematic, and thus to question the presumption that college students have already acquired it. Indeed, in these proliferating discussions of literacy, its simple definition as the ability to read and write is usually rejected at the outset. But in attempting to go beyond the simple definition, scholars begin to diverge. Consider, for example, the variety of essays collected under the title, The Right to Literacy (1990), a title which implies a unitary conception of literacy and a contest only over who possesses the desired object. In this volume, Andrea A. Lunsford, Helene Moglen, and James Slevin collect twenty-nine papers from the 1988 MLA "Right to Literacy" conference. Most of the essays, therefore, are short; and ranging through them, one gets a sense of the heterogeneous mixture of topics that accrue for Engli... ...Discourse Community." Curriculum Inquiry 12 (1982): 191-207. ---. "Literacy in Culture and Cognition." A Sourcebook for Basic Writing Teachers. Ed. Theresa Enos. New York: Random, 1987. 125-37. Brandt, Deborah. Literacy as Involvement: The Acts of Writers, Readers, and Texts. Carbondale: Southern Illinois UP, 1990. Hirsch, E.D., Jr. Cultural Literacy: What Every American Needs to Know. 2nd ed. New York: Vintage, 1988. Kintgen, Eugene R., Barry M. Kroll, and Mike Rose, eds. Perspectives on Literacy. Carbondale: Southern Illinois UP, 1988. Lunsford, Andrea A., Helene Moglen, and James Slevin, eds. The Right to Literacy. New York: MLA, 1990. Stuckey, J. Elspeth. The Violence of Literacy. Portsmouth, NH: Boynton, 1991. Taylor, Denny, and Catherine Dorsey-Gaines. Growing Up Literate: Learning from Inner-City Families. Portsmouth, NH: Heinemann, 1988.

Is Hip-Hop Culture Harming Our Youth?

Is Hip-Hop Culture Harming Our Youth? Hip-hop culture is everywhere. The culture, which encompasses rapping, deejaying, break-dancing and graffiti-writing, has become so popular that it has entered mainstream fashion and modern language. It doesn't stop there. The culture permeates everything from TV commercials to toys to video games. Currently, there is even a hip-hop exhibit at the Brooklyn Museum of Art. You name it, and hip hop is there representing. However, hip hop's most potent form is its rap music–embraced by urban Blacks and suburban Whites alike.It is raw self-expression that sometimes features profane lyrics, misogyny and violence. The music, along with rap videos that often present a disturbing mix of rap, hip-hop dance styles, fashion and language, leave many people asking: â€Å"Is hip-hop culture harming our youth? â€Å". â€Å"The hip-hop culture is just like electricity,† civil rights leader the Rev. Al Sharpton told JET. â€Å"It can be used nega tively or positively. The same electric current that lights up your house can also electrocute you.It is the misuse of hip-hop culture to attack our women and promote violence. We must encourage the proper use of hip-hop culture. We are all influenced by the hip-hop generation. † Sharpton, who recently hosted a special summit on social responsibility in the hip-hop industry, labeled gangsta rappers â€Å"well-paid slaves. † Advertisement â€Å"Don't let some record executive tell you that cursing out your mama is in style. Anytime you perpetuate a slave mentality that desecrates women and that desecrates our race in the name of a record†¦. I consider you a well-paid slave. Sharpton labeled the fashion of these rappers–loose-fitting pants and sneakers without shoelaces–prison clothes. Sharpton was joined at the summit by some of the industry's superstars, including Master P, Sean â€Å"Puffy† Combs, Chuck D and RZA. No Limit Records' CEO-rapper Master P apologetically admitted that some of his lyrics might be offensive to women. â€Å"Everything that came from me like that came out of ignorance. I hope to edit myself in the future,† he reportedly said during the event. However, he asserted, â€Å"I don't believe any form of entertainment is harming our youth.It is up to parents to raise their own children and teach them. Blaming entertainment is a scapegoat. † Dr. C. DeLores Tucker, chair of the National Political Congress of Black Women, Inc. , who has been a strong critic of hip-hop culture for more than a decade, continues to cite its reported negative influence over our youth. â€Å"The glorification of pornography, wanton disregard for civil authority, misogynistic disrespect for women and a penchant for violence are the unintended impact of hip-hop culture on today's youth,† the activist revealed. I say unintended, because hip hop †¦ was intended to celebrate the revival of the age-old rhym ed recitations of life's problems and aspirations set to music. † Unfortunately, somewhere along the way, some unscrupulous elements hijacked this influential conduit to our youth and loaded it with the evil and debasing, hate-driven messages in the lyrics we now know as gangsta rap. Hence the artistry of the rappers in the streets is used by the gangstas in the suites to spread cultural garbage among our youth. Hip-hop music mogul Russell Simmons, who dubs himself the â€Å"grandfather of hip hop,† says the culture has been helpful in allowing others to understand Blacks' inner-city plight. â€Å"It is not going to go away. I will stand by the door to keep it from being censored. It is easy to try to put a lid on what you don't like. But the real test, if you are freedom-loving people, is to protect even that which we don't like from the censorship by the government,† he explained. He points out the positive contributions from the hip-hop culture. The slam poetr y settings evolved out of the hip-hop community. Some of it does not have any curse words. Young folks have found a way to express themselves that was really inspired by rap. Kids are writing. They are thinking; brilliant thoughts are coming out in this creative poetry. † Concludes Simmons, â€Å"The hip-hop culture will evolve in ways that will be known as a significant art. The rap artists are not the poets that they are yet to become, but they are indeed poets. â€Å"

Children Always Need Love, Compassion, Support And Empathy...

