5D chess game where pieces time travel

So I think you can tactically play football and chess equivalents in 1D, but the actual movements required to execute the game still require three dimensions and Chess remains a game that is pretty naturally aligned with the requirements of two dimensional space.

This is very pedantic at this point but I think the naive and natural assumptions about game dimensionality are probably the most correct to stick with. They can be argued up and down (absolutely no game can actually be played in less dimensions than we exist in since we only exist in so many dimensions - we might not need to exercise them to play the game but a chess piece, a computer or any existing encoding of data that we have today requires representation in 3 (or however many you think we have) dimensions - similarly pretty much everything (everything, I think?) can be described in data that can be expressed linearly so all games and the entire world can be said to be 1D. I think the fair middle ground is to try and adhere to the meaningful definition of dimensions in the middle that actually lets us classify things differently instead of saying that everything in existence is both 1D and multi-dimensional.

[0] http://history.chess.free.fr/mediaeval-chess.htm

You are disagreeing with the definition made by somebody else and yet you are defining dimensionality as you please.

I don't find it useful in the slightest.

When I want to describe your movement from point A to B I need to use coordinates that have four dimensions, 3 of space and 1 of time. From our point of view it is not possible to reduce those dimensions (ie. have less numbers that can unambiguously describe your position).

That is not the case of a chess game. In case of chess game you can not only have just one number to describe your position on board, but you can also have one number to describe entire state of the board or just one number to describe entire game, completely.

Number of dimensions is about irreducibility. Of course, you can describe your position on piece of paper with three dimensions. But does it mean that piece of paper is 3D? No, not really. It is embedded in 3D space but the position on the sheet of paper is only 2D. A sheet of paper is a surface where each point might have different 3D coordinates but you might reduce it to 2D when you notice that the coordinates are not really independent.

Chess pieces are 3D objects in real world but as somebody already mentioned, that does not make the game 3D. We say that because when we are talking about the game, we really only care about game states that are independent from physical representation (ie. physical board and pieces). Game played with people as pieces standing on painted tarmac is the same as game played on rendered pieces on computer.

When people refer to 3D Chess they might refer to the fact that this is rendered in 3D on a computer. When the author named his game 5D he might want to refer to two additional dimensions of time.

But when you really want to strictly refer to game state space it is really just 1D and that's what I surmised after saying "strictly speaking". It is not useful to talk to people who may lack math skills that the game is 1D, but this is "strictly speaking" correct description of dimensionality.

If you go into argument about dimensionality you must understand what kind of definition the other person has. If you want to disagree it does not make sense to do it by inventing your own definition.

I personally agree with the description 5D because it points out to the feature of the game (ie. concurrent timelines) which in normal world would be described as fifth dimension.