Facebook Addiction Disorder Essay

Nowadays, the new thing in is Facebook. The big Facebook has changed the life of millions. But is that a good or a bad thing? Well some would think it’s good, but in many cases it isn’t. A new type of addiction was formed, Facebook addiction disorder. This addiction leads, mostly teenagers, to become very addicted to Facebook, and cannot live without it. Critics say that there is, at least, six symptoms of F. A. D. Some have come up with ideas to beat this new addiction. Facebook has completely changed society, for the good and for the worse. The article written by B.  Earl, â€Å" Facebook Syndrome: 8 Ways To Beat Your Facebook Addiction†, explains ways to find out if you are addicted to Facebook. He also explains ways to beat Facebook syndrome. The article written by A. Summers, â€Å"Facebook Addiction Disorder- The 6 Symptoms of F. A. D. † , explains how much Facebook has changed people, specially teenagers. She also mentions six symptoms of F. A. D. B. Earl of The Daily Mind writes, â€Å" If you ever late for a meeting or an appointment because you were checking your updates on Facebook or watching a related video on YouTube, then you know you are addicted†. He is referring to someone’s action, and how the result of that may effect their daily lives. This just to show that this actually happens to people. Many people over sleep due to being on Facebook until late hours, and sometimes lose their job because of too many late or absences to work. A. Summers wrote on the SocialTimes,â€Å" Tolerance- This term is used to described the desperate behavior or a Facebook addict. They spend an increasing amount of time on the site, coming to a stage where they need it on order to obtain satisfaction or on the other extreme, it is having a detrimental affect on them as a person and their life†. Ms. Summer’s quote also relates to that of Mr. Earl. She also is stating how someone who is used to being on Facebook for a large amount of hours per day will get addicted. When one cannot use Facebook because they have to participate in activities and is not allowed to use Facebook, withdrawal signs become visible. Some signs are anxiety, distress, and they require the need to talk about Facebook and what goes on while one is restricted from using it (Summers). She is referring to withdrawal symptoms, just as alcohol or cigarettes have withdrawal symptoms. B. Earl states â€Å"get off the computer. Really†¦do you need to spend that much time on the computer? Honestly ask yourself that†. This relates to what Summers said because if people spent less time on the computer, and more time socializing with people the real way, they would not get withdrawals. Facebook should not get in the way of either one’s individuals studies nor their careers. Nowadays, over 90% of young teenagers have a Facebook account (Adam). This just to show how much Facebook has changed our society, and it’s influencing teenagers to be less social. Adam blogged â€Å"Facebook games have become increasingly popular, and once again, what started out as basic games such as Sudoku or Scrabble has now advanced to games where you can create a whole new world within your laptop and smartphone†. People do this every day and waste money constantly on these foolish internet games. This is what Adam is trying to get at with his blog, people are starting to become so anti-social. Teenagers are starting not know how to communicate to people face to face.

Demonstration Speech

Duyen Pham INTRODUCTION: I would like to ask the class with a show of hands, who has never blew a bubble or played with bubbles? I have never met a kid or an adult who could resist bubbles. I believe that there is something unique about a bubble from its fragility, to its rainbow of colors, and to the perfect circle shape. A bubble's life expectancy is usually measured in seconds unless you know how to make a SUPER BUBBLE! So today, I am going to demonstrate how to make a bouncing bubble. MATERIALS: * 1 cup of distilled water * 2 tablespoons of dish soap * 1 tablespoon of glycerin * Pair of gloves * Small bubble wand, straw, or pipette STEPS: . Start with 1 cup of distilled water 2. Add 2 tablespoons of dish soap 3. Then, add 1 tablespoon of glycerin 4. Last, mix together all the ingredients EXPERIMENT: * Allowing your bubble solution to sit undisturbed for at least 24 hours in advance, will allow the bongs in the bubble solution strengthen, which means stronger bubbles. After making up a batch of Bubble Solution with the ingredients listed above. * Using a small bubble wand start by blowing a bubble. If you are using the pipette instead of the bubble wand, cut the bulb off the top of the pipette, dip it into the bubble solution, and blow into the other end of the pipette.If using a straw just dip and blow out the other end. * Bounce the bubble off of your gloves. It can also be bounced off other fabrics. As you'll soon see, some fabrics work better than others. CONCLUSION: Most people don’t know that the bursting of a bubble is caused by contaminates that instantly breaks down the bubble’s mixture and destroys its surface tension. That is why even lightly touching a bubble causes it to burst. So, even though it is just a puff of air trapped in a thin film of soap and water we just need to enjoy the little things in life.

Edgar Allan Poe and Nathaniel Hawthorne: a Comparison Essay

Edgar Allan Poe and Nathaniel Hawthorne were two of America’s finest Romantic writers. These two writers have stood the test of time and are read as much today if not more than they were in their own time. The major reason that both author’s were as popular as they are is because of the fact that they delved into the human mind to create their psychological literature. Edgar Allan Poe’s life spanned from eighteen nine until nineteen forty-nine, the years that were the beginning of the Romantic Movement. Poe was considered an educated man for his time. He attended the University of Virginia and West Point. Since West Point is a military school, he no doubt studied psychology because one who would be a commander in the army would need to know about the way the enemy thinks. Poe did not use this knowledge as a military officer, but used it to create excellent psychological terror in literature. During a time when the arts focused on the supernatural, Poe looked to the character’s own mind to provide terror. The narrator of The Tell-Tale Heart is so terrified by his guilt that he reveals the murder he has committed to the authorities, as does the narrator of The Black Cat. In the famous short story The Cask of Amontillado, the reader experienced the terror of one’s condemnation to be walled up in a small cellar room to die and to have the time to think about what is to happen in total darkness and isolation. The Fall of the House of Usher also leaves the narrator completely terrified, not because of his safety, but because of the information that his mind must process and the knowledge that he may begin to suffer from the same madness that Roderick Usher is doomed to endure. Nathaniel Hawthorne was also an expert in delving into the deepest regions of a character’s mind. The Scarlet Letter, one of Hawthorne’s best works is about a woman who must wear a scarlet A because she is an adulterer. The town minister is the man who is also responsible for the sin. However, because he is a male and cannot get pregnant, the community does not know of his guilt. Instead he punishes himself much more than his female counterpart until the sin takes on a supernatural quality. It does so only through the guilt that he must endure. The Minister’s Black Veil is about another minister who physically punishes himself for a psychological sin that he has committed. This penance has bothered the congregation to the point that they isolate the minister. Again, it is their psychological fear and guilt that is their terror. Hawthorne, in his attempt to prove that all are sinners and that all wrestle with good and evil in their minds, proves his point in Young Goodman Brown. In this short story, a young man must decide whether to sell his soul to become a successful man or to remain free. The resolution of the story is that the horrid scene the young man had witness the night before was only a dream, yet he is not sure that it took place in his mind or if it was real. Reality and what one perceived as reality was something that Hawthorne was a master. Both Edgar Allan Poe and Nathaniel Hawthorne made use of the human mind as an instrument a person’s demise rather than actions. They understood the power of the human mind even though they did not know what we do today. They are shining examples of psychological literature as an instrument of terror and guilt.

Nursing Application Essay Example | Topics and Well Written Essays - 1500 words

Nursing Application - Essay Example The purpose of this paper is to present a proper application of theory to practice and the theory this is applied in this part would be taking history in case of a patient with Chronic Obstructive Pulmonary Disease. This paper would demonstrate the history-taking techniques based on the developmental stage. This would include culture, religion; developmental and physical milestones gross & fine motor skills, language, and social development for the particular age group. (Kar, 2006) A 56 year old male patient was admitted in the hospital with the ailment of Chronic Obstructive Pulmonary Disease. He was suffering from Cough with phlegm. Alongside there was Wheezing and there was also Shortness of breath. It was needed to gather personal details for an intricate future diagnosis and treatment. For this it was important to communicate with the patient in a warm and personal manner by introducing oneself, ensuring patient's privacy, sitting at eye level when speaking with patient to comfort him as the patient was already in a situation of utter discomfort due to his ailment. For this it is important to use both verbal and nonverbal communications skills. Within this approach it is also important to explain the purpose of this interview in a heartily manner to sooth the patient telling him as in the case of legal advisor it is necessary to provide complete and accurate details as it would only help the doctors and nurses to diagnose perfectly and only then it would be possible to treat properly and thus this would help the patient to recover in a better and faster manner. It is also helpful and advantageous to use open-ended questions and summarize the interview for patient to be sure t he information is correct. (Fletcher, 2003) The details and summary of the patient's first hand vital particulars based on the interview performed are enumerated below. Culture: This patient was born and brought up in the United States however he seems to have as strong cultural overtone of his ancestral roots in South Asia but as a mainstream member of the American society he identifies himself as an American in the political and social context of the word. Religion: according to his birth certificate the patient could be enumerated as a Hindu by religion but like his cultural background he is attached to the American way of life and has no bias about any from of medical treatment or procedure. Physical milestones: The patient suffered from jaundice twice at the age of 16 and then again at the age of 27. He was diagnosed with diabetes at the age of 44 and he is still suffering from it however a report taken only 2 months back suggests blood sugar content sums up to 103. Gross & fine motor skills: Gross & fine motor skills were found to be at a normal stage however there was reported pain on the left shoulder and upper arm. Otherwise gross & fine motor skills were found to be normal. Language: The patient comes from an all American background and therefore he is fluent in English however he has a slight accent on his language of English like most South Asian. His mother tongue is Bengali. Social development: the patient was accompanied by his wife who is a native of India though she is well acquainted with the English

Aristotle's Concept of Happiness Essay Example | Topics and Well Written Essays - 1250 words

Aristotle's Concept of Happiness - Essay Example Aristotle uses Nicomachean Ethics in his theory of happiness to defend the view he takes on happiness. He begins by creating a big illusion that all things aim at some good. By saying that all things aim at some good, Aristotle means that everything has some aim or end to be achieved and the restricted good which every activity intends to achieve actuates the nature of that activity. Aristotle gives an example of health and the practice of medicine, the main aim of medical science is to attain health for everyone and health is in itself a good. Therefore the aim of medical science is good. Activities carried out in the real world achieve something desirable otherwise they would not be practiced. According to Aristotle, activities are hierarchically related to other activities and ends to ends (Broadie 11). Some ends are therefore subordinate to others. Hedonists and non-hedonists would disagree on what is subordinate to what between virtue and pleasure. Aristotle’s approach fo cuses on subordination-relations to cover individuals with different ethical attitudes. Subordination-relations are apparent to all who appreciate how diverse activities in a society are organized and the fact that all these activities aim at some common good. Aristotle argues that some end is ultimate for an activity and concludes that the ultimate is the good and the best but some activities may lead to others or each to various ultimate ends. Broadie states that â€Å"what is ultimate is not uniquely supreme, but it seems logically and ethically harmless, there could be conflict not resoluble by argument since it might not always be possible to act for the sake of one end without passing up an opportunity to act for the sake of another† (14). Since realistic people can avoid having different ends becoming adversaries’, anarchy or imposition of unreasonable decisions can also be avoided. Aristotle argues that knowing if there is a best should come before deciding wha t is the best. For him identifying a knowledge or skill first cultivates a good identification of the object or end. As far as ethics is concerned, the good is happiness. Despite the fact that everyone is mainly concerned for his own happiness, Nicomachean ethics does not ascertain or presume that a person can or should seek only his own good. It rather concentrates on activities and crafts in general. Aristotle argues that to form good decisions and carry them out, individuals need to understand impulse and not just apply philosophical ethics. â€Å"Lectures on ethics cannot act up for moral discipline.† (Broadie 20). It is not just enough to believe in theory; practicing things believed is a sure way of making progress. There is need to desire and act in congruence to reason. Reason does not just refer to philosophical light gained through studying ethics but rather to a progressive pursuit of the good life. According to Broadie, the pursuit is realistic not just for being established from an understanding of principles but because a good life is the kind of good that can only be achieved if individuals place some desires as secondary to others (21). This gives an individual a sound mind to choose what to do and discard what he may have felt like doing. In

