Taking a Look at Schizophrenia - 650 Words

A little over 1 percent of the world’s population has the acute mental disorder of Schizophrenia (World). It is one of the most common mental disorders in the world (World). Schizophrenia is a mental illness characterized by disordered thinking, delusions, hallucinations, emotional disturbance, withdrawing from reality (Gale), and thinking illogical, confused patterns (World). The disease causes impaired thinking, emotions, and behaviors in patients (Gale). The word Schizophrenia is a Greek meaning for a â€Å"splitting of the mind†, although it does not mean the patient has more than one personality (World). The disease is more common to start in people in their late teens to mid twenties, but men tend to develop the disease earlier and more severe than women. Schizophrenia has been proven to be incurable, but patients can be treated by being hospitalized, and can start therapy or treatment when their symptoms have come under control in reaction to the medications and drugs the patient was put on (World). Scientists and physicians do not know the exact cause or causes to developing this disorder (World). Many scientists believe that viral infections, drug abuse, trauma during birth (World), or even bad parenting (Gale) may lead to this disease and cause the chances of getting it to become higher (World). The disease can be passed down from family by genetics, and abnormal chemistry plays a role in the development also (World). Chemicals in the brain, called neurotransmitters,Show MoreRelatedTaking a Look at Schizophrenia793 Words   |  3 Pagesâ€Æ' Schizophrenia is a disorder that has an effect on about 25 million people around the world (Myers, 2010). Schizophrenia is a brain damage, naturally created by the human body, that is caused by the genetically determined vulnerability of the blood-brain barrier (Voronov, 2013). This psychiatric disorder, like most others, is characterized by changes in behavior, thinking, reduced ability to feel normal emotions, and mood (Abad et al., 2011). The unique thing about schizophrenia is that the symptomsRead MoreTaking a Look at Schizophrenia997 Words   |  4 Pagesrespectively. However, the more common symptoms of schizophrenia are hallucinations, delusions, and disorganized thought. This paper will discuss the causes, symptoms, and treatments of schizophrenia. Causes of Schizophrenia Schizophrenia can arise from biological and environmental factors. Genetics are thought to play a role in the development of schizophrenia. It is currently unknown which genes are specifically involved in causing schizophrenia, but the it has been observed that the more geneticallyRead MoreTaking a Look at Schizophrenia1249 Words   |  5 PagesA common mistaken belief is that people with schizophrenia have multiple personalities. Many people confuse schizophrenia with split personality or multiple personality disorder (Lilienfeld et al, 2010). The misunderstanding stems from the meaning of the word schizophrenia, as in Greek it means split mind (Boruck, 2008). In 1990, Carlson proposed â€Å"schizophrenia is probably the most misused psychological term in existence† . Vaughan (1977), performed a study which found that 77% of studentsRead MoreTaking a Look at Schizophrenia828 Words   |  3 PagesSchizophrenia â€Æ' Schizophrenia is a mental disorder that makes it difficult for someone to establish what is real and what is not real. Schizophrenia also makes it hard to think clearly or to establish your emotions. Having this disorder affects how a person acts and sees the world. Over 2.2 million people suffer from this mental illness. There are many symptoms for Schizophrenia. Although there is no cure, proper treatment can control these symptoms. A person with schizophrenia may often seeRead MoreTaking a Look at Schizophrenia729 Words   |  3 PagesWhat is schizophrenia? â€Å"Schizo† meaning split, and â€Å"phrenia† meaning mind. Schizophrenia is a disorder of the brain that has affected many individuals throughout history. Usually starting in childhood or early adulthood, it is rare for schizophrenia to start after one has reached adulthood. Before schizophrenia was discovered, those with the disorder were considered to be possessed, therefore causing them to be feared or locked up away from those that did not have the disorder. Schizophrenia is chronicRead MoreTaking a Look at Schizophrenia 1626 Words   |  6 PagesSchizophrenia is one of the most common mental disorders. The World Health Organization (WHO) identifies the disorder as the 7th greatest cause of disability in terms of disability-adjusted life-years worldwide affecting about 24 million people worldwide (Frangou, 2008). Many individuals arou nd the world are affected by this disorder directly and indirectly. This paper looks at Schizophrenia assessing its epidemiology, history, diagnosis, symptoms, causes, and treatment drawing support from relevantRead MorePersonality Paper1187 Words   |  5 PagesJanuary 14, 2013 Dr. Tracy Masiello Personality Theory Paper John Nash was a very interesting man. Many may just know of him because of the movie, â€Å"A Beautiful Mind†. Taking a look at John Nash and his personality and how psychologists, such as Jung and Freud would see John Nash through their diagnoses. Also taking a look at how different theories would go up against John Nash and his everyday life. The different theories that will be looked at are the Five-factor model and Maslow’s hierarchyRead MoreThe Horrible World of Schzophrenia1245 Words   |  5 PagesSchizophrenia is a horrible brain disorder where people mix up what is real and what is their imagination. People with Schizophrenia hear voices in their head that arent really there. People affected with this disease may be paranoid because they believe people are reading their minds, controlling what they think, or plotting to hurt them. Schizophrenics may not make sense when they talk or seem crazy to people around them. They can sit still for hours without moving a nd you really cant tellRead MoreThe Biological And Psychological Explanations Of Schizophrenia1405 Words   |  6 PagesIn this essay I will try to explain schizophrenia and talk about the main biological and psychological explanations, also showing how similar and different they are. Schizophrenia is defined in the oxford dictionary as a long-term mental disorder of a type involving a breakdown in the relation between thought, emotion, and behaviour, leading to faulty perception, inappropriate actions and feelings, withdrawal from reality and personal relationships into fantasy and delusion, and a sense of mentalRead MoreMental Health And Mental Illness1314 Words   |  6 Pagesthings such as anxiety and shock. Thus, this essay was based on a case study; it will look at the meaning of mental health and mental illness in relation to Schizophrenia. Also, it will look at the causes and the functional difficulties associated with Schizophrenia. Furthermore, it will reflect on the im pacts of a diagnosis of mental illness on individual and in general and particularly in relation to Schizophrenia. Finally, it will discuss the type of support and treatment that might be effective

The Good and the Bad of the 1920s - 909 Words

Although the 1920’s is often categorized by widespread prosperity and pleasure, there was no lack of tension. Struggles revealed themselves between those who were beginning to form a new approach to the world, and those who wished to stick to traditional ideals. The rise of consumerism, technological advancements, and conditions in a post-war society all caused America to change in different ways; leading to either support of this change or a desire to preserve the past. As both sides fought to have their way, this strain regarding the role of women, rights of minorities, religious teachings, and the growth of industry manifested itself in a variety of ways, including physical violence and government legislation. With the creation of Fordism came the mass production of a plethora of new technology and goods that were easily accessible to the American public. More patents were issued than any time before, and quickly the country saw its final departure from agriculture, no lon ger being a predominantly rural social. Some viewed the advents of automobiles and appliances and airplanes as fantastic, welcoming them with open arms. â€Å"The Bridge† depicts a new architectural structure with pride and beauty, displaying it in such a way that suggests opportunity (Doc B). After successfully flying across the Atlantic, Charles Lindbergh is hailed as a hero (Doc F). New wares, like cameras and water heaters, represented excellence for Americans and were viewed by some as sources of joyShow MoreRelated1920s Good or Bad?1665 Words   |  7 PagesJuly 15th , 2010 1920s Good Times or Bad Times? For many decades, there were numerous arguments stating whether the â€Å"Roaring 20s† were good times or bad times in Canadian history. Although there were many clear reasons that supported both sides of the argument, I believe that the 1920s were good times. The â€Å"Roaring 20s† were times of economic and social boom. New inventions which are still effective part of our lives in 21st century, growing power of multimedia and entertainment, and modern formRead MoreAdvancements During The Roaring Twenties Essay527 Words   |  3 Pagesprosperity, music, dancing, and happiness. The 1920’s are often referred to as the â€Å"roaring twenties,† but many histories purpose that this is not a correct interpretation of this time period. America may have not been good for the some of the lower class in this time period, but the 1920’s were fantastic for most of the middle and upper class living in urban cities. The advantages of this time period did out weigh the bad, which is why the 1920’s are called the â€Å"roaring twenties.† Women’s rolesRead MoreEssay on Life Changes of Americans in the 1920s568 Words   |  3 PagesLife Changes of Americans in the 1920s In the 1920s many American lives were improved greatly, but some lives were as bad as they had been before. The economy was booming, with cars being mass produced, and many other consumer goods such as radios, were widely available. Also more jobs became available, and many people recieved a par rise. However there were bad things such as racism about. Many ethnic minority groups were treated poorly. The most racist group aroundRead MoreRadio’s Impact during the 1920’s Essay965 Words   |  4 Pages After the First World War, many people were looking forward to good times. The 1920’s presented people with this time of fast-paced fun and adventure. Entertainment was the foremost part of everyday life during the 1920’s. Radio introduced a whole new practice of entertainment to people’s everyday lives. Likewise, through the utilization of the radio, people were able to experience a new medium to entertain themselves. Furthermore, the radio changed the face of society’s culture through its widespreadRead MoreEssay about Twists and Turns of the 1920s953 Words   |  4 Pages Depression Era Project. Throughout the 1920’s there were many bad times and many good times. From things like Flappers, women who began to do things that were considered â€Å"Un-lady like†, to the Stock Market crash all the way to the election of Franklin D. Roosevelt, the 20’s and 30’s were full of twists and turns. Even the fact that Herbert Hoover, who was beloved during WWI, was beaten by newcomer Franklin D. Roosevelt was a surprise. Though, after the Stock Market had crashed FDR’s electionRead More The 1920s Essay795 Words   |  4 Pages The 1920’s The 1920s were a decade of enjoyment, employment, and for some disappointment. It was a decade classified as the quot;roaring twenties.quot; Men returning from World War I had to deal with unemployment, wheat farmers and oil companies were striking it rich, new modern conveniences were being thought up, and fashion was a major issue among the rich. During the twenties the economy had a definite impact on the society. It benefited some, but hurt others. The people that benefited wereRead MoreRoaring Twenties : A Decade Of Extravagance939 Words   |  4 Pagesaftermath of the First World War. Returning from the horrors of war, writers were inspired by romance and the riches America had. Using their unique creative expression, many of the writings from the Twenties were a commentary on social life, the good and bad. Each story holds a different theme, different message, and different romance, however, each piece of work was individualistic to the writer, and to his experiences. America was entering a new era, and literature was at the forefront to changeRead MoreAmerica in the 1920s762 Words   |  4 PagesWhich were the more typical of 1920s of America: Prohibition and intolerance or the Jazz Age and increasing social freedom? The 1920’s were seen as a prosperous time for America, judging by the increasing economic strength, the development of new industries and new methods of production and, by the time of rebellion and liberation that came with it. The 1920’s are often reffered to as the ‘Roaring Twenties’ or the Jazz Age, a period of great fun and enjoyment. However, not everyone agreed withRead MoreThe Golden Age Of Sports Essay700 Words   |  3 PagesDestinee Holliday Ms. Biltz May 20, 2015 The Golden Age of Sports The 1920s was a great decade for the economy because of the popularity in sports. The number of fans increased, which created the need for new stadiums and raised the salary for sports stars. Sports in the 1920s went through many changes in the time period known as the Roaring Twenties. New heroes, new teams, and new leagues were emerging in sports. Some sports were just starting, some were broadening their horizons, while othersRead MoreNew York Of The Twenties956 Words   |  4 Pagestechnology and ways of life. They were also in prohibition, which led to corruption and organized crime groups like the mafia. New York in the 1920’s is authentically portrayed in the The Great Gatsby as the epicenter of wealth, crime, and good times. First of all, the culture in New York City and Long Island in the 1920’s was roaring with many good and bad opportunities. There were many choices to be had, from parties to nightclubs to movie theaters. â€Å"The twenties witnessed the large scale use

