Specificity of Rules
Let us take another look at the complex intersection of constituative and operational rules. Is it really true that for any given game, there exists a single set of constituative rules? Or are there many sets of constituative rules we might apply to the same game? What if the constituative rules of Chutes and Ladders were simplified in the following manner:
Players all begin with a value of zero.
Players alternate turns generating a number and adding it to their value.
The first player to reach a value of 100 wins.
Or simplified even further:
Players begin with a value of zero.
The first player to reach a value of 100 wins.
Or even further:
The first player to satisfy the victory conditions is the winner.
What is going on with these successive simplifications of the constituative rules? With each stylization, we not only move farther away from Chutes and Ladders, but we also move farther away from a set of constituative rules that could be contained within a particular set of operational rules. Because the operational and constituative rules together create the formal identity of a game, they must embody the qualities of rules we identified in the previous chapter: explicit and unambiguous, as well as shared, fixed, binding, and repeatable. The vague sets of constituative rules listed above don't meet these criteria: they are simply too general. A similar set of ambiguous operational rules could be created for Chutes and Ladders, such as by telling players to move on the board but not specifying exactly how they are supposed to move. As we know from earlier examples, ambiguity in operational rules leads to disagreements, which must be resolved before play can continue. The specificity of the rules for any game allows us to identify the game, by saying that it is defined by this set of rules and not that set of rules. There is no absolute measure for the moment when the identity of one game ends and another begins. But the identity of the game is usually self-evident. So if identity is self-evident, why are we going through such trouble to pin it down? Because the formal identity of a game emerges from the intersection of its constituative and operational rules, understanding how it operates will help us understand how rules construct a game.
The operational rules are not merely an expression of the constituative rules of a game. The relationship is more of a two-way street. Operational rules are concrete, real-world rules. Constituative rules are abstract, logical rules. They are very different, but every game ties them together tightly by virtue of its unique identity. What is the relationship between these two kinds of rules? Mathematician John Casti sheds some light on the problem:
Given a particular kind of mathematical structure, we have to make up a dictionary to translate (i.e., interpret) the abstract symbols and rules of the formal system into the objects of that structure. By this dictionary-construction step, we attach a meaning to the abstract, purely syntactic structure of the symbols and strings of the formal system. Thereafter, all of the theorems of the formal system can be interpreted as true statements about the associated real-world objects.[5]
Casti is not talking about games (he is discussing the relationships between purely formal systems such as math and the objects that those formal systems name and manipulate). But his thinking is relevant here. In the kinds of systems he describes, there is interpretation between the two levels of a structure, an interpretation that produces meaning as translation occurs between the levels. This same process occurs across all three levels of a game's rules. The formal meaning of a game is dependent on the intertwined constituative, operational, and implicit rules. How we make sense of a game relies on their interaction, as one form of rules allows for the expression of the others. The significance of rules as a system of expression arises out of the interdependence of its parts. Within the magic circle of a game, formal structures acquire meaning by virtue of these interrelationships. [5]John Casti, Complexification: Explaining a Paradoxical World Through the Science of Surprise (New York: HarperCollins Publishers, 1994), p. 123.