Uncertainty Reduction Theory Annotated Bibliography

Theory & Rhetoric Annotated Bibliography Uncertainty Reduction Theory 1). Witt, P. , & Behnke, R. (2006). Anticipatory Speech Anxiety as a Function of Public Speaking Assignment Type. Communication Education, 55(2), 167-177. doi:10. 1080/03634520600566074. * Research Questions: -Why does public speaking generate anticipatory anxiety? -Is public speaking anxiety dependent on assignment type? -How can anticipatory public speaking anxiety be controlled? Key Terms: Public Speaking, Speech Anxiety, State Anxiety, Trait Anxiety, Assignment Type * Thesis: Most individuals who enroll in communication courses do so in order to improve their presentational skills and to increase the enjoyment that they derive from their communication performances. * Theoretical Perspective: -Uncertainty Reduction Theory -Interpretive * Case Studies: -185 undergrads in entry level communication performance course -171 undergrads in entry level communication performance course * Implications: Therapeutic Intervention, Pedagogical Application * Future Research Questions: Can anticipatory public speaking anxiety not only be controlled but eliminated? -Is there any method that can help change trait anxiety as easily as state anxiety? -How can a better understanding of trait anxiety help ease anticipatory anxiety? 2). Pratt, L. , & Wiseman, R. (1999). Interrogative strategies and information exchange in computer-mediated communication.Communication Quarterly, 47(1), 46-66. Retrieved from Academic Search Complete database. * Research Questions: -Is there a difference between face-to-face communication and computer mediated communication? How does age coincide with computer mediated communication? -Are different styles of computer mediated communication dependent on geographical location? * Key Terms: Uncertainty Reduction, Asynchronous Communication, Interrogative Strategies, Question Typologies, Content Analysis * Thesis: Results suggest that the interrogative strategies we engage in to achieve interpersonal connectedness are sometimes different in computer-mediated communication (CMC) and a new standard for transacting relational message exchange may be emerging. * Theoretical Perspective: -Interpretive -Social Exchange Theory* Case Studies: 200 â€Å"epals† selected for content analysis of their emails to each other -316 messages analyzed between 10 pairs of â€Å"epals† * Implications: -People react differently to emails because they lack the requirement for an immediate response. -The shorter the time between a sent and read email will increase the chance of response. * Future Research Questions: -Why do â€Å"epals† want to know about others attitudes and opinions? -Is the medium redefining the type of message we send? – Is the quality of selective message construction found in asynchronous e-mail (Walther, 1996a) producing a new standard for interpersonal connectedness? ). Goldsmith, D. (2001). A Normative Approach to the Stu dy of Uncertainty and Communication. Journal of Communication, 51(3), 514. Retrieved from Academic Search Complete database. * Research Questions: -How can uncertainty reduction theory be applied outside of stranger to stranger interactions? -How do different communities treat uncertainty in communication? -What are the different levels of uncertainty in communication?* Key Terms: Frequency of Communication Behaviors, Level of Uncertainty, Level of Relational Qualities * Thesis: A normative pproach entails a shift in focus from measuring level of uncertainty to examining multiple and potentially conflicting meanings of uncertainty, a shift from measuring communication behaviors to evaluating communication practices, and a shift from predicting what people will do to predicting and explaining the effectiveness and appropriateness of what they do in response of uncertainty. * Theoretical Perspective: -Interpretive -Critical * Case Studies: -Puerto Rican Community -Western Apache Commu nity -Malagasy Community -White, College Educated North Americans* Implications: Uncertainty is a fundamental human experience. -Different communities react to communication uncertainty differently. -Uncertainty is not static there are many forms of uncertainty that need to be taken into consideration differently. * Future Research Questions: -What can uncertainty in other cultures teach us about our own uncertainty? -How has uncertainty in communication changed over time? -How does the frequency of behaviors affect the overall uncertainty of a relationship? 4). Maguire, K. (2007). â€Å"Will It Ever End? â€Å": A (Re)examination of Uncertainty in College Student Long-Distance Dating Relationships.Communication Quarterly, 55(4), 415-432. doi:10. 1080/01463370701658002. * Research Questions: -How does a long distance relationship affect a person’s daily life? -What kinds of uncertainty do long distance relationships lead to? -How does an individual in a long distance relati onship cope with stress compared to someone in a close relationship? * Key Terms: Coping, Distress, Long-Distance Relationships, Relationship Satisfaction, Uncertainty * Thesis: Research in the area of stress and coping suggests that a close relationship with a romantic partner helps individuals cope with stress * Theoretical Perspective: Uncertainty Reduction Theory -Uncertainty Management Theory -Interpretive* Case Studies: -Undergrads from a South-Central college -Norton’s Quality Marriage Index * Implications: -Any relationship where the partner is too far to visit every day is considered a long distance relationship. – Close relationships are more successful than long distance relationships. -Uncertainty is not inherently problematic in long distance relationships * Future Research Questions: -What can be done to ensure success in a long distance relationship in terms of uncertainty? Why is the visual/physical aspect of a relationship over power the uncertainty fo und in long distance relationships? -How is relational uncertainty not inherently an unwanted state? 5). Brumfield, E. (2008). Using Online Tutorials to Reduce Uncertainty in Information Seeking Behavior. Journal of Library Administration, 48(3/4), 365-377. Retrieved from Academic Search Complete database. * Research Questions: -How does asynchronous delivery differ from synchronous delivery? -How does the length of the tutorial affect its overall effectiveness?How does the design of the tutorial affect its quantity of use? Key Terms: Distance Learners, Distance Education, Information Seeking Behavior, Online Tutorials * Thesis: Information seeking behavior results from a determination of an information need and the realization that there is insufficient knowledge to address that need.. * Theoretical Perspective: -Uncertainty Reduction Theory -Interpretive * Case Studies: -Wilson, Ford Research -A&M University -Stephen F. Austin University * Implications: -The overall effectiven ess of tutorials is dependent on a large number of variables such as visual appeal. –The students skill and attitude play a big role it a tutorials effectiveness. Future Research Questions: -What can be done to help improve student’s attitudes towards tutorials? -How has the introduction of these tutorials help reduce uncertainty in personal relationships? -Can these findings be applied to cultures other than our own? 6). Rubin, R. , & McHugh, M. (1987). Development of Parasocial Interaction Relationships. Journal of Broadcasting & Electronic Media, 31(3), 279-292. Retrieved from Academic Search Complete database. * Research Questions: -How do viewers become attached to specific television characters? Are there any universal qualities that attract viewers to characters? -How can uncertainty reduction and uses and gratification theory help explain these character to viewer relations?* Key Terms: Social Interaction, Uncertainty, Interpersonal Communication, Telev ision Characters * Thesis: This investigation explored the possibility of a parallel pattern of relationship development with media characters, applying principles from both uses and gratifications and uncertainty reduction theories to understand further the development of parasocial interaction relationships. Theoretical Perspective: -Interpretive -Critical -Uses and Gratification Theory * Case Studies: – Parasocial Interaction Scale Survey Study -The 15 Item Scale Study * Implications: -Social attraction is key in developing parasocial interaction relationships. -Attraction occurs through a great level of exposure to a character. -Relationship importance is a construct that differs from attraction. * Future Research Questions: –How can the findings of these studies be applied to network television? How does the uncertainty reduction theory apply to non face-to-face relationships such as in a television character? – How can the results of these studies relate t o the concept of market research? 7). Theiss, J. , & Solomon, D. (2008). Parsing the Mechanisms that Increase Relational Intimacy: The Effects of Uncertainty Amount, Open Communication About Uncertainty, and the Reduction of Uncertainty. Human Communication Research, 34(4), 625-654. doi:10. 1111/j. 1468-2958. 2008. 00335. x. * Research Questions: Why are there 3 competing mechanisms that affect the amount of intimacy in romantic relationships? -Which of the 3 mechanisms is the most effective in romantic relationships? -Are there any variables that interrupt the effectiveness of the 3 mechanisms? * Key Terms: Uncertainty, Intimacy, Interpersonal Relations,* Thesis: Uncertainty and its management hold a prominent place in the study of interpersonal communication. * Theoretical Perspective: -Interpretive -Critical -Uncertainty Reduction Theory * Case Studies: -Longitudinal Study Distinguishing Uncertainty Implications: -There is something inherently rewarding about the process in r educing uncertainty. -Openness of communication about uncertainty has a positive impact on perceptions of intimacy. -The uncertainty reduction process is perceived as rewarding in close relationships. * Future Research Questions: -How can the findings of this study help intimate relationships in turmoil? -Are there any other factors that affect intimate relationships outside of the 3 mechanisms discussed in this study? -Are there any instances contrary to this study?

