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[increpare]

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.



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

So, anyone else wanna have a go at this?  (it's fun!)

[moi]

[Melly]

Ooooold.

[increpare]

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

[joshg]

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 dunno ... it kinda worked?

[increpare]

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 dunno ... it kinda worked?

Thematically it seems to work fine enough.  I can't think of a better way to phrase it off-hand.  (I've never actually played lode runner, but I did just read the wikipedia page    ).  Was it at all satisfying to formulate?

[joshg]

It was ... I dunno, kind of interesting?  Although it seemed more like a puzzle to fit the game into than something which unlocked a new revelation of how the game worked.  :D

It does force you to think about reversals and "turning the tables" in a game, though, which is interesting.

[increpare]

It was ... I dunno, kind of interesting?  Although it seemed more like a puzzle to fit the game into than something which unlocked a new revelation of how the game worked.  :D

You mean to say that you always thought about lode runner in terms of transference of freedom from the bad guy to the player?

It does force you to think about reversals and "turning the tables" in a game, though, which is interesting.

Sure.  I like that it gives some something concrete to think about and to in your efforts to conceptualise what a (certain mechanism in a) game's about.

Here're another two:

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).


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 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.

[joshg]

It was ... I dunno, kind of interesting?  Although it seemed more like a puzzle to fit the game into than something which unlocked a new revelation of how the game worked.  :D

You mean to say that you always thought about lode runner in terms of transference of freedom from the bad guy to the player?

No, more that it still doesn't seem like a very strong description of how to describe the relationship between enemy movement and player movement in the game.  Like it's kind of a forced choice of words to find something that can be reversed.

[Zaphos]

Isn't clear communication hard enough without introduction constricting, poorly defined notation and arbitrary layers of abstraction?

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. f tends not to mean anything and is ignored: often a^-1 is the opposite of a, but most of the time where I've managed to use it it's been to indicate some other sort of reversal.  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.

... that's comically ill-defined :D

[increpare]

No, more that it still doesn't seem like a very strong description of how to describe the relationship between enemy movement and player movement in the game.

Sure, it only partially describes one particular mechanism in the game.

  Like it's kind of a forced choice of words to find something that can be reversed.

That's pretty much exactly what it is.

Isn't clear communication hard enough without introduction constricting, poorly defined notation and arbitrary layers of abstraction?

Erm, it's certainly not an arbitrary layer of abstraction.  Its creation was motivated by an attempt by Levi-Strauss to (amongst other things) link together variations of myths(for him a myth was not a single story, but rather the collection of all variations of a single story).

(As for abstractness, see below).

... that's comically ill-defined :D

What do you mean by 'ill-defined' here?  Compare this to, say, the classical notion of  tragedy, a "form of drama defined by Aristotle characterised by seriousness and dignity and involving a great person who experiences a reversal of fortune", this reversal being brought about by a "tragic flaw" of the main character.  This involves four terms, and is a lot more semantically loaded than the CF.  Somebody might say, 'yes, but the idea of what constitutes a tragedy has some independent meaning in and of itself', to which I would say, 'yes, but so, in a slightly different way, does the CF'.

All that said, a whole lot of people, both in the field of anthropology and elsewhere have (and, to be fair, with good reasons) a lot of issues with this sort of stuff.

[Zaphos]

Erm, it's certainly not an arbitrary layer of abstraction.  Its creation was motivated by an attempt by Levi-Strauss to (amongst other things) link together variations of myths(for him a myth was not a single story, but rather the collection of all variations of a single story).

That it was created for a purpose doesn't mean it's not arbitrary.

What do you mean by 'ill-defined' here?

I mean it's trying to look like math but all of the terms are like, "we don't care how you use this," or even, "this one's meaningless."  It's as if somebody wanted a false sense of authority by co-opting the language of math, but then couldn't even be bothered to define their notation.  What that's probably going to do in practice is let people claim equivalences where there are none, because they can use the ambiguity to translate totally different things in to the same structure.  In other words, it looks like an intentionally lossy abstraction.

[joshg]

For what it's worth, I found it an interesting exercise exactly because it seemed a bit overly-specific and arbitrary.