Databases vs. Spreadsheets Essay Example | Topics and Well Written Essays - 500 words - 4

Databases vs. Spreadsheets - Essay Example This paper illustrates that there are many serious drawbacks of using spreadsheet for data storage, for instance, it is awkward to recover or access data from any, however, the unsophisticated queries, provides little or no data authentication and validity as well as little or no protection in opposition to data corruption from well-meaning but inexperienced and inadequately trained users. A database element can store simply the data for which it is created on the other hand spreadsheets offer the flexibility. In this scenario, any cell can be used to store and maintain numbers, text or charts. From the discussion, it is clear that a database is essential for storing a large amount of data in a secure way. A database is essential for storing banking data, human resource and other similar data where security and efficiency are critical. The researcher would recommend Oracle Database, which a well-known database development tool. The researcher has recommended Oracle Database because i t provides to its users some of the excellent capabilities such as scalability, leading performance, security and reliability in all the environments such as Windows, UNIX, and Linux. In addition, it offers a wide variety of tools and functionalities to effortlessly handle the most difficult business intelligence, transaction processing, and content management applications.

Saving Starbucks' Soul Essay Example | Topics and Well Written Essays - 750 words

Saving Starbucks' Soul - Essay Example Starbucks was one of the Fortune Top 100 Companies to Work For in 2005(Marketing teacher, 2010). Its global reputation and brand name has immense effects on global custoemrs.The immense resources are the major strength of Starbucks. The ability to forecast the market climate is another major strength of Starbucks. Most of the decisions taken by Starbucks during the last decade brought dividends to the company. Not even a single decision went wrong for Starbucks during this period. They were able to analyse the market opportunities and challenges provided by globalization and moreover they were able to redefine their strategies to make them suitable to meet the challenges and opportunities. They have adopted custom made strategies for each market as they realised that even for the same product, different marketing strategies required at different places. (BusineeWeek, 2009, p.3).This program was aimed at teaching the staff about the regional preferences. Commitment towards the environment made Starbucks one of the highly reputed companies in the world. They are keen protecting the environment by recycling all the industrial waste produced by their activities.Good customer relationships, good suppliers, leadership in the market, talented employees are some other major strengths of Starbucks. Starbucks tried to do too many things at a time. They have changed the romantic La Marzocca machines and introduced automatic espresso machines, in order to solve the major problem in terms of speed of service and efficiency (BusineeWeek, 2009, p.1). They failed to recognize the emotions the customers have on the earlier machine. Moreover the current machines are too big in size and small persons find difficulties in using it. The new machine also prevents the customers from enjoying the preparation of the drink. Flavor locked packaging helped the company in providing the fresh roasted bagged coffee, but, the loss of aroma,

Disclosure Analysis Paper Essay Example | Topics and Well Written Essays - 750 words - 1

Disclosure Analysis Paper - Essay Example According to Hilton (1994), finished products with The Coca Cola trade mark are presently selling in over 200 countries worldwide. The success of The Coca-Cola is its ability to reach the customers and providing them with unrivalled variety of products that satisfies their needs, desires and lifestyle choices. The Coca-Cola Company is a publicly traded and listed in the New York Stock Exchange (NYSE). Such company’s success is communicated to shareholders and other interested parties through the financial statements. Nevertheless, the financial statements provide summarized information and further detailed information in terms of notes. Notes to the financial statements are very essential for clear understanding of the financial reports. This paper seeks to analyze disclosures contained within the notes to the financial statements with respect to cash and cash equivalents, receivables and inventories. It goes further to provide a list identifying the components of cash and cas h equivalents. Cash and cash equivalents Cash Any information necessary for full understanding of the financial statements should be included as notes while at the same time avoiding information that is not needed to expound on financial statement. The Coca-Cola Company cash and cash equivalents comprise of both cash and short-term investments. ... credit risk by applying minimum credit standards and diversifies counterparties through application of procedures provided for monitoring credit risk concentrations. Cash equivalents The company considers short-term investments as cash equivalents due to their easy convertibility into cash. This category comprises other investments and time deposits with maturities of more than three months, but not more than one year. The investments grouped under this category comprises of securities that are easily convertible into cash. In this vein, the company can easily convert them into cash at any given time it is faced with cash flow challenges. Receivables Account receivables are referred to as dues from customers. According to Hopwood, (1974), these are amounts, which have not been received from customers by the close of an accounting period. There are different methods through which receivables are recorded in the books of accounts, and such information is provided as part of the notes t o the financial statements. In this regard, the notes provide that The Coca-Cola Company receivables are recorded at net realizable value. The notes further indicate that the value provided has an allowance for bad debts. Therefore, it records any foreseeable loss on trade account receivable by charging it to provision for doubtful debts. Moreover, the notes indicate that allowance for doubtful debts is computed based on historical values of the write-offs, an amount of unpaid accounts after considering the contractual terms and the ensuing relationship with the customers and bottling partners. However, the notes conclude by mentioning that the exposure posed by concentration of credit risk is adequately controlled due to diversity of geographical areas covered by the company’s

Strategic Management Unit 3 DB SA final Week Essay

Strategic Management Unit 3 DB SA final Week - Essay Example The reliability of the matrix is on decline as a result of the poor correlation between the profitability levels of the market as well as the functionality of market levels (Hubbard, Vetter, 1998). Though the Cadbury yogurt markets are currently operating at high levels due to the their high market shares and yields much profits , but due to the fact that they operate on larger markets they are most likely to consume a lot of cash in return making the matrix to become unreliable(Medicos MBA, 2014). In the second template, it is shown that though matrix can be reliable up to a certain point, it is not fully sustained since the matrix’s are utilized in the implementation of strategic decisions. There are as well some limitations to the kind of information that the matrix group offers (Medicos, 2012). It becomes very hard to retrieve valuable information as well as data concerning the market share. This matrix is consists of four different quadrants (Medicos, 2012). In the first quadrant is about the Question Mark which shows that the matrix has low relative position in market share (David, 2005). In the other quadrant, a good example is the iPhone which is considered a great product. Though the product holds a high market position, they do not sell at high growth industry at times (McClurg, 2013). The last quadrant, ‘Dogs’, have a low market share, weak internal and external position leading to liquidation (McClurg, 2013). Hubbard, R., Vetter, D. E., & Little, E. L. (1998). Replication in strategic management: Scientific testing for validity, generalizability, and usefulness. Strategic Management Journal, 19(3),

Understanding The Business Environment Term Paper

Understanding The Business Environment - Term Paper Example The capital comes from the treasury or the local rates. The public limited aim at providing services to the nation, and in case of profit generation, it has handed hack to the government or the local authority. The government appoints a minister to take responsibility. The minister then appoints a chairperson and the board of directors who respond to daily activities in running the industry. The chairperson and board of directors then give an annual report to the minister who presents it to the parliament for public debate. The information then published for public. The private limited companies are businesses owned by private people. The owners do control and management. They are the directors and managers. The private people raise capital, and their aim is to generate profit. The profit or losses made equally distributed according to the number of shares one own in the company. The voluntary group is an organization consisting of people who offer unpaid services to the organization . Its resources (cash, labor and services) obtained through voluntary means. The co-operatives form when a group works together to accomplish a common need. They are significant status in the tax law in most countries. The co-operatives assist members with their primary business e.g. selling of milk or other farm products. Type of organization Examples- Name of organization and why it exist What sector does this organization operate within Public limited company CDC – A centre for Disease Control ministry of Public health Private limited company Fly Emirates Transport industry Voluntary DISABLED AMERICAN VETERANS AUXILLARY- facilitate medical treatment of veterans Medical industry Co-operatives BONGARDS’ CREAMERIES CO-OPERATIVE Milk processing industry US CDC; CENTRE FOR DISEASE CONTROL CDC is a division of the public health systems and workforce development based in Atlanta, Georgia USA. Its strategy is to work with partners with the aim of strengthening public health systems and the public health workforce. It applies public health sciences and practices to demonstrate health impact. Vision, mission and goals Its vision is to enable countries worldwide have efficient and equitable public health systems to protect communities. It also visualizes the enablement of persons to live productive and healthy lives. It has a mission of working with Ministries of Health (MOH), and various health partners to strengthen public health systems. They collaborate to develop the workforce using innovative programs and science. The aim at building sustainable capacity maintaining strong public health systems and responding to the changing and increasing health challenges. They have a mission of coming together with public health partners to diversify global health problems, practices experiences and resources. (Allison, M & Kaye J 2001) Their main goal is to use system development programs to help the Ministry Of Health worldwide build strong, effective and sust ainable programs. The system development programs include; FETP, Field Epidemiology Training Programs, Field Epidemiology, Laboratory and Training Programs (FELTP), Global Public Health information program (GPHIP),Sustainable Management Development Program (SMDP) and the Integrated Disease Surveillance and Response (IDSR). They thus help the MOH to improve public health systems locally, regionally and nationally. The internal and external stakeholders of the CDC Stakeholders include persons or organizations invested in a program. They are interest in the results and evaluation of the program where their interests and requirements considered and budgeted for in the planning process. These

Factors That Have Led to An Increase in The Importance of Logistics as Research Paper

Factors That Have Led to An Increase in The Importance of Logistics as A Field of Study - Research Paper Example Strong links to the market (the customer) is the basis of corporate power. Since customer service drives the supply chain, professionals in logistics are best placed to implement value chain integration that yields customer satisfaction. The industries create future advantages based on the integration of logistics and international supply chains. Key words: Global economy, customer satisfaction, value, supply chain, diversity, technology, professionals. Factors that have led to an increase in the importance of logistics as a field of study Logistics refers to the process of scheduling, applying and controlling the effective, efficient storage and flow of services, goods and relevant information from origin to consumption. The management of the logistics process aims at meeting the users’ requirements. In a business sense, logistics is a critical aspect because it must support procurement, warehousing, inventory, distribution, human resources, financial, customer support and di stribution operations (Rodrigue, Comtois & Slack, 2006). Such operations are covered in the perspective of outbound, inbound, external and internal movements of materials and personnel. For materials, there is the additional aspect of return for environmental purposes. Apart from the physical items and personnel, logistics management also involves abstract items like information, time and energy, where the minimized use of capital is a universal concern (World Bank, 2010). This paper will discuss factors that have led to an increase in the importance of logistics as a field of study. The role played by logistics and supply chain management in a country’s economy makes the study of logistics critical towards increasing the country’s competitiveness in business. Because of the business objective of ensuring the correct items are available at the right time, place and quantity, logistics is inextricably linked to supply chains (Kahn & Kobayashi, 2007). It has become incre asingly important to study logistics and supply chain management because of the direct link to an economy’s revenues and cost structure as well as the competitiveness of producers in terms of quality of products and delivery times. Further, logistics affect the producers’ responsiveness to the requirements of consumers, which makes it important to understand how the growth in freight flow affects the current changes in local, regional and global economic systems (Waters, 2003). An understanding of logistics enables supply chain logisticians to associate optimum logistics performance with export diversification, trade expansion, economic growth and the capacity to draw direct foreign investments. This is because the competitiveness of an economy depends on how the logistics and supply chain perform (Hossein, 2010). When these factors are balanced, the value added to an economy by logistics exceeds the total costs. The growing complexity of supplying materials to busines ses as well as distributing products in a globalized supply chain also gives importance to the study of logistics (Christopher, 2010).