Chase Sullivan DR. Earnest FSL November 9, 2016 Fatherless Children always need love, compassion, support and empathy from their parents when growing up. They are better off without a father in certain circumstances such as abuse, but both boys and girls will suffer a negative effect as they develop into adults without a father in any situation. No one can agree that growing up fatherless is far from the worst thing other than Michele Weldon from the New York Times, and her article â€Å"When Children Are Better off Fatherless† as she states: In the cases where the father is far from heroic – even abusive – his absence is also the absence of the chaos, anger, pain and disruption he would bring to his family. Americans encourage women to leave abusive partners, but mothers who do this end up in a class we shame and pity. The government itself sends the message that children are better off with a father. The reality is, many children are better off without their fathers.† Ms. Weldon is right in the fact that children are better off without abusive fathers as they regularly risk beatings, psychological damage, and sexual abuse as they are near their abusive father. A child’s stress limit will always be pushed to unsafe boundaries as they constantly feel the pressure not to upset or anger their father and the fear of face unintended consequences. An unsafe home is not a place for any child to be nurtured or grow up in. Unfortunately, leaving the abusive husband or loosing aShow MoreRelatedParenting Styles And Their Effects On Children1572 Words   |  7 PagesParenting Styles and Their Effects on Children Parents play a key role in their children’s lives, including supervision, involvement, love, support, comfort, and a wide variety of discipline and punishment. The relationship between parenting styles and child is vital and impacts the child’s physical, mental, and emotional well-being. Parenting involves two dimensions, demandingness and responsiveness sometimes referred to as control and warmth. With the use of these dimensions four parenting stylesRead MoreIs The Family Dynamic?1767 Words   |  8 Pagestraditional family consists of a mother, father, children, and maybe a pet. A healthy family is based on respect for one another, honesty, trust, communication, acceptance, and unconditional love. A healthy home and family life fosters positive mental attitudes, good self-esteem, predictable and stable routines, and an unwavering bond between the members. In a healthy environment, the hierarchy is strong and children know that they are loved by the parents and, in turn, there is a reciprocated respect†¦Read MoreThe Pursuit Of Happyness Movie Review958 Words   |  4 Pagesdirected by Gabriele Muccino. The film narrated the life story of Chris Gardner, a single father struggling to support his son and accomplish his dreams. 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Students walk down the halls every day with their peers, never knowing what goes on after the dismissal bell rings, and they go their separateRead MoreThe Importance Of Social Work1704 Words   |  7 Pages The cornerstone of Social Work, comes from the kind, caring, supporting and loving the act of compassion for others. With the focus on helping others to better themselves for a better future. I originally became interested in the Social Work field when I started with the Department of Human Services-Child Welfare Services Unit as a Case Support Aide. I was drawn to the idea of helping people, in fact helping people has always been an important part of my life. As I advanced on in my career the passionRead MoreTherapy Vs Crisis Intervention1410 Words   |  6 Pagesremoval of a sibling group from their single parent drug addicted mother. The goal of crisis intervention in this case would be to minimize risk to the children and place them in the home of a relative or foster care. The mother would then be assessed, given a treatment plan, and provided a care plan by a psychotherapist to try, at the very least, to establish visitations as soon as possible. (This would aid in to minim izing further abandonment trauma to the children.) Psychotherapy in this caseRead MoreContemporary Australian Society Of The 1940 S Australian Dream1877 Words   |  8 Pages each aging population, each child that learns to be a citizen, a patriot. This empathy seems obvious but I’m asking you all to think intricately! Ponder over little things; the contagion of yawning, or of laughter 5, www.huffingtonpost.com/entry/contagious-behaviors_us_56f400d7e4b04c4c37616ff4 the urge to wince when someone else trips over and our often innate urge to go to their aid. Perhaps to some degree, empathy does occur on a cognitive level? 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The Essence Of Existence Joseph Conrad s Heart Of Darkness

