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Wednesday, December 31, 2008

hi there!! Happy New 2009!

Hey there!

3rd semesters over matey!! Seems like weve got plenty to do!!

Twas a very successful semester for me- I finished off the ten seasons of FRIENDS- although a meagre first viewing only! But 20X24X10=4800 mins=30 hrs of popcorn popping was not ALL I did!! I also passed a chemistry course in spectroscopy (having flunked the midsems by one point- but made up good time to claim 85% in the final assessment), passed a physics course in Quantum Mechanics which was over-the-line mathematical, loved a complex analysis course, proved myself a SENSITIVE scientist wannabe (humanities course in “Indian Heritage in sciences” baby!), and watched many more movies of my kind.

I also grew a goatee and shaved it, twice, notwithstanding my status as a bovine creature. There was also a great deal of growing up, yknow, philosophically and emotionally; but the present stand is to put all the growing up behind the linen!! We do need to grow sometime soon, mind our own business and manners- but give it a break grumpy; we aren’t 20 yet!!

New year is coming up, and the resolutions I take grow increasingly stupid!! Ahh , the time to start all over again!! We do need that now, don’t we? I wish I had a bunch of Donald Shimoda quotes to throw at you, but then do you know at all who he is?

Ayn Rand does write beautifully and she climbed into my hallowed unrankable authors list with Tolkien, Rowling, Richard Bach, Erich Segal- after I read only one chapter of “Atlas Shrugged” (talk of me being biased from the hype she has around people- but the factor is that she satisfied all my expectations- she could have let me down, like Rowling in “Deathly Hallows”- but AR didnt).

VARIABLE CHANGE from movie ‘21’

And last of all the insight into variable change that my musings revealed to me only this morning. You see, in the movie 21, the protagonist who goes by the name of Ben is a brilliant young student who gets into a ‘card counting’ club in MIT, and the subsequent repercussions on his lowly life. In my opinion, it is not a timeless piece at all, but enjoyable like all crap in this world is. There however Kevin Spacey stars as Miki Rosen, the MIT prof with a helluva gift of oratory and the leader of this card counting team who go into Vegas at weekends to beat the game of Blackjack using logic and cool head. So, Miki asks Ben an apparent paradox, also known as ‘Monty Hall Paradox’ which I will now proceed to explain.

Miki tells Ben to imagine ( I am trying my hands at my own version of Kevin Spacey’s inimitable style in this monologue) that he is in a game show; the host offers him three doors behind one of which is “brand new sports car” and two goats behind the others. Ben chooses door ‘1’ in this choice. Before declaring the result however the host spices things up when he undoes door ‘3’ behind which there is a goat. Then Miki asks Ben if he would switch his choice to ‘2’ or not.

Heres the key- Ben chooses to swich to door ‘2’.

This decision, he says, is propelled by cold hard logic, because the host knows everything and the unlocking of door ‘3’ changes everything; ‘1’ has a 33% percent chance of having the car, while ‘2’ has 66% odds of having the car and hence “thank-you-very-much for that extra 33%”, he says.

People are very confused by this explanation, as was I, because apparently the unlocking of the door ‘3’ redistributes the odds to 50:50 between ‘1’ and ‘2’. BUT what I forgot, and most people do, is that the choice to unlock the door ‘3’ by the host is a conscious choice, and in doing so he seals the odds to one-thirds and two-thirds respectively.

Lets examine the 33% case when the car is originally behind ‘1’; if Ben switches then, then he loses. Note that the host would not show ‘1’ and would not show the door with the car.

For the 66% case that the car is either behind ‘2’ or ‘3’, the host eliminates ‘3’ and now if one imagines that the car cannot be behind ‘1’ which IS our assumption here, one is 100% certain that it is behind ‘2’. If the host uncovers either ‘2’ or ‘3’, the response is the same, make the switch for a 66% chance of win.

Summing up quite, at the beginning:

‘1’=> 33%

‘2’ or ‘3’ => 66%

The host eliminates ‘3’, one is left with,

‘1’=> 33%

‘2’=> 66%

This required quite some thinking, but still people convince themselves that this is actually not a correct explanation at all; it requires one to keep track of the abstraction long enough to see the answer.


rvivekshanmugam said...

Happy New Year! :)

RaSh said...

Woow. Long time since I saw something here!

Happy New year to all those who are reading :)

Hamsa said...

Hello everyone!
This is Hamsa from Pune. I was at the Bangalore summer programme in May 2006. (KVPY Stream SA 2005) I was reading through the posts on this site for quite some time and thought I should introduce myself and come in. But haven't seen any posts for a long time now -- so was not sure whether this site is still in use?