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Another interpretation (this game's) is that pawns are supposed to move forwards as in towards the opponent's side, in this case either the opponent's side of the board or the opponent's side of the timelines.
and how that is refering to a movement forward, outside of the representation of those timeline on a cartesian display?
In other words, there's two sides to the multiverse : Your side, and your opponent's.
In addition, pawns move upwards, and your opponent's side of the multiverse is also up, meaning they move away from your side and towards your opponent's side.
beside so far from what I know the timelines are sorted as they are created instead of sorting them by how ancient they are.
and by ancient I mean the time in the past at which the start, not from which turn of gameplay they were made, that also is a shortsightedness imo.
It's allows to attack diagonally to the left despite the fact that on the X axis the pawn is moving backwards.
In 5D chess if the alternate timelines are on the Z axis and the past/future are on the W axis then we can say the pawn is moving "forward" on the Z axis and attacking diagonally either "forward" or "backward" on the W axis.
This is exactly the same as the pawn attacking diagonally forward/backward on the X axis while it moves forward on the Y.
so each player are on either side of the time and time is going left to right right?
that's just overlaying the spacial 2d into W and Z as you say intsead of thinking more conceptually about what is forward...
let's put it another way so if the dimension created by the other player are his side then what are the left and right side of the board? past and futur?
that's none sense...
if you make that parallele dimensions are left and right then futur being foward make more sense.
but let's explore another idea what if each players are actually fighting against the past since they actually travel in past to atteck their opponent, then the pawn could move forward only in the past.
when the player move in the past that's against their opponent and they are trying to protect the present/futur which is each player side.
The X axis is simply left-right and left-right changes based on whether you're white or black.
The Y axis is simply up-down and that also changes based on whether you're white or black.
The Z axis is towards and away. That changes based on whether you're white or black.
The W axis is forwards and backwards through time. That doesn't change regardless of who you are.
The only oddball is the W axis and the reason why it's an oddball is because everyone simply agrees that forward is objectively the next turn while backward is objectively the last turn.
That being said, for the other three axes, I think treating them as axes you can move forward and backward in is simple and intuitive.
P.S. It's fine to think of this as fundamentally wrong (your opinion is your opinion and it's not my place to tell you that you're wrong). However, do know that when you say "fundamentally" wrong, you're essentially disagreeing with the fundamental rules of 2D chess. 2D chess is fundamentally sided, 5D chess just extends the rules to include 2 additional axes.
That's why I argue that it is simple and intuitive the way it is; because it mirrors how pawns act in 2D chess.