Logic as Art

Bertrand Russell once expressed his sense of mathematical beauty in these words:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.^[1]

Games certainly have the capacity to entertain and enchant us. But is the logic of game design so separated from the narrative as to be irrelevant to the aesthetic qualities? I recently examined this question by conducting the following analysis:

Games, by definition are formal systems. First of all, let's look at the definition of a system:

sys·tem, n.

1. A group of interacting, interrelated, or interdependent elements forming a complex whole. 

2. A functionally related group of elements, especially:

a. The human body regarded as a functional physiological unit.

b. An organism as a whole, especially with regard to its vital processes or functions.

c. A group of physiologically or anatomically complementary organs or parts: the nervous system; the skeletal system.

d. A group of interacting mechanical or electrical components.

e. A network of structures and channels, as for communication, travel, or distribution.

f. A network of related computer software, hardware, and data transmission devices.

3. An organized set of interrelated ideas or principles.

4. A social, economic, or political organizational form.

5. A naturally occurring group of objects or phenomena: the solar system.

6. A set of objects or phenomena grouped together for classification or analysis.

7. A condition of harmonious, orderly interaction.
8. An organized and coordinated method; a procedure. 

9. The prevailing social order; the establishment.

All of the definitions in red are directly applicable to games. Now, let's examine what makes a formal system.


According to M. Alan Kazlev [1], a formal system is [a construct] in which statements can be constructed and manipulated with logical rules. So at the core, a game is basically a logical construct. Everything else is superficial, that is to say, the narrative, characters, music and art is all window dressing placed on top of the construct for aesthetic reasons.

Here's an example from Raph Koster of how a story tacked onto a formal game structure can have profound ethical implications:

The bare mechanics of the game do not determine its semantic freight. Let’s try a thought experiment. Let’s picture a mass murder game wherein there is a gas chamber shaped like a well. You the player are dropping innocent victims down into the gas chamber, and they come in all shapes and sizes. There are old ones and young ones, fat ones and tall ones. As they fall to the bottom, they grab onto each other and try to form human pyramids to get to the top of the well. Should they manage to get out, the game is over and you lose. But if you pack them in tightly enough, the ones on the bottom succumb to the gas and die.

I do not want to play this game. Do you? Yet it is Tetris. You could have well-proven, stellar game design mechanics applied toward a repugnant premise. To those who say the art of the game is purely that of the mechanics, I say that film is not solely the art of cinematography or scriptwriting or directing or acting. The art of the game is the whole….

 …All artistic media have influence, and free will also has a say in what people say and do. Games right now seem to have a very narrow palette of expression. But let them grow….It is not surprising that we wonder whether games or TV or movies have a social responsibility–once upon a time we asked the same thing about poetry. Nobody really ever agreed on an answer.

    The constructive thing to do is to push the boundary gently so that it doesn’t backfire. That’s how we got Lolita and Catcher in the Rye and how we got Apocalypse Now. As a medium, we have to earn the right to be taken seriously. [2]

But it is important to note that while all games are formal systems, they are also media. All media has the capacity to be art and in fact achieves the status of art when the communicative element is either exceptional or is open to multiple interpretations:

Raph Koster argues that Media becomes art when the communicative element is either novel or exceptionally well done. This communicative element should be open to multiple interpretations, for if there is only one possible meaning, the message no longer becomes an interactive dialog between the piece and the observer. He further argues that there is a crucial difference between games portraying the human condition and the human condition merely existing in games. [2]

Games, therefore, possess a unique duality, in that they are simultaneously constructs of logic and media. The implications of this formal duality is that games are constructs in which logic manifests as art in such cases where an underlying narrative exists within the game. While the narrative of a game can be distinguished from the game itself, the outcome of the narrative resulting from gameplay is inseparable from the formal system of the game itself.

[1] http://www.orionsarm.com/eg-topic/45b2b9be57dea
[2] "A Theory of Fun for Game Design" Raph Koster, 2004  http://www.theoryoffun.com/