The Role of Perception in Corporate Decision Making

Here is an office scenario wherein two senior executives are observing an employee who is a potential candidate for promotion:   At certain times, they both see the said employee just sitting on his chair, lounging, even minutes before the end of office hours.   Often chancing upon the employee during his idle time, Senior Executive A may see this as laziness on the employee’s part.   Senior Executive B views the situation, having kept track of prompt and quality reports done by the employee, as the employee being a fast worker who gets the job easily done and right, not as somebody who is just loafing around. This is the fundamental nature of perception.   Senior Executive B saw the employee’s circumstances in another approach from that of Senior Executive A’s.   Even though they both examined the same situation, each one had a different view on it.   The outcome of this observation shall depend upon how the executives had perceived the candidate’s performance.   This is an illustration of how perception plays a part in making decisions on a work setting.   The employee’s likelihood of getting promoted relies on others’ diverse insights. Perception Perception has a role when it comes to decision making on many business situations.   It can impact an organization’s behavior.   Also depending on every person’s background, traits, knowledge, and many other factors, perception can also shape ethical or moral decisions. Definition What is perception?   â€Å"Perception is the process we use to make sense out of our environment by selecting, organizing, and interpreting information from the environment† (Daft, 1997, p. 786). People have varied outlooks on a particular situation in his/her own way.   â€Å"Perception depends not only on the physical stimuli but also on the stimuli’s relation to the surrounding field and on conditions within the individual.   The key word in the definition of perception is individual† (Kotler, 2000, p.173). Impact on Organizational Behavior Because of the different perceptions each individual has on a working atmosphere, it is a necessity for managers to have a profound knowledge of anticipating diversity between the different levels within their organization.   For example:   If a manager only sees his/her staff as a means to an end, just a functioning machine in getting the job done, like without incentives or further trainings, etc., with this kind of perception that the employees may get, how would the employees react to it? There might be a number of them who would not think of it as an issue because they themselves may also only see their work as a means itself to meeting their own needs, financially speaking of earning a salary.   For some, they would like to be recognized and given value as employees, being humanely treated and could perceive their employers as insensitive to both their professional growth and personal welfare. In this case, when this type of perception prevails, it could possibly lead to a chain reaction amongst the employees.   A possible impact could be that the organizational behavior (employees’ performance) is not being concerned about their company’s productivity since the management itself does not look after their issues. How a person perceives others can greatly or minimally impact an organization either in a negative or positive way because people would act in response to it. Another citable circumstance in an office setting with regards to perception and its impact on behavior is rumors.   For instance, there is a new employee who was highly  recommended by an officer of the company.   Some may right away see this as special treatment being given on the said employee.   While others actually get facts and can see  exceptional work being done on the new employee’s part.   Yet, with a number of gossip mongers existing on a work environment, they are going to talk about misleading details.   Now with those who may be unaware of what is actually going on, just basing the events on hearsay, they might perhaps bear some resentment on management or even give it a shot themselves on apple polishing. â€Å"Individual perceptual awareness varies widely.   Recognizing the difference between what is perceived and what is real is a key element in diagnosing a situation† (Daft, 1997,p. 787). Using Perceptive ‘Shortcuts’ Every now and then, several business matters call for immediate decisions.   Some may resort to using perceptive ‘shortcuts’ when judging others.   Positive effects may include a decision being done without delay and can move on to attend to other business matters at hand.   This could result to increase in productivity.   Negative effects consist of hastiness in judgment.   Without studying all the facts and details, one fails to take into account everything that needs to be considered which may be leaving out a factor that could have brought out a different turn of events. The Real World Before a decision is made in real world organizations, an issue is addressed by gathering necessary data or a proposal is prepared for a project they will undertake.   There is an open discussion in order to reach a consensus of opinion (i.e. meeting).   Advantages and disadvantages are weighed out (e.g. project to be considered, acquisition of office equipment).   Strengths and weaknesses are pointed out (e.g. hiring of an applicant, promotion  among ranks).   A good management first makes a thorough study then arrives at a more solid decision this way than in making hasty assessments. Ethical/Moral Decisions How we see things are based on several factors.   People’s views are different because each one has his/her own distinctive background.   What values and beliefs a person has can influence an ethical or moral decision he or she makes.   For example:   A sales agent who proposes to a Human Resources Head the availment of a pension plan for the company’s employees, is also suggesting a share in the commission that he would give to the HR Head when he approves the proposal. If the HR Head perception of the agent’s offer is lucrative to his own pocket and does not see it as harmful to their corporation, viewing the agent’s approach as a normal sales tactic, then this shapes the moral decision he is about to make.   Clearly, this is against business ethics, undisclosed behind-the-scenes negotiations.   The employees, who are not aware of what had transpired between the sales agent and their HR Head, would naturally perceive the outlay in pension plan as a benefit for them.   Now if it was a different matter all together, with an honest HR Head who believes in hard work to earn a living, may see the sales agent as a dubious character and perhaps would choose not to deal with that agent anymore. â€Å"Perception in itself does not always lead to an accurate picture of the environment† (Daft, 1997, p. 562). References Daft, R. L. (1997).   Management.   Pennsylvania:   The Dryden Press. Kotler, P. (2000).   Marketing Management.   New Jersey:   Prentice-Hall, Inc.            

Monopolistic Competition Term Paper Example | Topics and Well Written Essays - 1250 words

Monopolistic Competition - Term Paper Example The paper also explains the fact that given the transition from a monopolistically competitive firm to a monopoly, what will be the changes with regard to prices and output in both of these market structures. And finally the paper explains given the transition from a monopolistically competitive firm to a monopoly, what will be the changes with regard to prices and output in both of these market structures. Benefits to the stakeholders: The price, output level, and the quality of the monopolistic competitor are resolved through â€Å"maximizing the difference between its revenue and its cost, where cost is measured exclusive of the rent on its product-specialized inputs† (Carson, 2006, p. 433). Such a business organization must have definite inputs that are specific to its definite product—as product differentiation is or else compatible with the perfectly competitive market—and the exclusivity of these inputs permits those producers to gain positive rent, yet in the long-term equilibrium. The addition of rent in the cost provides increment to the â€Å"traditional Chamberlinian solution†, where (â€Å"rent inclusive†) average cost lays tangent to the level of demand and thus downward-sloping. However, if rent is not included, average cost can be constant or even it can be upward-sloping at the equilibrium, and also, monopolistic competition does not necessarily induce ‘excess capacity or to production facilities that are too small’ (Carson, 2006, p. 433). In this context, the company, called ‘Wonks’ will not produce the monopolistically competitive level of output which is largely based on the competitive market conditions. The firm will produce the level of output which is lower than the perfectly competitive amount of output; however, it will produce an output even lower than the monopolistically competitive level of output. Hence, the amount of price charged by the firm for potato chips will be mu ch higher than the two competitive market structures. Hence, the amount of profits will be the highest in case of the production and sale of potato chips. Hence, this would benefits some of the stakeholders associated with the business organizations; however, this outcome will worsen the optimal level of benefit of some other stakeholders. The government of the country would benefit in the sense that the increased level of profit of the business organization will increase the amount of corporate profit tax earned by the business organization. Hence, the government would benefit in terms of the greater revenue earned. However, the government would loose in respect to the fact that some people, who are unable to purchase the product at higher prices, would either reduce their volume of purchase of the product, or stop purchasing the product (Boone and Kurtz, 2011, p. 98). The other business organizations also face loss or profit from the monopolization of the potato chips company. In the situation, where the original company has significant level of reputation as the economic agent of selling most popular potato chips, the market share of the new company would like to be very high. In this situation, the other business organization would suffer in terms of reduced market share which will reduce the amount of pro

Risk Factors and Challenges in the Technology Industry Essay

Risk Factors and Challenges in the Technology Industry - Essay Example Moreover, business enterprises are very concerned about "outsider" company having access to the sensitive commercial information. Escalating complexity of the products and solutions: It is hard to test all the scenarios for the applications involving extremely lengthy and complex code, which sometimes leads to "bugs" and malfunctioning. Growth of in-house IT: Many non-computer firms joined the industry by adding divisions or by acquiring computer services companies. Banks, publishers, airlines, and telecommunications companies were among those whose information technology divisions were involved in this industry (SIC Computer Related Services n/p). Dependability on the readiness of the customers to engage in electronic interactions or networking: Value of network grows in line with the number of participants. If the market does not successfully adopt the new technology on a wide scale, it will not exist long. The wave of year-2000-related new equipment purchases that took place at the end of the 1990s, as well as the availability of quality used equipment from bankrupt Internet companies in the early 2000s, had a negative impact on the corporate market for new electronic devices and computers. (Electronic Computers n/p) From 1998 to 2000, reported IDC, ave... 2. Communications and Networking Changes in the industry-related regulations: For example, adoption of the Telecommunications Reform Act of 1996 greatly influenced operations of the telecommunication industry players. Standardization and adoption of new protocols. Emergence of many competing formats, offering lower costs and improved services to the customers: for example emergence of PCS systems as strong competition to wireless phone systems. Integration of different services (e.g. mobile phones with PDA -functions, text and multimedia messages services, WAP-internet access). Transformation of the industry structure: mergers and acquisitions in the industry (for example, recently approved acquisition of Skype VoIP-operator by the EBay Corporation). Reaching saturation in the developed-countries markets and challenges of global expansion. Dependability on the readiness of the customers to engage in electronic interactions or networking: Value of network grows in line with the number of participants. If the market does not successfully adopt the new technology on a wide scale, it will not exist long. 3. Electronics and Computer Hardware: Temporary slowdown of early 2000s in the technology spending in both corporate and private sectors caused by economic conditions and changes in the consumer behavior: The wave of year-2000-related new equipment purchases that took place at the end of the 1990s, as well as the availability of quality used equipment from bankrupt Internet companies in the early 2000s, had a negative impact on the corporate market for new electronic devices and computers. (Electronic Computers n/p) High R&D costs and consequently high break-even volumes. Increasing competition of low-cost Asian electronic

Realizing My Potentials Essay Example | Topics and Well Written Essays - 1250 words

Realizing My Potentials - Essay Example Belonging to a place which is the hub of all activities such as culture, entertainment, sports, media, trade, and arts have influenced my personality in many ways. The purity of my land has affected my upbringing and has bought a positive impact on my personality. Miami Beach is a center of attraction for many has developed great affinity in me for beaches and has also helped in to build up my love for water sports. Being the youngest in my family with two elder brothers, I have always been pampered and that has also made me a real family oriented person. For me, my utmost priority is my family. My family takes its roots from the African Americans. Apart from that, I am personally a sports lover. Football has influenced me since childhood and has been an essential part of my life since then. Football has been my passion and I have played football for my school that is Hialeah High School. I have also represented the University of Central Michigan in football at various events bringin g laurels for them. The love for sports and other athletics has shaped my personality. I believe that I can compete in all areas of life irrespective of what obstacles and hurdles come my way. I am very determined and I have a firm belief in my capabilities. Education has always been the priority of my family. Belonging to an average middle-class sector of the society, the value of education has always been given in my family. Currently, I am enrolled in school to study criminology. The reason behind choosing criminology was because of my interest in crime and what causes crime, its nature and to what extent it can be affected. This inquisition made me opt for this subject so that I could study in depth the behavior of crime on individuals, as well as the society. Concepts The first and the foremost thing that has developed within me is conscientiousness. Conscientiousness deals with the "Common features of this dimension include high levels of thoughtfulness, with good impulse cont rol and goal-directed behaviors." (Coon, 394) This apparently means that I am very organized and I take care of the minutest details in everything I do. This trait has been really controversial for me as at times as I do not let go of myself and my feelings resulting in being quite reserved and losing people who make difference in my life because of lack of expression of my feelings. Anxiety is also something I possess. Nervousness and anxiety go hand in hand. Despite this fact, I have always been really confident, active and determined. Public speaking has always made me nervous. I find it really difficult to face masses of people and, therefore, I undergo issues like "headaches, stomachaches, breathlessness, hyperventilation, blushing, trembling, increase heart rate, muscle tension, and sweating." (Kearney, 103). These are the symptoms of nervousness mentioned by Kearney in his book. Because of the anxiety and nervousness, I tend to show all the symptoms I previously mentioned whi ch drain my confidence and leave me numb when I have to face the public. Another issue which is affecting my personality is my behavior in public. Socially, I do not tend to mingle with people that easily. Since I get reserved and show signs of nervousness, this has made me a bit quiet when it comes to dealing with people.  

