Music History Essay Example for Free

Music History Essay Music, as they say, is a universal language. Unlike dialects, music can be understood by many sans, the lyrics spoken in a different country. The simple humming of a child, done in mostly minor chords, can make everyone feel a little emotional or sad. A happy song filled with trumpets, saxophones and lively guitar tabs can make people excited and get them all to dance. Music can unite people regardless of their age, gender and race, which is why it is considered a universal language. Through Those Years The history of music dates back before the 1800s, but that is only to put a legal timeline to the evolution of music. Since music is universal, it is then safe to say that it has started even in the beginning of the world. The first human beings, or the first animals, for that matter, depended on sounds that make up a structure filled with patterns that were easily remembered, which conveyed a meaning and made people do things like hunt for food, identify where the predator or the prey is, or go where they should go. Music was a sign and a symbol that represented something (Murray, 2004, p. 773). Technically, though, music before the 1800s existed already, in a more technical sense of the concept. Music was then not just a collection of different sounds. It became a study where people researched about it. During the 18th century, the book entitled History of Music was written and published by GB Martini. Its original title was Storia Della Musica. Other books followed after GB Martins, and among the many books that were published after the first one were De Cantu de Musica Sacra and Scriptores Ecclesiastici de Musica Sacra. The types of music being studied, during these times, were classified as sacred music (Murray, 2004, p. 773). During 1800-1950, the evolution of music can be seen and musical history was being more defined. It didn’t take too long when Johannes Wolf started to do more studies about music, specifically the type of sound that emerged during the Medieval and the Renaissance times. Musicologists depended much on the studies conducted by Johannes Wolf. Because of this, a branch of art called historical musicology was termed and developed. This branch of study became a significant part of the Baroque music. It also became an instrument to the development of music during the Medieval and the Renaissance era. In particular, the movement of original performance has a lot to do with the scholarship associated with the history of music. Musicology became a big part of the arts, and became more and more developed as time passed by. It soon became a field of study. Consequently, journals, researches, articles and new analyses are being developed to branch them out altogether, in order to produce more studies to be published. Music was being more defined as years went by, and it was spreading like fire all over the world (Murray, 2004, p. 773). Ancient Music To understand the history of music and how it changes, it is then best to use a chronology to explain the turn of events. First there was ancient music. This type of music reflects all the types of music that developed in the different parts of the globe, like Mesopotamia, Egypt, Rome, Greece, China, India and Persia. In fact, music was already popular and rich in countries like Rome, Greece and Mesopotamia. Whatever was audible to the people were characterized through basic scales and tones, and then came music. Music spread throughout history through systems, either written or oral (West, 1994, p. 13). The definition of ancient music differs from time to time because of how much music is already revolving, and is continuously revolving. Today, if one defines ancient music, he can say that it is the modern sound that still resembles whatever is folk and traditional in that country. Today, there are modern sounds that Muslims, Egyptians, Jews, Asians, Persians, and Indians produce, but still has not left behind the oldest and most basic of original ancient music (West, 1994, p. 13). Persia, for example, flute, lute and guitars were already being played. Religious rituals were not complete in Persia without music. Music was significant in the lives of the Persians, especially in their spiritual life. It was in Mesopotamia where the first traces of writing were seen. It was the same time when researchers and historians traced instructions for music. The traces were fragmentary, but the authorities were sure that there was music during this time in this place. In fact, music was in made in thirds when it comes to harmony. The scales of the musical pieces produced were even diatonic (Leichtentritt, 2007, p. 14). Up to this day, though, how the researchers can interpret the symbols in the ancient Mesopotamia is not a hundred percent clear. There are still controversies that have yet to be discussed and settled. The interpretation of the symbols remains to be vague. But one thing is sure; all the notations made on the cuneiform tablets were clearly that of the tunings and strings of a musical instrument called a lyre. It was also during this time when harps were invented and became a big part of the history of music (Leichtentritt, 2007, p. 14). In India, ancient music was also active. Indians were always enthusiastic when it comes to the type of musical instrument they were playing. Musical instruments were all around India. This can be proven by how much instruments were amassed from the Indus valley civilization. Archaeological sites can prove all these. Indians had forms of music that includes Samaveda, Rigveda and Samagana. Their music was characterized from hymns, verses and melodies. It was in religious rituals where music was used the most. Indian music had basic ingredients to make a sound â€Å"Indian. † During the first part of a song, Shadja is always established. The grama, in this case, is being defined. Grama is the Indian term for the note of the scale. Indian music also lives by the two principles of consonance, which involves Avinashi and Avilopi. Avinashi is a fundamental note that should always be present in a musical piece, and with Avilopi it means that the note should never change, and that it should always stay there in that particular music piece, according to Leichtentritt (2007, p. 14). Greek’s music has evolved through time. The Greeks have original musical notation style. They developed their own, no matter how robust it is. While it is true that the best musicians in Greece did not necessarily use their musical notations produced originally, it cannot be denied that a lot of Romans and Greeks still use of that original musical notation. Greek music was not exactly monophonic, although this was almost established with their style of music (West, 1994, p. 13). There was always more than just a note to be sounded at a similar time. Double pipes and bag pipes were mostly used. These can be proven also by the ancient drawings seen on the vases and the walls of Greece. Even the oldest Greek books had authors who were able to describe what different musical techniques were being used during these times. Double flutes were also popular in Greece (West, 1994, p. 13). Middle Eastern After the Ancient music came the Middle Eastern music. Middle Eastern music was rich in that it was characterized by different styles from different regions. When one goes to the Middle East, there are different types of music that can be seen, like â€Å"zajal, Turkish folk music, Turkish classical music, sha’abi, Sufi music, rapbesk, rnbesk. Somali music, pizmonim, Persian folk, Nubian music, mawwal, Kurdish music, Egyptian Chaabi and el-Gil, Egyptian Classical music, Berber music, Arabic Andalusian, Arabesque music, Arabic rap, Arabic pop, Algerian rai and Arabic Classical Music (Stanley, 1997, p. 126). † The Islam community displays its great influence coming from the Middle East music. In fact, as the Islam used music in their rituals, Middle Eastern music spread even more quickly. The identity of Middle Eastern music is defined from the melody which is still present today in modern Middle Eastern pop and liturgical music (Stanley, 1997, p. 126). Classical Music Music evolves all around the world. In the West, music has gone a long way from the classical compositions of great masters like Wolfgang Amadeus Mozart, Ludwig van Beethoven, Carl Philipp Emanuel Back, and Franz Schubert to the catchy modern pop songs of today. It’s kind of hard to imagine how music has evolved from those grand compositions to the contemporary quirky beats we listen to today, but that just proves how quickly music transforms according to the needs of the people (Stanley, 1997, p. 154). The Classical period in the West dates from about 1750 to 1820. Classical music refers to various styles of music with roots in the secular and liturgical European musical traditions of the 9th century. This type of music is characterized by romantic melodies using instruments like violins and flutes (Stanley, 1997, p. 154). One striking characteristic of classical music is its elegance. This elegance is achieved by the composers’ close attention to balance and proportion. For this reason, classical music never becomes obsolete. Up to now, many people around the world, whether they live in the West or not, still listen to classical music. Some people study their structures and attempt to recreate classical music using modern instruments. Others simply enjoy their relaxing melodies, which may aid them to concentrate on their tasks or even sleep better. There is even a concept called â€Å"Mozart effect†, as explained by Stanley (1997), which says that children who are exposed to the classical music of the great genius that is Mozart are able to concentrate more on their tasks, thus resulting in better performance in school. This is just one example of the newly discovered benefits of music that are surprising ordinary people and experts around the world (Stanley, 1997, p. 8). Western Music through the Years As the power of the West became stronger and reached farther into different corners of the globe, music itself has gained the imprints of Western culture. More and more people heard and recognized the merits of Western music. Countries that were once colonies of Western countries are especially influenced by Western music because the language barrier is weaker. Today, the dominant music is the world comes from the West. Classical, blues, jazz, rock, hip-hop, ballads, R n B – all of these have roots in the West. The amazing thing is that since music is universal, people of different races and cultures around