^^ Well, as Asimov described in
Forward The Foundation, it uses complex mathematics (and futuristic computational power) that we don't have yet.
I love the entire
Foundation Series and the Robot Series and I love how he tied them together (and I also include
Nemesis in that Universe). The entire epic is about as classic as Science Fiction gets. Idea-driven stories, exotic alien worlds, galaxy-spanning empires. Yeah, baby.
As for Trevize's decision regarding Gaia (or, rather, Galaxia), he wasn't happy with it, either-- he was just doing what his Black Box was telling him. But, interestingly, just as he made his decision based on what he thought was an unwarranted assumption by Seldon, there were a couple of things he didn't know that would allow him reason to reverse his decision later; which he must have done, since the Encyclopedia Galactica indicates that the First Foundation ulimately triumphed.
As for the "Second Foundation Series" by the Killer Bs, that was an epic failure that even exceeded nuTrek in its wrongheadedness.