Forensic Accounting class discussion Assignment Example | Topics and Well Written Essays - 250 words

Forensic Accounting class discussion - Assignment Example Software applications use a combination of functions, some of which include sorting, joining files, as well as record selection and extraction among others. Sorting entails arrangement of the data in some order, which can be regarded as meaningful; this may include the customer number, date, name, and amount. Joining files entails the gathering of various parts of different files of data. Record selection and extraction entails making a request for the computer to find occurrences in a certain field, which matches a criterion that interests the investigator (Kranacher, Riley & Wells, 2011). Skimming involves the stealing of cash from an entity before it enters into the accounting system. Sales skimming is referred as an â€Å"off-book† fraud since the cash is stolen from the victim before its recording in books of the victim (Kranacher, Riley & Wells, 2011). Fraudsters may use various techniques with the sole aim of concealing a receivables scheming scheme. One of the techniques used to conceal this form of fraud includes the creation of fake accounts. The write-off of inventories is also another method used to conceal a receivables scheming scheme (Kranacher, Riley & Wells, 2011). The difference between skimming and cash larceny is that skimming entails the stealing of cash before the recording of the cash. As a result, it becomes one of the difficult frauds to detect. On the other hand, cash larceny involves the theft of cash by employees after its recording in the books of the entity. As such, larceny is can easily be detected than skimming (Kranacher, Riley & Wells,

Embracing the Concept of Democracy Essay Example | Topics and Well Written Essays - 1250 words - 1

Embracing the Concept of Democracy - Essay Example The intent of this paper is to lucidly determine these changes that were deemed to embrace the concept of democracy, and whether they actually achieved their intended purpose as expressed by the response of the people. An incident that can be viewed as the genesis of the Russian transformation is the defeat in the Crimean War. It resulted in the sought of scenarios where individuals reassess their own status so as to forge a route forward. Russia has expected to win the war with ease seeing that it had the largest army in Europe but overlooked the morale of the soldiers to fight. The defeat opened channels for reassessments, which were mainly carried out in the 1860s and came to be commonly referred to as the Great Reforms. Realizing the underbelly of the army and the possibility of being attacked in the future, Alexander II initiated a number of reforms.1 One aspect to Russia that stood up in the Crimean War as compared to its enemies was that the country still practised serfdom. The enemies disliked this fact about Russia and Alexander II saw this as an opportunity to commence the reforms that would transform Russia. Ending selfdom was a move supported by the liberal intellectual in the country, but fiercely contested by the landowners. In 1861, Alexander II pushed forward to end the practice, and the country was one of the last to do so in the European continent. â€Å"The new democracy,† as Pobedonostsev refers to it, is nonetheless questionable as it still left so many in suffering whilst it was supposed to do the opposite. 2 As a result of the liberation of the peasants, there was a surge in the number of citizens in the local governments. The peasants now had a voice that was recognized by the government, and this required it to be embedded into the government itself. Initially, the local government was run by the sole representation of the landlords who were viewed in turn as representatives of their serfs. A new form of government referred to as the zemstvos were put into place, it required fair elections to be conducted. Pobedonostsev cites this form of government as ’a fatal error, and one of the most remarkable in the history of mankind.  Ã‚  

Edit Submission Essay Example | Topics and Well Written Essays - 500 words

Edit Submission - Essay Example e common in the interaction with the political figures has been addressed by the numerous political forums that are available on the social media and networks. The grievances and complaints of the citizens of any country can be expressed to the officials in a far more reliable and fast manner than before. The emergence of any news on the web is analogous to fire in a dry forest in the modern times. Any act of misconduct by the government cannot be hidden since people have acquired greater power to voice their opinions with the advent of the internet. The recent uprising in the Arab countries, such as Egypt, Libya, could not have been arranged with such unity and effectiveness if the social media and networks had not been available. The risings were led by no apparent leaders but at the spur of collective thinking and ideas. The dictatorial nature of the leadership in those countries always forbade any expression of negativity towards the rulers; however the accumulation of agitation among the masses on the web transformed into a historical revolution that freed the people from years of dictatorship. The citizens are more aware about the prevailing political activities which make them capable of possessing a strong opinion about everything in their societies. These opinions are known to gain voice on the political forums which can prove to influence the core objectives of the political parties. Democratic parties tend to rely on such internet communication even more than dictatorial rule. Specifically, the communication and campaigning is noticed to escalate in the times of the elections. An apparent benefit of political communication over the internet is that the political parties can evaluate the responses and comments of their voters and strategize their actions accordingly. This proves to become an on-going survey for the political parties since the success or failure of any event or procedure can be retrieved on an immediate basis via social

How is the UK as a whole doing Essay Example | Topics and Well Written Essays - 1000 words

How is the UK as a whole doing - Essay Example Similar to this is the money or cash flow for output services, (Maher and Wise, 2005, p.85). The key economic players are administration, business trade, households, and the wider international globe. Their means of interaction with one another is explained as a transaction The national statistics office offers statistics of the economy that measure the economy of the United Kingdom in various ways. For instance, there are complete United Kingdom national and economic accounts that offer an overall economic view. The accounts sequence follows the laid out accounts if the national account systems of 1993, as well as the European Account systems of 1995. Similarly, short-term economic indicators like GDP, Index of Retail Sales, Production Index and Services Index exists. Additionally, there are some statistics offered on Payments Balance and Products and Services Trade. UK economic performance The performance of economy of UK is evaluated based on attainment of goals and targets the ec onomy. The goals may be long-term like effective development and growth of the economy, or temporary like economic stabilization in following abrupt and unpredictable factors mainly known as economic shocks. To evaluate economic performance against the above goals, economists use various economic indicators. These economic indicators estimate variables of economy, which directly or indirectly allow them to determine whether the performance of economy has enhanced or declined. Tracing such economic indicators is crucial to policy makers to allow them determine whether to intervene or if the intervention activities and plans have been successful or not. According to statistics, the first quarter GDP increase was about 0.3 percent – a yearly growth rate of about 1.2 percent, (Helpman, 2008, p.12). This was 0.6 percent increased from the previous years; these growth rates are low than the set target and 3% than the growth witnessed prior to the financial crisis. The IMF asserts t hat the 2009 advanced economies GDP - that entails the United States, Japan and popular economies of Europe – will be about 3.8% higher than in the 2007 and 2008 cycles. Although, the United Kingdom GDP has not recovered its initial 2008 level, extreme slowdowns have been witnessed in various economic sectors that make up lower than 21% output and approximately 10% of employment opportunities – services of finance, construction and gas or oil, (Steil and Victor, Nelson, 2002, p.56). Apart from the sector of finance, the services activities that the key UK economic pillars are improving, this is the reason behind increased and strong employment. The informal sector accounts for approximately a million United Kingdom’s employments in the last three years. Whereas UK does not have extensive manufacturing based that maintained its economy in both 19th and 20th centuries, it has various global and prominent manufactures – in aerospace, high engineering technol ogy and health care sectors. UK care industry attained in global record export level last year. UK manufacturing is still competitive in knowledge deployment, skills, and technology and has a competitive advantage over reduced wage; labor-intensive sectors of manufacturing that have shifted to developing economies. UK has also strong and competitive business sector services

Percy bysshe shelley Research Paper Example | Topics and Well Written Essays - 1000 words

Percy bysshe shelley - Research Paper Example The discussion becomes easy if a look at his poetic ideas is done first. Shelley is of the opinion that a poet is a moral teacher. He does not agree that a poet is merely an imitator. At the same time, he asserts that a poet is a creator, who not only creates but also provides ideas to the society, guides the people, and in a way teaches what should be done to improve one’s life. He rejects Thomas Love peacock’s remark that a poet is a â€Å"semi-barbarian†. He not only counters this negative remark about the poet but also declares that â€Å"Poets are the unacknowledged legislators of the world† (Defense). In his essay defending poetry, he explains the true role of a poet in his society and states that†Poetry turns all things to loveliness; it exalts the beauty of that which is most beautiful, and it adds beauty to that which is most deformed; it marries exultation and horror, grief and pleasure, eternity and change; it subdues to union under its li ght yoke all irreconcilable things† (Defense). Unlike Keats for whom poetry means beauty, Shelley finds poetry as a form of intellectual beauty. He treats politics, love, and nature on equal scale. He looks sometime melancholic, but his melancholy is closely related to his ideas. â€Å"Ode to West Wind† can be taken as an ideal poem to study Shelley as a poet and revolutionary. As a poem, it is very remarkable because in it the poet treats everything in nature as an instrument of melody. The poet becomes totally spellbound by the power of the wind, the cloud, the sun, the ocean, and all these in nature for him become the right subject for poetry. He is so much inspired that he prays, â€Å"Be thou, Spirit fierce, / My spirit! Be thou me, impetuous one!† (Ode). The poem deals with the regenerative power of nature. It praises how everything that is old and dead in nature is driven out to leave space for the birth of new and beautiful. In other words, it speaks abou t the likely situation in which the world has to exist with everything unwanted and decayed, if regeneration does not take place. The poet feels that this unfortunate situation is avoided in nature because of the support of the sweeping powers of west wind: â€Å"Thou, from whose unseen presence the leaves dead/ Are driven, like ghosts from an enchanter fleeing† (Ode). It is with similar spirit that the poet wants changes in the political situation in his society. However, he does not possess the sweeping powers seen in the west wind to drive out the old and conventional ideas in his society to pave the way for the new and creative ideas. That is how the poem becomes significant as an example of the poet’s political perspective. As Sydney Waterloo says, â€Å"He was a dreamer, but he never dreamed merely for the sake of dreaming; he always rushed to translate his dreams into acts† (Sydney). â€Å"Ode to the West Wind† shows how Shelley tries to translate his poetical and political dreams into reality. The poem, â€Å"Ode to the West Wind†, is in the form of a prayer. It is addressed to West Wind, and not to any particular God, as Shelley finds in the invisible power in nature what man generally finds in God. The political idea with which he was obsessed is identified with the power of the wind. Though he tried to impress his philosophical ideas upon the people through many pamphlets he found very poor response coming from the people. So he was disappointed.

