Future Musing

This age is when decisions are made that affect the whole life... Right now I and all my peers are making decisions and choosing paths...

I wonder sometimes, what my life will come to.

Twenty years from now, where will I be? And where will my peers be? Will my life have been successful? Will I be looking back twenty years from now, and be extremely happy with the path that I took at this time? Will I have attained what I want to?
Or will I be ruing it, surrounded by success stories of my peers? My mom told me stories of IITians of her batch. Of some she said, "He got through IIT at that time (in the 70s). But look at his life now. He did nothing special." What category would I belong to?

In my batch there have been so many talented people, and all have chosen different paths. Some took a job, some went for a PhD, some for a masters and then a job in the US, some would like to be professors, some went into consulting and some went for MBA.

Everyone is trying at this moment to set the direction of his life. Roughly twenty years from now, we would have a class reunion at IITB. At that time, it will be clear, who all succeeded, who all are happy with how their life has turned out, and who all belong to the category my mom talked about.

Only time will tell.

Twenty years from now, if this post remains, I will come back and look at it -- either with eyes aglow or eyes downcast, reminiscing about a life wasted.

Simplicity

There is something extremely awesome about simplicity. A problem should not be considered solved unless a simple solution is obtained.
Here is one such problem that was given us during my graph theory course. It is on graph coloring.
X(G) represents the chromatic number of the graph.

Question: Given a set of lines in the plane with no three meeting at a point, form a graph G whose vertices are the intersections of the lines, with two vertices adjacent if they appear consecutively on one of the lines. Prove that X(G) =< 3.

I pondered this for a long time applying theorems and making no headway. Finally an elegant and simple solution came to me. Even now I remember the contentment this solution gave me. As expected, it was much simpler than the one the professor offered in the tutorial session.

Solution: Assume some co-ordinate axis system, so that each vertex of the graph has a (x,y) co-ordinate.
Use the following algorithm:
1. Start coloring from the left, i.e. start coloring vertices according to increasing value of x- co-ordinate.
2. If two or more vertices have same x co-ordinate value, first color the one with lowest value of y - co-ordinate.
Its now immediate that while coloring any vertex, atmost two of its neighbors can be already colored and hence X(G) =< 3.
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I definitely wasn't the most brilliant student of the lot - far from it actually... but simple solutions do come unexpectedly, and they can come to anyone I guess.

I still remember sitting still for a long time afterwards.. savoring the beauty of this simple solution...

Benediction

May you experience joy that you never got through sex,
May you experience peace having which you never vex,
May you experience calm having which your life is never amiss,
May you know that all the joy you ever searched for is already you, your true nature is bliss!

Cut Songs

To a friend who has this very irritating habit of dissecting songs into parts he loves and does not love:

what sayeth the artist when,
in cometh the layman,
cleaveth apart the song--the artists heart,
and dumbly sayeth-- I love this part but this part I do not!!
-Sagar