The notion of approximation has brought forward a completely inherent phenomenon of the nature. The interesting fact that not all the problems in the nature have optimal solutions. And it is pretty evident that every action that happens around us, may not be the best way it can be done. Again the most interesting example of 'Human Brain' is valid here. Not all the time we do things optimally. Many times an approximately good choice suffices and we opt for it. We may not be interested in acting optimally every time (though it will be very interesting :P to get the optimal result).
The whole point here is, the study of Approximation is crucial. And the resemblance of computational processes with the natural processes has given a nice directions and platform to study it. Approximation Algorithms a recent field has given many directions to the problem solving domain. It is not solving the only computational problems but many problems that lie at the base of this world. The P versus NP question again has interesting significance here. If (P=NP) then a huge set of natural problems will be optimally tractable rather than being approximably tractable. (Which does seem unlikely but nobody knows yet for sure.) Again this kind of thought might lead to confusion. If nature does not act optimally then how does it manage to maintain such a huge equilibrium? Or are there many optimal solutions? The question is wheather the optimal solution needed or an approximate solution suffices. The approximate versus the optimal solution problem is actually a nice thing to obtain the truth about the optimality.
Truely the P versus NP problem has its own beauty. Its not just a mathematical or a computer science problem but one of the problems that lies at the crux of the nature.
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