A Raisin in the sun & The American Dream

The American is defined by reaching the top no matter who you are or where you come from. In the ‘50s this dream revolved around materialistic values. This play focuses on a family with each member having a different dream and their journey as an African Americans. Walter, Mama’s son learns the meaning of pride and keeping what his father has earned is more important than money. The play focuses on supporting each other through rough times and learning to love. In the end, they achieve their American dream despite the color of their skin.

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A Raisin in the sun & The American Dream
The American dream in the ’50s was close to materialism. The ownership of consumer goods was believed to bring joy into a family’s life. This stereotypical view governs the dream of one of the main characters in Lorraine Hansberry’s play. The title of the play is based on “Harlem” by Langston Hughes, a poem that raises a question about a dream that is deferred. “Does it dry up like a raisin in the sun? … Or does it explode?” (Rampersad, 1995, pg. 426) There are three main characters and all three of them of have dreams that have been prolonged for too long. A Raisin in the Sun is about the rocky journey they go through to acquire their dreams.
The Younger’s family has just received a $10,000 dollar check for their dead father’s life insurance policy. They live in a two bedroom apartment on the black side of town in Chicago. Racial prejudices against blacks in that era and a low income are the root of conflict in the family. Mama, deceased Mr. Youngers widow wishes to buy a house and fulfill the dream she once saw with her husband. Beneatha, Mama’s daughter, hopes to find her identity through looking towards true African heritage. Walter, Mama’s son, wishes to one day become rich. He wants to replenish his marriage and provide his son with all the opportunities he never had growing up.
Walter wants to invest money in the liquor business with a few of his friends. Although the idea appalls Mama at first, she trusts and supports her son with his decision. The night before making the investment Walter tells his son about the business transaction he about to make while tucking him into bed. He tells the little boy that their lives will change soon and paints an elaborate and vivid picture of the future. He tells his son that when he’s seventeen years old he’ll come home and park the Chrysler in the driveway. The gardener will greet him and when he’s inside the house he’ll kiss his wife and come up to his sons room to see him browsing through brochures of the best colleges in America. He then tells his son that he will give him whatever he wants. Although Walter is somewhat materialistic in what he wants at the core he just wants a happy family and a son who should have all the chances he never had. During this time Mama buys a house to fulfill the dream she saw with her husband; the only one she can afford is in a white suburban neighborhood. Mr. Lindner a man from the neighborhood comes to the Younger house trying to convince them to not destroy the white community. He offers a lot of money in exchange for their acceptance. Meanwhile Walter looses all the money he has invested in the liquor store because I friend has run away with it. When he looses the majority of their financial resources the entire family falls into a deeper level of depression. At this time, Walter decides to take the money the white man has to offer. The thought of selling away their right vexes Mama, Walter’s sister and his wife. They detest Walter for dealing with his dead fathers money so easily and feel that he has lost his soul when he days we wants to be bought out by the white Mr. Lindner.
Ultimately, loosing everything they have unites them because at the last moment Walter changes his mind about taking money from Mr. Lindner. Walter tells him that they have moved into the house because their father earned it for them. He continues by saying that they don’t want to disturb the neighborhood peace or protest for bigger causes, and that they’d be nice neighbors. He tells Mr. Lindner that he doesn’t want the money. At this moment the entire family’s spirits are lifted and they are proud of the decision Walter has made. This act of standing by your family to achieve the American dream of succeeding no matter who you are and where you come from unites them. They learn to support each other and put their families before their own. By owning a house, having a high morale, and the support of their family, each of them is on their way to fulfill their American dream.
Foulis, Rhona (2005, March, 14). A Raisin in the Sun. Retrieved March 8, 2008, from Culture Wars Web site: http://www.culturewars.org.uk/2005-01/raisin.htm
Potter , G and Struss, Joe. (2002, April, 02). Iowa State University. Retrieved March 8, 2008, from ISU Play Concordances Web site: http://www.public.iastate.edu/~spires/concord.html
Rampersad, A (Ed.). (1995). The Collected Poems of Langston Hughes. Alfred A. Knopf, Inc..

