# Cardinality Of Gameworld

Out of date. It has been superseded by something that has been published elsewhere.

The Cardinality of a Gameworld is an aggregate value of spatial freedom within a gameworld representing all possible dimensions in which movement can take place.

Many games are spatially-based in the sense that a player must interact with a gameworld that is defined and presented as having distinct spatial properties. The cardinality of any given gameworld is an encompassing description of all possible spatial movements available to entities within that world. The gameworld’s cardinality is also used to describe the space that these entities pass through. In more canonical game designs, these movements are often characterized by motion along a combination of orthogonal axes. Thus it is common to classify gameworlds as being one-dimensional, two-dimensional, three-dimensional, etc. based on the number of orthogonal axes available to game entities for motion.

It is important to note that these examinations may not concretely identify a gameworld as being a purely one-dimensional, two-dimensional, or three-dimensional gameworld, etc.. As with all Ontology entries, it is important that allotments are made for strong and weak examples of each instance.

In determining the cardinality of a gameworld it is important to consider the degrees of locomotive freedom that have been granted to each entity in the game. Additionally, the circumstances under which these degrees of freedom occur must also be taken into account. For example when considering consider the classic arcade game Space Invaders, which is spatially-based on a standard Cartesian reference system containing two orthogonal axes, we can note that the player controls a spaceship that can freely move left or right along an X-axis. The spaceship also fires missiles that can only ascend along a Y-axis. Finally there are ‘invaders’ that can only move left or right along an X-axis and descend along a Y-axis.

In consideration of these circumstances, we would conclude that cardinality of Space Invaders’ gameworld is a strong two-dimensional example since the invaders are free to move along two orthogonal axes. This is despite the fact that the player’s spaceship has only one degree of locomotive freedom (the player is unable to control missiles once they have been fired).

It is also possible that there may be cases where game entities possess equal degrees of freedom but along different axes. As an example, imagine that the invaders were only able to descend along the Y-axis (they have lost their ability to strafe along an X-axis). Under these circumstances, all entities in the game have been limited to one degree of freedom. However, the player’s spaceship moves along an axis that is orthogonal to that of the invaders. We would describe this game as a weak example of a two-dimensional gameworld.

In other cases, while the player may have the perception of a world, the actual dimensions of this may be unclear or undefined. This is commonly seen in text-based adventure games where the locations that the character visits may not follow normal rules of logic. For example, typing "North" to exit a location and then typing "South" may not lead the character back to the original location despite the logical assumption that moving "North" is the inverse to "South."

Also, in many games there is certain confusion caused by changes in representation between levels or episodes of the game. In fact, the mere existence of various levels makes this distinction more confusing. In a game such as Donkey Kong, where there are 3 distinct 2D levels, do we consider each level a place that is connected to the previous ones? Would that make Donkey Kong's game world 3D? For simplicity, we refer to the cardinality of space in terms of what is represented in a level or episode. Thus, for the case of Donkey Kong, we would maintain that it takes place in a 2D game world.

We note that the cardinality of space refers to the perception of the game world by the player and not to the actual degrees of freedom the player is allowed within the game world. To account for this, please refer to Cardinality of Gameplay.