It's fun and was worth buying, but I'm pretty sure it's 4D. In the in game manual, it even says that there is an unused spacial dimension in the in-game rulebook.
First, you have the 2 dimensions that pieces can move in in regular chess. The third dimension is the fact that pieces can move back in time a certain amount of boards depending on the move, creating a different timeline. The fourth dimension is how pieces can move into different timelines using one their movement dimensions.
I think it's 5D because it just skips the "our" 3rd dimension. Just because Chess movements are in a 2D space, doesn't make the 3rd dimension temporal. You can move in 2 spatial dimensions and 1 temporal one (the 4th), but when you move through the temporal one you create a split in the 4th one...
You can even play chess without any physical or digital 2D or 3D board. Blindfold Chess is a thing. The chess board in my mind is 3D, but this may vary from person to person. Game position and moves can be stored in 1D, just text. https://en.m.wikipedia.org/wiki/Portable_Game_Notation
Well you cannot play football, because this requires physical activity. But I think, yes, for games that just require 1D information exchange and thought, that's all it needs. Any 2D, 3D, 4D representation of that 1D information is just optional e.g. for convenience reasons, because people like to move around physical 3D chess pieces instead of having to remember chess positions and playing blindfold.
I can precisely record football in one dimension - in fact some folks over at EA have been making a whole bunch of money simulating football using a linear data stream for quite a number of years. If you dislike the simulation then bear in mind that most people who "observe football" are observing a 1D data stream that's being read in to cause some photons to bounce around.
Saying that you can describe something in X dimensions doesn't make that thing an X dimensional object - or well it might depending on how you define dimensionality, but if you do it that way then everything is 1 dimensional.
I mean the difference is that I can actually play (not only observe) chess with just 1D representation of the game. Whereas football requires you to act physically in 3D space. But you are right, I would also consider "virtual football" e.g. simulated by a computer as 1D.
I disagree - you can play a game with the same rules as chess in 1D but you can't move your pawn forward on the board in 1D. Chess is a cerebral game so it's easier to abstract it down to entirely be about the will of the movements but those movements aren't committed (in a normal game of chess) until the pieces are actually moved.
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.
Hmm. okay I understand that you still disagree but I don't get your point.
> 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
I don't know what you mean by tactically. I never played football in 1D in my life and I think no one ever has, except if you are referring to a computer game or computer simulation. But I have played blindfold games without a chessboard and without a computer.
> but you can't move your pawn forward on the board in 1D
you don't need a board to play chess. A chess board be it in 2D representation on a computer screen or in 3D in real life is just a optional representation of the chess game, but you don't need it.
> a computer or any existing encoding of data that we have today requires representation in 3 (or however many you think we have)
I think we most likely have (according to theories that are mathematically sound) four non-compact dimension and seven that are curled up, so 11, but obviously there's no proof for that.
Nitpick: text isn’t typically 1D. You would have to use a Morse code font or something similar (and, nitpicking even deeper, use infinitely thin dots and dashes)
In some ways it is a part of gameplay, since knights are the only piece that can travel through other pieces. One one hand, you could just say that there are additional movement rules pertaining to either just knights or to all other pieces besides them. On the other you could also say that a chess board is actually only a 2-dimensional representation of the game state and that you actually play in a 1-dimensional plane with more advanced movement rules.
How do you know it's not vice versa? :) Both pieces move. And when you castle on a real board, you're supposed to move the King first, then the Rook, so it is indeed vice versa, the King doesn't have to "jump".
Besides, note I responded to a comment that stated "knights are the only piece that can travel through other pieces".
So if we already conceptualize Knights as "travelling through" rather than jumping over...
I know because castling developed from the King's Leap [0] which came about as the game evolved to faster more exciting play. By allowing the Queen and Bishops to move an arbitrary number of spaces various mechanisms were tried for protecting the King revolving around moving multiple spaces or jumping pieces. A common sequence became to move one's Rook adjacent to one's King, then using the next move to "jump" the King to safety. This eventually became formalized as modern castling and can be seen by noticing how the pieces move when castling kingside vs queenside.