Life Without the Sun

According to scientist the sun is the nearest star to earth the only planet believed to be inhabited by the living creatures. This natural alignment is mysterious and it is hard to explain why the star is placed in such a position. The earth is a planet and it revolves around the sun leading to a series of seasonal changes. Science tells us that the gravity of the sun is the one responsible in holding the earth in its current position. The seasonal changes caused by the revolution of the earth have had tremendous effects in the lives of creatures living on earth as well as the physical terrain of the planet.

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Plants on earth which are the primary producers in the food chain rely on the light from the sun to manufacture their own food through the process of photosynthesis. In these case the light from the together with chlorophyll a pigment in green plants undergo a series of some chemical reactions that lead to manufacturing of food by the plants.(Kenneth 2006)
Consumers which are made of various animals and micro organisms rely entirely on plants for food. The sense we get here shows that without plants, it is difficult for consumers to live. Since the sun is the primary source of light that is needed by plants to survive, then it is very important because plants apparently form the basis for life here on earth. Plants which make up forests will attract rainfall that will ensure that human beings survive. Water is a very important requirement to all animals and plants in this world. People need water for both domestic and industrial uses. Without water it will be impossible to cook food, wash bath and drink. Plants need water to grow well and to produce the best yields. Food crops like fruits beans potatoes and corn need water in order to grow well.
Water is also needed for industrial use like generation of hydro electric power, supplying industries that engage in very important activities like manufacturing and processing of various products that we may need in our every day life situation. Water from the rain can also be harvested to be used in irrigating dry lands to produce subsistence food. Animals also need water whether domestic or wild. Pastoral communities rely on livestock as a lively hood and if these animals do not get enough water the live of the pastoral communities in danger.(Kenneth 2006)
Apart from these effects on plants, the sun also has some direct benefits on animals. For instance it provides warmth, source of vitamin D, source of light, source of solar energy, act as a stellar cue to migrating birds and animals. The sun also has let to economic benefits especially in the tropics where tourist allover the world troop to these places to enjoy the warmth provided by the sun. Tourists earns foreign income to a country that will create employment opportunities to the locals of tropical countries.
In conclusion, the sun is has a lot of benefits that if there was no sun then it means that life could not be there. In simple terms the sun is life.


Analysis of Brett from ‘In The Sun Also Rises’

The character that I chose to talk about from The Sun Also Rises is Brett. She stood out to me for a few reasons. I chose her because she is an empowered and independent woman, and also because she seems to be the character that the story finds a way to revolve around. Brett is a woman who seems to epitomize and really sum up what I thought the true theme of the book was.