the world can appreciate these Western genres of music. Western music may influence local music, but the traditional character of music never goes away. For instance, in Japan today, pop music has obvious Western overtones, but most pop hits are all sung in Japanese. J-pop, as Japanese pop is locally called, is influenced by Western music in a lot of ways, but its characteristics are still a lot different from Western pop music. The Music of the ‘40s and ‘50s The invention and mass production of radios during the 1940s and 1950s facilitated an amazing development in musical styles. In many ways, World War II has also changed the face of music dramatically as people expressed their disappointments and rebelliousness against the war through music (Melton and Weinstein, 2001, p. 17). Rock and roll has its roots in the 1940s, along with other musical genres such as country, jazz, swing, folk, and boogie woogie. In the United States, different musical styles were expressed by different races. Blacks had difficulty hitting the mainstream until the king of rock and roll, Elvis Presley, sang rock and R n B. Elvis was able to show the whites the excellent beats of rock music, which made its crossover into mainstream a lot easier. Elvis eventually became one of the biggest icons of rock and roll in the United States and around the world (Melton and Weinstein, 2001, p. 17). The Music of the ‘60s and ‘70s Music received huge social influences again during the 1960s and the 1970s because of the Vietnam war, the Cold War, and the spread of the Civil Rights movement. During this period, music clearly became a platform for various causes, including feminism, race empowerment, sexual freedom, and other liberal ideas (Frith, et. al. , 2001, p. 77). There are many musical icons that gained fame during this tumultuous period in musical history. Musicians like Joan Baez and Bob Dylan pioneered new techniques in lyrical composition. These new techniques inspired more artists such as Cat Stevens, Carole king, Elton John, and James Taylor to create their own groundbreaking chart-topping hits. The ‘60s were filled with R n B hits that were a combination of secular and gospel music. Different kinds of soul music emerged in this time, including Philly soul, Memphis soul and Motown. Popular artists such as Marvin Gaye and James Brown also found fame and fortune in the 1960s (Frith, et. al. , 2001, p. 77). Of course, music in the 1960s and 1970s cannot be discussed without mentioning the band that is probably one of the biggest influences of contemporary music: The Beatles. John Lennon, Paul McCartney, George Harrison and Ringo Starr drew huge crowds to their concerts and sold millions through their hits. The band not only became huge in England, but also in the United States and in other countries as far as the Philippines (Frith, et. al. , 2001, p. 74). One of the amazing things about The Beatles is their ability to change the musical landscape. While their early hits had rhythms and melodies that have the basics of rock and roll, their later albums explored new horizons. Their album, Sgt. Pepper’s Lonely Hearts Club Band was ranked by Rolling Stones magazine as the greatest album of all time. This recognition is due to the immense influence of this album on the musical styles of later genres of music (Frith, et. al. , 2001, p. 74). Music of the ‘80s and the ‘90s Western music continued to gain wide acceptance around the world during the 1980s. New Wave, hip-hop, punk rock, and heavy metal increased their markets and new musical stars were born. New Wave experimented with electronic sound and catchy, playful beats which people danced to. The various styles of rock music provided the youth the avenue to express their adventurousness and rebelliousness against the fast-paced modern world. During the 1990s, grunge musicians led by the band Nirvana took center stage in the music world. Their honest and rough lyrics reflecting the confusion and apathy of the youth, and their loud, distorted riffs gained millions of fans in the United States. Meanwhile, hip-hop also gained wider popularity as hip-hop stars such as Dr. Dre and Puff Daddy broke into the music scene with fresh raps and rhythms (Chambers, 2002, p. 166). The 1990s were also notable for the huge popularity of boy bands, which are boy groups that sang ballads with catchy beats and lyrics. Some of these boy bands included Backstreet Boys, NSYNC, Westlife, and A1. Boy bands became hugely popular because of their romantic songs which people can sing and dance to. Another group that is worth noting is the Spice Girls who originated from the United Kingdom. This group symbolized the power of women through their songs and videos. Interestingly, the Spice Girls were a hit for both males and females. After the Spice Girls, many other girl bands soon formed, but none of them reached their extraordinary level of popularity (Chambers, 2002, p. 166). The State of Music Today Today, contemporary music is still strongly influenced by the West. Pop, rock, hip-hop, R n B, and other genres have Western musicians leading the pack. Local music in different countries, though, are also gaining wider acceptance by fusing with the dominant music of the West or borrowing some of its elements. Music today is also crisper and clearer; thanks to the high level of technology that humans have achieved through science. Albums are released in CDs or DVDs, and they can also be downloaded on the Internet. Storage of music became a lot simpler, too. Before, you need bulky gramophone records to store music. Now, all you need is a tiny universal serial bus (USB) storage device to archive all the music you want. MP3 players have also made listening to music easier since these devices can be worn or slip inside a pocket. People can now go anywhere listening to their favorite songs. The West has no monopoly over music, though. All around the world, many people are rediscovering the beauty of their own local melodies, and they are breathing new life into them again in the form of world music. This musical style makes use of indigenous instruments and they usually are not accompanies by lyrics. Less popular genres like this are usually produced by independent producers, thus the term â€Å"indie. † Indie though, has its own market and continues to grow in popularity as people try to taste new musical types (Chambers, 2002, p. 166). The Human Experience of Music People change as music transforms as we’ve seen in our discussion of the long continuing history of music. Music is an expression of the culture that gives birth to it, and it constantly bends as various influences impinge upon it. It is an art form that never stays the same, but evolves through time. Music though doesn’t transform on its own. Historical events shape music as they shape the lives of people. The art form becomes a reflection of the hopes, dreams, and grievances of the people that create and listen to it. We can see this clearly in the rebellious attitude of the music from the ‘40s and ‘50s because of World War II, and the free spirit of the music from the ‘60s and ‘70s as it protested against the Vietnam War and the Cold War (Frith, et. al. , 2001, p. 77). In many ways, musicians deliberately voice out their protests through the songs that they sing. For example, John Lennon’s â€Å"Imagine† is a clear reaction to the dangers of the Cold War and other social inequalities at that time (Frith, et. al. , 2001, p. 77). However, music doesnt always send clear messages all the time. In fact, most of the time, composers unconsciously express their sentiments and the sentiments of their generation through the beat of their songs, or through their melodies. Perhaps the greatest thing about music is its universality. Since everyone can appreciate good music, the art form traverses national and ethnic boundaries, bridging people together no matter where they come from. Good music will always be good music regardless of a person’s educational or cultural background. Of course, a person may need to expose himself repeatedly to a new genre to appreciate its beauty. But it’s not difficult to do that if the genre is indeed good. The universality of music is now more apparent than ever before because of the Internet. Musical influences are easier to share ever since artists living in opposite sides of the globe can listen to each other’s work. It’s not only artists though who benefit from the cyberspace, but also the listeners. Downloadable MP3 songs are all over the Internet, some of them free, others for sale for a small price. With a click of a mouse, a person online can listen to Middle Eastern music, classical music, rock and roll, hip-hop, world music, or whatever genre he wants. Music is bringing people closer and closer to each other. Time and space are quickly becoming negligible factors as people find satisfaction and comfort in just enjoying different musical styles. Old styles themselves are disappearing as traditional barriers are broken and various genres fuse together to create new ones. The result is that people are able to understand each other better through listening to different kinds of music. People are becoming more tolerant of each other’s differences as they see that theyre all just human beings enjoying music The future is bright for musicians and listeners around the world as technology allows music to cross more borders. Soon, everyone will be able to appreciate a variety of musical genres regardless of their original countries or ethnic backgrounds. As people listen to their CDs, MP3s and musical devices, they will realize that their hopes and dreams are one. They will realize that while music came from different corners of the world, it speaks of the universal desire of human beings for unity and peace. Bibliography Chambers, Stuart. (2002) Yes: An Endless Dream of 70s, 80s and 90s Rock Music : an Unauthorized Interpretative History in Three Phases. General Store Publishing House. Frith, Simon, Will Straw and John Street. (2001) The Cambridge Companion to Pop and Rock. Cambridge University Press. Leichtentritt, Hugo. (2007) Music, History and Ideas. Read Books Publications. Melton, William and Randy Weinstein. (2001). The Complete Idiots Guide to Playing the Harmonica. Alpha Books. Murray, Christopher John. (2004) Encyclopedia of the Romantic Era, 1760-1850. Taylor Francis Publishing, Inc. Stanley, John. (1997) Classical Music: An Introduction to Classical Music Through the Great Composers Their Masterworks. Penguin Group USA. West, Martin Litchfield. (1994) Ancient Greek Music. Oxford University Press.

