My first month of research: parable of the door

Imagine you are trying to crack open a wooden door. It looks new; no one might have tried it before, so behind it might lie of unknown treasures. You take a few steps back, a deep breath, then run forward with all your might. Bang! You feel sharp pain on your shoulders, but the door seemed to budge at the impact. There is hope! You kick and pound on it with unbridled, fresh energy. Your hands and feet are numb, but the door remains. You realize it's probably better to try a smarter way...

You examine the lock. Wow, the locking piece seems to be a wedge, so if you slides something behind it and pull... Fresh hope renews your energy. You survey the surrounding area, and you find a sheet of plastic film, scraps of sheet metal, and a knife. Heartened by these new tools you set out to work.

You first try to slide the plastic film into the gap, but its end keeps folding: it's not strong enough. You then try the sheet metal: it's strong but a little too thick for the gap. Hence you start chipping at the gap with a knife. The wood peels off only little by little but the steady progress spurs you on. After much chipping, you take the sheet metal and try again to jam it in. It goes in a little bit. Undaunted by the difficulty of the task, you begin to forcefully slide the sheet metal up and down to force it in more, while plying with the knife to marginally increase the gap. This process creates many specks of wood shavings. Finally, you feel the sheet metal touching the wedge. So close! Carefully, you try to maneuver the sheet metal to cut under the wedge. But just at that moment it gets stuck! Aghhh!! You push your right foot against the door frame and pull, applying the full force of your legs and dorso. Pfrizz... Ouch, you tumble back as the sheet metal snapped out of the gap. You pulled too hard...

Wiping the sweat off your brows, you push yourself up. Your are too determined to let the setback affect you. Oh wait, you have a better idea! You use the knife to ply as before, and insert the plastic sheet. Your previous effort had enlarged the gap, so now with the knife you can insert the plastic without it bending. Once inside the gap, the plastic is a great improvement because it is thinner and smoother. You try to slide it under the wedge as before. You try once... the plastic slides against the wedge but doesn't push it in. You try again... same thing happened. You try the third time... Voila! The plastic pushed the lock wedge in. Nothing is now holding the door back! You can't control the wild smile on your face. This is it! You push forward and the door swing open. Life is great!

With pride you examine the now open door, the spoil of your ingenuity. What a triumphant moment! The small, metal wedge on the side of the door now seems so innocuous... Wait, the handle on the other side doesn't have a key hold. So how does one lock this? You turn the inside handle: the wedge obediently goes in. You turn the outside handle: the wedge goes in again. What? You could have done that all along? Wow you feel stupid...




This in essence captures my research experience in the last 3 weeks. I was excited about my problem, designing revenue maximizing auctions in the presence of budget constraints. It seemed to have many applications and not many people have approached it my professor's way before. Felt like a great research topic.

I first try brute force. Although this seemed to make some progress, but after pages of math I realized I needed some clever way. Then I stepped back and tried to build tools to help me. I proved structural theorems helping me to narrow down to the essence of the problem. I found my plastic, sheet metal, and knife.

Then I worked hard to apply my tools to the problem, averaging about 10 hours a day. The progress at first was slow but I persevered. I just couldn't stop thinking about the problem, even daydreaming about it in the gym. After much effort I felt very close to a solution, but there were many setbacks. Sometimes I realized a fundamental theorem I had assumed was wrong, hence rendering meaningless much of my argument and I had to restart. But eventually I found better ways of doing things: the plastic sheet simply fits better. Last week I finally made a break through: the door opened. I improved currently best-known results and diligently wrote a 10 page paper on it. I felt so good last Friday when I printed the paper. It's in the same template as for the conference I'm hoping to submit so at least from afar it looks legit. =)

Then came yesterday: my prof used the intuition from my paper but gave another proof, showing a better result in 5 lines, rendering redundant the last 9 pages of my write-up (3 full days of hard work just writing it). Clearly, the new approach is the correct one to take. Today I further improved the result in this direction, but now the proof is less than a page, and all the ideas are simple: it could have been some homework problem; I didn't need all those tools I was proud of. Ironic how the result is now much better, but the paper is no longer publishable. It looks way too simple...



Moral of the story: next time I need to open a door, try the handle first!