It is 5D because of following progression:
3D = spatial dimensions (space)
4D = single timeline in space
5D = all possible timelines (3D of space plus 2D of time)
The game is 5D because you don't only move through time, you can go back and generate multiple timelines.
Well, strictly speaking, it has no dimensions as long as all possible states can be enumerated.
To give example, the board could just as well be arranged in a single line with more complex, but equivalent rules. Is it really 2D if it can easily be brought to 1D?
"In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it."
Since we can define an order and enumerate all possible gameplays (not just states -- all possible gameplays) from 1 to however many possible games there are, the game is only 1D.
Which means you can describe any game from start to end with a single number.
Your assumptions about dimensionality are completely incorrect. Just because something can move in different directions doesn't mean these are different dimensions.
Think about idealized ant moving on idealized string. Well, you could say it is only 1D because you can describe its position by giving the distance from selected origin. Now, even if you crumple the string into a ball, the ant might be able to travel in different directions in 3D space, but the movement is still 1D movement on the string that can be described with a single number -- distance from origin.
With regards to chess, you can reduce the game the same way. Let's start from easy to more complicated:
1. You can reduce the board to 1D (line all fields one after another, preserving their names, but giving them order that will let you describe position of a piece with a single number).
2. You can reduce entire game state to 1D. Since there is finite possible game states, you just need a function that will map the board to an integer, so that you can refer to all possible board states with an integer that uniquely identifies it.
3. Just as with #2, you can do the same with an entire gameplay. In this case a single integer can describe not just board state but entire course of the game from start to finish. The game is now 1D.
I think the difference is that, in the ant example, it would appear that the ant can teleport if you are looking at it from a 1D perspective, while in the 3D ball, the ant would be moving through space in a continuous fashion. Now since we know that ants cannot teleport, the 1D perspective does not align with reality. I think that's the distinction between being able to unroll certain movements from higher dimensions into lower dimensions. Now the question is, do we want to define chess movements as continuous or teleportation? If it is defined as teleportation from the beginning, then unrolling it into 1D would not change aspect of movement. But if we define it as continuous movements, then unrolling it into 1D would break that rule.
When we use dimensions we are not talking about actions but about state space. Action implies time and time is just one of the dimensions.
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.
Ah, then when you were referring to the ant example, you are assuming the constraint that the ant is moving only along the string. You did not specify that constraint in your original phrasing, and I imagined it as -- if the string was rolled into a ball, the ant can travel in any direction on the ball. This would cause it to appear to teleport if observed from a 1D point of view.
My question about dimensionality would be about the decomposition of the 2D coordinate of the chessboard into a 1D state space. First of all, all games with discrete positions would be 1D games, correct? Even the 5D chess game, since time and timelines can also be encoded into state space. This would also seem to apply to every computer game as well, since the state space can be taken to be the snapshot of any data at a certain time step in the computer. And finally, if we take that to the limit, as we approach infinitely small time steps, the state space would get infinitely less granular, and we could map any N-dimensional space into 1D. That doesn't seem right, where is the fallacy in this line of reasoning?
> "In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it."
> Since we can define an order and enumerate all possible gameplays (not just states -- all possible gameplays) from 1 to however many possible games there are, the game is only 1D.
This argument only makes sense if you stop reading the wikipedia page after the first sentence. The rest of the page talks about coordinates being properties that can change independently of other properties of the system, and other things that contradict what you're arguing.
E.g.:
> 1. You can reduce the board to 1D (line all fields one after another, preserving their names, but giving them order that will let you describe position of a piece with a single number).
A mapping like that would be a bijection of a chessboard, but would not be homeomorphic to one. That is, points that are adjacent in one mapping can be distant in the other, so there's no reason to assume they have the same dimensionality. (To the extent that a set of discrete points has dimensionality, anyway.)