The Mathematical Mystery Behind Sudoku Mathematics Essay

The Mathematical Mystery Behind Sudoku Mathematics Essay Puzzle games can be very enjoyable and is popular amongst kids as well as adults. Many of you may know the game Sudoku; where by the goal of the game is to fill in the remaining empty cells with each number from 1-9 appearing no more than once from each column, each row and each of the nine sub-grids. Sudoku is a type of logic-based numerical puzzle game that has a unique solution once completed. The most common form of a Sudoku is constructed as a 99 grid with nine 33 sub-grids and is primarily partially completed. Sudoku has become appealing among puzzle enthusiasts and involves complex thinking and practice. Available daily in newspapers, mobiles and many more, this addictive and brain-teasing puzzle game has become one of the most popular games to play since the time of the Rubiks cube. This dissertation discusses the mathematical side involved in Sudoku. There is no mathematics in actually solving a Sudoku but more of how it is used from a creators side. The 99 grid will be considered in the majority of the report; however a glimpse into other size grids will be discussed briefly also known as variants. Mathematicians have been questioning How many unique solutions are there in a Sudoku? Essentially meaning what are the possible ways of filling in an empty Sudoku grid so that each row, column and sub-grid contains the numbers 1 through 9. Your first thought of an answer may be a couple of thousands, but as you understand the concepts behind a Sudoku, you begin to grasp a whole new aspect. Combinatorics and permutation group theory are largely interwoven with analysing Sudoku. For that reason, I aim to explore these theories and understand how it applies to the methods of enumerating Sudoku grids. In particular I will be looking at Felgenhauer and Jarviss approach to enumerating all possible Sudoku grids where they employ several mathematical concepts. Furthermore I will uncover the importance of Latin squares and its use of constructing Sudokus. There are many constraints in regards to when are similar solutions considered different such as solutions of similar structure, symmetry etc. Preserving symmetries are known as relabeling symbols, band permutations, reflection, transposition and rotation. Burnsides Lemma theorem is one of their techniques in computing the number of essentially different solutions. Many difficult problems are of the type called nondeterministic-polynomial known as an NP-complete problem. This will direct me onto the debate on whether Sudoku is an NP-complete problem. Sudokus can take many forms and shapes. These are called Sudoku variants and consist of rectangular regions, Sudokus with a large region having no clues (numbers), an empty row, column or sub-grid and many more! Here I will research the logic behind irregular Sudokus as well as examining any occurring patterns or whether it has occurred by chance. 1.2 Latin squares and Sudoku Sudoku is also a special case of Latin squares. The Swiss mathematician, Leonhard Euler made many fundamental discoveries during 1782 including Latin squares. A Latin square is an N x N matrix where by a set of N characters are arranged such that each row and column contains one of each character. This is also in the case of a Sudoku, when complete, with an additional constraint that the nine sub-grids must hold the numbers 1-9. A reduction can be made to any Latin square by permuting the rows and columns. This arrangement is an aspect of combinatorics and is most commonly referred to as enumeration. Enumerative combinatorics is a classic area of Combinatorics and involves counting the number of infinite class of finite sets. Counting combinations and counting permutations are two of the most common forms. The number of valid Latin squares is known to be approximately 5.525 x 10 ²Ãƒ ¢Ã‚ Ã‚ ·. Write about Colbourns proof 1.3 Combinatorics and Permutation group theory Combinations and permutations have slightly different meaning. Combinations are the number of different ways of selecting n objects from a set but the order of events is not important. From a set of 3 objects, lets call these 1, 2 and 3. If for example I was asked to pick the number of ways of selecting 2 objects out of the 3, there would be three combinations 12, 23 and 13. 12 = 21 since the order of each pair is not important. A permutation on the other hand does consider the position. Therefore if I was to use the above example, there would be six permutations. A simpler way to calculate a larger set would be to use formula 1: Formula 1. = = Where is the combination formula, is the permutation formula, n is the total number of objects and r is the number to be arranged Both methods are one way of computing the number of possible Sudoku solutions and this will be looked at later in the report. Chapter 2 Enumerating possible Sudoku solutions 2.1 Distinct Sudoku solutions There are many approaches to enumerating possible Sudoku solutions. To enumerate every possible Sudoku solution, a Sudoku differs from another if they are not identical. Thus all solutions will be consider unless they are like for like. Felgenhauer and Jarvis was the first to enumerate the Sudoku grid solutions directly in 2005. There approach was to analyze the permutations of the top row used in valid solutions. Their knowledge of the complexity in computing the number of Latin squares has made them aware of how they should go about getting an answer with fewer computations. Hence by using relabeling this could shorten the number of counts. To make it easier, each sub-grid is given an abbreviation seen in figure 3. B1 B2 B3 B4 B5 B6 B7 B8 B9 Figure 1. Abbreviated sub-grid with top band (Felgenhauer and Jarvis, 2006) Firstly they consider every solution to filling in blocks B2, B3, given that B1 is in standard form. To work out every possible way of arranging B1 on its own would essentially be computing the number of permutations of 9 symbols. There are 9! of filling in B1. The main operation they use is called relabeling. 1 2 3 4 5 6 7 8 9 Figure 2. B1 in standard form (Felgenhauer and Jarvis, 2006) Felgenhauer and Jarvis have found that B2 and B3 is the same as the transpose of B2 and B3. Therefore the number of ways of arranging B1, B2 and B3 and B1, B2 and B3 to a complete grid is equally the same. This means that computing one set of possibilities will cut down the number of solutions. Inevitably, there are few pairs of B2 and B3 that needs to be worked out and as well as using reduction the number of possibilities for the top band of a Sudoku grid is 9! x 2612736 = 948109639680. The next section involves brute force computation. As running through all 2612736 possibilities would be exceedingly tedious for B2 and B3, Felgenhauer and Jarvis attempts to identify configurations of the numbers in these blocks which give the same number of ways of completing to a full grid. This in return, will cut down the number possibilities. Permuting B2 and B3 in every way such that the result gives a unique solution will preserve the number of complete grids. This is the same for B5 and B6, and B8 and B9. However this changes B1 from its standard form, so an additional relabeling of B1 needs to be performed. Another approach to reducing the number of possibilities is to permute the columns in each block and permute the rows of any block. Reducing the number of possible ways by permuting. Lexicographical reduction Permutation reduction Column reduction As a result of these methods, Felgenhauer and Jarvis have found that there are approximately 6670903752021072936960 à ¢Ã¢â‚¬ °Ã‹â€  6.671 x 10 ²Ã‚ ¹ Sudoku solutions. In light of this result, there are fewer solutions than Latin squares due to the fact that there is that extra restriction of 9 sub-grids. That being said, there will be no shortage of Sudoku puzzles any time soon. Verification of this result has been confirmed by several other mathematicians Ed Russell to be more precise. 2.2 Essentially different Sudoku grids Whether symmetrical Sudoku grids are considered as two separate solutions is another method of enumerating the possible solutions. In this case, the only solutions are ones that are essentially different. Lets say two Sudoku grids are equivalent if one is a transformation of the other by applying any number of symmetries. If however, no such chain of symmetries can occur between two grids, it is essentially different. Two Sudoku grids are the same provided the first grid can be converted to the second by applying some sort of symmetry. For instance, take figure 3 4 below; the set of 3s in the first grid can be interchanged by the placements of the set of 1s, effectively producing the second grid. 1 7 2 8 6 4 9 3 5 4 9 3 5 1 7 2 8 6 6 5 8 2 9 3 1 7 4 2 4 7 3 5 9 6 1 8 8 6 5 1 7 2 3 4 9 3 1 9 4 8 6 5 2 7 5 8 6 7 2 1 4 9 3 9 2 4 6 3 8 7 5 1 7 3 1 9 4 5 8 6 2 Figure 3. Valid Sudoku grid 3 7 2 8 6 4 9 1 5 4 9 1 5 3 7 2 8 6 6 5 8 2 9 1 3 7 4 2 4 7 1 5 9 6 3 8 8 6 5 3 7 2 1 4 9 1 3 9 4 8 6 5 2 7 5 8 6 7 2 3 4 9 1 9 2 4 6 1 8 7 5 3 7 1 3 9 4 5 8 6 2 Figure 4. Another valid Sudoku grid from Figure 1 As well as this, a solution is said to be the same as another if any two columns or rows are swapped. The first column and second column in figure 3 can be exchanged to give figure 5. The two solutions are said to be symmetrical because the transformation still produces a valid Sudoku grid. 7 3 2 8 6 4 9 1 5 9 4 1 5 3 7 2 8 6 5 6 8 2 9 1 3 7 4 4 2 7 1 5 9 6 3 8 6 8 5 3 7 2 1 4 9 3 1 9 4 8 6 5 2 7 8 5 6 7 2 3 4 9 1 2 9 4 6 1 8 7 5 3 1 7 3 9 4 5 8 6 2 Figure 5. First and second column swapped from Figure 1. Another form of symmetries includes rotational grids. A rotation of Figure 3 by 90 degrees generates a new valid Sudoku grid shown in Figure 6. 