Convergence (math please, forgive me)

This is probably the whole idea that made math simply beautiful. i'm not qualified enough to give a discourse on this topic, but it's just so brimming with possibilities that i cannot stop myself...
'disclaimer' tipe:
fine even if you listen or not, i like to keep rambling on, so this is not for morons who just can't appreciate the significance of maths. and neither is this for those who just can't keep up with my extremely irritating style of writing..(oops, i just lost my readership!)..

so what's with this convergence anyway huh??well, the first glimpse that i got of this function, was back in the days when i was preparing for the great IIT-JEE, when the class was introduced to Taylor's and McLaren's series... actually, i think, it's way before that... Remember mathematical induction? remember all those expressions for the nth term and stuff, sums of series types? well all those formulae are i think some kind of convergence... i vaguely remember there was a polynomial expansion for pi too. dunno. but definitely, there is an expression that evaluates to the value of 'e', the base of the natural logarithm, and closer the value for higher the degree of the polynomial you evaluate. so you see, the point of concern here is that the polynomial 'converges' onto the value of e for some n.. another instance, one you might relate with, is that of functions.. say f(x)=sin(x)/x. we know:
-1/x <= sin(x)/x <= 1/x; (since -1 <= sin(x) <= 1) we also know that (1/x) -> 0 as x->inf; and -1/x -> 0 as x -> inf; (the symbol '->' being approaches to ).. so we can clearly see, that
sin(x)/x -> 0 as x -> inf.

until now, if you've thought either "mamma" or "tty" or "abbeeyy" you really shouldn't be reading this, because this is all high school math till now. the reason i put up this post, beside the negative publicity that i'm sure it will create, is that this is probably the first that time that convergence knocked on our head and we didn't recognise. here, the function is "bounded" on both sides by convergent functions. 1/x cannever be zero. but we can make it as arbitrarily close as we want to. this is the idea of convergence. that in the near future, the hope that stability can be achieved. ganga and yamuna converge on the banks of allahabad. 1/x and -1/x can be thought of two rivers that are coming ever closer as we go to larger x, in search of the elusive Prayag. since sin(x)/x keeps bouncing between these two rivers, it also is bound to meet at prayag, namely, zero. but since nobody can plot out all the values of x (remember, the real number set is uncountably infinite) no one can say that it cannot reach 0.

these are only instances of convergence. like i said before, to me the word means the hope that stability will be achieved sometime later. the reason i chose this topic, is that this semester, especially after mla last sem, really feels converging to a point. although irregular, like sin(x)/x in the beginning, maybe the theory i read will someday achieve a closure of some kind. the hope that all different branches of mathematics or physical sciences will converge, is one kind of convergence, and such a Unification Theorem will achieve closure over knowledge gained from observations and experiments alone. i may not be blessed to live long enough to see this happen, but atleast the subjects that i read, if they converge on a topic, or on a set of ideas, that will more than be enough for me. my holy grail will have been achieved. already, there are a few basic ideas that are common to all the courses i've taken this semester. the idea that everything is a set, introduced first in mla, is now quite evident in moc. moreover, sets can have such deeper meanings that there are whole branches of mathematics dedicated to the study of one particular types of sets. Topology is a spinoff from Group Theory, i think, and Group Theory is but the study of specialised sets. a mathematician would have killed me at this point, for the sheer callousness with which I brush aside these holy and revered subjects.

point to note: Inner Direct Product and External Direct Product of groups is very similar to the internal and external products of two vectors. and since groups and vector spaces are both Algebraic Structures (note the capitals), probably there is some unifying theory for these Structures.

We were taught (a debatable point, i agree...) right in the first semester that matrices and systems of linear equations weren't all that different. now i see that even groups and vectors aren't all that different, and everybody knows vectors can be represented by matrices. you see, everything is coming closer... or did it start off like that? were matrices first discovered or Algebraic Structures? is math creation of useful tools to work with, like integrals and derivatives, or is it understanding the true nature (think fibonacci and golden rectangle) of Nature? i think these doubts can be classified as consequences of three essential 'dichotomies' - a dichotomy is a split - discussed in a journal in the library. infact i suppose this urge to post a blog on math is the direct effect of a rare occurence, namely my reading a journal in the library. this article discusses three fundamental dichotomies that can be found in math, and also in languages in general. well, more on that later...

