ESSAY

When mathematicians, historians, and scientists say that they have explained something, are they using the word ‘explain’ in the same way?

A different approach to the topic -
What were the conclusions some of my fellow classmates came to?

“When historians explain something they mean something totally different from when mathematicians and scientists explain something.” – Natasha

“Thus different areas of knowledge are explained in different manners and each of these explanations has different implications.” – Kirtika

“History, Math and Science hence explain different things and in different ways.” - Aneesha

“However, when different people- mathematicians, scientists or even historians say they “explain” something are they referring to “explain” in the same way? Truly, looking at all the different meanings of the word, they don’t.” – Raghav

Everybody till now has agreed that when mathematicians, historians and scientists say they have explained something they are using the word explain in different ways. However I beg to differ.

As you must have noticed the main aspect of the title largely deals with the treatment of the word ‘explain’ in a wide variety of contexts. It is reasonable to consider that mathematicians, historians, and scientists would all explain their findings in their own way. However, their actions in essence are the same.

Why is this? All humans are constantly trying to explain the unexplained. They are providing reasons and judgments on the basis of data that they have collected and are presenting their conclusions to describe a phenomenon, idea or concept in their field. Therefore, we can conclude that the explainers themselves are all using the word ‘explain’ in the same way as they are all undergoing the same duty. It is only the listeners that truly distinguish the differences in these ‘explanations.’ The perception of listeners is directly related to ‘Areas of Knowledge’ in the specific field mentioned. Moreover, the ‘Ways of Knowing’ that are employed in each Area. Therefore, at one angle, the question above has an answer that is almost obvious- Explainers would of course be using the word ‘explain’ in the same way, but the connotations of their explanations evoke contrasting sentiments amidst us.

Mathematics is one such area that builds itself on ‘Logic and Reasoning’ that is to say it draws all its explanations in a very logical and rigid fashion. Through my experiences in math, and after discussing how tangible math is with various teachers of the IB, I have realized that Mathematics relies on its own rigid rules that cannot be altered to suit one’s interests.

Due to this very reason, I deem that this ebbs the possibility of one’s own interpretations and perceptions becoming occupied in the process and thus presents knowledge in its most factual form. It is my observation that Mathematics would thus lead to the most logical results that can very rarely, if at all, be debated on. The only possible errors in mathematics could lie in the logic employed.

Shifting to the next area of discussion - History. History seems to be the total opposite of what math is. History is one such Area of Knowledge where explanations are formed entirely on the root of interpretation. As a result this creates a great deal of bias. It has been my personal finding while working on a history project in the 10th grade that I have come across this great deal of bias. I have studied of numerous occurrences during the First World War, where countries like Britain projected that the Germans were wrong (look at cartoon attached), while the German projected that they were not entirely to be blamed for the war.

This was a fine exemplar of a case where many historians distorted facts to suit only one opinion, while disregarding others. This that would most definitely introduce a reasonable degree of doubt regarding the validity of the facts presented. Interpretation clearly allows room for one’s personal opinion, and more often than not, this tends to distort the true facts and the underlying truths.

Looking at the two areas of knowledge presented above, Science would seem to present a very unique perspective, a middle ground between the rigidity of Mathematics and the interpretation of History since it is based purely on experimentation and the evaluation of empirical evidence. Laws can always be modified, and are always open to interpretation. An example of this case is the evolution of science; man himself has progressed from four elements to a hundred and nineteen. Due to this very reason any person who does not trust in the concepts presented to him is able to observe the phenomenon for himself and derive his own independent conclusions out of the calculations he has made.

However, it is important to note that in the above paragraphs, the view of the Areas of Knowledge with respect to the explainers is considered. Although the means by which they arrive at their respective conclusions are completely diverse, the underlying theory is still the same. They are all trying to describe the world around them, and ‘explain’ the occurrences that happen in our world.

