How many dimensions are there in 5D Chess?
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- Опубліковано 5 вер 2024
- Because my original video on 5D Chess With Multiverse Time Travel proved so popular, I thought I'd make a follow-up asking and attempting to answer this contentious question.
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Original video: • 5D Chess With Multiver...
Jurassic Rook: • I Am Four Parallel Uni...
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Knife Skills
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Corrections (yes, I'm annoyed to have found errors already):
4:40 - 'Linear dependence means...' should read 'Linear independence means...' These are in fact opposites of one another.
When playing 5d chess do you ever use the history View or the parallel view. They both imply that the game is played on a 2d board in a 3d space thus making time the 4th dimension and the timeliness the 5th. Therefore there is a Z in this game in addition to an X,Y.
watched all your 5D chess videos... pretty good... wondering if all this nose bleeding is drain bamage...
#IStandWithMadVulcan
If you don’t think that the 5th dimension is multiple timelines at least state your reason cause it is theoretically and mathematically on point
From our current understanding, the 5th dimension allows us to treat both time and different timelines as if they were space so we could just traverse through them
But I ask you why don’t you think the 5th dimension is different timelines?
@@J11_boohoo state all 5 dimensions you think there are, it's easier to debunk this way
Maybe the 5th dimension was the friends we made along the way
B... baka~
Yes and the 4th was where a guy with a gun had to escapenor have a heart attack
W.....wh-w-w-which way?
I'm making a 45 dimensional platformer. The 43 extra dimensions are there, just unused.
That would be very impressive, given you’d still need to find a way to integrate those remaining 43 dimensions into the view. 5D chess calls itself 5D because the unused dimension can still be used for ease of viewing the board. Even if the game is 4D the 5th dimension still exists within the game’s graphics.
If you consider one multiverse with time travel and dimension-hopping and all that jazz as one single unit and have a copy of the unit be one "supertime" ahead with "supermultiverses" besides the single unit of multiverse, would that count as adding another 2 dimensions: supertime and supermultiverse?
@@Vearru that wouldn’t be as hard as u spect, by using matrices and some clever programming u can create a shadow of a n-dimension object in a 2D screen .
@@narudavidkun that would actually be very cool, I’d love to see such a platformer.
@@Vearru That is a nice thing to try it, if I have time I will do it and show the results to u =)
It's good there's someone out here spreading the word, don't let this game fall victim to the flat chess society.
I would argue that the dimension in which the boards turn and rotate to visualize how the time and multiverse vectors travel is the "unused extra spatial dimension."
That's still just a representation of two spatial dimensions in three. A square viewed from an angle on the Z-axis is still a two dimensional shape.
@@emuspy6761 yea, but 5 distinct dimensions still exists in the video game. 4 from the chess game, and 3 for visualization (x and y axis used for both)
This is the truest of true answers.
Ok, but consider: 5D Diplomacy: The Game of Knife with Multiverse Time Travel
For when you want to create a time travel franchise spanning uncountable timelines, each encapsulating a lifetime, that you and your friends can only finish by agreement to declare it finished.
(Also it answers the main strategic weakness of time travel in 5D Chess by creating more units each turn)
This game is called Achron, it's on steam since 2011.
You called it.
Ah, so this is the origin of the mind-shattering amalgam he posted recently.
U did it
The knight doesn’t jump, it merely teleports
Nah it jumps through the third, unplayable dimension. Jumping looks like teleporting if you view it without the dimension you're jumping into. If you look at a normal chess board as 2d only, the knight appears to teleport when infact it jumps in the third, unplayable dimension.
I would like to go with the fact that knights are actually just neutrinos
Or: Chess pieces are pointlike. The knight can move through the gaps in the pieces with their off-diagonal movement, but the other pieces, bound to 45° increments collide with each other.
But is it really the same knight? Maybe the old knight dies and a new one is born in the new location.
"...best left to philosiphers... sooo..."
**uses imaginary number** I fucking loved that.
any phylosopher that says imaginary numbers are less "existent" than real number will be extensively bullied by me.
You mean you sqrt(-1) loved that. ;-)
my favourite joke from this video
I wonder if the unused spacial dimension is because the game was originally planned to have a 3D camera, but it was decided that was too confusing
I'm not even sure what this channel is (music channel with some random reviews of stuff?) but it looks fun and interesting, so here i am, subscribed and all
I'm not entirely sure myself these days. It used to just be music but I've been branching into video editing lately, which seems popular. I've also been struggling to make music over this same period for a number of reasons, so that's a factor.
Overall I guess it's just whatever I happen to make, whether that be my own original work (music, videos) or something related to things I like (specific games, films, etc.). Hopefully people subscribe because they like one of those categories, and I fully expect most of them not to care about any others. That's fine, I just hope I can continue to provide things at least some people enjoy and I have fun making.
Apologies for the sudden ramble, this comment made me a bit introspective.
@@OliverLugg Well, i'm glad to see you plan on doing more reviews/essays, the 5d chess video is really fun and well edited, so it's nice to see you'll be doing more! As for the music, it's also great! I guess the important thing is to have fun, whatever you decide to do or people decide to like, and the quality will follow. Oh, and don't worry about the rambling, is cool to put a comment on a video and have the creator answer, especially so extensively, so thanks!
That 2+i in the "me vs comments" thing killed me xD.
Also I said I was going to sleep early today but I'm here at 3 am learning about 5d chess
*4d
Everything else aside can I just say that "The bottom half of the internet" is possibly one of the best phrases I've ever heard.
I also figured it kinda only has 4 dimensions that are being used. I think the most plausible explanation is that real time is the 5th dimension, because you can move pieces asynchronously in the in-game future, present and past. As you said, this would imply that regular chess is 3d as well. On the other hand we often don't count time as a dimension when we talk about things in the real world. So I think regular chess can be called 3d chess and the game can be called 5d chess.