7 9 5 3 8 2 6 4 1 3 2 8 1 6 4 5 9 7 1 4 6 9 5 7 8 3 2 9 6 7 4 1 3 2 5 8 4 3 2 8 7 5 9 1 6 5 8 1 6 2 9 3 7 4 8 7 4 5 3 6 1 2 9 6 5 9 2 4 1 7 8 3 2 1 3 7 9 8 4 6 5 Figure 6. Rotational of 90 degrees from figure 1 These operations performed above maintain the property of it being valid and this is known as symmetries of a grid. When an object is subject to these operations, certain properties are preserved. An example would be if one performs symmetry on to a Sudoku grid and repeats this operation once more, the final transformation is itself symmetric. In addition a symmetrical object can be transformed back to its original state by another form of symmetry. Performing several symmetries on a Sudoku grid can also be achieved by grouping its neighbouring pair. So the first symmetry can be paired with the second or the second can be paired with the third and so on. The resulting transformation is nevertheless the same either way. From these properties, it is inevitable to say that the set of symmetries form a group of any Sudoku grid. A group is a set G if it satisfies the following properties: CLOSURE If f and g are elements of G, then f ·g is also an element of G. ASSOCIATIVITY If f, g, and h are elements of G, then f ·(g ·h)=(f ·g) ·h must satisfy. IDENTITY ELEMENT There is an element e in G such that g ·e=e ·g=g for all g in G. INVERSE For any element g of G, there is another element d of G such that g ·d=d ·g=e, where e is the identity element. (The element d = g-1.) The symmetry group is thus generated by the transformations of: re-labelling the nine digits, permuting the three stacks (3 vertical blocks of a Sudoku), permuting the three bands (3 horizontal blocks of a Sudoku), permuting the three columns within a stack, permuting the three rows within a band, and any reflection or rotation. Any two transformations can be merged to shape other elements and together they comprise of the symmetry group G. Given that any element of G can be mapped so that it takes one grid to another, we can say that the set of valid Sudoku grids has a finite number of elements. Thus G has finitely many symmetries. The association between symmetrical Sudoku grids are in fact an equivalence relation and satisfies the following three properties: for grids A, B and C in set G Reflexivity A = A Symmetry If A = B then B = A Transitivity If A = B and B = C then A = C Let A be any valid Sudoku grid, we must consider all the grids that are equivalent to a valid Sudoku grid A. To do this, we firstly have to group together grids that are essentially the same so that we can partition the set of grids. This will break the set of Sudoku grids into subsets, with groups that contain no relating elements within each other. The term subset can be called equivalence classes. This can also be referred to as X/G. In any equivalence class, there are elements that are equivalent to each other by symmetry. The total number of elements in X/G is equal to the number of essential Sudoku grids. To enumerate all essential Sudoku grids, we shall look at all the symmetries neglecting the re-labelling of the nine digits for the time being. The number of distinct symmetries founded by Russell and Jarvis (2006) is said to contain 3359232 (pg 4). In this finite group H, we need to find the average number of grids fixed by an element of H, up to re-labelling. Next we need to verify the number of fixed points of all elements in H. Russell and Jarvis have found that there are 275 classes of symmetries using a software package called GAP. It is interesting to note that some of the elements in H contain equivalent fixed grids. In other words, it is now easier to work out as each of the classes contains one symmetry. However a number of symmetries in H have no fixed points. Subsequently, it is not necessary to calculate the number of fixed grids for those that have no fixed points. That being said, there are only 27 out of 275 classes that contain fixed points, meaning fewer computation s. Rotman. J. J (1995) demonstrate that if X is a finite G-set and |X/G| is the number of G-orbits of X, then Formula 2 holds where, for gцG, X is the number of xцX fixed by g (pg 58-61). Using this notion, we have established that the number of valid Sudoku grids is of a finite set and X/G is the number of essentially different Sudoku grids, so we can obtain the number of essentially different Sudoku grids by using the Burnside Lemma Theorem. Formula 2. Burnside Lemma Theorem (Rotman, 1995) Burnside Lemma Theorem is a useful tool when dealing with symmetry with a set of countable objects. When used to enumerate the essentially different Sudoku grid, the set of equivalent grids form an orbit of the symmetric group. The number orbits are essentially the number of different grid solutions. This may sound slightly (ALOT) trickier to compute, nonetheless Russell and Jarvis have shown that the number of essentially different Sudoku grids is 5,472,730,538 with the implementation of Burnsides Lemma Theorem. Chapter 3 Nondeterministic polynomials 3.1 NP-complete and Sudoku Sudokus may relate to a variety of problems, in particularly, whether Sudoku is an NP-complete problem. It is known that NP-complete problems are one of the most complicated cases in NP, also referred to as nondeterministic-polynomial. Its rival, P problems relates to NP as both being in the same complexity class. Mathematicians have yet to solve whether NP-complete problems can be solved in polynomial time or more commonly whether P = NP. Consequently being one of the greatest unsolved mathematical problems. The majority of computer scientists believe that P à ¢Ã¢â‚¬ °Ã‚   NP, as a result would mean that NP-complete problems are significantly trickier to compute than to verify. Unfortunately, nobody has yet found an efficient algorithm, not even with the use of computers available today. A problem is said to be NP-complete when its solution can be proved in polynomial time. And if that problem can be solved in polynomial time, all problems in NP can be solved too. An interesting characteristic of NP-complete problems is that the time frame to solve the problem increases rapidly as the size of the problem gets larger. If that is the case and Sudokus are NP-complete, solving a Sudoku of higher order (say 17 ² x 17 ²) will become increasingly challenging algorithmically then the standard 3 ² x 3 ² version were talking trillions of years. It has been shown that Sudoku does belong to the category of NPC problems by Takayuki Yato of the Univeristy of Tokyo (2003). An exchange for the notation ASP-completeness (shorthand for Another solution problem), led the proof of NP-completeness of ASP. Their proof uses reduction in order to obtain the required polynomial-time ASP from the problem of Latin squares by Colbourn (1984) who has verified, the NP-completeness of ASP of Latin square completion Another accountable source by Provan states that, It is known that solving general-sized Sudoku puzzles is NP-hard, even for square grids with blocks consisting of the sets of rows and columns (Latin Squares) or for p2 x p2 grids with blocks consisting of rows, columns, and the p2 partitioned p x p subsquares. Mathematical programmes such as the 0-1 linear programming and the knapsack problems are also cases of NP-complete problems. A full list of other problems that are NP-complete can be found in Garey and Johnson (1979). Chapter 4 Sudoku Variants 4.1 Variation The classic form of a 99 Sudoku are polyominoes. There are other variations of Sudokus that can be applied to the rules of Sudoku. There are puzzles of the size 66 with 23 regions or a 1212 grid of 43 regions. More so, there are other fascinating Sudoku variants such as Greater than Sudoku. Chapter 5 Personal Critical Review The progress I have made during the duration of this project, have been fairly slow but surely getting there. Having said this on many occasions, I have still not conquered my time management skills! The project started very slow which meant I was behind schedule. Nevertheless my organisational skills have kept me on balance. The GANT chart has been of great help in doing so. What has kept me going throughout this project in particular would be self discipline and motivation. This project has proven that I am capable of working to my own initiative, but also well within a group; my time during the group project. Furthermore, my time on this project has definitely promoted a better mentality of my future ambitions. I have learnt that it is crucial to read a lot, as well as reading as broadly as I can. This in turn have aided in the running of my project. With other coursework deadlines, I made that a priority and had no time to meet with my supervisor. I understand that meeting with my supervisor is equally important because a supervisor is there to encourage and to advice on any difficult obstacles I may encounter. An area of interest to proof whether NP-complete problems can be solved in polynomial time, was left open as future work. This could be the next step of extending this report that little bit further. Chapter 6 Conclusion A challenging problem for further research is to proof whether NP-complete problems can be solved in polynomial time. This has yet to be solved and anyone who has a formal proof will be rewarded $1 million dollars by The Clay Mathematics Institute.

