After acquiring and digesting information from various quarters, it is prudent for one to evaluate how one comes about to know what he or she knows. It is thus crucial for one to understand the impact of knowledge and its practicality. However, in pursuit to know how we know what we know it is prudent to focus on the two branches of the knowledge: practical and theoretical. The practical knowledge is inclined towards a persons day-to-day experiences. It thus helps one cope with different situations by honing various skills and techniques. Theoretical knowledge, on the other hand, dwells on answering the question why. It provides one with the understanding of why one approach works and other fails. It teaches one through other peoples accounts and experiences. It opens avenues for a deeper understanding of concepts by focusing on them on a whole context and the reasoning behind them. The two types of knowledge are pivotal to an individuals intellectual growth as they offer a multidimensional understanding. This paper, therefore, seeks to assert that with application to the real world the value of knowledge is enhanced. This leads to the question: what is the unit of measurement of knowledge value? What entails the real world? All these questions will be captured by the essays focus on the validity of the aforementioned statement by focusing on Arts and Mathematics.
In consideration of mathematics as an area of knowledge, it is prudent for one to understand that it has two distinct branches. The first branch is pure mathematics and the second, applied mathematics. The pure mathematics is constructed to study entirely abstract concepts. Much of those that subscribe to pure mathematics focus on solving problems for the sake of mathematics. Applied mathematics, on the other hand, has its practical aspect. It uses mathematical methods in engineering, business, science industry, and computer science. It enables mathematicians to solve problems through formulation and study of mathematical models. In many cases, even the most abstract of mathematics had a very unexpected application. The number theory, was previously, believed to be useless until it was incorporated in computer science. The number of the theory is the basis of the computer encrypts systems. Pure mathematics, on the other hand, can be separated from the physical world. It establishes facts, problems, and answers. It is also totally separated from the physical world. The two branches of mathematics, however, are somewhat correlated. In many instances, the two overlap. Many applied mathematicians rely on techniques, tools, and formulas that are deemed pure. The pure mathematicians, on the other hand, rely on social and a natural and social phenomenon is the inspiration behind their abstract workings. To expound clearly on pure mathematics, a famous theorem has arrived on the Banach-Tarski paradox. The theorem cites that although it is a verified fact that it is possible to convert one sphere into using two rotations and cuts. This transformation is ideal meaning that it is something that cannot exist in reality. The Banach-Tarski paradox highlights that the knowledge claim of the prompt can be perceived to be wrong as the paradox value is not diminished by the fact that it is not applicable in the real life situations.
By using Applied Mathematics, one might establish the extent to which the claim stated in the prompt might be true. This is so as the value of knowledge is greater through its application to the real world. As aforementioned, applied mathematics can be seen and used in various fields. Game theory is one of the many applied mathematics theorems. It is applied in some fields namely politics, economics, psychology, computer science, biology, and logic. It relates to an array of human behaviors incorporating logical decision-making process in animals, humans and computers.
Game theory as its known today founds its roots to John Von Neumann though some aspects related to the theory had been in existence since time immemorial. In his 1944 publication, Theory of Games and Economic Behavior, Neumann explored mathematical and scientific techniques to establish or arrive at optimal choices in real-life scenarios. One of the most popular games under the theory is the Prisoners Dilemma. The game tries to highlight a scenario where two rational individuals might not cooperate or work together even if the situation seems to be in their favor. It was created in 1950 by Melvin Dresher and Merrill Flood. The game was however formalized by Albert Tucker, who used the prisoner's context to establish the Prisoner's Dilemma. Tucker incorporated payoffs in the Prisoners Dilemma and by doing so, he made Flood's and Dresher's ideas more understandable and accessible. It acts as a game theory basis in many of its applications such as in the areas of probability and statistics.