This comment was way simpler at explaining what I was trying to say than my comment. I completely agree with this explanation
My body is ready for that FTL video.
In regards to the progression of time being a different dimension, one difference between 5d chess and other linear progression time games is that in 5d chess moves can be made that change the present.
Well to be fair, you don’t change the past, you create an alternative past, and then change it.
the thumbnail's text, "5? 4? 6??" reflects that the choice of either 5 or 4 is a mistake and 6 is an absolute blunder.
Technically speaking you can play chess in 1D by just writing moves down.
Example: 1. e4 e5, 2. Bc4 Nc6, 3. Qh5 Nf6 4. Qxf7#
That would imply that information is 1 dimensional.
@@La4geas It is one long string of characters. Navigating that string you can only go forwards and backwards thus 1 Dimensional.
@@MegaAgamon Navigating a single string of characters is not really "playing chess", it's looking back at a game that has already been played. And yea, your influence in that is purely 1D. However actually playing a game means creating new moves. Each move has multiple linearily independant pieces, it's an implied 2D vector. So no, that's not really 1D. You're taking higher dimensional moves and ordering them along a single dimension when creating the string but that doesn't remove the other dimensions.
@@lunkel8108 except a computer plays chess by navigating a long string of characters. Also that is how blind people play chess. By saying the moves out loud
@@MegaAgamon Again, each block is an implied 2D vector so the creation of a new move is a 2D task. That's like saying that 3D space is actually 1D because you can represent movement through it as a string of 3D vectors. Yea you can but you're still dealing with 3 (4 if you include time) independant variables.
Alright, I'm putting this to rest with the fact that it is in fact 5d, IF you are willing to accept that normal chess is actually 3d, it can help if we think about it in terms of coordinates, when describing a typical chess game in full detail, you could just say "pawn on e, 4" which is two coordinates, up and down, but that's not fully descriptive, what you actually need is to also describe what turn it's on, "pawn on e, 4, on turn 3" which would be 3 coordinates, up, down, and turn, so 3 dimensions, 2 spatial and 1 temporal. In 5d chess you would do a similar description "pawn on e, 4, T3, +1L, global turn 6", this is then 5 coordinates, those being: up, down, local turn, parallel universe, global game turn, therefore being 5 dimensions of the game.
Guy.
I have seen this "documentary videos"of yours.
And man, i am amazed.
Please, keep doing it, also, good music.
You have a great guion, great edition and great and acid sense of humor.
This is pure gold in internet
The game engine appears to represent the "unused" 3rd dimension. The animations, tooltips, arrows, etc. are representative of a world not fully known by the pieces.
The unused dimension is simply *interaction.*
Well the game is rendered in 3D, so that is also a possibility for the "unused" 5th dimension is just depth.
@@TinyDeskEngineer yeah but the 3rd dimension has no bearing on gameplay. It's like saying the original super mario bros is a 3d game because there are background elements. Or that enter the gungeon is a 3d game because it's rendered in 3d, even though the 3rd dimension has no bearing on the game.
i'm perfectly happy with saying that regular chess is 3d and 5d chess is 5d. the reason we usually don't is the same reason we say we live in a 3d space, when we really live in a 4d spacetime. we just kinda ignore time most of the time. but that doesn't mean it isn't a real part of the game/universe.
The game is 4D. 5D is simply used to avoid confusion because if it were called 4D chess, many would assume it's 3D with the added time dimension. It is 4 dimensions because we have 4 axes: X, Y, time, and multiverse. And yes, time is technically a factor in every game, but we don't express it because it's not a mechanic of those games, just a circumstance. This is similar to how we play normal (2D) chess in 3 dimensions despite the 3rd dimension not actually being relevant to the game or its rules.
I however think that in 2 D chess, time it is relevant to the rules, thats why there is a mechanic that prevents the future (such as Check), so it is accounting thay this game is played over time, and not on an instant, as Conway "Life" game is.
@@thelyghter7927 Every game is played in the space of time, as is every 2D game played in 3D space. In my opinion what makes a game 4 dimensional is the manipulation of time in the moves of the game, such as the time travel shown here.
Just imagine the nightmare of if it was truly 5d (3D chess with the time travel shit)
what kind of piece would have to be invented to move on a quintagonal?
Donovan Mahan I don't know and don't think I want to
@@donovanmahan2901 phoenix
@@donovanmahan2901 wyrm
@@donovanmahan2901 why do you think there WILL be new pieces? Doesn't 3d chess just use the regular pieces on 8 stacked regular boards?
The fifth D is actually the level of abstraction of the meta content around the game. A video discussing the video about the game is a movement of 2 in the fifth dimension
There's a second time dimension, that we use to observe the game independent of the game's internal time that allows time travel.
✨Game Vs. Universe✨
*the youtube algorithm works in mysterious ways*
Still less complicated than 5D chess
did not expect an indestructible pawn cube reference, thank you
The 5th demmention is the options menu you can move in the x y multiverse and time demention but when someone does a Jurassic Rook you forfeit the game and when you do this move you directly affect the board (you losing) so when you use this move you are moving in a dimension other then the 4 states requiring the forfeit button to be the 5th dimension
What?
@@guyinacage yes
What if you expressed the each piece type (king, queen, rook, bishop, knight, pawn) as value along an additional dimension? By this logic, we can consider promoting a pawn (which can become any other piece besides a king) as a transformation along that "piece" dimension. This would also make regular chess three dimensional.