It's kind of like writing poetry.  Sometimes writing within specific constraints forces you to think beyond the obvious and dig for a more meaningful and precise word.  Writing one of these formulas was sort of like writing a poem within a very strict thematic formula about a game.

In this specific case I probably got more out of the act of writing within the constraints than I got out of it as an analysis tool.  But it still forced me to reshuffle my thoughts about how Lode Runner's mechanics interact with each other, so I can see how it has potential to reveal things in a different light.

[increpare]

I mean it's trying to look like math

It's as if somebody wanted a false sense of authority by co-opting the language of math

Fwiw, I put in the fraction-notation and the arrow for readability.  Originally it was a big old-fashioned colon-fest, and looked like

f_x(a): f_yb :: f_y(x) : f_a^-1(y)

Its inspiration comes not (directly) from mathematics, but rather from structuralist linguistics (which, for what it's worth, has also had a measurable impact on modern mathematics).  Maybe it might help to think of this all as being a high-calibre form of those elementary school language relationships along the lines of

"hand : glove :: head : hat"

or

"hot : cold :: big : small".

I don't think it's at all unreasonable to represent the form of the above relationships  x:g(x) :: y:g(y) (where g has to be functionally related to x; and be might in the above instances 'garment', or 'opposite').  It's not a water-tight formalism (no linguistic formalism os/can ever hope to be perfect), but it's certainly has some substance.

but then couldn't even be bothered to define their notation. but all of the terms are like, "we don't care how you use this," or even, "this one's meaningless." 

Who said that?  Oh wait, I said that about f      I've amended my explanation of it now.  Look, I do hope I've allayed most of your concerns about that matter now by my explanation above.

What that's probably going to do in practice is let people claim equivalences where there are none,

Okay, this is a reasonable concern.  This sort of stuff is a method for representation, it's not a full-on method of inquiry and deduction.  If people slip up using these sorts of tools, it's pretty likely that they'd slip up without them.  However, they can slip up in extremely virtuosic ways when they use this, non more-so, maybe than L-S himself, who had sufficient knowledge of various mythological systems that he could find particular examples from different parts of the globe to illustrate some really far-out theory and, in the process, claim that this evinced the presence psychological invariant of the human mind, rather than, as it did in some cases, a dearth of evidence existing in any single continent   But the problems with his method in this case are general, rather than specifically oriented about structuralist tools.

because they can use the ambiguity to translate totally different things in to the same structure. 

I don't think you could do that any more than you could with standard "eyes:nose::sight:smell"-style expressions or try to treat a comedy as a tragedy.   What terms you can put in *are* constrained.  You can't just shove in whatever you like: you have to justify each element's presence.  There's some wiggle space, sure, and some people abuse it, but that sort of abuse certainly isn't widespread.



I'm going to take one possible game-related mechanic-interpretation that I'm really not comfortable with at all, dealing with experience points in RPGs.  If somebody was to say that "in battling an enemy, you aim to take his experience points and make them your own", I'd probably wince a little.  If they were to write it out in equation form, I'd probably wince even more.  But I wouldn't, I guess, be able to show that it was a bit nuts just by dealing with the formula, it would have to be with either this person's interpretation of the various relationships in the formula, or with their interpretation of the game, or with both.  In this case, I'd be all, like 'That seems pretty weak dude.  Enemies don't loose experience when you kill them, they die.  If there was a game where experience-trading actually took place (maybe in a hard-mode PvP battle in Diablo 2, where you loose some experience whenever you're killed), then I'd buy it, but not for, say, final fantasy".

[moi]

I mean it's trying to look like math but all of the terms are like, "we don't care how you use this," or even, "this one's meaningless."  It's as if somebody wanted a false sense of authority by co-opting the language of math, but then couldn't even be bothered to define their notation.

Well thank you, my thoughts exactly.
I went through a similar phase when I was 20 something with another epistemology related theory. I was amazed thinking that I could put everything into a simple equation.
Then I realized it was dumb.
(I don't want to talk too much about my particular experiences, but believe me, it was worse than this)