The Future and Stability of Taiwans Independence

Introduction For decades now, Taiwan’s international status has been in limbo. The Taipei’s government, which in the past represented China in the United Nations Security Council (UNSC), currently does not enjoy a lot of support. Only around twenty diplomats continue supporting the government.Advertising We will write a custom essay sample on The Future and Stability of Taiwan’s Independence specifically for you for only $16.05 $11/page Learn More Consequently, the government finds it hard to gain recognition in the international arena. Today, very few states recognise Taiwan as an autonomous country (Chu 2004). However, Taiwan has been self-governed for a long time and has enjoyed a democratic government for over fifteen years. Relative to China, Taiwan enjoys what it refers to as the status quo, a situation that paves room for flexibility, but curtails the likelihood of Taiwan becoming a sovereign state. Currently, Taiwan’s condition does not appear too complex. The truce it established with china has allowed it to continue with its activities without interferences. Furthermore, Taiwan partakes in numerous international organisations. For instance, the country became a member of the World Trade Organisation (WTO) in 2002. Besides, in 2009, the country became an observer in the World Health Organisation (WHO) (Hickey 2011). This paper will focus on the future of Taiwan’s independence in ten years and give some of the factors that affect the stability of Taiwan’s independence. The issue of independence Since early 1990s, the call for Taiwan’s democratisation stirred the subject about the identity of the Republic of China (Crane 2006). It unlocked the political continuum for parties that do not support the belief that the Republic of China stands for China’s government, but which posits that Taiwan is autonomous with a different national identity from China. In other words, the call for democratisation led to disagreement about the future of Taiwan as a sovereign state. These developments made it hard for Taiwan to hold public referenda, which could have helped the state to acquire its independence. Nevertheless, even if Taiwan gained independence, either as Taiwan or as the Republic of China, it would be very hard for it to change its international status (Hickey 2011). The state would only participate fully in the international affairs if other countries agreed to recognise it as a sovereign state. By declaring itself as a sovereign state, the move would not change the way other countries perceived it. Moreover, it would harm its relationship with numerous countries, especially those that recognise China as the only sovereign state in the region.Advertising Looking for essay on asian? Let's see if we can help you! Get your first paper with 15% OFF Learn More Most of the superpowers have openly expressed their opposition to the separation o f Taiwan from China. For instance, the United States has heavily invested in promoting good ties with China. Therefore, the United States does all it can to ensure that it discourages any move by Taiwan to gain its independence, no matter how Taiwan tries to disguise its intentions (Ross 2002). For instance, in 2008, the United States opposed the referenda that sought to see Taiwan become a member of the United Nations (Lowther 2010). It is evident that in the next ten years, it will be hard for Taiwan to gain independence due to pressure from the international community. For Taiwan to continue enjoying a cordial relationship with other countries, it will have to nurture and promote a peaceful co-existence with China as advocated by most of the influential countries. No possibility for unification Unification with China would help in defining Taiwan’s status in global affairs. Nevertheless, chances of unification between the two are minimal. Among all the available options fo r Taiwan, unification is treated as the last result. In an independent society, the move to embrace unification would only be decided by the Taiwanese people, who largely opt to keep the option pending and seek other alternatives (Kastner 2006). Nevertheless, it is hard to rule out that the two countries might end up unifying in the near future. There is a high chance that Taiwan may drop its call for independence in the next ten years if it continues to experience pressure from China and if it is promised that the unification will pave room for it to continue enjoying its current autonomy (Kastner 2006). Nevertheless, currently, no plans are underway to facilitate this move, and the Taiwanese population strongly opposes chances of union between China and Taiwan.Advertising We will write a custom essay sample on The Future and Stability of Taiwan’s Independence specifically for you for only $16.05 $11/page Learn More Taiwanese voters oppose the c laim by the Chinese government that the union would pave room for a â€Å"one state, two systems† policy, which would ensure that Taiwan maintains its current autonomy and probably help Taiwan take part in global organisations even though it is not a state member. Some scholars claim that even if the two countries agreed on the unification, the move would only benefit the two countries and would have no benefit to the world (Kastner 2006). The two countries would come up with a stronger economy, since most of the