Monday, September 17, 2007

perfect and the dirac function

A question i was asked you believe in perfect... it was an odd question to be asked. i probably wouldn't have pondered so much about it if it had been "perfection" and gone on a fairly long monologue on my idea of perfection. but 'perfect', had a sense of ambiguity and enigma surrounding it.
as i thought about it myself, i went back to our dynamic modeling class earlier today. it was a regular class like any other. concepts we learned in 12th std being refreshed, about the dirac-delta function, and how every function could be expressed as an infinite summation of weighted impulse functions convoluted over time. but somehow today, i was seeing things in a different light. i dunno now if it was Shorya's way of communicating it that made me see things in a new light, but the convolution integral had always been a conundrum for me. its one of those concepts you always understand when you are with it, but fades away, becoming hazy. somewhere in the beauty of all that mathematics that Dirac, Euler and Laplace defined for us, was the answer to my friend's question. I went back to the class time and again today, as i idly passed away the time in the lab, thought about wonderful way in which every mathematical aspect fell into place. starting from the definition of the dirac function, our consideration of an ideal impulse function, weighted with the function being mapped, its correlation with linearity and super position, and then finally the laplace integral. As we went deeper into the mathematics, and made our assumptions that the system considered was time invariant and linearised, i realized that so much for the mathematics, yet no one equation could be 'perfectly' used to define a real time system. despite all that, we still find a way around it, make a few assumptions, and viola, we had the foundations of the classical control theory.
There is no human relationship that is perfect, yet treated with slight adjustments, there is always a way to work around such imperfections and control it so that it reaches a comfortable equilibrium. Life itself could be treated as an infinite summation of impulse functions or events. some weighted high, like the moments of extreme happiness you get when you receive a letter from a loved one. intense spikes, that instantly attenuate. The effect of such an event or pulse is however felt later on. In a way, experience is the sum total of our response to such events collected from the finite time of our birth. the effects of which might be felt a long time after the actual event. the insignificant events damping out sooner, their poles being so much farther away in the left half of the s-plane. events that get under our skin.. irritating, marginally destabilizing. but not threatening. you can chose to ignore it, and get it under control. there are these intense moments of sadness as well, undamped and unconquerable,taking us away to the right half leaving us unstable, waiting for an external influence, a buffer, a support to prop us back into reality. yet no matter what control algorithm you use, they still leave behind a permanent scar, a steady state error. that remains with you. there will never be anything called a free lunch.always a trade-off. a compromise.. we as individuals will never be time invariant, yet, we are also adaptive, always changing. learning from past experiences. sometimes learning quickly. other times refusing to learn. letting the same repeated events bother us. letting others become routine.
getting back to the question, none of the classical control theory which we study would have been possible if its weren't for certain assumptions made. It all starts with an impulse. Somewhere back in time. Life itself is like that. there can never be a perfect spread of time. but if we are able to freeze every single point in time. and record our response to that instantaneous event. we would see there is indeed that elusive perfect.
PS: i think i will make this a floating blog. My own thoughts on this matter are a little incoherent as of now. should improve with time. hopefully.

Saturday, September 1, 2007

The Indian Chaos Theory

A friend of mine asked me a couple of day's back.... whatever happened to your blog? you don't seem to be writing anymore. guess the winter's setting in once again(its already chilly in the evenings in Ann Arbor). but more importantly, guess I have been doing a lot of other writing off-late.( now now. don't you think its erotica.) so decided, I would do something about my blogger's block.(er. can anyone tell me if there is something of that sort?)
I started thinking about this blog almost a month back, at the chicago o'hare. Somewhere in those multitude of terminals, was a corner of a foreign airport that I was completely feeling at home. Sitting there at the terminal, waiting for the flight that would take me home for the first time since my coming to uncle sam's land, I could already sense a little bit of India right there. It wasn't the cliche'd spices or the wafts of Hindi or Tamil you could over hear. You get that everywhere in the US. Its true, we Indians and Chinese are taking over the world. Its one conspiracy the FBI will never be able to do anything about. It was the CHAOS. If u ask me the one thing that I find most characteristic in us Indians(from an year old American perspective if you may) it would be our unimaginable ability to create and thrive in chaos.
It began right there at the terminal. an hour before the boarding, the PA called for a certain Mr.Mithra(well i don't remember the exact name) for an upgrade to first class. Then, the avalanche started. Within fifteen minutes there was a rumor doing rounds.
it seems there are a lot of seats in first class left. lets also go try for upgrade.
So they went. The ground crew there, who spoke with a curiously mixed accent that i couldn't place,(it definitely wasn't a gujju or tam or any of the regular hybrids u can immediately figure out) had a tough time convincing them otherwise.
please search once again madam. my mother. she is very old. need to stretch her leg. difficult no.. in economy class??
It took almost an hour to sort out the mess. and then, when the announcement for boarding was announced, u had people rushing to get in. Something that totally flummoxed the odd amru taking the flight. Everyone wanted to be the first to get into the flight! Maybe they wanted to get to the nearest window seat(a thing that actually happens in deccan airways flights back home, I heard)
And then, things just got better.. People stowing away luggage at any available slot. requests to the airhostess.
see that nice gentleman over there?? no no. there. g5 ..could you ask him to adjust a little and sit here. then my wife can come sit there. no no. my wife is here c5. i am at g6. small difference no?both aisle seats. he wont mind. its closer also to the the lavatory.