The Percentage by Mass of Calcium Carbonate in Eggshells Essay Example for Free

The Percentage by Mass of Calcium Carbonate in Eggshells Essay The purpose of this experiment is to determine the percentage by mass of calcium carbonate in eggshells. Introduction To avoid the breakage of eggs before reaching market, the eggshells needs to be as strong as possible. The strength of eggshells is mainly determined by the percentage of calcium carbonate in it. In order to monitor the quality of eggshells, the following experiment has to be done to determine the percentage of calcium carbonate in eggshells. In this experiment, back titration is used. First, excess acid is reacted with the calcium carbonate in eggshells: 2HCl(aq) + CaCO3(s) CaCl2(aq) + H2O(l)+ CO2(g) Later, if we can find out the number of mole of unreacted acid, number of mole of calcium carbonate can then be found out. The number of mole of unreacted acid can be found by titration with the following reaction: HCl(aq) + NaOH(aq) H2O(l) + NaCl(aq) Percentage by mass of calcium carbonate in eggshell can then be calculated by the following formula: % by mass of CaCO3 = Requirements eggshell burette, 50 cm3, and stand pipette, 25 cm3 pipette filler methyl orange indicator M NaOH solution, standardized 1 M hydrochloric acid, standardized ethanol wash-bottle with de-ionized water mortar and pestle forceps safety spectacles 2 beakers, 100 cm3 volumetric flask, 250 cm3 filter funnel, small magnetic stirrer pH meter electronic balance Procedures 1. The attached membrane of the eggshell was removed carefully by forceps and the remaining eggshell was ground into a fine po wder with mortar and pestle. 2. 2 g of powder was weighed accurately by the difference on an electronic balance and put into a beaker on a magnetic stirrer.