economic resources that are currently used in safeguarding their divergent policies would be used in enhancing the economy. Status quo as the ultimate solution Rather than fighting to gain independence, there are high chances that Taiwan will fight to maintain the status quo for the next ten years. In late 1980s, Taiwan lost the majority of its diplomatic allies. Furthermore, it was scrapped from the international organisations. This made it hard for Taiwan to reflec t anywhere on the political map (Tsang 2006). Therefore, to ensure that it reflected on the political map, the Taiwanese government had to come up with creative strategies. Lee Teng-hui’s regime came up with the notion of â€Å"flexible† or practical diplomacy that claimed that if it were not possible for Taiwan to have formal relationships with other states, then the country would work towards entertaining considerable relations (Tsang 2006). This meant that Taiwan would work towards establishing close ties with other countries in the absence of diplomatic recognition. In addition, the country had to look for measures to help it participate in global organisations by using different names to suit the demands of the organisations. All these measures sought to help Taiwan maintain its status quo in the eyes of other countries. The current pressures from global organisations and influential nations imply that, it will be hard for Taiwan to continue fighting for its separ ation (Tsang 2006). Instead, the next ten years will see Taiwan struggling to maintain its status quo as the only strategy for its survival both politically and economically. After years of wrangles between China and Taiwan, President Ying-jeou stated that Taiwan was not ready for unification. Besides, he claimed that his country would no longer fight for independence and his government would cease applying force (Tucker 2007).Advertising Looking for essay on asian? Let's see if we can help you! Get your first paper with 15% OFF Learn More The move led to stability in the region and economic ties between the two countries became strong. Since then, the two countries have engaged in numerous government-to-government talks and significantly enhanced the association between the Chinese and Taiwanese population. Taiwan has been the major beneficiary of this close relationship. The state’s economy has strongly improved. As china is opposed to any call for independence and is ready to use its military powers to ensure that Taiwan does not gain independence, Taiwan has no feasible alternative, but to maintain the status quo (Tucker 2007). This would be the only way that Taiwan would continue enjoying its ties with China. Taiwan will definitely have to come up with a solution to the current challenges facing it on matters to do with independence and self-determination (Tucker 2007). Most of the Taiwanese believe that the move to call for independence is not misguided. Nevertheless, they feel that the move would jeopard ise their close relations with the international community. Hence, currently, Taiwan is not only facing pressure from the international community, but it is also facing immense internal political disagreements. Some of the Taiwanese feel that even though they need to be independent, the independence will do more harm than good to them. Hence, they prefer maintaining the status quo since it helps in maintaining the country’s good reputation in the international arena (Wang 2010). Currently, Taiwan is a major attraction to the Chinese people. Hence, Taiwanese citizens do not want to ruin this relation. Most probably, in the next ten years Taiwan will continually drop its desire to become independent and work on enhancing its relations with China while maintaining its status. For a long time, Taiwan has been using different names to continue working with international organisations. Its absence in such organisations would be detrimental to its economy. On the other hand, the org anisations would not allow it use a name that is similar or contradicts with that used by China (Hickey 2011). In a bid to ensure that it remains as a member in most of the international organisations, Taiwan has continuously kept on changing its name whenever it realises that the existing name would contradict or interfere with the one used by People’s Republic of China. The main reason why most of the international bodies fail to support Taiwan’s call for independence is the influence that China has in the global economy (Hickey 2011). Supporting Taiwan would lead to China withdrawing all the support it extends to international organisations. In return, this would incapacitate them making it hard for the organisations to manage their operations. In this view, for Taiwan to ensure that it continues participating in global organisations, it has to drop its call for independence. Consequently, the possibility of Taiwan gaining independence in the next ten years is minim al (Crane 2006). Hence, Taiwan will only strive to maintain the status quo so that it can continue enjoying its current relations with international organisations. While Taiwan continues struggling to gain independence, it will be hard to gain it since it can only do that by negotiating with China. With most of the world states opting to support China due to its international influence, Taiwan is left with no state to turn to for support, in case