Here's a question: when I plot out the typical y = x² on an x y plane, is that 1D or 2D? Well, it really depends on precisely what you mean. Most relevant to this, I think, it is 1D, because x and y are *not* independent. You really only get to chose a value for x, then the y value is forced. It's a 1D scalar field, represented in a 2D space. Also, you might have some predicate P : (R, R) -> Bool, where P(x, y) = y == x^2 (in English, P(x, y) is true if y is the square of x, and false otherwise) which you could plot in a 3D space, although it would be a 2D scalar field that is 0 (or false) everywhere, except for a parabolic wall that's 1 tall. Having written that, I'm now trying to justify why it's relevant. It is more similar to what you're saying. Assign those pieces integer IDs so that we may visualize it easily, then we may represent the state of a board S : [0, 8)^2 -> IDEnum, where [0, 8) = { 0, 1, ..., 7 }, and IDEnum is all our assigned IDs, perhaps White Pawn: 1, White Rook: 2, ... Nothing: 0, Black Pawn: -1, Black Rook: -2 ... what we have then is a 2D scalar field, which we can again represent in a 3D space.
@@MCLooyversewoah that's actually interesting
That pawn cube comment is gold, I died when you showed it.
To add a bit. I think we should note that the rule set of chess in the abstract regardless of if we just include single state or “full history of moves” or “full set of timelines of moves” is a 0-dimensional discrete graph. However, this graph have notions of direction, some of which are similar and some of which are slightly different. But all the other issues of contention are a matter of embedding.
If we just consider game states of regular chess for a second, that graph can be embedded in a plane like in computer chess or in 3D as with a regular old chess board (or computer chess with 3D pieces, don’t get me started on projections).
The graph has directions, though they are not dimensions in the sense of a vector space. But it makes very much sense to talk about the board as being a bounded 2D region. And move sequence makes very much sense as a bounded interval. Obviously the state space must take into account of all possible piece states and may not even have a well defined dimensionality.m so I won’t bother.
The multiverse stuff doesn’t really make sense as a dimension either. The neighborhood simply doesn’t look the same everywhere. The multiverse history is more like a branching tree. But since the game state and single time line sequence parts are discrete we can kind of just lay it all out next to each other. But imagine the move sequences was a continuum. The you wouldn’t be able to enumerate branches and you’d might need an arbitrary number of dimensions to embed it. You just can’t get away with saying multiverse is a dimension. There is probably some infinite dimensional embedding. But even so that doesn’t make the actual state infinite dimensional. The game actually would have different number of dimensions depending on which neighborhood of it we consider.
With all these complications, I prefer to stick to 0-dimensional.
A pawn cube is completely possible in 5d chess. You can even have a pawn tesseract
No; just because a game is played on a 2D screen does NOT mean it is actually 2D. It is just a representation of a higher dimensional game.
Yeah, by that logic mario 64, for example, would be a 2d game.
But the representation is the reality, the hologram it projects from is imaginary.
@@edomeindertsma6669 and then every game is a 2d game, but because that classification is useless, we use the dimension of what we represent which is what we talk about
@@Odisher7 According to current string theories the universe has at least 10 dimensions, however we still perceive it has having 3 (or 4 at a stretch). However according to the Holographic principle, it could be true "that volume itself is illusory and the universe is really a hologram"², meaning that the universe has less dimensions, possible 3 space-time ones.
2 en.wikipedia.org/wiki/Holographic_principle
1D: Up and Down (or the other way around).
2D: Up, Down, Left and Right.
3D: X, Y, Z axis
4D: X, Y, Z axis + Constant 1 (Future gets overwritten).
5D: 4D meets grandfather multivere constant. (Future is in divisibility rules)
6D: 5D meets present multiverse hopping.
If it does help then your welcome.
You're playing a 4 dimensional game, but you're looking at it from the 5th dimension.
We can always use the argument that possibly everything you experience including logic is a still-going coincidence of nonsense and random static-like fluctuations of some pseudo-existence or something
though personally I believe logic is completely and independently immutable from any such construct
I think that its probably more convenient to consider the way we actually *move* pieces in a game. On a regular chess board, all possible moves are expressed as a 2D vector in space. However, the board changes from move to move, implying a third dimension of time. If you abstractly think about a chess game and not just possible movements from a given board state, then it is 3D (2+1 dimensional).
In the 5D chess game, the original time axis can be traversed like a spatial dimension. Multiverse adds a clear fourth spatial dimension, and the board state evolves in a time axis orthogonal to the other 4 dimensions.
So if we define the dimension of the game as how many spatial dimensions it has, youre right that 5D chess actually just has 4D. But I posit that moving through the original time axis makes movement through that axis behave more like a spatial dimension, and our experience of the game is from the next dimension up, a second "super-time" dimension we dont time travel in which is distinguished from the original time axis that we do.
Thus, i suggest that movement in this game takes place over 3 space-like dimensions and one time-like dimension plus one more time-like dimension we experience the board state in.
To summarize, the game can be expressed as 4+1 dimensional (if you think of the original time dimension as a pure spatial dimension) or, more informatively as 3+2 dimensional. That is, three spatial dimensions (x,y,multiverse) and two time dimensions (traditional time and "super time").
The reason i think 3+2 dimensional is more informative is because this expression is more generalizable to N+M dimensional chess. We would imagine a 3+1 dimensional chess game as, for example, moving chess pieces around a cube (3D) along normal time rules (1D in time). Additionally, we could consider 2+2 dimensional chess where the board occupies the normal 2D space but time travel is allowed *without spawning multiverses*.
Actually it's "5th" Dimensional chess, because 4D would make everyone think it has rumble, smells and shoots water at you, and this dimension is new and different to that.
Although it could also just be called "Chess with multiverse timetravel", because chess implies 2 dimensions, and so does multiverse timetravel, so no reason to put the dimensions in the title.
