The P versus NP problem is a major unsolved problem in computer science. “Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer” (Wikipedia).
This problem is also one of the 7 Millennium problems that Clay Mathematics Institute of Cambridge, Massachusetts (CMI) designated a $7 million prize fund for the solutions, with $1 million allocated to the solution of each problem.
CMI, however, formulated this problem as “determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure”, which can be formulated as a question by “is there a question whose answer can be quickly checked, but which requires an impossibly long time to be solved by a direct procedure?”.
These two questions about the same matter actually demonstrate the duality of reality. The answer to the first is “no”, whereas the answer to the second is “yes” – no, not every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer, and, yes, there is a question whose answer can be quickly checked, but which requires an impossibly long time to be solved by a direct procedure. The problem is that “questions” and “answers” are orthogonal, and thus that there has to be at least one question or answer that doesn’t have an answer or question.
Every question is generically also an answer, but in a finite context (ie, in Western thinking) there has to be at least one question (the first) that isn’t an answer and one answer (the last) that isn’t a question. The problem with this context is that it is contradictory by also predicting that there is a question that also is an answer AT THE SAME TIME. It thus contradictory predicts that there is a “truth” (ie, a question-answer).
It is this question-answer the P versus NP problem aims to find. Unfortunately, it is not to be found. So, do I now receive this Prize when I have clarified the solution of this problem? Can I be Prized for demonstrating that rational thinking can’t explain reality?
Another contribution to understanding of conceptualization http://menvall.wordpress.com/