Garlic And Abate As Larvicide Against Mosquito Larvae Biology Essay

Garlic And Abate As Larvicide Against Mosquito Larvae Biology Essay This experiment was designed to investigate and compare the effectiveness of garlic as the natural larvicide and Abate as the chemical larvicide against mosquito larvae. The effectiveness of the larvicides was determined by the time taken for all the mosquito larvae to be killed. The mosquito larvae were placed in separate plastic cups containing garlic extract and Abate respectively. They were monitored at fixed time intervals and the time taken for all the mosquito larvae to die was recorded. The experiment was repeated with different concentrations of garlic extract and Abate. A two-way ANOVA statistical test showed that Abate is more effective against mosquito larvae at 5% significance level compared to garlic, corresponding to the experimental hypothesis. Research and Rationale Mosquitoes originate from the family Culicidae.13 Like many other insects, they go through a life cycle from egg to larva, pupa and finally adult. They are generally well-known as blood-sucking insects to human and they are responsible for many fatal diseases such as dengue, malaria and yellow fever. Some commonly known genera are Aedes, Culex and Anopheles. Usually, mosquitoes breed in stagnant water like ponds, marshes and swamps and they thrive in warm climates.9 (210 words) In order to control mosquitoes, chemical larvicides are used. One commonly used larvicide, Abate is applied to stagnant water to kill larvae of a wide range of pathogen-carrying vectors (mosquitoes) to hinder their development into adult mosquitoes.2 Consequently, this prevents disease-carrying mosquitoes from hatching and transmitting the pathogens to human via bites. Although the active ingredient of Abate, temephos is said to be effective against mosquito larvae (affects the nervous system by inhibiting cholinesterase enzyme), it has its downsides. Research has shown that certain mosquito species (Aedes albopictus and Aedes aegypti) have developed resistance for Abate.4 In addition, rats exposed to temephus showed organic phosphorus poisoning while some fish are vulnerable to temephus. Temephus also harm inverterbates such as shrimps and crabs. Accumulation of temephus may also cause drastic impacts on cholinesterase activity involved in nerve signal transmission.6 Plant extracts such as those of garlic are potential alternatives to Abate. Crushing garlic releases thiosulfinates which convert into diallyl disulfide and diallyl trisulfide if mixed with water.10 These two products formed are effective against mosquito larvae. Trials conducted in Bombay have shown that several species of mosquito larvae are susceptible to garlic extracts. Allicin helps to curb malaria by preventing the formation of circumsporozoite protein (CSP) of Plasmodium sporozoites to infect host cells.10 They are effective, safe, environmental-friendly and economical. The objective of this experiment was to investigate and compare the effectiveness of garlic as the natural larvicide and Abate as the chemical larvicide against mosquito larvae. The results from this experiment indicate that the spread of pathogen-causing diseases by mosquitoes can be curbed by using natural substances such as garlic as well as chemical larvicide like Abate. Garlic is a potential alternative to Abate as it is effective, easily available and eco-friendly. Although it might not be as fast-acting as chemical larvicides, garlic has none of the downsides of Abate such as accumulating in the environment and killing other invertebrates. Thus, more research is being conducted to investigate the efficiency of garlic as a larvicide. (545 words) Experimental hypothesis There is a significant difference between the effectiveness of garlic and Abate as larvicide. Abate is more effective larvicide compared to garlic. Null hypothesis There is no significant difference between the effectiveness of garlic and Abate as larvicide. Variables Manipulated variable : Types of substances Responding variable : Time taken for all the larvae to die Fixed variables : Number of mosquito larvae, volume of distilled water, room temperature Apparatus 100mL measuring cylinder, electronic balance, plastic cups, label stickers, pestle and mortar, disposable droppers, glass rod Materials Mosquito larvae, garlic cloves, cinnamon powder, fennel powder, Abate 1.1G, distilled water Planning A trial experiment was conducted to determine which natural substance has the most significant effect on mosquito larvae. The three natural substances used were cinnamon powder, fennel power and garlic cloves. Three labelled plastic cups were used. About 1% of each respective natural substance extracts were made by either dissolving 1g of the powder in 100mL of distilled water or pounding 1g of garlic and then mix with 100mL distilled water. Using a disposable dropper, 5 mosquito larvae were inserted into each cup and they were allowed to sit for 24 hours. The number of mosquito larvae left after 24 hours was counted. (750 words) Types of natural substances Number of mosquito larvae left after 24 hours Cinnamon 3 Fennel 5 Garlic 0 Table 1: Number of mosquito larvae left after 24 hours with respect to natural substances The results imply that garlic showed the most significant effect on mosquito larvae since none of the mosquito larvae was left after 24 hours. A second trial was carried out to determine the method to measure the effectiveness of garlic and Abate. The first method was to count the number of mosquito larvae left after 24 hours while the second was to measure the time taken for all larvae to die. Three concentrations were used for each substance and method. Substance Number of mosquito larvae left after 24 hours for each concentration 1% 2% 3% Garlic 0 0 0 Abate 0 0 0 Table 2: Calculating the number of mosquito larvae left after 24 hours Substance Time taken for all larvae to die for each concentration (minutes) 1% 2% 3% Garlic 420 360 120 Abate 90 75 55 Table 3: Measuring the time taken for all larvae to die The results showed that method 1 was not practical to use since no mosquito larvae is left after 24 hours for both garlic and Abate. Therefore, method 2, which is to measure the time taken for all larvae to die, was used to compare the effectiveness of both substances as larvicides. (983 words) Real Experimental Procedures 1g of garlic clove was weighed using an electronic balance. The garlic clove was placed in a mortar and it was pounded lightly using the pestle to obtain garlic extract. 100mL distilled water was measured using a measuring cylinder and it was poured into the mortar to form an extract solution of concentration 1%. The solution was then transferred into a labelled plastic cup. Using a disposable dropper, five mosquito larvae were transferred into the beaker. At 5-minutes interval, the number of dead mosquito larvae in the beaker was counted and recorded to measure the time taken for all larvae to die. Dead larvae are those that cannot be induced to move when they are touched with the tip of the dropper. Steps 1 to 6 are repeated twice to obtain an average time taken. Steps 1 to 7 are repeated for garlic cloves of 2g, 3g 4g and 5g. The time taken for all larvae to die for each respective garlic concentration was tabulated. Steps 1 to 9 were repeated using 1g, 2g, 3g, 4g and 5g of Abate 1.1. A graph of mean time taken for all larvae to die against concentration of larvicides was plotted. A two-way ANOVA test was used to analyse the data statistically. Risk Assessment The experimental procedure is ranked low-risk. The risk of accidental introduction of mosquito into the environment had been considered and precautions were taken to ensure that pupae which had developed into mosquitoes were not released, but killed in the water. The container containing larvae were closed at all time. Gloves were worn to avoid direct contact with Abate which is toxic. Hands were washed before and after handling garlic extract, Abate and mosquito larvae. After using droppers, they were disposed properly. When the experiment had completed, the solution containing dead mosquito larvae were drained into the laboratory sink. (1307 words) Results Concentrations (%) Time taken for all mosquito larvae to die (minutes) Garlic Abate1.1G 1 2 3 Mean 1 2 3 Mean 1 360 345 370 358.3 90 85 90 88.3 2 300 310 300 303.3 75 75 70 73.3 3 120 115 120 118.3 55 50 60 55.0 4 100 90 110 100.0 45 40 40 41.7 5 80 80 70 76.7 30 35 35 33.3 Table 4: Time taken for all larvae to die for different concentrations of garlic and Abate Figure 1: Graph of mean time taken for mosquito larvae to die with respect to concentrations of larvicides (1409 words) Statistical Analysis Two-way ANOVA test was used to analyse the data to show whether there is a significant difference between the two larvicides. The Columns P-Value (8.58E-24) is less than the significance level (ÃŽ ± = 0.05). There is a significance difference between the larvicidal properties of Abate and garlic. Abate is a stronger larvicide than garlic. Therefore, the experimental hypothesis is accepted and the null hypothesis is rejected. From the analysis also, the calculated Sample P-value (3.62E-22) is less than the significance level tested as well (ÃŽ ± = 0.05). This shows that there are statistically significant differences between different concentrations of garlic and Abate. The Interaction P-Value (3.01E-19) indicates that there was a statistical significant interaction between the larvicides and the concentrations used. Higher concentrations of both larvicides are more effective against the mosquito larvae