No points for guessing who the nice gentleman was. But there were a whole lot of nice gentlemen along with me doing a lot of 'adjusting' before the flight actually took off. In the milieu one fellow's precious duty free maal came crashing down! someone else never got to drink his johnny walker.
Airline cost cutting meant there were only veggie meals on board, something met with very little fuss. Except for one particularly thin bedraggled amru sitting a row in front of me.
do u have any chicken meals? umm. no. we got vegetarian!(20kw smile)
anything with egg?
umm no. veggie... like i said<tiny little frown>
do i have a choice? oh yeah! u can eat or not eat! (40 kw smile)
can i get u something sir?
oh vegetarian meals are perfectly fine for me! (60 kw smile)
Imperceptibly, things that were uniquely Indian began to take shape. You had the men using one lavatory, the women congregating discretely at the other side. My order for an extra vodka, was met with disapproving looks from the aunty sitting at the other side of the aisle. When we finally landed at Delhi, I think there was a crowd building up near the exit even as it was taxi-ing towards the terminal. the first thing that struck me as i exited the airport with baldy and Ritesh, was the honking.We honk When we are angry, when we are startled. When we want to startle. Or sometimes, just because we are in a bindaas mood. :)
And then, when ritesh made his driver stop the car in the middle of the ring road leading to Gurgaon to wait for baldy to catch up, none of my protests were heeded.
Abey, tu ek saal mein NRI ban gaya kya?
baap ka sadak hai. kaun kya puchega!?
When I took Harsha's bike once he caught up with us. (a changeover made in the middle of a busy highway) and rode till gurgaon, I suddenly felt a release. I wasn't worried about not having a valid licence. I wasn't constantly looking at the speedo to check if i was doing 65. I wasnt worried about not having a proper insurance cover.i wasnt looking over my shoulder or worried about people in my blindspot. It was a sheer thrill to feel the wind in my hair! A rush of blood i hadn't experienced for more than a year. A few minutes into the ride, I started humming an old ad jingle.(not sure which brand. but it was definitely a bike ad)
Azaadi! dil ki....
mama i am back home!
Traffic was one thing that amazed me all through my trip. For someone who was zipping around, weaving in and out of traffic, riding on footpaths not more than a year ago, the chaos on the streets still struck me! Yet in all that chaos, there was some inherent order, that instinctively took shape. We have a million drivers causing every kind of traffic infraction imaginable. We overtake from the left, we jump signals, we ride on footpaths, we over speed, yet when u look at the number of accidents that actually occur due to them, its surprisingly very low. Made me wonder what that kind of chaos can do on roads in the US. We might not respect the red signal, yet, we do yield to the people with the green signal when we jump signals. And somewhere, somehow, we do have a way of making sense of it all. Guess everything gets done when everyone is ready for a litttle adjust maadi! On our bike trip to Shivanasamudra on independence day, we would often stop on the BM highway, PD, NS and pan-man lighting up, sometimes fertilizing the odd shrub besides the highway( a federal offense in many states here. ). it remained that way right till the end. Ritesh again driving like a madcap, reminiscent of our college days to get me to the airport on time. And then, the CHAOS in the airport took over again.