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I thought that there were a lot of interwoven lives and personalities in this story, and they all had a sense of being lost souls. I think that of all the characters she is truly a wanderer in life. Overall, the easiest first impression to make about Brett is one that shows her as a very shallow and selfish woman, which in my opinion seems to be a fair assessment.
Brett first comes into this novel with a crowd of men, and seems to have a very commanding presence. Throughout the novel we find out that this is exactly right. We learn that she somehow manages to create a hold, a force even, over the people, specifically men, that she meets. While there are some exceptions to her “power” (i.e. Bill), this is a rare occurrence. While this sense of female dominance continues, it brings a more negative connotation the farther into the novel it gets. In addition, it is quickly learned that Brett’s number one concern in her insatiable desire for sex. A relationship in her eyes is defined by the amount of and quality of sexual intercourse that she can get. While she is seemingly capable of loving someone, as we see in chapter 4 and beyond, love is not important enough to prevail. “Love you? I simply turn all to jelly when you touch me,”(Hemingway, p.34) is what she mentions to Jake during the first encounter that we see in the novel. Her relationship with Jake is never fully understood and definitely never reaches its full potential due to her inability to commit to anything of substance. Brett truly seems more interested in having a good time, which can be seen through her promiscuous actions and constant partying. In addition, she wanders through life by traveling and just sweeping in and out of people’s lives. She truly shows her shallow nature through these actions.
Another example of when we can see more of her shallowness appears in chapter 5 when we first become aware of the fact that she is actually engaged. Being first introduced to her by knowing her promiscuity and then later learning she is engaged, makes her appear even more of a negative character.
Besides being shallow, it can also be said that she is one of the most selfish characters in the entire book. She leads a very unsettling life and comes through others lives like a tornado. She does what she wants and never considers the effects that her actions have on others. We can really see this through her actions with Jake. She is constantly asking for reassurance of his love for her, yet has not intentions on following through with a relationship. Brett has a habit of making plans with Jake and then standing him up. Jake questions her, “You don’t remember anything about a date with me at the Crillon?” In which Brett replies, “No. Did we have one? I must have been blind” (Hemingway, p.61). She continually leads him on, and while he knows there really isn’t a chance that anything will come of their feelings for each other, it is like throwing salt on his wounds at every mention of her love for him. In addition to acting selfishly towards Jake, which is the most severe, she also is treating her fiancé Mike severely selfishly. She fairly openly has affairs and expects him to stand there and wait for her. Between the combination of her promiscuity and selfishness, we can get a complete picture of Brett as a truly inconsiderate person.
When we look at all these factors, and while I do have a much more negative view of Lady Brett than positive, I can’t help but wonder if this behavior is a result of being confused and afraid. Someone feeling unsure about the direction her life is going, may act in ways that they think will have no foreseeable consequences in the immediate future. What she is not looking at is the bigger picture. She is a live day-to-day kind of girl, and looking towards her future doesn’t appear to be a question in her mind.
It is mentioned in the book that this group has all experienced the hardships of WWI in some way or another. The disaster has really hit them all and they are struggling to find meaning in their lives post-war. Many of them never wanted the war to begin with, and they are now dealing with the detriments of life after war. “We would probably have gone on and discussed the war and agreed that it was in reality a calamity for civilization, and perhaps would have been better avoided” (Hemingway, p. 24-25).
In addition to dealing with the war, it is learned through a conversation between Jake and Cohn that Brett had married shortly after her true love died. “When did she marry Ashley?” “During the war. Her own true love had just kicked off with dysentery” (Hemingway, p.46). The fact that Brett suffered through the loss of her true love could be the root of all of her recent negative actions. She could have been so distraught from the loss of her love, that she now found it hard to allow herself to truly fall for another man, and if she seems to have feelings, like she does with Jake, she pushes them aside. All of her antics could actually be a defense mechanism and her real reason for being selfish stems from fear. Allowing herself to open up to another person would open her up for the possibility of heartbreak and distress. Overall, the war left her alone and without any direction as to where her life was going. She was left to basically start her life over. Afraid and unsure, she chose to live a life filled with sex and alcohol.
Another cause of her inability to commit to a man could be due to her disheveled and corrupt past marriage with Lord Ashley. He “always made Brett sleep on the floor. Finally, when he got really bad, he used to tell her he’d kill her”(Hemingway, p.207). This unstable and violent relationship most likely further damaged any remaining faith she may have had in relationships. The impression I got from reading the novel was that the only reason she was in an engagement was because they had a relationship of convenience and were comfortable enough in their dysfunctional relationship.
An example of finally seeing an ounce of morality in Brett is exposed during the last chapter when she leaves Romero. At first, Brett seemed to have a connection with him, and she most likely still did upon leaving him, but she claimed that he was young and she didn’t want to hurt him. She knew she wouldn’t be able to remain faithful. While this initially seemed to be an admirable move, this decision could have also easily been driven by selfishness or her fear of settling down and/or conforming. She knew Romero loved her, but wanted her to be something that she couldn’t possibly be. “He wanted to make it sure I could never go away from him. After I’d gotten more womanly, of course” (Hemingway, p. 246). Romero was trying to turn an independent woman into a dependent housewife, a lifestyle Brett couldn’t conform to.
Given all of the information the novel exposes to us about Brett, more than one interpretation can be made about her character. She could be a nice girl deep down, with fear of commitment lurking in her head. While I do think that there is definitely some truth to this, I still think that Brett has let her past circumstances dictate her life in a negative way, rather than growing from her pain and experience. I feel that Brett is using her pain as an excuse to behave in such a harmful way. She allowed herself to become an extremely selfish, inconsiderate woman, who is willing to hurt anyone in her way in order to get what she wants sexually.
The last quote being used to be analyzed is one that stood out to me immediately. In the last paragraph she states, “Oh Jake, we could have had such a damned good time together” (Hemingway, p. 251). This line proves that her self-centeredness has ironically not only caused other pain, specifically Jake, but also herself. She is her own worst enemy and her current lifestyle is ruining her chances of truly being happy again.