Brandon Banks AP Literature Per. 3 Mr. Backen 16 December 2015 The Essence of Existence The nature of human reality is one theory that has sent philosophers on a never-ending journey, in which they have tried to explain, define and hypothesis this theory. In turn, our civilization has seen philosophies rise and fall such as Intellectualism, Transcendentalism, and Existentialism. As a result, our human history is littered with philosophies that tried to establish their own comprehensive system of idealisms and ideologies. Joseph Conrad’s Heart of Darkness, published in 1899, is one of the first novellas to unequivocally evaluate and scrutinize the tyrannical imperialism that conquered the African nation, specifically the Congo. However, Conrad illustrated this dense novella in a particular method, in which he employed an anonymous passenger, who listens to Marlow’s story, and reiterates the story to the reader. In turn, the reader holds a certain distance from the story that is maintained throughout the whole novella. Conrad compose d an interesting passage that encompasses all the previously stated sentiments, however, he deliberately placed this passage towards the beginning of the novella as to enthrall the reader. At this particular moment, the fast-talking Brickmaker is further elaborating on his pursuit to be a manager in this ivory craze to a disinterested Marlow, who continues to hypothesize on the very essence of existence. This conceptualization of life and theShow MoreRelated Portrayal of Women in Joseph Conrads Heart of Darkness Essay874 Words   |  4 PagesPortrayal of Women in Heart of Darkness      Ã‚  Ã‚   In his novel, Heart of Darkness, Joseph Conrad exposes the evil lurking in the soul of mankind; but this corruption is hidden from the innocent European women. Conrad?s novel depicts women simplistically in black and white ? without any confusing shades of gray. 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But itRead MoreAnalysis Of Joseph Conrad s Heart Of Darkness1555 Words   |  7 PagesAlthough the author Joseph Conrad never met the German philosopher Gottfried Wilhelm Leibniz, who died more than a century before Conrad’s birth, their distinct philosophies still have numerous points of intersection, suggesting some fundamental truths within the structure of the human reality. Through the novella, Heart of Darkness, Conrad details his perspectives on the faults of man and reality as a whole, with views often coinciding with many of Leibniz’s own, as found in his numerous philosophicalRead More A Comparison of the Power of Will in Heart of Darkness and Apocalypse Now1893 Words   |  8 PagesThe Power of Will in Heart of Darkness and Apocalypse Now      Ã‚  Ã‚  Ã‚   The story of Heart of Darkness was adapted to film after many failed attempts. (Hearts of Darkness, Coppala E.). Finally, director Francis Coppala collaborated with his friend John Milius on writing a screen play for Conrads masterpiece. The two came up with Apocalypse Now, utilizing a more modern setting than the original story which was based in imperialistic Europe. The modern setting was that of the Vietnam war. ApocalypseRead More journeyhod In Quest of Self in Joseph Conrads Heart of Darkness4090 Words   |  17 PagesIn Quest of Self in Heart of Darkness      Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In Conrads Heart of Darkness Marlow comes to the Congo for experience and self in the ancient belief that a man is shaped by what he does, that character is formed by what happens to one. But surrounding all of mans efforts in the Congo is a presence: Kurtz listened to it and went mad, and Marlow recognizes it but refuses to listen, neutralizes the appeal of the unknown and survives Kurtz, who succumbed to the fascinating wilderness.   Read MoreThe Nature Of The African Landscape10552 Words   |  43 PagesThe Landscape: In this section, I seek to investigate how the nature of the African landscape has been depicted in Heart of Darkness. Questions such as 1.) How the Orientalist others the foreign landscape 2.) What is the psychological influence of the African landscape on the European colonisers? 3.) Does the psychological influenceon the Whites similar to that of the Blacks? 4.) And, what are the consequences of that psychological influence on the White invaders and the natives? These argumentsRead MoreMy research paper is entitled, Analyzing Heart of Darkness through a Feminist Lens. Through this3100 Words   |  13 PagesMy research paper is entitled, Analyzing Heart of Darkness through a Feminist Lens. Through this paper, I will investigate and examine Heart of Darkness by means of Feminist Criticism and literary theory. I aspire to thoroughly analyze the entire narrative, in order to pull out and pinpoint various aspects and examples linked to feminist theory. I want to investigate and spotl ight specific occurrences, in the novel, where characteristics of Feminist Criticism can be found or applied. I specificallyRead MoreThe s Theory Of Evolution2321 Words   |  10 Pagesand wouldn’t accept the idea of originating from such savages. Similarly, Sartre questioned the existence of man from an existentialist’s standpoint. He argues that as an existentialist, it is common belief that existence comes before essence. 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Essay How Romantic Was William Blake - 1517 Words

