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        Arimaa >> General Discussion >> a beautiful game?
        
(Message started by: arimaaphile on Aug 21^st, 2011, 6:48pm)

Title: a beautiful game?
Post by arimaaphile on Aug 21^st, 2011, 6:48pm

What makes arimaa beautiful, if you think or believe that there is beauty in arimaa? By the way, I'm not speaking about physical features of pieces.
Chess players talk about beautiful combinations (or moves?). I don't play much chess so I don't understand what that means specifically but I do appreciate beautiful shapes in Go and I know what they mean when they look at the board and say "that's an ugly (or beautiful) shape".
So my question is what is that specific/concrete X, Y that makes arimaa beautiful to you.

Title: Re: a beautiful game?
Post by Fritzlein on Aug 21^st, 2011, 9:11pm

Beauty in abstract strategy games, as in mathematics, has to do with simplicity and order emerging from complexity and chaos. This is why 1+1=2 is not considered a beautiful equation, but e^(i*pi)+1=0 is. Without understanding some subtle ideas, it is unclear that the latter equation is true, but when the understanding is present, it not only seems inevitably true, but also deeply reassuring that the truth can be so easily expressed.

A beautiful position in Arimaa is one that overcomes the combinatorial explosion of possible moves with a simple idea. Perhaps the idea is the need to immediately respond to any goal threat. Perhaps it is direct immobility of the elephant, or indirect immobility from the need keep a framed or hostaged piece from dying. Beauty is when you would expect there to be fifteen thousand choices of move, but understanding the position leads you to see that there is only one good move, or no good moves.

Beauty is not merely the move that wins or the move you have to play, if that necessary move is connected to no idea. You can win ugly if it is inefficient, with more force used than is necessary. A bulldozer may be as simple and effective as 1+1=2, but it is not subtle. You may know the winning move is there, and when you finally find it, nothing has been clarified or illuminated. Ugly is winning in some incomprehensible way, even if a computer verifies that there was in fact only one way to win.

Thus, beauty is not a function of the Arimaa move or position per se, but rather a function of how that move or position relates to our understanding of Arimaa. Does it bring order to apparent chaos, like a "magic eye" image of white noise suddenly becoming 3-dimensionsal? Does it hang in memory from then on as a way to understand other positions? Does it show pieces working in harmony, as they should work, so that you come away feeling that you now know what a cat's purpose in life is? Is it something you not only can't forget, but are also overjoyed to remember?

As Kahlil Gibran says of beauty:

All these things have you said of beauty,
Yet in truth you spoke not of her but of needs unsatisfied,
And beauty is not a need but an ecstasy.
It is not a mouth thirsting nor an empty hand stretched forth,
But rather a heart enflamed and a soul enchanted.

It is not the image you would see nor the song you would hear,
But rather an image you see though you close your eyes and a song you hear though you shut your ears.

Title: Re: a beautiful game?
Post by Hippo on Aug 22^nd, 2011, 1:17am

For me the beaty of arimaa is in the fact that two positions which differs by just one piece shifted one square could lead to absolutely different optimal strategies.

I like the fact even the best players are not able to play without occassional weak moves. They just do stronger moves in average :).

I like the rules simplicity generating the game complexity.

Title: Re: a beautiful game?
Post by arimaaphile on Aug 24^th, 2011, 12:42am

Wow, Fritz, I did expect you to use math formulas but not definitely Gibran’s poem; that was a pleasant surprise.

I somewhat agree with you. But I think there might be something specific to arimaa that would separate it from other games and would also characterize it as beautiful. Sure, beauty is connected to overcoming possibility of thousands of moves and finding the one that would illuminate us. But that move, that position, that harmony, that whatever, that collection of functions and factors should meet certain needs or conditions to be seen as beautiful. Yes, there is subjective element in beauty, the side of it which haunts us after we close our eyes. But there is some unexplainable, objective dimension of it too. Last few weeks I speculated a lot about that specific whatever. I’m unable to find it.

Nevertheless, I think there might be two kinds of candidates for hints/signs of beauty in arimaa. One is, as Hippo says, high frequency of drastic changes within play which require shift in strategy. Other games have drastic changes too but no other game allows you to move four pieces around or to cross half of the board with your elephant and land on opponent’s camp only to wake up and see your elephant choked. In addition, other games built tension much slower than arimaa. I mean when you play go growing tension is so slow to increase that it is difficult to find out what was the decisive move. One stone per move makes the game slow. But with arimaa you can play and believe that you are winning yet your opponent may find a comeback move and win. That element of suddenness or possibility to find a winning move until the last moment might be beauty of arimaa; it gives you lots of chances to come back.

The other candidate might be type of moves that combine only necessary number of steps and just one piece higher than the opposing/involved enemy piece in hierarchy to capture or to accomplish the purpose. Of course, not all moves which take only necessary things from the game are beautiful. But I’m suspicious that beauty of arimaa will be more visible in those type of moves than in anything else. These two features together might be something specific to arimaa. Anyway, that’s what I was speculating about few days ago.

Thanks for sharing your thoughts.

Title: Re: a beautiful game?
Post by chessandgo on Aug 26^th, 2011, 12:20pm

Cats' purpose in life is to eat mice, but unfortunately on an arimaa board they have to satisfy themselves by bullying rabbits around.

(sorry)

Title: Re: a beautiful game?
Post by Nazgand on Aug 26^th, 2011, 12:27pm

The reason mice do not exist is because then we'd need to worry about cyclic strength; sending pieces to send an elephant from a mouse would make Arimaa a very different game.

Title: Re: a beautiful game?
Post by lightvector on Aug 26^th, 2011, 5:24pm

What I find beautiful is the way Fritzlein and Chessandgo so often win the opening, simply by the sheer clarity of their strategic understanding and judgement.

Title: Re: a beautiful game?
Post by Fritzlein on Sep 1^st, 2011, 2:54pm

Example of Arimaa beauty: The Mob's position
Example of Arimaa ugliness: The Gang's position
;D

Title: Re: a beautiful game?
Post by megajester on Sep 2^nd, 2011, 1:05am

on 09/01/11 at 14:54:10, Fritzlein wrote:

Example of Arimaa beauty: The Mob's position
Example of Arimaa ugliness: The Gang's position
;D

Yeah sure you can be the beauty...
we are DA BEAST!!!

Title: Re: a beautiful game?
Post by Fritzlein on Sep 2^nd, 2011, 7:26am

A sure sign that what is beautiful doesn't exactly coincide with what works: We have the phrase "winning ugly".

Title: Re: a beautiful game?
Post by UruramTururam on Sep 2^nd, 2011, 10:36am

on 09/02/11 at 07:26:31, Fritzlein wrote:

We have the phrase "winning ugly".

But sometimes a move is both ugly and ineffective e.g. the latest Mob move. :D