Flotsam and Jetsam

LOTR enthusiasts will readily recognise this as a title of one of the chapters in the second book. Infact, that's where i looted it from. Flotsam and jetsam is the equivalent of debris, only flotsam and jetsam are the result of something drowning, whereas debris is the result of something exploding or falling apart. and why is this a title, no it's not the result of intensive GRE prep's like some of my colleagues are in right now, it's just a thought out of the blue that reflects my mood right now...

i suppose life is like a huge ocean. there are ebbs and tides, there are ups and downs. far away strangers might become friends, close knit 'coteries' might just break up. imagine a raft made of wood, slats tightly bound with unbreakable cords. or atleast, previously thought unbreakable. the moment you realise that you were mistaken, and that the cords can really break apart, is the moment you realise the real danger you are in. you might sink with only a wooden log to hold onto, if lucky, or not even that. what do you do? you make sure that they are bound extra tight, and that you have the sufficient skill to tighten them up if they slacken. what if you can't? you just make sure you don't do extra harm to these ties. all this is well and good, but what if you realised that the cords were indeed only mortal bonds, breakable by all means, and you realise this only after they break apart while you are in the middle of high seas? godsaveyou!!! something similar in line is going on right now in my mind. the friendships that i thought i was really a part of, the circles that i thought i belonged to, are long gone. people only talk to me if they think i'm intelligent enough to answer the few doubts they have. others just look away, or steer clear from me, OSTENSIBLY "sticking to their own thoughts", while all the time thinking "oh god, not him again". only now do i realise that the bonds that were tied need tending to, and need taking care of, if only to make sure they are tighter. and then there are people, survivors, who can make do with just one log, and then there are other groups either too selfish to share their raft or too many that their raft sinks due to sheer weight. where am i? what am i doing? do i even have a support? would i even know if i were drowning? dunno. a big Shunya. Cipher. Sifar. Zero. no naresh, you might prove to me that i am not an empty set, but i really don't think so.

just the other day i was actually counting my friends, still close to me. i know the very act is despicable, but one never knows. one always needs to take stock of one's company and one's self. taking stock of myself has never happened, can't happen, too tired, too fearful, so who are my real close friends is the more interesting question. and i wasn't really surprised that the set had a cardinality less than 10. i dunno if it's something i say, or it's somthing i do, but i do know that i'm a natural repellant for people in general. believe me, i have tried to improve on it. somehow, nothing works. being outright frank is probably not the right way, but sorry, i lack diplomacy. and if you don't have the guts to face the truth about yourself, probably you shouldn't have any friends at all. some might say who needs friends anyway. but there is always that something more that you get, if you believe that you are entitled to it, rather than just recieving it because you deserve it. imagine being stuck somewhere on the highway. you call up someone, get someone or the other somehow to help you out, and even your bike if possible. it's just that much more fun, if it's someone who accepts you as a friend. later you could even laugh about it. but imagine the guy who came came out of pure civic sense, with no emotional attachments, and even slight misgivings about the whole idea. he probably will curse you till the end of the day... you get the idea right?..

at a time when i should actually feel elated, i really don't know the reason why i'm so down.. it just could be the sympathy factor. or am i really just so boring that i put off people? i thought i was reasonably intelligent.. maybe infact i am low in IQ, or EQ, someQ.. donno...fine. gotta get outta this shit. there are people who care for me, and there are people that i care for. guess that should be enuff. life should go on..

woah wo woaa ah... aah aaahhCCCHOOOOOOoooo.. eeoww goo on my hands.. wash room where where wash room.. ah aah aaahhCCHHHoooooo.. eeoww run run... ah wash basin water clean hands clear nose.. bliss... oh no, .ah.. here it ..aaah.... comes again AaaaHCCHHOOooo woah that was me? hehe canteen is still resounding... eeoww again.. gotta clean my hands.. and nose for that matter. but does it matter? lotsa gooey matter in mah nose.. need to cut off my nose.. hmmm wonder how surpanakha felt?? she wouldn't have had this problem for sure.. acchoo.. head splitting ache.. need some pills.. hmm what pills do i take? oh ok there.. green pills... fave colour.. obviously green pills mean peace... world peace.. wheee... (pop) hmm wonder what medicine it has? dunno waoh dizzy whoozy wheezy hmm.. slapping my head certainly doesn't make any sense.. mmm.. oh no .. ah aaah aaaahhh hmm.. nothing? that hurts.. all that for noth-- AAHCCCHOOOO... oh well.. by god and all his holy angels... if i live this week, that'd be, like, woah...

The 'J' factor

oh c'mon guys, this was gonna come sooner or later. for cross reference, one can always check up on raj's blog, dealing with the D factor. so what's with J now? yup, thou guess't it right. another invisible sphere that differentiates the haves from the havenots. and what is it the haves have or the havenots haven't? it's a decent Job. believe me when i say there are times when it is just too damn difficult to even lift up my head while walking in the corridors. there's that invisible J halo around everyone else's sniggering face. and it really takes a lot to step up and congratulate those who have landed a coveted career when i'm still seething behind my mask of accepted-failure, especially when i think that i am much more worthy of especially that coveted thing than the congratulatee. but of course, whenever did what-i-think-of-myself matter anyway? walking along the edges of the corridors, trying best to avoid everyone's sypathetic gaze, ducking into corners to actually evade individuals... oh my frigging god! i'm a convicted criminal already! noooooo somebody bail me out!!! oh and incidentally, i think the usage of 'bail' is the same in either bailed out of prison, or bailing somebody out of a sinking ship...

neways, so getting back to my original lament, i think all the geniuses of this world have contrived to come up with a most ingenious plan to compel me to undertake Mortification of the Body.. by actually suggesting that i needed a tie. coz u see, same dress, same tests, same results for a week. would adding a tie alter the result? gonna find out 2moro. so my advice to all jobless loafers out there. don't change your dress for teh next interview, just put on a tie. and for cripe's sake let nature take it's toll on that facial hair. no need to hinder the natural growth process of a patch of hair.. you wouldn't be able to find them anyway in a few years.. so let them flourish while they can.. unless ofcourse, it hinders your eating habits. by which time you should have changed your eating habits... speaking of eating habits, this quasi-intellectual needs to stuff some stuff somewhere, so so long..

