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¶ the problem as a battle
Having trouble sleeping again. It's 6 am and I can't fall asleep.

I'm beginning to understand how to appreciate difficult problems. Lately, I've started thinking about the whole process as a battle. My opponent is the problem, and I must defeat it. Like any adversary worth fighting, this is one that must be carefully studied and analyzed before being approached. My opponent will expect and easily deflect the obvious approaches, otherwise he will have been defeated long ago by others who have come before me. Indeed, several have come this way before and retreated, declaring him an unsurmountable obstacle. Therefore, I must approach with caution.

Patience is often rewarded with success, as is diligence. If one type of attack fails at first, then it is beneficial to step back and determine why it did not work, and if there is anything to be learned. Eventually, by probing and exploring from every angle I know of, I will expose the weaknesses of the problem. Knowing where the opponent is weak gives me the confidence to approach and make a final assault. If my analysis was correct, then I will easily prevail. What seemed like an unbeatable foe a short time ago becomes the dust in my tracks.

If I was wrong, however, and acted hastily, then I will be defeated. With luck, I will escape mentally battered but intact. Without luck, my opponent will crush me, permanently impairing my ability to wage battle in the future (they say that's what happened to Sipser after he spent a couple years trying to solve P ?= NP... he does have this crazy look in his eye...)

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