Thursday, November 28, 2019

Conduction of The Holocaust

Introduction The Holocaust is the term used to denote the execution of more than six million Jews which was perpetrated by the National Socialist Germany Workers [Nazis] Party during the Second World War. Holocaust [Shoah] signifies the era of the reign of Adolf Hitler as the chancellor of Germany from 30 January, 1933 to 8th may, 1945.Advertising We will write a custom essay sample on Conduction of The Holocaust specifically for you for only $16.05 $11/page Learn More This genocide represented two-thirds of European Jewish population, and a third of the world Jewish population. Those Jews who were killed were victims of intentional and systematic efforts of the Nazi to annihilate all Jews in Europe, but not casualties of Second World War which devastate Europe (â€Å"Jewish virtual library,† par. 1). Following the success of the National Social Germany Workers Party in the 1932 elections, Adolf Hitler was appointed Germany chancellor. The Nazis, capitalized on the then unstable Germany government to gain an electoral foundation. The Nazis provoked conflict with the communist, organized numerous demonstrations, and conducted a ferocious propaganda crusade against its political rivals -the Weimar authority, and the Jews who they held accountable for the all the Germany evils (â€Å"Jewish virtual library,† par. 3). Why did it happen? Propaganda against Jews The common media the Nazis used for the campaign against the Jews was the Weekly Nazis newspaper, â€Å"The attacker.† At the bottom line of the front page of the newspaper, a slogan, â€Å"the Jews are our misfortune!† was inscribed in bold letters. The attacker often featured Jewish cartoons characterized with hooked-noses and ape statures. In fact about half a million copies of â€Å"The Attacker† were supplied per week (par. 4). Shortly after Hitler attained chancellorship, he organized for new elections in endeavors to acquire full power ov er Reichstag (parliament) for his party. The Nazis terrorized other parties using government’s resources. After the Reichstag house was burned down, the German’s democracy was placed in jeopardy. Immediately, the Nazi’s government eliminated various privileges including the sovereignty of press, freedom of expression, the right to assemble and the privilege for privacy. In the March 5 election the party succeeded by securing more than 50 percent parliament seats (par. 6). The Nazis immediately transformed their authority into dictatorshipvia the Enabling act passed on March 23. This act legitimized Hitler’s dictatorial ideas and allowed him to implement them over generally all areas. Additionally, the Nazis organized their propaganda machine, Der sturmer, and overshadowed their critics. In addition the put up a well organized military and police unit. Any opposition to the Nazis authority culminated to imprisonment in the concentration camps, which initia lly served as political prisoners (par. 7, 8).Advertising Looking for essay on history? Let's see if we can help you! Get your first paper with 15% OFF Learn More Eventually, Hitler gained full authority over Germany and reinforced his campaign against the Jewish community in Europe. The Nazis accused the Jews of contaminating pure German traditions with their â€Å"mongrel† and â€Å"foreign† exertion. They depicted an evil and cowardly impression of the Jews, as opposed to the Germans who they expressed as truthful, brave and industrious. The Nazis alleged the Jews for the weakened German’s economy and civilization, because they occupied considerable positions in finance, commerce, the press, art, theatre and literature (par. 9). Another element which contributed to the holocaust is race perceptions in which there was a misconception that the superior race was the â€Å"Aryans† which signifies the Germans (Leni Yahil 36). Anti-Semitic myth s It is believed that the holocaust was perpetuated by the sentiment European Christians had about the Jews. These sentiments are proven by various anti-semantic myths that were held across Europe (Ashliman, par. 1). These myths portrayed the Jews as very brutal and sacrilegious people, causing them to be hated by the rest of the communities in Europe. The proceeding paragraphs reviews one of the anti-Semitic myths. Most of these legends were propagated in Germany which explains why Germany was the setting of the holocaust. I am going to review one of the twelve anti-Semitic legends to emphasize why there was such ferocious hate for the Jews. â€Å"The Jews’ stone,† is a story of a peasant who sold his child to some Jews. The Jews then took the child and brutally persecuted her on a large stone till death. From hence forth the stone was denoted the Jews’ stone. The mother of the child who was working at the farm sensed that a terrible thing has befallen her chil d. She hurried home to inquire about the child from the father who told her, he had sold the child. In the mean time the money turned to leaves. The mother went to look for the child and she found her hanged on a tree and brought it down and took it to the church. The father was shocked and he lost his mind and shortly died. The stone was placed at the grave side of the child and it is believed that it is still lying there up to the present. Later on a shepherded shopped the tree down, but he broke his leg when trying to carry it home and he later died of the wound (Ashliman, par. 1). The other anti-Semitic legends include; â€Å"the girl who was killed by the Jews,† â€Å"Pfefferkorn the Jew at Halle,† â€Å"the expulsion of the Jews from Prussia,† â€Å"the bloody children of the Jews,† â€Å"the imprisoned Jew at Magdeburg,† â€Å"the chapel of the holy body at Magdeburg†, â€Å"the lost Jew,† â€Å"the story of Judas,† â₠¬Å"malchus the column,† â€Å"buttadeu, and the eternal Jew on the Matterhorn† (Ashliman, par. 