Becoming a Helper free essay sample

To observe and rationalize our motivations and needs for becoming helpers can help us develop competent and practical approaches within the helping profession. I view human struggle as a catalyst for unity, in various degrees because in the face of adversary, we are naturally inclined to confide in others, seeking what we need to rise above certain circumstances. To elevate and uplift is directly connected towards my need to care for others, which has been a driving force behind my decision to enter the helping profession. Growing up, I had a strong sense of empathy, being able to make connections with my peers, from different walks of life. A lot of the times, I felt as if it was my â€Å"duty† to ensure that no burdens had to be carried by anyone. Within the SSW program, I’m looking to cultivate my ability to care for others effectively. â€Å"One of the pitfalls of being a caregiver to significant people in your life is that very often no one attends to your needs† (Coreyamp;Corey, 2007, p. We will write a custom essay sample on Becoming a Helper or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 5). I agree with this statement because there are times where I feel so caught up with needs of others I begin to disregard my own. Finding balance between my emotional well being and the well being of my clients is imperative in order to deliver the quality service that they are entitled to. Rejuvenation is essential. â€Å"The reality is that many clients will not express appreciation for your efforts nor will some of them make changes in their lives† (Coreyamp;Corey, 2007, p. 6). Which is why we shouldn’t rely on our clients exclusively to feel like useful human beings (Coreyamp;Corey, 2007). Finding pride and self worth from other sources in order to maintain composure in the field is also essential.

Youth and Guns Violence in America Essay Example

Youth and Guns: Violence in America Essay Gun violence in the United States has become an epidemic. From the Civil War to the present, 567,000 Americans have died in combat; but since 1920, over 1 million American civilians have been killed by firearms (Children’s Defense Fund, p. 15). For thousands of teens, death from gun violence is the end of the pipeline. In 2007, 3,042 children and teens died from gunfire in the United States—eight every day—as a result of homicide, suicide or accidental shootings. Almost six times as many children and teens – 17,523 – suffered non-fatal gun injuries, which have serious physical and emotional consequences. Children’s Defense Fund, p. 3) Youth violence is a complex problem, influenced by psychological, economic, and social factors (Eron and Slaby, 1–22). The problem is substantially worsened because of the lethality and accessibility of firearms. Guns cause deaths and severe injuries more frequently than knives, clubs, or fists, and with guns, even violent impulses can have lethal outcomes. Guns also are easily available to young people, even though federal law, with a few exceptions, prohibits those under 21 from purchasing handguns and those under 18 from purchasing rifles and shotguns or possessing handguns. Exceptional lethality, combined with easy access, accounts at least in part for the fact that firearm-related injuries remain the second leading cause of death among children and youth ages 10 to 19. Only motor vehicle accidents claim more young lives. (National Center for Injury Prevention and Control, Web-based Injury Statistics Query and Reporting System) Suicide is the third leading cause of death among youth aged 10 to 19 years in the United States, accounting for 1883 deaths in 2001 (Brady Campaign to Prevent Gun Violence). Firearms were used in approximately half of suicides within this age group in 2001; however, as recently as 1994, 7 of every 10 suicides among teenagers involved firearms. (Kellermann, p. 263) Numerous studies have documented a clear association between the presence of firearms in the home and suicides, particularly suicides by adolescents and young adults. One study found that a gun in the home is 22 times more likely to be used in a completed or attempted suicide, criminal assault or homicide (7x), or unintentional shooting death or injury (4x) than to be used in a self-defense shooting, contrary to what many ro-gunners believe. The rate of nonfirearm suicides among 5- to 14-year-olds in the United States is roughly equal to the rate in other industrialized countries combined. However, the firearm suicide rate among children in this age group is nearly 11 times higher. As a result, children in the United States commit suicide at twice the rate of children in 25 other industrialized nations combined. (Children’s Defense Fund, p. 101) Unintentional shootings among young people most frequently happen when children or youth obtain a gun and play with it, not realizing that it is real, or loaded, or pointed at themselves or a friend. We will write a custom essay sample on Youth and Guns: Violence in America specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Youth and Guns: Violence in America specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Youth and Guns: Violence in America specifically for you FOR ONLY $16.38 $13.9/page Hire Writer In 1998, more than 7% of children and youth under age 20 killed by firearms died in unintentional shootings,36 and these shootings accounted for 27% of firearm deaths among children under age 12. Boys, African American children, and Hispanic children are more likely to die in accidental shootings than are other groups of children. The death rate from unintentional shootings among children is nine times higher in the United States than in 25 other industrialized nations combined (Children’s Defense Fund, p. 101). Although accidental shootings of children have declined significantly in recent decades, they still attract a great deal of public attention, perhaps because the victims, and sometimes even the perpetrators, are seen as blameless and the deaths preventable. If guns were not present in the home, if they were designed with safety features making them difficult for children to fire, or if they were stored safely—unloaded and locked, with ammunition stored separately from the guns—the risk to young children could be virtually eliminated. As previously stated, firearm homicide is the second-leading cause of death for young people ages 1-19 in the United States. The 3,042 children and teens killed by gunfire in the U. S. in 2007 is comparable to the total number of U. S. combat deaths in Iraq and four times the number of American combat fatalities in Afghanistan to date. The amount of preschoolers (under age 5) killed by gunfire (85) is more than the number of law enforcement officers (57) killed in the line of duty. (Children’s Defense Fund, pg. 2). Out of 3,042 children and teens killed by gun? re, another 17,523 suffered non-fatal gun injuries. In addition to the human toll, gun violence among young people imposes significant psychological costs on society. For children and youth, these costs can be especially high; those exposed to gun violence are at risk for significant and lasting psychological effects. Moreover, children do not have to be injured themselves to experience these negative effects. Exposure to gun violence at home, at school, in the community, or through the media all can cause harm. Some of these affects include posttraumatic stress, poor school performance, increased delinquency, risky sexual behaviors, substance abuse, and desensitization to violence. All of these effects can make children and youth more prone to violence themselves. (Chidren’s Defense Fund, p. 12) However, the children and youth at highest risk for psychological trauma from gun violence are those exposed to it directly: children who are injured, who witness gun violence at close proximity, or who are exposed to high levels of gun violence in their homes, schools, or communities. (Chidren’s Defense Fund, p. 2) A December 2001 study of 119 African American seven-year-olds living in inner-city Philadelphia, for example, found that three-quarters had heard gunfire, one-third had seen someone shot, and one-tenth had someone in their own family or household who had been shot or stabbed. Among children in the study, exposure to higher levels of violence was correlated with more anxiety , greater likelihood of depression, lower self-esteem, lower grade point average, and more absences from school. More than 60% of the children worried that they might be killed or die, and 19% sometimes wished they were dead. Hurt, Malmud, Brodsky, and Giannetta 1351–56) Despite widespread recognition of the psychological costs to children and youth associated with gun violence, physicians and mental health professionals have been slow to develop treatments that help young people cope with gun-related trauma. Even children and youth who are injured often go without psychological help. One group of doctors has observed, â€Å"When patients present with suicide attempts, evaluation for future risk and follow-up treatment are considered standard practice. However, individuals treated for violent injuries generally receive no further evaluation. †(Christoffel, Spivak, and Witwer 1202–03) Although they are rare, shootings at schools and universities are devastating to families and communities. The last nation-wide known shooting occurred on April 16, 2007. A Virginia Tech student by the name of Seung-Hui Cho killed 32 students and faculty and wounded 15 more at the University before killing himself. Following the incident, there was an overwhelming response from both sides of the gun control issue. While the pro-gunners believed that arming the students would help their chances of survival if an attack were to occur, the community and students of Virginia Tech went forward with a â€Å"Lie-In† to try to instill stricter gun laws. Despite the efforts towards stricter gun laws on school grounds and campuses alike, there have been at least 60 cases of mass school shootings involving kids and teens since 2007 (Brady). What will it take for us to stop this senseless loss of young lives? Common sense gun laws can make a difference. States with higher rates of gun ownership and weak gun control laws have the highest rates of firearm deaths of people of all ages. Although polls show that the majority of Americans favor common sense gun control laws that would stem the tide of gun violence, federal and state legislative reform has been difficult to achieve. We need political leaders who will protect our children by enacting legislation to limit the number of guns in our communities, control who can obtain firearms, and ensure that guns in the home are stored safely and securely. (Childrens Defense Fund, p. 6) There is no federal law that specifically allows or prohibits guns on college campuses. According to the American Association of State Colleges and Universities, 26 states prohibit guns on college campuses with the exception of public safety officers. Twenty-three states allow public campuses to determine their own gun policies, with nearly all choosing to be gun-free. Only one state — Utah — c urrently prohibits college administrators and security professionals from setting rules regarding firearms on campus, thus effectively allowing guns on campus (Brady Campaign to Prevent Gun Violence). No single policy solution will end youth gun violence in the United States; a wide variety of approaches is needed to address different aspects of the problem. Key strategies that may reduce youth gun violence include: reducing unsupervised exposure to guns among children and youth, strengthening social norms against violence in communities, enforcing laws against youth gun carrying, altering the design of guns to make them less likely to be used by children and youth, and, perhaps most importantly, implementing new legal and regulatory interventions that make it more difficult for youth to obtain guns. Numerous studies document the ease with which youth can obtain guns in the United States. In a 1998 national study of male high school sophomores and juniors, 6% of respondents had carried a handgun outside the home in the previous 12 months. Among the youth who had carried guns, 48% had been given or loaned the gun by a family member or friend. An equal percentage had obtained the gun through an illegal purchase or theft: 35% had bought the gun (of those, 53% bought from family or friends), 5% reported asking someone else to purchase the gun, and 6% had stolen or traded something for it (Sheller, Wright 1994). Youth can obtain guns illegally from licensed dealers or in private transactions. Although licensed firearms dealers are regulated by the federal government (and by many states) and are required to conduct criminal background checks on all purchasers, some dealers do sell illegally to youth, often by turning a blind eye to â€Å"straw purchases†, in which youth ask older acquaintances to buy guns for them. Only a small minority of licensed gun dealers are involved in illegal activity. According to federal statistics, guns sold by 1. % of retailers account for more than 57% of the weapons that are later traced by ATF after being recovered by law enforcement following a crime (Commerce in firearms in the United States). At the same time, guns sold by licensed dealers account for only about 60% of the guns sold in the United States. Guns sold by private parties, collectors, and unlicensed vendors at gun shows account for 40% of all gun sales. These sales are not regulated by the federal government, nor by most states. In an unregulated private sale, no background check takes place. Sellers are not required to keep records of their sales, and they do not even have to ask buyers for identification. Such lax requirements make it easy for youth to obtain guns. Decreasing the availability of illegal guns to youth is an important strategy to de-escalate the violence that plagues many communities, and to reduce the fear and need for self-protection that lead many youth to get guns in the first place. Researcher David Kennedy, who has written extensively about youth gangs and gun violence, has observed, Many of the kids involved in this life do not really want to live it. Less readily available weaponry would ease tensions and diminish the deadliness of incidents. (Kennedy, 76) Without stronger, sensible gun laws, thousands upon thousands of people will continue to die and be injured needlessly each year. We make it too easy for dangerous people to obtain dangerous weapons. We should make it harder for convicted felons, the dangerously mentally ill, domestic violence offenders and youth to get the guns in the first place. We can do this by passing strong, effective laws and stopping laws and policies that would allow guns on campuses. Works Cited Brady Campaign to Prevent Gun Violence. Brady Campaign, 2011. Web. 9 Dec 2011. . Childrens Defense Fund, Protect Children Not Guns 2010, September 2010 Christoffel, K. K. , Spivak, H. , and Witwer, M. â€Å"Youth violence prevention: The physicians role. † Journal of the American Medical Association (March 1, 2000) 1202–03. Eron, L. D, and LG Slaby. Reason to hope: A psychosocial perspective on violence and youth . Washington, DC: American Psychological Association, 1996. 1–22. Hurt, H. , M. Malmud, N. Brodsky, and J. Giannetta. Exposure to violence: Psychological and academic correlates in child witnesses. Archives of Pediatrics and Adolescent Medicine. (2001): 1351–56. Print. Fowler, Patrick J. , et al, â€Å"Community Violence: A Meta-Analysis on the Effect of Exposure and Mental Health Outcomes of Children and Adolescents,† Development and Psychopathology 21 (2009) Kellermann, Arthur L. , Injuries and Deaths due to Firearms in the Home, Journal of Trauma (1998) Kennedy, D. Can we keep guns away from kids? The American Prospect (June 23, 1994) 74–80 Miller, Matthew, Deborah Azrael, and David Hemenway. â€Å"Household Firearm Ownership and Suicide Rates in the United States. † Epidemiology 13 (2006) 517-724 National Center for Injury Prevention and Control, Web-based Injury Statistics Query and Reporting System. n. page. Web. 9 Dec. 2011. . Sheley, J. F. , and Wright, J. D. High school youth, weapons, and violence: A national survey. National Institute of Justice Research in Brief. Washington, DC. October 1998 United