A Raisin in the Sun: Analysis of Lena

Reading Journal 3

In the play A Raisin in the Sun, an African American family has an opportunity to have their dreams come true with the arrival of an insurance check after the death of the head of the house Walter SR.  Lena Younger moved into the small apartment with Walter, Sr when she was young and ever since she has dreamed of moving into her own home.  Receiving the insurance check means her dream could finally come true.  The characterizations that can be made of Mama Younger, who is now head of the household, would be that she is unselfish, loving, and a strong-willed woman.

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 Though Mama shows all of these characteristics her best would be how unselfish she is towards her family. Even her dream is based on wanting more for her family. She wants her own home for her family to have a better life. You can see Mama’s selflessness when she fixes Travis’ bed for him after he leaves for school.  Mama asks Ruth why Travis isn’t good at making up his bed and Ruth replies, “He don’t try at all ‘cause he knows you going to come along behind him and fix everything.” (pg. 40) You can also see it when Ruth starts ironing the family’s clothes; Mama’s unselfishness tells Ruth to let her do it.  “You aiming to iron all them things? Leave some for me.” (pg. 40) Though Mama is most unselfish when she tells Water Jr..,” I want you to take this money and take three thousand dollars and put it in a savings account for Beneatha’s medical schooling.  The rest you put in a checking account – with your name on it.” (pg. 107) This behavior shows how much she loves and cares for her family and how she is willing to do anything she can for the good of her family.

  Another characteristic of Lena would be how much she loves and cares about her family.  Though she does show how much she loves her family every day it is not always in the typical affectional way.  She shows her love by her actions and what she does for them.  One can see this when she starts to see that she may have prevent her son from following his dream.  “I ain’t got nothing, don’t own nothing, ain’t never really wanted nothing that wasn’t for you.  There ain’t nothing as precious to me… There ain’t nothing worth holding onto, money, dreams, nothing else – if it means- if it means it’s going to destroy my boy.” (pg. 106).  She takes a big step in showing how much she does care when she gives up her authority of the household to her son to do what’s best for the family.  It is best summed up when at the end of the play Mama says that, “There is always something left to love. And if you ain’t learned that, you ain’t learned nothing.” (pg. 145)

 The last characteristic to discuss is what truly holds the family together and that would be her strong-willed personality. Within the play you can see that this comes from her way of life, which is very much based in God. One can see this throughout the play as she doesn’t allow her children to use the Lord’s name in vein; one example would be when she says “If you use the Lord’s name just one more time- “(pg. 51) One antidote that she talks about was how her and Walter Sr. did all they could possibly do to get each family member to service every Sunday. Another time you can see how God-based her life is was when Beneatha states she no longer accepts the idea of there being a God; Beneatha is told to say, “In my mother’s house there is still God.” (pg. 51) However in the third act we start to question her strong willed personality. Mama is seen in a more vulnerable light after the insurance money was invested in the wrong person and is now gone. In the after aftermath of this devastation we see her walking out of her room like she is now a lost soul and she is described as if she’s trying to make sense of her former command of the world and that all of the dreaming she did of owning her own home was just a waste of time.   She tells Ruth about how people used to always tell her she was too big of a dreamer.  People used to say to her, “Lena Eggleston, you aim too high all the time.  You needs to slow down and see life a little more like it is.  Just slow down some.” (pg. 139). 

Start here You can see the wonderful characteristics of Lena by how her family loves her as they sacrifice to assist with her dream come true.              This is accomplished because Walter, Jr. calls the man from the neighborhood back to talk about their home, it seems like he is going to sell the house back to the neighborhood society however he decides to use his mother’s advice, “I come from five generations of people who was slaves and sharecroppers – but ain’t nobody in my family never let nobody pay ‘em no money that was a way of telling us we wasn’t fit to walk the earth.  We ain’t never been that poor. We ain’t never been that – dead inside.” (pg. 143). By following this advice from of his mother, he decides to tell the man that they were going to move into the home and live the dream of owning their own home. Thankfully Mama’s dream is only put on a hold for a short period because the way she chose to be made her a role model to her family, which helped them live a better, happier life in their new home.