Rogerian Argument Essay Example for Free

Rogerian Argument Essay The poem â€Å"Sex Without Love† by Sharon Olds is as controversial as the topic itself. The author describing the phenomenon that has become pervasive in modern life could not refrain from taking a stand on the issue, and this position can be either supported or refuted by the audience. When so many people are motivated by the contemporary American culture to engage in sexual intercourse without the trappings of love or even simple emotional attachment, it is interesting to review the poem dedicated to this situation and sort out issues covered in it. Doing so will help one tread with more confidence in the complex realm of human communication. Besides, it is even more interesting since Olds is the kind of poet who does not shun provocative topics and is not afraid to show her intimate life to the public. In analyzing the poem, we will try to understand whether Olds’ poem is a humanistic glorification of the body or a disgusting description that satisfies bad tastes. The latter view of Olds’ poetry is taken by William Logan. In his article â€Å"No Mercy† published in the journal New Criterion in December 1999, he indeed takes no mercy on Sharon Olds’ works and their artistic value. Perhaps the only positive trait Logan finds about Olds’ poetry is its spontaneity and unexpectedness of the next line that in itself should be applauded in the world of literature. However, Logan is disgusted by the sensual images that constantly surface in the poems and repel him with their openness. Therefore, he states that reading through Olds’ â€Å"hell-for-leather hubris you never know whats coming next, but youre sure its going to be a disaster† (Logan 1999:60). In short, Logan believes her work to be â€Å"shameless prose chopped up into lines of poetry, lurid as a tabloid† (Logan 1999:60). As such, he sees Olds’ work as a response to the society in our times constantly demanding from poets more descriptions of sexual lurid scenes, empty of any meaningful human emotions, and Olds is a vivid example of this trend. However, Logan takes care to dismantle the value of the poetess’ work on the grounds on which she seems to him to advance – the radicalism in the portrayal of sexual scenes. Olds to Logan ism despite her attempts to pass herself as a radical, â€Å"a homely Redbook moralist, believing in motherhood, family, and honey on her nipples† (Logan 1999:60). Thus, this view of Olds’ poetry proclaims her tasteless and lacking radicalism, totally denigrating her work and making it look worthless. There is, however, a different perception of Olds’ poetry, and in particular the poem â€Å"Sex Without Love†. To me, in particular, this poem presents an image that is rich in imagery, metaphors, and perceptive comparisons. This imagery comes out in comparisons that liken the participants of the act in turn to dancers, ice-skaters, and children at birth. The latter, true, is a somewhat brutal simile, but it is so to only some people who think that newborns are not particularly good-looking, while to others a newborn is as beautiful as anybody, being part of the life cycle. The first two comparisons, â€Å"beautiful as dancers† and â€Å"gliding over each other like ice-skaters† seem suitable for any taste, reinforcing the opinion that sexual intercourse, like any natural human action, is not disgusting, but beautiful and elegant (Olds). The poem also introduces an interesting perception of sexual intercourse, interpreting it in its own terms. It is unusual to someone who was brought up with the conviction that sex is pure and acceptable only when it is justified by love and preferably by marriage. In our society, love at one point came to serve as a convenient way to justify why people had sex outside of marriage. Therefore, with time it became almost as sacred as marriage itself. Olds takes love off its pedestal and proclaims that those who choose to have sex without it are â€Å"the true religious, the purists, the pros† (Olds). Those are the people who will not accept a false Messiah, love the priest instead of the God. They do not mistake the lover for their own pleasure (Olds). It seems that in this context sex for its own sake becomes the new norm, and love is something like a deviation from this norm. Many people can dispute this perception, but it is certain that each person can have one’s own viewpoint on these matters. In any case, the fact that Olds raises the issue and supports it with bright poetic images makes this poem worth attention. The value of Sharon Olds’ poem is also appreciated in the Free-written Comprehension of Sex Without Love available from the Richard Stockton College of NJ website. Also noting the strong imagery of the poem, the writer also adds that â€Å"the images are here not for enjoyment, but rather to exhibit the reality of the action† (Richard Stockton College). Besides, the interpretation also emphasizes the fact that, like in many pieces of poetry, Olds does not draw the ready-made conclusion that she wants the reader to follow. In fact, she allows several explanations and has the reader make the guessing on his or her own. So is Sharon Olds a lurid author who enjoys portraying sexual scenes with all the possible details or a philosopher who introduces a new opinion, supported with adequate imagery? It feels that the answer can lie somewhere in between. Returning to the denigrating opinion stated by William Logan in his article, one can see that this argument covers the whole poetry. â€Å"Sex Without Love†, compared to other poems by Olds, is relatively more Puritan in its imagery and does not use many shocking details. The emphasis is on the process as a whole, and the author uses broad metaphorical images like ice-skaters or runners to convey broader similarities. Abstaining from talking about details like her labia or other body parts that she mentions in other poems, Olds appears more appealing to a broad audience of people with different backgrounds and views, many of whom may be alienated by more naturalistic images. By the way, talking about the imagery in Olds’ poetry, Logan admits that â€Å"Aristotle would have loved her metaphors, her anatomy lessons† (Logan 1999:60). In â€Å"Sex Without Love†, Olds is at her best with building her imagery that serves to convey her message. Her images become a powerful tool for showing the event from new and new angles, creating the effect of unexpectedness noted by Logan. Most interestingly, there is a viewpoint supported by Free-written Comprehension of Sex Without Love and differing from my initial perceptions: that in the poem, Olds does not at all support the idea of meaningless, thoughtless sex without emotions, and that in fact she is disgusted by it as much as her more conservative audience. The latter view is grounded in the final part of the poem where Olds compares her lovers to runners: they are like great runners: they know they are alone with the road surface, the cold, the wind, the fit of their shoes, their over-all cardio- vascular healthjust factors, like the partner in the bed, and not the truth, which is the single body alone in the universe against its own best time. (Olds) It can be claimed that â€Å"stating that the people in bed together are just meager factors of life strongly indicates that there is distaste for sex without love† (Richard Stockton College). Speaking of cardio-vascular health as one of the factors, Olds expresses her sadness over such act of love that does not include any emotional attachment between the two. Even though on the surface, she claims that she admires sex without love, in fact she is repelled by it, as shown in her images. After deliberation, I agree that Olds’ poem should perhaps be read in a different sense – disputing the value and attraction of sex without emotion. Using this time less naturalistic images, Olds displays her strengths with metaphors by creating an unforgettable picture of the two runners rushing along a meaningless path of factors. In this poem, she may not be savoring the details of lurid sexual pictures. Instead, Olds puts in her poem a deep spiritual meaning that reiterates the old human value of love, attachment, and care. In this sense, she may indeed by lacking radicalism, but instead of this she professes values close to many in her audience. Works Cited Logan, William. â€Å"No Mercy.† New Criterion 18.4 (December 1999): 60. Olds, Sharon. Sex Without Love. 24 June 2002. 17 April 2006 http://plagiarist.com/poetry/4922. Richard Stockton College of New Jersey. Free-written Comprehension of Sex Without Love. 17 April 2006 http:///thebalance/stories/storyReader$9.