Most Opposition to Abortion Relies Essay Example for Free

Most Opposition to Abortion Relies Essay A Defense of Abortion Author(s): Judith Jarvis Thomson Source: Philosophy and Public Affairs, Vol. 1, No. 1 (Autumn, 1971), pp. 47-66 Published by: Blackwell Publishing Stable URL: http://www. jstor. org/stable/2265091 Accessed: 10/01/2010 00:54 Your use of the JSTOR archive indicates your acceptance of JSTORs Terms and Conditions of Use, available at http://www. jstor. org/page/info/about/policies/terms. jsp. JSTORs Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www. jstor. org/action/showPublisher? publisherCode=black. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [emailprotected] org. Blackwell Publishing is collaborating with JSTOR to digitize, preserve and extend access to Philosophy and Public Affairs. http://www. jstor. org JUDITH JARVISTHOMSON A Defense of Abortion Most opposition to abortion relies on the premise that the fetus is a human being, a person, from the moment of conception. The premise is argued for, but, as I think, not well. Take, for example, the most common argument. We are asked to notice that the development of a human being from conception through birth into childhood is continuous; then it is said that to draw a line, to choose a point in this development and say before this point the thing is not a person, after this point it is a person is to make an arbitrary choice, a choice for which in the nature of things no good reason can be given. It is concluded that the fetus is, or anyway that we had better say it is, a person from the moment of conception. But this conclusion does not follow. Similar things might be said about the development of an acorn into an oak tree, and it does not follow that acorns are oak trees, or that we had better say they are. Arguments of this form are sometimes called slippery slope arguments-the phrase is perhaps self-explanatory-and it is dismaying that opponents of abortion rely on them so heavily and uncritically. I am inclined to agree, however, that the prospects for drawing a line in the development of the fetus look dim. I am inclined to think also that we shall probably have to agree that the fetus has already become a human person well before birth. Indeed, it comes as a surprise when one first learns how early in its life it begins to acquire human characteristics. By the tenth week, for example, it already has i. I am very much indebted to James Thomson for discussion, criticism, and many helpful suggestions. 48 Philosophy ; Public Affairs a face, arms and legs, fingers and toes; it has internal organs, and brain activity is detectable. 2 On the other hand, I think that the premise is false, that the fetus is not a person from the moment of conception. A newly fertilized ovum, a newly implanted clump of cells, is no more a person than an acorn is an oak tree. But I shall not discuss any of this. For it seems to me to be of great interest to ask what happens if, for the sake of argument, we allow the premise. How, precisely, are we supposed to get from there to the conclusion that abortion is morally impermissible? Opponents of abortion commonly spend most of their time establishing that the fetus is a person, and hardly any time explaining the step from there to the impermissibility of abortion. Perhaps they think the step too simple and obvious to require much comment. Or perhaps instead they are simply being economical in argument. Many of those who defend abortion rely on the premise that the fetus is not a person, but only a bit of tissue that will become a person at birth; and why pay out more arguments than you have to? Whatever the explanation, I suggest that the step they take is neither easy nor obvious, that it calls for closer examination than it is commonly given, and that when we do give it this closer examination we shall feel inclined to reject it. I propose, then, that we grant that the fetus is a person. from the moment of conception. How does the argument go from here? Something like this, I take it. Every person has a right to life. So the fetus has a right to life. No doubt the mother has a right to decide what shall happen in and to her body; everyone would grant that. But surely a persons right to life is stronger and more stringent than the mothers right to decide what happens in and to her body, and so outweighs it. So the fetus may not be killed; an abortion may not be performed. It sounds plausible. But now let me ask you to imagine this. You wake up in the morning and find yourself back to back in bed with an unconscious violinist. A famous unconscious violinist. He has been found to have a fatal kidney ailment, and the Society of Music Lovers 2. Daniel Callahan, Abortion: Law, Choice and Morality (New York, 1970), p. 373. This book gives a fascinating survey of the available information on abortion. The Jewish tradition is surveyed in David M. Feldman, Birth Control in Jewish Law (New York, i968), Part 5, the Catholic tradition in John T. Noonan, Jr. , An Almost Absolute Value in History, in The Morality of Abortion, ed. John T. Noonan, Jr. (Cambridge, Mass. , 1970). 49 A Defense of Abortion has canvassed all the available medical records and found that you alone have the right blood type to help. They have therefore kidnapped you, and last night the violinists circulatory system was plugged into yours, so that your kidneys can be used to extract poisons from his blood as well as your own. The director of the hospital now tells you, Look, were sorry the Society of Music Lovers did this to you-we would never have permitted it if we had known. But still, they did it, and the violinist now is plugged into you. To unplug you would be to kill him. But never mind, its only for nine months. By then he will have recovered from his ailment, and can safely be unplugged from you. Is it morally incumbent on you to accede to this situation? No doubt it would be very nice of you if you did, a great kindness. But do you have to accede to it? What if it were not nine months, but nine years? Or longer still? What if the director of the hospital says, Tough luck, I agree, but youve now got to stay in bed, with the violinist plugged into you, for the rest of your life. Because remember this. All persons have a right to life, and violinists are persons. Granted you have a right to decide what happens in and to your body, but a persons right to life outweighs your right to decide what happens in and to your body. So you cannot ever be unplugged from him. I imagine you would regard this as outrageous, which suggests that something really is wrong with that plausible-sounding argument I mentioned a moment ago. In this case, of course, you were kidnapped; you didnt volunteer for the operation that plugged the violinist into your kidneys. Can those who oppose abortion on the ground I mentioned make an exception for a pregnancy due to rape? Certainly. They can say that persons have a right to life only if they didnt come into existence because of rape; or they can say that all persons have a right to life, but that some have less of a right to life than others, in particular, that those who came into existence because of rape have less. But these statements have a rather unpleasant sound. Surely the question of whether you have a right to life at all, or how much of it you have, shouldnt turn on the question of whether or not you are the product of a rape. And in fact the people who oppose abortion on the ground I mentioned do not make this distinction, and hence do not make an exception in case of rape. 50 Philosophy ; Public Affairs Nor do they make an exception for a case in which the mother has to spend the nine months of her pregnancy in bed. They would agree that would be a great pity, and hard on the mother; but all the same, all persons have a right to ife, the fetus is a person, and so on. I suspect, in fact, that they would not make an exception for a case in which, miraculously enough, the pregnancy went on for nine years, or even the rest of the mothers life. Some wont even make an exception for a case in which continuation of the pregnancy is likely to shorten the mothers life; they regard abortion as impermissible even to save the mothers life. Such case s are nowadays very rare, and many opponents of abortion do not accept this extreme view. Moreover, in killing the child, one would be killing an innocent person, for the child has committed no crime, and is not aiming at his mothers death. And then there are a variety of ways in which this 3. The term direct in the arguments I refer to is a technical one. Roughly, what is meant by direct killing is either killing as an end in itself, or killing as a means to some end, for example, the end of saving someone elses life. See note 6, below, for an example of its use. 51 A Defense of Abortion might be continued. i) But as directly killing an innocent person is always and absolutely impermissible, an abortion may not be performed. Or, (2) as directly killing an innocent person is murder, and murder is always and absolutely impermissible, an abortion may not be performed. Because unplugging you would be directly killing an innocent violinist, and thats murder, and thats impermissible. If anything in the world is true, it is that you do not commit murder, you do not do what is impermissible, if you reach around to your back and unplug yourself from that violinist to save your life. The main focus of attention in writings on abortion has been on what a third party may or may not do in answer to a request from a woman for an abortion. This is in a way understandable. Things being as they are, there isnt much a woman can safely do to abort herself. So the question asked is what a third party may do, and what the mother may do, if it is mentioned at all, is deduced, almost as an afterthought, from what it is concluded that third parties may do. But it seems to me that to treat the matter in this way is to refuse to grant to the mother that very status of person which is so firmly insisted on for the fetus. For we cannot simply read off what a person may do from what a third party may do. Suppose you find yourself trapped in a tiny house with a growing child. I mean a very tiny house, and a rapidly growing child-you are already up against the wall f the house and in a few minutes youll be crushed to death. The child on the other hand wont be crushed to death; if nothing is done to stop him from growing hell be hurt, but in the end hell simply burst open the house and walk out a free man. Now I could well understand it if a bystander were to say, Theres nothing we can do for you. We cannot choose between your life and his, we cann ot be the ones to decide who is to live, we cannot intervene. But it cannot be concluded that you too can do nothing, that you cannot attack it to save your life. However innocent the child may be, you do not have to wait passively while it crushes you to death. Perhaps a pregnant woman is vaguely felt to have the status of house, to which we dont allow the 53 A Defense of Abortion right of self-defense. But if the woman houses the child, it should be remembered that she is a person who houses it. 1 should perhaps stop to say explicitly that I am not claiming that people have a right to do anything whatever to save their lives. I think, rather, that there are drastic limits to the right of self-defense. If someone threatens you with death unless you torture someone else to death, I think you have not the right, even to save your life, to do so. But the case under consideration here is very different. In our case there are only two people involved, one whose life is threatened, and one who threatens it. Both are innocent: the one who is threatened is not threatened because of any fault, the one who threatens does not threaten because of any fault. For this reason we may feel that we bystanders cannot intervene. But the person threatened can. In sum, a woman surely can defend her life against the threat to it posed by the unborn child, even if doing so involves its death. And this shows not merely that the theses in (i) through (4) are false; it shows also that the extreme view of abortion is false, and so we need not canvass any other possible ways of arriving at it from the argument I mentioned at the outset. 2. The extreme view could of course be weakened to say that while abortion is permissible to save the mothers life, it may not be performed by a third party, but only by the mother herself. But this cannot be right either. For what we have to keep in mind is that the mother and the unborn child are not like two tenants in a small house which has, by an unfortunate mistake, been rented to both: the mother owns the house. The fact that she does adds to the offensiveness of deducing that the mother can do nothing from the supposition that third parties can do nothing. But it does more than this: it casts a bright light on the supposition that third parties can do nothing. Certainly it lets us see that a third party who says I cannot choose between you is fooling himself if he thinks this is impartiality. If Jones has found and fastened on a certain coat, which he needs to keep him from freezing, but which Smith also needs to keep him from freezing, then it is not impartiality that says I cannot choose between you when Smith owns the coat. Women have said again and again This body is my body! and they have reason to feel angry, reason to feel that it has been like shouting into the wind. Smith, after all, is 54 Philosophy Public Affairs hardly likely to bless us if we say to him, Of course its your coat, anybody would grant that it is. But no one may choose between you and Jones who is to have it. We should really ask what it is that says no one may choose in the face of the fact that the body that houses the child is the mothers body. It may be simply a failure to appreciate this fact. But it may be something more interesting, namely the sense that one has a right to refuse to lay hands on people, even where it would be just and fair to do so, even where justice seems to require t hat somebody do so. Thus justice might call for somebody to get Smiths coat back from Jones, and yet you have a right to refuse to be the one to lay hands on Jones, a right to refuse to do physical violence to him. This, I think, must be granted. But then what should be said is not no one may choose, but only I cannot choose, and indeed not even this, but I will not act, leaving it open that somebody else can or should, and in particular that anyone in a position of authority, with the job of securing peoples rights, both can and should. So this is no difficulty. I have not been arguing that any given third party must accede to the mothers request that he perform an abortion to save her life, but only that he may. I suppose that in some views of human life the mothers body is only on loan to her, the loan not being one which gives her any prior claim to it. One who held this view might well think it impartiality to say I cannot choose. But I shall simply ignore this possibility. My own view is that if a human being has any just, prior claim to anything at all, he has a just, prior claim to his own body. And perhaps this neednt be argued for here anyway, since, as I mentioned, the arguments against abortion we are looking at do grant that the woman has a right to decide what happens in and to her body. But although they do grant it, I have tried to show that they do not take seriously what is done in granting it. I suggest the same thing will reappear even more clearly when we turn away from cases in which the mothers life is at stake, and attend, as I propose we now do, to the vastly more common cases in which a woman wants an abortion for some less weighty reason than preserving her own life. 3. Where the mothers life is not at stake, the argument I mentioned at the outset seems to have a much stronger pull. Everyone 55 A Defense of Abortion as a right to life, so the unborn person has a right to life. And isnt the childs right to life weightier than anything other than the mothers own right to life, which she might put forward as ground for an abortion? This argument treats the right to life as if it were unproblematic. It is not, and this seems to me to be precisely the source of the mistake. For we should now, at long last, ask what it comes to, to have a right to life. In so me views having a right to life includes having a right to be given at least the bare minimum one needs for continued life. But suppose that what in fact is the bare minimum a man needs for continued life is something he has no right at all to be given? If I am sick unto death, and the only thing that will save my life is the touch of Henry Fondas cool hand on my fevered brow, then all the same, I have no right to be given the touch of Henry Fondas cool hand on my fevered brow. It would be frightfully nice of him to fly in from the West Coast to provide it. It would be less nice, though no doubt well meant, if my friends flew out to the West Coast and carried Henry Fonda back with them. But I have no right at all against anybody that he should do this for me. Or again, to return to the story I told earlier, the fact that for continued life that violinist needs the continued use of your kidneys does not establish that he has a right to be given the continued use of your kidneys. He certainly has no right against you that you should give him continued use of your kidneys. For nobody has any right to use your kidneys unless you give him such a right; and nobody has the right against you that you shall give him this right-if you do allow him to go on using your kidneys, this is a kindness on your part, and not something he can claim from you as his due. Nor has he any right against anybody else that they should give him continued use of your kidneys. Certainly he had no right against the Society of Music Lovers that they should plug him into you in the first place. And if you now start to unplug yourself, having learned that you will otherwise have to spend nine years in bed with him, there is nobody in the world who must try to prevent you, in order to see to it that he is given something he has a right to be given. Some people are rather stricter about the right to life. In their view, it does not include the right to be given anything, but amounts to, 56 Philosophy Public Affairs and only to, the right not to be killed by anybody. But here a related difficulty arises. If everybody is to refrain from killing that violinist, then everybody must refrain from doing a great many different sorts of things. Everybody must refrain from slitting his throat, everybody must refrain from shooting him-and everybody must refrain from unplugging you from him. But does he have a right against everybody that they shall refrain from unplugging you from him? To refrain from doing this is to allow him to continue to use your kidneys. It could be argued that he has a right against us that we should allow him to continue to use your kidneys. That is, while he had no right against us that we should give him the use of your kidneys, it might be argued that he anyway has a right against us that we shall not now intervene and deprive him of the use of your kidneys. I shall come back to third-party interventions later. But certainly the violinist has no right against you that you shall allow him to continue to use your kidneys. As I said, if you do allow him to use them, it is a kindness on your part, and not something you owe him. The difficulty I point to here is not peculiar to the right to life. It reappears in connection with all the other natural rights; and it is something which an adequate account of rights must deal with. For present purposes it is enough just to draw attention to it. But I would stress that I am not arguing that people do not have a right to lifequite to the contrary, it seems to me that the primary control we must place on the acceptability of an account of rights is that it should turn out in that account to be a truth that all persons have a right to life. I am arguing only that having a right to life does not guarantee having either a right to be given the use of or a right to be allowed continued use of another persons body-even if one needs it for life itself. So the right to life will not serve the opponents of abortion in the very simple and clear way in which they seem to have thought it would. 