The time period typically associated with the Romantic Poets and writers was one of the most turbulent to hit Europe ever. With the French Revolution sweeping the fields of Alsace, Lorraine and beyond, most monarchs, including those in England were wary of the new notions that were becoming common place among the commoners. Not since the Reformation of the 16th century was the continent in more turmoil. Yet with this build up of angst came a fertile bed for a new style of writing to grow in. This new style embraced many things that were ignored for one reason or another in the previous period of writing among the Augustans. To generalize, but not trying to be an idiot, one would have to attribute a heightened sense of nature to the†¦show more content†¦The aforementioned characteristics are what are generally associated with Romantic. However, there must be more than a simple synopsis in an attempt to define what the Romantics were all about. The official definition a s seen in the Oxford English Dictionary is, Of a fabulous or fictitious character; having no foundation in fact (OED def 2). Now if in keeping with this definition, are we to assume that the Romantic writers were writing works that had no basis in real life and fact and only on fuzzy-minded ideals? This does not seem to be the case at all. Actually the opposite is probably the case. The Romantics used what they saw in life and nature to symbolize what they felt themselves. In this way, they could create elaborate metaphors and link seemingly incongruent things to each other. As Perkins states in the General Introduction, [t]he illusion was that in lyrics one heard not a fictional, but a real person speaking on a real occasion...in reading a lyric, was the speakers inner life, his or her mind or emotion (Perkins 13). In this manner, Romantics were able to convey their emotions and feelings through a third person or narrator. The lyrics themselves were generally not as formula ic as the pre-cursor Augustans, but what was lost in form was made up forShow MoreRelatedRomanticism in The Marriage of Heaven and Hell by William Blake1393 Words   |  6 PagesRomanticism in William Blakes Poem William Blake was a poet, painter, and a printmaker all during the period in literature known as the Romantic time period. The Romantic time period, also known in Literature as Romanticism began in Europe, mainly France and Britain around the 1800s (Barker) and it was first defined as a tool to in literature and literary criticisms (Galitz). The Romantic period did not just focus on literature, but also on the subjects of art and knowledge which was fueled by theRead MoreInnocence and Experience Essay1422 Words   |  6 PagesAs a new way to criticize the Romantic period, desperate times call for desperate measures and it did through the use of children’s point of view in Romantic poetry. A period of fifty years called Romantic period included the French Revolution, the American Revolution and wars of national independence in Europe. William Blake, one of well known Romantic poets, commented on his society by viewing it through the child’s eyes in the two sets of â₠¬ËœSongs of innocence and of Experience’. It is said thatRead MoreWilliam Wordsworth And The Echoing Green905 Words   |  4 PagesWhile researching about poets in the Romantic period that created beautiful poetry filled with overflowing powerful feelings designed to capture the reader’s imagination in nature. These Poets often placed the literature they were studying into a documented context by discussing the important events in which the literary works were published (â€Å"I Wandered Lonely as a Cloud† by William Wordsworth and â€Å"The Echoing Green† by William Blake). 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Medieval life Essay Example For Students

Medieval life Essay I will consider five different characters in this study of medieval life. These will be the Shipman who gives a view of the importance of shipping in medieval times, the Knight who is a good example of military life and its importance at the time, the Miller who gives a view of agriculture at the time which was very important because it was the main form of employment, the Parson who an the example of what the church was supposed to be like and the Pardoner who is a good representation of the corruptness in the church at the time. From these I hope to give a good slice of medieval life at the time of Chaucer. With many a tempest hadde  his berd been shake  The Shipman like most of his fellow pilgrims is very skilled at his profession and has spent a long time in perfecting it. He is a master mariner, woninge fer by weste dwelling from the west of England, with a wide experience and ability. He comes from Dartmouth, he was of Dertemouthe, and has a ship called the Magdelene His understanding of coasts and tides is very good. Chaucer suggests by the dagger hanging under his neck that he has an easy