# Difference between revisions of "Talk:2465: Dimensional Chess"

Line 22: | Line 22: | ||

True n-dimensional chess, where there are an unlimited number of dimensions, would probably be unplayable by any Turing machine, including, of course, humans. [[User:Geek Prophet|Geek Prophet]] ([[User talk:Geek Prophet|talk]]) 23:58, 19 May 2021 (UTC) | True n-dimensional chess, where there are an unlimited number of dimensions, would probably be unplayable by any Turing machine, including, of course, humans. [[User:Geek Prophet|Geek Prophet]] ([[User talk:Geek Prophet|talk]]) 23:58, 19 May 2021 (UTC) | ||

:If you have an infinite number of dimensions to work with, there is a straightforward means for a king to escape forever - just alternate linear moves with diagonal moves, always away from the opposing pieces, and always along a dimension not previously traversed (there are an infinite number of these, so always one more). Any opposing piece will be one dimension behind, at the very least. [[Special:Contributions/108.162.237.4|108.162.237.4]] 01:45, 20 May 2021 (UTC) | :If you have an infinite number of dimensions to work with, there is a straightforward means for a king to escape forever - just alternate linear moves with diagonal moves, always away from the opposing pieces, and always along a dimension not previously traversed (there are an infinite number of these, so always one more). Any opposing piece will be one dimension behind, at the very least. [[Special:Contributions/108.162.237.4|108.162.237.4]] 01:45, 20 May 2021 (UTC) | ||

+ | ::That surely only works if you don't end up stuck in an infinitely-dimensioned corner (infinite dimensions but still finite+nowrapping extent in each dimension). | ||

+ | ::I'm not sure if there's a foolproof way not to find yourself in that corner, by evading through heretofor unused dimensions strictly around the centre of the board (where a finite number of pieces may not be able to coordinate an all-sides trap) but once there a single infinitely-dimensional queen moved one square away from all the relevent edges, protected by some handy rearward piece, could force the endgame. | ||

+ | ::If the king itself is in that one-space-out position (not yet immediately restricted by the edge, ''any'' edge) I ''think'' it can still be considered corralled by a suitably-placed finite smattering of sufficiently-positioned (for their respective powers of projection) pieces, so even if the centre squares are freely dodgable round (which they might not be, if the opposing king is already safely stationed there, denying 3x3x3x...3 spots to the victimised king) there's a potential to be tactically/psychologically forced towards a definitely entrapping position the moment you stray towards any edge. | ||

+ | ::(If the queen/etc is '≤2D in movement, like a 2D queen except throughout the ∞D of choice' (i.e. confined to a planar diagonal), then it may be less potent for a given distance and not be able to project a no-king-may-pass barrier even without confounding pieces, so might not be the key to the corner-shoving tactic. But then the king would surely be 'choose your single plane' too, in the moves available in its attempt to escape.) | ||

+ | ::Boundaryless arenas (including wrap-around finite boards, or at least 'only' 8<sup>∞</sup> in their infiniteness) might well be trivially always in an escapable position. But I have my doubts even about the fully-wrapping version, as the attacker's 'left behind' pieces may be considered significant danger again as they are then actually ''ahead'' of any king's fleeing move, and the question now is whether the king can still dodge ever-'sideways' against a concerted and sufficiently analytic opponent still with enough (2? 16? However-many-you-can-initially-start-with-on-such-a-board?) pieces of the right kinds. | ||

+ | ::That said, whatever my proficiency with dimensional projections, I'm definitelt rubbish at chess in its standard form. So ICBW. [[Special:Contributions/141.101.98.60|141.101.98.60]] 09:24, 20 May 2021 (UTC) | ||

