What Is Research?

July 8, 2006

A breakthrough

“And then he saw her. Those hours of waiting under the moonlight, that pacing up and down, those nervous glances at the watch, those frantic glances at the sky, all seemed to fade out as he saw her gliding across the lawns. And then he realized that she had always been there… if only he had looked that way!”

I had a chat with DP the next day again. I had already sent him the writeup and I presented my ideas. He had marked some corrections in my piece — mostly incorrect symbols here and there.

I had used a little piece of notation: “BIR” for “Base is a Retract”. I am all for defining all my notation but I had split my work across multiple files and I had just sent DP the main file. In case you’re curious, by “BIR” algebra I mean an algebra with a retraction (viz an idempotent endomorphism) to the base ring. Every connected graded algebra is naturally a BIR algebra.

DP asked me what this means and I explained. But once he realized it was just something I had cooked up for the purpose, he lost interest. But it was a reminder of an important lesson I have often ignored: avoid introducing too many terms of your own.

DP gave me a little more pep talk. He said that I have made good progress, but it is high time to actually get down to the proofs. I told him that I had started going through it, but hadn’t achieved mastery over the proofs. We chatted for some more time, and before leaving, DP told me: I am happy that you are at last happy… it is nice to know you have started enjoying it. I won’t be here for the week but I think you’ll manage now.”

DP then left, and my progress continued. But somehow, it started losing steam again. This went on for 4-5 days, even as I was blogging out my experiences. Then, I pulled myself up and said “Hey! I am here in TIFR to learn and do great stuff. I am here to do great stuff and I am going to do it. And that great stuff begins with doing the task I have been allotted with full commitment.”

And then I asked myself: “With all these cycles of highs and lows, what am I really achieving? have my lows actually been all that low? Have my highs actually been genuine?”

I realized that my progress and commitment had been there throughout. The difference was that there were times when I had a feeling and a desire to do the paper and at other times when I was just plodding my way through. And when I was just plodding my way through, I was more prone to distractions. But, repeat repeat: progress had been there throughout.

But now there was a week left, and I wanted to do a lot. And I knew it : I was going to do a lot. I had spent a lot of time absorbing the background material: now was the time to plunge into the proof.

The next day, I just managed to master one part of the paper in an hour’s time. Yes, this hour came after a lot of days of struggling, but I know that I could have brought the hour on earlier if I had really wanted to. And I started consolidating on that hour.

And I have since been hard at work, pushing my way through the paper. There have still been distractions but there are now no regrets in my mind about having taken the paper. The paper is part of me: it is part of my history, my experience, and it defines a part of my present.

Which brings me to a question I want to discuss further with you: why does research take so long. Why are (as I had put it earlier) the few periods of activity interspersed so thinly in long periods of inactivity? Is it really that necessary? Is incubation time so high, or is a lot of the gap redundant? Do we set a limitation for ourselves when we say: “I have three years to do my B.Sc., two years to do M.Sc. and five more years to do research, so let me relax. It anyway can’t be speeded up”?

Do we give up our attempts to learn, lose heart, and wander here and there too easily? Or is that wandering necessary? Of course, these things differ from person to person, and situation to situation. I look forward to your posts. On a somewhat related note, you want to have a look at Steve Pavlina’s webpage.

Do give your comments…

2 Comments »

  1. I read the last 3 posts.
    You are a very systematic person – to be documenting your experiences irrespective of the nature of progress. A good analysis of the reasons for the slow progress is a sure way towards improvement rather than the common tendency to avoid the work altogether. Your lucid analysis indicates a great research potential. Best of luck.

    Comment by Anonymous — July 9, 2006 @ 6:16 pm

  2. Yes, I too have been asking these questions about the pace at which things are done since at the end of it I always end up feeling that this could have happened earlier, maybe there are some phases when we uncounsiously put it away to some other time. For instance I could be blogging when Im supposed to work on a problem that has been bugging me and not feel an urgency related to this fact. I wonder what bearing this has on our output in the long run and wether people like erdos spent such periods of long inactivity.

    Comment by Sagar — August 2, 2006 @ 6:46 am


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