7 ms·

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

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... "5 - a split" https://www.youtube.com/watch?v=0ca4miMMaCE https://www.youtube.com/watch?v=0ca4miMMaCE Of course I'm assuming you're all playing the game in the same universe I am! In other words - the game USES 4 dimensions, but is PLAYED in 5D.

gibspaulding 6y ago
One could argue that traditional Chess still has 3 dimensions since knights wouldn't be able to "jump" in true 2-space.
- tomjakubowski 6y ago
  The knight is just a little more polite than the other pieces and so can readily scoot past them.
- tutfbhuf 6y ago
  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 https://en.m.wikipedia.org/wiki/Portable_Game_Notation
  - munk-a 6y ago
    Eeeh I'm not buying 1D - by the same logic all shapes can be stored in 1D by writing their descriptive formulae in a linear series of text.
    - tutfbhuf 6y ago
      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.
      - munk-a 6y ago
        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.
        tutfbhuf 6y ago
        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.
        munk-a 6y ago
        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.
    - grenoire 6y ago
      Everything was analog all along!
  - mypalmike 6y ago
    Slightly OT... Just a quick plug for my pvp chess bot https://twitter.com/chessbot2020 https://twitter.com/chessbot2020 on twitter which works using the related FEN notation (https://en.m.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Notation https://en.m.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Nota...).
  - Someone 6y ago
    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)
- danaur 6y ago
  You are assuming physical properties about the pieces like that they can collide which is invalid and not part of gameplay
  - xboxnolifes 6y ago
    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.
    - V-2 6y ago
      Depends on your definition. King and Rook sort of travel through eachother when castling.
      - c22 6y ago
        Technically the king jumps the rook.
        V-2 6y ago
        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...
        c22 6y ago
        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. [0] http://history.chess.free.fr/mediaeval-chess.htm http://history.chess.free.fr/mediaeval-chess.htm
RobRivera 6y ago
That simply distills the conversation into semantics
lmilcin 6y ago
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.
- Arnavion 6y ago
  Except that the game doesn't use three spatial dimensions.
  - lmilcin 6y ago
    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?
    - Arnavion 6y ago
      There's no "strictly speaking"s about it. https://news.ycombinator.com/item?id=24066521 https://news.ycombinator.com/item?id=24066521
      - lmilcin 6y ago
        If you really insist, I can correct myself and you, too. https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension "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. In general, if the state space of the game is finite or countably infinite (https://en.wikipedia.org/wiki/Countable_set https://en.wikipedia.org/wiki/Countable_set) the game IS 1D.
jml7c5 6y ago
While we typically think of a fourth dimension as time, that is just convention. One could easily say [x, time, z, y] and the math works out the same.

gibspaulding 6y ago

One could argue that traditional Chess still has 3 dimensions since knights wouldn't be able to "jump" in true 2-space.

tomjakubowski 6y ago
The knight is just a little more polite than the other pieces and so can readily scoot past them.
tutfbhuf 6y ago
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 https://en.m.wikipedia.org/wiki/Portable_Game_Notation
- munk-a 6y ago
  Eeeh I'm not buying 1D - by the same logic all shapes can be stored in 1D by writing their descriptive formulae in a linear series of text.
  - tutfbhuf 6y ago
    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.
    - munk-a 6y ago
      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.
      - tutfbhuf 6y ago
        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.
        munk-a 6y ago
        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.
  - grenoire 6y ago
    Everything was analog all along!
- mypalmike 6y ago
  Slightly OT... Just a quick plug for my pvp chess bot https://twitter.com/chessbot2020 https://twitter.com/chessbot2020 on twitter which works using the related FEN notation (https://en.m.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Notation https://en.m.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Nota...).
- Someone 6y ago
  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)
danaur 6y ago
You are assuming physical properties about the pieces like that they can collide which is invalid and not part of gameplay
- xboxnolifes 6y ago
  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.
  - V-2 6y ago
    Depends on your definition. King and Rook sort of travel through eachother when castling.
    - c22 6y ago
      Technically the king jumps the rook.
      - V-2 6y ago
        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...
        c22 6y ago
        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. [0] http://history.chess.free.fr/mediaeval-chess.htm http://history.chess.free.fr/mediaeval-chess.htm

RobRivera 6y ago

That simply distills the conversation into semantics

lmilcin 6y ago

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.

Arnavion 6y ago
Except that the game doesn't use three spatial dimensions.
- lmilcin 6y ago
  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?
  - Arnavion 6y ago
    There's no "strictly speaking"s about it. https://news.ycombinator.com/item?id=24066521 https://news.ycombinator.com/item?id=24066521
    - lmilcin 6y ago
      If you really insist, I can correct myself and you, too. https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension "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. In general, if the state space of the game is finite or countably infinite (https://en.wikipedia.org/wiki/Countable_set https://en.wikipedia.org/wiki/Countable_set) the game IS 1D.

jml7c5 6y ago

While we typically think of a fourth dimension as time, that is just convention. One could easily say [x, time, z, y] and the math works out the same.