I would argue that in virtually every description of the rules of chess, the Knight is described as "Jumping Over" other pieces. It's not moving through or having other pieces get out of its way. Canonically in the Chess Lore, Knights have a unique passive ability to jump over any piece that would otherwise block its movement. So even though you can describe its velocity with 2 dimensions, as it must always land back on the board, its movement necessitates that it must be able to move through another dimension in order to bypass one of the other rules which is that pieces normally block each other's movement.
Thus in a game where there are 4 movement dimensions, and the knight is still able to jump over any other piece no matter what direction it is moving, and even if every single space in between its starting and ending position is occupied by another piece, it is still able to reach its destination, then it must be moving through the third spatial dimension, (or whatever other dimension of choice I guess) in order to reach its destination. Thus creating 5D chess.
The real question is what the fuck is happening when you Castle.
While the game rules use 4D movement over 2 spatial dimensions and 2 temporal dimensions, the 3rd spatial dimension is actually used by the game's interface, similarly to playing 2D chess on a 3D board. Specifically, the camera rotates 3-dimensionally when switching to history/parallell view.
I guess so but the game mechanic is independent of it's visual representation. you can play chess in 3d space, or blind chess simply with the 2d coordinates, they're both 2d games.
if you believe knights do not require the third spatial dimension to travel over other pieces, then you must accept they are able to pass through pieces. now, spacial dimensions are ultimately unneeded.
You could play 2D chess on a line of 8 cells if you put colored hats on the pieces to represent what row they are on. All the pieces in a column would be existing in the same location. You could even condense the entire board into a single cell if you have those colored hats also have different types to represent what column. Sombreros for column 1, fedoras for 2.
Ultimately, dimensions are just a visual representation of these kinds of arrays, and theres certainly more than two when it comes to normal chess. On the 2D chess board, the different shapes of the pieces are ultimately a representation of a dimension just as the colored hats. You could absolutely represent the dimension of piece type as a third spatial dimension.
You may now say "no, that doesn't count because there's no movement between levels!" but you would be wrong. Pawn promotion is exactly that.
One could even conceive of a chess variant where pieces are able to move through this third dimension freely. A rook would be able to travel orthogonally in any direction, meaning it would be able to transform into any piece. Pawns would be able to promote to a knight on the spot, or even to a bishop if they're on the second rank (but be weary of third dimensional en passant). Queens would be able to move in any orthogonal direction and move the corresponding piece levels.
There would also be a lot of strategy with kings. There would need to be a rule that you must have a king on the board at all times, but theres no reason why you cant create a second king somewhere and then remove your original king in order to evade a potential checkmate.
Anyway, yeah. The game is 5 dimensional, not 4 dimensional.
I think what you meant to express with that first section is that spatial dimensions are only one visual representation of mathematical dimensions (which you may concretely think of as arrays).
But yea, I completely agree that piece promotion is an extra dimensional move, very good point.
try using this argument to say mario is a 3d game and no one will take you seriously
Shoutout to Eric Rosen for his creation of pawn cubes. Thus proving chess is indeed played in three dimensions.
Having just heard of pawn cubes, how do they prove chess is in 3D? Really cube seems like a misnomer and it's really a pawn square.
@@eduardog3000 Just a joke. Chess players know better.
Knights are the only pieces that have access to a "hyperspace" and that is what allows them to jump over other pieces. This also explains why the rest of the pieces cannot jump over the other pieces. I think it could make sense mathematically (disclaimer my multivar calculus is rusty). If you defined the rules of chess in a computer for example, you would need an extra variable to tell when a piece can jump over other pieces, and that extra variable could be represented by a third dimension in regular chess and fifth in 5D Chess with Mutliverse Time Travel.
Just submitted across your channel not so long ago. So professional. I didn't even realize I don't normally watch your videos. Well done. Laughed for a while here.
Does that mean regular chess is actually 3D, with 2 spatial and one temporal (number of moves) dimension?
Parmon : is 3D chess, it can use similar mechanics to utilise all 5 dimensions.
in order to increase dimensions in sets of 3 just keep adding 3 spatial dimensions.
adding multiple simultaneous time and probability dimensions is possible but requires more powerful tools ( software, hardware || Turing , quantum trans Turing ).
huh
Here is another game that you might love - Achron. It is RTS about time travel and from 2009. A true hidden time travel gem.
The third spacial dimension is used in other views of the board that rotate the boards into the third dimension. But that is just for viewing, not a game mechanic.
Here's a simpler explanation for the argument that forward and backward in the multiverse/time is that for the same reason left and right are on the same axis, forward and backward in time are too.
I think the knight argument is actually the strongest one, and really the only argument for a third spatial dimension existing or at least implied in the game of chess without being an additional movement vector.
My first argument for this is from a perspective of written rules, in many representations of rules for chess it is written that knights "jump" or "skip over" other pieces and since the act of a jump necessitates 3D it is 3D. As to the argument of things "moving out of the way" in the second dimension I don't see any chess rules written this way, probably because the idea of something moving out of the way could potentially cause confusion and ambiguity with things like, "do the other pieces need valid moves to move out of the way?" or "if they move out of the way do they stay in their moved position?" which would complicate things at least from a written rules perspective. I have seen it written that nights "move through" other pieces but that kind of implies the existence of an astral plane which knights can use to travel through, which would then also be a 3rd dimension.
The second argument is that without the existence of technology to fly, we do not fly, and yet we as humans manage perfectly well getting over obstacles. If you have to step/jump over some kind of barrier to get to the other side of a room your net movement (at least relative to that space) was only in 2 spatial dimensions, so did you only move in 2D? Well no, you had to go over something to get where you are, but because you cannot fly and gravity exists you had to return to the ground to meet your final end point on the other side of the barrier. The act of jumping over an obstacle is a fine explanation for non flight based movement over a flat plane.
