Timeline for What is a chess piece mathematically?
Current License: CC BY-SA 3.0
44 events
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| Oct 4 at 17:38 | comment | added | Nikodem | Concerning the physics analogy of @TerryTao, I would rather see chess figures as particles (of different flavors) moving in a discrete space and interacting via long-range interactions (including annihilation processes), similar to cold atoms in optical lattices or quasi-particle excitations in solid states. I wonder which other analogies can be found. | |
| Aug 11 at 1:51 | answer | added | Marco Ripà | timeline score: 0 | |
| Sep 2, 2023 at 1:21 | answer | added | dbdb | timeline score: 0 | |
| Apr 24, 2021 at 17:24 | answer | added | The Red Fox | timeline score: 1 | |
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| S Apr 2, 2019 at 20:25 | history | suggested | Rodrigo de Azevedo |
Since Joel talks about Tic-Tac-Toe, I believe the CGT tag is quite on-topic.
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| Apr 2, 2019 at 19:50 | review | Suggested edits | |||
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| Dec 15, 2017 at 3:00 | review | Close votes | |||
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| Dec 10, 2017 at 14:30 | history | edited | Morteza Azad | CC BY-SA 3.0 |
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| Dec 9, 2017 at 17:56 | comment | added | RBarryYoung | Ah, I found it. It's called "Computers, chess and long-range planning" M.M.Botvinnik, Heidelberg Science Library, 1970. But now that I look at it, it doesn't seem like it would be that helpful. It's pretty primitive from a CS standpoint and it doesn't really talk about mathematical representation of the pieces, so much as the mathematical representation of the process of chess itself. | |
| Dec 9, 2017 at 17:42 | comment | added | RBarryYoung | IIRC, Mikhail Botnivik wrote a book on this back in the late 60's/early 70's (be aware, this was when CS was still part of Mathematics, so it is oriented toward the mathematical formulation of a computer program/process). I think I still have it somewhere in my library, so I'll see if I can find it for reference. | |
| Dec 9, 2017 at 5:10 | history | edited | Morteza Azad | CC BY-SA 3.0 |
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| Dec 9, 2017 at 2:44 | answer | added | Nissim Levy | timeline score: 1 | |
| Dec 8, 2017 at 13:05 | answer | added | Michael Kay | timeline score: 13 | |
| Dec 8, 2017 at 11:11 | comment | added | Morteza Azad | @NeilBarton (+1) Indeed, I do agree with you. By the way, there is a MathOverflow question addressing the same "lack of proper definition" problem for large cardinal axioms: What is the definition of a large cardinal axiom? | |
| Dec 8, 2017 at 10:59 | comment | added | Neil Barton | I second @Joel David Hamkins' diagnosis, but want to point out that this isn't always a devastating problem for mathematical research. The notion 'large cardinal axiom', for example, has no rigorous mathematical definition, but we tend to know one when we see one. | |
| Dec 8, 2017 at 10:04 | history | edited | Morteza Azad | CC BY-SA 3.0 |
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| Dec 7, 2017 at 20:49 | comment | added | Morteza Azad | @CarloBeenakker (+1) Interesting article! Thanks for sharing, Carlo! Here is more information about Shogi (Japanese chess) for those who might be interested. | |
| Dec 7, 2017 at 20:47 | comment | added | Carlo Beenakker | in this connection, reading how chess (and its Japanese variant) were implemented on a neural network is instructive: arxiv.org/abs/1712.01815 (today on arXiv) | |
| Dec 7, 2017 at 18:59 | comment | added | James Smith | Maybe prepending 'the behaviour of' to most of the occurrences of 'a chess piece' in the question would make it a bit more readable. | |
| Dec 7, 2017 at 18:27 | comment | added | OrangeDog | @NikWeaver that’s why they’re comments, not answers | |
| Dec 7, 2017 at 18:16 | review | Close votes | |||
| Dec 7, 2017 at 22:32 | |||||
| Dec 7, 2017 at 17:37 | comment | added | Morteza Azad | @TerryTao What an amazing analogy, Terry! Actually, I didn't get it at the first glance but I gave it some thought and now I feel I can understand what you mean. It would be great if you explain the idea behind such an analogy in an answer or a more extended comment. What do these two (chess and fluid dynamics) have in common exactly? | |
| Dec 7, 2017 at 16:39 | comment | added | Terry Tao | If one draws an analogy between chess and fluid dynamics, then the chess pieces are the possible values of Lagrangian coordinates, while the 64 squares of the chessboard are the possible values of Eulerian coordinates. en.wikipedia.org/wiki/… | |
| Dec 7, 2017 at 16:19 | comment | added | user94041 | "There is a long-standing discussion amongst chess players concerning the best possible configuration of chess pieces which makes the game more exciting and complicated." I am not so convinced chess players care about this. Even those that like to play and advance chess960 are doing it for the purpose of making chess more varied, but are not necessarily preferring one configuration over another. | |