Life is just a huge real time MMO-RPG

Glory be to thee, O proud runner,
and since i'm not a good punner
i'll stop writing such shit
that your eyes don't see fit
to sit beside so many a stunner...

idiotic and stupid as it sounds, this was inspired by my blog being accepted into the da-iict's rss feed (i'll leave finding out the connection for you, i'm not that stupid :P) and as for akshat, i appreciate this gesture, but i'll feel better only after i've seen some of those elusive comics!!!

at this juncture, when all the world is busy fighting their lives for their future, i take a moment to bring to your notice, that the future is but fickle, and lost souls like myself shouldn't be feeling too sad, just bad. or not. for where in lies the adventure, if the next five years become predictable? where will your spirit soar, if it is fettered by shackles of bonded labour? anyways like i said, souls like myself feel a need to justify their complete uselessness somehow, so we pretend to not notice what's going in the real world, and tend to slip into our very own world. where kalimdor is at war with azeroth, and character files tend to get corrupted. but a better world (mmo/rpg, that is) would be where every CJ can choose his own Kendl, and still go to war with the ballas fools. or where Sweet is really your brother, and not just a useless bot. idea courtesy the original thinker, a.k.a. g.o0o.se. or maybe where the ballas fools had the help of orcs, and humans had to side with grove street as their only hope. hmm. got to work out the details. and oh, btw, did i mention that people in my world tend to lose touch with your world to the extent that they don't care about their future? no? not that they really do care at all...

been too much outta touch, so get back ta ya l8r...

The moonglade is lovely, dark and deep,
But i have quests to complete,
And blogs to read before i sleep,
And blogs to read before i sleep.

searching for a better thing to do while i while away my time in the hope of an all-out night out, i start blogging. but since i'ev got no topic in mind, and too lazy to do any thinking, here's a list off the top of my mind...

some things i like:

words like pleonasm (don't confuse with neoplasm) and adventitious
that i come across in friends' blogs (which incidentally make me look up dictionaries)
Amul ka Rs.5 wala chaas packet.
jeans, faded or torn by natural usage, not artificially altered.
recieving calls from long-lost friends, especially female.
wind blowing in my face, like right now, where i'm sitting beside a window.
raj's pc, coz there's always something interesting.
my roomy's attitude toward life.
frogs croaking and crickets chirping under a full moon lit night.
MD PC and his antics, especially on tours :D.
Volvo buses and reclining seats.
cute chicks in pink and blue furry lingerie.
nightly walks on lonely roads, especially with ones whom i can talk freely.
a dinner wholly on chawal and homemade achar.
my friends and my batchmates, their quirkinesses and solidarity.
keyboards that have non-sticky keys and heavy bases (like andy has right now).
not having to switch off the lights when other ppl are sleeping in the room.

things i don't like:

getting up early in the morning to attend shitty GRE classes, taken by Neeru, especially if its AWA.
loud music from movva's room, especially when i'm trying to sleep.
lalla trying to throw his weight around.
ppl who have reservations against me watching naruto manga.
security guards who force you to quit lab, even if it's before closing time.
having to sms out-stationed friends, rather than call, since they are on roaming.
ppl who say they will reply but never do, to your mails.
me.
videos and movies trying to pass off uncensored material as "demanding by the plot" rather than accepting it's pure porno sleaze.
misunderstandings, especially the ones caused because i really can't articulate my thoughts and feelings.
having to be a parasite on other's comps, coz i don't have the face to ask my parents buy me one.
excessive usage of first person reflexive pronouns (i, me, my, ..) in my writings.
that urge to have a puff whenever i see ppl smoking.


cya guys.

I can still feel you, o Wind
The fleeting glances
The nightly sojourns
from a caring touch
to a loving embrace

I can still see you, o Wind
rushing past, looking back
filling me up to let me dry
lolling around in the gardens
flying around the whole world

I can still recall, o Wind
those private moments
from atop the hills of Vizag
to the jain temples of Abu
moments that i cherish even now

I do remember you, o Wind
at times so angry
to knock me down
at times so willing
to hold me up

under different skies, i met You
dawn-fresh red and lazy noon white
young nightly black and cool evenin'blue
in the grounds of a Ba'hai temple
and again in the resorts at Munnar

But do I know you, o Wind
do you really see me?
faceless yet facing me
pointless yet pointing away from me
what is thy will, o heavenly Wind?