It looks like the 3rd row adds a cube on a stack of alternating colored squares, and then the 4th row does something similar with a tesseract. It gets a little crowded, so hard to be sure. [[User:Orion205|Orion205]] ([[User talk:Orion205|talk]]) 01:36, 20 May 2021 (UTC) | It looks like the 3rd row adds a cube on a stack of alternating colored squares, and then the 4th row does something similar with a tesseract. It gets a little crowded, so hard to be sure. [[User:Orion205|Orion205]] ([[User talk:Orion205|talk]]) 01:36, 20 May 2021 (UTC) |

## Revision as of 09:24, 20 May 2021

How best to describe the addition of dimensions? The admirable first author goes as far as the second row, but there appear to be more... ahem... 'depths'. The first is 'sideways', though from this non-playing angle it's depthways; the second adds verticality; the third initially looks to be '4d represented in 3d' perspective (now further represented in 2d, by perspective method), but the sole cube atop confuses me; the fourth is... busy... and seems to go with a hyper(hyper)cubic continuation. 141.101.99.161 18:05, 19 May 2021 (UTC)

not quite what is demonstrated in the comic but there is a game called 5 dimensional chess with multiverse time travel --172.68.57.189 19:00, 19 May 2021 (UTC)

I think this would require 5 dimensions rather than 4 as the middle rows are 4d slices of a 5d space just as the second row is a 2d slice of a 3d space 172.69.35.193 20:23, 19 May 2021 (UTC)

- I see it as there being a basic 1D between the opponents. On the Nth row away from you (on your half of the board) there's an additional N lateral dimensions. Row 1, sideways (8 columns). Row 2, sideways and up/down (7 levels). Row 3, those plus some form of superimposition indicated by scale/perhaps a sub-gridlevel elevation (6 of these?). Row 4, all those plus ??? (gonna assume 5). (...Row 5=Profit?) 162.158.158.131 22:25, 19 May 2021 (UTC)

Is there an error on the top board of this image? If I look at the sequence of squares on the vertical, they alternate black/white except for the top board. Even if I were missing some aspect of the logic, I feel like there should be some symmetry between top and bottom. 108.162.221.70 20:52, 19 May 2021 (UTC)

Note that white made a horse move on the left side of the board, forward one and up two 172.68.57.189 21:11, 19 May 2021 (UTC)

- There's at least one black piece on (its) row 3, possibly a knight, and both players have at least one of their pieces on (their) row 4. There are four obvious white pieces forward of the two starting ranks (with no obvious sign that these are established starting positions in this esoteric board*) so there may be a third black piece out there, obscured from clear view. Or more likely that black Knight's movement (two squares forward, three up, one sideways and 0+ squares in the fourth-way direction) is multiple moves (2f1u then 2u1s would be the most simple projected moves).
- (* - The starting ranks appear to be as per 2D chess, with white's far bishop no longer in starting position, but if that's the one now in the nearest start-level 4th rank then it must not have made just one single 2D-like bishop's move to get there, nor is it obviously a pawn brought forward (2f starter then 1f second move, with or without an en-passant), so it may not be quite so simple, or else we've seen more than 4 white moves (and 3/4 black ones). Or both plus some possible exchange of pieces already.) 162.158.158.131 22:25, 19 May 2021 (UTC)

I interpreted the comic as the first row is normal chess- 2 dimensional. The second row starts the boards above and below- 3d. The third row would be 4d, and the 4th row would be 5d. ----

Pretty sure this is just funny commentary on people making more and more complex variations of chess, Quantum Chess, 4D Chess, 5D chess with time travel etc... but part of me looks at this and goes "that could be a real game... that could actually be a good game." just me? 108.162.221.20 21:35, 19 May 2021 (UTC) Sam

Looking at this, I note that there seems to be an assumption in the explanation that n-dimensional chess means chess with an unlimited number of dimensions. I believe that what Randall was actually saying with the "N" was "any number N", not "all numbers N together", i.e. "The problem with 3, 4, 5, 6, ... , N dimensional chess is", and that his objection is that you always only get one number for N. His board, of course, is designed to give you as few as two dimensions up to five dimensions available for any particular piece depending upon the row.