1).Advertising We will write a custom essay sample on Conduction of The Holocaust specifically for you for only $16.05 $11/page Learn More The way the Holocaust was conducted Isolation The Nazis reinforced their genocidal activity against the Jews with their racist hypothesis in conjunction with Darwinian Theory of evolution. Hitler started terrorizing the Jews and he imposed harsh legislation on them. These racist intents entailed a wide range of activities including exclusion from public proceedings, investment and assets confiscation; exterminating their professions and public learning institutions, and burning books of Jewish author(s). The most notorious of the anti-Jewish policies were the Nuremberg laws. This legislation constituted the legal foundation for the Jews elimination from Germany (â€Å"Jewish virtual library;† par. 12). T hese reforms triggered a massive Jewish emigration from Germany to the neighboring European nations. Nevertheless, tough immigration policies hindered the Jews from leaving Europe. In fact such frustrations compelled a Jewish boy aged 17 to shoot and kill a third secretary in the Germany Embassy in France. Nazi hooligans used this assassination as the excuse for initiating a famous night of destruction known as Kristallnacht. They plunder and spoiled many Jewish possessions including their residence, enterprises and place of worship, the synagogue. During these skirmishes, many Jews lost their lives and 30,000 of them were arrested and taken to the concentration camps (par. 13). Jews confinement in the ghettos During the onset of the Second World War, Germany invaded Poland and developed ghettos for the Polish Jews. There were about three million Jews in Poland, representing about 10 percent of the entire polish population. The Nazis authority forced the Jews from their homes to liv e in ghettos isolated from the rest of the ethnic groups. This concentration in ghettos facilitated the Jews deportation to concentration camps by the Nazis authority. The ghettos were characterized by shortage of food, water, sanitary amenities, and space. Deprivation and starvation contributed to the deaths of many Jews in the ghettos (par. 17). The â€Å"final solution† In 1941 the Nazi invaded the Soviet Union and culminated into a plan of execution which they termed the â€Å"final solution.† In the same year four itinerant the Nazi developed einsatzgruppen A, B, C, and D, whose duty was to move around killing the Jews. The duties of this group were to systematically collect Jews from towns, parade them to pre-dug pits, strip them, align them, and execute them with sub-machineguns. One such popular massacre is the Babi yar’s in which between 30,000 to 35,000 Jews were murdered within a period of two days (par. 18).Advertising Looking for essay on history? Let's see if we can help you! Get your first paper with 15% OFF Learn More The pinnacle of Nazi authority met to develop the a system to use to implement mass killing of the Jews. This discussion, the Wannsee Conference, indicated the preliminary for massive, thorough Jewish execution, and developed the plan for its administration which ensued shortly following the completion of the conference (Yahil, p. 328, qtd in â€Å"Jewish virtual library,† par. 19). Although the Nazis killed other nationalities and communities including various soviet prisoners of war, gypsies and polish academics, just the Jews were targeted for methodical and complete annihilation. The Jews were specially exterminated by often chlorine gas poisoning (par. 20) Noteworthy, all the execution points were situated along the railway lines to allow for easy transportation of the Jewish victims. A huge structure of camps backed-up the execution camps. The support camps played various roles such as serving as workforce camps, transportation camps, concentration camps, while others a s death camps (par. 21). In almost all the colonies of the Nazi, the Jews were obliged to wear badges to distinguish them from the other ethnic groups, so that they could be gathered into ghettos or alternatively concentration camps to be gradually conveyed to the death camps. Thousands of Jews were conveyed to the death camps from all the Nazi colonies. Shortly after their arrival, the victims will be gas poisoned’ and the bodies blazed. An estimated 3.5 million Jews were murdered via death camps (22). Nevertheless, the able bodied young Jews were spared, to be used in the Nazi’s war effort and to provide forced free labour. They were confined in labour and concentration camps, and forced to labour in Germany’s munitions and other manufacturing plants including I. G. Farben and Krupps, and in every place the labour was necessary. These slave laborers were exerted from dawn till night with inadequate food and cover. Many of these Jews were essentially labored to death by the Nazi in conjunction with their collaborators (22). Eventually, in the final months of Adolf Hitler’s reign, the Nazi military began to parade the survivors in the concentration camps to the regions they still governed. The Nazi military pressured the emaciated and sickly Jews to trek so many miles to reach other concentrations camps in nation that were still their subjects. Approximately 250,000 Jews died naturally or were shot during the marches (23). Works Cited Ashliman, D. L.(ed.). Anti-Semitic Legends. Jewish virtual library; The American Israel Cooperation Centre. 2010. Web. Jewish virtual library. History of the holocaust – an introduction. West Bloomfield: Holocaust memorial center; The American Israel Cooperation Centre. 2010. Web. Leni, Yahil. The Holocaust: The Fate of European Jewry, New York: Oxford University Press, 1990. Print. This essay on Conduction of The Holocaust was written and submitted by user Janiyah S. to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Monday, November 25, 2019

