Keeping that study in mind, let's assume there exists a deity who is infinitely intelligent. Would that deity appear to us infinitely stupid?
I think the problem would come from "the stupid" not being able to understand and thus reverting to "dumbing down" of said deity in their own minds...... not the deity's mind. So I guess it is yes and no....
If so, would we be under any obligation to worship that deity?
I think about half would feel obligated to worship it, out of lack of understanding and thus making the deity a God when perhaps it isn't. How would you look to a "caveman" if you went back in time with a lighter? Some probably would turn you into a fire-god for lack of understanding. But to answer, NO we would not be obligated to worship that deity just because it was more intelligent than humans.
Again, would it make any sense to follow any rules or directions that deity set out for us?
What would give it the right to set out rules and directions for us..... we are talking about something that is more intelligent, but not to say that it is our "parental guidance", creator, etc...... I guess some would follow out of the knowledge that it is more intelligent than us and probably therefore knows better than us.
Is there any way we could know that deity was infinitely smart, rather than infinitely stupid?[/
NO- because OUR "smarts" are limited......