Space is the most logical constraint to consider after time. It is also one of the most obvious constraints I might talk about, due to its widespread use.
When I refer to space, I talk about the spatial attribute of the Magic Circle of play. As (the translator of) J. Huizinga put it:
All play moves and has its being within a play-ground marked off beforehand either materially or ideally, deliberately or as a matter of course. Just as there is no formal difference between play and ritual, so the ‘consecrated spot’ cannot be formally distinguished from the play-ground. The arena, the card-table, the magic circle, the temple, the stage, the screen, the tennis court, the court of justice, etc., are all in form and function play-grounds, i.e. forbidden spots, isolated, hedged round, hallowed, within which special rules obtain. All are temporary worlds within the ordinary world, dedicated to the performance of an act apart. (in Homo Ludens, 1955)
In a nutshell, the amount of space this magic circle covers can be measured as the physical zone in which are contained all game objects in each of their possible states. As the game objects go through their different states, a boundary emerges, effectively separating the “game-world” from the “normal-world”. Many games do not require for this boundary to be materialized, but most do for practical purposes. In that case, the boundary becomes herself a game object. As an example, it is very easy to measure the space occupied a game of “Rock, paper, scissors”, even if there is no obvious boundary. It would also be possible to play a game of chess without a checkered board, but then the manipulation of the game objects would consume too much time and would be detrimental to play. The chess board is not required to play chess, but it identifies the different possible states and embodies the boundaries of play in such an elegant way that it became indispensable to the game.
Gaming, like every other human activity, is inherently constrained in space. Even games that seem boundless, like pervasive games, are in fact bound by our own spatial limits. Would you be willing to get on a bus, a train or a plane, just to carry out a single game action? You set the boundary at the limit of your own possibilities. The ultimate boundary is our current inability to leave the surface of our planet. The world is our ultimate playground (for now).
On the other side of the spectrum, each game has a required minimum amount of space to be playable. This amount is determined by our own average human scale and manipulation possibilities. For board games, the mere size of your fingers limits how small pieces can become, sports and physical games are limited by the size and endurance of your body and video games are limited by your eyesight. Even if you augment your senses and abilities using mechanical methods, you’re just scaling up a small space to make it accessible.
All games require a certain amount of space to represent the current state of their objects. The player cannot play without knowing the current state of the objects he manipulates.
Following this, all games are limited by space in the amount of information they can hold at once, thus implying the general rule stating that “smaller games tend to be simpler than larger ones”.
Every game space is (implicitly or explicitly) divided in several discrete sections. Each of these sections can be occupied by one or many game objects, effectively becoming a container of game state information. This rational division of a continuous space can be called the “resolution” of said space, in the same way a computer screen (continuous surface) is rationally divided into pixels (discrete sections). As an example, Rock, Paper, Scissors has a resolution of 2, Tic-Tac-Toe a resolution of 3×3, Chess is 8×8, etc. The complexity of a game can be understood trough its resolution value.
Resolution explains the above rule in a very simple manner: the smaller the available space becomes, the harder it is to divide it into functional sections.
Video games still follow this rule, albeit in an indirect way. Modern screens have a high resolution value, with up to millions of functional elements (pixels) able to be in millions of different states (colors). This amount of information is so dense, video games actually use many elements to represent one virtual, functional element. Your character in a 3D game, for example, is composed on-screen with thousands of pixels, yet when you play, you don’t care about the individual pixels, you see a character moving in a given space. This virtual space, like the “real” space, is also divided into functional sections and thus has a resolution of its own.
A computer screen is actually a very good tool for experimenting with space, since it provides you with a fairly large amount of space you can program its behavior very precisely. Thanks to pixel density and scrolling, you could also represent spaces smaller or larger than the screen.
How would a 1-pixel game look like? What is the largest game you can make?