Priemgetallen

Priemgetallen Voorwoord Het stond vast, ons onderwerp werd priemgetallen. Onze kennis in verband met priemgetallen reikte niet verder dan de getallen die deelbaar zijn door 1 en zichzelf. En we vroegen ons af wat er nog meer over te zeggen valt. Na even te surfen op het internet bleek al snel dat er veel informatie te vinden was. Priemgetallen hebben vele wiskundigen door de geschiedenis geboeid. Zo heb je Euclides, Fermat, Mersenne, Euler. Dit waren stuk voor stuk grote wiskundigen die geboeid waren door priemgetallen en er velen jaren over nagedacht hebben. Het grote voordeel aan een onderzoekscompetentie (OZC) met twee maken, is dat je elk maar de helft moet doen. Maar met als nadeel dat je verschillende afspraken moet maken, het werk eerlijk moet verdelen en samenkomen om alles te overlopen en tot in de details uit te werken. Onze OZC is in vier hoofdstukken ingedeeld. Eerst hebben we het over de geschiedenis van de priemgetallen en over de wiskundigen die er mee bezig waren. Hoe men steeds nieuwe priem getallen blijft vinden zien we in hoofdstuk 2. Hoofdstuk 3 gaat over de eigenschappen van de priemgetallen. Zo hebben we eerst het vermoeden van Goldbach, de belangrijkste stelling bij de priemgetallen. Daarna gaan we het hebben over de soorten priemgetallen en priemgetallen met speciale eigenschappen. Tenslotte gaat hoofdstuk 4 over de toepassingen van priemgetallen, en dit blijkt vrij veel te zijn. We hopen dat het voor u een even interessante en leerrijke ontdekkingsreis door de priemgetallen zal worden als dat het voor ons was. Hoofdstuk 1 De geschiedenis van de priemgetallen Wanneer precies de priemgetallen ontstaan zijn, kan nooit met zekerheid gezegd worden. Het zou kunnen dat de Babylonià «rs de eerste ontdekkers waren. Wel staat vast dat rond 400 voor Christus, Pythagoras de priemgetallen had gedefinieerd als getallen alleen deelbaar door 1 en zichzelf. Daarmee staat hij bekend als de uitvinder van de priemgetallen. In 530 v.C. stichte hij in het zuiden van Italià « een gemeenschap die zich onder andere bezighield met wiskunde. Er was een grote interesse in natuurlijke getallen en hun eigenschappen. Natuurlijke getallen en hun verhoudingen waren volgens de gemeenschap de basis van het leven en het heelal. Dankzij hun grote interesse, ontdekten ze iets bijzonder over bepaalde getallen. Stel een getal voor als een aantal knopen. Je kan dan sommige getallen rangschikken als een rechthoek, zoals het getal 6 (een rechthoek van 2 op 3 knopen). Er zijn getallen die je onmogelijk kan rangschikken als een rechthoek, zoals het getal 5. Er werd zo het verschil gemaakt tussen de rechtlijnige en de rechthoekige getallen. Deze rechtlijnige getallen worden nu priemgetallen genoemd. Rond 300 v.C. kwam Euclides, à ©Ãƒ ©n van de grootste wiskundigen uit de oudheid. Hij schreef een 13-delig werk De Elementen, waarin onder andere een bewijs staat dat er oneindig veel priemgetallen bestaan. Bewijs: Veronderstel dat er een grootste priemgetal pn bestaat. Dan maken we een lijst van alle priemgetallen: 2, 3, 5,,pn. Definieer dan N = 2, 3, 5, , pn. N + 1 is niet deelbaar door 2 want N is dat wel. De rest is 1. N + 1 is niet deelbaar door 3 want N is dat wel. Ook hier is de rest 1. N + 1 is niet deelbaar door 5, 7,,pn. De rest is telkens 1. Als N + 1 niet deelbaar is dan moet N + 1 zelf priem zijn. Als het wel deelbaar is, dan bestaat er een priemgetal p dat N + 1 deelt maar dat niet was opgenomen in de lijst, dus moet dat priemgetal p groter zijn dan pn. Hierdoor is er dus geen grootste priemgetal en zijn de priemgetallen oneindig. In 200 v.C. werd De Zeef van Erastosthenes (zie 2.4.1) beschreven en daarna bleef het een aantal eeuwen stil rond priemgetallen. In de 16de eeuw veronderstelde Pierre Fermat dat 22n- 1 enkel priemgetallen opleverde. Indien n een priemgetal voorstelde. Marin Mersenne dacht hetzelfde over 2n 1. In 1753 toonde Goldbach aan dat geen enkele formule voldoet om alle priemgetallen te definià «ren. Vanaf de 19de eeuw werd er intensief op zoek gegaan naar grote priemgetallen en de mogelijkheden om ze toe te passen in de samenleving. Hoofdstuk 2 Het zoeken naar priemgetallen Welke getallen zijn priem? De definitie: Een priemgetal is een natuurlijk getal dat slechts 2 verschillende delers heeft. Die delers zijn 1 en het getal zelf. In het begin is het simpel. Je kan getallen à ©Ãƒ ©n voor à ©Ãƒ ©n gaan uitproberen. Zijn ze niet deelbaar door een ander getal dan 1 en zichzelf, dan is het een priemgetal. Zo zijn 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 alle priemgetallen kleiner dan 100. Veel mensen vragen zich af waarom 1 ook niet gewoonweg een priemgetal is. Natuurlijk heeft 1 maar à ©Ãƒ ©n deler en geen twee. Dan waarom is de definitie niet gewoon een natuurlijk getal dat enkel gedeeld kan worden door 1 en zichzelf? Wel hierdoor zou de hoofdstelling van de rekenkunde (Elk natuurlijk getal valt te ontbinden in priemfactoren op juist à ©Ãƒ ©n manier) niet meer gelden. Een natuurlijk getal zou dan op oneindig veel manieren kunnen worden geschreven als een product van priemgetallen. Eà ©n voor à ©Ãƒ ©n de getallen gaan uitproberen om na te gaan of ze priem zijn is na een tijdje toch vrij vervelend. Het zou daarom wel handig zijn een patroon in een lijst van priemgetallen te herkennen. Helaas is er tot op het heden geen enkel goede formule gevonden. Euler, in de 18de eeuw, vond de formule f(x) = x ² + x + 41 en alle f(x) zijn priem. Maar het werkt enkel voor x∈(0 t/m. 39). De principià «le hoofdtheorie De principià «le hoofdtheorie houdt in dat de kans een getal x priem is, ongeveer gelijk is aan 1/ln(x), voor een x groter dan rond de 5000. Als x rond het getal 10000 ligt, dan is de kans dat het priem is ongeveer 1/9. Ligt een getal ergens bij de 1.000.000.000 dan is de kans ongeveer 1/21. Dit betekent dat de priemgetallen zeldzamer worden naarmate we kijken naar grotere getallen. Mersenne-getallen Marin Mersenne onderzocht in het begin van de 17de eeuw ook de priemgetallen en hij probeerde net zoals Fermat een formule op te stellen. Ook hij is er niet in geslaagd, maar hij heeft wel ander belangrijk werk verricht. Hij was de eerste die zich volledig toelegde op de formule Mp = 2p -1, waarin p priem is. Euler had deze formule opgesteld in De Elementen. Deze formule werkt niet altijd. Toch is al jarenlang het grootst bekende priemgetal altijd een Mersenne-priemgetal geweest. Vanaf juni 2009 zijn er 47 Mersenne-priemgetallen bekend. Het grootst bekende priemgetal is 243112609 -1. Het was het eerste bekende priemgetal met meer dan 10 miljoen cijfers! De vlugge testen De zeef van Erastosthenes De zeef van Eratosthenes is de oudste methode voor het vinden van priemgetallen. Ze is ontstaan circa 240 voor Christus. Het werkt heel simpel. Je schrijft bijvoorbeeld alle getallen op van 2 tot en met 120 Dan nemen we het eerste getal, 2, en arceren we alle veelvouden van dit getal, groter dan het getal zelf in het rood. We nemen nu het volgende, nog niet gearceerde getal, 3, en arceren alle veelvouden van 3 in het groen. De veelvouden van 4 zijn reeds gearceerd dus kunnen we deze overslaan. Daarna arceren we alle veelvouden van 5 (blauw), van 7(geel) en van 9 (groen) De resterende getallen arceren we in het paars en dit zijn de priemgetallen van 1 t/m. 120 Met deze methode kan je alle priemgetallen t/m. n achterhalen door alle veelvouden t/m. n te arceren. Dit valt ook te bewijzen: Stel dat de zeef maar van 2 t/m 100 gaat. Stel dan dat er toch een samengesteld getal x ≠¤ 100 nog niet gearceerd is. Omdat x samengesteld is, geldt x = a.b , met a ≠¤ 100 of b ≠¤ 100. (Als a en b beide groter zijn dan 100 , is a.b = x immers groter ( 100) ²=100). x Is dus een veelvoud van een getal kleiner dan 100, Al deze veelvouden hebben we gearceerd. Elk niet gearceerd getal kleiner dan 100 kan dus niet samengesteld zijn, en moet een priemgetal zijn. Het ontbinden in priemfactoren Euclides bewees eveneens in De Elementen dat elk natuurlijk getal te ontbinden valt in priemfactoren op juist à ©Ãƒ ©n manier (als we de volgorde verwaarlozen). Dit wordt ook wel de hoofdstelling van de rekenkunde genoemd. Valt een natuurlijk getal niet te ontbinden in priemfactoren, dan is het getal priem. Bijvoorbeeld met het getal 211. Je kijkt of het deelbaar is door 2,3,5,7,11 en 13. Omdat 17 > 211mag je bij 13 stoppen. Het getal 221 is niet deelbaar door deze 6 priemgetallen, dus is het zelf priem. Deze methode wordt alleen gebruikt voor getallen met maximum 25 cijfers. Fermat In de 17de eeuw stelde Pierre de Fermat dat elk getal van de vorm Fn = 22n+ 1 (met n ∈ N een priemgetal is. Echter in 1732 zei Euler dat dit onzin is. Het werkt enkel voor n = 0 t/m 4. Je hebt enkel 2 proefdelingen nodig om deze factor te vinden. Euler toonde aan dat elke deler van een Fermat-getal Fn met n > 2 de vorm 2n+2.k + 1 heeft. In het geval van F(5) is dat 128.k + 1. De getallen 129, 385 en 513 zijn niet priem dus gaan we 257 en 641 uitproberen, met succes. Waarschijnlijk zijn alleen de eerste 5 Fermat-getallen werkelijk priemgetallen. Fermats kleine stelling daarentegen is van meer nut. Het houdt in als p een priemgetal is, dan geldt voor ieder geheel getal a dat ap = a(mod p) Als het priemgetal p geen deler is van a, dan heeft ap-1/p een rest van 1. Stel dat je een bepaald getal a hebt. Als je een priemgetal p kunt vinden waarvoor ap-1/p niet als rest 1 oplevert, dan is a deelbaar door p en dus samengesteld. Bijvoorbeeld: a=4 en p=5; dan is 1024/5 = 1020 + 4. De rest is 4, dus is het getal 1024 samengesteld