Multiplayer Interactive-Fiction Game-Design Blog

The authoring equation

9 December 2004

by Mike Rozak

A 3D computer graphics image is generated from hundreds of equations and algorithms that simulate how light reflects and refracts off of objects. There are so many equations and algorithms that it's easy to be overwhelmed.

However, computer graphics has a single unifying equation, called "The Rendering Equation". I could write it out, but most people would be afraid of the math, so I'll use words instead. All the rendering equation says is that the colour and brightness of a pixel is determined by the light reflected, refracted, or shined into that pixel by the objects in the scene. The light reflected or refracted by the object (to the pixel), is in turn determined by light reflected, refracted, or shined by other objects in the scene. Repeat as many times as necessary.

One simple equation makes sense of all the 3D graphics buzzwords, such as radiosity, ray tracing, global illumination, etc. The reason why all these buzzwords exist, however, is because the rendering equation is very slow (to draw). The buzzwords are just optimisation techniques whose complexity masks the simplicity underneath.

The authoring equation

In an effort to understand how to write a good story, I read several books about the subject. For the most part, the authors come to the conclusion that stories are about conflict, and provided a few other tidbits of wisdom. When I read game development books, the authors reiterated the same pearl of wisdom, "Stories are about conflicts". The game-development book author would often reverse the logic and conclude, that if stories are about conflict, then conflict results in a story. (I suspect game developers like to reach this conclusion because the it puts a game on a pedestal with Hollywood movies.)

Both of these conclusions are wrong. Stories are not about conflict, although conflict is an a very common technique in stories. And even if stories were about conflict, adding conflict to a game would not necessarily result in a story.

My techie brain came up with a different definition for what makes a good story, one that works on a more fundamental level. It involves three parts:

1. 
   At some point a potential reader must be convinced to read the story. Therefore, the story's plot must be summed up into a few sentences that are good enough to entice the reader to buy the book and begin reading.

   If you look at the back of any book, you'll see a such a summary. For fantasy books, it's usually of the form: "Jelson, an unassuming Frobin, is minding his farm when one day he discovers a magical shoe that changes his world forever. Journey with Jelson as he meets up with the wizard Lootish, and eventually confronts the evil overlord, Kalziban, who a shape-shifter of devious cunning."

   To a potential reader, the proper names are absolutely meaningless, so they may as well be replaced with the variables, X, Y, and Z. Once the names are removed, it's easy to see how little information is conveyed in the summary... The previous summary boils down to "X finds a magical shoe, meets wizard Y, and confronts the shape-shifting evil overlord Z." I could easily replace "shoe" with "M", since the shape of the magic item is irrelevant too.

   Is this enough information to make an informed decision about the book? No.

   With so little information, people's brains do pattern matching against all the other summaries they've seen and conclude, "This is just like story X, but with a shape-shifting bad guy." It is upon this "delta" over previous works of fiction that readers make their choice, along with the author's reputation. If they liked books about X, and they like the idea of a shape-shifting bad guy, they'll buy the book. If they didn't like X or can't see how shape-shifting bad guys makes for a more interesting story it gets put back on the shelf.

   I find this conclusion a bit depressing, but that's the way it generally works. Consequently, a story must be a derivative of other stories the reader has experienced. If it is completely different than anything the potential reader has experienced, the summary won't convey any information at all, and most readers will put the book down. A few will persist, and they may eventually tell their friends, "Try it, you'll like it," but this will produce a very slow ramp-up in book sales.

   
   
2. 
   Once the reader has purchased the book, the narrative must maintain the reader's interest throughout the duration of the book. That's all; one fundamental rule. Conflict is not necessary...

   Conflict doesn't hurt though, along with a number of other literary devices. For a list of some devices, see Evolutionary explanation for entertainment, The attraction of impossibility, and books about how to write stories.

   Basically, a story keeps a reader's interest by introducing a number of characters designed so that the reader will quickly like and/or empathise with them. The characters' narratives are then followed by the story. The narratives are designed to place the characters in interesting situations so that the reader (as their friend) wants to hear what happens. (If the author doesn't manage to make the reader like or empathise with the characters, then the reader won't really care what happens, and won't stay interested.) The interesting situations usually involve conflict, romance, challenges, danger, etc.

   I won't go into any more detail because so much is written about the subject... just don't believe it when the authors say that conflict, or any other technique is a requirement. They're not. What is a requirement is to maintain the reader's interest.

   
   
3. 
   After the reader has finished the story, it's distilled and shelved into long term memory. The long-term memory of the story must be satisfying. If it isn't, the reader won't purchase any more books by the author, and the reader won't recommend the book to friends. An author who doesn't get return readers or recommendations won't do well.

   How does a story produce a good long term memory?

