I had my final exam today and the paper being easy,the exam was a breeze.So 3 weeks of rest follow for me after a busy month of classes.After my exam,I happened to read this:
http://21writersblock.blogspot.com/2007/08/youve-got-mail-again.html
Now the author happens to be someone I am very fond of,and her earnest appeal to people in general to find a way to explain the idea of arranged marriage didnt fall on deaf ears.I took upon my frail shoulders the onerous task of removing the stigma(if I may call it that) associated with an "arranged" marriage.I know that the tone of my writing puts the word "arranged" at about the same level as the word match "fixing" in cricket.A thousand pardons for that inadvertent error.At the outset, let me issue the usual disclaimers that am neither married nor in love,and any views that I may express may be taken with many grains of salt.
To any prospective girls who might have an outside chance of falling in love with yours truly--I agree that after reading this your feelings for me would probably be not far from that you share for a brick on the road,or the friendly neighbourhood bulldozer, for that matter.I hasten to add that I am a romantic at heart,and its just my other side taking over for a brief period.I may be guilty of bringing down something as intangible as love,to something as mundane as mathematics.However,there are similarities-both are abstract:)) to start with.But if you look beyond the obvious ,am sure the parable am going to narrate will prove most instructive.
I shall assume that most of my readers are familiar with some numerical techniques for finding roots of equations.But the person for whom the post is intended, though clever, almost certainly doesnt,so a quick introduction.
A function f(x) is said to have a root at c if f(c)=0.Now consider an equation like f(x,y). The point (i,j) is a root if f(i,j)=0.
Consider an equation like x-cos(x+4)=0 or better still sin(x)-log(y) +6=0
I ask you to find a root of the equation.
To come to my point,I need 2 names.Lets take,err...preetha and preethi,for want of any better names:)).I give this problem to both of them, and allow them use of an elementary calculator.
Preetha,being a highly whimsical girl and a good programmer,insists on the following idiosyncrasy.She wants to arrive at the solution by chance alone,so with the help of a random number generator,she tries out numbers one after the other and tries to find if any of them is a root.Sometimes its love,oops! sorry, root at first sight.But often the random numbers turn out too random,and try as she might,picking a root by trial seems too difficult for some equations.But she is delighted whenever she does stumble on the root by chance:)
Preethi on the other hand is a girl singularly devoid of such eccentricity.She consults a book of numerical recipes and hits upon tried and tested techniques like the Golden Search method,Newton Raphson method,bisection method or for more complicated functions,Steepest Descent method and so on.The way these methods work is as follows.
Instead of choosing at random,from the general behavior of the given function,a smaller region is identified in the search space,where a root is likely to occur.Once the region is identified,simply do what Preetha does at random-try out numbers in the region and see which one fits.Notice that in the end, you dont accept a number as a root without checking its functional value.So you are not compromising in any way:))
The general name for such techniques is quite appropriate-Directed Search methods:))
Some more comments on this technique are warranted.An equation can have more than one root.But they all might not lie in the same search space.Also let us recognise a tacit assumption we have made that the equation in question has a real root,which might even be false.(sorry!!)
Assuming that both Preetha and Preethi arrive at the same solution,lets now explore the matter further.For one thing,would you expect that Preetha is happier than Preethi just because she "found" her root by chance alone?Likely not.Now how viable is Preetha's method? If she has time till kingdom come,its a foolproof method.But if you are short of time, then trusting the God of Randomness is not highly advised.
Then there is the problem of "irrational" roots:) In such cases people stop their search once they find an integer value sufficiently close to the root.:)How close?That's decided by the Convergence Criterion -the mathematical term for this.
Also let us remind ourselves that the best method actually would be to graph the function and simply determine all the roots by inspection. But such a process is feasible if you are looking from above ,which we are not.
Having said all that,when I have an equation of my own to solve,I will give the random numbers a chance first:)To my dearest random root finder I have this to say-I do wish with all my heart that the correct number pops up soon.Randomly,or with an algorithm,does it really matter ?:)
I believe in the fact that if you wish something for others,it comes true.And I say this in all seriousness.
Wednesday, August 08, 2007
Friday, August 03, 2007
Important dates of the second kind ! :)
If you are starting to read it thinking its about my dates,you are wrong.I have given up on that and am resigned to the fact that nothing like that will ever happen to me :))
This post is more to remind myself than about writing anything funny or concrete.
Today is August 3rd.Exactly a year ago on this day, I got my visa. Maybe not everyone will think that event noteworthy,but I know otherwise.I was put through an emotional shredder for a month before finally getting it.And so how does it feel,I ask myself, a year hence?