it collides with China (Crane 2006). China is not likely to heed to these demands in the near future implying that it is hard for Taiwan to gain independence in the next ten years. Factors that affect the stability of Taiwan’s independence One of the factors that destabilise Taiwan’s independence is the â€Å"Anti-secession Law† signed by China in 2005. According to this law, the People’s Republic of China declared that it would use non-peaceful measures and ensure that Taiwan does not detach itself from China (H ickey 2011). Hence, this declaration destabilises the move by Taiwan to call for secession since it fears that China might attack it. Taiwan is weaker in terms of military powers relative to China. Hence, it would be hard for Taiwan to defend itself from china. In addition, most of the influential countries are against the secession calls. Failure to gain support from the international community also makes it hard for the country to demand its independence. For instance, the United States is opposed to the call since most of its military forces are involved in other battlefields. Hence, it would be hard to rescue Taiwan from any attacks. Moreover, the existing laws that define the relations between Taiwan and the United States do not commit the United States to protecting Taiwan. They only give the United States an option to protect Taiwan in case of any incursion. An internal political wrangle in Taiwan is another factor that destabilises its independence. In as much as Taiwanese a re calling for independence, there are some people within the country that do not approve this move (Chao 2003). Those opposed to the call claim that calling for secession would affect the country’s young economy, and ruin its current relationship with China and other global countries. Besides, they believe that the move would lead to the country suffering from disfavour from the international community. This disunity among the Taiwanese makes it hard for the country to pursue its goals with one voice. The divisions weaken the call for secession from the People’s Republic of China (Carpenter 2006). After the 2000 presidential elections, there emerged two opposing forces in Taiwan. The Pan-Green and the Pan-Blue supported the Taiwanese identity and the Chinese identity respectively. The two forces destabilised the effort by the country to fight for its independence. The Pan-Green supporters claimed that there was an imbalanced economic dependence on China (Carpenter 200 6). They warned that such an economic dependence might jeopardise Taiwan’s national security. Consequently, the Pan-Green politicians started looking for support from individuals that did not benefit from the economic ties between China and Taiwan. On the other hand, the Pan-Blue politicians asserted that the Taiwan-China economic relations would have positive effects on the country’s economy. Hence, they sought the support of individuals that benefited from the economic ties. Since then, the country has been split between these two groups of politicians (Carpenter 2006). While one of the groups supports the unification, the other one calls for separation. It is hard for the country to speak in one voice thus making it hard for people to make an informed decision on whether to advocate for independence or not. The cost of seceding from China is high for Taiwan. The current relationship with China allows Taiwan to enjoy a cordial relationship with the international comm unity. Most of the countries acknowledge the one-China Principle; hence, if Taiwan happens to declare itself as a sovereign state and cuts its relationship with China, there are high possibilities that the international community would stop associating with it (Chao 2003). The pursuit for the one-China policy destabilises the Taiwan’s independence. Gaining independence would push most of the nations that are members of the international community to stop supporting the country financially. Hence, the move would render Taiwan economically handicapped making it had for it to manage its operations. Furthermore, China supports Taiwan financially, which destabilises Taiwan’s independence since Taiwan fears that it would lose this support upon becoming independent. These economic costs associated with independence compel Taiwan to abandon its independence calls (Wang 2010). Rather, the country uses other methods to ensure that it develops its economy to a self-reliant level. Today, China is under no pressure from the international community to assist Taiwan to gain its independence. Hence, China uses its influence to destabilise the fight for independence in Taiwan. China uses its power to lure other countries into opposing the Taiwan’s call for independence (Barbieri 2003). As Taiwan seeks to enhance its membership in the international organisations, it faces stiff challenges from China, which has significant influence on most of the organisations. China uses its influence to ensure that other member states compel Taiwan to compromise on some of its conditions. The influence from China has affected the stability of Taiwan’s independence, and thus Taiwan has been forced to ensure that it maintains the status quo to enjoy cordial relationship with international organisations. Conclusion For decades now, the Taiwan’s international status has faced immense challenges. Unlike in the past when the Taiwanese