Can lightning be used to solve N!=NP
I'm a MS/BS computer science guy who is wondering about why lightning can't (or can?) be used to solve NP complete problems in P time (considered by some to be the greatest problem in the field of computer science), but I don't understand the physics behind lightning, so I'm posting here.
What seems peculiar to me about lightning is that it knows how to follow the "easiest" path to a given destination (as opposed to just the shortest path). This seems analogous (identical?) to the weights in the traveling salesman problem.
Since the lightning process ionizes the air (or seems to) and pick the easiest route in non-polynomial time, I have 2 questions:
1) Does lightning use a method similar to <PERSON>'s approach (such that a "good enough" path is found in p-time, but not necessarily the "best of all options")? Is it basically an NP "solver"?
If the answer to the above question is "no" and it is indeed the best pick:
1) Could the selection process of lightning be used in a computer algorithm to solve a traveling salesman-type problem in P time and
2) If not, could an arbitrary series of weighted nodes be physically set up somewhere and have electricity passed through it and have the results fed back into some kind of computer mechanism for every time a user wants to know a shortest path?
If you could use this approach to solve NP-hard problems in P time, you would have your name on the news and maybe in the history books. 180
So why hasn't anyone used lightning to solve this problem?
UPDATE: Another aspect I find interesting: when lightning strikes it ionizes the air to find the shortest path. If the world were totally flat (and the clouds were also) this would ionize all the air equally. Which leads me to believe the route "picked" by the lightning incorporates all points, which seems to be a requisite for finding the best of all solutions.
Originally posted here: http://stackoverflow.com/questions/10586781/can-lightning-be-used-to-solve-n-np And re-posted here by a suggestion from the comments. 229