An Explanation of the Origins of the Cold War in Europe

An Explanation of the Origins of the Cold War in Europe In the aftermath of the Second World War two power blocs formed in Europe, one dominated by America and capitalist democracy (though there were exceptions), the other dominated by the Soviet Union and communism. While these powers never directly fought, they waged a cold war of economic, military and ideological rivalry which dominated the second half of the twentieth. Pre-World War Two The origins of the Cold War can be traced back to the Russian Revolution of 1917, which created a Soviet Russia with a profoundly different economic and ideological state to the capitalist and democratic West. The ensuing civil war, in which Western powers unsuccessfully intervened, and the creation of Comintern, an organization dedicated to the spreading of communism, globally fuelled a climate of mistrust and fear between Russia and the rest of Europe/America. From 1918 to 1935, with the US pursuing a policy of isolationism and Stalin keeping Russia looking inward, the situation remained one of dislike rather than conflict. In 1935 Stalin changed his policy: afraid of fascism, he tried to form an alliance with the democratic Western powers against Nazi Germany. This initiative failed and in 1939 Stalin signed the Nazi-Soviet pact with Hitler, which only increased anti-Soviet hostility in the West, but delayed the onset of war between the two powers. However, while Stalin hoped Germ any would get bogged down in a war with France, early Nazi conquests occurred quickly, enabling Germany to invade the Soviet Union in 1941. The Second World War and the Political Division of Europe The German invasion of Russia, which followed a successful invasion of France, united the Soviets with Western Europe and later America in an alliance against their common enemy: Adolf Hitler. This war transformed the global balance of power, weakening Europe and leaving Russia and the United States of America as global superpowers, with massive military strength; everyone else was second. However, the wartime alliance was not an easy one, and by 1943 each side was thinking about the state of Post-war Europe. Russia ‘liberated’ vast areas of Eastern Europe, into which it wanted to put its own brand of government and turn into Soviet satellite states, in part to gain security from the capitalist West. Although the Allies tried to gain assurances for democratic elections from Russia during mid and post war conferences, there was ultimately nothing they could do to stop Russia from imposing its will on their conquests. In 1944 Churchill, Prime Minister of Britain was quoted as saying â€Å"Make no mistake, all the Balkans apart from Greece are going to be Bolshevised and there’s nothing I can do to prevent it. There’s nothing I can do for Poland, either†. Meanwhile, the Allies liberated large parts of Western Europe in which they recreated democratic nations. Two Superpower Blocs and Mutual Distrust World War Two finished in 1945 with Europe divided into two blocs, each occupied by the armies of, in the west America and the Allies, and in the east, Russia. America wanted a democratic Europe and was afraid of communism dominating the continent while Russia wanted the opposite, a communist Europe in which they dominated and not, as they feared, a united, capitalist Europe. Stalin believed, at first, those capitalist nations would soon fall to squabbling among themselves, a situation he could exploit, and was dismayed by the growing organization among the West. To these differences were added fear of Soviet invasion in the West and Russian fear of the atomic bomb ; fear of economic collapse in the west versus fear of economic domination by the west; a clash of ideologies (capitalism versus communism) and, on the Soviet front, the fear of a rearmed Germany hostile to Russia. In 1946 Churchill described the dividing line between East and West as an Iron Curtain.​ Containment, the Marshall Plan and the Economic Division of Europe America reacted to the threat of the spread of both Soviet power and communist thinking by commencing the policy of ‘containment’, outlined in a speech to Congress on March 12, 1947, action aimed at stopping any further Soviet expansion and isolating the ‘empire’ which existed. The need to halt Soviet expansion seemed all the more important later that year as Hungary was taken over by a one party communist system, and later when a new communist government took over the Czech state in a coup, nations which until then Stalin had been content to leave as a middle ground between the communist and capitalist blocs. Meanwhile, Western Europe was having severe economic difficulties as the nations struggled to recover from the devastating effects of the recent war. Worried that communist sympathizers were gaining influence as the economy worsened, to secure the western markets for US products and to put containment into practice, America reacted with the ‘Mars hall Plan’ of massive economic aid. Although it was offered to both eastern and western nations, albeit with certain strings attached, Stalin made sure it was rejected in the Soviet sphere of influence, a response the US had been expecting. Between 1947 and 1952 $13 billion was given to 16 mainly western nations and, while the effects are still debated, it generally boosted the economies of member nations and helped freeze communist groups from power, for example in France, where the communists members of the coalition government were ousted. It also created an economic divide as clear as the political one between the two power blocs. Meanwhile, Stalin formed COMECON, the ‘Commission for Mutual Economic Aid’, in 1949 to promote trade and economic growth among its satellites and Cominform, a union of communist parties (including those in the west) to spread communism. Containment also led to other initiatives: in 1947 the CIA spent large amounts to influence the result of Italy’s elections, helping the Christian Democrats defeat the Communist party. The Berlin Blockade By 1948, with Europe was firmly divided into communist and capitalist, Russian supported and American supported, Germany became the new ‘battleground’. Germany was divided into four parts and occupied by Britain, France,  America, and Russia; Berlin, situated in the Soviet zone, was also divided. In 1948 Stalin enforced a blockade of Western Berlin aimed at bluffing the Allies into renegotiating the division of Germany in his  favor, rather than them declaring war over the cut off zones. However, Stalin had miscalculated the ability of airpower, and the Allies responded with the ‘Berlin Airlift’: for eleven months supplies were flown into Berlin. This  was, in turn, a bluff, for the Allied planes had to fly over Russian airspace and the Allies gambled that Stalin wouldn’t shoot them down and risk war. He didn’t and the blockade was ended in May 1949 when Stalin gave up. The Berlin Blockade was the first time the previous diplomatic and po litical divisions in Europe had become an open battle of wills, the former allies now certain enemies. NATO, the Warsaw Pact and the Renewed Military Division of Europe In April 1949, with the Berlin Blockade in full effect and the threat of conflict with Russia looming, the Western powers signed the NATO treaty in Washington, creating a military alliance: the North Atlantic Treaty Organisation. The emphasis was firmly on  defense  from  Soviet  activity. That same year Russia detonated its first atomic weapon, negating the America advantage and reducing the chance of the powers engaging in a ‘regular’ war because of fears over the consequences of nuclear conflict. There were debates over the next few years among NATO powers over whether to rearm West Germany and in 1955 it became a full member of NATO. A week later eastern nations signed the Warsaw Pact, creating a military alliance under a Soviet commander. A Cold War By 1949 two sides had formed, power blocs which were deeply opposed to each other, each believing the other threatened them and everything they stood for (and in many ways they did). Although there was no traditional warfare, there was a nuclear standoff and attitudes and ideology hardened over the next decades, the gap between them growing more entrenched. This led to the ‘Red Scare’ in the United States and yet more crushing of dissent in Russia. However, by this time the Cold War had also spread beyond the boundaries of Europe, becoming truly global as China became communist and America intervened in Korea and Vietnam. Nuclear weapons also grew more power with the creation, in 1952 by the US and in 1953 by the USSR, of thermonuclear weapons which were vastly more destructive than those dropped during the Second World War. This led to the development of ‘Mutually Assured Destruction’, whereby neither the US nor USSR would ‘hot’ war with each o ther because the resulting conflict would destroy much of the world.

