That Carl Sagan video keeps bouncing around in my head. Some thoughts though. What if there are barriers to bringing "beings" from different dimensions into dimensions above their own? For instance, a true flatlander has difficulty existing in a 3 dimenional context because in 3 dimensions we can't truly lack height. What if going into the fourth dimension would means needing some quality that we lack. We could find some sort of way to represent 3 dimensions, but it wouldn't quite be the same, or maybe you just inherently gain some qualities just by transitioning. What if you can only go so many levels beyond your own or you would simply distort the original thing to the point of breaking it?
Also, little square gained what seemed to it like uncanny ability when lifted out of it's dimension. For instance, it could see inside of it's fellow flatlanders, and their buildings. Not to mention it would have perceived the "familiar" aspects differently. They would be used to dealing with each other edge on, but from above you could see all the sides at once and see edges as outlines instead. How would you make sense of sensing some kind of "all at once" quality? And do things like reading minds or seeing things that you aren't supposed to be able to see, just represent tapping into some sense from a higher perspective as it were? Something that would be perfectly normal if you were looking down as it were onto the 3 dimensional world?
And what happens if you metaphorically throw several squares in the air. It's the blind men and the elephant. Everyone preceived an aspect but no one got the whole picture and by the sound of it everyone described a completely contradictory animal. Yet, they were all grasping in a limited way the aspects of the whole creature even if they lacked the ability to tell how much of the whole that piece constituted. If all the squares are thrown out of flatland into a much larger and more complex context, who knows what they might all take away from it. But all of it will sound crazy as the squares will have to simplify descriptions in terms of what exist in flatland which will make for issues in coming up with a description. It wasn't flatland they got thrown up into. Then imagine that over time, the story gets repeated, distorted, and some outright fabrications get thrown in, and you've got a real mess. But that didn't mean that the initial squares did not in fact try and explain as accurately as possible something for which they had poor points of reference, and perhaps they didn't have exposure long enough to be able to recognize what points of reference they could use. Maybe they didn't see a sphere long enough to recognize it as a more complex form of circle, so imagine trying to explain it while also looking around for a point of reference while missing the best point of reference.
Then, the other dimensions are probably not physical as we typically perceive it as in three dimensions, we have to approximate even the more simple dimensions to represent them in out own. So for all we know, trying make sense of that other dimension in terms of 3 dimensional physical point of references would be the equivalent of trying to make sense of a whole universe of Escher stairs without any nice doorways to hide the process of how someone went between two seemingly unrelated points. You'd just see it happen and your brain would spazz.