compared to lower concentrations. (1548 words) Substances Garlic Abate Total 0.01 Count 3 3 6 Sum 1075 265 1340 Average 358.3333 88.33333 223.3333 Variance 158.3333 8.333333 21936.67 0.02 Count 3 3 6 Sum 910 220 1130 Average 303.3333 73.33333 188.3333 Variance 33.33333 8.333333 15886.67 0.03 Count 3 3 6 Sum 355 165 520 Average 118.3333 55 86.66667 Variance 8.333333 25 1216.667 0.04 Count 3 3 6 Sum 300 125 425 Average 100 41.66667 70.83333 Variance 100 8.333333 1064.167 0.05 Count 3 3 6 Sum 230 100 330 Average 76.66667 33.33333 55 Variance 33.33333 8.333333 580 Total Count 15 15 Sum 2870 875 Average 191.3333 58.33333 Variance 14458.81 445.2381 Table 5: Summary of the data (1656 words) Source of Variation SS df MS F P-value F crit Sample 137903.3 4 34475.83 880.234 3.62E-22 2.866081 Columns 132667.5 1 132667.5 3387.255 8.58E-24 4.351243 Interaction 69970 4 17492.5 446.617 3.01E-19 2.866081 Within 783.3333 20 39.16667 Total 341324.2 29 Table 6: Calculations for two-way Anova test (1701 words) Data Analysis The two-way ANOVA test revealed that Abate is a stronger larvicide than garlic. The Columns P-value is less than the significance value (ÃŽ ± = 0.05), which indicated that Abate and garlic are significantly different in terms of larvicidal properties. This supports the experimental hypothesis that the effectiveness of Abate is greater than that of garlic. Table 4 shows that for all Abate concentrations, the mean time taken for all the mosquito larvae to die are shorter compared to that of garlic. For both larvicides, as their concentrations increased, the mean time decreased. From the data in Table 4, it can be evaluated that there is a bigger percentage difference in the mean time taken between garlic and Abate for the first two concentrations (about 75%). For 3%, 4% and 5% concentrations, the percentage differences in mean time range from 54% to 58%. This is illustrated in Figure 1. It clearly suggested that Abate is much more effective than garlic. Abate is a chemical larvicide while garlic is a natural larvicide. Both contain the active substances which are capable to kill mosquito larvae. Within 24 hours, all mosquito larvae would have died in Abate as well as garlic solutions. It was therefore not practical to calculate the number of live mosquito larvae after 24 hours. Hence, the time taken for the mosquito larvae to die was used as a measure of the substances effectiveness. The shorter the time taken, the more effective the compound is. Dead larvae can be identified by touching them with the tip of a rod or dropper. They cannot be induced to move. Abate contains temephos which is an organophosphate compound.11 It is able to inhibit acetylcholinesterase enzyme which is required to stop a nerve impulse after it has crossed the synapse. As a result, there is a continuous stimulation of the nerve, resulting in tremors and uncoordinated movement.11 Garlic, when crushed and mixed with water, will convert thiosulfinates to diallyl disulfide and diallyl trisulfide,10 both which are organosulfur compounds. They are effective against mosquito larvae. (2043 words) The experiment showed that Abate is a more effective larvicide compared to garlic. Both organophosphorus and organosulfur compounds worked against mosquito larvae. This explains that during the trial experiment, after allowing both solutions to sit for 24 hours, all mosquito larvae died. Nevertheless, the experimental results showed that Abate which contains organophosphorus compounds took a shorter time to kill all the mosquito larvae compared to garlic (organosulfur compound), implying that organophosphorus compounds are more effective against mosquito larvae. However, this may also be due to the purity of the active substances. The industrially-produced Abate contain pure temephos, whereas allicin found in garlic is impure. For an active ingredient to work effectively, it has to be extracted and processed to give optimum results. Although results showed that Abate is a more effective larvicide, it should be noted that Abate is harmful to certain animals such as mice and fish, as well as to some invertebrates. Abate is also liable to accumulate within the natural environment, posing risks to human health. Garlic is an option to replace Abate as it is easily obtainable, cheap and does not pose harm to the environment. Nevertheless, garlic takes a longer time to kill mosquito larvae compared to Abate. Time is a crucial factor when dealing with disease-carrying mosquitoes such as Aedes aegypti. Therefore, although garlic might be effective against mosquito larvae, it may not be practical to use such a time-consuming substance to alleviate the problem with mosquito larvae. (2287 words) Evaluation To increase the accuracy, the base of the garlic, together with its skin was removed before the garlic cloves were weighed using an electronic balance. The garlic cloves were pounded lightly using a mortar and pestle to prevent heat from destroying the chemical contents of garlic, which might decrease the effectiveness of garlic. Disposable droppers were used to avoid contamination of substances being tested and in the container used to collect mosquito larvae. Besides, plastic cups were used instead of laboratory glassware in order to prevent contamination as well. Each cup was closed with a perforated cover to ensure that air flows into the cup. The cup was covered as a precaution to prevent the introduction of any mosquito into the environment in case any larvae managed to complete its life cycle. Results from the trials showed that all mosquito larvae were killed by the larvicides within 24 hours. Therefore, if the number of live mosquito larvae were noted after 24 hours, there would not be any significant differences. As an alternative, the time taken for the mosquito larvae to be killed was measured. It was also impossible to run a stopwatch to measure the time as it would be difficult to estimate when to stop it. Instead, the mosquito larvae were observed every five minutes and any dead larva was noted. Hence, the time measured was estimation as it would be hard to check on the larvae every minute for hours. To increase the precision of results, the experiment was repeated twice to obtain an average time. It was also impossible to differentiate the types of mosquito larvae. Different larvae species might have different response towards larvicide. However, in this experiment, they were assumed to be of the same species. The larvae were also of different days old. Larvicides might have different effects on larvae of different days old. Besides, the solutions might not contain the exact concentration which was supposed to be tested. This is because garlic juice might not be able to be extracted and dissolve in distilled water completely. Abate granules also did not dissolve completely in distilled water. (2641 words) An ethical issue that may be questioned is the accidental introduction of mosquitoes into the environment. In this experiment, mosquito larvae are collected from ponds, which are mosquito breeding grounds. These mosquito larvae are actually prevented from turning into adult mosquitoes, which may transmit certain diseases. Larvae collected are placed in a covered container and are monitored to prevent accidental introduction of mosquitoes in case any larva managed to complete its life cycle. This investigation could be modified by grinding the garlic cloves and dissolve it in ethanol to form garlic solution of a particular concentration. This would increase the reliability of the results. Besides, mosquito larvae of the same species could be used to ensure that the effects of larvicides on that particular type of mosquito larvae only are determined. This reduces the probability of results occurring by chance. Mosquito larvae of a specific species could be cultured rather than collecting them from a pond. The number of mosquito larvae could also have been increased to obtain a more reliable result. Conclusion Chemical larvicide, Abate is significantly more effective than garlic in killing mosquito larvae. This was determined by the notably shorter time taken by Abate to kill all the mosquito larvae than shown by garlic. (2848 words) Source Evaluation Source 2 contains information on agricultural products such as vector control by BASF, the worlds leading chemical company and a corporate group. Hence, it is trustable and reliable. Source 4 is a journal, so contains sound scientific information. It contains a research note written by authors from several research universities. Therefore, it should be trustable and reliable. Source 6 is a data sheet on temephos, the active ingredient in Abate. The data sheet is provided by IPCS INCHEM, cooperation between International Programme on Chemical Safety (IPCS) and the Canadian Centre for Occupational Health and Safety (CCHOS). IPCS INCHEM compiles information regarding management of chemicals and their risks based on data from World Health Organization (WHO) and Food and Agriculture Organization (FAO). Therefore, this source is reliable and not biased. Sources 8 and 13 are published books. Therefore, they are credible sources with reliable contents written by notable experts in the respective fields. Source 10 is a trustable review as it is written by credible experts in the particular area. Source 12 is a reliable and credible governmental website by the U.S. Environmental Protection Agency in regulating pesticides; therefore, all facts and information provided are updated. Source 14 is guidelines for laboratory and field testing of mosquito larvicides by World Health Organization, so should contain sound scientific information.