Unless they teleport... *X files music* ... but even that in and of itself might mean that nights move through some unseen extra dimension so...
If you count the knight movement to justify another dimension then you could say any 2D game with an intractable background a 3D game
I would argue its 4+1, because the board is kinda described by a 4D tensor: 2 dimensions for each board, and two dimensions of boards, and then at each turn you change this 4D configuration (which is different from the configuration itself having a dimension called "time"). But by this definition regular chess is 2+1D. And no, not every game involves progression in time. Consider the prisoners dilemma played exactly once.
5D absolutely, not 4D. You aren't noticing that the TIME moves are in 3D space? Take the bishop, from inside a cube it can move through the 12 edges (4 top 4 side (2D), and 4 bottom), the top and bottom 8 are time moves. I've played 3D chess many times and that was one of the first things that noticed. It's why there is an odd time move at the end of the Knight move, because the L shape tip passed through time and space. I haven't played enough to know if it is allowing all (6x4) 24 knight moves, but I do know that allowing the Queen to move through time on the 2D diagonal is a Unicorn move, through the corners of the cubes. So the movement it is not 2D plus time, it is 2D plus time though a 3rd dimension. When the rook does non-2D moves it either moves through time like a column in 3D chess (say up) or to other existing boards (say down). I have also drawn Tesseracts in 2D that lets me count the many parts the way you would count the parts of a cube, So if you count backwards you can count to 5D: (5th) the dimension you pass back to known timelines, the 4th dimension is time, 3rd like gravity how time is visualized in the game, 2nd and 1st the axis of the moves of chess. I think what you are missing is due to the restrictions that prevent paradoxes. Most people that care know that a Queen can move 26 directions in 3D, and 80 directions in 4D, so I hope it can be verified, factoring paradox restrictions. Lastly, these 80 directions are combinations of dimensions that the Queen can move, and just llike looking over a 2D chess, you can't really evaluate the moves if you are also 2D, so in the case of your 4D chess you are playing in a 5D perspective.
@OliverLugg, woah, did I write that at 3am? Thanks for your videos, but I do my own thinking. Rereading what I wrote, I see the fallacy that I created, no one calls international classic chess 3D. But the moves in time through the 3rd dimension are undeniable. The bishop is my favorite, because the boards don't alternate B/W patterns like in really 3D chess I can change the color of my Bishop!
You need vectors with 4 components to properly describe the movement of every piece. It's 4d
Considering all the boards fill a 2d plane, I believe a complex enough function could define the movements with just 2 axis.
@@ceresgc No, the 2d planar representation of the game is a 2d plane of 2d planes. Each sub-2d plane consists of the x and y directions (normal chess), while the outer-2d plane consists of the time and multiverse directions. It is a 2d representation of a 4d game-state.
@@gadrill4285 true, but since all of the 2d cheeses board are FINITE 2d planes, their totality can be expressed without occupying more than a single infinite 2d plane. So it can be both
I don't know if 5D chess has this feature, but if you can play the game with a global clock, then it would be 5D: 2 spacial dimensions, parallel universes, The causality dimension (referred to in the game as the time dimension) and the proper time dimension (the one dictated by the clock and can guarantee that the amount of committed boards always stays the same or increases with the passage of time). By committed boards, I mean the ones that you can't undo anymore, because undoing would break the statement above.
Even with a board-local clock you would have more than 4 dimensions for the same reasons, though you can debate if this is 5D or 4+D.
It’s 6 dimensions, but only because of a very unique ruling in 5D chess involving knights.
Imagine you have a chess piece that you want to send two timelines over, but there’s a gap between the those two timeline. You can visualize it with emojis, where the black square is effectively ‘void space’:
⬜️⬛️⬜️
Well, with any other piece, moving from one, to the other would be impossible. Knights, however, can jump from one side to the other, this is because they can ‘jump’ through the 6th dimension. Meaning 5D chess is technically 6D; at least for the knights.
As for your argument about regular chess being 2D. I would still argue it’s a 3D game, just played on a 2D plane. You wouldn’t look at us walking on the ground and say “we’re two 2D creatures because we cannot fly”. The same logic applies to chess. And if the ruling for 5D chess is that knights are able to jump through the 6th dimension across void space, the same logic applies to regular chess, where knights can jump through the 3rd dimension, to reach a position that would normally be impassable.
So yes, ultimately chess is 6 dimensional. At least to a certain degree.
I feel like you surely have to concede that all games involve the dimension of the progression of turns as otherwise the game simply couldn't happen, this does make most games 3D but that isn't really that much weirder than our universe being 4D when you count time. The only games that could be said to not involve this dimension are games that are instantly resolved like rock papers and scissors.
By definition a dimension has two vectors, with 1d it's up and down with 2d it's 1d+left and right, etc. Games that have soley linear progression of time, as in standard chess where you cannot move pieces backwards in time, time is no longer considered a dimension. Reality considers time to potentially be a 4th dimension, but it won't be proven untill we prove that backward time travel is possible.
The 5th dimension was the friends we made along the way.
there is a RTS called achron with similar mechanics
I’ll solve this debate by giving everyone a thing to DISagree on. The game does not have 138 dimensions.
I disagree. The game actually does have 138 dimensions.
It actually does but 134 of them are unused.
Well, I tried.
There are many ways to express chess with many degrees of dimensionality. I will now discuss 2.
Chess is 3-dimensional, there are 2 quantized spatial dimensions and a 3rd ordinal piece dimension that represents the piece on that square. This means adding 2 dimensions to chess produces a 5d game.