The Architectural Pediment and How to Use It

The Architectural Pediment and How to Use It A pediment is a low-pitched triangular gable originally found on temples in ancient Greece and Rome. Pediments were reinvented during the Renaissance and later imitated in Greek Revival and Neoclassical house styles of the 19th and 20th centuries. Use of pediments has been freely adapted in many styles of architecture, yet remains most closely associated with Greek and Roman (i.e., Classical) derivatives. The word pediment is thought to have come from the word meaning pyramid, as the triangular pediment has a spatial dimension similar to the pyramid. Use of Pediments Originally the pediment had a structural function. As the  Jesuit priest Marc-Antoine Laugier explained in 1755, the pediment is one of only three essential elements of what Laugier called the basic primitive hut. For many Greek temples, first made of wood, the triangular geometry had a structural function. Fast forward 2,000 years from ancient Greece and Rome to the Baroque period of art and architecture, when the pediment became an ornamental detail to be extravagantly modified. Pediments are most often used today to create a solid, regal, stately look-and-feel to the architecture, such as is used for banks, museums, and government buildings. Often, the triangular space is filled with symbolic statuary when a message need be proclaimed. The space within a pediment is sometimes called the tympanum, although this word more commonly refers to the Medieval-era arch areas over a doorway decorated with Christian iconography. In residential architecture, pediments are commonly found above windows and doorways. Examples of Pediments The Pantheon in Rome proves just how far back in time pediments were used - at least 126 A.D. But pediments were around before that, as can be seen in ancient cities around the world, like the UNESCO World Heritage site of Petra, Jordan, the Nabataean caravan city influenced by Greek and Roman rulers. Whenever architects and designers turn to ancient Greece and Rome for ideas, the result will likely include the column and the pediment. The Renaissance in the 15th and 16th centuries was such a time -- a rebirth of Classical designs by the architects Palladio (1508-1580) and Vignola (1507-1573) leading the way. In the United States, American statesman Thomas Jefferson (1743-1826) influenced the architecture of a new nation. Jeffersons home, Monticello, incorporates Classical design by using not only a pediment but also a dome - very much like the Pantheon in Rome. Jefferson also designed the Virginia State Capitol Building in Richmond, Virginia, which influenced the federal government buildings being planned for Washington, D.C. Irish-born architect James Hoban (1758-1831) brought Neoclassical ideas from Dublin to the new capital when he modeled the White House after the Leinster House in Ireland. In the 20th century, pediments can be seen throughout America, from the New York Stock Exchange in Lower Manhattan to the 1935 U.S. Supreme Court Building in Washington, D.C. and then on to the 1939 mansion known as Graceland near Memphis, Tennessee. Definition pediment: the triangular gable defined by the crown molding at the edge of a gabled roof and the horizontal line between the eaves. -   John Milnes Baker, AIA Other Uses of the Word Pediment Antique dealers will often use the word pediment to describe an ornate flourish in Chippendale-era furniture. Because the word describes a shape, it is often used to describe man-made and natural shapes. In geology, a pediment is a sloping formation caused by erosion. Five Types of Pediments 1. Triangular Pediment: The most common pediment shape is the pointed pediment, a triangle framed by a cornice or ledge, with the apex at the top, two symmetrical straight lines  sloping to the ends of a horizontal cornice. The rake or angle of the slope can vary. 2. Broken Pediment: In a broken pediment, the triangular outline is non-continuous,  open at the top, and without a point or vertex. The broken space is usually at the top apex (eliminating the top angle), but sometimes at the bottom horizontal side. Broken pediments are often found on antique furniture. A swan-necked or rams head pediment is a type of broken pediment in a highly ornamented S-shape. Broken pediments are found in Baroque architecture, a period of experimentalism in detail, according to Professor Talbot Hamlin, FAIA. The pediment became an architectural detail with little or no structural function. Baroque detail thus became a matter of the increasingly free modification of forms originally classic, to made them sensitive to every possible nuance of emotional expression. Pediments were broken and their sides curved and scrolled, separated by cartouches, or urns; columns were twisted, moldings duplicated and reduplicated to give sharp emphasis, and broken suddenly out and in where a complexity of shadow was desired. - Hamlin, p. 427 3. Segmental Pediment: Also called round or curved pediments, segmental pediments contrast with triangular pediments in that they have a round cornice replacing two sides of the traditional triangular pediment. A segmental pediment might complement or even be called a curvilinear tympanum. 4. Open Pediment: In this type of pediment, the usual strong horizontal line of the pediment is absent or nearly absent. 5. Florentine Pediment:  Before Baroque, architects of the early Renaissance, when sculptors became architects, developed a decorative styling of pediments. Over the years, this architectural detail became known as Florentine pediments, after their use in Florence, Italy. It consists of a semicircular form placed above the entablature, and as wide as the enclosing columns or pilasters. Usually a simple ban of moldings runs around it, and the semicircular field below is often decorated with a shell, although sometimes molded panels and even figures are found. Little rosettes and leaf and flower forms are usually used to fill the corner between the ends of the semicircle and the cornice below, and also as a finial at the top. - Hamlin, p. 331 Pediments for the 21st Century Why do we use pediments? They give a sense of tradition to a home, in the Western Classical architecture sense. Also, the geometric design itself is innately pleasing to the human senses.  For todays homeowners, creating a pediment is a rather simple, inexpensive way to add decoration - usually over a door or window. Have pediments gone sideways? Todays modern skyscraper architects use triangles for structural strength as well as beauty. David Childs design for One World Trade Center (2014) is a good example of aesthetically pleasing grandeur. Norman Fosters Hearst Tower (2006) is filled with triangulation; its beauty is up for discussion. Sources American House Styles: A Concise Guide by John Milnes Baker, AIA, Norton, 1994, p. 175Architecture through the Ages by Talbot Hamlin, Putnam, Revised 1953, pp. 444, 427, 331Furniture with broken pediment Agostini/A. Dagli Orti/Getty Images (cropped)Broken Pediment on Residential Portico Richard Leo Johnson/Getty Images (cropped)Contrasting pediments Julian Castle/ArcaidImages/Getty ImagesPediments over windows Brian Bumby/Getty Images