Congratulations on having invented a definition that nobody finds useful. If you don't mind, the rest of us will continue treating the game as having four dimensions.
Maybe 5D is a joking one-up reference to a certain politician's supposed, metaphorical 4D abilities. (Or simply a desire to avoid 3D and 4D, which already have meanings.)
The playing higher-dimensional version of a board game idea predates that politician. TOS had 3D chess. And there are various memes about some character archetypes metaphorically engaging in similar games.
Is this an actual part of Hikaru no Go, or is it fan made? It doesn't seem to fit with the style of the story (although I've only seen the beginning few seasons of the animation).
yep, im pretty sure they're just calling it 3D because of playing on a physical chess board but we can obviously play it in 2D. if i was creating the game, i would've done the same because of all those jokes about playing chess in multiple dimensions
isn't regular chess already a 3D game? you have two spacial dimensions (rank and file) and then wouldn't the sequence of turns constitute a temporal dimension? maybe the turns are conventionally ignored (and not counted), since all games have them?
The way I think of it, the time dimension isn't relevant because you can make moves because of it. In regular chess, you don't need to keep track of a 3-dimensional game when playing, only the most recent 2D board (and sometimes the one before it for en passant). For that reason, I consider it 2D.
I get your point, but you also have to keep track of castling rights. If King or Rook have moved at any point (not necessarily on previous move), you can't castle even if they're in their starting position again.
I've enjoyed Alice Chess[1], which is played with two boards and on each move a piece on one board goes "through the looking glass" to wind up on the corresponding position on the other board.
Also fun was Suicide Chess[2], where the winner is the first to get all their own pieces captured.
About 20 years ago, I found a book in The Strand which had collected something like 300 chess variants... I'm sure by now there are many more.
Within 5d chess, there's a mode called "Timeline invasion". In this mode, there are 2x 5x5 boards. On one board, you have BRKBN and five pawns, and I only have five pawns. On the other board, I have BRKBN and five pawns and you only have five pawns. These two boards are parallel dimensions that then follow the rest of the rules.
This is a weird little game - regular checkmates are often not, because the king can just escape back in time or across timelines, but threatening a king's past self is pretty easy - it can't escape having been where it was. And you only need one checkmate to win, because you have to make a move on all boards where it's your turn (even if you have no pieces there - you have to move one there!).
You can also give check with a king, because of the quirk that only "the present" can threaten check. At least, I think that's why it works.
Quite an interesting puzzle game, but it's not all that similar to chess given the extra dimension. This means that a knight might move two spaces forward and one back in time: a lot of patterns you may be used to seeing & responding to in normal chess will need to be rethought or thrown out.
With that in mind it is a lot of fun to figure out new strategies and patterns!
The alpha go team is working with Chess grandmasters to determine which variations to the rules of chess result in a larger state space with more complexity.
They believe this will allow them to find a game that has more space for human creativity (since most games now are very constrained in the first 40 moves or so).
Would be cool to submit this game to see where it falls :)
The press kit section of the page says it has AI opponents. At first this didn't seem remarkable to me since it's a standard feature of most chess games.
But, how would that work? Would they have to create a new AI implementation? An off-the-shelf chess AI presumably doesn't understand the best strategies for multiverses. Unless there is some trick to apply an off-the-shelf AI to this.
Off the shelf techniques for zero sum games of perfect knowledge would work though. Minimax and Monte Carlo Tree Search and reinforcement learning from self-play. Leela has been adopted to play both go and chess, I suspect it would be practical to adopt it to play any game.
Doesn't chess AI just create a tree of all possible moves (up to a certain depth (limited by difficulty setting and computer resources)) and choose the best one. As long as the board mutation rules are well defined, it should be straightforward to create an AI.
In this context it is, it's defined as the bi-directional line between game state transitions, and can be measured quantitively like any other spatial dimension.
I'm talking specifically about time in the context of this game, which is what this thread is about, not time in the universe.
Those lines are an aspect of the dimensions of the board, not an addition to them. The measure of time does not make it a dimension (we can measure time in the universe too).
