I wrote a new little piece of my how-to-write book today, thought you all might like to see it. :) This builds on my journal entry Plot III where I talk about characters' goals and methodologies. Plot As Thematic Argument, Characters As Thematic Vectors (In geometrical terms, plot is the time or X-axis of a story, and the other axes should be Y=possession/political alignment and Z=theme, with characters being the vectors that move through this space.) The thematic vector value of the character is found by multiplying the character's goal by the character's method. There must also exist a character with either an opposing goal or an opposing method; there may exist one character with an opposing goal and another character with an opposing method. There may additionally exist a character with both an opposing goal and an opposing method (although this would be a bit redundant). Finally, if the goal and/or method are not binary choices, there may exist multiple characters with goals and/or methods which oppose the first characters and each others'. For example, let us imagine a world with 3 types of magic: black, white, and gray. These are philosophies or methods of doing magic. Thematically, there are three possible conflicts we could choose to explore: black vs. white, black vs. gray, or white vs. gray. If we want to explore all three conflicts in the same book this gives us a nice conflict triangle: black vs. white vs. gray (vs. black again). To illustrate this conflict we need at least one character to represent each faction. (Although, keep in mind that a character does not have to be a person, and even if they are a person they might only exist off-screen, in the other characters' thoughts and dialogue.) There are lots of ways this set-up could be developed, but I'll pick one particular way to illustrate: Let's suppose the author wants to convey that extremes are dangerous and the correct method is balance. Therefore, the gray mage is the 'good guy' and the white and black mages are the 'bad guys'. But, the gray mage is not necessarily the viewpoint character; if he started out already having the right method, what would there be for him to learn during the story? - Perhaps the viewpoint character is a student mage who has not picked his color yet, and the gray mage is his positive mentor or guardian. - Or perhaps the viewpoint character is the white mage who is friends with the gray mage and enemies with the black mage. The white mage would always be arguing with his friend about whether white magic or gray magic was better, and at the end of the story the white mage might decide gray magic is better and change his color to match that of his friend. - Or, perhaps the viewpoint character is the gray mage. He is in love with the black mage, but cannot marry her because they belong to opposing factions. So they argue throughout the story and at the end the black mage realizes grayness is better and changes to become a gray mage and they live happily ever after. - Or perhaps the viewpoint character gray mage is torn between being in love with twins, one of whom is a black mage and one of whom is a white mage, and who are always fighting with each other. The twins have a climactic fight and accidentally get magically merged into one body, averaging their blackness and whiteness into grayness. - Or perhaps there is no gray mage; the black mage and the white mage start out as enemies, fall in love, and relize that when they work together their magic averages out to gray. So there are many possibilities, but the point is that the author picks a theme (black/white/grayness) and a moral argument to make within this theme (i.e. grayness is correct and blackness and whiteness are both incorrect), creates characters to represent the various sides of the argument, argues the point through the conflict between the characters, and shows the superiority of one side by neutralizing the characters representing the other sides. A character can be neutralized by being killed, by being shown to be incompetent and thus harmless, by being permanently locked in a struggle with an equal and opposite character such that they have no time to bother anyone else, or by being convinced to change and join the 'correct' side. [Edited by - sunandshadow on March 31, 2006 5:04:35 PM]

Very interesting, although I think I might need some more sleep before my mind is in the right state to fully understand it [smile].

When you use mathematical terminology such as coordinate systems and vectors, are you using this purely as an allegory, or to describe how theme and changing character traits could be abstracted to a form that could be represented by mathematics (and therefore also by a computer program)?

Lol, I just spent half an hour trying to answer that question for my roommate. I guess my primary goal is to find a way to represent the structure of stories visually; I would really like it if this also gave computers a mathematical way to 'understand' and generate/manipulate stories, but I'm not sure I'm at that point yet. The problem is that vector physics is deterministic, whereas character interactions are somewhat arbitrary. If two billiard balls with known mass, direction, and velocity crash into each other, anyone can predict exactly what will happen, but if two characters with known traits have a fight there are several reasonable outcomes, and the author can pick whichever makes the rest of the story work.

So, spacifically I am using the word vector here to mean "an object with known traits, the 'inner urge' to move in a thematic 'direction', and the propensity to interact with other vectors and be affected by environmental conditions." But a character does not necessarily have the same number of dimensions as a regular vector, does not necessarily have a steady velocity, and does not obey Newtonian physics but instead behaves according to a sort of 'dream logic' or 'social calculus' which I am still trying to understand.

Do let me know what you think about the idea when you are more awake. [smile]

"Y=possession/political alignment"

Possession? What about ownership? indentity? affinity?
political alignment? What about group affiliation?

"character interactions are somewhat arbitrary"

Smacks of probabilities and metaverses, perhaps some fuzzy math and weighted graphs, a nueral network or a terrain explorer - social terrain.

'dream logic' or 'social calculus'

There are different approaches to understanding these. One approach that might lend itself well to virtualization and "gamification" is "Constitutive Rules". Here are a few links:

Constitutive Rules and Institutions
Coordinated Management of Meaning
The new role of the constitutive rule
The social ontology of virtual environments
Articles in Jan 2003 issue of American Journal of Economics and Sociology
The construction of social reality

It sounds a bit analogous to some of the robotic control systems I've seen in my research, actually. If you send a robot a command to move forward two metres, you don't know if it will go 1.9m, 2.1m, or a wheel will stick on the carpet and it will careen into the wall [smile]. While there are mathematical models to deal with this kind of situation, they're more for when you want to combine a whole bunch of measurements with a level of error, which isn't really the case when you have complete control over the system.

