Quality logical reasoning that can later prove
Quality can be defined as thestate of possessing a higher degree of excellence when compared to othermatters of similar nature. To measure the quality of a piece of knowledge, onemust identify the criterions that distinguish high-quality knowledge from poorquality knowledge and is easily refuted. Poor quality knowledge would be onethat is vulnerable to criticism. Quality knowledge needs to have a strong andclear line of argument or basis upon which the knowledge is developed.
Therefore, knowledge of high quality should possess a high degree of accuracy.It is also important for knowledge to be highly adaptable and remain relevantas time passes. So it can be assumed that in order to produce such knowledge,one must exert exhaustive efforts to eliminate any bias or errors. Forknowledge to be directly proportional in terms of quality and its historicaldevelopment, the production of the knowledge must be dynamic in nature. This means that knowledge needs to be continuouslyimproved to remain relevant and this may be through trial and error,experiments and other methods that constitute it to disprove or uncoverpreviously unknown areas of the discipline. Continuous improvement ensures thatold knowledge is continuously replaced with a more accurate knowledge that issuperior to the previous in terms of precision and validity. This essay willfocus on the dynamic versus static nature of knowledge and their role inproducing quality knowledge in the area of Mathematics and Natural Sciences.
Mathematics is a purelylogical system of knowledge. Reasoning is the basis on which knowledge in thearea of mathematics is produced, which relies on logic and rationality. Thepursuit of complete subjectivity is the highest priority in knowledgeproduction, justifying the dynamic nature of the discipline.
Knowledge production in mathematics followsunder the strict rule that every knowledge produced should be objective andimpartial therefore limiting the scope in which a knowledge can be claimedwithout rigorous evidence. Before a mathematical statement is accepted as atheorem, the opinion that was formed by the mathematician from his observationsmust go through an order of logical reasoning that can later prove or disprovethe conjecture. This means that when a mathematician has claimed to discoversomething, he is obligated to go through a process to convert personalknowledge into shared knowledge to eliminate any bias. A notable example of aconjecture that was later disproved was the findings of German mathematicianPeter Gustav Lejeune Dirichlet in 1838 who proposed the mathematical inequalityli(x)>?(x). Later in 1914, an English mathematician John Edensor Littlewoodclaimed the inequality was false although he had no evidence to support thisclaim. However, South African mathematician Stanley Skewes supportedLittlewood’s claim when he provided the evidence to support it.
One example that defies theconcept of direct proportionality is the physical law of buoyancy or theArchimedes’ principle that coined the term “eureka” itself. “Eureka”, in Greek,means “I have found it!” and those were the exact words said my Archimedeswhile running down the streets of Syracuse after he discovered a method tomeasure the volume of gold, which was impossible at that time. Archimedes waschallenged with the task of proving that the new crown given by the goldsmithfor King was not pure gold although his efforts were unproductive. One day, hewent to take a bath when he noticed that the water level rose and overflowed ashe submerged himself in. At that instant, he knew that the amount of water thathad been displaced was equal to the volume of his body he has submerged.Instead of logical reasoning, Archimedes relied on his intuition, which isconsidered personal and defies against the notion that mathematics should bepurely free of bias.
While serendipitousdiscoveries are assumed to happen by pure chance, other factors also play arole such as the time period and any prerequisite knowledge that the individuallearned that may increase the chances of the individual discovering something”by luck”. Such was the case for Archimedes. He was deemed as a mathematicalgenius even before his discovery. It is highly unlikely that the king entrusteda normal man with the task of finding a method to determine real gold from fakeand even more unlikely that his discovery was almost immediately accepted. Thestory of Archimedes was first published in the first century B.
C but the realevent took place long before that when the proof of knowledge was not asdemanding as it is now. The abundance of knowledge present in the 21st centurywould not have allowed Archimedes to claim such a discovery without substantialevidence and therefore the likeliness of events repeating itself in the mordernworld in highly unlikely. Moreover, the traditional use of the Archimedesprinciple that was limited to measuring the volume of irregular objects, hasexpanded throughout history and greatly contributed to many developments inseveral areas of society, most notably in the development of infrastructure andthe design of the submarine, in which the principle is relied upon. Therefore,significant developments in the applicability of knowledge supports that theduration of time spent on improving knowledge will improve its quality.