Welcome to Gaia! ::

This paper, written by a guy with very good credentials, is the current best bet for a proof that P≠NP. It uses an analogy between solution space complexity and thermodynamic entropy to show that the class of polynomial-time-solvable problems is a proper subset of the nondeterministic-polynomial-time-solvable algorithms.

There are a lot of people getting very excited about this since the guy is not just a random crank but actually has a lot of authority and the paper itself looks very, very good. However, it is a little bit suspicious that many top theoretical computer scientists who have spent full time on this have admitted total defeat and this guy who has a day job at HP managed to get it.

Here are some people discussing possible issues with the proof. I am totally not equipped to evaluate the paper in any meaningful way, but however it turns out this is a pretty big event.

Well, in linear functions Y is completely dependent on what X is.

For P to Equal NP, by some stroke of luck, N would have to be equal to 1; Exactly. Which would be a mathematical anomaly, and seeing how it's a variable and not a constant (?) I think it's easy to assume that only in vary rare circumstances could P be equal to NP- and should it be proved a constant in some form, or to hold a constant value (such as NP not equaling P) then I still highly doubt it would ever be equal to 1.




Still, P = NP is mainly a metaphorical symbol for the question (yes?): "Suppose that solutions to a problem can be verified quickly. Then, can the solutions themselves also be computed quickly?"- The answer to that is, yes. If you know the answer, then computing a problem is instant, as you already know the answer. If you already know part of the answer, such as f(x) = 2 in f(x)= x + 2, then the answer is theoretically easier to solve. But, for P to equal NP, you would have to already be aware of the answer. Defeating the purpose of computation in it's original goal. Unless the computer has a decision making engine, computations will always be dependent on the computers ability to compute, whatever that computer may be (Human, electric, little beads etc.)




And regardless, my Calculator says that X = 1.125 ninja

So it's easy to assume that within a single distinctive linear form that you could formulate an answer but when multiple variables are introduced, as the problem suggests, the answer is potentially unsolvable. Who knows what one page of his 102 page essay could hold a mistake- maybe his calculator randomly set the value of N to everything but 1. xp