I came across an old Carl Sagan explanation of higher dimensions that is incredibly simple...and slightly unsettling.

Imagine a creature that lives entirely on a two-dimensional sheet of paper. It understands length and width, but “up” doesn't exist in its universe. Now imagine pushing a 3D apple through that sheet of paper. The 2D creature wouldn't see an apple. It would see a tiny circle suddenly appear, grow larger, shrink again and then disappear. From its perspective, something seemingly appeared from nowhere and vanished into nowhere. But nothing supernatural happened. The creature simply couldn't perceive the dimension the apple was moving through.

Now move the thought experiment up one level. We're the flatlanders. If a four-dimensional object intersected our three-dimensional world, theoretically we wouldn't perceive the whole thing either. We'd perceive whatever 3D cross-section happened to intersect our space and just as you could reach “over” the walls of a 2D enclosure without crossing them, a hypothetical higher-dimensional being could potentially access the interior of a closed 3D space through a direction we can't perceive.

That's where this gets weird. Something could seemingly appear inside a locked room without passing through the walls. Something could disappear without traveling anywhere we could observe. Something could potentially interact with the inside of a 3D object without crossing its surface. Not because physics was violated, but because our perception of the event was incomplete.

None of this proves higher-dimensional beings exist, much less explains ghosts, UFOs or anything supernatural. It's simply geometry. But Sagan's analogy raises a fascinating question, if something existed beyond the dimensions humans can perceive, would we even be capable of recognizing what we were looking at?