06.02.2015 Views

Towards a new Paradigm of Board Games

"There is no reason that forces the game industry to restrict itself on a paradigm of games that is repetitive, addictive, regressive and is denying the right of the user to develop his/hers intellectual capabilities of creativity. It is a strategic decision of the game industry to stupidify its costumers." ThinkArt Lab To introduce the paradigm of morphic (board) games, I start with two simple questions. Why are classical games producing regressive addiction and boredom? What are the differences between classical and morphic games? My first answers to the questions might be summarized as follows: Classical games are based on the perceptive acts of identification and separation of the elements of the game by the rules of the game. Morphic Games are involved into differentiations and structurations of interactive and reflectional patterns (morphograms) in complex constellations. For a more conceptual answer of the two questions I connect the proposed new kind of games to the theory and practice of morphogrammatics. What do I understand by morphogrammatics? Morphogrammaitics is a pre-semiotic theory of inscription. It is studying and formalizing the 'deep-structure' of semiotics. Mathematically, morphograms, as the fundamential patterns of morphogrammatics, are representations of Stirling numbers of the second kind. Formal semiotics consists of an sign repertoire and rules of maipulating its signs. This is established by a strict difference of operators and oprands (signs). In contrast, morphograms are playing a double role: they are involved in a chiastic interplay of patterns (operands) and rules (operators). This is in decisive conterast to identity-based semiotic systems that are based on atomic signs. Strings of signs are based on a set of signs with cardinality m and its potentiation (n): m^n. Hence for m=4 and n=4, there are exactly 4^4 = 256 different semiotic strings possible. But on a morphogrammatical level there are just exactly Sn(4,4) = 1+6+7+1=15 morphograms for m=n=4 possible. In this sense, those 15 morphograms are presenting the 'deep-structure' of the set of semiotic strings of length 4.

"There is no reason that forces the game industry to restrict itself on a paradigm of games that is repetitive, addictive, regressive and is denying the right of the user to develop his/hers intellectual capabilities of creativity.
It is a strategic decision of the game industry to stupidify its costumers." ThinkArt Lab


To introduce the paradigm of morphic (board) games, I start with two simple questions.

Why are classical games producing regressive addiction and boredom?

What are the differences between classical and morphic games?

My first answers to the questions might be summarized as follows:

Classical games are based on the perceptive acts of identification and separation of the elements of the game by the rules of the game.

Morphic Games are involved into differentiations and structurations of interactive and reflectional patterns (morphograms) in complex constellations.

For a more conceptual answer of the two questions I connect the proposed new kind of games to the theory and practice of morphogrammatics.

What do I understand by morphogrammatics?

Morphogrammaitics is a pre-semiotic theory of inscription. It is studying and formalizing the 'deep-structure' of semiotics.

Mathematically, morphograms, as the fundamential patterns of morphogrammatics, are representations of Stirling numbers of the second kind.

Formal semiotics consists of an sign repertoire and rules of maipulating its signs. This is established by a strict difference of operators and oprands (signs).

In contrast, morphograms are playing a double role: they are involved in a chiastic interplay of patterns (operands) and rules (operators).

This is in decisive conterast to identity-based semiotic systems that are based on atomic signs. Strings of signs are based on a set of signs with cardinality m and its potentiation (n): m^n. Hence for m=4 and n=4, there are exactly 4^4 = 256 different semiotic strings possible.

But on a morphogrammatical level there are just exactly Sn(4,4) = 1+6+7+1=15 morphograms for m=n=4 possible. In this sense, those 15 morphograms are presenting the 'deep-structure' of the set of semiotic strings of length 4.

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Morpho<strong>Board</strong><strong>Games</strong>.nb 5<br />

w e s u s e l z v l l<br />

s w z m m l w z w m n<br />

e s w s s l l n m u n<br />

n m m l e n s l s s z<br />

v u e z v l l u w n e<br />

v l w z v w m n l u e<br />

l n l v v s n m z m s<br />

v w z m m e u u v v e<br />

s n l v w u l l m n w<br />

Interpretation <strong>of</strong> a <strong>Board</strong><br />

The category <strong>of</strong> interpretation <strong>of</strong> a board is not necessarily a specific topic <strong>of</strong> a classical definition <strong>of</strong> a<br />

game. Classical games are conceived as ruled by the identity during a play <strong>of</strong> its board (width,<br />

height), modality (randomness, usw), elements (patterns) and rules.<br />

This is in concordance with the definition <strong>of</strong> an elementary formal system (EFS) in the sence <strong>of</strong> Melvin<br />

Fitting and Raymond Smullyan.<br />

But there are other approaches to an interpretations <strong>of</strong> a board and its use available.<br />

This proposal is distinguishing, at first, between Leibniz, Brownian, Mersennian and Stirling games.<br />

Classical games are understood as Leibniz games.<br />

Play<br />

“By definition, a play is one step <strong>of</strong> the playing phase. At each play, the player has to select which<br />

action, among the legal (valid) ones, to perform. “<br />

For poly-<strong>Games</strong>, this decision function <strong>of</strong> selection is complemented with the election function that<br />

decides what kind game (Leibniz, Stirling, etc.) shall hold for the next steps.<br />

Rules<br />

“The rules are the set <strong>of</strong> constraints that determine what can be played and how the status <strong>of</strong> the<br />

game should be modified by a play.”<br />

Additional features: Undo, repetition detection<br />

“How to Undo Remember we said our board representation needed to handle undo operations.There<br />

are two possible methods :<br />

(1) Keep a stack in which each stack item holds a whole board representation; to make a move push<br />

it on the stack and to undo a move pop the stack.Probably this is too slow ...<br />

(2) Keep a stack storing only the move itself together with enough extra information to undo the<br />

move and restore all the information in the board position. E.g. in chess you would need to store the<br />

identity <strong>of</strong> a captured piece (if any) and enough information to restore castling and en passant capturing<br />

privileges.”<br />

http://www.ics.uci.edu/~eppstein/180a/970408.html<br />

MorphoGame interpretation <strong>of</strong> a <strong>Board</strong><br />

For a Stirling approach to <strong>Board</strong> <strong>Games</strong>, the fact that the concept <strong>of</strong> patterns,where the ordered<br />

strings or morphograms <strong>of</strong> identity-free elements, are crucial, leads to the following elementary rules.<br />

MorphoGame rules<br />

Rules in colors<br />

Rule1. Ê = ‡<br />

Rule2. Ê Ê = ‡ ‡<br />

Rule3. Ê ‡ = ‡ Ê<br />

Rule4. Ê Ê Ê ¹≠ Ê Ê ‡ ¹≠ Ê ‡ Ê ¹≠ Ê ‡ ‡ ¹≠ Ê ‡ Á<br />

Rule5. Ê Ê ¹≠ Ê.<br />

Rule5 is resolved in metamorphic Morpho<strong>Games</strong>.

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