Does p equal np for some np problems yes well sort of and the proof is simple
lets say your traveling sales man lives on a straight street with 3 houses 200m apart he lives in the first house and needs to go to the second and third house to sale his chairs. his optimal route is salenumber*200m due north. in an unoptimal np approach to this problem he looks up the street checks the distance from the nearest house to the furthest house tests if going to the second house first cuts time tests if walking round the block leading away from the first house back round to the second house cuts time and realises it doesn't matter on this occasion whether he starts at the first or last house as long as he walks in a straight line to the end and back because hes walking back home after anyway and decides to start at the second house so he can get that out the way and have a bit of time trying to sell more chairs to the person in the closest house. He ends up spending too much time trying to convince house number 3s occupant to buy just one chair without any luck such that number 2 has already gone out for lunch with a friend.
How did I come to the p conclusion through mental np type analysis and here in lyes the problem and the solution.
lets say now my traveling sales man is immortal and sales to ten different houses in a town of 4500 houses every day.
he sells to ten different houses than the day before and he uses various differernt ways of calculating with different multiples of numbers representing 1 to 10000 to work out his journey every day each day homming in on a more optimal p type solution that works for all the routes he could take eventually considering the map never changes he finds eventually the optimal p type solution for all optimal routes given any possible 10 sales but realises some thing very significant. simply finding the p type solution was an np problem.
Is it possible to use a p type solution instead by which to find an np solution of course it is you could map every possiblity in a type of p form that ultimatly gives you the optimal travelling sales man solution for every 10 different sales would this be quicker than using an np solution every day it can be yes depending on how many days he does this but you need to work in np to work it out quick enough. what im talking about is a relatavistic paradox.
Whats the purpose of stating this paradox well because the p to np problem is a relatavistic paradox theres infinitley many ways to prove this.
The simplist proof being it required you np time in the first place to work out how to count from 1 to what ever in integers more np time to realise fractions and decimal places yet more np time to make good use of 0 and you've barely scratched the surface so does p = np yes it does because theres all possible solutions in p time but also no because you need np time to discover the right possibilities. so at the point of an able p working up too infinity to the power of infinity of complexity such a polynomial equation can solve all np problems from here to infinity but you need infinite np time just to understand the p logic required for such an polynomial time function.
why is this of any relavence actually its of major relevence.
this means as intelligence evolves it achieves ever closer to optimal solutions for all encountered complex problems.
In other words the pursute is required by which to find the solution but there is always a p time solution with the exception of problems involving infinite degres of complexity unless you are working with infinite complexity as you method of counting with p time. in other words the p to np problem is a paradox that converges at the point of infinite complexity.