The Good in Mathematics
The attribute of good is a concept that is central to mathematics. Mathematics is a subject that is evident in nature and very many processes of life. Many professions rely on mathematical concepts to accomplish their discourse objectives. It is the attribute of good in mathematics through its various concepts that helps us understand nature and its laws. This is evident through the various discoveries made by scientists in the present day academic world and that of a long time ago. The attribute of good implies that something can be explained through mathematical models. The attribute of good is manifested through the laws of nature, its application in the various activities in daily life. Through the attribute of good in mathematics, the philosophies by which we understand nature and the mechanisms of our daily life are understood.
Occurrence of the Attributes of Good in Mathematics
The attributes of good in mathematics have helped in the advancement of concepts within the discourse. Mackenzie (123) argues that for the longest time, the Euclid’s geometry was thought to be the sole approach to deductive reasoning. This was a school of thought was exalted to fame by Kantian theory of knowledge in which Euclid’s geometry was regarded foolproof knowledge of the universe. However, the Kantian theory noted that such knowledge was derived from reasoning instead of through observations. The reliance on reasoning instead of observations was a common approach to problem resolution in the early academic communities. It is through the reliance of human reasoning which is at times prone to subjectivity that the belief in Euclid’s geometry as foolproof knowledge flourished.
However, the birth of non-Euclidean geometry was the result of the pursuit of the attribute of good in mathematics. Mackenzie (124) reports that the discovery of the non-Euclidean geometry by Bolyai was the opening for other discoveries. The discovery of the hyperbolic geometry, another non-Euclidean geometry challenges the existing knowledge and traditions that were based on reasoning, hence not self-evident. The discovery of other geometry has enabled the advancement of different areas of study. For instance, the whale geometry has enabled the study of the movement of waves under water. Mackenzie (125) also reports that the discovery of the whale geometry has also enabled the development of knowledge on how sound travels in water, concepts that are important in modern-day activities such as submarine warfare.
The attributes of good in mathematics explain the occurrences in daily life. In his letters explaining why mathematics is important, Stewart (4) underscores the use of mathematical concepts in modern communication systems. For instance, Stewart (4) argues that the search engines used over the internet employ mathematical concepts such as probability theory, matrix algebra, and combinatorics of networks to determine the pages on the world wide web that have the highest likelihood of containing the information searched. It is through the application of these mathematical concepts that search engines such as Google are able to sift the World Wide Web for web pages that are most relevant to the search words used. This application has enabled the use of the internet for research among other applications.
It may not be apparent to the users that the availability of the pages with the relevant content is the product of mathematical models. This is why Stewart (4) holds that the ignorance of the most people regarding the worth of mathematics on the mechanics of the daily activities is not an argument to undermine its value. Stewart (4) also reports that the telephony communications employ mathematical concepts such as Fourier analysis, coding theory, and signal processing to transmit the signal from one end to another and make error corrections to avoid the distortion of messages.
Stewart (4) argues that mathematics has enabled the development of telephony communications from the erstwhile days when the switchboard operators used to connect manually callers to different locations. Through the use of the concepts highlighted above, the messages can be carried through the same channels and reconstructed by the receiving devices on the other end. Through the attribute of good in mathematics, the modern communication systems are able to keep up with the demands of the contemporary environment.
Mathematics is also in many of the transportation systems used presently. For instance Stewart (5) reports that the global positioning system that is used in the navigation of airplanes employs to determine their location and the location of other places within the accuracy of a few feet. This is achieved through the concept of geometry by analyzing the signals emitted by various satellites using mathematical models to pinpoint the location of the plane in the sky and other landmarks in which the pilots might have interest. The scheduling of planes also benefits from mathematical concepts to ensure that the planes are available when they are required.
The design of the planes and ensuring that they remain airborne is also a product of mathematical applications. The concepts of aerodynamics and fluid flow make use of mathematics in order to come up with calculations that inform the design process. Stewart (5) also argues that when operating an automobile, drives are subconsciously making mathematical calculations to determine various variables and use the input in decision making. The approach of the author is to show that many of the communication systems that we use incorporate mathematical concepts and that even if it is not apparent to many people; it is not an indication of its inexistence.