en niet priem. Jammer genoeg werkt de stelling niet altijd in de andere richting, maar door deze kleine stelling van Fermat kunnen we al meteen een hele hoop getallen elimineren als priemgetallen. De andere getallen kunnen daarna verder gecontroleerd worden. PRPs De hedendaagse computertests hebben hun snelheid niet alleen te danken aan de snelle hardware, maar veeleer aan de software. Men gaat eerst een aantal waarschijnlijkheidstesten uitvoeren. Ze gaan op zoek naar pseudo-priemen. De getallen die deze testen doorstaan. De simpelste test werkt met de kleine stelling van Fermat. (zie 2.4.3) Het omgekeerde van die stelling is niet altijd geldig. Als voor een gehele a en k geldt dat ak = a(mod k) dan is k niet noodzakelijk een priemgetal. Vroeger was elke k een pseudo-priemgetal. Nu is het alleen nog maar een pseudo-priemgetal als het nog meer testen doorstaat en toch geen priemgetal blijkt te zijn. Een getal k dat in een test slaagt waarin a=2 noemt met een 2-PRP (waarschijnlijk priemgetal, een vertaling van probable prime). Als de test slaagt met a=3 noemt met het een 3-PRP enzovoort. Omdat deze priemtesten veel sneller verlopen dat de exacte controles, gaat men er meerdere na elkaar uitvoeren. Men begint bij a=2, dan a=3 enzoverder. Als een getal k positief test over verschillende testen, dan is het waarschijnlijk dat het ook een priemgetal is. Bijvoorbeeld: Een 2-PRP met k=341. Het blijkt geen priemgetal te zijn want het is deelbaar door 11 en 31. Er zijn 1.091.987.405 priemgetallen kleiner dan 25.000.000.000, maar slechts 21.853 pseudo- 2-PRP priemgetallen. Dus een getal k kleiner dan 25 miljard, die in een 2-PRP-test slaagt, in 99.998% van de gevallen ook werkelijk priem is. En hoe groter k wordt, hoe groter de slaagkans wordt. SPRPs Wanneer k het getal is dat we onderzoeken of het priem is, d oneven is en s positief. Dan is in k 1 = 2s.d , k een sterk waarschijnlijk priemgetal (vertaling van strong probable prime) als aan à ©Ãƒ ©n van de volgende condities voldaan wordt op basis a. ad = 1(mod k) (ad)2r = -1(mod k) waarbij r positief is en r Ook hier zijn alle getallen k > 1 die niet in de test slagen, niet priem. En de getallen die wel slagen kunnen priem zijn. Deze waarden voor k zijn dus niet priem. Zo een SPRP-test is redelijk snel, zeker als het gecombineerd wordt met het zoeken naar de kleinste priemfactoren. Het is aangetoond dat dergelijke testen in 75% van de gevallen priemfactoren oplevert. Op zichzelf is een SPRP-test dus tamelijk zwak, maar als we enkele van deze testen combineren, maken we een krachtige test voor kleine getallen k, die priemheid aantonen. Wat wilt zeggen dat een getal zeker priem is of zeker niet. Bijvoorbeeld: Als k k priem. Als k k priem. Als k k priem. Als k k priem. Als k k priem. Als k k priem. Deze resultaten geven ons een manier om een zeer snelle priemheidstest te maken. We beginnen met het zoeken naar de kleinste priemfactoren, daarna voeren we SPRP-testen uit op basis 2, basis 3, tot wanneer een van de bovenstaande criteria is bereikt. Bijvoorbeeld, als k De klassieke testen Merkwaardig is dat de grootste priemgetallen tot nu toe gevonden, p-1 of p+1, zeer makkelijk te ontbinden zijn. Dit komt omdat dit priemgetallen zijn waarvan het gemakkelijk is om te bewijzen dat ze priem zijn. Bij deze klassieke testen kunnen we aantonen dat een getal priem is. Dit zijn dus geen waarschijnlijkheidstesten, maar bewijzen van de priemheid. Stelling 1 (Lucas-Kraitchik-Lehmer) Lucas heeft op het einde van de 19de eeuw de kleine stelling van Fermat omgevormd tot een praktische test, die later versterkt werd door Kraitchik en Lehmer. Stel n > 1. Als voor iedere priemfactor q van n-1 er een natuurlijke a bestaat zodat an-1 = 1(mod n) a(n-1)/q ≠  1(mod n) dan is n priem. Dit is zowat de basis van alle moderne priemtesten. Stelling 2 (Pocklington) Stelling 1 heeft een volledige ontbinding in priemfactoren nodig van n-1. Pocklington had daar een oplossing voor. Stel n-1 = qkr waar q priem is en r niet deelt. Als er een natuurlijk getal a bestaat zodat an-1 = 1(mod n) en de g.g.d. van(an-1q- 1,n) = 1, dan heeft iedere priemfactor q van n de vorm qkr + 1. Stel dan n-1 = FR, waarbij F > R, g.g.d. (F,R) = 1 en de ontbinding van F gekend is. Als voor iedere priemfactor q van F er een a > 1 bestaat zodat an-1=1(mod n) g.g.d. (an-1q- 1,n) = 1 dan is n priem. Er kunnen verschillende a gebruikt worden voor ieder priemgetal q. Deze formules zijn de basis van de bekendere formules, zoals die van Pepin en Proth. Pepins test Pepin heeft in 1877 een formule gevonden die Fermat-getallen (van de vorm 22n+1) op de priemheid test. Stel dat Fn het n-de Fermat-getal is met n > 1. Fn is priem als en slechts als 3(Fn-1)/2 = 1(mod Fn). Bijvoorbeeld: F2 = 222+ 1 = 17 Dan is 3(17-1)/2 = 38 =6561 = 1(mod 17) Want (6561+1)/17 = 386 Proths test Proth maakte in 1878 de formule: n =2kh +1 met 2k > h. Als er een natuurlijk getal a bestaat zodat a(n-1)/2 = -1(mod n), dan is n priem. Lucas-Lehmertest Om na te gaan of een Mersenne-getal, een priemgetal is kan je de Lucas-Lehmer test gebruiken. Als p een priemgetal (groter dan 2) is, is het Mersenne-getal 2p -1 priem, als S(p-1) deelbaar is door 2p -1, waarbij S(n+1) = S(n) ² -2 en S(1)=4. Bijvoorbeeld: Als we willen weten of M3 = 7 een priemgetal is, dan zoeken we S(2).   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  S(2) = S(1) ²-2   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  = 4 ²-2   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  = 14 Dan controleren we of 14 deelbaar is door 2p -1 = 7. Dat klopt dus 7 is een priemgetal. De theorie voor de test heeft Lucas uitgevonden rond 1870. Hij heeft dan de test vereenvoudigd in 1930 tot wat hierboven uitgelegd staat. Voor heel grote Mersenne-getallen wordt het wel moeilijk de test uit te voeren. Zelfs moderne computers kunnen slecht overweg met zeer grote getallen. APR, APRT-CL In 1970 begon Williams samen met enkele anderen op een andere manier de priemheid te testen. Ze gingen nu niet meer de factoren van n-1 gebruiken, maar factoren van n2+1, n ²+n+1, n ²-n+1 en nm 1 waarbij soms m heel groot was, zoals 5040. Elk priemgetal q waarvoor q 1 een deler is van 5040 (welke n niet deelt) moet dan n5040 1 delen. Er is aangetoond dat er altijd een m is waarvoor geldt dat m q die nm 1 delen met q 1 een deler van m op zijn minst een product geven dat gelijk is aann. Zo goed als altijd ligt m rond de 100.000.000 voor een n die een 3000-tal cijfers bevat. GIMPS GIMPS (Great Internet Mersenne Prime Search) is een project waarbij men zoekt naar steeds grotere Mersenne-priemgetallen. Dankzij GIMPS kunnen we enorm grote getallen controleren op priemheid, doordat het werk wordt verdeeld onder een aantal deelnemers. Het project heeft tot op het heden 12 Mersenne-priemgetallen gevonden. Iedereen die een computer heeft en over internet beschikt kan deelnemen. Er is wel veel tijd voor nodig, à ©Ãƒ ©n priemheidstest kan gemakkelijk een hele maand duren. GIMPS is een efficià «nt systeem, het zoeken naar Mersenne-getallen gebeurt in verschillende stappen. Het aanmaken van een lijst met priemgetallen (want de formule die ze gebruiken is 2p-1 met p als priemgetal) Het zoeken naar de priemfactoren, wat op verschillende manieren kan gebeuren. Bij GIMPS zullen ze de exponent eerst omzetten naar het binair talstelsel. Bijvoorbeeld: 223 1 wordt getest en wordt daarbij gedeeld door 47. In het binair is 23 = 10111. Daarna passen ze de volgende werkwijze toe (het binair rekenen): De Pollard-methode om te ontbinden in priemfactoren. De P-1-methode werkt nogal simpel. In stadium 1 kiezen ze een vaste B1. Als q = 2kp + 1, dan zal het P-1-ontbinden in factoren deze factor q bepalen zolang alle factoren van k kleiner zijn dan B1. Dan wordt x = 3E.2.P berekend. Daarna controleren ze de g.g.d. van(x 1,2p -1) om te zien of er een factor is gevonden. In stadium 2 gebruiken ze een ander vast getal, B2. Hier zal de factor q gevonden worden als k exact à ©Ãƒ ©n factor heeft tussen B1 en B1 en alle andere factoren van k kleiner zijn dan B1. (Dit stadium maakt gebruik van zeer veel geheugen) GIMPS gebruikt deze methode om de grote factoren te vinden. Bijvoorbeeld 22944999 1 dat deelbaar is door 314584703073057080643101377. B1 en B2 worden gekozen door kansberekening. De Lucas-Lehmer test. (zie : 2.5.2.2) Om een getal te controleren zijn er heel veel vermenigvuldigingen nodig. Er worden zorgvuldig algoritmes geschreven die gebruikt worden om zeer snel te vermenigvuldigen. De kans dat zo een Lucas-Lehmer test succesvol een priemgetal ontdekt is ongeveer 1/80000. De zoektocht naar het grootste priemgetal Sommige mensen hebben er een hobby van gemaakt steeds op zoek te gaan naar het grootste priemgetal. De traditie is al gaande sinds 300 v.C. toen Euclides zijn werk De Elementen schreef. Hij merkte op dat de perfecte getallen (positieve getallen gelijk aan de som van zijn delers) nogal dicht lagen bij de priemgetallen van de vorm 2p -1 voor een priemgetal p. Vanaf toen begon de jacht op de Mersenne-priemgetallen. Grote getallen van deze vorm zijn al bestudeerd door grote wiskundigen zoals Fermat, Mersenne, Euler, Lucas, Leibniz enzovoort. Veel mensen willen de eer om hun naam bij het lijstje te voegen. De traditie om grote Mersenne-priemgetallen te vinden zal zeker blijven duren. En er valt heel wat meer met mee te bereiken. Er zijn programmas om priemgetallen te zoeken bij het testen van hardware. Dit wordt al gedaan sinds het ontstaan van de computer. Zo werden stukjes software van het GIMPS project (Zie 