If particles snap to grid once you get down far enough, then there are a finite, though very large, number of ways you could configure atoms and stuff them into a limited amount of space. Which trivially implies that the maximum amount of intelligence you could fit into a finite amount of space is bounded.
And of course you could also update perfectly on every piece of evidence, simulate every possibility, etc.. in this hypothetical universe. This is the theoretical maximum bound on intelligence.
If our universe can be well approximated by a snap to grid universe, or really can be well approximated by any Turing machine at all, then your statements seem trivially true.
If particles snap to grid once you get down far enough, then there are a finite, though very large, number of ways you could configure atoms and stuff them into a limited amount of space.
It's called the Bekenstein bound and it doesn't require discreteness.
I was very interested in the discussions and opinions that grew out of the last time this was played, but find digging through 800+ comments for a new game to start on the same thread annoying. I also don't want this game ruined by a potential sock puppet (whom ever it may be). So here's a non-sockpuppetiered Irrationality Game, if there's still interest. If there isn't, downvote to oblivion!
The original rules:
Enjoy!