When mathematicians, historians and scientists say that they have explained something, are they using the word “explain” the same way?
Simply put, mathematicians define explain as 'proofs', scientists define the word explain as 'analysis' while historians explain by 'imagination'. They all inter-link in defining explain as 'analyze'. Mathematicians have less imagination than scientists, less than historians and this is what makes their “explanation” so different from each other’s.
Scientists use induction, reasoning from detailed facts to general principles (previously explained), looking into the relationship between cause and effect, without excluding justifiable possibilities, since natural occurrences cannot adequately explain everything. Repeatability is also very important in the method to test that such an observed effect or cause is constantly valid or has a pattern we can use. If something is not repeatable, and leaves no traces, it may have happened in real life, but science cannot deal with it. So unlike what some believe, science proper doesn't have all the answers. It is limited. The apple falling on Sir Isaac Newton’s head, lead him to question- “why?” He went on to explain what we understand as “gravity.” Later, Albert Einstein based his theory of relativity on the findings of Sir Isaac Newton; although rejected under the pretext of being less thorough in explanation at first, every Physics high school text-book has chapters on gravitation and relativity. Scientists are continually through curiosity and observation forming hypotheses, experimenting upon them and proving cause and effect to themselves and then putting it simply for the world to understand.
If however, the explanation is too complex for simple minds, could it really be said to have been “explained”? Every home has a computer, whether it is a PC or a mobile phone. We all know how to work these machines but more importantly, do we know how these machines work? I’ll leave you thinking about that while I talk about how mathematicians “explain” things
Mathematics as we know is simply playing with numbers and manipulating them to prove axioms and eventually conjectures. Similar to hypotheses in science, mathematicians set about trying to prove conjectures keeping in mind certain prepositions known as axioms. They try to show consistency in patterns using mathematical induction, but for what purpose? So that models are explained easily. Golbach’s conjecture took more than 140 pages to prove successfully but if the world cannot understand this explanation, is it truly “explained” as scientists use the term? No it’s not! Mathematicians follow the Oxford American Dictionary definition of the term “explain”- ‘make (an idea, situation, or problem) clear to someone by describing it in more detail or revealing relevant facts or ideas.’ For mathematicians, a proof, in any form is considered an explanation.
Let’s now consider the historians’ explanations. Historians merely interpret events that occurred in the past using artefacts and certain pieces of evidence. However, an explanation as historians put forward maybe considered the most inaccurate- simply put historians’ explanation is biased; it’s entirely based on their perception. Every coin has two sides and every historical event has two different accounts. A Jew’s account of the holocaust, it would totally condemn Hitler and the Nazi Germany reign whereas a Nazi account would in all senses, respect Hitler for what he did. Our knowledge is hence hindered because we don't know which account is true, and we can only give our own interpretations and analysis to what we read. There are two explanations for the same incident, one true-one false, both true or both false but how can we tell? We can’t!
At this point one must also consider this- explanations are given using concepts already explained however, regarding concepts we have created? What if the initial preposition itself is incorrect? The explanation for that preposition may be right but it’s explaining something that maybe wrong completely. Also, it must be noted that different explanations are accepted by different people who have a different concept of truth in their head. What maybe an explanation for one person may not be for another. Since there is no one universal truth, there is no universal explanation, especially in the case of science and obviously history. Math is a concept created by us to assist explanations in science, history, economics and practically everything else. It uses models to explain what needs explanation.
Explanations may not necessarily be purely based on fact but on theory. Take for example the theory of black holes. There is substantial evidence suggesting their existence and this evidence is piling on everyday. There is a possible explanation as to their origin but it can never be completely investigated. The same way tornadoes were investigated by going inside them (over a 100 micro-cameras were launched into a tornado), to know the arbitrary absolute truth about black-holes we must go inside them. Even if somebody survives this, there is no way it can thereafter be explained as he/she can escape it. This is only suggestive of how not everything can be explained whether it be science, math or history.
Science is used to explain things in the hypothetically distant past and even in hypothetically extreme distances in the universe by using methodological naturalism and hence going beyond science's proper boundaries of human experience. In such a worldview, everything in the natural world must have a natural explanation. "Jonathan Wells: Let me finish. On the other hand, you have just heard another definition of science here which is not the same as the one we agreed upon a few minutes ago. The definition of science I gave--the essence of science is the testing of hypotheses against the evidence. The definition we just heard is that science starts with the assumption that everything in the world can be explained without recourse to supernatural causes.”
Coming back to the question I left you thinking about- we all know how to work the machines but how many of us know how the machine really works? This is the simplest analogy (a comparison between two things, typically on the basis of their structure and for the purpose of explanation or clarification) to suggest that the term ‘explanation’ is very relative. What mathematicians, scientists, historians, economists, engineers etc. try to ‘explain’ is only from their perception of what ‘explaining’ is. Every person has a different interpretation of what “explain” means and neither of them are wrong.
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