When a mathematician, historian and scientist say that they have explained something, do they all use the word ‘explain’ in the same way?
To answer this question, we must first come to the very basis of the question. What exactly are they trying to ‘explain’? A mathematician will try and explain a phenomenon totally different from that of the historian or the scientist. The areas of knowledge which they are trying to interpret have a very different significance in today’s world. Thus when understanding the meaning of what each one has to say, we have to talk about the ways of knowing, which plays a very significant role in what they have ‘explained.’
“You are not thinking. You are merely being logical.”
- Neils Bohr, 1885-1962 to Albert Einstein.
This is the principal a mathematician lives by. Mathematics is all about logic. It has no relation at all with the understanding of the subject. If you can prove something in a logical sequence, using correct mathematical terms, it has been correctly explained. This is what a mathematician does when he ‘explains’ something.
Why does 2 and 2 make 4 and not 3. Why is the integration of sin(x), cos(x) and not tan(x) ? Well, this all seems to be logic as I really don’t understand why this happens, even though it does. If someone tells me he has one $10 bill, and one $20 dollar bill. I know that he has $30 in total. Using my logic I know that to calculate the total amount of money, I simply have to add and not subtract or multiply. I do not need to think what to do.
“All generalizations are false-including this one.”
- Henry David Thoreau, 1817-1862.
This is what a scientist seeks to achieve. In science, something is believed to be true until it is so proved otherwise. Therefore, when a scientist says that he has ‘explained’ something, it means that he has just disproved a previous ‘truth’, and has come up with his own model for explaining the phenomenon which will now be deemed as the truth until disproved again.
The structure of an atom is one such example. With the discovery of the atom, scientists have created a vast number of models to help explain it. Each one different from the other, yet each one was considered as the “truth” by society for a period of time. With the discovery of electrons, Neils Bohr’s newest addition of sub-shells and orbitals has now become the “true” structure of an atom. It will not be long before this will be disproved too. Who knows, it might be one of us who will finally do it.
“What is history but a fable agreed upon.”
- Napoleon Bonaparte, 1769 – 1821
The past can never have concrete evidence, which does not have some fault in it. Everything a historian uses as proof can have another meaning to it. But it is the most agreed upon one which is finally written down in our text books, and termed as “history”. Thus when a vast variety of people believed that something really did happen, it becomes part of our history. A good example of this is that of the legendary King Arthur. When I was a young child I remember my mother would tell me to eat my cereal, even though I hated it as it would make me strong like King Arthur who was the only person who could remove the sword, the Excalibur, from the stone it was wedged in. No historian has yet found any proof of the Knights of the Round Table or of the Excalibur, except for the tales passed down from generation to generation.
Mathematics is oft considered as a language used to convey some message. Just like our English language, mathematics too consists of rules which must be followed for it to make sense. It consists of a large number of terms and symbols like the long list of vocabulary we all see in our SAT books, many of which we have not even heard of and many funny sounding, which makes you think who uses such words. To be clear in mathematics, we must be able to use a vast variety of symbols which to some people will be a simple and logical sequence. For example, when I first studied calculus I was told to find the derivative of (x3 + x2 + 99x ). This meant nothing to me and my brain could not process what I was reading. This was not eased when my teacher said that it was really simple, and all we had to do was apply the formula: xn = nxn-1. But now, after correctly understanding the language, it seems so simple. Thus, for mathematics to be explained, its own language must be used, and for someone to understand this language, just like any other language he must be able to be fluent in it.
Scientists believe that everything has a reason, and nothing in this world can spring up because God wanted it to. There has to be some controlling factor, or some catalyst which caused whatever happened, to happen the way it did. Therefore, when the try to “explain” something, they have to have a fool proof reason for it, and therefore Reason plays an important role for them. In science, both inductive as well as deductive reasoning is used. There are some generalizations which can be applied such as; All halides are coloured. Chlorine is a halide. Therefore chlorine must be coloured. This is true as chlorine is greenish-yellow in colour. An example of inductive reasoning is; Methane has 1 carbon atoms and 4 hydrogen atoms. Ethane has 2 carbon atoms and 6 hydrogen atoms. Propane has 3 carbon atoms and 8 hydrogen atoms. Therefore all alkanes must have the general formula CnH2n+2. But scientists are wary of this, as inductive reasoning may not always be very reliable. There are always a few exceptions such as that of Cyclopentane, which even though is an alkane, has the general formula CnH2n which is that of an alkene. Thus when explaining something, scientists use the deductive method of reasoning as compared to the inductive.
“It is only with the heart that one can see rightly; What is essential is invisible to the eye.”
- Antoine De Saint-Exupery, 1900-1944.
This is the role perception plays. In history, evidence can never be 100% in the right direction. There are various ways in which it can be interpreted and explained. But perception is mostly affected by our Emotion. When a historian explains something there are various factors which causes him to say what he has. Which side did he originally believe ? If he found some evidence did he consider it or discard it ? Is he dealing with an emotional subject ? An example of this would be in my own country, that of the “Revolt of 1857.” This was the first time in the history of
Thus from the above examples, we can conclude that when a historian, a mathematician and a scientist seek to explain something to us, they are all using the term “explain” in different contexts as they are all trying to explain to us different areas of knowledge, which are related to different ways of knowing. This will affect how they perceive the word “explain.”
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