government represented China, today the international community does not recognise this government. Currently, Taiwan enjoys what it refers to as the status quo, which allows it to enjoy numerous privileges in the international arena and manage its affairs. However, the status quo does not allow the country to gain full independence. Since 1990s, Taiwan came up with the issue of democratisation, which sought to help the Taiwan Strait break away from the mainland China. However, the call for independence led to Taiwan facing opposition from other countries that advocated for the one-China policy. In a bid to ensure that Taiwan continues enjoying its interaction with the international community, some parties call for unification. However, the Taiwan citizens are against unification, thus leaving it as the last option. Taiwan is not likely to achieve its independence in the next ten years. Instead, the country will continue working on maintaining the status quo to help it gain financial support from the internatio nal community. Since President Ying-jeou called for Taiwan to maintain the status quo, the country has enjoyed a good relationship not only with China, but also with other global states. China has vowed to use its political and military powers to ensure that Taiwan does not gain independence. Hence, the fear of being attacked by China may hamper Taiwan’s ability to gain independence in the next ten years, thus opting to maintain the status quo. Numerous factors affect the stability of Taiwan’s independence including the anti secession law signed by China in 2005. The law gives China the power to use military means to ensure that Taiwan does not gain independence. Another factor is the internal political wrangles among the different groups of politicians. While the Pan-Green group calls for secession, the Pan-Blue calls for unification thus hampering the collective efforts to pursue independence. Reference List Barbieri, K 2003, ‘Economic Interdependence: A Path t o Peace or a Source of Interstate Conflict?’ Journal of Peace Research, vol. 33 no. 1, pp. 29-49. Carpenter, T 2006, America’s Coming War with China: A Collision Course over Taiwan, Palgrave Macmillan, New York. Chao, C 2003, ‘Will Economic Integration between Mainland China and Taiwan Lead to a Congenial Political Culture’, Asian Survey, vol. 43 no. 2, pp. 280-304. Chu, Y 2004, Taiwan’s National Identity Politics and the Prospect of Cross-Strait Relations’, Asian Survey, vol. 44 no. 4, pp. 497-503. Crane, G 2006, ‘China and Taiwan: Not Yet ‘Greater China’, International Affairs, vol. 69 no. 4, pp. 705-723. Hickey, D 2011, ‘Rapprochement between Taiwan and the Chinese Mainland: implications for American foreign policy’, Journal of Contemporary China, vol. 20 no. 69, pp. 233-245. Kastner, S 2006, ‘Does Economic Integration Across the Taiwan Strait Make Military Conflict Less Likely’, Journal of East Asian Studies, vol. 6, pp. 319-346. Lowther, W 2010, US, PRC discussing ways for Taiwan to join world bodies, http://www.taipeitimes.com/News/front/print/2010/12/09/2003490463 Ross, R 2002, ‘Navigating the Taiwan Strait: Deterrence, Escalation Dominance, and US-China Relations’, International Security, vol. 27 no. 2, pp. 48-85. Tsang, S 2006, If China Attacks Taiwan: Military Strategy, Politics and Economics, Routledge, London. Tucker, N 2007, ‘If Taiwan Chooses Unification, Should the United States Care’, The Washington Quarterly, vol. 25 no. 3, pp. 21-24. Wang, Y 2010, ‘China’s Growing Strength, Taiwan’s Diminishing Options’, Taiwan-U.S. Quarterly Analysis, vol. 23 no. 3, pp. 34-47. This essay on The Future and Stability of Taiwan’s Independence was written and submitted by user Crystal Carson to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

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Prime Numbers Divide

Prime Numbers Divide Prime Numbers: History, Facts and Examples Prime Numbers: An Introduction Prime number is the number, which is greater than 1 and cannot be divided by any number excluding itself and one. A prime number is a positive integer that has just two positive integer factors, including 1 and itself. Such as, if the factors of 28 are listed, there are 6 factors that are 1, 2, 4, 7, 14, and 28. Similarly, if the factors of 29 are listed, there are only two factors that are 1 and 29. Therefore, it can be inferred that 29 is a prime number, but 28 is not. Examples of prime numbers The first few prime numbers are as follows: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc. Identifying the primes The ancient Sieve of Eratosthenes is a simple way to work out all prime numbers up to a given limit by preparing a list of all integers and repetitively striking out multiples of already found primes. There is also a modern Sieve of Atkin, which is more complex when compared to that of Eratosthenes. A method to determine whether a number is prime or not, is to divide it by all primes less than or equal to the square root of that number. If the results of any of the divisions are an integer, the original number is not a prime and if not, it is a prime. One need not actually calculate the square root; once one sees that the quotient is less than the divisor, one can stop. This is called as the trial division, which is the simplest primality test but it is impractical for testing large integers because the number of possible factors