TOK be misunderstanding the term “accurate” all by itself.

TOK Essay

Q.
Over time knowledge has become more accurate. Discuss his statements with
reference to two areas of knowledge

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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/

 

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