Thursday, November 21, 2019

Mountain Resort and its Outlying Temples, Chengde Essay

Mountain Resort and its Outlying Temples, Chengde - Essay Example Mountain Resort and its Outlying Temples, Chengde It is also the shortest river in the world, only 14.7 kilometers long. There are 11 magnificent temples in the outlying area, standing on the hills in a semi circle. They were usually referred to as the â€Å"Eight Outer Temples† because they were divided into eight sections under the administration of the Beijing-based Harmony and Peace Lamasery- a monastery for lamas. Only seven temples remained intact, including Puren Temple, Temple of Sumeru and Puning Temple. They consist of the largest temple building complex in China. The mountain resort and it outlying temples were inscribed as UNESCO World Heritage Sites at the 18th session of the World Heritage Committee in Phuket Thailand, December 12-17, 1994. It is described as a huge complex of temples, palaces, administrative offices and ceremonial buildings and these structures harmoniously blend into the landscape of lakes, pastures and forests. Moreover, they represent a variety of architectural styles and reflect the aesthet ic aspiration of imperial China of that period. I have chosen this site to write about for it has a fascinating architectural diversity, as well as a contrast between well developed bio diversity and a lack of water, deforestation and desertification. It is also very fascinating how after a disaster, a â€Å"heaven† can return to its prior heavenly state with the help of people who give their best to maintain the nature and keep the environment healthy as possible. Furthermore, it was most amazing to learn about the outlying temples and the divinity of the whole area and its uniqueness. Chengde mountain resort is divided into two sections: a palace section and a garden section.  The palace area is situated in the southern part of the resort, which is made up of the Main Palace, Pine-Crane Hall, Pine Soughing Valley and East Palace. The Main Palace consists of the Front Court and the Back Imperial Bedroom. The main hall of the Front Court was the place where all important ce remonies were held during the emperors staying in the mountain resort. The garden section can be further divided into a lake section, plains section, and mountain section. The lake section is on the north of the palace section and covers about 80 hectares; going north, you will get to the plains section where the Qing emperors held banquets and recreational activities. This area is mainly covered with grassland and woods; the mountain section is located in the northwestern part and four-fifths of the Mountain Resort is mountainous, sloping down from the northwest to the southeast. The Kuixing Pavilion is a tourist spot newly that was built upon the foundations of a former, ancient pavilion that had fallen into ruin. It is located atop Banbi Mountain in the south of city, the three main areas of this complex comprise a palace, square and garden zones. The whole architectural style is bright and colorful, and some cultural sights  Ã‚  can still be seen in this beautiful scenic spot. There are also many forest parks in and around Chengde, including Qingchuifeng and Liaoheyuan National Forest Parks, Beidashan Stone Sea Forest Park, and Liuliping Forest Park, etc. The Qingchui Cliff National Park, lying to the east of the city, is a natural park that features with a dramatic, lofty and steep formation called the Danxia Landform. The highlight of the park is the Qingchui Cliff, which is nearly 60 meters (197 feet) high and

Wednesday, November 20, 2019

Survey Research Paper Example | Topics and Well Written Essays - 250 words - 1

Survey - Research Paper Example g to the survey, more than half of the respondents applauded the efforts made by the service provider as a step in the right direction especially for the young population, who constitute the largest bulk of the fast food clients. Among the sample of four hundred students, a hundred were optimistic that the proposed small sustainable lifestyle changes would indeed go a long way in improving their general wellness and fitness. One of the key determinants of the success of a program is gathering the right information. Out of those surveyed, at least fifty of them reported that they had no concrete information on the program and how it would affect their fitness and health. Great hindrance to the same being lack of interest on matters health, the general stereotype as pertain fast foods. Diet plays an important role in fitness and health, and the need for a well-balanced nutrition is key. Service providers such as KCAL’s with calorie-controlled, refreshingly wholesome tasty and affordable fast foods have made this possible. There was an admission by the majority of not having the right information pertaining the right components of the various foods.There was an admission by at least a hundred out those surveyed that the first key consideration was cost, rather than the nutrition component. The high demand for fast and tasty foods among the young population is a great attraction for most of the respondents, with at least half of the population admitting to the same. The efforts to provide rich flavors,tantalizing tastes and health promoting nutrients dishes by KCAL was a reason for most admitting that they would seek to try out the program and that it would actually help them achieve their envisioned goal of a better