Richard Howe - Royal Navy Richard Howe

Richard Howe - Royal Navy Richard Howe Richard Howe - Early Life Career: Born March 8, 1726, Richard Howe was the son of Viscount Emanuel Howe and Charlotte, Countess of Darlington. The half-sister of King George I, Howes mother wielded political influence which aided in her sons military careers. While his brothers George and William pursued careers in army, Richard elected to go to sea and received a midshipmans warrant in the Royal Navy in 1740. Joining HMS Severn (50 guns), Howe took part in Commodore George Ansons expedition to the Pacific that fall. Though Anson eventually circumnavigated the globe, Howes ship was forced to turn back after failing to round Cape Horn. As the War of the Austrian Succession raged, Howe saw service in the Caribbean aboard HMS Burford (70) and took part in the fighting at La Guaira, Venezuela in February 1743. Made an acting lieutenant after the action, his rank was made permanent the next year. Taking command of the sloop HMS Baltimore in 1745, he sailed off the coast of Scotland in support of operations during the Jacobite Rebellion. While there, he was badly wounded in the head while engaging a pair of French privateers. Promoted to post-captain a year later, at the young age of twenty, Howe received command of the frigate HMS Triton (24). The Seven Years War: Moving to Admiral Sir Charles Knowles flagship, HMS Cornwall (80), Howe captained the vessel during operations in the Caribbean in 1748. Taking part in the October 12 Battle of Havana, it was his last major action of the conflict. With the arrival of peace, Howe was able to retain sea-going commands and saw service in the Channel and off Africa. In 1755, with the French Indian War underway in North America, Howe sailed across the Atlantic in command of HMS Dunkirk (60). Part of Vice Admiral Edward Boscawens squadron, he aided in the capture of Alcide (64) and Lys (22) on June 8. Returning to the Channel Squadron, Howe took part in the naval descents against Rochefort (September 1757) and St. Malo (June 1758). Commanding HMS Magnanime (74), Howe played a key role in capturing Ile de Aix during the former operation. In July 1758, Howe was elevated to title of Viscount Howe in the Irish Peerage following the death of his older brother George at the Battle of Carillon. Later that summer he participated in raids against Cherbourg and St. Cast. Retaining command of Magnanime, he played a role in Admiral Sir Edward Hawkes stunning triumph at the Battle of Quiberon Bay on November 20, 1759. A Rising Star: With the war concluding, Howe was elected to Parliament representing Dartmouth in 1762. He retained this seat until his elevation to the House of Lords in 1788. The following year, he joined the Admiralty Board before becoming Treasurer of the Navy in 1765. Fulfilling this role for five years, Howe was promoted to rear admiral in 1770 and given command of the Mediterranean Fleet. Elevated to vice admiral in 1775, he held sympathetic views pertaining to the rebelling American colonists and was an acquaintance of Benjamin Franklin. The American Revolution: As a result of these feelings, the Admiralty appointed him to command the North American Station in 1776, in the hope that he could aid in quieting the American Revolution. Sailing across the Atlantic, he and his brother, General William Howe, who was commanding British land forces in North America, were appointed as peace commissioners. Embarking his brothers army, Howe and his fleet arrived off New York City in the summer of 1776. Supporting Williams campaign to take the city, he landed the army on Long Island in late August. After brief campaign, the British won the Battle of Long Island. In the wake of the British victory, the Howe brothers reached out to their American opponents and convened a peace conference on Staten Island. Taking place on September 11, the Richard Howe met with Franklin, John Adams, and Edward Rutledge. Despite several hours of discussions, no agreement could be reached and the Americans returned to their lines. While William completed the capture of New York and engaged General George Washingtons army, Richard was under orders to blockade the North American coast. Lacking the necessary number of vessels, this blockade proved porous. Howes efforts to seal American ports were further hampered by the need to provide naval support to army operations. In the summer of 1777, Howe transported his brothers army south and up the Chesapeake Bay to commence its offensive against Philadelphia. While his brother defeated Washington at Brandywine, captured Philadelphia, and won again at Germantown, Howes ships worked to reduce the American defenses in the Delaware River. This complete, Howe withdrew the fleet to Newport, RI for the winter. In 1778, Howe was deeply insulted when he learned of the appointment of a new peace commission under the guidance of the Earl of Carlisle. Angered, he submitted his resignation which was reluctantly accepted by the First Sea Lord, the Earl of Sandwich. His departure was soon delayed as France entered the conflict and a French fleet appeared in American waters. Led by the Comte dEstaing, this force was unable to catch Howe at New York and was prevented from engaging him at Newport due to a severe storm. Returning to Britain, Howe became an outspoken critic of Lord Norths government. These views kept him from receiving another command until Norths government fell in early 1782. Taking command of the Channel Fleet, Howe found himself outnumbered by the combined forces of the Dutch, French, and Spanish. Adroitly shifting forces when needed, he succeeded in protecting convoys in the Atlantic, holding the Dutch in port, and conducting the Relief of Gibraltar. This last action saw his ships deliver reinforcements and supplies to the beleaguered British garrison which had been under siege since 1779. Wars of the French Revolution Known as Black Dick due to his swarthy complexion, Howe was made First Lord of the Admiralty in 1783 as part of William Pitt the Youngers government. Serving for five years, he faced debilitating budget constraints and complaints from unemployed officers. Despite these issues, he succeeded in maintaining the fleet in a state of readiness. With the beginning of Wars of the French Revolution in 1793, he received command of the Channel Fleet despite his advanced age. Putting to sea the following year, he won a decisive victory at the Glorious First of June, capturing six ships of the line and sinking a seventh. After the campaign, Howe retired from active service but retained several commands at the wish of King George III. Beloved by the sailors of the Royal Navy, he was called upon to aid in putting down the 1797 Spithead mutinies. Understanding the demands and needs of the men, he was able to negotiate an acceptable solution which saw pardons issued for those who had mutinied, pay raises, and the transfer of unacceptable officers. Knighted in 1797, Howe lived another two years before dying on August 5, 1799. He was buried in the family vault at St. Andrews Church, Langar-cum-Barnstone. Selected Sources NNDB: Richard Howe Napoleon Guide: Admiral Richard Howe

Control Room - a video by Al Jazeera Assignment Example | Topics and Well Written Essays - 500 words

Control Room - a video by Al Jazeera - Assignment Example The channel depicted the massive casualties of innocent people, which was seen as detrimental or somehow derogatory to US operations. Also, the documentary outlined alleged propagandas that America has done to veer people’s attention away from casualties of war and focus on the success of the allied forces in ousting Saddam’s regime. Based on the video documentary, it is primarily aimed to provide the world, especially their Arab fellows, a clear view of the events that have transpired during the war. It presented war-related issues and the sentiments that the Iraqi people had. Though at some point the video delivers point-of-views that might somehow be biased in nature since they are catering their network to their Arab viewers, they remained keen on providing an overview of the war at the perspective of the Iraqi people and the Arabs. Media is truly a powerful tool that can significantly contribute to the overall perspective of an individual on certain issues. For instance, members of the Al Jazeera has shown an event wherein the US allegedly done a publicity stunt to drive away attention from three incidents involving the death of media personnel to US airstrikes. One of the most notable and commendable actions that Al Jazeera took was its courage to go against the tide of all other media coverage during the war. Correspondents have been vigilant in providing its viewers with the actual events that Iraqi people are experiencing; their fear, their pain, and their struggle. However, the video also takes a direct attack on the credibility of the network on issues since some viewers may perceive their actions during the war Iraq are just propaganda to further promote conflicts between the Middle East and the US. In addition, Kirkpatrick’s article on the alleged collusion of the Al Jazeera top news director with a US official to take down two images which an involved a woman and a child who was affected by the on-going war that time. It was clearly conveyed in the video that with any kind of war, there will be deaths of innocent children, men and women; as if there is very little, or nearly absent, consideration on the lives that will be lost, families that will be broken, and communities that will have to start again from scratch after the war has ended.     

Essay 2 Example | Topics and Well Written Essays - 1250 words - 9

2 - Essay Example From Tito’s story, the theme of family relationship emerges, and one learns about the disadvantages of having poor relationship with family. The immigrant, Tito Urena, is portrayed as one that had poor relationship with his family members. He is shown as having not communicated with his family for a long time. Additionally, he was involved in a conflict with one Haydee, who was once his wife, with whom he had separated for 16 years (Spack 156). The story also shows the remarkable isolation of Tito during the time of his death, as well as after his death. A highlight of this story is where Tito suffers a heart attack that cuts his life short while in his office. At the time of his death, Tito had no one around him in his office, as he was all alone. He lived far away from his family whom he never contacted. His poor relationship with family could not allow him to call any of them before succumbing to the heart attack. Therefore, Tito died all alone. After his death, no one realized that Tito was dead. In fact, his body spent two days in the office before being noticed (Spack 159). His body remained unclaimed, and only his mistress could be traced by police. Therefore, this kind of alienation and failure to embrace family relationships made Tito live and die a lonely death. The second story, â€Å"Albert and Esene† by Frances Khirallah also bears the significant theme of family relationships. The author depicts Esene, a widow, as having good relationship with her family members and relatives. This story teaches on the advantages of embracing good relationship with family. There are different aspects in this story that are an evidence of the good relations that Esene had with her family. For instance, Esene shares jokes and a light moment with her husband’s, Albert’s, sisters that came to visit her (Spack 162). The mere fact that these two ladies, Safiyah and Amelia, visited Esene shows just how strong their

In His Tragedies Shakespeare Often Presents Women Merely as the Tragic Victims of Men Essay Example for Free

In His Tragedies Shakespeare Often Presents Women Merely as the Tragic Victims of Men Essay In His Tragedies Shakespeare Often Presents Women Merely as the Tragic Victims of Men. To What Extent Do You Consider This Applies to Desdemona In Othello? There are no Antigones in Elizabethan Drama, Lyndsey Turner. Turner is here expressing the view that Shakespeare does not use his women as heroines. Instead she is of the opinion that they are used as devices on which the tragic impulses of the plays male characters are enacted. They are a device to produce a cathartic response from Shakespeares audience. In order to discuss to what extent Desdemona complies with this view, it would appear logical to define a tragic victim. Many say that a tragic victim is a character in a tragedy who suffers at the hand of circumstance and the fates. They suffer through no fault of their own and are brought down by others, they are totally powerless to change their fate and dont contribute to their own tragedy; they are solely the victims of others. It is also vital that they produce a cathartic response from the audience in order for their suffering to be tragic. Looking at these criteria it becomes clear why Shakespeare often uses women as his tragic victims. In the time Shakespeare was writing women had very little influence on their destiny having to submit either to their father or husband. They were the objects of men. When Iago warns Brabantio of his daughters escape he says Look to your house, your daughter and your bags. This shows of how little importance women were, being so powerless they would then be a natural choice for tragic victims, powerless to avoid their fate because of their weakness in society. However, when Desdemona is first presented to us she does not seem anything like a stereotypical woman of the time. Her character is presented as much stronger than that. Her father has not tried to force her into marriage even telling Roderigo that, My daughter is not for thee, even though it is clear that Roderigo is a rich man. At the end of Act one he goes to, sell all his land, in order to pursue Desdemona. As Brabantio is not therefore being in any way a tyrant to his daughter; her ability to escape from the house and deceive him shocks us and surely would have shocked a contemporary audience even more. This woman is not the kind of person you would expect to become a victim. Before the audience have even seen her she is described as a woman of, Beauty, wit and fortunes. She has gone to Othello in the dead of night protected by a, Knave of common hire, a gondolier. This shows Desdemonas bravery and strength. All of this increases her status with the audience and detracts from the image of a weak submissive woman. In Act 1 Scene 3 she defies what the Duke says, when he requests that she stay at her fathers house while Othello is in Cyprus saying that, She did love the Moor to live with him. For a woman to speak in front of a council of the most powerful people in Venice, not invited to do so, would be shocking to a contemporary audience and really show her strength of character. It is almost as though she is a feminine version of Othello, as Patsy Hall says, She cannot be the man, but she can be the husband of the man. She has shunned the Wealthy curled darlings of her nation unlike most women and instead chooses Othello. She doesnt care about his age or race she sees Othellos visage in his mind. The language Shakespeare gives her when talking of her wooing shows how deeply immersed in Othellos world she is; she, Falls in love with the battles even her language is strong. My downright violence and storm of fortunes, She is presented as incredibly strong certainly not a figure of pity. It is seemingly no wonder that Othello calls her, his fair warrior. Although Desdemona is first portrayed as quite a heroic figure by Shakespeare he soon starts to use her as a cathartic device, as the audience watch her previous strength fall away. It becomes clear that Shakespeare made her so strong willed deliberately in order to shape our response to Desdemona. Doing this makes it that much more painful for the audience. A major episode wherein Desdemona is presented as an object of pity is in the handkerchief episode. Desdemona loses her handkerchief and Othello sees Cassio with it. Despite Othellos growing suspicion, Desdemona remains ignorant claiming that, The sun where he was born drew all such humours from him. We feel tremendous pity for Desdemona when she says this because Shakespeare has shaped our response using structure and also the irony of her language. In the last scene we saw that Othello was seething with jealousy and vowed to kill her. This amplifies hugely our feeling of catharsis for her because we feel so helpless. Our pity for her is only added to when Shakespeare shapes events in the play so that all her qualities that were viewed as good in the first act of the play cause her to fall even further. However, she is still a victim because she is powerless to stop it; she is a victim of circumstance and ignorance that Iago has been planning her destruction. She continues to mention Cassio even when it is clear it is causing Othello irritance, she thinks that it is a trick to put her from her suit. The audiences feeling of catharsis is amplified as we can do nothing while her language puts her fidelity in more doubt in Othellos mind The time when we pity her most however is when Othello strikes her. Again she says precisely the wrong things, through no fault of her own but rather because her loving nature wishes to help Cassio, saying that, She would do much for the love she bears to Cassio. All the audience can do is sit and despair for her. When he hits her we think that maybe her strength will come back but she simply responds by saying that she, Will not stay to offend Othello. We despair because we know that if she submits to Othello she will die at his hands. This is yet more evidence of Desdemonas good proving to be her downfall. Shakespeare shapes events very cleverly in the next section in order to get the largest cathartic reaction. For a moment it seems like we might see a glimpse of Desdemonas fight. She claims, She has no Lord. The audience think for a moment she will be fine, however soon she is asking Iago, What shall I do to win my Lord again. The assertive Desdemona from the earlier scenes is gone and the audience despair for her. Even when Othello kills her she does not blame him. When asked who has killed her she says, Nobody, I myself. She dies a symbol of goodness and love, the way Shakespeare shapes her demise is unquestionably tragic. However, is she actually a victim? The audience on the most part at the time would say she is because she does not fall through a flaw in her character. However was she totally helpless and unable to change her fate? Patsy Hall argues that Othello and Desdemona have a, Mutual ignorance of each others nature, saying also that she is, so selflessly devoted that she cannot acknowledge imperfection in her husband. I would agree with this statement by Hall. The audience are constantly perplexed throughout the play as to why Othello will not listen to anyone but Iago. This could be perhaps a comment on how women have had to suffer under the patriarchal society in which Shakespeares original audience was living, perhaps through Desdemona he is trying to show the unfair nature of their society. But in many ways the same is true for Desdemona. Emilia tries to tell her that, Jealous souls are not ever jealous for the cause, but jealous for they are jealous. But even after this warning Desdemona takes no heed of anyone but Iago, therefore it could just perhaps be confirmation of Iagos intelligence, this backs up Desdemonas role as a victim as she is a victim of others. So in conclusion there is no doubt that Desdemonas demise is very much tragic. Also having examined the criteria it would be accurate to say that in many ways Desdemona is a victim. She suffers through no fault of her own and is the victim of circumstance. However, I am not sure that one could say that she was totally powerless to stop her eventual fate. I would say that Desdemona was not a victim of Iagos scheming or Othellos jealousy as she could have stopped these. She was a victim of her own love for Othello. Therefore, I would say that the statement in the title applies to Desdemona so far as she was the tragic victim of her own love for a man.

