It looks amazing, and I really want to play it, but however I count I only end up with 4 dimensions. A chess board is 2D, time back-and-forth is 3D, and going up/down across universes is 4D. What's the 5th? Are they counting real-life-time as the 5th? In which case normal chess is 3D, which seems like an abuse of terms.
You are correct that the game is 4D. Every piece's coordinates are made up of four numbers - x, y, turn number, and timeline number. Depending on the piece, it can manipulate one or more of these numbers to go up or down. [1]
However, I would say that real chess is sort of "2.5" D by this definition rather than full 3D, since the turn number coordinate of every piece can only go up, not down.
[1]: The game's formalism is slightly complicated by the fact that a piece could make a move of (x, y, t, L) -> (x, y, t - 1, L) which would count as moving one square in one dimension, but then the game's "system" automatically transforms that move into a (x, y, t - 1, L +/- N) move. (The choice of +/- depends on which player made the move. The value of N depends on how many other timelines there are at that t.) This happens because of the rule that the past cannot be changed, so altering the past requires branching the timeline.
Similar things also happen with a move of (x, y, t, L) -> (x, y, t, L2), because within a single turn there is a concept of whether the board has already had a move played on it or not. So if the board at L2 has already had a move played on it, this new move is instead transformed into (x, y, t, L3). So it counts as a move of (L2 - T) squares for the purpose of validity, but is actually a move of (L3 - T) squares.
I think you're right. Even if we classify classical Chess as 3D (2D board + a time axis for game states), time travel re-uses that same time dimension.
If you wanted to shift the complexity into ludicrous speed (this is inspired by archgoon's comment [0]), you could introduce another dimension by putting a classical chess board inside each square of the 4D board. The 4D move only succeeds if you win the game on the mini-board. Just, please, don't bring recursion into this, unless you're captain Kirk and absolutely need to nerd-snipe a rogue AI. (“They've gone to plaid!”)
There's another possibility I've hinted at by calling standard Chess ‘classical’. On second thought, let’s not go to Quantum Chess. 'Tis a silly place. (I tried to imagine what a Schrödinger's king would look like. I've seen things you people wouldn't believe. Queens checked en passant from the future. I watched knigths glitter in the parallel time-line near the Hadamard Gate. All those moments will be lost in time, like tears in rain. Time to resign.)
It's only 4D. I believe they called it 5D chess because they didn't want people to interpret this as 3D chess + time. If I recall correctly, the tutorial mentions at some point that the 5th dimension is "unused".
5. The timeline of how the game actually evolves, building out the tree. This is a bit of a stretch, since you can't move pieces through it in the same way as the other four.
It would have been nice if 4D only ever meant four spatial dimensions, and then we'd have (3+1)D for three spatial dimensions and a time dimension. (And (2+2)D for two spatial and two time dimensions :-))
I count it thusly: Ordinary chess is 2D. Adding in the ability to bifurcate the timeline and play distinct possibilities in parallel is 3D since it is a distinct degree of freedom. Adding in the ability to go back and forth along a timeline is 4D. Adding in the ability to also jump back and forth to ANY timeline (sideways rather than strictly back and forth) requires a fifth degree of freedom. So it's 5D as far as I'm concerned.
Hmm, I think I see what you're saying, but in my opinion the way that one bifurcates the timeline is by traveling back and forth in time, which is already counted, and moving back and forth among bifurcated dimensions is already counted as well, so there's not extra dimension there.
For instance, if you have a stick you can push back and forth in a groove and count that as one dimension, if you push hard enough against an obstacle the stick might break and rotate out into the plane, but that's still only two degrees of freedom.
If the chess board is 2d, how does the Knight move, doesn't it need the third dimension to go "over" other pieces? I assume, graphics notwithstanding, the board is logically represented in 3 dimensions.
I can't tell if this is sarcasm, but anyways: obviously an actual chessboard is indeed 3d - as are all physical objects in our world. Yet a chessboard is effectively a 2d space: any piece position is completely defined by a row and a column.
It's true that at the beginning and end of each move, every piece has a specific coordinate in a 2D space, but it is still nice to imagine that knights' moves (and castling) involve travelling through a third spatial dimension. And yes, the pieces themselves are conventionally thought of as volumes in 3D space rather than areas of a 2D plane.
Yes, but to maintain the conceit of chess being like a battlefield, it is nicer to think of knight pieces as being jumping cavalry (however unrealistic that is) rather than ghosts or owning a portal gun.
I suppose the actually intended analogy is that by riding a horse, the character is more evasive and can slip past another unit without being blocked. Also, I suppose that rooks must have wheels on, and a door that a king can only walk through in rare circumstances.
There's a similar discussion upthread where someone points out this is a matter of representation -- you could "unwind" the chess board into 1d just as easily.
I interpreted the description as normal chess board = 2 dimensions. time = third dimension. moving on the x axis in the multiverse as 4th dimension and moving on the y axis in the multiverse as 5th dimension. So yes, in this wacky world a standard game of chess in progress is 3D.