Monday, November 18, 2019

How did Stanton recalculate the definition of self-evident truths Essay

How did Stanton recalculate the definition of self-evident truths - Essay Example lution do not only consist of change process via ethnic relations, but since movements in the aim to advance civil rights emerged as well at various points in history, their heavy criticisms upon the four models of social change managed to recalculate the view of self-evident truths. Eventually, for Elizabeth Cady Stanton, recalculation of truths applies further to more specific issues of evaluating differences between the dominant and the non-dominant groups. Ethnic social relations that were classified by Frederickson as hierarchy, assimilation, pluralism, and separatism each possess a characteristic definition. For one, hierarchy manifests the conspicuous evidence of truth in the manner nature takes its course as men of dominant race or culture share privileges among themselves, excluding their weaker counterparts whom they consider to be inferior. It may be widely perceived herein that social inequality is the natural order of truth and there seems no way of having the non-dominant blend with the dominant of the society for the borders that distinguish one from the other are fixed and significantly rigid. Assimilation, on the other hand, takes on a more subtle, rather considerate treatment by approving outcasts as in a situation where the superior in-groups tolerate acceptance of the inferior out-groups for as long as the latter make the effort to ‘assimilate’ or establish conformity to the attitude, sense of fashion, or beliefs of the former. Even more flexible in structure is pluralism the theory of which promotes respect for cultural diversity so that this enables abolition of typically unfavorable judgments upon ethnicities on the basis of color and racial origins. Instead, a pluralistic society encourages distinctions and social relation that supports the prevailing state of democracy from which to measure the level of civilization attained. Separatism being a form of pluralism, in the definition of Frederickson, may then be achieved upon full

