Tayzwi

I have never heard the Who's music; and scientists have always wondered about the Why's; Science mostly explains the How's; Today's question is the What.

On first glance, the What appears to be tame compared to its illustrious peers. While beginning Jaynes's tome on probability, I came across this quote said around 1948 and attributed to von Neumann - "For those who believe that comptuers cannot do all that we humans can; please explain in finite, precise steps, what it is that you can do; I will make the computer do precisely that."

This is precisely the importance of the What. What is it that we are doing here? What is it that we want? What is it that happens when we breathe? What is emotion? What is thought? What is pride? What is light? What is everything....

A what can mostly be answered by enumerating all the members of the answer set, and hopefully some abstraction will come out of it so that the next time, we use the abstraction instead of enumeration. But the first time, or till the time the abstraction comes out, we are stuck with the enumeration of all members of the answer set. Here is precisely where things might go out of hand. We might not be able to enumerate all that we think contribute to the answer to a single What. There might be just too many of them.

Let me elaborate that with an example. If someone asks me - What is poetry? - I can either come up with an absract answer which encapuslates all forms of poetry, all poems ever written, all poems that will be written in the future, all poems' purposes, all this, for all languages. The abstract encapuslation of these needs to be simple, concise, and should give a precise description of poetry.
OR
I can simply enumerate ALL possible poems there are, all of them, in a set, and give the enumeration set as the answer to "What is poetry?".

It seems that for all the NP-complete problems, we are stuck with the enumeration till the abstraction for all enumerations is found. We don't even know if such an abstraction exists. This is the famous P vs NP question, and well, there is a chance that this question itself is beyond answer.

My next post will elaborate on my current thoughts on the relevance of the P vs Np question in the eternal human-vs-machine debate.

ps - while writing about that poetry example, I remembered that there was something called Information Complexity which I had read about somewhere, and here it is. It goes by the name of Kolmogorov Complexity.

Labels: computer science