Shakespeares Macbeth - The Character of Macbeth :: GCSE English Literature Coursework

Macbeth Character Shakespeare The character of Macbeth is not an easy one to understand. At the beginning of the play Macbeth is praised by many people as being a hero when he has defeated the Norwegians. The captain says: "Brave Macbeth "When Duncan hears the news he adds: "o valient cousin "and "Noble Macbeth ". However Macbeth is becoming tied up with things that are not good. The three weird sisters said they would meet with him. When the three weird sisters do meet with Macbeth and Banquo: "All hail, Macbeth! Hail to thee Thane of Glamis! ", " All hail, Macbeth! Hail to thee Thane of Cawdor! ", "All hail, Macbeth! Hail to thee that shalt be king here after. "Macbeth knows he is the Thane of Glamis but how can he be the Thane of Cawdor, the Thane of Cawdor lives a prosperous life and becoming king is just unthinkable. This gets Macbeth thinking about what they mean. At the start of the play the audience hail Macbeth as a hero but as he begins to think about murdering the king the audience feels he isn't so heroic after all, and they begin to dislike him. We learn from Lady Macbeth, the person who knows him best that he is too nice to be able to kill anyone especially the present king: "is too full o' th' milk of human kindness, "says Lady Macbeth. She then devises a plan to kill Duncan while he is staying with them. Duncan has arrived and is having dinner. Macbeth leaves and decides not to murder Duncan. Lady Macbeth accuses him of being less than a man for not killing him. Macbeth is not a natural born killer, Lady Macbeth has to persuade him to murder the king; he is initially reluctant to do such a deed: "We will proceed no further in this business: "Macbeth says this because he thinks he might become king without killing the present king, it might just be fate. But Lady Macbeth then begins to persuade him and soon a chink forms in Macbeth's armour. Macbeth says: "If we should fail "which shows us that Macbeth has once more changed his mind this shows us that he is very unwilling to murder Duncan. Once Duncan is asleep and Macbeth is on his own he sees a dagger before him. Shakespeare's Macbeth - The Character of Macbeth :: GCSE English Literature Coursework Macbeth Character Shakespeare The character of Macbeth is not an easy one to understand. At the beginning of the play Macbeth is praised by many people as being a hero when he has defeated the Norwegians. The captain says: "Brave Macbeth "When Duncan hears the news he adds: "o valient cousin "and "Noble Macbeth ". However Macbeth is becoming tied up with things that are not good. The three weird sisters said they would meet with him. When the three weird sisters do meet with Macbeth and Banquo: "All hail, Macbeth! Hail to thee Thane of Glamis! ", " All hail, Macbeth! Hail to thee Thane of Cawdor! ", "All hail, Macbeth! Hail to thee that shalt be king here after. "Macbeth knows he is the Thane of Glamis but how can he be the Thane of Cawdor, the Thane of Cawdor lives a prosperous life and becoming king is just unthinkable. This gets Macbeth thinking about what they mean. At the start of the play the audience hail Macbeth as a hero but as he begins to think about murdering the king the audience feels he isn't so heroic after all, and they begin to dislike him. We learn from Lady Macbeth, the person who knows him best that he is too nice to be able to kill anyone especially the present king: "is too full o' th' milk of human kindness, "says Lady Macbeth. She then devises a plan to kill Duncan while he is staying with them. Duncan has arrived and is having dinner. Macbeth leaves and decides not to murder Duncan. Lady Macbeth accuses him of being less than a man for not killing him. Macbeth is not a natural born killer, Lady Macbeth has to persuade him to murder the king; he is initially reluctant to do such a deed: "We will proceed no further in this business: "Macbeth says this because he thinks he might become king without killing the present king, it might just be fate. But Lady Macbeth then begins to persuade him and soon a chink forms in Macbeth's armour. Macbeth says: "If we should fail "which shows us that Macbeth has once more changed his mind this shows us that he is very unwilling to murder Duncan. Once Duncan is asleep and Macbeth is on his own he sees a dagger before him.

Ancient Greece :: Ancient Greece Essays

I found chapter two particularly interesting because it deals with the ancient Greek culture and life. It is so different than the American way of living, yet there are some similarities that are strikingly close. I feel this is especially relevant in their religion. They had oracles, who were these people who delivered messages from the Gods. I think that is kind of like a priest or minister of some sort, but in the Greek world the oracles were the say all ? be all. Apollo was one of the most well known and respected Oracles. I interpreted this as him being like the pope. Everyone respects what the Pope says, and everyone in the ancient Greek world respected what Apollo said. They also had decorative doors to the religious places. Today, many doors to churches are very decorative or have symbols. The way the Greek people justified the world was through their gods and goddesses. They had a god or goddess for everything ? love, war, trouble, sun, the world, the moon, and many other s. My favorite goddess is Pandora. You always hear about Pandora?s Box when someone is about to get into some trouble. To me, she was the rebel goddess. The ?black sheep? if you will. I feel like everyone can relate to her in some way or another. I know there are many times I feel like the odd one out. Or that I am always getting in trouble. Poetry and really good fiction started to flourish in the times of the Greeks. They were very into the whole entertainment thing. Some great pieces of literature came from their time period. For example The Odyssey, The Iliad, and the Trojan War. Homer is the most well known author from the era.