John Lennon :: essays research papers

I like music. Whenever I listen to my favorite music, I feel good. My favorite musician is John Lennon. I have reasons why I like him and why I choose John Lennon as famous person. I like songs of John Lennon because of his song is kind and beautiful. In addition to we always impressed with his songs. I consider that John Lennon was one of the best musician in history because of his songs had a lot of influence on us. Everybody knows John Lennon regardless of the generation gap. John Winston Lennon was born October 9,1940 in Liverpool England. His parents separated and his mother married another man and he ended up living with his aunt Mimi. John entered Dovedale Primary School in Liverpool in 1945. He showed a natural aptitude for drawing and word play. When Lennon was 17 his mother was killed by a bus. In 1952 John entered Quarvy Bank High School. John was well behaved in the house because of his aunt was strict woman but in school he was very bad. In 1956 his aunt bought John a guitar that started he shows his music ability and then he created the group called the ?gQuarry Man?h. The band had shifting member until 1957 when the second permanent member was in. His name was Paul Mccartney. John came up with the name Beatles for the group. They were performing in the cavern. In 1961 the Beatles debuted at the Cavern Club and then they released their first single ?gLove me Do?h. John met a woman in 1966. Her name is Yoko Ono. John fell love with her and he divorced his first wife and re-married Yoko Ono. After the Beatles broke up and John started doing this by releasing solo album Imagine. But on December 8, 1980,Lennon, returning to their apartment on New York City?

Explain the difference between Anxiety and Depression

Two mental disorders that are closely associated with another and share similarities are anxiety and depression. Anxiety is a psychological and a physical state in which a person exhibits excessive fear, nervousness, apprehension, or worry (eMedicineHealth, 2008). Usually people with anxiety cannot stop worrying about things, especially if these are beyond their control. In addition, anxiety also causes people to exaggerate problems and fears, which eventually disrupt their normal way of life because they believe that these problems and fears cannot be solved.In most cases, anxiety is caused by stress or other external factors that cause people to worry a lot (United States National Library of Medicine and National Institutes of Health, 2008). Its most common symptoms may include sweating, palpitations, trembling, nausea, shortness of breath, dizziness, and chest pain, among others (eMedicineHealth, 2008). On the other hand, depression is a condition wherein a person is excessively s ad, hopeless, and/or discouraged (Mayo Clinic, 2008).Like anxiety, it also affects people’s perception and behavior towards several things, especially problems (Mayo Clinic, 2008). One of its most common symptoms include irritability, restlessness, sleeping problems, inability to focus or concentrate, feeling worthless, suicidal thoughts, excess fatigue, and even lose of interest in sex, among many others (Mayo Clinic, 2008). The main difference between anxiety and depression is that the latter is a more severe condition of the latter.A person suffering from depression actually feels sad and excessively discouraged and usually knows what they are depressed about but are unable to control it (Lowrance, 2008). On the other hand, a person with anxiety usually fears something that might happen or something that he or she has not experienced or seen yet (Lowrance, 2008). In other words, anxiety usually involves fear of the future or fear of what might happen due to the present pro blems.

