Some time ago I came up with this “to ambitious for your own good” prop that could be used in essentially any setting. It could be an ancient artifact, weird piece of mysterious alien technology, magical arcana, mystical object and etc. Essentially it’s a toy you can safely lock away along with all the other game master/dungeon master/storyteller notes that you will never, ever get to use in any game session, or story.
Here is the idea – imagine a Rubik’s Cube like puzzle with a nasty twist. You can twist it, rotate it, and change the positon of the faces in some way. To solve it you must align them in some sort of a pattern. It’s important to make the pattern clear, and easy to grasp – such as for example the original Rubik’s cube goal – to make each face a solid color. Solving the puzzle will unlock something. Maybe there is a hidden message inside? Perhaps it triggers some bound spell or activates the artifact in some way. Or maybe the process of solving it teachers you the correct thinking you will need in order to understand some other, more powerful artifact.
Here is the twist: the puzzle is unsolvable. The “faces” are not well defined, and there is just no possible way to arrange the moving pieces in a way that that would produce the desired pattern. A smart character with a good grasp of math or science can figure this out mathematically – either on paper, or perhaps build a computer simulation. The pattern just can’t be produced. There is just no way to do it.
And yet, there is evidence that it was solved in the past. No notes on how it was achieved survived, but someone before did unlock the great mystery it hides, and lived to tell about it. You can find vague, cryptic hints, but no complete solution.
Why is that? Why can’t anyone solve it? Because the object you see is not the puzzle itself. It is just a 3 dimensional projection (ie. a “shadow”) of a 4 dimensional object. If you need a visual, it would be something like this:
This is actually a picture of a real sculpture at Penn State designed by a math professor to illustrate representation of 4d object in 3d. If you are unfamiliar with this, let me explain.
Consider a map of the world. It is a representation of the 3 dimensional globe, in 2 dimensions. Each location on earth can be found on the map, but their relative position in space is change, and altered. Now imagine a randomly generated state of Rubik’s Cube projected onto paper this way. The rules for rotating the faces are still the same, so when you move one piece, the whole picture shifts around in a weird way. In this representation, solving the puzzle is still possible? If you “unroll” the cube into the familiar cross like shape made out of squares, then yes. You can identify the faces and figure out how to manipulate it. But what if the cube is unrolled in a different way – for example, starting at a corner, and slicing it into triangular shapes? Can you still solve it then without knowing that in the 4D shape, a face is really a square, and not a triangle?
This is exactly what we are dealing with with our puzzle. It can’t be solved unless you recognize that it is merely a projection of the 4d object, reconstruct the object, and re-evaluate the goal. Of course we tend to think in 3 dimensions, and can’t really imagine 4d objects. But, we could mathematically figure out what would be the shape of a face, or segment, or component of our puzzle and what would be it’s relation to other pieces. Furthermore we can directly map it onto our “shadow”.
So there it is – that’s the concept. It’s ridiculously complex to even explain, few people will get it, and there is just no way to role-play solving the puzzle in a meaningful way. The only thing that the players could solve is the dimensionality issue, but I’m not sure how would introduce the problem in a way that would hint at it without giving it away. So I gave up on introducing it in a game. But I still think it is an interesting idea. If you want to use it, it’s under CC, Attribution, Non-Comercial, Share Alike, 3.0.
[tags]4 dimensions, 3 dimensions, rubik’s cube, 4 dimensional rubik’s cube, rpg, role playing, penn state[/tags]