Alternately let's get radical, rather than representing pieces as a single ordinal dimension we can represent them as 6 separate dimensions with sign representing the color of the piece. Assuming that pieces are quantized and the magnitude of this vector is either 0 or 1 then you get chess as we know it described using 8 dimensions and adding 2 dimensions produces a 10d game.
I think 5-d is accurate. x,y,t,m, and piece: the pieces are a dimension. Pieces are orthogonal to x, y, t, and m. You could say color is a partial dimension. There is, unfortunately, no smell dimension, nor is there a flavor dimension (but then, smell impacts flavor, so that might be a fractal). For 8th dimensional chess, add spin, smell, and flavor.
"Playing 3D chess" is an expression meaning that you think so far ahead of your opponent that they can't keep up. This is the 3rd dimension in regular chess. In 5D chess neither player can keep up, therefore it is in actuality 6D chess.
Just an opinion, but I personally agree with MrCoolGuy on the grounds that the game is 5D due to the moving forward in time being another dimension. I feel like it’s not that much of a stretch to assume that normal chess is three dimensional because of two special dimensions and another time dimension. By this logic you take normal chess with three dimensions, moving vertically in space, horizontally in space, and forward through time, you can add the two new time dimensions that 5D chess introduces.
I confused myself writing this and am now doubting myself but I wanted to hear from you guys to see if this logic makes any sense at all. With all the kinds of dimensions we live in (special and time) we live in one dimension higher than what we experience. For example, we see in 2D but live in 3D. If we saw in 3D we would be able to see all sides of an object at once. And we live in one time dimension but see in 0D time. Meaning we can only see the single instant that we exist in the present on the one dimensional line that is time. So my thinking is that inside 5D chess there are three space dimensions, but we only see two of them because of this limitation of always seeing n-1 dimensions.
To describe these time dimensions; The first time dimension is moving forward and backwards on the board game’s time
Second is moving sideways through the multiverse
And third, the one we cannot see, is all the moves we’re ABOUT to make in the game itself, like the move that checkmates the enemy king 30 moves in the future that neither player has thought of yet. It is essentially the real life time dimension that is stopping us from seeing the future ending of any 5D chess game. In order for there to be a game, you must have an extra time dimension that we cannot see or else the game would already be completely laid out in front of us and everything would be visibly pre determined.
Another way to think about it as if every turn, the entire game state moves forward one move in this third time dimension. Not just one single chess game, but the entire game itself moves forward in this time as we play
Is this in any way logically correct or am I stupid
I would argue, that it is played in 4 dimensions, as u said, but it still makes sense, to call it 5D, because as u said, technically every game has time as the extra dimension, but since this game decided to call an extra dimension time, that is not the played time, it would be strange to not count the actual second real timeline, the game is being played in. So I'm fine with 5d, but not for the reason, the dev said :P
Chess is actually either a 1D, 3D or a 20D Game!
Chess doesn't have the markov property. To know if it is legal to castle you either need to know the history of a board, or store the "right to castle" in another dimension. Same is true for the en passant rule.
Of course you could store all these informations in a 1D Bit vector, but then any computer game would be 1D, since the game state is stored in a 1D array (the computer's memory).
my view on this is that it only uses 4 dimensions, but it utilizes the by-definition fifth dimension. Basically, everybody wins
Pretty sure it has 2 of space and 2 of time, for a total of 4, and the player is a hypothetical 5d observer.
Time is only one dimension. You go forward and backward in time like you go forward and backward in the x direction. The 4th dimension is the multiverse dimension, and the observer isn't a dimension, you cannot go "forward" in "observer."
2:55
Time is not "the fourth" dimension. It is *one of the four* dimensions.
I argue the 5th dimension is our time dimension.
Normal chess has 2+1 dimensions x, y, and time. So when we add the multiverse we now need a fourth dimension to designate what you universe you are referring to. But now the chess time dimension is no longer related to out time dimension. An example is you capture the queen at 3:00 but the queen is saved from the capture at 3:05. This means we have disconnected the chess time dimension from our own time dimension.
It sounds weird but I am saying 5d chess has 2 time dimensions, 2 spacial dimensions, and 1 multiverse dimension or a 2+2+1 number of dimensions.
Also following this logic any time time travel is possible in media the universe it takes place in is actually a 3+2 dimension with 3 spatial and 2 time.
"How many sides an octagon has, Hajime?"
4 dimensions are in use, the 5th (the 3rd spatial) is merely the distinction between board and piece.
yeah it's like saying the original mario is a 3d game because there is a background, it doesn't really have any bearing on the game so it's not really fair to say it adds a whole dimension
4:40
While I appreciate the detailed explanation, it's much simpler than this:
They've done the equivalent of splitting the x axis into two dimensions:
Moving forward along the x-axis
Moving backward along the x-axis.
More like just taking one plane and placing it inside another.
You move along the x and y axis of the chess board and then move along the x and y axis of time.
Castling, en passants, and draws via repetition all directly imply the normal chess must be 3D with the 3rd dimension being time. That being said, it is correct that "5D chess" is really just 4D.
I would argue that 5D chess is actually 1D and so is everything else.
Actually, anything game or construction the set of whose possible states has countable cardinality could be one dimensional, because Cantor's diagonalization argument can be used to show that any n dimensional continuum has the same cardinality as any n+1 dimensional continuum, for all n != 0. Therefore, since any game with finite states can obviously be represented with a discrete natural number and any game with a continuous set of possible states can be represented using the real numbers between 0 and 1 (which represent a 1D continuum), basically everything ever is 1D.
I would also like to pint out that time is discrete in chess, so at no point in time the knight is actually occupying the 3rd dimension
What can be said about the space, in game, not occupied by chess boards?
Also, is each game played in its own new dimensions or in the same dimensions? Is each game it’s own? What about online play where each game exists twice?