4. There is another way to bring out the difficulty. In the most ordinary sort of case, to deprive someone of what he has a right to is to treat him unjustly. Suppose a boy and his small brother are jointly given a box of chocolates for Christmas. If the older boy takes the box and refuses to give his brother any of the chocolates, he is unjust to -him, for the brother has been given a right to half of them. But 57 A Defense of Abortion uppose that, having learned that otherwise it means nine years in bed with that violinist, you unplug yourself from him. You surely are not being unjust to him, for you gave him no right to use your kidneys, and no one else can have given him any such right. But we have to notice that in unplugging yourself, you are killing him; and violinists, like everybody else, have a right to life, and thus in the view we wer e considering just now, the right not to be killed. So here you do what he supposedly has a right you shall not do, but you do not act unjustly to him in doing it. The emendation which may be made at this point is this: the right to life consists not in the right not to be killed, but rather in the right not to be killed unjustly. This runs a risk of circularity, but never mind: it would enable us to square the fact that the violinist has a right to life with the fact that you do not act unjustly toward him in unplugging yourself, thereby killing him. For if you do not kill him unjustly, you do not violate his right to life, and so it is no wonder you do him no injustice. But if this emendation is accepted, the gap in the argument against abortion stares us plainly in the face: it is by no means enough to show that the fetus is a person, and to remind us that all persons have a right to life-we need to be shown also that killing the fetus violates its right to life, i. e. , that abortion is unjust killing. And is it? I suppose we may take it as a datum that in a case of pregnancy due to rape the mother has not given the unborn person a right to the use of her body for food and shelter. Indeed, in what pregnancy could it be supposed that the mother has given the unborn person such a right? It is not as if there were unborn persons drifting about the world, to whom a woman who wants a child says I invite you in. But it might be argued that there are other ways one can have acquired a right to the use of another persons body than by having been invited to use it by that person. Suppose a woman voluntarily indulges in intercourse, knowing of the chance it will issue in pregnancy, and then she does become pregnant; is she not in part responsible for the presence, in fact the very existence, of the unborn person inside her? No doubt she did not invite it in. But doesnt her partial responsibility for its being there itself give it a right to the use of her 58 Philosophy ; Public Affairs body? 7 If so, then her aborting it would be more like the boys taking away the chocolates, and less like your unplugging yourself from the violinist-doing so would be depriving it of what it does have a right to, and thus would be doing it an injustice. And then, too, it might be asked whether or not she can kill it even to save her own life: If she voluntarily called it into existence, how can she now kill it, even in self-defense? The first thing to be said about this is that it is something new. Opponents of abortion have been so concerned to make out the independence of the fetus, in order to establish that it has a right to life, just as its mother does, that they have tended to overlook the possible support they might gain from making out that the fetus is dependent on the mother, in order to establish that she has a special kind of responsibility for it, a responsibility that gives it rights against her which are not possessed by any independent person-such as an ailing violinist who is a stranger to her. On the other hand, this argument would give the unborn person a right to its mothers body only if her pregnancy resulted from a voluntary act, undertaken in full knowledge of the chance a pregnancy might result from it. It would leave out entirely the unborn person whose existence is due to rape. Pending the availability of some further argument, then, we would be left with the conclusion that unborn persons whose existence is due to rape have no right to the use of their mothers bodies, and thus that aborting them is not depriving them of anything they have a right to and hence is not unjust killing. And we should also notice that it is not at all plain that this argument really does go even as far as it purports to. For there are cases and cases, and the details make a difference. If the room is stuffy, and I therefore open a window to air it, and a burglar climbs in, it would be absurd to say,Ah, now he can stay, shes given him a right to the use of her house-for she is partially responsible for his presence there, having voluntarily done what enabled him to get in, in full knowledge that there are such things as burglars, and that burglars 7. The need for a discussion of this argument was brought home to me by members of the Society for Ethical and Legal Philosophy, to whom this paper was originally presented. 59 A Defense of Abortion burgle. It would be still more absurd to say this if I had had bars installed outside my windows, precisely to prevent burglars from getting in, and a burglar got in only because of a defect in the bars. It remains equally absurd if we imagine it is not a burglar who climbs in, but an innocent person who blunders or falls in. Again, suppose it were like this: people-seeds drift about in the air like pollen, and if you open your windows, one may drift in and take root in your carpets or upholstery. You dont want children, so you fix up your windows with fine mesh screens, the very best you can buy. As can happen, however, and on very, very rare occasions does happen, one of the screens is defective; and a seed drifts in and takes root. Does the person-plant who now develops have a right to the use of your house? Surely not-despite the fact that you voluntarily opened your windows, you knowingly kept carpets and upholstered furniture, and you knew that screens were sometimes defective. Someone may argue that you are responsible for its rooting, that it does have a right to your house, because after all you could have lived out your life with bare floors and furniture, or with sealed windows and doors. But this wont do-for by the same token anyone can avoid a pregnancy due to rape by having a hysterectomy, or anyway by never leaving home without a (reliable! army. It seems to me that the argument we are looking at can establish at most that there are some cases in which the unborn person has a right to the use of its mothers body, and therefore some cases in which abortion is unjust killing. There is room for much discussion and argument as to precisely which, if any. But I think we should sidestep this issue and leave it open, for at any rate the argument certainly does not establish that al l abortion is unjust killing. 5. There is room for yet another argument here, however. We surely must all grant that there may be cases in which it would be morally indecent to detach a person from your body at the cost of his life. Suppose you learn that what the violinist needs is not nine years of your life, but only one hour: all you need do to save his life is to spend one hour in that bed with him. Suppose also that letting him use your kidneys for that one hour would not affect your health in the slightest. Admittedly you were kidnapped. Admittedly you did not give 6o Philosophy Public Affairs anyone permission to plug him into you. Nevertheless it seems to me plain you ought to allow him to use your kidneys for that hour-it would be indecent to refuse. Again, suppose pregnancy lasted only an hour, and constituted no threat to life or health. And suppose that a woman becomes pregnant as a result of rape. Admittedly she did not voluntarily do anything to bring about the existence of a child. Admittedly she did nothing at all which would give the unborn person a right to the use of her body. All the same it might well be said, as in the newly emended violinist story, that she ought to allow it to remain for that hour-that it would be indecent in her to refuse. Now some people are inclined to use the term rightin such a way that it follows from the fact that you ought to allow a person to use your body for the hour he needs, that he has a right to use your body for the hour he needs, even though he has not been given that right by any person or act. They may say that it follows also that if you refuse, you act unjustly toward him. This use of the term is perhaps so common that it cannot be called wrong; nevertheless it seems to me to be an unfortunate loosening of what we would do better to keep a tight rein on. Suppose that box of chocolates I mentioned earlier had not been given to both boys jointly, but was given only to the older boy. There he sits, stolidly eating his way through the box, his small brother watching enviously. Here we are likely to say Youought not to be so mean. You ought to give your brother some of those chocolates. My own view is that it just does not follow from the truth of this that the brother has any right to any of the chocolates. If the boy refuses to give his brother any, he is greedy, stingy, callous-but not unjust. I suppose that the people I have in mind will say it does follow that the brother has a right to some of the chocolates, and thus that the boy does act unjustly if he refuses to give his brother any. But the effect of saying this is to obscure what we should keep distinct, namely the difference between the boys refusal in this case and the boys refusal in the earlier case, in which the box was given to both boys jointly, and in which the small brother thus had what was from any point of view clear title to half. A further objection to so using the term rightthat from the fact that A ought to do a thing for B, it follows that B has a right against A 6I A Defense of Abortion that A do it for him, is that it is going to make the question of whether or not a man has a right to a thing turn on how easy it is to provide him with it; and this seems not merely unfortunate, but morally unacceptable. Take the case of Henry Fonda again. I said earlier that I had no right to the touch of his cool hand on my fevered brow, even though I needed it to save my life. I said it would be frightfully nice of him to fly in from the West Coast to provide me with it, but that I had no right against him that he should do so. But suppose he isnt on the West Coast. Suppose he has only to walk across the room, place a hand briefly on my brow-and lo, my life is saved. Then surely he ought to do it, it would be indecent to refuse. Is it to be said Ah, well, it follows that in this case she has a right to the touch of his hand on her brow, and so it would be an injustice in him to refuse? So that I have a right to it when it is easy for him to provide it, though no right when its hard? Its rather a shocking idea that anyones rights should fade away and disappear as it gets harder and harder to accord them to him. So my own view is that even though you ought to let the violinist use your kidneys for the one hour he needs, we should not conclude that he has a right to do so-we should say that if you refuse, you are, like the boy who owns all the chocolates and will give none away, self-centered and callous, indecent in fact, but not unjust. And similarly, that even supposing a case in which a woman pregnant due to rape ought to allow the unborn person to use her body for the hour he needs, we should not conclude that he has a right to do so; we should conclude that she is self-centered, callous, indecent, but not unjust, if she refuses. The complaints are no less grave; they are just different. However, there is no need to insist on this point. If anyone does wish to deduce he has a ight from you ought, then all the same he must surely grant that there are cases in which it is not morally required of you that you allow that violinist to use your kidneys, and in which he does not have a right to use them, and in which you do not do him an injustice if you refuse. And so also for mother and unborn child. Except in such cases as the unborn person has a right to demand it-and we were leaving open the possibility that there may be such cases-nobody is morally required to make large sacrifices, of health, of all other interes ts and concerns, of all other duties 62 Philosophy Public Affairs and commitments, for nine years, or even for nine months, in order to keep another person alive. 6. We have in fact to distinguish between two kinds of Samaritan: the Good Samaritan and what we might call the Minimally Decent Samaritan. The story of the Good Samaritan, you will remember, goes like this: A certain man went down from Jerusalem to Jericho, and fell among thieves, which stripped him of his raiment, and wounded him, and departed, leaving him half dead. And by chance there came down a certain priest that way; and when he saw him, he passed by on the other side. And likewise a Levite, when he was at the place, came and looked on him, and passed by on the other side. But a certain Samaritan, as he journeyed, came where he was; and when he saw him he had compassion on him. And went to him, and bound up his wounds, pouring in oil and wine, and set him on his own beast, and brought him to an inn, and took care of him. And on the morrow, when he departed, he took out two pence, and gave them to the host, and said unto him, Take care of him; and whatsoever thou spendest more, when I come again, I will repay thee. (Luke I0:30-35) The Good Samaritan went out of his way, at some cost to himself, to help one in need of it. We are not told what the options were, that is, whether or not the priest and the Levite could have helped by doing less than the Good Samaritan did, but assuming they could have, then the fact they did nothing at all shows they were not even Minimally Decent Samaritans, not because they were not Samaritans, but because they were n ot even minimally decent. These things are a matter of degree, of course, but there is a difference, and it comes out perhaps most clearly in the story of Kitty Genovese, who, as you will remember, was murdered while thirtyeight people watched or listened, and did nothing at all to help her. A Good Samaritan would have rushed out to give direct assistance 63 A Defense of Abortion against the murderer. Or perhaps we had better allow that it would have been a Splendid Samaritan who did this, on the ground that it would have involved a risk of death for himself. But the thirty-eight not only did not do this, they did not even trouble to pick up a phone to call the police. Minimally Decent Samaritanism would call for doing at least that, and their not having done it was monstrous. After telling the story of the Good Samaritan, Jesus said Go, and do thou likewise. Perhaps he meant that we are morally required to act as the Good Samaritan did. Perhaps he was urging people to do more than is morally required of them. At all events it seems plain that it was not morally required of any of the thirty-eight that he rush out to give direct assistance at the risk of his own life, and that it is not morally required of anyone that he give long stretches of his lifenine years or nine months-to sustaining the life of a person who has no special right (we were leaving open the possibility of this) to demand it. Indeed, with one rather striking class of exceptions, no one in any country in the world is legally required to do anywhere near as much as this for anyone else.

