It can be found here.

There is a very rough key to the symbols that I assembled when I was writing it here.

After having played about a little bit today with things relating to structuralism, I thought it might be fun to try to apply Levi-Strauss‘s canonical formula of mythology to some games. (the closest I could find to a discussion of this nature on the web was this rather elementary discussion on gamedev.net).

The canonical formula looks like:

It’s supposed to depict some sort of transformation, with the fraction on the left representing some sort of relationship between the numerator and the demoninator, the arrow in the middle representing the transformation, and the fraction on the right a relationship between the permuted contents of its numerator and denominator. Basically, you can fill it out however you want. a^-1 is supposed to be some sort of opposite of a. Also, generally either a and b represent characters, and x and y represent some properties, or vice versa. And generally f doesn’t mean anything. (I take that back. f indicates that there’s a functional relationship between its two arguments. ‘functional relationship’ means that one of its arguments is a property of the other, or is an action performed on/by the other. Basically by ‘meaningless’ I mean ‘not a variable’).

It all is a bit arbitrary, but there’s certainly a knack to describing things using it. Actual analyses follow below the fold

Example 1: Megaman boss battles

a: Shoot with x-buster
a^-1: Shot by x-buster
b: Shoot with boss’s weapon
x: Megaman
y: Boss
=>:beat boss

So, ignoring f, the formula looks like

This can be read as: before you beat a boss, you each are equipped your respective weapons, but you kill him and take his weapon by shooting at him; in short:

=>

Exampe 2: Tetris

This is a little weaker, but anyway.

a: falling
a^-1: rising
b: stationary
x: controlled piece
y: main body of blocks
=>: drop piece

That is to say that, when you’re dropping a piece, the mass of blocks at the bottom don’t do anything, but when the piece has finished dropping, it stops moving itself, and adds to the mass of the main body of blocks at the bottom. (no, this doesn’t deal with getting lines: that would require another diagram … ).

Example 3: Pacman

a: eats
a^-1: edible
b: freedom of movement
x: pacman
y: ghost
=>: get power pill

Before you get the power-pill, you gotta be real careful where you go, but once you have it you don’t need to fear anybody, for the time being. And the ghosts become edible (and they also start trying to avoid you). Mmmm.

	=>

It’s one of these fun things to do. Kirby can be dealt with in a manner similar to megaman, but yoshi seems a lot more difficult (the most obvious candidate for inclusion in any formula here being the between the opposition between eating and giving birth. to an egg).

Interpreting things using the canonic formula can seen a bit arbitrary. Semiotic squares are much simpler, and can be handy for classifying entities in a game. For an off-the-cuff example, take pacman again. We take a two pairs of binary opposites, in this case “round/non-round” and “moving/stationary”, and we get the following diagram

	moving	not moving
round
not round

Maybe I could have thought of slightly better categories if I had put more thought in ;), but they do at least allow us to distinguish these four entities from eachother. This sort of stuff is far less arbitrary than the canonical formula stuff: you get a computer to do the searching for things, and you don’t find yourself back-tracking half as often in attempts to squish your things into a big ol’expression like the CF.

The CF is chiefly used in anthropology to talk about differences between related myths. It should also be applicable to computer games to talk about the differences between different games in the same genre (indeed, it’s when one starts doing this that things end up getting a lot less arbitrary).

If one was being a little bit pretentious, and was okay with using Levi-Strauss’s (rather non-standard) terminology, one could describe the above interpretations using the CF as the study of megaman/tetris/pacman as myth :D

Example 4: Tetris Line Removal

Ah, here’s something for the tetris line-removal mechanism. So before, you have a piece that you control that is added at the top of the screen, while a line, only partially filled, sits at the bottom. When you actually fill a line, the line is removed, and the piece you controlled presumably ending up getting partially/wholly destroyed in the process.

a: added
a^-1: removed
b: partial/non-existence
x: controlled piece
y: line
=>: line filled

So, in less mathematical form, you have the transition from a picture of pieces being added at the top of the screen while you have all of these partially filled rows, but when a line is filled and removed, the piece that you controlled looses some (possibly all of) its blocks, as if to retore some cosmic balance ;)

Example 5: Lode Runner

A good fellow on the forum called joshg gave the following example (ref)

I’ll take a shot at it.

Let’s see, which game … how about Lode Runner.

Player(trapping)		Player(freedom)
—————-	=>	————–
Robots(freedom)		Trapped(Robots)

So the robots begin with the freedom to chase you down, and all you can do is lay traps. Once you trap them, you then have freedom to escape.

I found this to be quite a nice analysis myself.

Here’re another two:

Example 6: Yoshi’s Island

a: eating
a^-1: eaten
b: life
x: yoshi
y: bad guy
=>: swallow bad guy

That is to say, Yoshi, in the process of eating the bad guy, takes his life, and gives birth to a new one (the egg).

Example 7: End-of-level Bosses

In general, boss sequences in game take place in enclosed spaces, where your movement is restricted. Also, bosses generally have much more elaborate movement patterns than normal bad guys. So there’s some sort of transfer going on: you’re loosing some freedom of movement, and the AI is getting it. And how does this happen? Well, by just progressing through a level, you’re eventually going to get to the boss (usually).

a: progresses
a^-1: encountered
b: relatively restricted movement
x: player character (PC)
y: non-player characters (NPCs)
=>: encounter the boss

So, thus far we have the following oppositions between a and b in the various games

shoots with X/shoots with Y
falling/stationary
eats/freedom
adds/partial
trapping/freedom,

eating/life
progress/restricted movement

In each case, doing the former will, in a sense, get you the latter

Also, in each case so far x has been under the control of the player and y has been computer-controlled. I can’t think of any examples off hand where this is not the case, though there must be some. I’m going to have to go now and compare these examples to the traditional ones, see how they match up.

Given two pairs of ‘opposites’ (a,b) and (c,d), one can construct a square by juxtaposing different elements from each pair.

For instance, we might get this

While reading this book, I came across a similar interpretation of Levi-Strauss’s canonical formula (more about which I will write in a future post) the form of which I’m sure you’ll be able to see by looking at a single example for a moment:

This interpretation is given by Racine, and is not explicit in Levi-Strauss’s original work. I don’t find it especially rich either as interpretations go, but it was interesting to look at the results it could produce.

The resulting program may be seen here.