Works Cited

Hansberry, Lorraine. A Raisin in the Sun.


Do the Teachings of Clausewitz or Sun Tzu Produce the Better Military Leader?

Do the teachings of Clausewitz or Sun Tzu produce the better military leader?



The teachings of Clausewitz and Sun Tzu provide the military leader with different approaches on how war should be conducted, both theorists and their theories being the product of very different times. Sun Tzu’s Art of War was written during the late 6th century BC, whilst Clausewitz On War was written during the 19th century. The two teachings therefore have very different conceptions of the nature of warfare as they are based on their own observations of warfare during their lifetime. Sun Tzu’s Art of War doctrine is very much based on the assumptions of ancient warfare, whilst Clausewitz’s teachings are based on his observations of the Napoleonic Wars, and therefore offer a very Western centric view of warfare. Whilst it is evident that both the teachings of Clausewitz and Sun Tzu offer the military leader advice which is beneficial, both approaches are not without fault. The best military leader is aware of the limitations of both Sun Tzu and Clausewitz and draws strengths from each doctrine and applies them to war. However, if one was to only be allowed to follow one doctrine it can be seen that the adaptability and totality of warfare taught by Sun Tzu is of more applicable to modern war than the Western centric view on the warfare offered by Clausewitz.

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The teachings presented by Clausewitz in On War do provide the modern military leader with some transferrable methods. Perhaps the greatest advantage of the teachings of Clausewitz over that of Sun Tzu, is the importance he places on the strategic triad between government, the armed services and the people. The importance Clausewitz places of this “remarkable trinity” in waging an effective war stems from his belief that “war is nothing but a continuation of policy with other means” (Clausewitz, 1976, p.69). The effective use of this triad of government, armed forces, and the population can be seen as key factor in achieving success in a modern war. Clausewitz’s teachings were shaped by the Napoleonic Wars, meaning that his views were influenced by the total nature of warfare he witnessed. Whilst in ancient times there was a clear distinction between the military sphere and the political sphere, the extensive nature of warfare and the purpose for which it was being fought, i.e. the survival of the status quo against the revolutionary ideas of the Republic, meant that the waging of war had to be considered from a more holistic standpoint. For Clausewitz each component of this “remarkable trinity” has an important role to play in strategy; the government gives the fighting a political purpose, the armed services provides the means for achieving this goal, and the people provide the will. (Cronin, 1984, p.41-2). It is evident that each component is equally essential to one another in waging an effective war. Perhaps the best example of when this triad came into full affect can be seen in the way society was mobilised in Europe during the Second World War.

The relationship between the government and the military is a relationship in the triad which Clausewitz gives particular attention to. For Clausewitz by giving the political goal paramount importance its avoids the military leaders from viewing the “capture of certain geographical points or the seizure of undefended provinces [as] of value in themselves” (Clausewitz, 1976, P.182). This is beneficial to military leaders at any time as it avoids the view of war in terms of military achievements, but rather encourages the military leader to view military actions in relation to the political goal which is sought to be achieved. This use of a political motive in fighting a war, and it’s relationship with morale and will, can be seen as one of the driving factors behind Clausewitz teaching incorporating the defensive advantage in warfare. For it could be argued that the intensity of will and morale associated with protecting one’s own sovereignty, compared to that of the attacker who is not concerned with loss but purely gain, attributes the defender a greater strength in his morale due to the intense nature of his motivation (Sumida, 2009, p.19).

Another useful teaching of Clausewitz is the emphasis which he places on approaching theory as simply a guide. Clausewitz’s teaching that a theory of war cannot be subject to rigid scientific principles is beneficial in that it teaches the military leader to be flexible and to adhere the conduct of war to only what is being observed. It can be seen that this flexibility of strategy was one of Napoleon Bonaparte’s greatest attributes, and given the context of Clausewitz’s writings, would have been a major driving force behind this inclusion in On War. For Clausewitz argues that the ‘friction of war’, the difficulty of applying theory to real life due to the intrinsically dangerous nature of war, the physical effort, and the ambiguous information received in war, will mean that any rigid war plans will ultimately fail (Cronin, 1984, p.44-5). This is perhaps one of the most useful teachings that Clausewitz has to offer the modern military leader, as it gives focus to the very human nature of warfare and the difficulty of applying rigid pseudoscientific formulas to the battlefield.