Theorems Related To Mersenne Primes Mathematics Essay

Theorems Related To Mersenne Primes Mathematics Essay Introduction: In the past many use to consider that the numbers of the type 2p-1 were prime for all primes numbers which is p, but when Hudalricus Regius (1536) clearly established that 211-1 = 2047 was not prime because it was divisible by 23 and 83 and later on Pietro Cataldi (1603) had properly confirmed about 217-1 and 219-1 as both give prime numbers but also inaccurately declared that 2p-1 for 23, 29, 31 and 37 gave prime numbers. Then Fermat (1640) proved Cataldi was wrong about 23 and 37 and Euler (1738) showed Cataldi was also incorrect regarding 29 but made an accurate conjecture about 31. Then after this extensive history of this dilemma with no accurate result we saw the entry of Martin Mersenne who declared in the introduction of his Cogitata Physica-Mathematica (1644) that the numbers 2p-1 were prime for:- p= 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 and for  other positive integers where p So simply the definition is when 2p-1 forms a prime number it is recognized to be a Mersenne prime. Many years later with new numbers being discovered belonging to Mersenne Primes there are still many fundamental questions about Mersenne primes which remain unresolved. It is still not identified whether Mersenne primes is infinite or finite. There are still many aspects, functions it performs and applications of Mersenne primes that are still unfamiliar With this concept in mind the focus of my extended essay would be: What are Mersenne Primes and it related functions? The reason I choose this topic was because while researching on my extended essay topics and I came across this part which from the beginning intrigued me and it gave me the opportunity to fill this gap as very little was taught about these aspects in our school and at the same time my enthusiasm to learn something new through research on this topic. Through this paper I will explain what are Mersenne primes and certain theorems, related to other aspects and its application that are related with it. Theorems Related to Mersenne Primes: p is prime only if 2p  Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢Ã‚  1 is prime. Proof: If p is composite then it can be written as p=x*y with x, y > 1. 2xy-1= (2x-1)*(1+2x+22x+23x+à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦..+2(b-1)a) Thus we have got 2xy à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 as a product of integers > 1. If n is an odd prime, then any prime m that divides 2n à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 must be 1 plus a multiple of 2n. This holds even when 2n à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 is prime. Examples: Example I: 25 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 = 31 is prime, and 31 is multiple of (2ÃÆ'-5) +1 Example II: 211 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 = 23ÃÆ'-89, where 23 = 1 + 2ÃÆ'-11, and 89 = 1 + 8ÃÆ'-11. Proof: If m divides 2n à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 then 2n à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod m). By Fermats Theorem we know that 2(m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod m). Assume n and m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 are comparatively prime which is similar to Fermats Theorem that states that (m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1)(n à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod n). Hence there is a number x à ¢Ã¢â‚¬ °Ã‚ ¡ (m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1)(n à ¢Ã‹â€ Ã¢â‚¬â„¢ 2) for which (m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) ·x à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod n), and thus a number k for which (m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) ·x à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 = kn. Since 2(m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod m), raising both sides of the congruence to the power x gives 2(m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1)x à ¢Ã¢â‚¬ °Ã‚ ¡ 1, and since 2n à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod m), raising both sides of the congruence to the power k gives 2kn à ¢Ã¢â‚¬ °Ã‚ ¡ 1. Thus 2(m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1)x/2kn = 2(m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1)x à ¢Ã‹â€ Ã¢â‚¬â„¢ kn à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod m). But by meaning, ( m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1)x à ¢Ã‹â€ Ã¢â‚¬â„¢ kn = 1 which implies that 21 à ¢Ã¢â‚¬ °Ã‚ ¡ 1 (mod m) which means that m divides 1. Thus the first conjecture that n and m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 are relatively prime is unsustainable. Since n is prime m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 have to be a multiple of n. Note: This information provides a confirmation of the infinitude of primes different from Euclids Theorem which states that if there were finitely many primes, with n being the largest, we have a contradiction because every prime dividing 2n à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 must be larger than n. If n is an odd prime, then any prime m that divides 2n à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 must be congruent to +/-1 (mod 8). Proof: 2n + 1 = 2(mod m), so 2(n + 1) / 2 is a square root of 2 modulo m. By quadratic reciprocity, any prime modulo which 2 has a square root is congruent to +/-1 (mod 8). A Mersenne prime cannot be a Wieferich prime. Proof: We show if p = 2m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 is a Mersenne prime, then the congruence does not satisfy. By Fermats Little theorem, m | p à ¢Ã‹â€ Ã¢â‚¬â„¢ 1. Now write, p à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 = mÃŽÂ ». If the given congruence satisfies, then p2 | 2mÃŽÂ » à ¢Ã‹â€ Ã¢â‚¬â„¢ 1, therefore Hence 2m à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 | ÃŽÂ », and therefore . This leads to , which is impossible since . The Lucas-Lehmer Test Mersenne prime are found using the following theorem: For n an odd prime, the Mersenne number 2n-1 is a prime if and only if 2n -1 divides S(p-1) where S(p+1) = S(p)2-2, and S(1) = 4. The assumption for this test was initiated by Lucas (1870) and then made into this straightforward experiment by Lehmer (1930). The progression S(n) is calculated modulo 2n-1 to conserve time.   This test is perfect for binary computers since the division by 2n-1 (in binary) can only be completed using rotation and addition. Lists of Known Mersenne Primes: After the discovery of the first few Mersenne Primes it took more than two centuries with rigorous verification to obtain 47 Mersenne primes. The following table below lists all recognized Mersenne primes:- It is not well-known whether any undiscovered Mersenne primes present between the 39th and the 47th from the above table; the position is consequently temporary as these numbers werent always discovered in their increasing order. The following graph shows the number of digits of the largest known Mersenne primes year wise. Note: The vertical scale is logarithmic. Factorization The factorization of a prime number is by meaning itself the prime number itself. Now if talk about composite numbers. Mersenne numbers are excellent investigation cases for the particular number field sieve algorithm, so frequently that the largest figure they have factorized with this has been a Mersenne number. 21039 1 (2007) is the record-holder after estimating took with the help of a couple of hundred computers, mostly at NTT in Japan and at EPFL in Switzerland and yet the time period for calculation was about a year. The special number field sieve can factorize figures with more than one large factor. If a number has one huge factor then other algorithms can factorize larger figures by initially finding the answer of small factors and after that making a primality test on the cofactor. In 2008 the largest Mersenne number with confirmed prime factors is 217029 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 = 418879343 ÃÆ'- p, where p was prime which was confirmed with ECPP. The largest with possible pr ime factors allowed is 2684127 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 = 23765203727 ÃÆ'- q, where q is a likely prime. Generalization: The binary depiction of 2p à ¢Ã‹â€ Ã¢â‚¬â„¢ 1 is the digit 1 repeated p times. A Mersenne prime is the base 2 repunit primes. The base 2 depiction of a Mersenne number demonstrates the factorization example for composite exponent. Examples in binary notation of the Mersenne prime would be: 25à ¢Ã‹â€ Ã¢â‚¬â„¢1 = 111112 235à ¢Ã‹â€ Ã¢â‚¬â„¢1 = (111111111111111111111111111111)2 Mersenne Primes and Perfect Numbers Many were anxious with the relationship of a two sets of different numbers as two how they can be interconnected. One such connection that many people are concerned still today is Mersenne primes and Perfect Numbers. When a positive integer that is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself then is it said to be known as Perfect Numbers. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors. There are said to be two types of perfect numbers: 1) Even perfect numbers- Euclid revealed that the first four perfect numbers are generated by the formula 2nà ¢Ã‹â€ Ã¢â‚¬â„¢1(2n  Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢Ã‚  1): n = 2:    2(4 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) = 6 n = 3:    4(8 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) = 28 n = 5:    16(32 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) = 496 n = 7:    64(128 à ¢Ã‹â€ Ã¢â‚¬â„¢ 1) = 8128. Noticing that 2n  Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢Ã‚  1 is a prime number in each instance, Euclid proved that the formula 2nà ¢Ã‹â€ Ã¢â‚¬â„¢1(2n  Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢Ã‚  1) gives an even perfect number whenever 2p  Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢Ã‚  1 is prime 2) Odd perfect numbers- It is unidentified if there might be any odd perfect numbers. Various results have been obtained, but none that has helped to locate one or otherwise resolve the question of their existence. An example would be the first perfect number that is 6. The reason for this is so since 1, 2, and 3 are its proper positive divisors, and 1  +  2  +  3  =  6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: (1  +  2  +  3  +  6)  /  2  =  6. Few Theorems related with Perfect numbers and Mersenne primes: Theorem One: z is an even perfect number if and only if it has the form 2n-1(2n-1) and 2n-1 is a prime. Suppose first that   p = 2n-1 is a prime number, and set l = 2n-1(2n-1).   To show l is perfect we need only show sigma(l) = 2l.   Since sigma is multiplicative and sigma(p) = p+1 = 2n, we know sigma(n) = sigma(2n-1).sigma(p) =  (2n-1)2n = 2l. This shows that l is a perfect number. On the other hand, suppose l is any even perfect number and write l as 2n-1m where m is an odd integer and n>2.   Again sigma is multiplicative so sigma(2n-1m) = sigma(2n-1).sigma(m) = (2n-1).sigma(m). Since l is perfect we also know that sigma(l) = 2l = 2nm. Together these two criteria give 2nm = (2n-1).sigma(m), so 2n-1 divides 2nm hence 2n-1 divides m, say m = (2n-1)M.   Now substitute this back into the equation above and divide by 2n-1 to get 2nM = sigma(m).   Since m and M are both divisors of m we know that 2nM = sigma(m) > m + M = 2nM, so sigma(m) = m + M.   This means that m is prime and its only two divisors are itself (m) and one (M).   Thus m = 2n-1 is a prime and we have prove that the number l has the prescribed form. Theorem Two: n will also be a prime if 2n-1 is a prime. Proof: Let r and s be positive integers, then the polynomial xrs-1 is xs-1 times xs(r-1) + xs(r-2) + + xs + 1.   So if n is composite (say r.s with 1 Theorem Three:   Let n and m be primes. If q divides Mn = 2n-1, then q = +/-1 (mod 8)  Ã‚  Ã‚  Ã‚   and  q = 2kn + 1 for some integer k. Proof: If p divides Mq, then 2q  =  1 (mod p) and the order of 2 (mod p) divides the prime q, so it must be q.   By Fermats Little Theorem the order of 2 also divides p-1, so p-1  =  2kq.   This gives 2(p-1)/2 = 2qk = 1 (mod p) so 2 is a quadratic residue mod p and it follows p = +/-1 (mod 8), which completes the proof. Theorem Four: If p = 3 (mod 4) be prime and then 2p+1 is also prime only if 2p+1 divides 2p-1. Proof: Suppose q = 2p+1 is prime. q  =  7 (mod  8) so 2 is a quadratic residue modulo q and it follows that there is an integer n such that n2  =  2 (mod  q). This shows 2p = 2(q-1)/2 = nq-1 = 1 (mod q), showing q divides Mp.       Conversely, let 2p+1 be a factor of Mp. Suppose, for proof by contradiction, that 2p+1 is composite and let q be its least prime factor. Then 2p  =  1 (mod  q) and the order of 2 modulo q divides both p and q-1, hence p divides q-1. This shows q  >  p and it follows (2p+1) + 1 > q2 > p2 which is a contradiction since p > 2. Theorem Five: When we add the digits of any even perfect number with the exception of 6 and then sum the digits of the resulting number and keep doing it again until we get a single digit which will be one. Examples. 28  ¬10  ¬ 1, 496  ¬ 19  ¬ 10  ¬ 1, and 8128  ¬ 19  ¬10  ¬ 1 Proof: Let s(n) be the sum of the digits of n. It is easy to see that s(n) = n (mod 9). So to prove the theorem, we need only show that perfect numbers are congruent to one modulo nine. If n is a perfect number, then n has the form 2p-1(2p-1) where p is prime which see in the above theorem one. So p is either 2, 3, or is congruent to 1 or 5 modulo 6. Note that we have excluded the case p=2 (n=6). Finally, modulo nine, the powers of 2 repeat with period 6 (that is, 26 = 1 (mod 9)), so modulo nine n is congruent to one of the three numbers 21-1(21-1), 23-1(23-1), or 25-1(25-1), which are all 1 (mod 9). Conjectures and Unsolved Problems: Does an odd perfect number exist?   We have so far known that even perfect numbers are 2n-1(2n-1)from the Theorem One above, but what about odd perfect numbers?   If there is an odd perfect number, then it has to follow certain conditions:- To be a perfect square times an odd power of a single prime; It is divisible by at least eight primes and has to have at least 75 prime factors with at least 9 distinct It has at least 300 decimal digits and it has a prime divisor greater that 1020. Are there infinite numbers of Mersenne primes?   The answer is probably yes because of the harmonic sequence deviation. The New Mersenne Conjecture: P. T. Bateman, J. L. Selfridge and Wagstaff, Jr., S. S., have conjectured the following:- Let n be any odd natural number. If two of the following statements hold, subsequently so does the third: n = 2p+/-1  Ã‚   or  Ã‚   n = 4p+/-3 2n-1 is a prime (2n+1)/3 is a prime. Are all Mersenne number 2n-1 square free? This is kind of like an open question to which the answer is still not known and hence it cannot be called a conjecture. It is simple to illustrate that if the square of a prime n divides a Mersenne, then p is a Wieferich prime which are uncommon!   Only two are acknowledged lower than 4,000,000,000,000 and none of these squared divide a Mersenne.    If C0 = 2, then let C1 = 2C0-1, C2 = 2C1-1, C3 = 2C2-1à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦ then are all of these prime numbers?   Dickson Catalan (1876) responded to Lucas stating 2127-1 (which is C4) being a prime with this sequence: C0 = 2 (which is a prime) C1 = 3 (which is a prime) C2 = 7 (which is a prime) C3 = 127 (which is a prime) C4 = 170141183460469231731687303715884105727 (which is a prime) C5 > 1051217599719369681875006054625051616349 (is C5 a prime or not?) It looks as if it will not be very likely that C5 or further larger terms would be prime number.   If there is a single composite term in this series, then by theorem one each and every one of the following terms would be composite.   Are there more double-Mersenne primes? Another general misunderstanding was that if n=Mp is prime, then so is Mn; Lets assume this number Mn to be MMp which would be a double-Mersenne.  As we apply this to the first four such numbers we get prime numbers: MM2 = 2(4  -1) -1= 23-1  Ã‚   =  7 MM3 =  2(8-1)-1  Ã‚   =  127 MM5 =  2(32-1)-1  =  2147483647, MM7 =  2(128-1)-1 =  170141183460469231731687303715884105727. Application of Mersenne Prime: In computer science, unspecified p-bit integers can be utilized to express numbers up to Mp. In the mathematical problem Tower of Hanoi is where the Mersenne primes are used. It is a mathematical puzzle consisting of three rods, and a number of disks of different sizes, which can slide onto any rod. The puzzle begins with the disks in ascending order of size on the first rod, the largest at the bottom to the smallest at the top. A diagram given below illustrates the Tower of Hanoi. The objective of the puzzle is to move the entire stack to another rod, obeying the following rules: Only one disk may be moved at a time. Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod. No disk may be placed on top of a smaller disk. Now to solve this game with a p-disc tower needs the minimum of Mp no of steps, where p is the no of disc used in the Tower of Hanoi and if we use the formula of Mersenne then we get the required result. An example of this would be if there were 5 discs involved in this Tower of Hanoi then the least number of steps required to finish this game would be 31 steps minimum. Conclusion After investigating the entire aspects, functions, and few applications of Mersenne Primes I believe that there is still many unsolved theories when it comes to Mersenne primes. These primes are also useful to investigates much further and deeper into the number system and help us to understand more sets of numbers such as Fermat prime, Wieferich prime, Wagstaff prime, Solinas prime etc.