conscience towards pirates and theft, with no pity for his victims. When he is away in other provinces he depends on himself because there are no laws or any justice to protect him, he must enforce his own as he wishes. He chooses a very harsh and violent way. He is very self-sufficient, he uses no charts or maps because he navigates using his compass and knowledge of the stars and the moon. Chaucer makes us recognise the strength of his character, he is tanned and hardened by exposure, and deeply immersed in the craft of the sea. The Shipman is a coarsely dressed man who gives a glimpse of the medieval sea dog. A stout carl  The Miller is my next character, he isnt really portrayed as a human but as a wild animal or a beast. He is quite a spectacle with his powerful muscular arms, frightening and ugly looks, black bristles protruding from his nose along with its wart, sly nature and his coarse brutality and insensitiveness. His face is more like that of a Gargoyle. He likes to sing a lot and play his bagpipes with an awful din; his voice isnt pleasant either with its raucous sound and drone. His voice is propelled by his giant, cavernous mouth which is like a furnace a great forneys with his hot breath, like that of a dragon. He also has the unusual ability to knock down doors with his head, possibly for breaking in- is he a bit of a thief? Chaucer mentions his thumb of gold which shows that he, like the Shipman, is skilled at his profession. It may have been have been a common and almost expected occurrence for a miller to take some of the grain to sell for himself. The Miller after all has a fiery red beard like that of a fox which is traditionally thought of as a sly and cunning animal. He is quite a source of entertainment for the other travelers because he is really full of himself, he is good at telling stories but as might be expected these are mainly of sin. a most distinguished man  The knight is a very noble man and is a good example of the importance of the military in medieval times. He spends much of his time going off to crusades in far of lands. He is very wealthy and a large ransom would be paid out for him if he were caught. He is in sharp contrast with many of the pilgrims as he is the only one of true noble birth and is very well off. At the time there was a big difference between the poor village folk and the nobles who had a  lot of power over their land. A knights life was very much truth and chivalry, this was full of wars and conquest. Such knights as him would have been bringing in a lot of money into the country from pillaging in crusades.  a good man was ther of religioun .ueeb8dff622222dff7a694973a5d05454 , .ueeb8dff622222dff7a694973a5d05454 .postImageUrl , .ueeb8dff622222dff7a694973a5d05454 .centered-text-area { min-height: 80px; position: relative; } .ueeb8dff622222dff7a694973a5d05454 , .ueeb8dff622222dff7a694973a5d05454:hover , .ueeb8dff622222dff7a694973a5d05454:visited , .ueeb8dff622222dff7a694973a5d05454:active { border:0!important; } .ueeb8dff622222dff7a694973a5d05454 .clearfix:after { content: ""; display: table; clear: both; } .ueeb8dff622222dff7a694973a5d05454 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ueeb8dff622222dff7a694973a5d05454:active , .ueeb8dff622222dff7a694973a5d05454:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ueeb8dff622222dff7a694973a5d05454 .centered-text-area { width: 100%; position: relative ; } .ueeb8dff622222dff7a694973a5d05454 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ueeb8dff622222dff7a694973a5d05454 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ueeb8dff622222dff7a694973a5d05454 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ueeb8dff622222dff7a694973a5d05454:hover .ctaButton { background-color: #34495E!important; } .ueeb8dff622222dff7a694973a5d05454 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ueeb8dff622222dff7a694973a5d05454 .ueeb8dff622222dff7a694973a5d05454-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ueeb8dff622222dff7a694973a5d05454:after { content: ""; display: block; clear: both; } READ: What is the Meaning of Life? EssayThe Parson is an example of what the church was supposed to stand for at the time. He is an embodiment of moral virtues which is what is missing in the church at the time which Chaucer expresses in the other pilgrims. With church being such a major part of everyday life compared to that of today so the corruptness is of major importance because a few people are making a lot of money from a lot of very poor people which is what the Pardoner is mainly about. He represents the truthful, patient faith that holds firm as standards collapse on all sides. There is a strong sense of personality that comes from the parson, what is a very humble per son who is very kind and Chaucer acknowledges thisa gentle pardoner The Pardoner is the contrast of the Parson. It is ironic that he is a gentle pardoner because he very much the opposite. He is the crumbling exterior of the church as the Parson holds up the middle. The Pardoner claims to have just come