grows exponentially as the number of digits in the number to be tested increases. Primality tests: A primality test algorithm is an algorithm that is used to test a number for primality, that is, whether the number is a prime number or not. AKS primality test The AKS primality test is based upon the equivalence (x a)n = (xn a) (mod n) for a coprime to n, which is true if and only if n is prime. This is a generalization of Fermats little theorem extended to polynomials and can easily be proven using the binomial theorem together with the fact that: for all 0 (x a)n = (xn a) (mod n, x r 1), which can be checked in polynomial time. Fermat primality test Fermats little theorem asserts that if p is prime and 1≠¤ a a p -1≠¡ 1 (mod p) In order to test whether p is a prime number or not, one can pick random as in the interval and check if there is an equality. Solovay-Strassen primality test For a prime number p and any integer a, A (p -1)/2 ≠¡ (a/p) (mod p) Where (a/p) is the Legendre symbol. The Jacobi symbol is a generalisation of the Legendre symbol to (a/n); where n can be any odd integer. The Jacobi symbol can be computed in time O((log n) ²) using Jacobis generalization of law of quadratic reciprocity. It can be observed whether or not the congruence A (n -1)/2 ≠¡ (a/n) (mod n) holds for various values of a. This congruence is true for all as if n is a prime number. (Solovay, Robert M. and Volker Strassen, 1977) Lucas-Lehmer test This test is for a natural number n and in this test, it is also required that the prime factors of n − 1 should be already known. If for every prime factor (q) of n − 1, there exists an integer a less than n and greater than 1 such as a n -1 ≠¡1 (mod n) and then a n -1/q 1 (mod n) then n is prime. If no such number can be found, n is composite number. Miller-Rabin primality test If we can find an a such that ad ≠¡ 1 (mod n), and a2nd -1 (mod n) for all 0 ≠¤ r ≠¤ s 1 then ‘a proves the compositeness of n. If not, ‘a is called a strong liar, and n is a strong probable prime to the base a. â€Å"Strong liar† refers to the case where n is composite but yet the equations hold as they would for a prime number. There are several witnesses ‘a for every odd composite n. But, a simple way to generate such an ‘a is known. Making the test probabilistic is the solution: we choose randomly, and check whether it is a witness for the composite nature of n. If n is composite, majority of the ‘as are witnesses, therefore the test will discover n as a composite number with high probability. (Rabin, 1980) A probable prime is an integer, which is considered to be probably prime by passing a certain test. Probable primes, which are actually composite (such as Carmichael numbers) are known as pseudoprimes. Besides these methods, there are other methods also. There is a set of Diophantine equations in 9 variables and one parameter in which the parameter is a prime number only if the resultant system of equations has a solution over the natural numbers. A single formula with the property of all the positive values being prime can be obtained with this method. There is another formula that is based on Wilsons theorem. The number ‘two is generated several times and all other primes are generated exactly once. Also, there are other similar formulas that can generate primes. Some primes are categorized as per the properties of their digits in decimal or other bases. An example is that the numbers whose digits develop a palindromic sequence are palindromic primes, and if by consecutively removing the first digit at the left or the right generates only new prime numbers, a prime number is known as a truncatable prime. The first 5,000 prime numbers can be known very quickly by just looking at odd numbers and checking each new number (say 5) against every number above it (3); so if 5Mod3 = 0 then its not a prime number. History of prime numbers The most ancient and acknowledged proof for the statement that â€Å"There are infinitely many prime numbers†, is given by Euclid in his Elements (Book IX, Proposition 20). The Sieve of Eratosthenes is a simple, ancient algorithm to identify all prime numbers up to a particular integer. After this, came the modern Sieve of Atkin, which is faster but more complex. The Sieve of Eratosthenes was created in the 3rd century BC by Eratosthenes. Some clues can be found in the surviving records of the ancient Egyptians regarding their knowledge of prime numbers: for example, the Egyptian fraction expansions in the Rhind papyrus have fairly different forms for primes and for composites. But, the first surviving records of the clear study of prime numbers come from the Ancient Greeks. Euclids Elements (circa 300 BC) include key theorems about primes, counting the fundamental theorem of arithmetic and the infinitude of primes. Euclid also explained how a perfect number is constructed fro m a Mersenne prime. After the Greeks, nothing special happened with the study of prime numbers till the 17th century. In 1640, Pierre de Fermat affirmed Fermats little theorem, which was later on proved by Leibniz and Euler. Chinese may have identified a special case of Fermats theorem much earlier. Fermat assumed that all numbers of the form 22n + 1 are prime and he proved this up to n = 4. But, the subsequent Fermat number 232+1 is composite; whose one prime factor is 641). This was later on discovered by