Babylonian Mathematics Essay

1 Introduction Our first knowledge of mankind’s use of mathematics comes from the Egyptians and Babylonians. Both civilizations developed mathematics that was similar in scope but different in particulars. There can be no denying the fact that the totality of their mathematics was profoundly elementary2 , but their astronomy of later times did achieve a level comparable to the Greeks. Assyria 2 Basic Facts The Babylonian civilization has its roots dating to 4000BCE with the Sumerians in Mesopotamia. Yet little is known about the Sumerians. Sumer was first settled between 4500 and 4000 BC by a non-Semitic 1  °2002, c 2 Neugebauer, G. Donald Allen 1951 Babylonian Mathematics 2 people who did not speak the Sumerian language. These people now are called Ubaidians, for the village Al-Ubaid, where their remains were first uncovered. Even less is known about their mathematics. Of the little that is known, the Sumerians of the Mesopotamian valley built homes and temples and decorated them with artistic pottery and mosaics in geometric patterns. The Ubaidians were the first civilizing force in the region. They drained marshes for agriculture, developed trade and established industries including weaving, leatherwork, metalwork, masonry, and pottery. The people called Sumerians, whose language prevailed in the territory, probably came from around Anatolia, probably arriving in Sumer about 3300 BC. For a brief chronological outline of Mesopotamia see http://www.gatewaystobabylon.com/introduction/briefchonology.htm. See also  http://www.wsu.edu:8080/ËÅ"dee/MESO/TIMELINE.HTM for more detailed information. The early Sumerians did have writing for numbers as shown below. Owing to the scarcity of resources, the Sumerians adapted the ubiquitous clay in the region developing a writing that required the use of a stylus to carve into a soft clay tablet. It predated the 1 10 60 600 3,600 36,000 cuneiform (wedge) pattern of writing that the Sumerians had developed during the fourth millennium. It probably antedates the Egyptian hieroglyphic may have been the earliest form of written communication. The Babylonians, and other cultures including the Assyrians, and Hittites, inherited Sumerian law and literature and importantly their style of writing. Here we focus on the later period of the Mesopotamian civilization which engulfed the Sumerian civilization. The Mesopotamian civilizations are often called Babylonian, though this is not correct. Actually, Babylon3 was not the first great city, though the whole civilization is called Babylonian. Babylon, even during its existence, was not always 3 The first reference to the Babylon site of a temple occurs in about 2200 BCE. The name means â€Å"gate of God.† It became an independent city-state in 1894 BCE and Babylonia was the surrounding area. Its location is about 56 miles south of modern Baghdad. Babylonian Mathematics 3 the center of Mesopotamian culture. The region, at least that between the two rivers, the Tigris and the Euphrates, is also called Chaldea. The dates of the Mesopotamian civilizations date from 2000-600 BCE. Somewhat earlier we see the unification of local principates by powerful leaders — not unlike that in China. One of the most powerful was Sargon the Great (ca. 2276-2221 BC). Under his rule the region was forged into an empire called the dynasty of Akkad and the Akkadian language began to replace Sumerian. Vast public works, such as irrigation canals and embankment fortifications, were completed about this time. These were needed because of the nature of the geography combined with the need to feed a large population. Because the Trigris and Euphrates would flood in heavy rains and the clay soil was not very absorptive, such constructions were necessary if a large civilization was to flourish. Later in about 2218 BCE tribesmen from the eastern hills, the Gutians, overthrew Akkadian rule giving rise to the 3rd Dynasty of Ur. They ruled much of Mesopotamia. However, this dynasty was soon to perish by the influx of Elamites from the north, which eventually destroyed the city of Ur in about 2000 BC. These tribes took command of all the ancient cities and mixed with the local people. No city gained overall control until Hammurabi of Babylon (reigned about 1792-1750 BCE) united the country for a few years toward the end of his reign. The Babylonian â€Å"texts† come to us in the form of clay tablets, usually about the size of a hand. They were inscribed in cuneiform, a wedge-shaped writing owing its appearance to the stylus that was used to make it. Two types of mathematical tablets are generally found, table-texts and problem texts. Table-texts are just that, tables of values for some purpose, such as multiplication tables, weights and measures tables, reciprocal tables, and the like. Many of the table texts are clearly â€Å"school texts†, written by apprentice scribes. The second class of tab lets are concerned with the solutions or methods of solution to algebraic or geometrical problems. Some tables contain up to two hundred problems, of gradual increasing difficulty. No doubt, the role of the teacher was significant. Babylon fell to Cyrus of Persia in 538 BC, but the city was spared. Babylonian Mathematics 4 The Darius inscription on cliff near Bisotun The great empire was finished. However, another period of Babylonian mathematical history occurred in about 300BCE, when the Seleucids, successors of Alexander the Great came into command. The 300 year period has furnished a great number of astronomical records which are remarkably mathematical — comparable to Ptolemy’s Almagest. Mathematical texts though are rare from this period. This points to the acuity and survival of the mathematical texts from the old-Babylonian period (about 1800 to 1600 BCE), and it is the old period we will focus on. The use of cuneiform script formed a strong bond. Laws, tax accounts, stories, school lessons, personal letters were impressed on soft clay tablets and then were baked in the hot sun or in ovens. From one region, the site of ancient Nippur, there have been recovered some 50,000 tablets. Many university libraries have large collections of cuneiform tablets. The largest collections from t he Nippur excavations, for example, are to be found at Philadelphia, Jena, and Istanbul. All total, at least 500,000 tablets have been recovered to date. Even still, it is estimated that the vast bulk of existing tablets is still buried in the ruins of ancient cities. Babylonian Mathematics 5 Deciphering cuneiform succeeded the Egyptian hieroglyphic. Indeed, just as for hieroglyphics, the key to deciphering was a trilingual inscription found by a British office, Henry Rawlinson (1810-1895), stationed as an advisor to the Shah. In 516 BCE Darius the Great, who reigned in 522-486 BCE, caused a lasting monument4 to his rule to be engraved in bas relief on a 100 Ãâ€" 150 foot surface on a rock cliff, the â€Å"Mountain of the Gods† at Behistun5 at the foot of the Zagros Mountains in the Kermanshah region of modern Iran along the road between modern Hamadan (Iran) and Baghdad, near the town of Bisotun. In antiquity, the name of the village was Bagastà ¢na, which means ‘place where the gods dwell’. Like the Rosetta stone, it was inscribed in  three languages — Old Persian, Elamite, and Akkadian (Babylonian). However, all three were then unknown. Only because Old Persian has only 43 signs and had been the subject of serious investigation since the beginning of the century was the deciphering possible. Progress was very slow. Rawlinson was able to correctly assign correct values to 246 characters, and moreover, he discovered that the same sign could stand for different consonantal sounds, depending on the vowel that followed. (polyphony) It has only been in the 20th century that substantial publications have appeared. Rawlinson published the completed translation and grammar in 1846-1851. He was eventually knighted and served in parliament (1858, 1865-68). For more details on this inscription, see the article by Jona Lendering at http://www.livius.org/be-bm/behistun/behistun01.html. A translation is included. Babylonian Numbers 3 In mathematics, the Babylonians (Sumerians) were somewhat more advanced than the Egyptians. †¢ Their mathematical notation was positional but sexagesimal. to some sources, the actual events described in the monument took place between 522 and 520 BCE. 5 also spelled Bistoun  ¯  ¯ 4 According Babylonian Mathematics †¢ They used no zero. 6 †¢ More general fractions, though not all fractions, were admitted. †¢ They could extract square roots. †¢ They could solve linear systems. †¢ They worked with Pythagorean triples. †¢ They studied circular measurement. †¢ They solved cubic equations with the help of tables. †¢ Their geometry was sometimes incorrect. For enumeration the Babylonians used symbols for 1, 10, 60, 600, 3,600, 36,000, and 216,000, similar to the earlier period. Below are four of the symbols. They did arithmetic in base 60, sexagesimal. 1 10 60 600 Cuneiform numerals For our purposes we will use just the first two symbols ∠¨ = 1 ≠º = 10 All numbers will be formed from these. Example: Note the notation was positional and sexagesimal: ≠ºÃ¢â€° º ≠ºÃ¢â€° º= 20  · 60 + 20 ≠ºÃ¢â€° º ∠¨ ∠¨ ∠¨ = 57 ≠ºÃ¢â€° ºÃ¢â€° º ∠¨ ∠¨ ∠¨Ã¢Ë† ¨ ∠¨ ∠¨ ∠¨Ã¢Ë† ¨ ≠º ∠¨ = 2  · 602 + 2  · 60 + 21 = 7, 331 The story is a little more complicated. A few shortcuts or abbreviation were allowed, many originating in the Seleucid period. Other Babylonian Mathematics 7 devices for representing numbers were used. Below see how the number 19 was expressed. Three ways to express the number 19 = 19 Old Babylonian. The symbol means subtraction. = 19 Formal = 19 Cursive form Seleucid Period(c. 320 BC to c. 620 AD) The horizontal symbol above the â€Å"1† designated subtraction. There is no clear reason why the Babylonians selected the sexagesimal system6 . It was  possibly selected in the interest of metrology, this according to Theon of Alexandria, a commentator of the fourth century A.D.: i.e. the values 2,3,5,10,12,15,20, and 30 all divide 60. Remnants still exist today with time and angular measurement. However, a number of theories have been posited for the Babylonians choosing the base of 60. For example7 1. The number of days, 360, in a year gave rise to the subdivision of the circle into 360 degrees, and that the chord of one sixth of a circle is equal to the radius gave rise to a natural division of the circle into six equal parts. This in turn made 60 a natural unit of counting. (Moritz Cantor, 1880) 2. The Babylonians used a 12 hour clock, with 60 minute hours. That is, two of our minutes is one minute for the Babylonians. (Lehmann-Haupt, 1889) Moreover, the (Mesopotamian) zodiac was divided into twelve equal sectors of 30 degrees each. 3. The base 60 provided a convenient way to express fractions from a variety of systems as may be needed in conversion of weights and measures. In the Egyptian system, we have seen the values 1/1, 1/2, 2/3, 1, 2, . . . , 10. Combining we see the factor of 6 needed in the denominator of fractions. This with the base 10 gives 60 as the base of the new system. (Neugebauer, 1927) 4. The number 60 is the product of the number of planets (5 known at the time) by the number of months in the year, 12. (D. J. Boorstin, 6 Recall, 7 See the very early use of the sexagesimal system in China. There may well be a connection. Georges Ifrah, The Universal History of Numbers, Wiley, New York, 2000. Babylonian Mathematics 1986) 8 5. The combination of the duodecimal system (base 12) and the base 10 system leads naturally to a base 60 system. Moreover, duodecimal systems have their remnants even today where we count some commodities such as eggs by the dozen. The English system of fluid measurement has numerous base twelve values. As we see in the charts below, the base twelve (base 3, 6?) and base two graduations are mixed. Similar values exist in the ancient Roman,  Sumerian, and Assyrian measurements. teaspoon tablespoon 1 teaspoon = 1 tablespoon = 1 fluid ounce = 1 gill = 1 cup = 1 pint = 1 quart = 1 gallon = 1 firkin = 1 hogshead = 1 3 6 24 48 96 192 768 6912 48384 inch 1 inch = 1 foot = 1 yard = 1 mile = 1 12 36 — fluid ounce 1/6 1/2 1 4 8 16 32 128 1152 8064 1/3 1 2 8 16 32 64 256 2304 16128 foot 1/12 1 3 5280 yard 1/36 1/3 1 1760 Note that missing in the first column of the liquid/dry measurement table is the important cooking measure 1/4 cup, which equals 12 teaspoons. 6. The explanations above have the common factor of attempting to give a plausibility argument based on some particular aspect of their society. Having witnessed various systems evolve in modern times, we are tempted to conjecture that a certain arbitrariness may be at work. To create or impose a number system and make it apply to an entire civilization must have been the work of a political system of great power and centralization. (We need only consider the failed American attempt to go metric beginning in 1971. See, http://lamar.colostate.edu/ hillger/dates.htm) The decision to adapt Babylonian Mathematics 9 the base may have been may been made by a ruler with little more than the advice merchants or generals with some vested need. Alternatively, with the consolidation of power in Sumeria, there may have been competing systems of measurement. Perhaps, the base 60 was chosen as a compromise. Because of the large base, multiplication was carried out with the aide of a table. Yet, there is no table of such a magnitude. Instead there are tables up to 20 and then selected values greater (i.e. 30, 40, and 50). The practitioner would be expected to decompose the number into a sum of smaller numbers and use multiplicative distributivity. A positional fault Which is it? ≠º ≠º = 10  · 60 + 10 = 10  · 602 + 10 = 3, 610 10 = 10 + 60 = 20() 1. There is no â€Å"gap†Ã‚  designator. 2. There is a true floating point — its location is undetermined except from context. ? The â€Å"gap† problem was overcome in the Seleucid period with the invention of a â€Å"zero† as a gap separator. We use the notation: d1 ; d2 , d3 , . . . = d1 + d2 d3 + 2 +  ·Ã‚ ·Ã‚ · 60 60 The values d1 ; d2 , d3 , d4 , . . . are all integers. Example ∠¨ ≠º ∠¨Ã¢Ë† ¨ ≠ºÃ¢â€° º ≠º ∠¨ ≠º ≠º ∠¨Ã¢Ë† ¨ ≠ºÃ¢â€° º 1; 24, 51, 10 = 1 + 24 51 10 + 2+ 3 60 60 60 = 1.41421296 Babylonian Mathematics 10 This number was found on the Old Babylonian Tablet (Yale Collection √ #7289) and is a very high precision estimate of 2. We will continue this discussion shortly, conjecturing on how such precision may have been obtained. The exact value of √ 2, to 8 decimal places is = 1.41421356. Fractions. Generally the only fractions permitted were such as 2 3 5 12 , , , , †¦ 60 60 60 60 because the sexagesimal expression was known. For example, 1 10 = = ;≠º 6 60 1 ∠¨ ∠¨ ∠¨ ≠ºÃ¢â€° º =; , 9 ∠¨ ∠¨ ∠¨ ≠ºÃ¢â€° º 1 Irregular fractions such as 1 , 11 , etc were not normally not used. 7 There are some tablets that remark, â€Å"7 does not divide†, or â€Å"11 does not divide†, etc. A table of all products equal to sixty has been found. 2 3 4 5 6 8 9 10 12 15 30 20 15 12 10 7,30 6,40 6 5 4 16 18 20 24 25 27 30 32 36 40 3, 45 3,20 3 2,30 2,25 2,13,20 2 1;52,30 1,40 1,30 Babylonian Mathematics You can see, for example that 8 Ãâ€" 7; 30 = 8 Ãâ€" (7 + 30 ) = 60 60 11 Note that we did not use the separatrix â€Å";† here. This is because the table is also used for reciprocals. Thus 7 30 1 = 0; 7, 30 = + 2 8 60 60 Contextual interpretation was critical. Remark. The corresponding table for our decimal system is shown below. Included also are the columns with 1 and the base 10. The product relation and the decimal expansion relations are valid in base 10. 1 2 5 10 10 5 2 1 Two tablets found in 1854 at Senkerah on the Euphrates date from 2000 B.C. They give squares of the numbers up to 59 and cubes up to 32. The Babylonians used the formula xy = ((x + y)2 − (x − y)2 )/4 to assist in multiplication. Division relied on multiplication, i.e. 1 x =x · y y There apparently was no long division. The Babylonians knew some approximations of irregular fractions. 1 =; 1, 1, 1 59 1 =; 0, 59, 0, 59 61 However, they do not appear to have noticed infinite periodic expansions.8 the decimal system, the analogous values are 1 = 0.1111 . . . and 9 Note the use of the units â€Å"0† here but not for the sexagesimal. Why? 8 In 1 11 = 0.090909 . . .. Babylonian Mathematics 12 They also seemed to have an elementary knowledge of logarithms. That is to say there are texts which concern the determination of the exponents of given numbers. 4 Babylonian Algebra In Greek mathematics there is a clear distinction between the geometric and algebraic. Overwhelmingly, the Greeks assumed a geometric position wherever possible. Only in the later work of Diophantus do we see algebraic methods of significance. On the other hand, the Babylonians assumed just as definitely, an algebraic viewpoint. They allowed operations that were forbidden in Greek mathematics and even later until the 16th century of our own era. For example, they would freely multiply areas and lengths, demonstrating that the units were of less importance. Their methods of designating unknowns, however, does invoke units. First, mathematical expression was strictly rhetorical, symbolism would not come for another two millenia with Diophantus, and then not significantly until Vieta in the 16th century. For example, the designation of the unknown was length. The designation of the square of the unknown was area. In solving linear systems of two dimensions, the unknowns were length and breadth, and length, breadth, and width for three dimensions. √ Square Roots. Recall the approximation of 2. How did they get it? There are two possibilities: (1) Applying the method of the mean. (2) Applying the approximation √ b a2  ± b ≈ a  ± 2a Babylonian Mathematics 13 Yale Babylonian Collection 1;24,51,10 30 42;25,35 Square with side 30 The product of 30 by 1;24,51,10 is precisely 42;25,35. Method of the mean. The method of the mean can easily be used to find the square root of any number. The idea is simple: to find the square root of 2, say, select x as a first approximation and take for another 2/x. The product of the two numbers is of course 2, and moreover, one must be less than and the other greater  than 2. Take the √ arithmetic average to get a value closer to 2. Precisely, we have 1. Take a = a1 as an initial approximation. √ √ 2. Idea: If a1 < 2 then a21 > 2. Babylonian Mathematics 3. So take a2 = (a1 + 4. Repeat the process. Example. Take a1 = 1. Then we have 2 3 a2 = (1 + )/2 = 1 2 2 17 3 )/2 = 1.41666†¦ = a3 = ( + 2 3/2 12 17 2 577 a4 = ( + )/2 = 12 17/12 408 14 2 )/2. a1 Now carry out this process in sexagesimal, beginning with a1 = 1; 25 using Babylonian arithmetic without rounding, to get the value 1;24,51,10. √ à º Note: 2=1; 25 = 1.4166†¦ was commonly used as a brief, rough and ready, approximation. When using sexagesimal numbering, a lot of information can be compressed into one place. Solving Quadratics. The Babylonian method for solving quadratics is essentially based on completing the square. The method(s) are not as â€Å"clean† as the modern quadratic formula, because the Babylonians allowed only positive solutions. Thus equations always were set in a form for which there was a positive solution. Negative solutions (indeed negative numbers) would not be allowed until the 16th century CE. The rhetorical method of writing a problem does not require variables. As such problems have a rather intuitive feel. Anyone could understand the problem, but without the proper tools, the solution would be impossibly difficult. No doubt this rendered a sense of the mystic to the mathematician. Consider this example I added twice the side to the square; the result is 2,51,60. What is the side? In modern terms we have the simple quadratic x2 + 2x = 10300. The student would then follow his â€Å"template† for quadratics. This template was the solution of a specific problem of the correct mathematical Babylonian Mathematics 15 type, all written rhetorically. Here is a typical example given in terms of modern variables. Problem. Solve x(x + p) = q. Solution. Set y = x + p Then we have the system xy = q y−x = p This gives 4xy + (y − x)2 = p2 + 4q (y + x)2 = p2 + 4q x+y = 2x + p = q q p2 + 4q p2 + 4q √ −p + p2 + 4q x = 2 All three forms x2 + px = q x2 = px + q x2 + q = px are solved similarly. The third is solved by equating it to the nonlinear system, x + y = p, xy = q. The student’s task would be to take the problem at hand and determine which of the forms was appropriate and then to solve it by a prescribed method. What we do not know is if the student was ever instructed in principles of solution, in this case completing the square. Or was mathematical training essentially static, with solution methods available for each and every problem that the practitioner would encounter. It is striking that these methods date back 4,000 years! Solving Cubics. The Babylonians even managed to solve cubic equations, though again only those having positive solutions. However, the form of the equation was restricted tightly. For example, solving x3 = a Babylonian Mathematics was accomplished using tables and interpolation. Mixed cubics x3 + x2 = a were also solved using tables and interpolation. The general cubic ax3 + bx2 + cx = d can be reduced to the normal form y 3 + ey 2 = g 16 To do this one needs to solve a quadratic, which the Babylonians could do. But did the Babylonians know this reduction? The Babylonians must have had extraordinary manipulative skills and as well a maturity and flexibility of algebraic skills. Solving linear systems. The solution of linear systems  were solved in a particularly clever way, reducing a problem of two variables to one variable in a sort of elimination process, vaguely reminiscent of Gaussian elimination. Solve 2 1 x − y = 500 3 2 x + y = 1800 Solution. Select x = y such that ËÅ" ËÅ" x + y = 2ËÅ" = 1800 ËÅ" ËÅ" x So, x = 900. Now make the model ËÅ" x=x+d ËÅ" We get y =y−d ËÅ" 1 2 (900 + d) − (900 − d) = 500 3 2 2 1 ( + )d + 1800/3 − 900/2 = 500 3 2 7 d = 500 − 150 6 6(350) d = 7 So, d = 300 and thus x = 1200 y = 600. Babylonian Mathematics 17 Plimpton 322 tablet Yale Babylonian collection Pythagorean Triples. 5 As we have seen there is solid evidence that the ancient Chinese were aware of the Pythagorean theorem, even though they may not have had anything near to a proof. The Babylonians, too, had such an awareness. Indeed, the evidence here is very much stronger, for an entire tablet of Pythagoreantriples has been discovered. The events surrounding them reads much like a modern detective story, with the sleuth being archaeologist Otto Neugebauer. We begin in about 1945 with the Plimpton 322 tablet, which is now the Babylonian collection at Yale University, and dates from about 1700 BCE. It appears to have the left section Babylonian Mathematics 18 broken away. Indeed, the presence of glue on the broken edge indicates that it was broken after excavation. What the tablet contains is fifteen rows of numbers, numbered from 1 to 15. Below we list a few of them in decimal form. The first column is descending numerically. The deciphering of what they mean is due mainly to Otto Neugebauer in about 1945. 1.9834†¦ 1.94915 . . . 1.38716 119 169 3367 4825 56 1 2 106 15 Interpreting Plimpton 322. To see what it means, we need a model right triangle. Write the Pythagorean triples, the edge b in the column thought to be severed from the tablet. Note that they are listed c B a b decreasing cosecant. b (c/b)2 120 (169/120)2 3456 (4825/3456)2 . . . 90 (106/90)2 Right Triangle a c 119 169 3367 4825 56 106 1 2 15 c csc2 B = ( )2 b A curious fact is that the tablet contains a few errors, no doubt transcription errors made so many centuries ago. How did the Babylonian mathematicians determine these triples? Why were they listed in this order? Assuming they knew the Pythagorean relation a2 + b2 = c2 , divide by b to get c a ( )2 + 1 = ( )2 b b Babylonian Mathematics u2 + 1 = v 2 (u − v)(u + v) = 1 Choose u + v and find u − v in the table of reciprocals. 19 Example. Take u + v=2;15. Then u − v = 0; 26, 60 Solve for u and v to get u = 0; 54, 10 v = 1; 20, 50. Multiply by an appropriate integer to clear the fraction. We get a = 65, c = 97. So b = 72. This is line 5 of the table. It is tempting to think that there must have been known general principles,  nothing short of a theory, but all that has been discovered are tablets of specific numbers and worked problems. 6 Babylonian Geometry Circular Measurement. We find that the Babylonians used Ï€ = 3 for practical computation. But, in 1936 at Susa (captured by Alexander the Great in 331 BCE), a number of tablets with significant geometric results were unearthed. One tablet compares the areas and the squares Babylonian Mathematics 20 of the sides of the regular polygons of three to seven sides. For example, there is the approximation perimeter hexagon = 0; 57, 36 circumference circumscribed circle This gives an effective Ï€ ≈ 3 1 . (Not bad.) 8 Volumes. There are two forms for the volume of a frustum given Frustum b b h a a V V a+b 2 )h ÃÆ'2 ! a+b 2 1 a−b 2 = h ( ) − ( ) 2 3 2 = ( The second is correct, the first is not. There are many geometric problems in the cuneiform texts. For example, the Babylonians were aware that †¢ The altitude of an isosceles triangle bisects the base. †¢ An angle inscribed in a semicircle is a right angle. (Thales) 7 Summary of Babylonian Mathematics That Babylonian mathematics may seem to be further advanced than that of Egypt may be due to the evidence available. So, even though Babylonian Mathematics 21 we see the development as being more general and somewhat broader in scope, there remain many similarities. For example, problems contain only specific cases. There seem to be no general formulations. The lack of notation is clearly detrimental in the handling of algebraic problems. There is an absence of clear cut distinctions between exact and approximate results. Geometric considerations play a very secondary role in Babylonian algebra, even though geometric terminology may be used. Areas and lengths are freely added, something that would not be possible in Greek mathematics. Overall, the role of geometry is diminished in comparison with algebraic and numerical methods. Questions about solvability or insolvability are absent. The concept of â€Å"proof† is unclear and uncertain. Overall, there is no sense of abstraction. In sum, Babylonian mathematics, like that of the Egyptians, is mostly utilitarian — but apparently more advanced. Exercises 1. Express the numbers 7 6, 234, 1265, and 87,432 in sexagesimal. 2. Compute the products (a) 1, 23 Ãâ€" 2, 9 (b) 2, 4, 23 Ãâ€" 3, 34 8 3. A problem on one Babylonian tablets give the base and top of an isosceles trapezoid to be 50 and 40 respectively and the side length to be 30. Find the altitude and area. Can this be done without the Pythagorean theorem? 4. Solve the following system ala the Babylonian â€Å"false position†  ´ method. State clearly what steps you are taking. 2x + 3y = 1600 5x + 4y = 2600 (The solution is (200, 400).) Babylonian Mathematics 22 5. Generalize this Babylonian algorithm for solving linear systems to arbitrary linear systems in two variables? 6. Generalize this Babylonian algorithm for solving linear systems to arbitrary linear systems? √ 7. Modify the Babylonian root finding method (for 2) to find√ the square root of any number. Use your method to approximate 3. Begin with x0 = 1. √ 8. Explain how to adapt the method of the mean to determine 3 2. n n3 + n2 1 2 2 12 9. Consider the table: 3 36 Solve the following prob4 80 150 5 6 252 lems using this table and linear interpolation. Compare with the exact values. (You can obtain the exact solutions, for example, by using Maple: evalf(solve(x3 + x2 = a, x)); Here a=the right side) (a) x3 + x2 = 55 (b) x3 + x2 = 257 10. Show that the general cubic ax3 + bx2 + cx = d can be reduced to the normal form y 3 + ey 2 = g. 11. Show how the perimeter identity is used to derive the approximation for Ï€. 12. Write a lesson plan wherein you show students how to factor quadratics ala the Babylonian methods. You may use variables,  ´ but not general formulas.

