If P = NP because there's a O(N^{Graham's Number}) polynomial algorithm - a 'galactic algorithm' indeed - then the lay description is theoretically correct, but

If P = NP because there's a O(N^{Graham's Number}) polynomial algorithm - a 'galactic algorithm' indeed - then the lay description is theoretically correct, but meaningless in practice. In particular, the hand-waving is the phrase 'sufficiently many examples.' This may be impossible to provide even if only a googol (10^100) examples are needed, because of mass and energy limitations of the universe - there's only so much you can do with 10^80 atoms, and the speed of light is too slow. "Only a googol" because Graham's Number is mind-boggingly huge - https://en.wikipedia.org/wiki/Graham%27s_number https://en.wikipedia.org/wiki/Graham%27s_number The Wikipedia entry for "galactic algorithm" at https://en.wikipedia.org/wiki/Galactic_algorithm https://en.wikipedia.org/wiki/Galactic_algorithm even mentions SAT: "a hypothetical large but polynomial O(n^2^100) algorithm for the Boolean satisfiability problem, although unusable in practice, would settle the P versus NP problem". Algorithmica may therefore be very little different than our world, other than that people no longer debate if P = NP.