However, despite these useful teachings which Clausewitz has to offer, On War cannot be used as a set military doctrine to base all future military action on. The teachings of Clausewitz are very much the product of its time, based heavily in the conventional western view of warfare as a conflict between two large armies fighting each other on large battlefields each searching for a decisive battle. Although perhaps useful in fighting conventional conflicts, the doctrine of On War has somewhat been outdated by the development of new technologies and the new type of warfare which is being fought. ‘Modern warfare’ is perhaps characterised by its lack of large open conflicts between two large ground forces, and this development in the way in which war is fought can be seen to outdate a lot of Clausewitz’s lessons on war. The teaching of Clausewitz which is perhaps most outdated is the idea of concentration of one’s forces on the oppositions “centre of gravity” (Clausewitz, 1976, p.595-6). For it can be seen that although there are benefits to knowing the opponent’s “centre of gravity”, the hub of all power and movement in order to effectively direct force towards it. However, with the rise of new more precise artillery and the nuclear threat, the concentration of forces provides the opponent with the perfect opportunity to wipe out a large percentage of one’s force. Sun Tzu in comparison teaches the military leader to be able to hide one’s forces and to never concentrate them until it is necessary. Therefore, when one views the teachings offered by Clausewitz in On War it should be remembered the limitations of much of his teachings in relation to the modern world and his teachings should instead be used with care.

The teachings offered by Sun Tzu in The Art of War due to its focus on the abstract nature of warfare can be seen as of great use to the modern military leader. The fact that Sun Tzu was writing during the 6th century BC can be seen as advantageous in shaping his teachings, due to the lack of any major technological advances at the time, Sun Tzu teachings are not bogged down by the preconceived ideas about how warfare is to be fought and instead focus on the very essence of conflict. This can be seen in Sun Tzu’s focus on the concept of deception as a tool in ensuring conflict, for Sun Tzu “all warfare is based on deception” (Sun Tzu, 1993, p.101). The use of deception in waging war is advantageous to the modern military leader and can be seen to be used by great affect in modern warfare. As mentioned previously, warfare no longer consists of long open battles between two large forces but is characterised by small skirmishes. The use of deception during warfare can be seen to have been used by great affect by small terrorist groups in the middle east fighting large foreign forces. For Sun Tzu a major part of ensuring success in conflict is to shape the adversary perception he has of you. For Sun Tzu the best commander will confuse his opponent and not allow them to gain an understanding of what they are facing. For it can be seen that to deceive the enemy makes it very hard to plan against an attack. This idea of deception can be seen as of great use regardless of the time period one is fighting and is one of Sun Tzu’s teaching which transcends the period of conflict.

Also central to the idea of deception is the belief of Sun Tzu that a good military leader will ‘attack the enemy’s mind’. For it can be seen that this is very much constant with perhaps one of Sun Tzu’s most famous teachings from The Art of War, that “to subdue the enemy without fighting is the supreme excellence” (Sun Tzu, 1993, p.105). For it can be seen that for Sun Tzu to attack the will of one’s force to fight is just as, if not more important, than the destruction of an opponent’s army (Yuen, 2008, p.192). For if the opponent no longer wishes to fight one has already defeated the opponent, without the mass loss of life.  This is yet another of Sun Tzu’s teachings which has proven to be more applicable today than ever, with the development of weapons of mass destruction. Furthermore, it can be seen that Sun Tzu’s belief that one should only fight a war when one has studied all aspects of the potential “friction of war” and all conditions seem in place to ensure victory can be seen as of benefit to any military leader. A follower of Sun Tzu will not be afraid to retreat when the odds are against him[1], and will only engage in battle when he is certain that the odds are in his favour. This leads to less unnecessary loss of life and produces the better military leader in today’s world.