Prehistoric Life During the Silurian Period

Prehistoric Life During the Silurian Period The Silurian period only lasted 30 or so million years, but this period of geologic history witnessed at least three major innovations in prehistoric life: the appearance of the first land plants, the subsequent colonization of dry land by the first terrestrial invertebrates, and the evolution of jawed fish, a huge evolutionary adaptation over previous marine vertebrates. The Silurian was the third period of the Paleozoic Era (542-250 million years ago), preceded the Cambrian and Ordovician periods and succeeded by the Devonian, Carboniferous and Permian periods. Climate and Geography Experts disagree about the climate of the Silurian period; global sea and air temperatures may have exceeded 110 or 120 degrees Fahrenheit, or they might have been more moderate (only 80 or 90 degrees). During the first half of the Silurian, much of the earths continents were covered by glaciers (a holdover from the end of the preceding Ordovician period), with climatic conditions moderating by the start of the ensuing Devonian. The giant supercontinent of Gondwana (which was destined to break apart hundreds of millions of years later into Antarctica, Australia, Africa and South America) gradually drifted into the far southern hemisphere, while the smaller continent of Laurentia (the future North America) straddled the equator. Marine Life During the Silurian Period Invertebrates. The Silurian period followed the first major global extinction on earth, at the end of the Ordovician, during which 75 percent of sea-dwelling genera went extinct. Within a few million years, though, most forms of life had pretty much recovered, especially arthropods, cephalopods, and the tiny organisms known as graptolites. One major development was the spread of reef ecosystems, which thrived on the borders of the earths evolving continents and hosted a wide diversity of corals, crinoids, and other tiny, community-dwelling animals. Giant sea scorpions - such as the three-foot-long Eurypterus - were also prominent during the Silurian, and were by far the biggest arthropods of their day. Vertebrates. The big news for vertebrate animals during the Silurian period was the evolution of jawed fish like Birkenia and Andreolepis, which represented a major improvement over their predecessors of the Ordovician period (such as Astraspis and Arandaspis). The evolution of jaws, and their accompanying teeth, allowed the prehistoric fish of the Silurian period to pursue a wider variety of prey, as well as to defend themselves against predators, and was a major engine of subsequent vertebrate evolution as the prey of these fish evolved various defenses (like greater speed). The Silurian also marked the appearance of the first identified lobe-finned fish, Psarepolis, which was ancestral to the pioneering tetrapods of the ensuing Devonian period. Plant Life During the Silurian Period The Silurian is the first period for which we have conclusive evidence of terrestrial plants - tiny, fossilized spores from obscure genera like Cooksonia and Baragwanathia. These early plants were no more than a few inches high, and thus possessed only rudimentary internal water-transport mechanisms, a technique that took tens of millions of years of subsequent evolutionary history to develop. Some botanists speculate that these Silurian plants actually evolved from freshwater algae (which would have collected on the surfaces of small puddles and lakes) rather than ocean-dwelling predecessors. Terrestrial Life During the Silurian Period As a general rule, wherever you find terrestrial plants, youll also find some kinds of animals. Paleontologists have found direct fossil evidence of the first land-dwelling millipedes and scorpions of the Silurian period, and other, comparably primitive terrestrial arthropods were almost certainly present as well. However, large land-dwelling animals were a development for the future, as vertebrates gradually learned how to colonize dry land. Next: the Devonian Period

