This is another rant about the author's bugaboo.

It would be great to prove that there is or isn't a non-galactic polynomial-time algorithm for NP-complete problems. But we can't even solve the easier problem of proving there is or isn't a galactic polynomial-time algorithm, so what hope is there for the harder problem?

If you could prove that any polynomial-time algorithm for NP problems had to be galactic, you would be the most celebrated computer scientist since Turing. It's just no one has any idea how to do that.