Misnomers in math

I think the title is self explanatory, math people have often come up with misleading names which when literally taken carry a very different meaning to the actual mathematical definitions they represent. To defend these ambiguous nomenclatures, often the terms are initially coined in German, French or Russian and the literal translation have a slightly different meaning in English or maybe the people who coined them didn't care much for words, and just chose the first word that came to their mind to capture the abstract phenomenon. Take for example the term "uniform continuity", the powerseries $$ \sum_{k=1}^{\infty} z^{i} $$ indeed converges uniformly to $$\frac{z}{1-z}$$ on $$|z| \le .5$$. However this doesn't mean the series literally converges at an uniform rate everywhere, as the name would seem to suggest. At z=0, it converges instantly to zero, and as you go away it's tail dies ever more slowly.

To explain uniform continuity, suppose you are teaching a class calculus. Suppose the class has "countably" infinite students: Student 1,Student 2, Student 3, ....... . You can think of non convergence as the situation when there are people who will never be able to learn calculus. Convergence would be when everybody has the ability to learn calculus in some given time. However if you actually want to teach everyone calculus, this alone doesn't help you much. Suppose the ith student will learn calculus on the ith day. Given this situation, if you teach the class for N days (whatever be the N). Student N+1 onward will not have learnt Calculus. The analogue to what is mathematically called uniform continuity would be when not only every student can learn calculus, but there is a N, such that all students will have learnt calculus by the Nth day. For example , say student i learns calculus on min(i, 10)  th day. Here by the 11th Day your job is done. This doesn't mean all the students learn calculus uniformly, the first student learns it on the very first day ahead of all else. 

Anyway just writing random stuff on a Friday night, if you read enough math literature, you will grow accustomed with the mathematical meaning of terms and forget their English meaning while reading math. It's just sometimes a little confusing when people new to the subject read them. I doubt however the huge volume of mathematical literature can ever be revised to accommodate this problem, I think frankly it would be easier if the English dictionary was amended to solve the problem.

Towards the Crimson Tide Moment

The sound of isolated birds chirping is the first signal that a “night out” is about to be completed. It is to this familiar noise that I walk down the C-D catwalk to fill up my water-bottle.  I decide to sit on the wall and stare at the ever-brightening eastern sky, something’s always look beautiful, no matter how many times you see them. It’s well into the summer break, D-block is empty, no one to spot me being “hallu”.  When I was little someone very wise told me, “ to feel another person’s sorrow is one of the great joys of being human”.  Right now this funda seems very stupid, why would anyone want part in this absolute anguish I feel right now. These surrounding blocks staring down at me, so soothing in their familiarity, yet there is no solace in their eyes. They have seen far too many like me, to feel any sorrow or attachment. I remember the first room I walked into in Azad. It was a small room, freshly white-washed, staring back at me blank and impassionate. Then I think about Koley’s room, me and Ramiz sitting on the sofa, Koley deep on the bed, Pagla in front of the lappy, the disco ball spinning behind him, the bed sheet beneath dotted with cig burns, left behind from half a decade of parties, the 5.1 speaker system, the curtains which used to be a single bed sheet in our first year. I can imagine all these layers being removed over two weeks leaving behind just a white room, staring back disinterestedly, bearing no signs of having ever been personalized. I see my life poised to be changed forever and I find that the world doesn't give a fuck, at that moment I feel like the loneliest person on planet earth.  Another surge of anguish burns through me, I cannot accept all this, I want to see a silver-lining, I want to believe that to kgp we were not just passers by, that I was a part of this world and not just a guest, that our rooms underneath their blankness remember all the epic nights from previous owners, I want to hear those stories, I want to feel that our lives here mattered.