2.7) gebruikt door Intel om de processors Pentium II en Pentium Pro te testen alvorens ze verscheept werden. De software dat priemgetallen berekent, belast de processor meer dan andere programmas doen en duurt niet lang om uit te voeren. Als je een heel groot priemgetal invoert, moet de processor een miljoen berekeningen uitvoeren om na te gaan of het wel klopt. En hoe meer priemgetallen er gevonden worden, hoe meer de verdeling ervan kan worden bestudeerd en worden begrepen. Er is al veel onderzoek gedaan naar patronen in de verdeling van priemgetallen. Tevens is het allemaal niet voor niks. Er wordt een serieuze geldprijs van minstens $ 150.000 uitgereikt aan degene die als eerste het priemgetal vindt bestaande uit 100-miljoen cijfers. De eerste die er eentje kan vinden bestaande uit een miljard cijfers, krijgt zelfs een prijs van minstens $ 250.000. Het grootste priemgetal is dus heel bruikbaar en gewild. Hoofdstuk 3 Een priemwereld vol verrassingen Inleiding Zoals al gebleken is zijn er oneindig veel priemgetallen maar kunnen we deze nog onderverdelen in aparte groepen? Ja, er zijn zelfs zeer veel onderverdelingen met elk hun specifieke eigenschappen. Zo heb je de palindroompriemgetallen, Mersennepriemgetallen, Illegale priemgetallen, Maar eerst beginnen we met het uitleggen van enkele vermoedens in verband met priemgetallen. Enkele vermoedens Inleiding Er zijn vele stellingen in verband met priemgetallen. Deze gaan van zeer simpel tot echte breinbrekers. We vooral de meest bekende en de meest belangrijke stellingen voor de priemgetallen bespreken. En daarom beginnen we ook met de stelling die van het grootste belang was voor de priemgetallen, namelijk het vermoeden van Goldbach. Het vermoeden van Goldbach Goldbach was een Duitse wiskundige en is in 1690 geboren in Kà ¶ningsberg. Hij werd zelfs leraar bij de Tsaar in Moskou omdat hij een zeer belangrijke wiskundige was in zijn tijd. Deze job gaf hem dan ook de mogelijkheid veel te reizen zodat hij overal in contact kwam met andere belangrijke wiskundigen zoals Euler, Leibniz. Hij bleef in contact met deze geleerden door middel van brieven. Ook het begin van zijn vermoeden schreef hij in 1792 in naar Euler. In deze brief schreef hij dit vermoeden: Als een geheel getal n > 5 is dan kan dit getal geschreven worden als de som van 3 priemgetallen. Bij deze 3 priemgetallen kan herhaling optreden. Wat wel vreemd is aan het hele verhaal is dat Euler een brief terugschreef met daarin de stelling dat dit vermoeden geldt voor ieder getal n > 2 maar toch is het vermoeden enkel bekend als het vermoeden van Goldbach. Euler beschouwde de stelling van Goldbach als waar maar hierbij was de stelling nog niet bewezen. Zelfs nu is de stelling nog niet bewezen desondanks er als publiciteitsstunt 1 miljoen dollar aan te verdienen was. Maar dit betekent niet dat er geen belangrijke ontdekkingen zijn gedaan. In 1939 bewees Schnirelmann dat je elk even getal groter dan 2 geschreven kan worden als een som van ten meeste 300000 priemgetallen. In 1995 bewees Ramarà © dat een som van maximum 7 priemgetallen meer dan genoeg is. Het oude vermoeden van Goldbach Dit is het vermoeden dat Goldbach als eerst vermelde in zijn brief naar Euler: als een geheel getal n > 5 is dan kan dit geschreven worden als de som van drie priemgetallen. Dit vermoeden wordt ook wel het oneven vermoeden van Goldbach genoemd. Dit oneven vermoeden is eigenlijk een zwakkere vorm van het eigenlijke vermoeden. Want we kunnen bij n > 2 telkens het priemgetal toevoegen zodat we elk oneven getal n > 5 bekomen maar het oorspronkelijke vermoeden volgt niet uit het oneven vermoeden van Goldbach. Het oneven vermoeden staat al veel dichter bij het bewijs dan het oorspronkelijke want in 1937 bewees Vinogradov dat dit vermoeden geldt voor alle voldoende grote oneven getallen. Het probleem was wel dat Vinogradov niet wist hoe groot voldoende groot nu juist was. In 1956 kon men uiteindelijk op voldoende groot een getal plakken, namelijk groter dan 3315. De waarde die gelijk is aan voldoende groot is het getal n > 1043000 bewezen door Wang. De exacte waarde zal men pas kunnen vinden als men computers kan ontwikkelen die dit soort berekeningen aankunnen. Nog meer vermoedens We zullen vlug nog even enkele vermoedens vermelden: Voor ieder even getal 2n bestaan er oneindig veel priemgetalkoppels waarvoor het verschil tussen beide priemgetallen gelijk is aan 2n. Maar indien n = 1 dan hebben we te maken met een priemtweeling en bij n = 3 dan moet het verschil 6 zijn en is het priemgetalkoppel een koppel sexy priemgetallen. (zie 3.7.2) Ieder even nummer is een verschil van 2 priemgetallen. Priemgaten Opvallend bij priemgetallen is dat er geen logische volgorde zit in de opeenvolging. Hoe verder we gaan zoeken naar grote priemgetallen hoe moeilijkere deze te vinden zijn, want ze komen dan steeds minder voor. De gaten tussen twee priemgetallen worden steeds groter hoe verder je gaat. Deze gaten oftewel priemgaten zijn de ruimtes tussen 2 opeenvolgende priemgetallen. De grootte van deze gaten wordt dus bepaald door het verschil van de 2 opeenvolgende priemgetallen. Al een gehele tijd hebben wiskundigen een patroon proberen te ontdekken bij de opeenvolging van priemgetallen door de priemgaten te bestuderen. Priemgaten hebben geen beperking in grootte want als n ≠¥ 2 de minimale grootte is dan zijn de volgende gatallen allemaal samengesteld: (n + 1)! + 2, (n + 1)! + 3, (n + 1)! + 4, , (n+ 1)! + (n + 1) Vb. n = 2 dan zijn de eerste 3 getallen van het priemgat 8,9,10 Deze formule is niet alleen nuttig om het priemgat met grootte n te geven maar ook om het priemgat te geven met minimale grootte n. Hierdoor is de aanwezigheid van minimum n ontbindbare getallen verzekerd. Wat wel nog een probleem vormt is de mannier om de grootte van een priemgat te berekenen. Want men gebruikt het eerste priemgetal a en het tweede priemgetal b om de priemgaten te berekenen door priemgetal a af te trekken van priemgetal b. Het probleem is dat men oftewel bij de uitkomst 1 moet optellen of niet, want zonder 1 toe te voegen wordt het priemgetal a ook meegerekend met het priemgat. Illegale priemgetallen In 2001 ontdekte Phil Carmody dat de gezipte broncode C, wat men op computers gebruikt om DVDs te decoderen, overeenkomt met een priemgetal. Hij ging als volgt te werk: Eerst comprimeerde hij de C-Code met het computerprogramma Gzip. Het getal wat nu weergeven werd in het verkleinde bestand was priem. Er bestaan dus heel wat illegale priemgetallen. Hieronder volgt het allereerste illegale priemgetal, gevonden door Phil Carmody. Later zette Joerg Dietrich het priemgetal om zodat deze kon worden weergegeven in baseparen. Hij kwam een Dna-sequentie uit die 43016 basen telt. Hij kwam ook tot volgende vaststelling: het zinloos zou zijn om een wet te maken tegen het gebruik van het priemgetal want als men ooit het priemgetal in ons DNA mocht vinden dan zouden 6 miljard mensen de wet overtreden. Hier is een klein deeltje van de Dna-sequentie: Merkwaardige priemgetallen Congruente priemgetallen Een priemgetal dat een regelmatige figuur vormt noemt men een congruent priemgetal. Een regelmatige figuur oftewel een regelmatige n-hoek zoals een vierkant of een gelijkzijdige driehoek. Het middelste getal of centrum vormt dan het priemgetal omgeven door cijfers van binnen naar buiten toe. Als voorbeeld geven we volgende regelmatige figuren gevormd door een priemgetal. Vb. 1 met priemgetallen Palindroompriemgetallen Priemgetallen die je zowel naar voor als naar achter hetzelfde leest noemt men palindroompriemgetallen. Als voorbeeld kunnen we volgende priemgetallen gebruiken: 2, 11, 101, Maar ook gigantische priemgetallen zoals 14 ·10^6343-4199. Dit priemgetal telt 6343 cijfers en dit is gewoon heel de tijd 1 en 4 afgewisseld: 14 ·10^6343-4199 = 1414141414141414141 Zo heb je ook het grootste palindroompriemgetal van 3 cijfers namelijk 717. Er zijn ook priemgetallen die de decimale loop van p weergeven: 3, 31, 314159, Het 4de palindroompriemgetal bevat al 38 cijfers en het 5de al 500. Nog een zeer mooi palindroompriemgetal is het volgende: 923032900000000 00000000000006660000000000 00000000000000009230329 Het bestaan uit 666 en wordt omgeven door 32 nullen en 9230329 aan elke kant. En nog wat eigenschappen van dit palindroompriemgetal: 9230329 is exact het 666ste palindroompriemgetal 666.32 = 21312 wat een palindroompriemgetal is. 666.64 = 42624 wat ook een palindroompriemgetal is. De palindroompriemgetallen zijn nog verder ingedeeld zo heb je: De Titanic-palindroompriemgetallen gevonden door Samuel Yates: deze bevatten minimum 1000 cijfers. Samuel Yates zei dat dit een zeer lage grens is en later bleek waarom. Doordat men nu verder kon rekenen met machines werd de onderverdeling Gigantische palindroompriemgetallen gemaakt: dit zijn palindroompriemgetallen met ten minste 10 000 cijfers. De Megapalindroonpriemgetallen: deze bevatten ten minste 1 000 000 getallen en er waren er in 2003 slechts 4 gekend. Een pandigitaal palindroompriemgetal: bijvoorbeeld 1023456987896543201 Als we het getal in 2 verdelen in het midden en links en rechts het midden meetellen dan hebben we elk getal 1 keer. Een zeer bijzondere eigenschap van de palindroompriemgetallen is dat ze allen oneven zijn buiten 11 want moest men een palindroomgetal vinden dat even is dan is dit misschien wel palindroom maar zeker niet priem. Nog een palindroompriemgetaleigenschap is de palindroompriempiramide: Hier begin je met een priemgetal bij de volgende rij plak je aan beide kanten deze

