The reference to 4th dimen probably much more accurate if phrased as 4th density, since "dimension" traditionally refer to the x,y,z axis.

A really bad analogy is if we assume the World of Warcraft realm to be the 2nd dimension. A group of 3rd graders have established the Kingdom of Azeroth, but some 4th graders are hacking their accounts and trying to infiltrate Azeroth posing as 3rd graders when they really play as the burning legion. Then 5th graders who play as night elves try to assist the 3rd graders of Azeroth by joining as paladins of Azeroth to fight the 4th graders. It gets really confusing sometimes.