from the Vatican with fresh pardons for people to buy, of course he hasnt really but has just made them himself.He has yellow hair like wax which hangs straight down over his shoulders. He thinks he is in the height of fashion but is not. He has a satchel at his side which he has all his pardons in which are selling like hot cakes- al hoot. Chaucer uses him as the typical person who uses the church as their chance to make lots of money. He is mainly a confidence trickster, he tricks his apes. He is probably though in quite good favour with the church because he can persuade people to give money to the church. He can get as much money of a poor person as they will earn in one month. But despite all of this he does have respect for the church and is very well behaved there, he is very good at singing hymns. Life in Medieval times was very much based upon the Feudal system as demonstrated by the Knight. This consisted of the poor folk who owned land of the noble just like the humble ploughman who is the brother of the Parson. These nobles could gain knighthood that would involve doing and owning certain things and then proving devotedness to a lady. Chaucer gives a very strong contact with that of fourteenth-century England. Chaucers Canterbury Tales certainly prove the extent of the churches influence in the medieval persons life. But it was rotting away, filled with priests who would sooner mover to London for a good life than help their people like the Parson. Of this group of supposedly dedicated men and women, only the Parson-in social status and appearance the least distinguished of them all-remains true to his ideals. The worldliness of contemporary outlook and the declining spiritual authority of the church are evident in the pilgrimage itself. There was also a strong running of profession and apprenticeship, in the case of the Squire. The Shipman and the Miller are both very skilled at what they do, if not rather corrupt. There was a real need at the time to learn a skill because there was no real education and this could then be passed on to the next generation so they could continue the business. Times were very difficult then and the Shipman demonstrates how hardy these people were, with none of the basic technology we have today they had to cope without, just like the Shipman who is skilled at navigating without instruments and the Miller who can tell the quality of grain just by feeling it. These hard lives did lead some people to become thieves to make a living or just to have a better life; this had then spread to the church. .u91de04e14b09e5bff8bf454e102f82bb , .u91de04e14b09e5bff8bf454e102f82bb .postImageUrl , .u91de04e14b09e5bff8bf454e102f82bb .centered-text-area { min-height: 80px; position: relative; } .u91de04e14b09e5bff8bf454e102f82bb , .u91de04e14b09e5bff8bf454e102f82bb:hover , .u91de04e14b09e5bff8bf454e102f82bb:visited , .u91de04e14b09e5bff8bf454e102f82bb:active { border:0!important; } .u91de04e14b09e5bff8bf454e102f82bb .clearfix:after { content: ""; display: table; clear: both; } .u91de04e14b09e5bff8bf454e102f82bb { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u91de04e14b09e5bff8bf454e102f82bb:active , .u91de04e14b09e5bff8bf454e102f82bb:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u91de04e14b09e5bff8bf454e102f82bb .centered-text-area { width: 100%; position: relative ; } .u91de04e14b09e5bff8bf454e102f82bb .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u91de04e14b09e5bff8bf454e102f82bb .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u91de04e14b09e5bff8bf454e102f82bb .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u91de04e14b09e5bff8bf454e102f82bb:hover .ctaButton { background-color: #34495E!important; } .u91de04e14b09e5bff8bf454e102f82bb .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u91de04e14b09e5bff8bf454e102f82bb .u91de04e14b09e5bff8bf454e102f82bb-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u91de04e14b09e5bff8bf454e102f82bb:after { content: ""; display: block; clear: both; } READ: The Secret Life Of Bees EssayDespite this, though, the group of pilgrims whom Chaucer joins at southwark does not provide a complete cross-section of English society, but it is still very accurate. Their background of inns, farmyards, city streets and middle class houses has a very wide range. From the farms and benches of the poor to the walled gardens and banquets of the rich, Chaucer seems to have covered the whole texture of medieval life. Maybe this was what he was trying to show, a sort of record of life in his time. It is evident that these men and women were very individual due to the social and economic pressures, which had warped and shaped them. They have great self-confidence, which suggests a society whose growing wealth was encouraging the middle classes to assert themselves. For instants the Wife of Baths red stockings which are very bold due to her expensive tastes. The Miller defrauds his customers by stealing part of the corn which he grinds, and the Shipman mixes piracy and theft with his lawful affairs at sea.