Enigma of the numbers, from within or the alfresco?

Numbers, to the eye of the common man, is by far the most important thing in life, it surmises in itself a multitude of things that happens and might be said that its the determinant of people’s life. It starts from money, benefits, clothes to more complicated terms such as wife/wives, computation, sciences, economy and so on. G.K. Chesterton, a very celebrated English literature person, writes in his book ‘The man who was Thursday’- “It may be conceded to the mathematicians that four is twice two. But two is not twice one; two is two thousand times one”. He very confidently writes “as conceded to the mathematicians”, of course it is understandable that he was talking about a more general perspective, but I chose this piece of quote for the reason that people make use of numbers in such freedom, as though they are an entity that is embedded in them. Before I throw more entangled arguments about numbers and their mystery, I shall quote a more sarcastic and in ways, a funny quote- “Natural numbers are better for your health.” People have a very casual mentality of treating numbers, they are so accustomed to it that one does not see the underlying mystery and paradoxical nature of numbers. To this, I sternly blame every academic programme that originates with the history of numbers, though I agree on the fact that people who have worked on the field need to be mentioned for their extraordinary line of thought, I disagree that that is what kids should start learning numbers from. If one is introduced to the┬ástartling mystery these mathematical entities hold, there may be a more interactive interest in mathematics, what I mean is that that people would understand the deep mystery numbers hold in themselves.

Consider a square of each side 1( in any metric system of measure of length), something we should be easily able to achieve in physical reality, now, the length of the line that connects any two vertices of this square has a very strange value, in our considered example, it is squareroot of 2. A very easy calculation given one knows how to apply the pythogoras theorem. Well, any calculator can possibly tell you what that number is, but the question being, do you understand the number? Do yu understand the physical sense the number portrays? Have you bothered to question WHY it is so? To peck brains, I would suggest you brush up on your knowledge of the real number system, why you ask? Well, if you understand the entirety of the simple paradox I am pointing toward, squareroot of 2 as a number is up to infinite length after the decimal, i.e. 1.4214….. and can go as long as you your patience wears or your computer’s capability to find till. But the diagonal of a square is a definitive physical reality, it exists, we can measure it, infact we all might have, at points in school if you had geometry. To the student of mathematical and physical sciences this may lead to two questions, two unanswerable questions, first- how can a theoretical, rather imaginative structure of computation describe a physical reality? Well, that is the beauty of mathematics. Second- this is something most people miss, it seems very non intuitive but it is true, I have experimented this myself and the results are most shocking. The fact that we have drawn a square and computed the length of the diagonal only means we have done it as much as it seems accurate to the naked eye. What this piece of puzzle leads you toward is the fact that if we had better methods, we could make the square more precise, how much you ask? Well, as much as the number expands, this is a very non intuitive idea but a very interesting one, the fact that we have joined opposite vertices of the square only means we have done it as far accurate as we can seem to see and think. Theoretically, this position is very hard to find, we may only approximate this and hence the complicated number related to it.

Why are numbers significant? Trivially, numbers have a part to play in almost every situation in our routine. But going further, with the ability to think of a number system that can be used for computation of any physical reality, comes a great idea, one which is often mistaken to be a derivative of the physical sciences- error propagation. In the 17th century, when the rationals and irrationals were known, mathematicians who had a core understanding of calculus felt that to explain mathematically the observable reality, the rationals and irrationals were a very ill serving number system, in situations their combination(in the most crude way of putting it) the real number system was also faced with the same consequence. All these concepts are a layered within themselves, often unasked, the disadvantage of asking the “why” question. What is questionable is how we have a desire for definitiveness in our views, while naturally all there exists is approximation and an underlying chaos. The complex number system is the most descriptive number system, but alas, not a very useful physical application. But as a computational tool to be used, these are the most powerful of numbers. Hence the conundrum, and a puzzling one at that- are numbers universally existing and we have merely discovered them? Or are they a human invention and we have the greatest gift analytically analysing our surroundings? Take a journey through the numbers, they are as scenic and beautiful as a holiday destination. I shall surmise with a quote that led me to think about this-” God made the integers; all the rest is the work of Man.” by Leopold Kronecker.


Legerdemain and throe of the Society, annals of poignant foragers.

Science, a stream of knowledge that has been subject to intense criticism and equally appreciated from the early 15th century. Since a long time, since I have fallen in love with the beauty of the scientific way of life( a philosophy toward life which I shall discuss about), I have always had a very daunting question to which I have not found answer for- how did we come to agnize upon this marvelous knowledge of the world around us? Many have expressed on this question I have had as too philosophical, something a person can never get an answer for and so on. I agree, it is a philosophically deep question, and what angered me more than people who just shrugged to answer this question were people who answered- “Well, that is the way the world is, your question is as redundant as to ask why leaves fall or why we die, it is stupid to ask such questions”. Much opposed to what is the true meaning of the question, it is misinterpreted as though I’m asking as to why things are as they are, no, what I’m asking is that how come we are able to see the design in such detail and depth while other species or even, other being of our own species fail to see. In this post, after I want to delve deeper into this question, so as to bring some peace to my chain of thought.

“The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. … No problem is too small or too trivial if we can really do something about it.” Says the famous theoretical physicist R.P. Feynman. The most fascinating thing about the science enthusiast’s mind is that they accept nothing based on just a word of mouth, the infamous act of debate sets in almost immediately when one disagrees with the other. I see this as the most requisite mentality to study sciences, to live life where one spends learning more about the world. Let me make this more clear with an example, something from my personal life- my mother and myself have been on indifference about a lot of things since when I was a child. My attitude came from extensive reading of the news paper and my mother’s from her social circle. On a Sunday, she said to me “Eat a lot vegetables, carrots especially, if you do not want big bad spectacles like I wear”, this she said because carrots were not my favorite, I always put them aside on my plate. Just days after, I read the article in the dailymail that said the misconception of carrots being the super-vegetable for the eye was a falsely led propaganda by the British during world war-2. I revealed this to her and she discredited the article. Why? Well, because our family doctor told it was nothing but a hoax, something to fill a column in a news paper, apparently. I was quick to understand that not all people were readily accepting change in my surroundings, and frankly, it was very annoying.

So, what is the the scientific way of life you ask? Its very simple, do not accept what anyone tells you, find out more, think about it, put it to experiment mentally or in physical realms and if you think it makes sense to you, then it matters no more. And thus standing upon this philosophy of life, I intend to bring many things I have learnt and known to a strong criticism and speculation. Because simply understanding something is of no use, its as good as we have sown a seed, if we intend to see a plant grow to a big tree, we have to water it, let its leaves spread and branches grow. Then, maybe one day, I might witness the huge tree, in its beauty and magnificence.