Friday, November 15, 2019

Overview of Famous Mathematicians

Overview of Famous Mathematicians Mathematicians’ Manifesto A young man who died at the age of 32 in a foreign land he had travelled to, to pursue his craft. A clumsy eccentric who could visualize his complete work in his head before he put it to canvas. A Russian who shuns the limelight and refuses recognition for his work. A traveller who went from country to country on a whim in order to collaborate with others. A man whose scribblings inspired the life work of hundreds. A woman, who escaped the prejudices against her gender to make a name for herself. A recluse who spent close to ten years working on one piece. A revolutionary child prodigy who died in a gun duel before his twenty-first birthday. What do you picture when you read the above? Artists? Musicians? Writers? Surely not mathematicians? Srinivas Ramanujan (1887-1920) was a self-taught nobody who, in his short life-span, discovered nearly 3900 results, many of which were completely unexpected, and influenced and made entire careers for future mathematicians. In fact there is an entire journal devoted to areas of study inspired by Ramanujan’s work. Even trying to give an overview of his life’s work would require an entire book. Henri Poincare (1854-1912) was short-sighted and hence had to learn how to visualise all the lectures he sat through. In doing so, he developed the skill to visualise entire proofs before writing them down. Poincare is considered one of the founders of the field of Topology, a field concerned with what remains when objects are transformed. An oft-told joke about Topologists is that they can’t tell their donut from their coffee cup. A conjecture of Poincare’s, regarding the equivalent of a sphere in 4-dimensional space, was unsolved till this century when Grigori Perelman (1966- ) became the first mathematician to crack a millenium prize problem, with prize money of $1million. Perelman turned it down. He is also the only mathematician to have turned down the Fields Medal, mathematics’ equivalent of the Nobel Prize. Have you heard of the Kevin Bacon number? Well mathematicians give themselves an Erdos number after Paul Erdos (1913-96) who, like Kevin Bacon, collaborated with everybody important in the field in various parts of the world. If he heard you were doing some interesting research, he would pack his bags and turn up at your doorstep. Pierre de Fermat (1601-65) was a lawyer and ‘amateur’ mathematician, whose work in Number Theory has provided some of the greatest tools mathematicians have today, and are integral to very modern areas such as cryptography. He made an enigmatic comment in a margin of his copy of Diaphantus’ ‘Arithmetica’ saying: ‘It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.’ Whether he actually had a proof is debatable, but this one comment inspired work for the next 300 years. In these intervening 300 years, one name has to be mentioned Sophie Germain (1776-1831). Germain remains one of the few women who have broken the glass ceiling and made significant contributions to mathematics. She was responsible for proving Fermat’s scribblings for a large amount of numbers. I apologise to Andrew Wiles (1953- ) for calling him a recluse, but he did spend close to 10 years on the proof of Fermat’s Last Theorem, during most of which he did not reveal his progress to anybody. Saving the best for last, Evariste Galois (1811-32), a radical republican in pre-revolutionary France, died in a duel over a woman at the age of 20. Only the night before, he had finished a manuscript with some of the most innovative and impactful results in mathematics. There is speculation that the resulting lack of sleep caused him to lose the duel. Galois developed what became a whole branch of mathematics to itself Galois Theory, a sub-discipline which connect two other subdisciplines of abstract algebra. It is the only branch of mathematics I can think of which is named after its creator (apart from Mr. Algebra and Ms. Probability). This might appear to be anecdotal evidence of the creative spirit of mathematics and mathematicians. However, the same can be said about the evidence given for Artistic genius. In fact there is research which shows that the archetype of a mad artistic genius doesn’t stand on firm ground. So, lets move away from exploring creative mathematicians, to the creativity of the discipline. Mathematics is a highly creative discipline, by any useful sense of the word ‘creative.’ The study of mathematics involves speculation, risk in the sense of the willingness to follow one’s chain of thought to wherever it leads, innovative arguments, exhilaration at achieving a result and many a time beauty in the result. Unlike scientists, mathematicians do not have our universe as a crutch. Elementary mathematics might be able to get inspiration from the universe, but quickly things change. Mathematicians have to invent conjectures from their imagination. Therefore, these conjectures are very tenuous. Most of them will fail to bear any fruit, but if mathematicians are unwilling to take that risk, they will lose any hope of discovery. Once mathematicians are convinced of the certainty of an argument, they have to present a rigorous proof, which nobody can poke any holes in. Once again, they are not as luck as scientists, who are happy with a statistically signific ant result or at most a result within five standard deviations. As a result of this, once you prove a mathematical theorem, your name will be associated with it for eternity. Aristotle might have been superseded by Newton and Newton by Einstein, but Euclid’s proof of infinite primes will always be true. As Hardy said, â€Å"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.