Euler and now no further Fermat numbers are recognized as prime numbers. A French monk, Marin Mersenne looked at primes of the form 2p 1, with p as a prime number. They are known as Mersenne primes after his name. Euler showed that the infinite series 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + †¦ is divergent. In 1747, Euler demonstrated that even the perfect numbers are in particular the integers of the form 2p-1(2p-1), where the second factor is a Mersenne prime. It is supposed that there are no odd perfect numbers, but it is not proved yet. In the beginning of the 19th century, Legendre and Gauss independently assumed that because x tends to infinity, the number of primes up to x is asymptotic to x/log(x), where log(x) is the natural logarithm of x. Awards for finding primes A prize of US$100,000 has been offered by the Electronic Frontier Foundation (EFF) to the first discoverers of a prime with a minimum 10 million digits. Also, $150,000 for 100 million digits, and $250,000 for 1 billion digits has been offered. In 2000, $50,000 for 1 million digits were paid. Apart from this, prizes up to US$200,000 for finding the prime factors of particular semi-primes of up to 2048 bits were offered by the RSA Factoring Challenge. Facts about prime numbers 73939133 is an amazing prime number. If the last or the digit at the units place is removed, every time you will get a prime number. It is the largest known prime with this property. Because, all the numbers which we get after removing the end digit of the number are also prime numbers. They are as follows: 7393913, 739391, 73939, 7393, 739, 73 and 7. All these numbers are prime numbers. This is a distinct quality of the number 73939133, which any other number does not have. (Amazing number facts, 2008) The only even prime number is 2. All other even numbers can be divided by 2. So, they are not prime numbers. Zero and 1 are not considered to be prime numbers. If the sum of the digits of a number is a multiple of 3, that number can be divided by 3. With the exception of 0 and 1, a number is either a prime number or a composite number. A composite number is identified as any number that is greater than 1 and that is not prime. The last digit of a prime number greater than 5 can never be 5. Any number greater than 5 whose last digit is 5 can be divided by 5. (Prime Numbers, 2008) 1/2 0.5 Terminates 1/3 0.33333 Repeating block: 1 digit 1/5 0.2 Terminates 1/7 0.1428571428 Repeating block: 6 digits 1/11 0.090909 Repeating block: 2 digits 1/13 0.0769230769 Repeating block: 6 digits 1/17 0.05882352941176470588 Repeating block: 16 digits 1/19 0.0526315789473684210526 Repeating block: 18 digits 1/23 0.04347826086956521739130434 Repeating block: 22 digits For some of the prime numbers, the size of the repeating block is 1 less than the prime. These are known as Golden Primes. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 9 primes out of the 25 (less than 100) are golden primes; this forms 36% (9/25). (Amazing number facts, 2008) Examples of mathematicians specialized in prime numbers Arthur Wieferich, D. D. Wall, Zhi Hong Sun and Zhi Wei Sun, Joseph Wolstenholme, Joseph Wolstenholme, Euclid, Eratosthenes. Applications of prime numbers For a long time, the number theory and the study of prime numbers as well was seen as the canonical example of pure mathematics with no applications beyond the self-interest of studying the topic. But, in the 1970s, it was publicly announced that prime numbers could be used as a basis for creating the public key cryptography algorithms. They were also used for hash tables and pseudorandom number generators. A number of rotor machines were designed with a different number of pins on each rotor. The number of pins on any one rotor was either prime, or co-prime to the number of pins on any other rotor. With this, a full cycle of possible rotor positions (before repeating any position) was generated. Prime numbers in the arts and literature Also, prime numbers have had a significant influence on several artists and writers. The French composer Olivier Messiaen created ametrical music through natural phenomena with the use of prime numbers. In his works, La Natività © du Seigneur (1935) and Quatre à ©tudes de rythme (1949-50), he has used motifs with lengths given by different prime numbers to create unpredictable rhythms: 41, 43, 47 and 53 are the primes that appear in one of the à ©tudes. A scientist of NASA, Carl Sagan recommended (in his science fiction ‘Contact) that prime numbers could be used for communication with the aliens. The award-winning play ‘Arcadia by Tom Stoppard was a willful attempt made to discuss mathematical ideas on the stage. In the very first scene, the 13 year old heroine baffles over the Fermats last theorem (theorem that involves prime numbers). A popular fascination with the mysteries of prime numbers and cryptography has been seen in various films. References Amazing number facts, 2008. Retrieved April 28, 2008 from http://www.madras.fife.sch.uk/maths/amazingnofacts/fact018.html Prime Numbers, 2008. Retrieved April 28, 2008 from http://www.factmonster.com/ipka/A0876084.html Solovay, Robert M. Strassen, V. (1977). A fast Monte-Carlo test for primality. SIAM Journal on Computing 6 (1): 84-85. Rabin, M.O. (1980). Probabilistic algorithm for testing primality, Journal of Number Theory 12, no. 1, pp. 128-138.