Well, it mostly feels like a dream, as though all that never happened.And yet there is a residue of the disappointment, the uncertainty,the prospect of seeing your dreams crumble, that gets me disturbed simply by thinking.Now sitting in the future,it sometimes feels that it was not anything to worry about.And thats the peculiar quality of the human psyche.
I once read a book by Dan Gilbert titled Stumbling on happiness,and it is this quality that he often talks about.
The inability of the human mind (or heart, whichever you prefer) to reconstruct effectively or accurately the emotions felt in the past.I have felt dissapointment before, joy and elation too,but every time is like a first time. It is as if my own past experiences are vicarious to my own self.
As I wrote once before, I remember dates.So it is that I recall some important events that happened in August in my life.
Two years ago I wrote the GRE exam on August 1st. I rushed back to college immediately from Bangalore because Delphi was coming to campus on the 2nd.I remember walking bleary eyed past the ad-block as I saw my friends ,dressed smartly, rush towards A-2 hall.I remember being congratulated for what then seemed like a great score.Next thing I saw was the written test paper- had lots of microprocessors and programming in it and so that was the end for me:)).
However it was not the end for Pattu.The only mech guy who cleared the written,I can recall vividly,his face flushed, outside my room window,waking me up from my afternoon nap,saying: "Shriram mera ho gaya!!!" :-) There are few times in ones life that you really,and I mean really feel delighted at another's success, but life in college gave me numerous such occasions.
There were more things that happened that month.On the 10th I wrote the TOEFL.On the 27th,Pawan and I got placed (but never joined the Tatas:). Infact I landed here on the 13th last year.Maybe August is a great month for me!
But Pattu's story doesnt end there. Very soon after there was a report in the ET that Delphi filed for bankruptcy.There is no end to the fun it brought us at Pattu's expense.I kept the copy of the newspaper in Pawan's room, and whenever this pest would bother us as we were having some discussion of great import (generally of a nature too scandalous to be mentioned in a blog:), Pawan would point to that newspaper by the corner.Pattu the Pest would then slink away sheepishly ;)
Let me dedicate this post to Pattu-that pestilential creature who figures in most of the good times that I have had- and due to whom I gained so much and despite what am gaining now, realise all that am losing.
This post is more to remind myself than about writing anything funny or concrete.
Today is August 3rd.Exactly a year ago on this day, I got my visa. Maybe not everyone will think that event noteworthy,but I know otherwise.I was put through an emotional shredder for a month before finally getting it.And so how does it feel,I ask myself, a year hence?
Well, it mostly feels like a dream, as though all that never happened.And yet there is a residue of the disappointment, the uncertainty,the prospect of seeing your dreams crumble, that gets me disturbed simply by thinking.Now sitting in the future,it sometimes feels that it was not anything to worry about.And thats the peculiar quality of the human psyche.
I once read a book by Dan Gilbert titled Stumbling on happiness,and it is this quality that he often talks about.
The inability of the human mind (or heart, whichever you prefer) to reconstruct effectively or accurately the emotions felt in the past.I have felt dissapointment before, joy and elation too,but every time is like a first time. It is as if my own past experiences are vicarious to my own self.
As I wrote once before, I remember dates.So it is that I recall some important events that happened in August in my life.
Two years ago I wrote the GRE exam on August 1st. I rushed back to college immediately from Bangalore because Delphi was coming to campus on the 2nd.I remember walking bleary eyed past the ad-block as I saw my friends ,dressed smartly, rush towards A-2 hall.I remember being congratulated for what then seemed like a great score.Next thing I saw was the written test paper- had lots of microprocessors and programming in it and so that was the end for me:)).
However it was not the end for Pattu.The only mech guy who cleared the written,I can recall vividly,his face flushed, outside my room window,waking me up from my afternoon nap,saying: "Shriram mera ho gaya!!!" :-) There are few times in ones life that you really,and I mean really feel delighted at another's success, but life in college gave me numerous such occasions.
There were more things that happened that month.On the 10th I wrote the TOEFL.On the 27th,Pawan and I got placed (but never joined the Tatas:). Infact I landed here on the 13th last year.Maybe August is a great month for me!
But Pattu's story doesnt end there. Very soon after there was a report in the ET that Delphi filed for bankruptcy.There is no end to the fun it brought us at Pattu's expense.I kept the copy of the newspaper in Pawan's room, and whenever this pest would bother us as we were having some discussion of great import (generally of a nature too scandalous to be mentioned in a blog:), Pawan would point to that newspaper by the corner.Pattu the Pest would then slink away sheepishly ;)
Let me dedicate this post to Pattu-that pestilential creature who figures in most of the good times that I have had- and due to whom I gained so much and despite what am gaining now, realise all that am losing.
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