Another teaching offered by Sun Tzu which is of benefit to the military leader of today is that of creating an army which is fluid and able to change tactics and formation in accordance to the situation of the opponent. Sun Tzu remarks that the army should be able to adapt in accordance to the situation of the enemy, the same way water flows in accordance to the ground (Sun Tzu, 1993, p.113). Both Clausewitz’s and Sun Tzu’s teachings rightfully place importance on the army’s ability to be flexible as a major attribute in achieving victory. The ability of strategy to be flexible is essential in today’s warfare. The ever-expansive nature of where war is being waged and the use of new tactics such as guerrilla warfare mean that the army needs to be able to respond to new challenges.

In conclusion, it can be seen that both the teachings of Clausewitz and Sun Tzu provide lessons and teachings which are beneficial to any military leader in learning how to fight an effective war. However, it can be seen that it is ultimately the student of Sun Tzu that will produce the better military leader, as the teachings of Sun Tzu leads one to view warfare outside of just the battlefield, and will produce a military leader who takes into consideration not just the acts of battle but one who is able to effectively wage war through all mediums. The student of Sun Tzu views warfare in relation not just to numbers and battles but the metaphysics of warfare and conflict, producing a military leader who is more competent and skilled in the art of warfare.


Clausewitz, Karl von. (1976) On War. Edited and Translated by Howard, M. & Paret, P. Princeton, New Jersey: Princeton University Press.

Cronin, Patrick M. (1984) Clausewitz Condensed. Accessed on Moodle

Tzu, Sun. (1993) Art of War. Ware, UK: Wandsworth Press. Accessed on Moodle

Sumida, Jon T. (2009). ‘The Clausewitz Problem’ in Army History Journal, No. 73 Fall 2009.

Yuen, D. (2008) ‘Deciphering Sun Tzu’ in Comparative Strategy: An International Journal, vol. 27 no. 2.

[1] Apologise for constant use of “him” can also be applied with “her” etc. Just used for narrative style.

Thickness of Earth to Sun

Popular claims suggested that it is impossible to fold a piece of paper in half more than seven times no matter its size or thickness.  Previous mathematicians have worked out the number of folds required to reach the moon from the Earth which was worked out to be 42 folds[1] using a m thick paper. The size of the paper however, was not found. In theory, the average folds for a normal size A4 (m) paper is seven.
This is an interesting topic because it is incredible how, by exponential growth, a miniature of m thick like a piece of paper can be folded in half to reach the distance of the planet Saturn.
Britney Gallivan[2] was able to fold a piece of toilet paper of 1200 meters a number of 12 folds. She derived two mathematical expressions based on geometrical sequences, taking into consideration the amount of paper lost in every fold. These formulas make it possible to calculate the hypothetical length L and width W of a piece of paper that would be folded n times to equate the distance from the Earth to Saturn.

Gallivan established some rules that would need to be followed when folding a sheet of paper in half:    

A single rectangular sheet of paper of any size and uniform thickness can be used.
The fold line has to be in the same direction each time.
The folding process must not tear the paper.
When folded in half, the portions of the inner layers which face one another must almost touch one another.
The average thickness or structure of material of paper must remain unaffected by the folding process.
A fold is considered complete if portions of all layers lie in one straight line.

Hence, the length L of the paper influences the number of times it can be folded in half.
Hypothesis – The distance from the Earth to Saturn will be obtained by folding a piece of paper ≥50 times with a hypothetically large enough paper.
This exploration used exponential growth and logarithms in order to find out the number of folds required to reach Saturn. Before any calculation was done, it was indispensable to collect all the data required for the investigation. All the values were used were in the international system of units (metres) and standard form in order to keep the exploration standardized.
Taking into consideration the elliptical orbits of the planets, sometimes they are closer to Earth and sometimes they are further away. Therefore, the value used during this mathematical exploration was the mean value of when they are the furthest apart and the closest together. Astronomical units (AU) are the standard unit measure used when dealing with distances within the Solar System. 1 AU is equal to the distance from the Earth to the Sun which is equivalent tom.
Distance from the Earth to Saturn when closer together – 8.00 AU[3]
Distance from the Earth to Saturn when further apart – 11.0 AU3
Mean distance from the Earth to Saturn –  AU
The thickness of a normal A4 paper (0.210 297m) was calculated by taking a measurement of an office pack of 500 pages (80gsm) which was found to be about 0.05m. The thickness of each individual page is calculated by dividing the total thickness (0.05m) by the amount of sheets (500); giving a result of m.
Whenever a paper is folded in half, the number of layers is doubled so the thickness increases by two. When there is only one layer of paper (not folded), its thickness is m. Once it is folded in half for the first time, its thickness will be multiplied by 2 hence,
Folding it one more time means multiplying it by two again,
Thus, an expression can be established, showing the exponential growth;