Why is Juliet Under Pressure in a Scene :: essays research papers

There are two families that hate each other Romeo's family the Montague's and Juliet's family the Capulet's. The families have hated each other for many generations. Romeo and Juliet met at a party even though Lord Capulet has found Juliet a husband but she doesn't like him and falls in love with Romeo who was previously in love with Rosaline. Romeo and Juliet get married in secret hoping in the long run that this deed will end the family feud but Juliet's family don't know about the wedding. Mercutio Romeo's best friend and Tybalt Juliet's cousin get into a fight and Mercutio dies but Romeo turns up and kills Tybalt. Romeo is banished to Mantua for killing Tybalt so Juliet isn't happy because she has lost two of the people she cares about most. At the start of this scene Romeo has sneaked into Juliet?s bedroom and has stopped the night in her bed. In the morning Juliet does not want Romeo to leave as she exclaims ?it was the nightingale, and not the lark.? Which means that the nightingale sounds in the night and the lark sounds in the morning meaning that if it is the lark Romeo must go but Juliet believes it was the nightingale so that Romeo can stay? Romeo knows he must go and pronounces ?it was the lark, the herald of the morn.? Meaning that the lark is the sign of the morning and the nightingale sing?s at night so if it was the lark it would be time for Romeo to go but Juliet can?t stand it when Romeo is gone so she is convinced it was the nightingale. When the nurse comes in and tells Juliet that Romeo must leave because her mother is coming Juliet finally realises that Romeo has got to go and she starts weep for Romeo. When her mother comes in she assumes that Juliet is in mourning for Tybalt, ?Evermore weeping for your cousin?s death.? So Juliet just goes along with it ?feeling so loss, I cannot choose but ever weep the friend.? Lady Capulet tells Juliet her daughter that she will have happy days, ?sudden day of joy,? meaning that amongst all of this madness she will have a happy day. Juliet asks what will happen on this day and when this day is. Lady Capulet. ?Marry, my child, early next Thursday morn.? Juliet is very shocked by this, ?