Thus, differences in the usage of the word ‘explain’ cannot arise, as it still means the same thing to each explainer. The difference lies in the perceptions of the listeners who retain their own analysis as well as prior knowledge while evaluating an argument and are thus able to generate their own opinions regarding each field. An analysis of these skills does in fact reveal a great deal about the human thought process and how, as individuals, we pick and observe flaws out in others arguments and thus ascertain its level of credibility. A perfect example of this would be quoting my fellow classmates at the beginning of my essay.

All three Areas of Knowledge listed above can be used connected to logic to evaluate an argument also called -Aristotelian ‘logos’. Each Area involves the analysis of data to arrive at some conclusions. Thus, reasoning skills that will be analyzed would keep in mind the ‘logos’ nature of each area and thus assist in the understanding of the leading question. Obviously these areas require certain other skill but the foundation is primarily the same.

Mathematics is often coupled with Inductive Reasoning. In maths we develop our own hypothesis or so called ‘conjectures’ and proceed to verify the observations by the Principle of Mathematical Induction. For example when a mathematician sees a familiar pattern between a certain group of numbers, i.e. when he attempts to generalize a pattern in that group of numbers, he first comes up with a conjecture using Induction. His peers prove his conjecture carefully as goes through a tough check; the statement of his conjecture finally becomes a Theorem when his peers agree and will always remain so. Elevation to the height of a theorem is an irreversible process- the results proved are largely irrefutable at this stage. Due to the logical nature of Mathematics and the rigidity of its founding principles, opponents of math cannot seldom debate on any of the laws established simply because its logical foundations are far too strong. There are no observable degrees of uncertainty and so we tend to treat mathematical knowledge as pure fact.

As for History, it works on causality and effect-to-cause reasoning. Historians seek to describe the past by analyzing its effect on the present. For a historian, the world is a place where every action has a reaction. This would, of course, present readers with a degree of uncertainty. For example when you read a history book written by a Nazi about the holocaust, you are going to get a different view about it than if you read a book written by a Jew. In history there are always two sides to every event, this hinders our knowledge because we don't know which is true, and we can only give our own interpretations and analysis to what we're read - and this depends on our own paradigm and cultural background. Effects discussed may not necessarily have been created by causes outlined by the historians. As said, the world does not function in isolation. When historians explain something, those who are listening to their analysis often note the element of bias within the minds of the historians. Historians can often make several errors in judgment and overlook key fats while backtracking from effect to cause.

Science presents a unique perspective that makes use of several aspects of reasoning employed in both mathematics and history. The basis of science is Conditional Reasoning, or the formation of a hypothesis. This means that while conducting an experiment one must carry it out in ideal conditions. However it is also important to have a independent and a dependant variable. The “If…Then… because…” nature of Conditional Reasoning allows spectators to effectively comprehend the idea being established in the laboratory and question the procedures employed for any flaws. They also note the degree of uncertainty in experimental measurements and are mindful of the errors generated. Science involves both qualitative and quantitative measures. However what may be true for one point of time may not for anther. For example, in the 17th century people did not believe that they could travel from one place to another by flying. Today in the 21st we use aircrafts that transport us in a span of no less than 2 hours from Delhi to Bombay.

This example again explains the point that each Area evokes a dramatically different sentiment within any listener. However, we can conclude that listeners would view Mathematical facts as most logical, and least open to debate, due to its nature of being based on a harsh system of rules. Historical interpretations are always doubted, mainly due to the abundance of errors that are inevitably present in any account. This is the reason why the nature of sources in history is extremely important as it defines the element of bias within the account and allows readers to become aware of the said bias. Lastly, science is a unique blend of both History and Mathematics. Listeners are always allowed to maintain their own opinions but still note the logical framework of scientific reasoning and would thus take scientific explanations to be far more factually accurate than an opinion in History.

Therefore the leading question still remains answered. The connotations of the word ‘explain’ as used in the guiding question differ only from the perspective of the viewer. Explainers are merely carrying out their job of generating generalizations to describe our world.