Tuesday, November 3, 2009

On Randomness

Most people know me as a studious kid. But I will now uncover some of the hidden truths of my life. I was never able to do things that I hate. An early example comes when I was 11 years old. I had to study a 3rd language- Hindi. I hated it like hell. I was very good in all subjects, but ordinary in hindi. In my highschool, my marks sheet looked unusual, with high 90's in math and science, and low 60's in social science. Once I failed in biology, in 12th. People around me, were emphasizing a lot on 'orderliness' and stuff...which I was never able to acheive; however, those suggestions, initiated an intellectual conflict in my mind. However, the first time I got the freedom to experiment on this conflict was when I came to IIT.

I planned a systematic waste of time in IIT. (good utilization of freedom!) As it turned out, all sensible and useful works that I did, was during the hours I planned to waste! It was the effect of the freedom given to the flow of thought. Finally, I understood that, the world is governed by randomness. Getting 'ordered' is a challenge to randomness. And hence, it failed..atleast in my case. These thoughts are deeper than they appear. They dont actually mean that one should live like a lazy drunkard.

The Story Of The Dog And The Monkey

In the last summer, back at home, I didnt feel like sleeping, one night. Towards the end of the night, one thought occured to my mind. It's the story of the dog and the minkey. A dog, never denies his masters order. It does exactly what the master wants it to do. On the other hand, a monkey, is known for it's restlessness. It does a lot of random stuff. The dog, cannot do what his master can't think of . A monkey, is capable of that. It goes beyond the span of it's master's mind, simply because it is more random in its approach. That is where is the hidden power of randomness. It's the monkey's attitude, which brings out something new to the world; not the dog's attitude. More precisely, it is the respect given to randomness in the monkey's attitude, which does the trick. So, if being notorious is useful, be notorious!.

However, the conflict is still on, in my mind. Confusion, which persists, looks to be a very essential entity. Thought says, life is not about getting out of such confusions quickly; it is the conflict of contradicting thoughts in the mind. Again, these thoughts too are in the conflict!(:D :D...the last one was a joke, a self reference)

Monday, September 28, 2009

The story of billiard balls

This blog is my first one, based on my thoughts, as mentioned at the end of the blog. I conceived this thought and the idea of blogging while travelling in a train, back from Kanpur to Bangalore.

A little kid, who does not know what 'color' is, comes across a bag of colorful billiard balls. what would be his reaction? His childish curiosity drives him towards the bag. He is attracted by the appearance of the balls...I mean, the colors, though he doesn't know what it is....

Most children stop there. But, imagine, an extraordinary( hypothetical, if you feel so) child, who can proceed further. The next thing he would do is, look for similar balls (balls which look like each other) The child has a way to tell whether two balls look like each other or not, by visual inspection. (looking like each other in our language means same color).

Next, the child can divide the bag of balls in to groups of like balls. Every pair of balls within a group would look alike. Hence, each group can be represented by a single ball. If the child is given new balls, he can easily put them in to respective groups. Or, if it doesn't look like any of the group representatives, it makes a new group.

Now, he is close to defining color. The representatives of each group are not balls, they are colors. He can name each group at his will. This is precisely what man did, over generations. The names he gave were red blue green et al.

Now, a formal look at the procedure adopted by the child. An important comment to be made at this point is about the way the child decides if two balls are alike. If balls 1 and 2 are alike , and balls 2 and 3 are alike, inevitably, balls 1 and 3 will fall in the same group. Hence, they should look alike. Formally speaking, his definition of alike should be trasitive. By using 'two balls look alike', and not 'one looks like the other', I have already meant that the like is symmetric. A little more thought will convince you that the like needs to be reflexive as well, for successful classification. Thus, it gives a reason to the mathematical definition of equivalence relation. Formally, those groups arising out of the equivalence relation are called classes. Once the classes are made, a mathematician may do various things with his classes....order them etc.

This is how most of the seemingly undefinable terms like color, size, mass, charge, cardinality, etc are defined(?).

The purpose of this blog is to express my thought flow, which at the moment says, mathematics is a way of thinking, formalized.