Perhaps it is five dimensional as the first four dimensions include the X, Y, multiverse, and time from the game which can be traversed forwards and backwards, and the fifth is the dimension of time from real life that you spend playing the game which you can only traverse forwards. Of course, using the "two dimensions of time" argument could then imply an additional number of necessary dimensions for the player to exist within... or the computing machine processing the game... But if a circuit board can be represented in a 2D diagram... Okay, 17 dimensions. That's my final offer.
The problem with calling this 4D chess, even though it’s more accurate, is that most would assume use of the three spatial dimensions and one time. It doesn’t immediately convey that two “temporal” style dimensions are involved the way “5D” does.
The first dimension you could represent as 2 dots and everything in the dimensions is between those dots (X) if you want to add a dimension just dubble the amount of dots (X&Y) and keep going
There's a term for 2D games that seem 3D but are fundamentally 2D: 2.5D. Doom is 2.5D because while it uses raycasting to paint the world in a way that looks 3D, the game is mechanically 2D and fully playable from just looking at the automap. Doom is 2.5D.
In the same way, Miegakure is a 3.5D game because while it abstracts a fourth spatial dimension and uses it as part of its puzzles, you are still fundamentally playing a 3D game, and can think of it as several 3D rooms overlapping each other. The fourth dimension is functionally superficial. Miegakure is 3.5D.
Which is why I argue that 5D Chess is 4.5D. The third spatial dimension is "there", but it's superficial, unused, and when it is used, it's for the game's UI. Fundamentally the game is 4D, but it's presented in a way that's consistent with time-as-a-fourth-dimension. 5D Chess is 4.5D.
But "4.5D" isn't as catchy as "5D".
Side note: I have also played a 1.5D game which presents itself as a 1D game. I cannot remember the name of it, though.
It's 5D. The knight needs that extra dimension since any pieces in the way do not move
You're right that the game has 4 playable dimensions, but I'd argue that it is still fair to title the game 5d chess. Regular chess may have 2 playable dimensions, but many people would still think about it as a thing in 3d space. Given that as a reference point, and assuming the point of titles is to convay useful information efficiently, it may be more appropriate to imply that this game has 2 more dimensions of freedom then what you would be used to, rather then strive for perfect accuracy at the cost of semantic usefulness.
"it may be more appropriate to imply that this game has 2 more dimensions of freedom then what you would be used to"
since chess is a 2D game, a quicker way to write that is 4D chess. The dimensions of freedom is what defines the dimensionality of a game if you ask me?
@@shiinondogewalker2809 Fair
I feel like if the game has 4 playable dimensions, you call it 4d chess. Arguing anything else would be, as you say, "striving for perfect accuracy at the cost of semantic usefulness". It's like arguing that mario is a 3d game because you're traveling along the time dimension, or arguing that mario is a 4d game because the background elements make it a 3d game with a 4th time dimension. If you try to actually use these arguments, people won't care. Mario is a 2d game to any reasonable person. 5d chess with multiverse time travel is a 4d game to any reasonable person.
irrational numbers, i'll take it
The pieces move thru 4 dimensions.
1 and 2 are normal chess, 4 is back/foward in time, and 5 is is up/down timeline/wordlines.
Dimension 3 is not used to move pieces, instead its used ro help the player see the movements easier when clicking the views. The game shows a moment thru time by linning the past boards in a way we can see it as a 3d move.
I made a game with 45 dimensions but 43 of them are unused
@@defaultusername1145 not an acurate joke, as all 5 dimensions in game are used. 4 of them for piece movenent and 1 to help the player understand and visualise the new movements.
@@matheusm.santana6527 so then almost every 2D game ever made is a 3D game because they have a background which represents a 3D game
@@defaultusername1145 if you want to be pedantic about it, then every video game ever made on a screen is 2d with at most just the ilusion of 3d, but we generally don't say that about them do we?
Its not using the 3rd dimension just for decoration like a normal 2d chess with 3d pieces mimicking real chess.
Paper mario for example is a 2d game set in a 3d world. different from other 2d marios, you can actually turn the camera on the 3d world changing the perspective, the game only uses 2 dimensions at a time amd you can switch which one you are not using.
5d chess is like that. The pieces move thru 4d space and you can use the last dimebsion to align the boards and Project those movements in a way our 3d mind can understand more easily.
@@matheusm.santana6527 so yes or no every “2D game” that has a background is a 3D game
Ok, so Time and Space are not separate, but the same as space time, meaning a change in time is a change in space and vise versa, so while some view space as a sheet, for a 3d world it is better to view space a pool, with gravity and other forces being like objects in that pool, and time as every-instance that your pool could be in, and all the pools in the world as other areas of space time. This is for a 3d world, while chess on no outside context is a 2d game (knights probably just create a wormhole and travel though it by bending 2d space through time). Now what dimension 5d chess takes place on depends on how the game is. Is each instance actually the same board, or are they boards that have arrangements that have been decided. If they are a physical representation of a singular board, then time could not be considered a dimension, or it could, if the time it travels though is what the player of the board experiences or the pieces, if it is the player then by the view of the pieces the game is 2 dimensions, although they most likely would not know, but by the view of the player with out outside context that the world is 3d then the game is 3d, with the context that it is in the view of the player and the game takes place in a 3d world, then by the view of that player they would say the game is 4d. It also could be thought the view of the pieces though the understanding that they take place in 3d space, and if time is separate for them then the player, and they know this then the game could be 5d chess with 2 different times, not time lines, existing, the board being 2d, adding the third dimension it takes place in and the player takes place in adding a third dimension, then the time the board take s place in and the time the player take place in adding 2 more time dimensions, them being different because the progression fo the boards time requires the progression of the players time, and the player themselves.
