Complexity of life.

Since this is my first blog I thought I would put little thoughts on "Complexity of Life".

I believe that figuring out how to make your life best or ideal (optimal in mathematical terms) is one of those complex decision problems called Non-Deterministic Polynomial-time (NP). I don't have a proof to this argument. Consider the verifier based definition of problems in NP. If there exists a verifier running in polynomial time (P) for the solution of the algorithm then then we call that the problem in in NP class.

Now imagine you are 84 years old and had a pretty good life so far (maybe a good career in computer science) and you are sitting in the park thinking about your past life. Suddenly God appears in front of you and he starts discussing about your the decisions in your past life. He wants to explain what could have been the best decisions for your life (optimal decisions) that he had written in his book.

He tells you if you had done BS Mathematics instead of Computer Science you would have topped university. And then if you chose to attend Princeton mathematics discarding the Stanford admit your Phd thesis on combinatorics (again a choice) would have won the best thesis award. After graduating from Princeton if you chose to become a professor letting go a lucrative job offer, you would have won a "Fields Medal"......

Or he tells you if instead of working for others all your life, if you had trusted your gut and started your own finance company, you would have been the richest man on earth...

And You faint ..

You have done good enough with your life, but you could have done better. It is easy to verify (in P TIME) the decisions in God's book (answer to the decision problem) about doing BS in Mathematics and going to Princeton were clearly the best choices for your life because they led to Optimal solution. But the question is can we find this answer in a considerable amount of time at the start of your life? (or at the end. but that wont help.) The answer is unknown.

If we consider every choice of your life and try to find a solution the time to find this will be approximately 1000000.......(I dont know where to stop) in any time-unit. Thats what makes it hard.

But human is an ingenious creature. Though we cant figure out what is ultimately (optimally) best choice for us we have some lookahead and by using that we can find an approximate solution to our lives (OPT/alfa). In some cases it performs very well (alfa=1) and for some cases its not that good.

At the end what I want to say is finding the optimal solution to the "life problem" is a NP problem. Since its not yet proven that P=NP we can still hope... But we have approximate solutions that do well if we give our best as an input to the algorithm.

So there is an approximation solution to the life and it performs best when we do our best .. Obviously we can check how well did we do in the the God's book later on in the heaven ...

Vinay