† The beauty of mathematical results and proofs is a fraught terrain, but there are certain results, great masters such as Euler’s identity and Euclid’s proof, which are almost universally accepted as aesthetically pleasing. So, why are people so afraid of mathematics? Why do they consider it to be boring and staid? Well, the easy answer is that they are taught shopkeeper mathematics. In school, you are taught to follow rules in order to arrive at an answer. In the better schools, you are encouraged to do so using blocks and toys. However, basically the only skills you are getting are those which help you in commercial transactions. At the most, you get the skills to help you in other disciplines like Economics and the Sciences. There has been a huge push in the recent past for the Arts to be taught in school ‘for art’s sake.’ There would be uproar tomorrow amongst artists and the liberal elite if art class turned into replicating posters (not even creating them). There would even be a furore if the only art students did was to draw the solar system for Science class and the Taj Mahal for Social Studies. What good art classes involve is teachers introducing concepts such as particular shapes and then encouraging students to experiment and create based on those concepts. What about ‘maths for maths’ sake?’ Students should be encouraged to come up with their own conjectures based on concepts introduced by the teacher. This class would have to be closely guided by a teacher who is conceptually very strong, so that they can give examples in order to get students to come up with conjectures. They would also be required to provide students with counterexamples to any conjecture they have come up with. I am not suggesting completely doing away with the current model of mathematics education involving repeated practice of questions. Just as replication probably helps in the arts and the arts can serve as great starting points for concepts in other disciplines, repetition is important in mathematics as it helps you intuit concepts and certain mathematical concepts are important for the conceptual understanding of other disciplines and for life. So, there needs to be a blend of mathematics classes (those which teach mathematics) and shopkeeper classes (those which teach mathematical concepts for other disciplines and for life). These would not work as separate entities and might even be taught at the same time. This requires a complete overhaul of the mathematics curriculum with a much lighter load of topics so that teachers can explore concepts in depth with their students. It also requires a larger emphasis on concepts such as symmetry, graph theory and pixel geometry which are easi er to inquire into and form conjectures in than topics like calculus. Now we come to the logistics. How many teachers are there in the country who have a strong enough conceptual understanding required to engage with mathematics in this manner? I would be pleasantly surprised if that were a long list, but I suspect it isn’t. In order to build up this capability, the emphasis at teacher colleges and in teacher professional development has to move from dull and pointless concepts like classroom management and teaching strategies, to developing conceptual understanding, at least in Mathematics. The amount of knowledge required to teach school mathematics is not all that much. All that is required is a strong conceptual base in a few concepts along with an understanding of mathematics as an endeavor, and a disposition for the eccentricities of the discipline. Even so, this will not be easy to accomplish and will take time. In the meanwhile, wherever possible, professional mathematicians could come in to schools and work with teachers on their lesson plans. In other cases, these mathematicians could partner with educationalists and come up with material, which can more or less be put to use in any class (this is not ideal as lesson plans should be created by the teachers and evolved based on their understanding of their class, but this will have to do in the interim). Not only will this help in developing a disposition for mathematics and hopefully churn out mathematicians, but it will also help in the understanding of shopkeeper mathematics. Pedagogy and conceptual understanding are not separate entities. In fact a strong conceptual understanding is a prerequisite for effective pedagogy. Mathematics is unfortunate in its usefulness to other disciplines and the utility it provides for life. In the meanwhile, the real creative essence of the discipline is lost. I don’t blame students for hating mathematics in school. In fact it is completely justified. Mathematics is missing out. Who knows, one of these students would have proved the Riemann Hypothesis in an alternate reality. Artists have been very successful in campaigning for the creativity of their discipline to be an integral part of schools. Mathematicians, on the other hand, really need to pull up their socks and join the fight for the future of mathematics. In the spirit of Galois, Mathematicians of the World Unite! You have nothing to lose but the chains of countless students!

