For a moment, let’s pull out from the external world and dwell into our inner self. The process of generating thoughts is swiftly and smoothly going on through our mind without any pauses. The process is absolutely automatic like our heart is beating, the breathing process and the blinking of our eyes. If we take a pause and try to observe, we realize the creation of thoughts happens through our mind consciously or otherwise which are then scripted into words or actions. Certainly, an infinite number of thoughts strike our mind, most of which is a waste but a few are good and useful to create a meaningful reality. Here I am going to deliberate upon the convergence in the pure thought and would like to start with my conjuncture that, “purity of a thought is inversely proportional to the external interjections”. I would like to quote some examples from diverse fields of knowledge with the commonality that the transcription of the thoughts coincides.
Some statements are simply inventive. We quite often hear a very famous Kashmiri maxim, ‘wahrach manz chu dandus aksei hengus rood pyomut’ that is in summers only one horn of an ox has received the rain. The aphorism describes the unevenness of a summer’s rainfall in very simple words portraying brevity, which according to Socrates is the soul of wit. On the one hand, the statement upholds universality or generality in terms of the distance between two horns of a bull, which is some inches, and on the other explains uniqueness, peculiarity of a place that one part receives rain and the other half doesn’t. The statement is an ultimate model of duality explaining singularity through universality. Looking at it through the prism of Mathematics the statement is optimally scientific and a felicitous example of discontinuity or a discontinuous function. This is just a casual talk which we speak quite often; there are many such examples in literature in general and poetry in particular which explain a Mathematical phenomenon and here are a few.
In (pure) Mathematics, we define many notions by making use of two famous symbols ε and 𝛿 (epsilon and delta). For example we define a continuous function as a function, which behaves smoothly, and to define it graphically we say a function without breaks is continuous. The novelty and ingenuity comes once the function is defined analytically by making use of ε and 𝛿. These two undefined quantities play a pivotal role in defining and proving most fundamental concepts of Mathematics. The nature and size of the epsilon and delta is assigned in consonance with the need and nature of the ambient Mathematical phenomenon these are being used for. In layman’s language epsilon and delta are being used as fundamental units of measurement which deal with duality that is treating specifically the generality. We have the analogous situations/phenomena in literature too where exactly the same kind of a situation is metaphorically described with same symbols, many literary giants have demonstrated such novelty in their supreme thought and here I would like to present a few examples: the first and foremost is a verse of Ghalib:
aah ko chahiye ik umr asar hote tak
kaun jeeta hai teri zulf ke sar hote tak
Here Ghalib makes use of the same epsilon and delta which we use in Mathematics umr and zulf. He metaphorically uses umr (life) for a shorter period of time and zulf (length of hair) for a longer period of time and a similar metaphoric ingenuity has been manifested in the following verse of Khusro
shebaan e hijraan daraaz chun zulf ve roz e waslat chun umer kotah
Which again gives the feeling of such a Mathematical phenomenon.
Carrying the series of pure thoughts forward I think quoting another example not from poetry but from prose work of one of the legendary novelist Saadat Hassan Manto becomes inevitable? In one of his works on the gruesome and barbaric acts during the partition ‘siyah haashay’ the black margins he writes, “are bhai tum ne petrole bhi radi qism ka diya eak bhi dukaan nahin jali”. This again signifies duality and a fundamental principle that two minus’s (negative sign) when multiplied gives us a plus (positive sign). The line too is fortified and grounded with a philosophical taste which at the face of it depicts barbarism in terms of being candid.
The point I want to make here is that, the commonality/convergence in the pure thought which of course may fall in a very diverse field of study when transcripted but the idea or the philosophical aspect is the same. This indeed describes the divinity, the beauty of a pure thought which relates an abstract Mathematical sophistication with literature and other disciplines. Finally, I would like to make a hint towards another point that being a student, or a teacher, of Mathematics a very simple and straightforward but irritating question I am being asked after explaining any Mathematical notion is, “what are its applications in the real world”. A general or what I think a universal answer to the question is that we are not bothered about the applications or implications of any Mathematical concept or result, we do it for the sake of doing it. As poets do poetry, Mathematicians do Mathematics, if the offshoot or waste of the subject is used somewhere in physics, engineering, economics etc, so be it. But the beauty of Mathematics does not lie in its applications but something else which I have tried to explain in this piece.
Dr. Nisar A. Lone is Assistant Professor of Mathematics, Higher Education Department.