However some sort of probabilistic approach might be worth considering. You might estimate for a particular confrontation there's a 75% chance of outcome X, a 20% chance of outcome Y, or a 5% chance of outcome Z. Of course, since the author is completely in control of the whims of Lady Luck, maybe calling it something like thematic desirability would be better than probability...

Perhaps it's possible to model arbitrary interactions in a manner similar to modeling the collision of billiard balls, except the various forces, masses, velocities and so forth acting on the collision aren't physical properties but descriptive approximations of aspects of the social terrain. For example, a set of cultural rules guiding interactions. An agent or a player behaves in accordance with his/her group affiliation, an agent aligned with a "good" group would be more likely to abide by the rules, an agent aligned with a "bad" group would be more likely not to abide by the rules. An agents position in the social hierarchy could be used to determine the ability of that agent to get away with bending the rules, possibly crafting new rules. In a conflict between two agents, their relative social positions might be used to limit outcomes of the interaction - superiors, peers, inferiors - verticle and horizontal distances. At least it seems to me that reducing the field of possibilities to a manageable set would make it easier to randomly select a plausible outcome from a range of possibilities. Ultimately, it seems to me that the calculus of such interactions would have to be constructed by the author of the story - along with story setting and themes. It might be possible to conceive of this as a construction project of sorts.

Quote: Original post by LessBread
"Y=possession/political alignment"

Possession? What about ownership? indentity? affinity?
political alignment? What about group affiliation?

Ooh, interesting responses! I will have to carefully read through these and investigate the links (my turn to be too sleepy to think about hard stuff at the moment), but I figured I would answer this first point since it was a simple matter of cutting and pasting. I described the concept of this Y axis in the Did anyone ever make any progress with Interactive Storytelling? thread:

Quote: A protagonist by definition is a character who is driven by a motivation to try to accomplish a goal. An antagonist (a very common but not universally necessary ingredient in a story) is also a character who is driven by a motivation to accomplish a goal, and this goal is one in opposition to the protagonist's. The protagonist and antagonist thus represent opposing thematic vectors.) Every goal that every character can have in a story is to affect the alliance/ownership state of an object (where the object could possibly be another character.

What do I mean by the alliance/ownership state of an object? Well, here are a bunch of examples: The protagonist wants to acquire the treasure. The antagonist wants to own the protagonist. The protagonist wants to stop being enemies (the negative version of being allied) with the antagonist, either by removing the antagonist's ownership of threatening weapons or by removing the antagonist's existence as an enemy by killing him. The protagonist and antagonist struggle over the ownership of a powerful foozle, or the rulership (ownership) of the kingdom, or the love of (alliance with) the princess.

So, the essential quality of every character and other object in our game is its relationships of ownership/alliance with any of the other objects in the game. And the plot of our game's story is the pattern of change in these relationships of ownership/alliance. A pattern of plot is like a sentence structure with different grammatical slots where you plug in nouns and verbs and things. Thus we can generate the characters and objects with which to initially populate the level of our game by analyzing our plot pattern to find out what slots we need to fill, and analyzing the theme we desire to convey to find out what details each object filling each slot should have.

To embellish what I wrote earlier: There are a lot of "maps" in games, that is the concept of mapping is applied in many places and many different ways - height maps, light maps, shadow maps. Perhaps social maps could be applied in a manner similar to light related maps as it could be said that reality is "bathed" in the social in a manner similar to the way that light "bathes" reality. Perhaps the social map would be crafted to change dynamically rather than remain static, but this change would be gradual rather than rapidly, perhaps like a slow moving wave.

I'll have to take some time to consider your response and the content of that link before responding to it. It just seems to me that "political" describes an allegiance to a larger group rather than say the family (not necessarily a nuclear family) and that these more intimate bonds have the potential to produce more powerful stories, stories that resonate somewhat organically. On the other hand, allegiances to larger groups, in so far as it requires an effort to construct them, might be considered more vulnerable to disruption and thus more fruitful for story telling.

Also, in case you missed it, I added some remarks to Plot III too.

I'm taking a look at these links and they are tangentially relevant to what I mean by 'dream logic' or 'social calculus'. In the last link in that list, it says:

Quote: [Searle's] ontology of social reality thus rests on four components:
1. certain physical objects

2. certain cognitive acts or states in virtue of which such physical objects acquire certain special sorts of functions

3. these functions themselves

4. contexts in which the given cognitive acts or states are effective.

What I am interested in here is point two, or more specifically the logic according to which functions are evaluated as 'appropriate' to be assigned to particular objects. Or to phrase it a different way, our subconscious evaluation of what behavior is 'appropriately' expected from a particular object. What I am looking for is a theory of psychology/sociology, not ontology.

Quote: Original post by Trapper Zoid
...since the author is completely in control of the whims of Lady Luck, maybe calling it something like thematic desirability would be better than probability...

Oooh, nice pharase! I'm gonna steal that, hope you don't mind. [wink]

That makes things nice and orderly: 'dream logic/social calculus' tells us what results are possible in any interaction between two vectors, then thematic desireability is a calculation of which of these results is preferable in that it will contribute the most to the soud construction of the story and clear, efficient conveyance of the story's meme. [smile]