The anatomy of a question

When I was younger, much younger in fact, in school, we were taught about writing a notice. In case you don't know, writing a notice involves answering 5 key questions, Who/What, When, Where, How, and Why. The interesting part, I realised later, was that you could actually decompose pretty much anything that ever was asked, into one of these basic questions, or at worst, a combination of them. That, in itself, isn't very special, you'll probably say. To the mathematically minded, this will probably seem somewhat more interesting, cause you're defining a basis of a space, orthogonal or not, you decide. The real kicker comes when you actually try to see this in action.

The first, the obvious, is probably art. Understanding art, in fact anything at all, requires that you ask the right question. It is like the principle of resonance, you really can't see any substantial affects unless the frequency's right, i.e. the right questions are asked. But then again, the point of a lot of art is simply to make you ask the question. Why is that interesting, useful even? When we usually ask a question, we ask it in a context. When you try to ask the same question in a different context, or even simply try to see the same answer in a different context, you'll see very different results. That's why people who advocate abolishing the death penalty, would probably hesitate, if say, Hitler was involved, assuming of course, that he were alive.

In saying so, the act of asking the question, the "right" question seems to be the most important thing of all. Ask someone doing a Ph.D. , they'll vehemently agree. The "right" part is the hard thing, it seems you need to use some magic to do so. Let me offer an interesting parallel. In theoretical computer science, there are 2 classes of problems, P and NP. The class of problems P are such that can be solved in time proportional to some polynomial function of the size of the input problem, for example, sorting a list of numbers. The other class, NP, intuitively means ones that cannot, more specifically, they stand for the class of problems whose solution can be verified in polynomial time. To actually find a solution would take exponential time. If this seems gibberish to you, understand this much, that problems belonging to the group P, are easily solveable, while the ones in NP, are not, they can be verified easily. Now, one of the areas of research in computer science is to see whether these 2 sets are the same set or not, i.e. is it that problems of NP actually cannot be solved in polynomial time, or we've just been that dumb for so long that we didn't see the answer.

Now that we've taken that detour, let me point out where I'm going. We always ask questions that have no "right" answer, or atleast one whose answer's "right"ness you cannot check until you try it out. That, to me, is pretty much what I'd consider NP material. However, you answer a lot of easy questions everyday, which you don't think twice about, more P material. I know a lot of you would scream blasphemy and point out holes in the argument at this point, but keep your pants on, take a leap of faith here. So, our dilemna is, are there 2 kinds of questions, or are we simply just dumb enough that it seems so to us. After all, different questions seem to pose different levels of difficulty to different people. But, when told the answer, we can all "easily" see that the answer's right, or wrong. Well, sometimes, we can't even do that, cause that itself is asking a new question. So does that prove whether P=NP or the negation? difficult to say. If human nature has shown us anything, it's that the same questions pose different scales of difficulty at differing times in our lives, so in a way, all questions are hard, which would seem to suggest that thinking P=NP isn't that bad after all. But then think of questions like "Where am I" at a more cosmic level, you'll have to stop at universe, but where is the universe?. Or even seemingly more mundane questions like "Who am I", or "Did I do the right thing". The thing is, hard questions exponentially explode to pose a number of other hard questions, which is exactly why they're hard. But the thing is, the answer to whether such hard questions can be answered (pun unintended), could be suggested by computer scientists!, if and when they prove the P=NP problem. Until then, we can do something most other computer scientists do, use approximations. The key lies in realising that the right answer may not be worth the effort, so there's no point in killing yourself over it. All you should probably care about, is that the answer is good enough to a certain level of tolerance, and then not care so much about the repercussions. After all, you did your "best", and you have a somewhat hacky argument to prove that you couldn't have done a better job given your restrictions. After all, the best algorithms for perfection are non-terminating. My favorite is a dialogue that Richard Gere said in a very cheesy movie called First Knight: to win a duel, you have study your opponent, wait for the critical moment, and not care about your life.

Of course if you try to use this post as an argument as to why you couldn't complete an answer in your paper, in front of your instructor, then ask yourself, is god/luck with you (and the exploding series of questions that follow :P ).

Ramblings

Rainy Day
In that moment time stood still,
Her beauty washed over me,
She was in front of me, within me, and all around me,
Born anew, glistening in the moonlight

-- Me