To be honest, right now I am venting. Usually when I write I want to develop and show an idea, or try to describe a situation in manner that seems pleasing.  Here, I am writing because it makes me feel better. I am trying to cope, I must say I am failing miserably. The only thing that’s keeping this sea of anguish at bay is the prospect of still having one more week left with my friends. To see a few more sunsets, to hear a lil more Floyd on our 5.1, to have some more Tinku’s for breakfast. After that how will I cope?  I wish I was young  and just had to hear mom say, “It’ll be all right” to feel better. I curse this stupid thing called rationality that makes you sceptical even after mother says it’ll be fine. Mathematics is another thing I can do to escape. I guess mathematics is what I do/ want to do professionally. It is an engaging exercise, when you are in the middle of a proof or finally beginning to realize where the whole chapter has been leading to, you are totally immersed and have little interest for the pains of the real world.  Mathematics can bring it’s own pains,  the frustration when you are scrapping to sharpen your bound  just a little bit, so that your entire “beautiful”  proof pushes through, then the agony of finding your last bound was tight, the complete darkness of starting all over again etc.  But these are familiar pains and they have the possibility of a silver lining at the end.

And so the final week is up as well. Time seems to have taken offence at the mere fact  I could try keeping my pains at bay with the thought of one week worth’s happiness. What was one week to time, who has seen off mighty emperors and great civilizations, at whose feet stars and galaxies have been born and fallen. It’s the morning when Sourav Roy is leaving, I leave the day after. The last week has been one of saying goodbyes to people. People I loved, people I liked, people I got along with, people I just knew, the girl I had a crush on. “Kab ja rahe ho?”, “8th /11th / chowda”. These were not distant dates on which they had reservations, these were today and tomorrow. I wish I could take time mourn them one by one , but things just seem to whizz by, you wind up saying, “ See you”, like you are leaving the mess table after dinner. Roy is packing furiously; his granson guitar is staring at me. I look at all the marks and stuff we wrote on it in five years, the picture of a stranger’s face Koley drew on it in second year, even it seems sad at this hour of farewell. A part of me hopes when I come back tomorrow, Roy will still be here, having missed his train by over-sleeping as he has done so many times before. But I don’t really want that, I don’t want to challenge time with one more day, I do not want to enjoy another wild night, if it means having to feel this pain afresh tomorrow morning. Here is the last truth I learnt in kgp, if you make something beautiful, it doesn’t mean it will last forever. You shouldn’t resent time for this, she washes away all evil things as well, she wants to give humanity a fresh slate to start over. You should be happy that what you made was beautiful. When time destroys something really beautiful, you can almost sense her sorrow as she takes it away. Finally I feel a little sensible, giving some “wise” funda as the great “junta” of kgp would put it. I want to say goodbye, goodbye to the vanilla skies above kgp, to the monsoon winds down lallu-way, to the beautiful summer nights, to the great trees of 2.2.  And  my friends, do not feel bitter this little world that we, you and I made is about to be washed away, about to become a memory, growing ever more distant, be glad that it existed and we were so happy(for the most part) in it. As I like you all have done or will do stand here trying to muster up the courage to say goodbye to a world of such incredible familiarity, I would like to thank you for making me feel so loved and I hope I have made you feel the same.

Birth of an Idea

About the phenomenon described below very little has been conjectured and even less is known for certain. This is the phenomenon of how an idea strikes you. Regarding this scientists note it takes roughly 35 nanoseconds for an idea to strike your brain. As is well known in any interval no matter how small, one may find infinite discrete points. Here we go through some number of such discrete points in these 35 n.seconds leading up to the birth of an idea.

We start at some point of your body, it’s location is not important. Let us say we are at some lymph node on the nervous system. The environment is rife with the noise of all the mundane chemical reactions in the adjacent parts of the body. But a beat is growing ever stronger, this is not the noise of some local phenomenon, this is a global wave spreading all through the body. Soon it drowns all the bytes and signals of our lymph node. It seems the whole body, driven by the beat, is on the threshold of a revolution. A whole new set of sounds have joined the beat, this is the crescendo of the awakening. And then it stops, there is only a light distant music. This is that briefest moment after the idea strikes, before greed and pride blind the mind, that you realize “I was lucky”. And then a new great mixture of components join the soft distant melody. A loud excited throbbing beat can be heard. When a drummer plays a song, besides a particular rhythm he also enforces the essence of his mood in the beat. This beat differs from our original beat by only this essential character. The song is morphing and changing with every second, most of the elements of the initial distant melody are long gone. This is the time when the human ego begins to believe that it is most definitely worthy of such a beautiful idea, when greed makes the human mind dream of all the profits and possibilities of the new idea. Now the music has climaxed into an excited feverish, oozing and growing relentlessly on an unstoppable crash-course with the very doom of human character.