Adding another dimension to an n dimensional array -- [0,0,0] becoming [0,0,0,0], the extra zero is another dimension.
It doesn't matter what the numbers represent, x,y,z + time, or whatever - so we can describe the position of a particle using 4 numbers, x, y, z spatial co-ordinates and time. The same with this game of chess, board coordinates and time to describe the positions of the pieces.
Is that right? I've always read "dimension" used in this way in arxiv papers on math and comp sci, time is another dimension when it is used to describe internal state.
You read the papers correctly, bc those are abstract dimensions, neither time nor space nor precise facial features. Adding another element to an array is changing it's arity, as arguments to a function (which nobody confuses as a function's dimensions).
The chessboard case is an example of mixing disparate, concrete properties, and calling them all dimensions. But that is exactly the error in saying that time is the 4th dimension: mixing the concrete concept of dimension with the abstract one. Blame physicists, for they seem to really think time is our forth dimension, ergo fundamental, whereas time is an emergent property not of spatial dimensions alone, but motion in that space.
Here is an example of purely abstract dimensions. When the researchers at OpenAI want to add the position of words in a sentence, they literally add time, in form of co/sines, to the data. They don't "add" as-in append/concat another dimension to the data, the add as-in sum the existing data with the co/sines, changing the data. They literally merge time into the dimensions of the input. Before and after are temporal, for clocks and words in a string (ie their relative position gives meaningful relativity to the concepts the words represent, or we are lost), but really ALL time is a position WITHIN the dimensions, and the changing of time is the change of position. Ergo time is not additional dimension to the space.
We would not experience time if there was no motion, and objects moving faster experience faster time relative to a slow moving object, as Einstein proved.
> We would not experience time if there was no motion
> whereas time is an emergent property not of spatial dimensions alone, but motion in that space.
Is that proven true generally? I have often really wondered this myself, but Ive not had anyone to ask for a fundamental proof of this. I appreciate your thorough answers could you please explain or point me in the right direction?
I am using motion quite generally, to include the motion of particles, heat, etc. I don't know if the emergent property stuff is proven or discussed much, but I think the field is coming around to it, if for no other reason than they are running out of ideas.
Physics has been working in the top-down direction. That is not how you find emergent properties, it is an attempt to explain things from the properties they seem to possess.
For instance, the relatively gigantic boson is somehow "sub-atomic", to particle physicists. Whereas I think it that particles emerge from the breakdown of the bosonic field, and when we smash together the particles which reveal the boson, we are briefly seeing what happens when we have put them back together. See my comment here https://news.ycombinator.com/item?id=21039542
A very good primer on this is "Intensive Science and Virtual Philosophy" by Manuel DeLanda.
This is just the same as playing the computer and hitting "Undo" when you get screwed until you find where it all went wrong. Then you play that new timeline and can "Undo" again to create another timeline.
"Undo chess" is a single timeline that a (human) player can rewind to a previous board state. Movements in time are constrained to moving the board state. Pieces cannot move independently of the board state in time. Additionally, you still play all the timelines that have been created.
In 5D chess, the knight moves two spaces in one dimension and one space in another. In a 2d board, this is the description of how a knight moves. In 5d chess, a knight can move one space back in time and two spaces in the Y dimension on the board two one space back in time. That is fundamentally different than Undo chess.
Additionally, this puts a new knight on the board timeline that is forked off of the previous move - so there are now three knights.
Lastly, as pieces can move through time as well as space, one of the standard wins is a piece that is attacking the king in the past. I had a game where I moved the queen to the same file as the king (which was currently protected) - it was five spaces away. I moved another piece, and then won as the queen was now attacking the king five turns in the past. The timeline for that board is https://slack-files.com/T0VD96U9G-F01A45YRLTG-cf2d776bd3 . You can see that there is no piece at [T-1, Y+1], [T-2, Y+2], [T-3, Y+3], ... until the king at [T-5, Y+5].
