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The Difference in Explanations - An Opinion Piece

When a mathematician, a historian and a scientist are asked to explain something, they are not using the word explain in the same manner, as their explanations are rooted from their contrasting methodologies and disciples that govern their profession. Instead of the word explain as being defined as “make comprehensible”, their definition of explain is more specific and geared towards their audience, in which they are explaining their work to. For the historian, his explanation is directed towards the public, as he attempts to provide an interpretation relating the cause and the effect of some significant event that happened in history. For the mathematician, the manner in which he explains something is different than the historian as his explanations are directed to his colleagues. Thus, he does not attempt to explain any of the mathematical concepts that were used in his proof, as he uses mathematics as a language to communicate his thoughts. Instead his definition of explain is synonymous to describe or prove, as he is merely proving the method that he took to reach to his conclusions to his peers so that they can review his work for any illogical jumps in reasoning. The scientist is similar, in which his explains to a target group of people; his colleagues. But the manner in which he explains something is derived from the scientific method, in which they base their explanations on observations that either support or refute their hypothesis. Thus his definition of explaining is characterized by the scientific method, as they attempt to conform to their hypothesis. All in all, the word ‘”explain” has a different meaning in these three disciples of knowledge.

A historian’s explanation differs greatly from that of the mathematician and the scientist as he has to construct the past based on written records, or evidence that has survived to the present day. Because the past is non-existent and thus unobservable; the historian must rely on sources; either primary or secondary to help him produce an interpretation; in other words, his explanation. The problem with these sources is that they always have a certain degree of bias towards them, which can be shaped from their culture and their interests. The implications of this are more severe in the ancient societies as the number of records that survived today is small. Consider the Ancient Sumerian culture which is typically associated with being dour. What if the Sumerians were not actually gloomy, and that the accounts that portray them in this manner were underrepresented? That would mean that we would never know how Ancient Sumerian culture was actually like. Unlike scientists’ explanations which do not necessary omit any collected data to the extent of the historian, the interpretations of historians are highly selective. The need is more evident in modern times, as the amount of records produced can reach insane amounts like 50 million, which the amount found in Hitler’s secret archive. The historian’s selectivity of the facts is based on the personal biases of the historian itself, and in some cases, after significant events such as war; it depends on their native country; whether they are losers or winners. This was the case after the US dropped the atom bomb on Hiroshima and Nagasaki, as many historians glorified the need to drop the bomb by portraying the Japanese as ruthless through the use of negative connotations, which misinformed the public; since President Roosevelt had motives to bring his troops out of the war as soon as possible. It can be seen that the historian’s explanations must have conformity to society, as if the American historian takes the side of the Japanese, condemning the actions of his own country, then it is likely that his account will not be published. From the very nature of history (unobservable past), it is suggested that the explanations from historians are biased, as they are biased, the witnesses to the historical event could be biased and it may even been recorded by biased individuals, thus completely undermining any knowledge from history. However, when the historian explains something, like for example, the reasons for the First Opium War in China, the historian knows the sheer difficulty in with achieving certainty and he is aware of the different cultural perspective. Instead of relying on the Chinese records’ perspective of the British not recognizing the superiority of the Middle Kingdom as a reason for the Opium War, he would be open to other accounts with different perspectives; such as the British, who felt that they were not being treated equality by the Chinese. Thus, when the historian explains something, he tries seeks plenty of evidence and tries to develop an interpretation that is reasonable and has some consistency with the evidence.

Unlike historians, the explanations that scientists give are in the form of laws or theories based on the scientific method, which consists of a hypothesis, observations, and an experiment. When the scientist explains something, he is actually trying to support or refute his hypothesis through the data that he has collected. The explanations that the scientists give; or in other words, the laws or theories have one distinguishing feature from that of the historians and the mathematicians; the fact that their generalized findings cannot be ever proven experimentally that it is correct. To a great extent, it is like the experiment that I have conducted for my chemistry extended essay in which, through many trials I have discovered that as the SPF factor increases, the UVA protection that the sunscreen provides decreases. If I conduct a zillion more trials and each one of them follows my generalized relationship that I have found, I cannot say that I have proven that my claim is correct. This is essentially the problem of induction, which is what the scientific method is based upon. The results are generalized from the observed to the unobserved so it cannot be said with absolute certainty that our generalizations are true, however, it could be said that as there are more instances that confirm the generalization, there is more confidence in the generalization. However, these generalizations can be proven false by exceptions to these generalizations. The content of the explanations are also in contrast to that of the historian, as the scientist explains using models to accurately predict the occurrence of phenomena in the natural world. When scientists explain something they have many factors to consider as it can lead to unsubstantial generalizations. Scientists must have a focused hypothesis to refer back to after they have observed the certain aspects, because vague hypothesis are difficult to refute or confirm. Furthermore, when they are testing their hypotheses, they must aware that there is a natural tendency for people to seek evidence that confirms their predictions and completely ignore the rest. This is very common during science labs, for example, during the chemistry lab, where indicators were used to test for acids and bases, my friend obtained a different result from the majority of the class and changed his own results. Although when the scientist explains something, there is no certainty in his explanations, the skeptical route should not be taken as it is ridiculous to dismiss scientific claims. As long as the theory is consistent and it is practical, it should be accepted as the truth momentarily until perhaps, it will be replaced by a more encompassing theory.

Contrary to the scientist and the historian, when the mathematician explains something, it refers to the process of deductive logic that he communicates through. If the mathematician was asked to explain the fact that the angles on a line equate to 180 degrees, the mathematician would not explain why it is like that, instead, he would prove it. Thus, when a mathematician explains something; he is merely proving it; a demonstration of his logical proof. The method of proving involves the use of basic assumptions and definitions which are known as the axioms. These axioms are taken to be true because if they are tried to be proven, it would result in circular reasoning. In order for the mathematician to prove mathematical problems, axioms are necessary as it provides the basis in which the rules of logic can be applied. When the mathematician successfully proves something, there is absolute certainty as the generalizations; the axioms are accepted as true, thus the conclusion that follows from deduction can be certain. However, when the mathematician proves something his knowledge is only based on axioms that are assumed to be true. It was the pursuit of mathematicians to find the one set of axioms that were true and thus all theorems can result from that. But, Gödel’s Theorems of Incompleteness state otherwise, as he says that if the axioms that the mathematicians use are true, it cannot be proven in the theory. Thus, although the mathematician’s proofs claim to be certain, they are not absolutely certain because their axioms are assumed to be true.

Like the contrasting underlying disciples in their areas of knowledge, the historian, the mathematician, and the scientist all have different meanings when they use the word explain. This is due to the methodologies in which they use to acquire knowledge. Because of the past does not exist, historians explain by analyzing the records of the past to provide interpretations of events. The scientist explains through his hypothesis; whether or not, his data from his experiments conform or reject his hypothesis. And finally the mathematician’s explanation concerns deductive reasoning, in which he applies logic to a set of axioms to prove a certain statement.


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