TOK Essay

Q.

Over time knowledge has become more accurate. Discuss his statements with

reference to two areas of knowledge

It

is possible for several people to state that knowledge does become accurate and

also the opposite. However, they might not exactly be referring to accuracy but

instead may be misunderstanding the term “accurate” all by itself. Before that,

we need know what “knowledge” is. “Knowledge” refers to the acquaintance with

facts, truth or principles 1. What is

“accurate”? If something is accurate it could be used as a model or a reference

for something because it is free from error or defect 2. This made me

arrive at my knowledge question. “What

are the issues that arise in the progression of knowledge over time?” In

different areas, knowledge gained and the accuracy can vary due to different

way of knowledge production. Hence the accuracy of knowledge would also differ

from one area to the other which. The accuracy may differ due to difference in

ideologies and thought processes of authorities. In some cases knowledge might

not be accurate but if that piece of knowledge is well reasoned for the facts

known to us, it can be well accepted in the society. For example, Mathematics

can be more accurate since it is less interpretive as compared to History which

is based on interpretations made from facts present. Looking back in time at

our ancestors, I concluded that the thought processes have changed and have

become more refined. Hence, I referred to History as one of my Area of knowledge

since I wanted to compare the ideologies of the authorities in the past and the

present.

The first claim of

this essay is, Mathematics is one of the

only subject which has the least ambiguity and highest accuracy in the

knowledge produced. Mathematics is very directive and leaves no chances of

ambiguity or in other words, there is no scope of interpretations. This causes

the facts produced in Mathematics to be highly acceptable and backed with

reasoning. It is known that calculus was discovered few thousand years ago but

only taken into serious considerations in the 17th century3. It has been observed that

there has been no sign of neglect towards calculus since then. However, there

have been modifications in calculus to meet with the current generations’

needs. Calculus has evolved over time and been used in areas of Mathematics

which would be impossible without it.

For example

calculating the exact acceleration of an object requires knowing the exact

position of the object at a given time. Moreover, without calculus there would

be many areas of mathematics undiscovered and we would not have been able to

progress any further. The evolution calculus began with the shaping of a new

era. Mathematicians started to discover new applications of calculus to enhance

the pre-existing concepts and patterns. This in return makes the knowledge

production in mathematics accurate as it not overthrown the old system but only

added onto it and refined it. It is widely acceptable and no scope for a

different answer. It is simplistic and straightforward in terms of arriving at

an answer. Having investigated calculus in school, I have never truly

questioned the accuracy of mathematics until now, truly realising its worth.

However, Mathematics

can also be counterintuitive in certain cases. This brings me to my first

counterclaim of the essay, Mathematics

is not entirely accurate even though the knowledge produced in Mathematics is

reasoned and backed by facts. Even though mathematics is based heavily on

facts and reasoning, there are several cases in which lack of sufficient

exploration has caused production of highly counterintuitive solutions and in

some cases, nearly impossible. Mathematics can become highly complicated and

may not be understood by a layman. This causes a lack of acceptability in the

society as no one knows what to truly believe. There are different way to solve

the same problem. However, irrespective of the method, the result is always the

same but that is only the case for problems that are commonly asked and have

had years of research behind them. Although, this is not the cases for problems

which have not been the centre of research for as long as the common problems.

For example, the famous problem that several mathematicians stumbled upon. The

sum of natural numbers up to infinity. 4

1 + 2 + 3 + 4 + … + ? =?

This seemingly easy

question is often overlooked. Intuitively, the answer should be a very large

number which has countless digit.

Nonetheless, the answer is shockingly as follows:

Although there have

been several proofs that the above conjecture is true, when tried to prove by

mathematical induction, a method I recently learnt in school, it does not give

the above solution. However this has been proved by the Riemann Zeta function.

As a matter of fact, this result has been used widely in areas of physics to

learn more about quantum mechanics and string theory.5 My interest in

quantum physics made me question the reliability of the result above as it can

be proved by one method and be completely superficial and non-calculative by

another. This in return reduces the accuracy of results produced as the level

of reliance on certain claims in mathematics can overpower the fact that the

ambiguity is being overlooked. Thus it can be said that knowledge in

Mathematics becomes accurate to an extent

On the other hand,

knowledge in history is produced by interpretations. History is not necessarily accurate in terms of the true facts but is

sufficient enough to give some insight about the possibilities. Historians

interpret possible occurrences based on the artefacts and evidences found. It

is this relevance and acceptance of the interpretations that determines the

knowledge produced in History. The Indus

valley civilisations was one of the most advanced civilisations and has

provided in-depth detail about the era before Christ in the Indian

subcontinent.6

There have been various manuscripts and sculptures excavated that have provided

historians with promising ideas of the roots of the modern Indian and Pakistani

cultures and traditions.7 On the other hand,

although there are promising interpretations about how the civilisation

flourished, there is still uncertainty about the declination of the

civilisation. There have only been

theories and no concrete evidence for the end of the civilisation. 8 Even after

thousands of years of evolution and advancements and differences in mind-sets

and technologies used by archaeologists, there are certain questions remained

unanswered which question the accuracy of knowledge. Hence, the interpretations

might not be entirely accurate but are sufficient to give a possible

explanation of the past.

On the contrary, the accuracy of the knowledge produced in

history may reduce over time. It is possible for the interpretations of

historians change over time as the thought processes of various generations

differ from one another creating an ambiguity in the knowledge produced. As of

now we know more facts about the World War than the Stone Age. This is because

the World War is a recent event in the timeline as compared to the Stone Age.

This arises due to the availability of resources. Since World War is more

recent there are more available facts regarding the war. The duration of the

Stone Age is a very rough estimate 9 whereas historians

have more precise knowledge of the World War. The ruins and available sources

of knowledge deplete over time enabling areas of ambiguity reducing the scope

of absolute surety. In the case of the War, there is ample evidence to give insight

into what would have happened. This can also be verified since many of the

World War survivors can help verify and validate the facts making it more

accurate with which, it can be concluded that knowledge produced in History may

not be necessarily accurate and even if it is, it would not stay accurate due

to the dynamism of ideologies of people from different generations and cultural

backgrounds.

It needs to be kept

in mind that accuracy itself is a dynamic term depending on its scenarios.

There can be various instances where knowledge may be prone to ambiguity yet be

accurate due to the acceptance and the usage of the piece of knowledge. The

accuracy is determined by how close it can get to the actual facts, yet facts

are determined by interpretations and reasoning. Hence there are some questions

that remain unanswered such as who could possibly determine what is or could be

classified as accurate since the accuracy differs from one area of knowledge to

the other. The production and perception of knowledge creates a divide in the

usage of the word “accurate”

1 www.dictionary.com/browse/knowledge

2 www.dictionary.com/browse/accurate

3 https://www.math.uh.edu/~tomforde/calchistory.html

4 http://adsabs.harvard.edu/abs/1999math……9178L

5 https://physics.stackexchange.com/questions/105635/which-values-of-the-riemann-zeta-function-at-negative-arguments-come-up-in-physi

6 www.ancient.eu/Indus_Valley_Civilization/

7 www.ancient.eu/Indus_Valley_Civilization/

8 https://www.boundless.com/world-history/textbooks/boundless-world-history-textbook/early-civilizations-in-the-indian-subcontinent-4/the-indus-river-valley-civilizations-23/disappearance-of-the-indus-valley-civilization-103-13207/

9 www.ancient.eu/Stone_Age/