Last modified: Mon 2/10/97 1700 PST
The Waldzell Glass Bead Game is a specific concretization of the game described in more general terms in Hermann Hesse's 1943 novel, Das Glasperlenspiel. The Waldzell Game can be played by any number of players (including single-player solitaire) at one of four levels, referred to as orders of the game because lower-order games are incorporated wholesale into higher-order games. The following overview presents a broad sketch of the Waldzell concretization; links are provided to more detailed explanation of all aspects of the game.
The single most important concept of the Game, essential for its coherent interaction with the Waldzell Canon, is that of ontological commitment: players agree to restrict assertions made in a game to those which are consistent with one particular ontology (which can be as constrained or as open as the players desire), agreed upon before the game starts. Fruitful interaction between the Game and the Canon is guaranteed by providing an ontology upon which the Canon is based and to which players of the Glass Bead Game may usefully commit, should they wish to contribute directly to the Canon.
The purpose of a formal ontology, in the context of the Waldzell Glass Bead Game, is to establish the conceptual language in which the Game will be played. This language defines at least the kinds of referring terms that may be invoked and the kinds of relations which players may assert about those term. An ontology may go beyond the definition of kinds of terms and relations to establish an inventory of particular terms and relational assertions as well.
The Waldzell Glass Bead Game can be played with any ontology. In order to ensure a clean semantic interface to the Canon, however, games may be played under commitment to the Waldzell Canon Ontology.
The Waldzell Glass Bead Game provides no rules concerning the manner in which assertions and their component parts are represented and communicated among the players. Representations may involve some combination of graphical network schematics, expressions in the Waldzell Conlang, expressions in the players' vernacular (e.g. English), or any other mechanisms that allow any assertion that is consistent with the chosen ontology to be recorded and communicated. The online-playable version of the Waldzell Glass Bead Game will of course provide a particular means of representation that is particularly conducive to play based on the Canon Ontology.
A zeroth-order game, when completed, is a semantic network of assertions involving such relational concepts, for example, as Generalization, Instantiation, Behavior, Composition, Causation and Identity linking terms representing such referents as, for example, Objects and Events. What kinds of relations and terms are playable is a function of the ontology to which the players have committed.
In contrast to all the games of higher order, a zeroth-order game is not subject to consideration as input into the Waldzell Canon -- this form of the game exists only to serve as the skeleton for a first-order game.
For more information, consult the current version of the rules for zeroth-order games.
A first-order game is built upon a selected zeroth-order game, its skeleton. The skeleton can be retrieved from the Game Archive or played previously in anticipation of the first-order game, but it must be based on an ontology which is compatible with that to which the first-order players are committing, and it must contain at least as many assertions as the square of the number of first-order players (this is the number of assertions contained in a zeroth-order game completed by that number of players).
First-order play involves the cooperative enrichening of the skeleton, by adding assertions as allowable in the chosen ontology. Many, if not most, of the new first-order assertions will refer to terms already introduced in the skeleton, and the first-order game is complete (i.e. may be submitted to the Game Archive) when all skeleton terms have been referred to in at least one first-order assertion. Actual game play stops when the players agree to stop, but only at the end of a complete round (all players make the same number of moves).
For more information, consult the current version of the rules for first-order games.
A second-order game is built upon a selected first-order game, its template. The template can be retrieved from the Game Archive or played previously in anticipation of the second-order game, but it must be based on an ontology which is compatible with that to which the second-order players are committing. The template needn't even have been played as a first-order game as long as it has the property (common to all first-order games) that every term is referred to in at least two assertions. The intended level of complexity for a second-order game is represented best by a template which was played as a first-order game by the same number of players, but players can choose a game of any formal complexity (since formal complexity is only a weak indicator of semantic complexity).
Second-order play involves the cooperative construction of a new network, the analogue, by creating assertions which parallel those in the template (i.e. which have the same relation but different terms). The analogue will mirror the template in the sense that all the template terms have been replaced by new terms. Players may also add additional terms and assertions to the analogue which do not mirror anything in the template.
The second-order game is complete (i.e. may be submitted to the Game Archive) when all the template terms have been mirrored by new terms in the analogue. Actual game play stops when the players agree to stop, but only at the end of a complete round (all players make the same number of moves).
For more information, consult the current version of the rules for second-order games.
A third-order game is built upon a selected second-order game, its skeleton. The skeleton can be retrieved from the Game Archive or played previously in anticipation of the third-order game, but it must be based on an ontology which is compatible with that to which the third-order players are committing. The intended level of complexity for a third-order game is represented best by a skeleton which was played by the same number of players, but players can choose a completed second-order game of any degree of complexity as their skeleton.
Third-order play involves the cooperative enrichening of the skeleton, by adding assertions. Many, if not most, of the new third-order assertions will bridge the gap between the underlying template and analogue sub-networks, linking (directly or transitively) a term in the one with a term in the other. The third-order game is complete (i.e. may be submitted to the Game Archive) when all terms in both the template and the analogue have been referred to in at least one such (perhaps only transitively) net-bridging assertion. Actual game play stops when the players agree to stop, but only at the end of a complete round (all players make the same number of moves).
For more information, consult the current version of the rules for third-order games.