Mathematics is not an exclusive discourse; on the contrary, it has contributed to the development of other discourses. Pursuing the concept of mathematical certainty endorsed the applicability of mathematics as the universal language for sciences. Grabiner (223) finds that the element of mathematics that makes it applicable in many areas is its pursuit of certainty. This means that even that which is not apparent at the moment has some objective truth and that the truth can be expressed through mathematical models. In this way, mathematics is used to prove the existence of a body of knowledge and eliminate any skepticism.
As discussed earlier, it is through mathematics that non-Euclidean geometry was proven as reported by Mackenzie (124). Mathematics helped prove the existence of other geometries, and from which grew a new body of knowledge. The belief that the Euclidean geometry was foolproof was also challenged by mathematical models. The certainty of mathematics also means that scholars could determine the fundamental attributes of knowledge by studying and analyzing mathematics. Thus, mathematics was predominantly used in physical science such as physics. Mathematics was also used to determine the level of development of a science depending on how easily the discourse is approached using mathematical calculations. It is through this process that social sciences developed because of the use of statistics (Grabiner 225).
Mathematics enhances the perception of beauty in nature and art. In explaining the importance of mathematics and its applications in real life, Stewart (7) alludes to the beauty of the rainbow and the fact that it can be explained using mathematical concepts. This is an attempt to explain that mathematics aids in the perception and understanding of beauty and art and does not serve as an impediment to perceiving beauty. Stewart (7) argues that mathematics can provide adequate answers to questions regarding the fact that the rainbow assumes a circular arc, the brightness of the light emanating from a rainbow as well as its colors. Stewart (7) reports that the concept of geometry in mathematics enhances the understanding of the laws of nature as they relate to the beauty of the rainbow.
Owing to this geometry, one understands why the colors of the rainbow do not overlap. As the light bounces inside a drop of rain, the spherical nature of the drop gives the rays of the sun a very sharp focus as they emerge from the drop towards a given direction. The different colors of light form their unique cones which have unique angles. When the human eye beholds a rainbow, they perceive the cones of light emanating from raindrops within a certain dimension (Stewart 8). The understanding of the influence of the geometry of the raindrop on the appearance of the rainbow helps improve the understanding of its beauty. Stewart (8) concludes that contrary to prevailing belief, the role of mathematics in this instance is not to cloud the beauty of nature, and more specifically the rainbow. Instead, understanding how it forms aids in the appreciation of its beauty. Understanding the laws of nature and their influence on the art we see enhances our appreciation.
Summary
The attributes of good in mathematics are evident in many things in nature. Mathematics, its models and concepts have a lot of significance in everyday life. As discussed, mathematics helped advance its discourse. Through mathematics, there was a shift from the reliance of reasoning to observation. It is through observations that other forms of geometry were discovered. The discovery of other forms of geometry has helped generate a body of knowledge that is important to many of the activities in the contemporary life. The attribute of good in mathematics also manifests itself in the transport and communication systems of the present world. Major transportation means such as air travel relies on the use of mathematical concepts in many of its applications. These include the design of the planes, the scheduling, and purchase of tickets and the actual air travel.
The attribute of good also has an influence in major communication systems. These include the use of the internet and mobile telephony where mathematical concepts such as probability matrix, Fourier analysis, and coding are used. Mathematics is also important in understanding the laws of nature, beauty, and art. The example of the rainbow and how mathematics enhances the perception of the colors, their formation, and the explanation of various peculiarities regarding the formation o the rainbow helps challenge the misconception that mathematics inhibits beauty. In addition to helping one to understand nature through its laws, mathematics is also an integral part of the mechanics of various systems of everyday life.
Works Cited
Grabiner, Judith. The centrality of mathematics in the history of Western thought, Mathematics Magazine. 61.4(1988): 220-226.
Mackenzie, Dana. The universe in zero words. The story of mathematics as told through equations.
Stewart, Ian. Letters to a young mathematician. Cambridge. Perseus Books Group. 2006. Print.