Ethics of Autonomous Drones in the Military

Jared May Professor Elfstrom February 25, 2013 Intro to Ethics A Soldier, Taking Orders From Its Ethical Judgment Center In this article the author Cornelia Dean has three major points that are supported by arguments made by others. The first major important point is the hopeful idea that autonomous robots can perform more ethically in combat situations than any soldier in the same scenario.She states that even the best and most trained soldiers that are in the midst of battle may not always be able to act accordingly with the battlefield rules of engagement that were stated by the Geneva Convention because of possible lashing out from normal human emotions such as anger, fear, resent, and vengefulness. The second major point Dean wants to show, by the views and studies of others, in her article is that with this possible step in our evolution of military technology we do not want to let this idea fade away.Another major point is if we do develop this technology how would we do so, a nd if not, would we regret not advancing in this field further many years from now. With all of this information Dean uses to present her ideas there are still major flaws such as, the majority of these ideas and beliefs are theoretical, they still have not been fully tested, there is error in all technologies, and where else would the technological advancements lead artificial intelligence.The first argument providing support for Dean’s major point comes from the research hypothesis and thoughts of a computer scientist at Georgia Institute of Technology named Ronald Arkin. Arkin is currently under contract by the United States Army to design software programs for possible battlefield and current battlefield robots. The research hypothesis of Arkin is that he believes that intelligent autonomous robots can perform much more ethically in the heat of the battlefield than humans currently can.Yet this is just a hypothesis and while there is much research done towards this hypoth esis there are still no absolutely positive research information that states an autonomous robot drone can in fact perform better than any soldier on the ground or up in a plane could do. In Arkins hypothesis, he stated that these robots could be designed with no sense of self-preservation. This means that without one of the strongest fears for humans, the fear of death, these robots would be able to understand, compute, and react to situations with out outside extraneous emotions.Although the men and women designing these robot programs may be able to eliminate this psychological problem of scenario fulfillment, which will cause soldiers to retain information that is playing out easier with a bias to pre-existing ideas, it is not always the case that this happens to soldiers. You have to realize that from the second a soldier begins his training he is trained and taught to eliminate the sense of self-preservation. There are isolated incidents with soldier error, but they are and wi ll be corrected by superior officers or their fellow soldiers.Another factor that affects Cornelia Dean’s arguments is that there are errors in all things including technology. Throughout history there have been new uses of technology in warfare but with these come problems and error flaws that have cause and can cause more casualties than needed. With the use of an Automated drone the belief by Dean is that it will be able to decide whether or not to launch an attack on a high priority target whether or not if the target is in a public are and will decide if the civilian casualties would be worth it.But what happens if that drone is only identifying the target and the number of civilians surrounding it? It will not be able to factor in what type of people would be around him such as men, women, or children and any variance of them. The error in this situation would be the drone saying the target is high enough priority and a missile is launched and the civilians were women a nd children around while a school bus was driving by.The casualties would then instantly out weigh the priority to eliminate a specific target and a human pilot would much easier abort a mission than a predetermined response of an autonomous robot. Although Ronald Arkin believes there are situations that could arise when there may not be time for a robotic device to relay back what is happening to a human operator and wait for how to respond in the situation that could complete a mission, it may be that second of time delay between the robot and human operator that the ethical judgment is made.Also the realization that many robots in which are operated by humans are widely used to detect mines, dispose of or collects bombs, and clear out buildings to help ensure extra safety of our soldiers is a way that robots are already used today as battlefield assistants supports Dean. But all of these machines in the field have moments of failure or error. When the machines do fail it takes a soldier who has trained for that experience to fix and then use it again. If an autonomous drone fails while on a mission it is completely by its self and no human operator to fix it.Then can arise the problem of enemies realizing they were even being monitored and they could gain access to our military technology and can eventually use it against us. Another major point that Cornelia Dean discusses upon is with this possible step in our evolution of military technology we do not want to let this idea fade away. A large part of that is if we do develop this technology how would we do so, and if not, how much would we regret or how much would it affect us for not advancing in this field further many years from now.The argument that if other countries advance upon this faster and better than the United States military we could become less of a world power and be more at risk of attack and war with greater human fatalities is not necessarily true. This situation is important in the sen se of keeping up with the other world powers but I believe that the risk for reward is not worth the amount of damage and civilian casualties that could happen from any number of robotic drones and their possible errors.There is a possibility as the technology develops and robots become more and more aware to the point were, Arkin believes that, they can make decisions at a higher level of technological development. Yet if these autonomous robots truly can think for themselves and make decisions brings a whole new possibility of problems of what if the robot can decide something differently than what the developers originally had programmed. Also comes the actual use problem of can the government ethically accept that in early stages of use, even after extraneous testing, there may be accidental casualties.If a robot has any error of making decisions because of how new and un-tested they are any of the possibly terrible results would not be the responsibility of the robot but of the country and government that designed it. The supporting evidence of this article strongly shows that Cornelia Dean will hope that use of these ethically superior autonomous robots will be apart of our military in the near future before the United States fall behind to other super powers in the world.Yet with all of this information Dean uses to present her ideas there are still major flaws such as, the majority of these ideas and beliefs are theoretical, they still have not been fully tested, and that there is error in all technologies. With these major points being enforced with plenty of evidence throughout the article, and with all of the possible negative sides and errors of this argument, it is safe to say that this will be and is a controversial topic of discussion by many governments and all parties involved with this technological advancement.