True n-dimensional chess, where there are an unlimited number of dimensions, would probably be unplayable by any Turing machine, including, of course, humans. Geek Prophet (talk) 23:58, 19 May 2021 (UTC)

- If you have an infinite number of dimensions to work with, there is a straightforward means for a king to escape forever - just alternate linear moves with diagonal moves, always away from the opposing pieces, and always along a dimension not previously traversed (there are an infinite number of these, so always one more). Any opposing piece will be one dimension behind, at the very least. 108.162.237.4 01:45, 20 May 2021 (UTC)
- That surely only works if you don't end up stuck in an infinitely-dimensioned corner (infinite dimensions but still finite+nowrapping extent in each dimension).
- I'm not sure if there's a foolproof way not to find yourself in that corner, by evading through heretofor unused dimensions strictly around the centre of the board (where a finite number of pieces may not be able to coordinate an all-sides trap) but once there a single infinitely-dimensional queen moved one square away from all the relevent edges, protected by some handy rearward piece, could force the endgame.
- If the king itself is in that one-space-out position (not yet immediately restricted by the edge,
*any*edge) I*think*it can still be considered corralled by a suitably-placed finite smattering of sufficiently-positioned (for their respective powers of projection) pieces, so even if the centre squares are freely dodgable round (which they might not be, if the opposing king is already safely stationed there, denying 3x3x3x...3 spots to the victimised king) there's a potential to be tactically/psychologically forced towards a definitely entrapping position the moment you stray towards any edge. - (If the queen/etc is '≤2D in movement, like a 2D queen except throughout the ∞D of choice' (i.e. confined to a planar diagonal), then it may be less potent for a given distance and not be able to project a no-king-may-pass barrier even without confounding pieces, so might not be the key to the corner-shoving tactic. But then the king would surely be 'choose your single plane' too, in the moves available in its attempt to escape.)
- Boundaryless arenas (including wrap-around finite boards, or at least 'only' 8
^{∞}in their infiniteness) might well be trivially always in an escapable position. But I have my doubts even about the fully-wrapping version, as the attacker's 'left behind' pieces may be considered significant danger again as they are then actually*ahead*of any king's fleeing move, and the question now is whether the king can still dodge ever-'sideways' against a concerted and sufficiently analytic opponent still with enough (2? 16? However-many-you-can-initially-start-with-on-such-a-board?) pieces of the right kinds. - That said, whatever my proficiency with dimensional projections, I'm definitelt rubbish at chess in its standard form. So ICBW. 141.101.98.60 09:24, 20 May 2021 (UTC)

It looks like the 3rd row adds a cube on a stack of alternating colored squares, and then the 4th row does something similar with a tesseract. It gets a little crowded, so hard to be sure. Orion205 (talk) 01:36, 20 May 2021 (UTC)

It might make sense to just add a link to chessvariants.com, since there are a surprising number of multidimensional chess variants in existence besides the aforementioned 5D chess with time travel. JakobWulfkind (talk) 02:38, 20 May 2021 (UTC)

Ah yes, the Ra̷s̵̡̡̛͍̖̗͖̟̞͊̀̓̉͂̈́̇̉p̵̛̤̔̂͐͗̄̿̋͛̿͗͒͒̚͘̚̚͝u̵̞̿̒̃̾̑͒̎ṱ̶̨̧̡͍̜̙͖̣̗͙̥͈̳̱̼̫͗͊̌͑̇̆͝i̵n opening. A good choice! Also, when is someone going to make a playable version of this??? 108.162.249.74 04:58, 20 May 2021 (UTC)

I don't think the explanation really needs anything to do with intelligence. "Fourth-dimensional chess" is lingo for complexity or cunning, so I think the comic is a joke based on that phrase. 172.69.142.50 05:36, 20 May 2021 (UTC)