Quality can be defined as the

state of possessing a higher degree of excellence when compared to other

matters of similar nature. To measure the quality of a piece of knowledge, one

must identify the criterions that distinguish high-quality knowledge from poor

quality knowledge and is easily refuted. Poor quality knowledge would be one

that is vulnerable to criticism. Quality knowledge needs to have a strong and

clear 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 relevant

as 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. For

knowledge to be directly proportional in terms of quality and its historical

development, the production of the knowledge must be dynamic in nature. This means that knowledge needs to be continuously

improved to remain relevant and this may be through trial and error,

experiments and other methods that constitute it to disprove or uncover

previously unknown areas of the discipline. Continuous improvement ensures that

old knowledge is continuously replaced with a more accurate knowledge that is

superior to the previous in terms of precision and validity. This essay will

focus on the dynamic versus static nature of knowledge and their role in

producing quality knowledge in the area of Mathematics and Natural Sciences.

Mathematics is a purely

logical system of knowledge. Reasoning is the basis on which knowledge in the

area of mathematics is produced, which relies on logic and rationality. The

pursuit of complete subjectivity is the highest priority in knowledge

production, justifying the dynamic nature of the discipline. Knowledge production in mathematics follows

under the strict rule that every knowledge produced should be objective and

impartial therefore limiting the scope in which a knowledge can be claimed

without rigorous evidence. Before a mathematical statement is accepted as a

theorem, the opinion that was formed by the mathematician from his observations

must go through an order of logical reasoning that can later prove or disprove

the conjecture. This means that when a mathematician has claimed to discover

something, he is obligated to go through a process to convert personal

knowledge into shared knowledge to eliminate any bias.

A notable example of a

conjecture that was later disproved was the findings of German mathematician

Peter Gustav Lejeune Dirichlet in 1838 who proposed the mathematical inequality

li(x)>?(x). Later in 1914, an English mathematician John Edensor Littlewood

claimed the inequality was false although he had no evidence to support this

claim. However, South African mathematician Stanley Skewes supported

Littlewood’s claim when he provided the evidence to support it.

One example that defies the

concept of direct proportionality is the physical law of buoyancy or the

Archimedes’ principle that coined the term “eureka” itself. “Eureka”, in Greek,

means “I have found it!” and those were the exact words said my Archimedes

while running down the streets of Syracuse after he discovered a method to

measure the volume of gold, which was impossible at that time. Archimedes was

challenged with the task of proving that the new crown given by the goldsmith

for King was not pure gold although his efforts were unproductive. One day, he

went to take a bath when he noticed that the water level rose and overflowed as

he submerged himself in. At that instant, he knew that the amount of water that

had been displaced was equal to the volume of his body he has submerged.

Instead of logical reasoning, Archimedes relied on his intuition, which is

considered personal and defies against the notion that mathematics should be

purely free of bias.

While serendipitous

discoveries are assumed to happen by pure chance, other factors also play a

role such as the time period and any prerequisite knowledge that the individual

learned that may increase the chances of the individual discovering something

“by luck”. Such was the case for Archimedes. He was deemed as a mathematical

genius even before his discovery. It is highly unlikely that the king entrusted

a normal man with the task of finding a method to determine real gold from fake

and even more unlikely that his discovery was almost immediately accepted. The

story of Archimedes was first published in the first century B.C but the real

event took place long before that when the proof of knowledge was not as

demanding as it is now. The abundance of knowledge present in the 21st century

would not have allowed Archimedes to claim such a discovery without substantial

evidence and therefore the likeliness of events repeating itself in the mordern

world in highly unlikely. Moreover, the traditional use of the Archimedes

principle that was limited to measuring the volume of irregular objects, has

expanded throughout history and greatly contributed to many developments in

several areas of society, most notably in the development of infrastructure and

the design of the submarine, in which the principle is relied upon. Therefore,

significant developments in the applicability of knowledge supports that the

duration of time spent on improving knowledge will improve its quality.