| Dec 7, 2017 at 14:59 | history | reopened |
Morteza Azad Carlo Beenakker Joel David Hamkins Joseph O'Rourke Pace Nielsen |
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| Dec 7, 2017 at 14:05 | review | Reopen votes | |||
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| Dec 7, 2017 at 13:44 | history | closed |
domotorp user1688 R W Chris Godsil Stefan Kohl♦ |
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| Dec 7, 2017 at 13:35 | answer | added | Joel David Hamkins | timeline score: 134 | |
| Dec 7, 2017 at 13:22 | comment | added | Morteza Azad | @ToddTrimble Hmmm... Seems (disappointingly) true! :-( Anyway, I did my best to "MathOverflowize" the ambiguous yet intrinsically natural question. | |
| Dec 7, 2017 at 13:13 | comment | added | Morteza Azad | @JoelDavidHamkins My question is somehow related to what you have mentioned. Anyway, I think it is still interesting to consider non-standard chess pieces which highly affect the game value and the winning strategies. For example, consider the piece corresponding to the complete graph in the chessboard with the jumping ability. It is a super powerful piece (superman) which ends the game in the first move because there is nowhere to hide from its fierce threat for the opponent's king! Modifications of superman covering "almost all" (but not all) places on the board are also interesting. | |
| Dec 7, 2017 at 13:11 | comment | added | Todd Trimble | If Joel's interpretation is correct, then the question seems to have little hope of being solved (as he said). After all, even in ordinary chess there are such bizarre rules (like castling, capturing en passant, even pawn promotion) -- how to draw a strict line between that type of game and checkers? Capturing in checkers could be seen as just a variant of capturing rules for pawns, and king-ing in checkers just a variant of pawn promotion. | |
| Dec 7, 2017 at 12:57 | answer | added | J.G. | timeline score: 8 | |
| Dec 7, 2017 at 12:56 | comment | added | Morteza Azad | @ToddTrimble Well, my question is actually not about the way one can define a "game piece" in general. Though, I relied on the "common sense" for what is called a chess game. However, I assume an exact definition of a "chess piece" (which works for all standard and fairy chess pieces) can't exist without a clear definition of a "chess game" including all variants of this game. Not to mention that I personally see a chess piece (chessman in your words) a graph with certain properties. But I have problems identifying the abstract properties that such a graph should satisfy. | |
| Dec 7, 2017 at 12:46 | comment | added | Joel David Hamkins | I interpret the question essentially as asking for a definition of what it means to be a chess variant. For example, checkers or draughts is not ordinarily viewed as a chess variant, but Fischer chess, bughouse and horde chess are. My opinion is that the category of chess variants does not have sharp boundaries, and any proposed definition will admit counterexamples. So I don't think there will be a fully satisfactory account. | |
| Dec 7, 2017 at 12:39 | comment | added | Todd Trimble | The terminology "chess piece" is confusing and probably should be replaced. Clearly you don't mean physical pieces, and I don't think you mean the specific game of chess. (Also, among chess players, "piece" often means a non-pawn chessman.) My guess is that "abstract game piece", using chess as an example, comes closer to your intended meaning. | |
| Dec 7, 2017 at 12:33 | review | Close votes | |||
| Dec 7, 2017 at 13:44 | |||||
| Dec 7, 2017 at 12:31 | history | edited | Morteza Azad | CC BY-SA 3.0 |
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| Dec 7, 2017 at 12:25 | comment | added | Nik Weaver | These comments don't really address the question. | |
| Dec 7, 2017 at 12:23 | comment | added | Morteza Azad | @MichaelGreinecker Of course for every variant of chess, we have rigorous well-defined rules but as a game with a long history, "chess" has many variants with different rules and pieces. For example, there are chess games played on a three-dimensional chessboard! (The theory of infinite three-dimensional chess has been studied in some of Joel Hamkins' works. See page 443 of this slides for more information: jdh.hamkins.org/wp-content/uploads/2014/08/… ). I don't see how and why one can consider one of them the standard version and the rest just "non-chess". | |
| Dec 7, 2017 at 12:15 | comment | added | Carlo Beenakker | Since chess can be played "in the head", there is no need for chess pieces at all. | |
| Dec 7, 2017 at 12:05 | comment | added | Michael Greinecker | The chess rules are already abstract and define the structure of chess rigorously. | |
| Dec 7, 2017 at 12:00 | history | edited | Morteza Azad | CC BY-SA 3.0 |
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| Dec 7, 2017 at 11:48 | history | asked | Morteza Azad | CC BY-SA 3.0 |