Wednesday, November 13, 2019

Compare and contrast the way the poets show the problems affecting the :: English Literature

Compare and contrast the way the poets show the problems affecting the culture they are writing about in Nothing's Changed and Blessing. Tatamkhulu Afrika, author of 'Nothing's Changed' has written a probably autobiographical poem, where he is revisiting scenes of his childhood; a reflective poem, that is very emotional. The poem set in South Africa, illustrates a society where rich and poor are divided. He remembers when he was a boy and the laws, enforced by police that separated the whites from the blacks. He has come back to Cape Town and seen that 'Nothing's changed' in the apartheid. Imtiaz Dharker author of 'Blessing' has written a descriptive poem, set in a hot country, where there is a shortage of water, as told in the opening lines of the poem where the human skin is compared to a seedpod, drying out till it cracks. The poem is set in India, in a village where there is poverty. We know that this because firstly there is a shortage of water, and secondly they live in huts. Consider also the last line, 'their small bones'. This could mean that there is also a shortage of food or it can also emphasis the size of the small children. In line 18, when it says 'and naked children', this also shows us that they have no clothes or it can emphasise the need of water to wash. Tatamkhulu Afrika shows us a society divided between the blacks and the whites. He also shows the difference between their cultures. 'District Six' is the name of a poor area of Cape Town. This area was bulldozed as a slum in 1966, but never properly rebuilt. Although there is no sign there, the poet can feel that this is where he is: 'but my feet know, and my hands.' Similarly the 'up-market' inn (brash with glass' and the bright sign, 'flaring like a flag', which shows its name) is meant for the white customers only. The 'whites only inn' is elegant, with linen tablecloths and a 'single rose' on each table. It is contrasted with the fast food 'working man's cafe which sells the local snack ('bunny chows'). There is no tablecloth, just a plastic top, and there is nowhere to wash one's hands after eating: 'wipe your fingers on your jeans.' This is all totally different from the poem written by Imtiaz Dharker, in which everyone as a community runs for the water and everyone has a right to the water, ('every man woman child for streets around'). There are many religious beliefs in 'Blessing', as you can see straight away from the title, which emphasises how holy the water is