The essay!!

When scientists, historians and mathematicians explain something, do they mean the word “explain” in the same way?

One of the goals of human beings is to derive meaning from what’s around them, from things that happened in the past, and use this ability of reasoning in them to reason further. The cycle of discovery, invention, interpretation, reasoning out and making logical conclusions continues throughout the life span of humans. It is this eagerness in human beings to understand everything around them that leads them to “explain” various phenomena’s, processes, steps, observations, circumstances and situations. Every time a scientist, a mathematician or a historian discovers or interprets something, how do they present and explain their observation or findings to the common man? Do they explain it by putting forth their perception and views and supporting it through evidences? Or do they explain it on the basis of experimentation and proof? Or finally do they explain it through logic and reasoning? These are the questions that I would be answering in my essay as to how people in different fields of study “explain” things differently.
The word “explain” is a very ambiguous term as people might mean different things when they say that are “explaining” something. When historians explain something they mean something totally different from when mathematicians and scientists explain something. For historians, their perception plays a key role in their explanations. Therefore it is a common occurrence that two historians, asking the same questions and using the same sources of information, would still come up with different answers! The reason behind this is that the explanation of historians is governed by the way they perceive their subject of discussion. The fact that there are still heated discussions and debates as to whether Mohandas Karamchand Gandhi, popularly called the “Father of India” did the right thing by signing the pact of the division of India and Pakistan, is a proof of how perception and interpretation governs history. Some historians believe that the division of India and Pakistan in two separate dominions was the right thing to do in order to free the territory of India (consisting of India and Pakistan along with Bangladesh and parts of Myanmar) from the various communal riots that were tearing the territory of India apart and making it difficult to govern. While some historians believe that Mohandas Gandhi is to be blamed for the animosity that is prevalent till today between India and Pakistan, and the Kashmir issue would be non existent had India and Pakistan been one nation. Another example is during the Cold war where the policies of Soviet Bloc and the American Bloc were interpreted in different ways to suit the ideology of the historians. While American historians criticized policies of the Communists, the Russian historians, spoke in favour of Communism, criticizing the Capitalists. Therefore, ‘Conformation bias’ plays an important role in the way historians perceive and explain things.
In science however, this difference in perception is rarely present. This is owing to the fact that scientists seek to explain natural processes that are present around us and which they can observe through their five sensory organs; things that they can feel, touch, see, smell and hear. They have nothing to interpret like historians have, as their research is carried out through observation of natural phenomena, and/or through experimentation that tries to simulate natural events under controlled conditions. Historians on the other hand rely on relics that have trickled down from the past to explain and support their ideas. They explain things through evidences and facts about the past, and these explanations are in the form of a story that they narate. They ask questions to which the answer is a story. That is to say, it's a series of human reactions to particular circumstances that take place in time and thereby produce a narrative and a story.
Mathematics is a science purely dealing with logic and reasoning. Abstraction, Deduction and Induction are the three modes of thinking and explanation that distinguish mathematics from other fields of study. Like scientists make use of Induction, by attempting to make generalizations from a number of circumstances, Mathematicians too make use of the course of Induction but in a special way. For scientists, conclusions using Induction have the status of as that of an experimental law. If it stands the test time, i.e. agrees with and even predicts, subsequent observations, then it becomes widely accepted. Such a process is slow and can be partly or wholly reversed (medical sciences provides many examples of reversibility and hullabaloo). For mathematicians, however, the result of Induction is a hunch. If the hunch is strong then it shapes up into the form of a conjecture. For example when a mathematician sees a common pattern between some sets of numbers, i.e. when he attempts to generalize a pattern in a set of numbers, he first comes up with a conjecture using Induction. As his conjecture is proved formally, and goes through scrupulous checks by his peers, the statement of his conjecture finally becomes a Theorem and will always remain so. Elevation to the height of a theorem is an irreversible process. The progress from a hunch to a conjecture is an example of the process of Induction, but the final irreversible commencement from a conjecture to a theorem has no parallel outside mathematics.
In the natural sciences, the first step that a scientists follows while explaining something is to develop a Hypothesis; (A hypothesis is a contention that has neither been well supported nor has it been completely ruled out). This is similar to the conjectures that are made by mathematicians. After the hypothesis has been stated by the scientists, experiments are carried out to prove the hypothesis. Conclusions and various theories are based on the results obtained through these experiments. These conclusions are explained using various models, set-ups, etc that refer to a description or depict something. However, scientists can never claim absolute knowledge of their subject of study as there can never be complete certainty about a particular phenomena. Unlike mathematical proof, scientific proof is empirical, and is always open to “falsification”, if new evidence is provided. Even the most basic theories may be proved false if new observations are made that are inconsistent with them. The most famous example is of Newton’s law of Gravitation. While proving this theory, Newton had made the assumption that the mass of a body always remains constant. This theory had been widely accepted until it was later found to be false for bodies moving at the speed of light. In such conditions the body did not have a constant mass. Therefore, as in this case, it is possible that in natural sciences, earlier accepted theories are proven false if new observations are made.
Ways of explaining things by Induction and Deductions, which mathematicians use, are in fact scientific methods. In actuality, mathematics is based on many abstract concepts that have no self evident truths. This is why it is very difficult for mathematicians to explain things. Math is simply based on the logical relationship between two or more symbols. Like in the game of chess where there are pieces which are moved according to certain rules, similarly math too has certain rules on the basis of which logical steps are carried out. In chess, the pieces have no meaning and do not represent any higher truth or anything; similarly the symbols in math have no meanings. Math can be explained only by teaching the rules and concepts in math’s, but the rest is all logic.
Thus, it is evident through the above discussions, that the meaning of the word “explain” is different for scientists, historians and mathematicians as they make use of different ‘ways of knowing’ to explain their subject. While historians are governed by perception, scientists are governed by reason and mathematicians by logic and intuition. Each of them also have different ‘truths’ as their basis of explanation. For a scientist, something that is true by experimentation becomes the ‘truth’ for them. For mathematicians something that’s proved using correct axioms is the ‘truth’, while finally for historians, knowledge based on the relics of past which acts as evidence is the ultimate ‘truth’.