The expression can be represented in a graph to illustrate graphically the exponential growth because of folding.
Graph 1:

From Graph 1, it is possible to visualise how, something that seems unrealistic like folding a sheet of paper to reach Saturn becomes possible. The graph also illustrates how rapidly exponential growth occurs.
Since the expression needs to be equal to the distance from the Earth to Saturn to work out (the number of folds), an equation to find can be solved:

To find, the rules of logarithms were put in place due to the exponential nature of the equation. The answer has been rounded up to 54 because it is not possible to have a half fold.
Gallivan derived the following formula for the minimum length of a piece of paper of thickness t to be folded n times in a single direction

To prove this formula, it is neccesary to understand that after each fold, some part of the paper is lost and becomes a rounded edge. I folded an A4 sheet of paper seven times in order to illustrate this:
As you can see from the picture, there is a rounded edge on the side which is paper being lost and is not contributing to the real thickness but just joining the layers. The curved portion becomes bigger in correlation with the number of folds and begins to take a greater area of the volume of the paper.
At the first fold, a semicircle of radius t (thickness) is formed, which has a perimeter . Thus, units of the paper are being used in the fold.  A paper smaller than this cannot be folded since there is not enough paper to form the fold. After the fold, there is a two-layer sheet of paper with a thickness of 2t. Another fold results in folding the second layer over the first layer. The second layer has a radius of , so it uses units of paper. The total amount of paper used by the second fold, for both layers, is resulting in a four-layer piece of paper.
The ith fold begings with layers, and folding the jth layer uses units of paper. Hence, the total length of paper used for the ith fold is given by

Therefore, to obtain the total length of paper required for n number of folds, sum this over i from 1 to n, which gives Gallivan’s formula:

The thickness can be substituted into t and the number of folds can be substituted into n

which gives L to be equal to 1.70-1028m.
The other expression proposed by Gallivan can be used to calculate the width of the paper.

If the length lost in the radii of earlier folds is not considered, the length lost must be considered in the last fold. At the final fold n, the side of the square must be at least equal to the length lost in the final fold which is (amount of length lost in each fold. Taking into consideration that the total area of the sheet (area = nb of sheets in penultimate step area of square in penultimate step) is preserved, Gallivan’s equation can be derived:

Again, the thickness and number of folds can be substituted and an answer for W can be found

giving W to be 2.69-1020m.
In conclusion, the initial hypothesis was right since the number of folds was 54 which is, indeed, greater than 50. The hypothetical paper that could, in theory, be folded 54 times so that its thickness equates the distance from the Earth to Saturn of m would be long and wide (taking into consideration that its thickness would bem). The dimensions of this paper would be bigger than the actual distance from the Earth to Saturn so, unfortunately, we do not have a paper that big that would allow us to reach to Saturn just by folding it in half.
This mathematical exploration used logarithms to find out the number of folds needed to reach Saturn with a m thick paper. However, the dimensions of this sheet of paper would be too big and hence, impossible to find in the Earth’s surface. Nevertheless, the exploration could have looked at using a thinner piece of paper to see if its dimensions would have been smaller and perhaps, we would have been able to find it in the surface of the Earth and we would have been able to reach Saturn.
Astronomy, S. (2012). How Far away is Saturn? [Online] Space.com. Available at: http://www.space.com/18477-how-far-away-is-saturn.html [Accessed 16 Jan. 2017].
IFLScience. (2016). Fold A Piece of Paper in Half 103 Times and It Will Be As Thick As the UNIVERSE. [Online] Available at: http://www.iflscience.com/space/fold-piece-paper-half-103-times-and-it-will-be-thick-universe/ [Accessed 16 Jan. 2017].
Pomonahistorical.org. (2002). Folding Paper in Half Twelve Times. [Online] Available at: http://pomonahistorical.org/12times.htm [Accessed 16 Jan. 2017].