The value of knowledge in theoretical and practical knowledge can also be established through arts as a discipline of study. A good example of art application in the real world and how it influences knowledge is George Orwell's book Animal Farm. The book was published in 1945 as a reflection of events that led to the 1917 Russian revolution and later the Stalin era. The book was a revolt against Stalinism with its strong imagery and symbolism heavily grounded on Orwell's democratic socialism. Orwell's narrative was found on his belief that the Soviet Union had been changed to a tyranny, enforced by a reign of terror and personality worship. The context of the book is in between the years 1943 and 1944 during which the Soviet Union was in alliance with the United Kingdom. Much of the UK residents and administration held Stalin in high esteem as an ally. The book was written with much incorporation of satire to depict the Soviet Union under Stalin and why socialism was not the best system of governance. It was the true embodiment of art and political purpose. The novel core message was that all violent revolutions often precipitate the emergence of tyrannical rule after a brief period. It uses symbolism and metaphors to relay these themes. Animals are the main characters and are used to depict the events and parties surrounding the then Russian revolution. Napoleon and Old Major are the main characters taking the form of pigs. The two represent Stalin and Lenin respectively. Just like Stalin in the Soviet Union, Napoleon the pig is depicted as the main villain in the story. Napoleon, just like Stalin, has his way in takeovers. Stalin exhibited the same characteristics as he eliminated people that stood in his way to Russia's leadership. The Old Major, on the other hand, is used to illustrate Lenin, who was seen as the founder of the Communist-led revolution in China. Old Majors skull is put on public display same as Lenin's case where on his demise, his body was put in public display. Another pig character, Snowball represents Trotsky, who was forced to flee Russia amidst the revolutions. Squealer is another character that depicts Vyacheslav Molotov. Molotov was in charge of propaganda in the Stalin regime. The humans, Mr. Pilkington, represents England and her allies while Mr. Fredrick represents Germany. The novel is relevant to date with many literature students using it to highlight inequality and dictatorships that are present even under democratic dispensations. Many countries just as in The Animal Farm have undergone revolutions, which end up being a recipe for new totalitarian regimes. A good case is Iraq during Saddam Hussein's tenure. Saddam ascended to power via a revolution but later turned out to be one of the worst dictators in the world.
On another dimension, in arts, the value of knowledge is not related to the practicality of knowledge. Michelangelo is one of the greatest Italian painter, sculptor, architect, engineer, and poet. He is hailed as one of the revolutionaries in the Renaissance period. He is best-established as one of the prolific forces behind the Mannerist art. Mannerist art dwelled on creating art that appeals to intellectualism as well as artificialness. It usually fuses highly styled poses and elongated proportions. Much of this style focused on style rather than substance. The art further incorporated alterations or exaggeration of postures and expression as well as proportions. Much of the art by Michelangelo adopted such characteristics. The Tomb of Giuliano de Medici is one of the Mannerist sculptures adopted by the sculptor. The tomb art fuses use of allegory by including four figures. The art stretches one's imaginations. Michelangelo uses male and female figures to represent night and day. A clutch of poppies and an eagle are other allegorical figures incorporated in the tomb art to highlight the artists dalliance with Mannerist art that was associated with high renaissance.
The Tomb of Giuliano de Medici to date is considered as one of the finest Michelangelo arts. Though the art was never finished, many lovers of art adore it and appreciate Michelangelo's artistry. Despite the much attention accorded to threat it has no actual relevance to the real world. It is only mentioned in historical and artistic context. It does not foster link with the contemporary society nor does it represent events that many people can relate to. The art is simply a celebration of art and artistry in the eyes of art lovers.
In conclusion, mathematics and arts posit the different spheres knowledge: practical and theoretical. When it comes to mathematics, there are two branches applied and pure. The two though found on the same discipline have different interpretations of scenarios. Applied mathematics is diversified to incorporate other themes and disciplines such as economics, computer science, and biology. A good example of applied mathematics theorem is the Game Theory, which is objective and applicable in various contexts. Pure mathematics, on the other hand, is founded on abstract concepts. It thrives away from the physical world. A good example of pure mathematics theorem is the Banach-Tarski paradox. Art on the other hand as a subject also highlights the various dimensions. Literal texts such as George Orwell's The Animal Farm employ artistic tools to depict true events that occurred in the Soviet Union. Using animals as some of the characters, the author manages to relay his intended message, which also resonates with the world to date. The other form of art dwelled on is Michelangelo's mannerist art, The Tomb of Giuliano de Medici. The art simply illustrates Michelangelo's artistry and his love for mannerist art but not on its applicability in the real world. Through the various examples highlighted it is safe to cite that the value of knowledge is strongly related to its applicability in the real world.
Gardner, Helen, and Fred S. Kleiner. Gardner's Art Through the Ages: A Global History. Australia: Wadsworth, Cengage Learning, 2013.
Lass, Harry. Elements of Pure and Applied Mathematics. Mineola, N.Y.: Dover Publications, 2009.
Rodden, John. Understanding Animal Farm: A Student Casebook to Issues, Sources, and Historical Documents. Westport, Conn: Greenwood Press, 1999.
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