I personally thought that the fifth dimension is the point of observation.
You are viewing the game from where and when pieces are moved and to be moved. It's like viewing multiple chess games on one screen.
so by that logic, super mario bros is a 3d game. it doesn't really make sense to describe it like that.
id argue that regular chess is 3d since the pawns lay *on top* of a board, indicating depth. this might be dumb reasoning but its worth a shot defending 5D
I think it's 5 dimensional because of how you would store the board in memory in the code. You'd make a 5-dimensional array: Board(x, y, time, multiverse, chess_piece). Knowing the chess piece is also an information you need to play correctly.
that's not what a dimension is, how would moving forward/backward in the chess_piece dimension work? is there a reason you don't include color as a dimension?
@@shiinondogewalker2809 hmm maybe when you promote a pawn? and the color can be nested in the chess_piece, I guess.
@@formdusktilldeath Code isn't an axis. There are not 2 directions you can move along in code.
The argument that it is 5D because the progression of the turns is its own dimensions sold me. It's 5D.
You can't specify a game of chess using only 2 dimensions. You can specify a single board, but not the whole game. Even a move in chess implies that the board is moving through a dimension akin to time. So, in 5D chess, there are actually two dimensions of time, one of which you can move freely through, the other which merely happens like every other game.
When I think '5D' Chess, I think the first 2 dimensions are the spatial ones, then the 3rd dimension is the normal flow of time, then the 4th dimension is the movement back and forth in time, and then the 5th dimension is moving to parallel dimensions (and by extension in time). Also, this was uploaded on my birthday! :D
Well "normal flow of time" is the same as moving forward in time, the only difference being how quickly you are moving through it. A forward-time-jump is moving forward in time at a high speed, whereas the normal flow of time is moving forward in time, but at the normal speed. They go in the same direction (therefore it must be the same dimension) just different speeds.
It's just a bit odd, since all pieces are constantly moving through the time dimension. Any movement in the spatial dimensions (x,y) also moves the piece forward in time by one unit (for chess, one time unit would be one turn.) So a pawn moving +1 in the y direction would move (1y, 0x, 1t, 0d).
our time and game's canon time?
saying going forward in time is a whole different dimension than going backward and forward in time is like saying left and right are different dimensions, or up and down are different dimensions
Basically, short answer: it's a 4D game that uses the 1st, 2nd, 4th and 5th dimensions.
5:10 thy is the expression of the second (real, untraversable) time dimension
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1 LR
2 UD
3 time (move to board left right)
4 side (move to parallel universe)
5 reeee
In 5D Chess, space is represented by a plane (ie the chessboard). Time is also represented as a plane.
There is no height in Chess or Time in the universe of the game. We only contextualize knight movements as "jumps" because we live in three dimensions, not two.
we live in four dimensions, not three
@@beaclaster
Spatially, we live in three, because you can't move through time (yet). Functionally, time is just a continuous line, unable to be changed in any meaningful amount.
@@RaeIsGaee can't we? we can use time and our senses to create memories which are useful in many ways. also if you're interested about time changing in some way, i highly recommend you about general and special relativity. and as you said that line is just a continuous line, remember a line is a dimension.
@@beaclaster
Memories are just our perception of time, and relativity is practically meaningless for most people. Any significant time dilation would take an immense amount of effort to induce and therefore can't be moved across like the 3 spatial dimensions.
@@RaeIsGaee you mean, things that are very small practically have no size? because they still have. i mean, memories aren't just perception, they are our way to integrate time into actions as references for how to do things. as we can't perceive our 3d space objectively, wouldn't it just being similar conditions? and just because most people doesn't understand relativity, it never means that it doesn't exist. also, ever heard of time crystals? not a sci-fi one, the scientific one. if you think doing nothing doesn't mean travelly across time and you need to do something for you do it, remember the rotation of earth. even if you're just sitting or laying somewhere, you still move according to earth rotation and velocity.
I need more of that last one
Doesn't the 3rd dimension exist within the game because of our perspective of the game itself? In a 3D game, the camera is usually something we can clearly imagine as being within that space, usually behind your character or something of the like. But in a 2D game like Chess, we're seeing the entire plane laid out before us. If it were truly 2D We could not clearly see everything before us like we do. Kind of like that weird video of the 3D person talking to a 2D being. Yes, I'll concede that by that definition, EVERY 2D game is actually 3D because of the perspective that we see the game from. I'd argue that while the pieces don't move in the 3rd dimension, it does still exist there within the game. I concede that by that logic that means ALL 2D games be it top down or platformer are technically "3D" games. But maybe that's the point. We don't categorize games by what they scientifically are achieving but by the gameplay functionality. That's why a 2D Platformer with 3D graphics is still considered a 2D Platformer. So by that logic, this game is still 5D, as functionally speaking we're playing along the multiversal axis which we perceive to be the 5th dimension. That or I guess we could call it 4.5 chess?
Q: How many dimensions are there in 5D chess?
A: Four, for all of the reasons in this video.
Q: So it should be called “4D Chess,” no?
A: No. The ‘5’ in “5D chess” is an ordinal, not a cardinal. The unabbreviated name would be “Fifth Dimensional Chess,” not “Chess in Five Dimensions.”
The game uses the first, second, fourth, and fifth dimensions. There is an ordering to the dimensions. The three spatial dimensions that humans can freely move through come before any other dimensions. Time is “the fourth dimension” because it is the first physical dimension that we comprehend beyond space. Multiverse comes after that, so it is the fifth dimension.
Next someone is going to make a 5d checkers with time travel and multiple dimensions
the easy excuse is that the knight uses height as the 3rd spatial dimension to jump over other pieces, i will take no critiscism of my infallible and true opinion
no