The Internet Essay -- Technology Computers Essays

The Internet The Internet and World Wide Web are commonly used words among people today. As a college student especially, the Web and Internet play a huge part of life. What is sometimes tough to realize though is the newness of the Internet and the Web. Because the two have become such a huge part of life, it is shocking to consider that the Internet itself has only been in existence for the past thirty years or so. It is important to understand the history of the Internet and the creation of the Web to better prepare for the future of the two and to ensure that the use of the resources is maximized, focused, and beneficial to all mankind. The History The roots of the internet can be traced to the year 1957. 1957 was a year dedicated to atmospheric research and was the year in which the USSR launched a small orbiting satellite into the Earth’s atmosphere. Shortly after the satellite was launched, the United States created the Advanced Research Projects Agency (ARPA) within the Ministry of Defense. This agency was created to number one, protect the U.S. against the threat of technological advances made by other countries and number two, to ensure the United States was keeping on top of state-of-the-art technology. Initially the focus of ARPA was on space, missiles, and nuclear tests. Several scientists worked within the agency along with several sub-contractors to create the latest technology. Even though computing was not the main priority of the agency, directors of the agency had a vision to create a direct link between the computers of the ARPA headquarters and all of its subcontractors. In 1962, John Licklider, an MIT scientist, was appointed by ARPA to lead a computer research development program.... ...22 October 2004. . Internet2. 22 October 2004. . Kristula, Dave. â€Å"The History of the Internet.† March 1997. 21 October 2004. . Leiner, Barry M. and Vinton G. Cerf. â€Å"A Brief History of the Internet.† Internet Society (ISOC). 22 October 2004. . â€Å"Next generation research networks†. Library and Archives Canada. 3 March 2004. 22 October 2004. < http://www.collectionscanada.ca/pubs/netnotes/notes42.htm>. â€Å"Usage and Population Statistics.† Internet World Stats. 22 October 2004. . Webopedia. 23 October 2004. . World Wide Web Consortium. 22 October 2004. .

The Lady of Shalott Essay -- essays research papers

1.  Ã‚  Ã‚  Ã‚  Ã‚  Introduction This paper will try to analyze the growth of consciousness of the Lady of Shalott. Ranging from her state of mind in total isolation, her 'childhood', to her changing 'adolescence' and eventually reaching 'adulthood' and death, all in a sort of quick-motion. It will further deal with the development of tension throughout the poem. By making a distinction between tension through formal aspects, such as rhyme scheme, and tension through content it will try to show the interconnection between both of them. Additionally, the paper will deal with the possible effect of tension on the reader and how the poem might be perceived by him/her. 2.  Ã‚  Ã‚  Ã‚  Ã‚  Growth of Consciousness and Development of Tension 2.1.  Ã‚  Ã‚  Ã‚  Ã‚  Initial Isolation Lord Alfred Tennyson's poem starts out with the total seclusion of the beautiful, young Lady of Shalott surrounded by '…four grey walls, and four grey towers…';. (Tennyson, line 15). She is largely unaware of the world outside and of her own existence as a woman, only being able to see shadows of reality, which are reflected by her magic (?) crystal mirror and worked into her web. At this point of time it is unknown to the reader whether the Lady of Shalott is forced to be in this situation or chose to live this life of isolation. Reasons for a self inflicted seclusion might be homophobia, the fear of rejection by the exterior world, or simply a lack of interest for it. However, the Lady of Shalott is quite content with what she has and what she does. Her life of art in front of the loom and the crystal mirror is all she needs singing her ';…song that echoes cheerly…'; (30) throughout the land. She is as innocent as a careless child giving little thought about her future. The Lady of Shalott has no urge to leave her own interior world because she is not aware of any other options. Little is known about her outside '…many-towered Camelot.'; (5) and apparently she intends to keep it that way: But who hath seen her wave her hand ? Or at the casement seen her stand ? Or is she known in all the land, The Lady of Shalott ? (24-27) By now the reader might ask him-/herself why the Lady of Shalott is stuck in such a dreadful situation and why she does not attempt to do anything about it. There is a cons... ...martyrdom and so the story ends, leaving the reader in anger about the carelessly spoken words of Lancelot. 3  Ã‚  Ã‚  Ã‚  Ã‚  Conclusion   Ã‚  Ã‚  Ã‚  Ã‚  'The Lady of Shalott'; was and is subject for countless interpretation by readers and artists, especially pictorial. Although, or maybe because the whole setting is quite vague and shadowy there have been many attempts to explain why the Lady of Shalott was cursed. Maybe she was not cursed al all. What was this whisper she heard ? Was she schizophrenic, hearing voices inside her head ? Another question is why she had to die in the end. Is it possible she eventually commit suicide, because she had realized that her love for Sir Lancelot was futile ? These are some questions that stay in the back of your head after reading Tennyson's poem. Even today you can feel the infinite struggle the Lady of Shalott had to undergo. Tennyson impressively shows the development of a young woman who is faced with one of the most difficult times in life- growing up in a world full of restrictions and rules and becoming a woman. His subtle description of a girls problems at his time is, slightly altered, even valid today.