Impact of Air Power Theory in WW2

Impact of Air Power Theory in WW2 Did â€Å"air power theory† do more harm than good before the outbreak of â€Å"and during† the Second World War? This essay will examine the meaning and impact of â€Å"air power theory†, a theory which took shape after World War One, which predicted that air power would be the single most important factor in the outcome of future wars. We will briefly examine the impact this theory had on the interwar Military planning and strategies of the major powers, as well as the influence of air power theory during the Second World War itself. The first part of our essay looks at what â€Å"air power theory† is, we shall look at the two major air power theorists, Giulio Douhet[1] and Billy Mitchell[2] and examine the differences and similarities between the two. Secondly we shall examine the negative impact of the â€Å"air power theory†, both in its implementation by the US and Britain and the shortcomings of the theory as demonstrated during the Second World War. The third part is concerned with the successful implementation of air power theory by the US and Britain before and dur ing the Second World War which led to positive military outcomes for the respective nations during the War. Finally we will attempt to conclude on whether the overall impact of â€Å"air power theory† during this time period can be judged positively or negatively. The most famous of the air power theorists, General Giulio Douhet was a passionate advocate on the fundamental importance and potentially revolutionary application of air power, specifically strategic bombing, as the most important means to win future wars. Douhet served with the Italian armed forces in Libya during the Italy – Turkey war of 1911 and during World War One, during which time aircraft were being used for the first time in military engagements. In 1921 he published â€Å"The Command of the Air† , arguably one of the most important works in air power theory and a endorsement of the power of precision bombing to win quick, decisive but devastating future wars. â€Å"I have maintained, and continue to do so, that in the wars to come the decisive field of action will be the aerial field†[3] It is not necessary to go into complex detail regarding Douhet’s theories of war, as we may summarise them into five key points. Firstly Douhet stated that modern and future warfare would give no distinction between civilian and combatant, that the previously taboo targeting of civilians and civilian infrastructure would be a thing of the past. Secondly, Douhet believed, no doubt influenced by his experiences from the First World War, that a quick, decisive victory using purely ground forces was no longer possible. Thirdly, that there was at the time, and most importantly for Douhet, would never be an effective anti aircraft measure that could prevent heavy strategic bombing from destroying its target. â€Å"Consequently I say, no aerial defence, because it is practically useless†[4] . Following on from this point, and arguably the most controversial in terms of the suffering it was seen to have led to, Douhet stated that the only way to defend against an enemy strategic bombing and to ultimately win a war was to launch a massive bombing campaign that would devastate the target’s government, industrial infrastructure and ability to make war, as well as so demoralising the enemy population that the shattered civilian population would force their Government to sue for peace or surrender unconditionally. Finally, and sharing a similar viewpoint with Mitchell, [5] there was a need for a nation’s air force to be completely independent of both the army and navy, and to constantly maintain a state of readiness in the event of needing to deal the knockout blow to the enemy. [6] Although borrowing many of his ideas from Douhet and others, American General Billy Mitchell did combine many air power theories at the time to create a structured, well thought air power theory which some might argue was more comprehensive and realistic than the ideas of Douhet.[7] Like Douhet, Mitchell wanted a centralised, independent air force, but unlike Douhet Mitchell wanted a centralised structure for all types of airpower, each given equal importance, whereas Douhet was concerned primarily with strategic bombers, any other type of aircraft was for him possibly useful but certainly secondary to the importance of the bombers. Mitchell also did not share Douhet’s view of strategic bombing being impossible to defend against. Mitchell wanted equal resources dedicated to both offensive and defensive air capabilities, and envisioned a wider role for ground attack and fighter aircraft that could be used as bomber escorts.[8] What both theories have in common however is their firm belief that air power would be absolutely vital, indeed the most important factor, in any future wars. Both men died before seeing that in the awful carnage of the Second World War, their theories were far from entirely accurate. When looking at the use of air power in the Second World War, it is clear that air power, in particular strategic bombing, did not make land and navy forces obsolete, and that both Douhet and Mitchell had both overestimated the destructive and defensive capabilities of strategic bomber aircraft. â€Å"Successful warfare still depended upon the movement of armies to occupy land, and the movement of ships to provide supplies and men,†[9] Although it played an important role throughout the War, the majority of fighting in Europe, in particular on the Eastern front was done with conventional land armies. Douhet had predicted that Britain’s mighty navy would be useless against a co-ordinated air assault, yet the British navy and merchant fleet was the lifeline supported the war effort with supplies from America and beyond. And certainly Douhet’s assertion that land forces were no longer capable of achieving quick, decisive victories does not stand up when looking at t he German Blitzkrieg campaigns between 1939-1941. In the 1930s Britain had slashed military spending, partly as a result of having to support the mass of unemployed during the great depression and partly due to an increasing anti war feeling in some parts of British Society. The exception to this was spending on Bomber Command, the part of the RAF responsible for strategic bombing. Strategic bombing offered a solution to the horrors of the First World War’s trench warfare, a decisive, relatively humane way in which to fight and end a war. Before the beginning of the war the emphasis was fortunately shifted to air defence, investing in innovations such as radar and fighter interceptors to shoot down German bombers. Following through with Douhet’s theories, as Bomber Command wished to, could have been a disaster for the defence of the British Isles, leaving them literally defenceless in the face of the Luftwaffe. [10] Both the USAF and Bomber Command continued throughout the war, as well the interwar period, to seriously miscalculate both the destructive capabilities and accuracy of strategic bombing. Technology had not solved the problems that both Douhet and Mitchell had overlooked in their theories, which failed to seriously take into account weather conditions, inaccurate targeting of enemy targets, as well as being able to ascertain which type of industrial targets would cause the most damage to the enemy’s war making capabilities. Air power theory also seriously overestimated the ease to which Bombers could make their targets without being shot down. Even after Bombers were given fighter escorts, the losses to Bomber crews were horrific. â€Å"The night bombing offensive against German cities and transportation targets between 3 September 1943 and 2 September 1944 cost the command 17,479 flying personnel killed in action or dead of wounds†[11] When considering the harm inflicted by air power theories, undoubtedly we cannot ignore the huge loss of civilian life lost in strategic bombing raids, committed by German, British and American Bomber crews against civilian targets during the Second World War. It is estimated that more German civilians were killed by allied bombing, than the combined casualty rate of British servicemen during the war, a staggering 543,000 dead.[12] At the heart of this bombing campaign against civilians was one of the most important aspects of air power theory. The theory that a targeted bombing campaign designed to kill civilians and spread terror amongst a population that would then force its Government to capitulate. The theory was fatally flawed against a totalitarian regime where citizens knew that talk of surrender was likely to get one shot. The campaign undoubtedly affected German civilian morale, yet unlike the targeted bombing against industrial infrastructure it did not significantly affec t the Nazi war making capabilities nor convince them to consider surrender whilst Hitler was in power. [13] Despite many aspects of air power theory being flawed and causing what many consider a waste of lives and resources; I believe that the broad application of air power theory by both the British and the Americans played a serious impact in their final victory over the axis powers. Both Douhet and Mitchell believed that in order to maximise the potential of air power, a nation’s air force must be independent of both the army and navy. Williams in particular promoted the idea of a centralised, independent air command for all types of air power, equal in importance and as independent as the army and navy. Despite the near legendary status of the Luftwaffe, it was primarily meant and used as a support for the army, both in the interwar period and throughout the Second World War. The Germans had a limited air strategy, the Luftwaffe lacked complete independence and was not always given the same amount of resources as the army and navy. The British and the Americans both before and during the War placed a huge emphasis on a general air power strategy, giving the RAF and the USAF operational independence to formulate an independent strategy and the huge amount of investment, personnel and resources necessary to carry out that strategy successfully. [14] The comprehensive general air strategy that Britain possessed during the Battle of Britain, with equal emphasis on offence and defence, allowed it to resist the strategically limited Luftwaffe which from the beginning lacked the scientific air power knowledge of the better supported, more independent, RAF. When the allies went on the offensive, gaining air superiority over Europe was vital in both protecting allied land forces and speeding up the advance by inflicting serious damage on German forces of any kind. Once Germany lost control of the skies they were forced back onto the defensive, unable to effectively counter attack without sufficient air cover and with in adequate defence against air power. Although we have previously criticised the civilian bombing of German cities, strategic bombing of German industrial targets undoubtedly slowed down their ability to rebuild their forces and severely hampered the Nazi war economy. [15]Although enthusiastic advocates of air power, by not following through with the main principles of air power theory, the German war machine found itself at a distinct disadvantage against the Western allies. Once USA and Britain had gained domination of the skies, as Douhet and Mitchell had insisted was vital, it was never in doubt that the defeat of Nazi Germany was inevitable. â€Å"The influence of air power on the ability of one nation to impress its will on another in armed contest will be decisive.†[16] During the final stages of the War in the Pacific, the USAF demonstrated that one of Douhet’s most controversial theories, the use of strategic bombing to target not only military and industrial infrastructure but also civilians, could effectively bring a war to an end without the need for military conquest on land. Although the atomic bombs dropped on Hiroshima and Nagasaki were credited for ending the war, the conventional heavy bombing of Japan actually inflicted more casualties on Japanese civilians, and played a greater part in destroying Japan’s war making capabilities.[17] Undoubtedly the effect of heavy bombing and dropping of the atomic bombs was the single most important factor in forcing political pressure inside Japan to convince the leadership that surrender was the only option, Japan could simply not continue to fight the war.[18] The atomic bombs were the only time that the Douhet and Williams theories of the destructive potential of a short, decisive ove rwhelming bombing raid that could bring an enemy to its knees proved accurate. For many academics and observers, the strategic bombing of Japan is still considered one of the greatest crimes of the Second World War. Despite the awful suffering it caused however, I would argue that it ultimately did more good than harm, preventing a military land assault on Japan that would have cost potentially the lives of hundreds of thousands of American Soldiers and millions of Japanese citizens. Even without an invasion, conventional heavy bombing would have soon equalled then surpassed the amount killed in Nagasaki and Hiroshima in a relatively short space of time, so devastating was its effectiveness. The unconditional surrender was without doubt the best thing for both Japan and America, and it might never have happened if the atomic bombs had not been dropped. In conclusion then, I believe that ultimately, for the allies, the adoption of the broader aspects of air power theory was a positive thing. Many of what Douhet and Williams said about air power did not come true in the Second World War. It did not replace armies and navies as the pre-eminent factor in warfare. It did not lead to wars being settled in a matter of days with a short, destructive bombing campaign and their predictions of the destructive capabilities and accuracy of conventional strategic bombing, with the possible exception of Japan, were to prove ludicrously optimistic. Undoubtedly however, by adopting Mitchell’s theory of creating a centralised, independent air force that was given the necessary resources to achieve its strategic goals, the United States and Britain had a massive advantage over Nazi Germany’s more limited air strategy. This advantage allowed them to eventually gain air dominance, put the German forces on the back foot and never allow them to re-gain the initiative. Strategic bombing, although causing huge civilian casualties in both Germany and Japan, played a crucial role in crippling the German war machine, and the most important part in forcing an unconditional Japanese surrender. It is for these reasons that I believe that air power theory was overall, a positive and important body of work. Bibliography Collier, Basil – â€Å"A History of Air Power† – Wilmer Brothers (1974) DeSeversky, Alexander – â€Å"Victory Through Air Power† – New York, Simon and Schuster, (1942) Douhet, Giulio – â€Å"The Command of the Air†. – Faber and Faber (1927) Hurley, Alfred – Billy Mitchell, Crusader for Air Power – Bloomington IN: Indiana University Press, (1964). Lee, Asher – â€Å"Goering – Air Leader† Duckworth (1972) MacIsaac, David – â€Å"Voices from the central blue: The Air Power Theorists† In Paret, Peter â€Å"Makers of Modern Strategy- From Machiavelli to the Nuclear Age†. – Clarendon Press – Oxford (1986) Mitchell, Billy – Winged Defence – Dover Publications (1989) Murray, Williamson – â€Å"Strategic Bombing: The British, American and German experiences. In Murray, Williamson â€Å"Military Innovation in the Interwar Period.† Cambridge University Press (1998) Overy, R.J. – â€Å"The Air War 1939 – 1945† – Europa Publications Limited (1980) Warner, Edward – â€Å"Douhet, Mitchell, Seversky: Theories of Air Warfare† in â€Å"Makers of Modern Strategy† Princeton University Press (1952) 1 Footnotes [1] Douhet, G – â€Å" (1927) [2] Mitchell, B – (1989) [3] Douhet (ibid) p.199 [4] Douhet (ibid) p.157 [5] Mitchell, (ibid) [6] Warner, E – â€Å" (1952) p.630 [7] MacIsaac, D (1986) p .631 [8] Collier, B (1974) p.93 [9] Overy, R.J (1980) p203 [10] MacIsaac, D (ibid) p.633 [11] Murray, W (1998) p.99 [12] Overy, R.J. (ibid) p.207 [13] MacIsaac, D (ibid) p.637 [14] Overy, R.J. (ibid) p.204 [15] Overy, R.J. (ibid) p208 [16] Mitchell, B (ibid) p.7 [17] Overy, R.J (ibid) p.100 [18] Overy, R.J. (ibid) p.93

