The importance of a peer group

I have to say at the start that people have different personalities, and consequently the kind of interaction that gives them satisfaction is a parameter that varies largely from person to person. I would like to divide people into two classes (neither exclusive nor exhaustive) - one who is extremely sure of what he wants to do, how he plans to do it, and what his opinions are on several issues. Such a person may be charachterised by an environment invariant measure - his thoughts and actions are seldom a function of where he is, or who he is keeping company with. Let us for the sake of simplicity call him a closed set. There is another class of persons, who are amenable (very highly) to draw inspiration from their surroundings. These surroundings mostly inlcude their sphere of interaction, available avenues for recreation and learning, etc. The latter person is in my opinion, one that I identify with closer. I should clarify at the outset, that this persona is NOT one who follows the herd, and has no mind of his own. This has more to do with the psychological metric known as Agreeableness (one of the Big 5 personality traits).
I find that my interests and curiosity are easily triggered by (interests/knowledge) of people i interact with. It is not up to you and I to categorize such behaviour under those broad clasifiers of good OR bad, but it may have its own merits and demerits on varying occassions. This ablity to inspire that a person has, has a very strong correlation with the interests and aptitude of the beneficiary of such inspiration. So, i value my peers very highly, especially those i like to interact with and consequently draw inspiriation , ideas from. Also, it is my humble belief that this interactive exchange of knowledge, ideas and more broadly perspective of opinion that we share - is mutual, and i feel very glad whenever i possess within me, the capacity to shed light on some topic, or obliviate my own ignorance on another.
A toast to all my friends, and a toast to the collective knowledge that we have helped each other attain and enrich.
cheers

(written a week ago i think, was too lazy to post )

IEEE down under

Yesterday I attended an IEEE lecture in bedford street north melbourne. It was evening, i was hungry, and it was raining. When i turned up, i was the youngest attendee, the average age being at least 50 ! I was mentally prepaered for an hour of boredom, reminising about food. The speaker is a certain Dr. Robert Hill, a very senior IEEE member having served in US army and navy as a radar specialist. "what the hell are you doing here on a monday evening in such a beautiful city? When you should be chasing women, or having a glass of wine, You chose to attend a seminar on the autocorrelation function !! the autocorrelation function for gods sake. Well, All i can say is that you all seem to lead pretty boring lives !!"
What ensued then on, was one of the most intersting and lively seminars i had ever attended. Starting from what his 14 year old grandson asked him at the breakfast table, at the end of 60 minutes, we were talking about binary phase coding, and the best ways to use radar systems to identify fast moving targets. In the process, i noticed that some of the portion was basic sophomore stuff : but each and every member in the audience had eyes and ears only for the speaker. Each one of them , so senior - probably knowing the autocorrelation function from the back of their palm, are so eager to take a fellow researchers perspective, and to revell in the basics of the subject - it became clear that these were men who loved every bit of what they did. The lecture also reaffirmed my belief - in the power of the instructor.
Having an immensly short attention span, it requires instances of such magnitude to stir me into action and fill me with a hunger that only the subjects that i love can satiate. There are several things that can be better at my college, but if at the end of my undergraduation - i can sustain an iota of the temperement and curiosity that i witnessed this day, i will be very highly satisfied. A toast to knowledge ! and all those who seek it !
Amen

PS: The melbourne journal is in the process of being written, readers are advised to keep checking this space :)

Of Information and Puzzlement

A couple of days ago, I came across this very interesting puzzle. What is more interesting about this puzzle than the usual ways in which all puzzles of this kind are interesting, is the information theoretical aspect of the solution, or a way in which the problem may be perceived. Information theory deals with quantification of information, and gives us those limits beyond which we cannot compress data any further. It is obviously of great relevance to all communication systems and computation paradigms.

First the puzzle -

A king decided to play a game. There are a bunch of 100 people, who are to be lined up and then a colored hat (Blue or White) is to be placed on their heads. Now the really sardonic king decided that he will walk up to the person at the back end of the line (who can see the other 99 in front of him) and ask him the color of his hat. This he would do for everyone. If a person answered wrongly, he would be silently killed, else he would be silently allowed to escape (those standing in front of him will not know if he answered correctly or not). What is the maximum number people that can be guaranteed to be saved if they evolve some strategy for this ?(the game is explained to them beforehand, and we can assume them to be sufficiently intelligent, self-less and whatever else you may want them to be)

Consider the obvious solution. Every alternate person yells out the color of the hat worn by the person immediately in front of him. That person, of course gets to live. In this manner at least 50 can be saved. But one gets the feeling that this can be improved upon. The interesting part starts here. Consider the sequence of 100 hats to be an ordered sequence of bits. It is clear that all 100 cannot be saved. Now, suppose I tell you that the answer is 99 (which is the case, as we shall shortly observe). Doesnt it sound absurd? Does this imply that through the answer of the first person (1 bit) only, 99 people are able to figure out their hat colors? Can the information of 99 bits be conveyed/compressed into a single one !? Admittedly, this perplexed me and my friend for a small second. From an Information Theoretical perspective this seems too wierd to be true. But then this statement is not correct after all. What took us some time to figure out was that the answers of K persons should contain sufficient information for the (K+1)th person to figure out his hat color. This seems logically sound, and the solution to our puzzle of the 100 wise men is as follows:

Let the man at the back count the number of White hats he can see, and shout out "Blue" if they are ODD in number, and "White" if they are EVEN in number. The person immediately in front of him will count the number of White hats 'he' can see, and based upon the first guys answer, he will know his hat color (how?). Subsequent people will know that the second guy onwards are correct in their response, and hence they will be able to figure out the color of their hats as well. In this intelligent manner they can save at least 99 amongst themselves.

Now this puzzle is probably like many others you have seen, but the bit sequence analogy aroused enough interest in me to write a post on it !! The whole idea of discussing this problem started when a couple of friends of mine (V1 and V2) were giving an interview (with a high paying oil company) for a lucrative summer internship. Incidentally they answered wrongly, and so did I and so did my other friend(P1) when they asked us the following question....

"There is a cold drink vending machine, with three buttons COKE, SPRITE and COKE/SPRITE. The COKE/SPRITE button can dispense either of the two drinks with equal probability. You are told that the labels are mismatched. What is the minimum number of coins you require to correctly label the buttons of the machine?"

PS : Read the question carefully. For those who are interested, my friends who couldn't answer this question in the interview got selected (:P), and another one who did answer correctly (P2) wasn't !!

And I obviously cant end the post without celebrating Chelseas total annihilation by Manchester United last night !!
Cheers ...