   
   
   1. 
      The first rule is to provide the story promised by the summary in #1, along with the norms of stories such as happy endings. Otherwise, the reader feels cheated.
      
   2. 
      Make sure the story produces memories worth remembering in long-term memory, preferably enjoyable ones. Long term memory tends to remember dangers and unique occurrences.

      For example: I saw Bambi when I was four. The only memories I have of Bambi are his mother's death, the forest fire, thumper talking about wobbly legs, and all of Bambi's friends leaving him to go "twitterfitting" (which I saw as social abandonment). The rest of the movie need not exist as far as my memories are concerned, although if the rest of the movie didn't exist then the scenes that I remember wouldn't be as compelling, and I wouldn't have remembered them.

      Long-term memory also ferrets out inconsistencies and parts of the story that seem to be irrelevant. Consequently, a good story is very tight and all parts of the story are important for the conclusion to be reached. After all, an important part of (artificial) intelligence is identifying what data is erroneous or irrelevant and tossing it out of the training set.
      

   3. 
      Only make the story long enough so that the important scenes have impact, and so the reader feels like he's gotten value for money. A story that's too long will either bore the reader so much they don't finish, or be so boring that all they remember about the story is how bored they were. (How many books that your high-school English teacher assigned only left memories of boredom?)
      

If you look at my three requirements from the right angle, they almost look like a recipe for evolution:

1. 
   An individual animal must be attractive enough to mate. After all, "good looks" are just a biological summary of a creature's DNA.
   
2. 
   An individual animal must survive long enough to breed, just like a story being interesting long enough to get readers to finish it.
   
3. 
   A individual animal must successfully raise its offspring... A story must create good long-term memories that cause readers to buy the author's next book or recommend it to a friend.
   

If the authoring equation is applied to virtual worlds (or any computer games), the following conclusions can be drawn:

1. 
   The "summary rule" causes almost all virtual worlds to become clones of one another since VW summaries must be worded so that users get the impression: "It's like Everquest, but with better graphics and more crafting." A virtual world that cannot be compared to its predecessors so easily may sell in the long run, but at first its sales will be slow.
   
2. 
   A virtual world must keep the player's attention. I have written up several papers with thoughts about this: See Evolutionary explanation for entertainment, The attraction of impossibility, Stop the buffet, Junk food entertainment, Choice, and Choice 2.

   The technique of using choice as a way to keep a player's interest is important to point out because it differentiates virtual worlds (and computer games) from stories, which have no choice. If a game provides no choices, players will (subconsciously) feel like they're reading a story, and a poorly-written one at that. A choice-less game is like chocolate cake without any chocolate in it... it's a let down.

   Not to sound too pessimistic, but a virtual world only needs to maintain a player's interest long enough so that (a) they recommend the world to friends (see below), and (b) they produce such strong social ties within the world that they are reluctant to leave. After that, virtual worlds can get boring, as they often do. Stories, because they are only recommended once they're completed, and because they produce no social ties, must keep a player's interest all the way through.
   

3. 
   A virtual world must also (theoretically) leave a good long-term memory. However, contemporary virtual worlds break my long-term memory rules in interesting ways.

   Because contemporary virtual worlds last so long, approximately 1000 hours, players recommend the world to friends long before they're finished playing. People reading novels rarely recommend them until they have finished with the novel, and if asked about the novel part-way through they'll say, "It's good so far, but I'm not done. Ask me in a few weeks." VW players cannot provide the equivalent reply of, "I'm not done. Ask me in a year."

   The real reason why players recommend VWs to friends before completing them is because they want their friends to be part of the VW, since playing with friends makes the VW experience more enjoyable. (This tendency also provides problems for a 100-hour virtual world, as written up in The anti-MMORPG. A person will probably play a VW one or two weeks before recommending it to friends. It then takes the friends another week or two before they purchase their own copy. By that point, the original player has finished 40-80 hours of content. If the content is only 100 hours long, there won't be much point recommending the VW to friends.)

   A VW author wouldn't want players reviewing the VW when they're finished with it anyway... because virtual worlds have no endings, players usually stick with them until long after they get bored, which means one of their long-term memories of the VW experience is that it was boring. Players often whinge that "Virtual world X was great when I started, but then the player base changed and became full of idiots, and the live team ruined it by adding feature Y." (Usually in more graphic terminology.) Did the player really leave because of these changes, or because they became bored, and the changes are used to rationalise their decision?

   
   

My analysis about what makes a good story or virtual world seems a bit mercenary. I'm basically saying a good story or VW is one that manages to attract readers/players, and keep them interested long enough to form strong memories so they'll recommend the story/player to their friends.

The concept has evolutionary similarities and ties into memes, which are viral ideas. Stories and virtual worlds are just very-long viral ideas.