Why Do Some People Modify Their Bodies and What Light Does Sociology

Body modification has been prevalent in society for centuries. It is defined as "the deliberate altering of the human body for any non-medical reason, such as aesthetics, sexual enhancements, a rite of passage, and religious reasons, to display a group affiliation, to create body art, shock value, or self expression." (Wikepidia.org). Put in its simplest term body modification is defined as â€Å"deliberately alter one’s physical appearance† (St. Leone, 2012, para.2). Throughout history, people have modified their bodies to follow certain traditions or as a way of identifying with their culture. There are many reasons why people modify their bodies and these reasons are viewed differently depending on several factors. Body modifications can be carried out purely for aesthetic reasons to create the ‘perfect body’ or one in which the individual believes will make them socially accepted within their group or society. Some forms of body modification involve legitimate practices and are considered to be perfectly acceptable in certain cultures. However, other modifications are said to involve the violation of moral boundaries and overstep social boundaries. This essay will identify some of the different ways in which people modify their bodies. It will also consider the sociological concepts that are related to body modification to provide answers as to why people carry out these changes. In recent decades there has been a greater focus on body modification practices in society and the reasons why people change their bodies. Body modification involves the deliberate altering of one's physical appearance. Although body modification is often associated with piercing and tattoos there are a number of other methods and practices so... ... Sage. Ferrante, J. (2013). Seeing Sociology: An Introduction. London: Cengage Learning. Fixers. (2014). Body Modification Fix. Retrieved fromhttp://www.fixers.org.uk/news/9479-11226/body-modification-fix-on-itv.php Giddens, A. (1991). Modernity and Self-Identity: Self and Society in the Late Modern Age. Cambridge: Polity. Langman, L. (2003). Culture Identity and Hegemony: The Body in a Global Age. Current Sociolgy 51(3-4) 223-247. doi:: 10.1177/0011392103051003005 Patterson, S. (2001). Tattoos and Women. [Weblog] Retrieved from http://www.indiana.edu/~urbanflk/body_art/patterson1.html Shilling, C. (2003). The Body and Social Theory. London: Sage Publications. St. Leone, L. (2010). The Art and History of Body Modification. Lightspeed Magazine. Retrieved from http://www.lightspeedmagazine.com/nonfiction/the-art-and-history-of-body-modification/ Why Do Some People Modify Their Bodies and What Light Does Sociology Body modification has been prevalent in society for centuries. It is defined as "the deliberate altering of the human body for any non-medical reason, such as aesthetics, sexual enhancements, a rite of passage, and religious reasons, to display a group affiliation, to create body art, shock value, or self expression." (Wikepidia.org). Put in its simplest term body modification is defined as â€Å"deliberately alter one’s physical appearance† (St. Leone, 2012, para.2). Throughout history, people have modified their bodies to follow certain traditions or as a way of identifying with their culture. There are many reasons why people modify their bodies and these reasons are viewed differently depending on several factors. Body modifications can be carried out purely for aesthetic reasons to create the ‘perfect body’ or one in which the individual believes will make them socially accepted within their group or society. Some forms of body modification involve legitimate practices and are considered to be perfectly acceptable in certain cultures. However, other modifications are said to involve the violation of moral boundaries and overstep social boundaries. This essay will identify some of the different ways in which people modify their bodies. It will also consider the sociological concepts that are related to body modification to provide answers as to why people carry out these changes. In recent decades there has been a greater focus on body modification practices in society and the reasons why people change their bodies. Body modification involves the deliberate altering of one's physical appearance. Although body modification is often associated with piercing and tattoos there are a number of other methods and practices so... ... Sage. Ferrante, J. (2013). Seeing Sociology: An Introduction. London: Cengage Learning. Fixers. (2014). Body Modification Fix. Retrieved fromhttp://www.fixers.org.uk/news/9479-11226/body-modification-fix-on-itv.php Giddens, A. (1991). Modernity and Self-Identity: Self and Society in the Late Modern Age. Cambridge: Polity. Langman, L. (2003). Culture Identity and Hegemony: The Body in a Global Age. Current Sociolgy 51(3-4) 223-247. doi:: 10.1177/0011392103051003005 Patterson, S. (2001). Tattoos and Women. [Weblog] Retrieved from http://www.indiana.edu/~urbanflk/body_art/patterson1.html Shilling, C. (2003). The Body and Social Theory. London: Sage Publications. St. Leone, L. (2010). The Art and History of Body Modification. Lightspeed Magazine. Retrieved from http://www.lightspeedmagazine.com/nonfiction/the-art-and-history-of-body-modification/

Illusions and Realities in Ibsen’s Plays The Wild Duck and Ghosts Essay

Illusions and Realities in Ibsen’s Plays The Wild Duck and Ghosts In Ibsen’s The Wild Duck, illusions and reality are set into a conflict within the story of a son’s personal desire to confront idealism. Throughout much of the play, the son, Greger, argues the value of truth with the reluctant Dr. Relling. Relling insists on the importance of illusions, but fails to discourage Greger’s intentions and a play that begins as a comedy quickly turns into a tragedy because of these conflicts. At the heart of the illusions in this play are the ways that people assume many roles in a family, impersonating multiple ideals as ways for managing their relationships. This theme of impersonation is also developed in Ibsen’s Ghosts, where family relations are slowly undone as the illusions and deceptions are stripped away. In both plays, deceptions are strategic and designed to protect the children from the pains and struggles of their families’ histories. Ultimately, in these plays, families are held together by illus ions, yet torn apart by truths that have been concealed to protect the children. In The Wild Duck, as Relling continues to discourage Greger from revealing damaging truths about family secrets, Relling insists, "If you take away make-believe from the average man, you take away happiness as well" (Ibsen, 294). Relling is referring to the ways the Ekdal family is structured on particular deceptions; however, these are designed to protect the innocent as well as the guilty. Hedvig, the fourteen year old daughter, represents one of the innocents, and Greger’s father, Old Werle, represents a part of the guilty side. The key to these dualisms of false and truth, innocent and guilty, illusion and reality, lies in... ... necessary illusion. Both The Wild Duck, and Ghosts are tragedies that involve what might be understood as â€Å"the sins of the fathers;† however, Ibsen seems to suggest that some truths are better maintained as illusions. In both plays, the truth destroys the lives of those who have been protected from the past and in both cases the past involves relationships that have indirect consequences on the children’s understandings of their lives. In the end, whether it is right or wrong to maintain the illusions is not as significant as the question of who has the right to determine what is real, and what is true for others. Works Cited Works CitedWorks Cited Henrik Ibsen, â€Å"The Wild Duck,† Four Great Plays by Henrik Ibsen, NY: Bantam Books. Henrik Ibsen, â€Å"Ghosts,† Playreader’s Repertory, M.R. White and F. Whiting, Eds., London: Foresom and Company.

How E.E. Cummings uses form in his poems Essay

Form is an integral part of poetry. The form used by E. E. Cummings is quite unique, and is different in each of his poems. His poems, â€Å"nobody loses all the time,† â€Å"pity this busy monster,manunkind,† and â€Å"r-p-o-p-h-e-s-s-a-g-r† illustrate this fact. The poem, â€Å"nobody loses all the time† is a good representation of Cummings’ work, written in no traditional form. It is 37 lines long, divided into six stanzas of six lines each, and one line standing alone at the end. This poem is unique in that it does not contain any punctuation other than apostrophes and parentheses. Cummings does not follow the traditional practice of capitalizing the first word of each line, either. In fact, the capitalization in this poem is quite unusual. Cummings does not have sentences, since there is no punctuation, so almost all of the words are written in lower-case. He does not even capitalize the word ‘I.’ He capitalizes only the proper nouns â€Å"Uncle Sol,† â€Å"Victor Victrola,† â€Å"Missouri† and â€Å"McCann,† as well as the words in line five, â€Å"He Was a Diver on Xmas Eve like Hell Itself.† Written in open form, this poem has a very conversational tone. The lines vary in length, showing no pattern, and there is no consistent meter. The number of accents and syllables per line varies throughout the poem as well, and all of this poem’s lines are enjambed except the last. Another interesting characteristic of this poem is that it contains no clear caesurae, or pauses within a line, as it lacks punctuation. The reader can only estimate where caesurae should be. Finally, the poem has no rhyme scheme, or rhyme of any kind. These characteristics all aid in giving this poem its conversational tone, and makes it very different from his poem, â€Å"pity this busy monster,manunkind.† Unlike the previous poem, â€Å"pity this busy monster,manunkind† is written in a very specific form. It is fourteen lines long, and written in blank verse– iambic pentameter with no end rhyme. This particular poem has no internal rhyme in it, either. Like others written in blank verse, this poem contains what are called verse paragraphs. These are stanzas containing varying numbers of lines. In this poem, there are seven of these verse paragraphs, with one, two, three, two, one, three, and two lines, respectively. Cummings does manage to stray slightly away from the restrictions of iambic  pentameter by using metrical substitution. Throughout the poem, a handful of trochees, as well as pyrrhics, can be found. In another digression from tradition, this poem does not have capitalization at the beginning of each line, only at the beginning of each sentence. On a similar note, only two of the poem’s lines–two and fourteen–are end-stopped. This makes for many other pauses, found within the lines of the poem. Caesurae are present in lines one, two, six, eight, nine, ten, twelve, thirteen, and fourteen. Overall, for E. E. Cummings, this poem is very structured–unlike some others he has written. The poem â€Å"r-p-o-p-h-e-s-s-a-g-r† is unique, to say the least. Seen written on a piece of paper, this poem looks like a hand in a scrabble game. Comparing this poem to most other poetry is like comparing a Pablo Picasso painting to a Leonardo da Vinci. This poem is in no way written in any traditional form. It is composed of fifteen lines, and has only one stanza. The fifteen lines of this poem are indented in eight different ways, with no apparent pattern of indentation. Spacing between ‘words’ within the lines also varies throughout the poem. Those words, are barely decipherable at first glance, and with seemingly haphazard placement of punctuation and use of capitalization, this poem can be easily mistaken for a meaningless jumble of characters. It has no meter and it has no rhyme. One might say that this poem must not be a poem at all, but through careful scrutiny, a reader can see that this jumble of letters and symbols does, in fact say something. This poem revolves around the letters in its title: r, p, o, p, h, e, s, s, a, g and r. These letters are seen together four times throughout the poem, only arranged in different orders and with different capitalization. By the last line of the poem, and the fourth time the letters appear, they spell the word grasshopper. The third time the letters appear, they are set up so that every other letter is capitalized, with the lower-case letters being the first six of the word, and the capitals being the last five (â€Å"gRrEaPsPhOs†). The second time the letters appear, they are written as â€Å"PPEGORHRASS,† not significantly altered from the original â€Å"r-p-o-p-h-e-s-s-a-g-r.† The other words of the poem are a puzzle as well. Only the words ‘who’ and ‘to’ are written as simple as they are written here. In line three, the words ‘as,’ ‘we,’ and ‘look,’ are written as â€Å"a ) sw (e loo )k.† In line four, the words ‘up’ and ‘now’ can be drawn out of â€Å"upnowgath.† Two other words, ‘become’ and a word that Cummings himself probably invented, ‘rearrangingly,’ are intertwined as â€Å"rea(be)rran(com)gi(e)ngly† in line fourteen. Within the parentheses are fragments of one word, and outside of the parentheses are fragments of the other. All of the other words of this poem are split up between two or more lines. Altogether, there are fifteen to sixteen words in this poem, and there are a number of different conclusions that can be drawn from the form they take. One conclusion could be that the poem reads, ‘r-p-o-p-h-e-s-s-a-g-r who as we look up, now gathering into PPEGORHRASS, he leaps, arriving at gRrEaPsPhOs, to rearrangingly become grasshopper.’ Another conclusion could be that E. E. Cummings used form in a way that only he could ever duplicate. Form, in many different varieties, is found in all poetry. E. E. Cummings poetry, though often atypical, and sometimes downright peculiar, is a perfect example of that.