American Views Before and After World War II

America is well-know for its wealth and independence. Proud Americans come together to fight for democracy and freedom, while fighting against extremists and their desire for world conquest. War stories usually favor the victor. As a result, after World War II, many of the stories that began to circulate added to an already inflated US ego. After World War II, depending upon the country, the impressions of Americans are diverse.On one hand, Americans were saviors; however, the other hand, many were offended because of America’s tentativeness to join the war efforts, plus the overconfidence Americans displayed with they eventually joined the war. Although, the US declared themselves as isolationists, they continued to provide defense supplies to the Allied states. These defense supplies came by way of Roosevelt’s Lend-Lease program. This program contributed to Allies collaborative efforts to resist German advancements. The Axis powers took considerable offense to this po licy, which resulted in hostility towards the US.By the time, the US officially entered the war; a devastated, Nazi-occupied Europe was struggling for survival. The wealth gained from Lend-Lease resulted in a secure and confident economy for the US. This great wealth, massive military, and America’s ability to harness atomic power, added to the audacity to use that power, were the factors that elevated the US into superpowerdom. Although, the economy was not the only reason for America’s ascent to become a superpower, it was also the combined efforts of the American citizens to support the war effort, which attributed to their elevated status.However, according to Stoler, most Americans did not attribute the end of World War II to combined efforts; they perceived it as a return to â€Å"normalcy† (p. 385). Stoler continued his opinion by stating that both Britain and the Soviet Union were slightly aggravated and annoyed at the US for assuming the superior status at the end of World War II (p. 388). Americans believed their arrival secured the defeat over Nazi Germany and the Japanese Empire. However, Britain and the Soviet Union’s opinions differ slightly regarding the US.According to Stoler, the British considered Americans â€Å"latecomers† to the war and felt abandoned during the first two years (p. 388). When the US finally decided to join the war, they entered with the â€Å"naive, arrogant, and incorrect belief that they should dictate both combined wartime strategy and a new, self-serving postwar international order† (p. 388). From the Soviet’s point of view, America’s role was â€Å"relatively insignificant† as compared to the Soviet role; plus, the US deliberately procrastinated entering the war with the intention to exploit the Soviet Union by using the Lend-Lease program (Stoler p.388). Memory serves as an important element during war-time. Many people consider memories of specific event s irrelevant. These recollections of selectively retrieved events can possibility deliver incorrect details of said events. Earl Kelly with the McClatchy-Tribune Business News even quoted Carol Gluck while speaking at the 31st annual Bancroft Lecture at the Naval Academy, â€Å"history and memory are often in collision, rather than collusion, with each other† (2010).Even the most overrated misconceptions of World War II were sometimes included into movies. Often, the US Government embedded them selves into the movie industry. The reason being was to influence Americans on the importance of entering the war by means of propaganda. Worland states, that the Office of War Information affected most popular war-time films; especially films that â€Å"depicting the armed forces, images of America as a united, democratic society, the ideology of the Axis enemy, and so on† (p.48). This governmental influence pushed Americans to support the war effort. The U. S. brought to the w ar added military, supplies, and ideas for the Allies. While the US may have been imprudent and arrogant in their attempt to assume control, but the U. S. did bring alternative solutions to the table. To some countries, Americans are egotistical and lazy. Fortunately, America’s pompous attitudes gave the added incentive and strength to the Allied powers that helped end the war. Works Cited Kelly, E.(2010). Historian says memories fuel inaccuracies. McClatchy – Tribune Business News. Retrieved November 20, 2010, from ProQuest Newsstand. (Document ID: 2155533071). Stoler, M. (2001). The Second World War in U. S. History and Memory. Diplomatic History, 25(3), 383. Retrieved from Academic Search Premier database. Worland, R. (1997). OWI meets the monsters: Hollywood Horror Films and War Propaganda, 1942 to 1945. Cinema Journal. 37(1), p. 47-65. Stable URL: http://www. jstor. org/stable/1225689

Scarlet Letter- Grey

Scarlet Letter Assignment Topic: Gray Part I- Cite six times in the book where your topic appears and analyze how those instances relate to the meaning of the work as a whole. 1. â€Å"A throng of bearded men, in sad-colored garments and gray† (33). The color gray adds to the atmosphere of the day, the day of judgment for Hester. The people of this Puritan town are close-minded and dull, all represented by the color grey. 2. She bore in her arms a child, a baby if some three months old, who winked and turned aside its little face from the two vivid light of day; because its existence, therefore, had brought it acquainted only with the gray twilight of dungeon, or other darksome apartment if the prison† (36) When in the dungeon Hester spoke to no one and would not admit to anything, because she concealed her secrets. The color gray connotes secrets and hiding. Once Hester and Pearl depart from the prison for the first time the gray of the dungeon disappears and the secret s can now be found out—this admission being a major plot in the novel.This is the moment when the secrets break free and begin to unfold. 3. â€Å"Standing on that miserable eminence, she saw again her native village, in Old England, and her paternal home: a decayed house of grey stone, with a poverty-stricken aspect, but retaining a half obliterated shield of arms over the portal, in token of antique gentility† (40). When leaving the jail, Hester gazed at her hometown. However, she was not filled with nostalgia or wistfulness. Rather, she looked out and saw her family’s poverty stricken house, though it was noticeable that it was once of high nobility.Those who were once elite and considered noble people are now in poverty and being trialed for murder. Grey connotes this transition. It is dull, boring, and is not red, blue, and purple, which are the colors that aristocrats wore at that time. When leaving the jail Hester realizes that everything has turned to gr ey—life will not be as luxurious and she will be repudiated by society because of her sins. 4. â€Å"The wide circumference of an elaborate ruff, beneath his grey beard, in the antiquated fashion of King James's reign, caused his head to look not a little like that of John the Baptist in a charger† (74)This description of Governor Bellingham is to show how he is esteemed and of high class in Puritan society. Puritans desire to live like their ancestors; no room for change at all. Governor Bellingham is illustrated in the novel and is compared to those living in King James’ time. To the Puritans this is positive, this dullness and inability to change their ways: it is the way of life. But to others, like Hester it is a negative aspect of the society. The color gray is therefore used in this context to highlight this. The Puritan society is gray, devoid of color and excitement.In today’s day, a black-and-white movie suggests that it is old and outdated. So too here, adding the fact that Governor Bellingham’s beard is gray is to elucidate Hester’s opinion that the society is and should be obsolete. 5. â€Å"An unwearied pall of cloud muffled the whole expanse of sky from zenith to horizon. If the same multitude which had stood as eye-witnesses while Hester Prynne sustained her punishment could now have been summoned forth, they would have discerned no face above the platform nor hardly the outline of a human shape, in the dark grey of the midnight† (101).The use of grey in this instance defines the mood Nathaniel Hawthorne is attempting to portray. Dimmesdale mounts the scaffold and screams out, confessing his sin. It is in the depths of the night and is dark, somber reflecting Dimmesdale’s desire of penitence for his sin. He wishes to be found out and for his guilt to be palliated. 6. â€Å"Mr. Dimmesdale throughout the long hereafter. But as he came down the pulpit steps, the grey-bearded sexton met him, holding up a black glove, which the minister recognized as his own† (108).The day after Dimmesdale’s profession of his sin in the midst of the night, the church sexton comes over to Dimmesdale and hands him his black glove that was found on the scaffold. The sexton decides that it was Satan’s doing and not that of Dimmesdale. Everything around Dimmesdale suddenly begins to turn gray. He sees everything as gray—full of sin and darkness void of life and purity. Part II- Explain how your topic sheds light on at least one character’s development in the novel Grey symbolizes many different ideas in the novel, The Scarlet Letter. However, a main theme of the color gray is that of darkness and the presence of sin.Throughout the novel, Dimmesdale’s status and health slowly deteriorate and the color gray helps track this decline. At first the society is looked at as gray, boring, and dull in the eyes of Hester. Dimmesdale was a prize pastor giving the best sermons. However, once Hester is reestablished in society, Dimmesdale’s guilt begins to take over. Especially after he and Hester talk about leaving the town by ship, his shame gets the best of him. He ascends the scaffold hoping someone will hear him confess his sins, but everyone thinks it is a witch. Everyone and everything around him appears gray, all reminding him of his sin.Dimmesdale even gives a sermon in which he reveals that he too has sinned, so as to alleviate some of his guilty conscience, but it makes the people like and revere him even more. At last he cannot take it and he mounts the scaffold, Hester and Pearl in hand, confessing his sins to all and dying there as Pearl kisses him. The guilt was too much for him and finally the pain is gone for Dimmesdale. Part III- Choose three biographical facts about Nathaniel Hawthorne and/or historical facts about the time period, and explain how the facts add to your understanding of the overall book 1.Nathaniel Ha wthorne’s ancestor, John Hathorne, originated in the Massachusetts Bay Colony and was a judge in the Salem witch trials. Hawthorne was fascinated by his kinship to John Hathorne and inspired several of his novels. This was a great inspiration for The Scarlet Letter, as witchcraft, sin, and Puritan society are all main themes of this novel. 2. Nathaniel’s father died when he was at an early age. This was therefore the inspiration for Hester being a single mother in the novel. He felt the same way that Pearl did and at the same time empathized with Hester because he watched his mother go through the same thing. . One important influence on The Scarlet Letter is money. Hawthorne never made much money as an author and the birth of his first daughter just added to the financial burden. He received a job at the Salem Custom House, but lost it three years later and was forced to return to writing to support his family. Consequently, The Scarlet Letter was published a year aft er being fired by his job in the Salem Custom House. At first, the work was only intended to be a long short story, but the extra money a novel would bring in was needed to support his growing family.