Obamas Inspiring 2004 Democratic Convention Speech

Obamas Inspiring 2004 Democratic Convention Speech On July 27, 2004, Barack Obama, then a senatorial candidate from Illinois, delivered an electrifying speech to the 2004 Democratic National Convention. As the result of the now-legendary speech (presented below), Obama rose to national prominence, and his speech is regarded as one of the great political statements of the 21st century. OUT OF MANY, ONE by Barack Obama Keynote Speech Democratic National Convention in Boston, Mass. July 27, 2004 Thank you so much. Thank you so much... On behalf of the great state of Illinois, crossroads of a nation, Land of Lincoln, let me express my deepest gratitude for the privilege of addressing this convention. Gratitude for Family Heritage Tonight is a particular honor for me because - let’s face it - my presence on this stage is pretty unlikely. My father was a foreign student, born and raised in a small village in Kenya. He grew up herding goats, went to school in a tin-roof shack. His father - my grandfather - was a cook, a domestic servant to the British. But my grandfather had larger dreams for his son. Through hard work and perseverance my father got a scholarship to study in a magical place, America, that shone as a beacon of freedom and opportunity to so many who had come before. While studying here, my father met my mother. She was born in a town on the other side of the world, in Kansas. Her father worked on oil rigs and farms through most of the Depression. The day after Pearl Harbor my grandfather signed up for duty; joined Patton’s army, marched across Europe. Back home, my grandmother raised their baby and went to work on a bomber assembly line. After the war, they studied on the G.I. Bill, bought a house through F.H.A., and later moved west all the way to Hawaii in search of opportunity. And they, too, had big dreams for their daughter. A common dream, born of two continents. My parents shared not only an improbable love, they shared an abiding faith in the possibilities of this nation. They would give me an African name, Barack, or †blessed,† believing that in a tolerant America your name is no barrier to success. They imagined me going to the best schools in the land, even though they weren’t rich, because in a generous America you don’t have to be rich to achieve your potential. They are both passed away now. And yet, I know that, on this night, they look down on me with great pride. I stand here today, grateful for the diversity of my heritage, aware that my parents’ dreams live on in my two precious daughters. I stand here knowing that my story is part of the larger American story, that I owe a debt to all of those who came before me, and that, in no other country on earth, is my story even possible. Tonight, we gather to affirm the greatness of our nation - not because of the height of our skyscrapers, or the power of our military, or the size of our economy. Greatness of America Our pride is based on a very simple premise, summed up in a declaration made over two hundred years ago: We hold these truths to be self-evident, that all men are created equal. That they are endowed by their Creator with certain inalienable rights. That among these are life, liberty and the pursuit of happiness. That is the true genius of America - a faith in simple dreams, an insistence on small miracles: - That we can tuck in our children at night and know that they are fed and clothed and safe from harm. - That we can say what we think, write what we think, without hearing a sudden knock on the door. - That we can have an idea and start our own business without paying a bribe. - That we can participate in the political process without fear of retribution, and that our votes will be counted at least, most of the time. This year, in this election, we are called to reaffirm our values and our commitments, to hold them against a hard reality and see how we are measuring up, to the legacy of our forbearers, and the promise of future generations. And fellow Americans, Democrats, Republicans, Independents - I say to you tonight: we have more work to do. - More work to do for the workers I met in Galesburg, Ill., who are losing their union jobs at the Maytag plant that’s moving to Mexico, and now are having to compete with their own children for jobs that pay seven bucks an hour. - More to do for the father that I met who was losing his job and choking back the tears, wondering how he would pay $4,500 a month for the drugs his son needs without the health benefits that he counted on. - More to do for the young woman in East St. Louis, and thousands more like her, who has the grades, has the drive, has the will, but doesn’t have the money to go to college. Now don’t get me wrong. The people I meet - in small towns and big cities, in diners and office parks - they don’t expect government to solve all their problems. They know they have to work hard to get ahead - and they want to. Go into the collar counties around Chicago, and people will tell you they don’t want their tax money wasted, by a welfare agency or by the Pentagon. Go into any inner city neighborhood, and folks will tell you that government alone can’t teach our kids to learn - they know that parents have to teach, that children can’t achieve unless we raise their expectations and turn off the television sets and eradicate the slander that says a black youth with a book is acting white. They know those things. People don’t expect government to solve all their problems.  But they sense, deep in their bones, that with just a slight change in priorities, we can make sure that every child in America has a decent shot at life, and that the doors of opportunity remain open to all. They know we can do better. And they want that choice. John Kerry In this election, we offer that choice. Our Party has chosen a man to lead us who embodies the best this country has to offer. And that man is John Kerry. John Kerry understands the ideals of community, faith, and service because they’ve defined his life. From his heroic service to Vietnam, to his years as a prosecutor and  lieutenant governor, through two decades in the United States Senate, he has devoted himself to this country. Again and again, we’ve seen him make tough choices when easier ones were available. His values - and his record - affirm what is best in us. John Kerry believes in an America where hard work is rewarded; so instead of offering tax breaks to companies shipping jobs overseas, he offers them to companies creating jobs here at home. John Kerry believes in an America where all Americans can afford the same health coverage our politicians in Washington have for themselves. John Kerry believes in energy independence, so we aren’t held hostage to the profits of oil companies, or the sabotage of foreign oil fields. John Kerry believes in the Constitutional freedoms that have made our country the envy of the world, and he will never sacrifice our basic liberties, nor use faith as a wedge to divide us. And John Kerry believes that in a dangerous world war must be an option sometimes, but it should never be the first option. You know, a while back, I met a young man named Seamus in a V.F.W. Hall in East Moline, Ill.. He was a good-looking kid, six two, six three, clear eyed, with an easy smile. He told me he’d joined the Marines, and was heading to Iraq the following week. And as I listened to him explain why he’d enlisted, the absolute faith he had in our country and its leaders, his devotion to duty and service, I thought this young man was all that any of us might hope for in a child. But then I asked myself:  Are we serving Seamus as well as he is serving us? I thought of the 900 men and women - sons and daughters, husbands and wives, friends and neighbors, who won’t be returning to their own hometowns. I thought of the families I’ve met who were struggling to get by without a loved one’s full income, or whose loved ones had returned with a limb missing or nerves shattered, but who still lacked long-term health benefits because they were Reservists. When we send our young men and women into harm’s way, we have a solemn obligation not to fudge the numbers or shade the truth about why they’re going, to care for their families while they’re gone, to tend to the soldiers upon their return, and to never ever go to war without enough troops to win the war, secure the peace, and earn the respect of the world. Now let me be clear. Let me be clear. We have real enemies in the world. These enemies must be found. They must be pursued - and they must be defeated. John Kerry knows this. And just as Lieutenant Kerry did not hesitate to risk his life to protect the men who served with him in Vietnam, President Kerry will not hesitate one moment to use our military might to keep America safe and secure. John Kerry  believes in America. And he knows that it’s not enough for just some of us to prosper. For alongside our famous individualism, there’s another ingredient in the American saga. A belief that we’re all connected as one people. If there is a child on the south side of Chicago who can’t read, that matters to me, even if it’s not my child. If there’s a senior citizen somewhere who can’t pay for their prescription drugs, and has to choose between medicine and the rent, that makes my life poorer, even if it’s not my grandparent. If there’s an Arab American family being rounded up without benefit of an attorney or due process, that threatens my  civil liberties. It is that fundamental belief, it is that fundamental belief, I am my brother’s keeper, I am my sister’s keeper that makes this country work. It’s what allows us to pursue our individual dreams and yet still come together as one American family. E Pluribus Unum. Out of Many, One. Now even as we speak, there are those who are preparing to divide us, the spin masters, the negative ad peddlers who embrace the politics of anything goes. Well, I say to them tonight, there is not a liberal America and a conservative America - there is the United States of America. There is not a Black America and a White America and Latino America and Asian America - there’s the United States of America. The pundits, the pundits like to slice-and-dice our country into Red States and Blue States; Red States for Republicans, Blue States for Democrats. But I’ve got news for them, too: We worship an awesome God in the Blue States, and we don’t like federal agents poking around in our libraries in the Red States. We coach Little League in the Blue States and yes, we’ve got some gay friends in the Red States. There are patriots who opposed the war in Iraq and there are patriots who supported the war in Iraq. We Are One People We are one people, all of us pledging allegiance to the stars and stripes, all of us defending the United States of America. In the end, that’s what this election is about. Do we participate in a politics of cynicism or do we participate in a politics of hope? John Kerry calls on us to hope. John Edwards calls on us to hope. I’m not talking about blind optimism here - the almost willful ignorance that thinks unemployment will go away if we just don’t think about it, or the health care crisis will solve itself if we just ignore it. That’s not what I’m talking about. I’m talking about something more substantial. It’s the hope of slaves sitting around a fire singing freedom songs. The hope of immigrants setting out for distant shores. The hope of a young naval lieutenant bravely patrolling the Mekong Delta. The hope of a millworker’s son who dares to defy the odds. The hope of a skinny kid with a funny name who believes that America has a place for him, too. Hope in the face of difficulty. Hope in the face of uncertainty. The audacity of hope! In the end, that is God’s greatest gift to us, the bedrock of this nation. A belief in things not seen. A belief that there are better days ahead. I believe that we can give our middle class relief and provide working families with a road to opportunity. I believe we can provide jobs to the jobless, homes to the homeless, and reclaim young people in cities across America from violence and despair. I believe that we have a righteous wind at our backs and that as we stand on the crossroads of history, we can make the right choices, and meet the challenges that face us. America! Tonight, if you feel the same energy that I do, if you feel the same urgency that I do, if you feel the same passion I do, if you feel the same hopefulness that I do - if we do what we must do, then I have no doubts that all across the country, from Florida to Oregon, from Washington to Maine, the people will rise up in November, and John Kerry will be sworn in as president, and John Edwards will be sworn in as vice president, and this country will reclaim its promise, and out of this long political darkness a brighter day will come. Thank you very much everybody. God bless you. Thank you. Thank you, and God bless America.