> This argument is useless since polynomial time is just as intractable as exponential time if the exponent is large. For example, lets say that we found a way

> This argument is useless since polynomial time is just as intractable as exponential time if the exponent is large. For example, lets say that we found a way to solve all np problems in n^1000 time, would that change anything? No, there aren't even 2^1000 atoms in the universe so we will only be able to solve it for the case n=1. That seems to be an argument for the uselessness of the distinction between P-with-large-exponent and not-P, not for the uselessness of having a reduction of NP to P. Also, it's worth noting that, if one is a theoretical computer scientist, then there is more of interest in the study of computing than what can be done in the universe. (I am a mathematician, and am, as I suspect most of my colleagues, serenely unconcerned with the applicability or non- of my work.)