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The Mathematics of Fiction

The Story Cube

Recall that a story is composed of matter and form.  The matter is what the story is about; the form is the style in which it is written.  The two are in the physical world inseparable: "Every thing is some thing."  So no matter what the story is about, it must be written in a certain genre, style of writing, length, etc.  In fact, the kind of story may influence the style of writing; and vice versa.  We cannot imagine James Thurber, in his usual voice, writing Moby Dick.  A comic essay wants a different style than a tragic novel. 

But let's take a look at the story matter: a story has four dimensions. 
  1. Theme, or Ideal.  This is the Prime Matter.  It is what the story is about, the point it is trying to make.  For example, the idea behind Huckleberry Finn is a indictment of slavery.  Ideas need not be profound (unless you envision people reading your novel or story a hundred years from now).  From Here to Eternity: "how life in a peacetime army degrades character."  Madame Bovary: "the life of a physician's wife in a small French village, whose adultery, extravagance, and self-indulgence drive her to suicide."  And so on.  A novel may develop more than one idea:  To Kill a Mockingbird is the story of a child's love for her father growing up in a motherless home and it is a story about racial intolerance.  The idea behind The January Dancer was merely the search for a powerful object and how it affects the various people who seek it.  Up Jim River had two ideas: the search of Mearana for her mother and Donovan's search for himself. 
  2. Character.  These are who the story is about, typically someone whom the Idea hurts in some way, at the very least by knocking him out of his accustomed rut.  Ishmael is bored with life on land, and so signs on to the Pequod to go a-whaling.  In The Grapes of Wrath, the main character is plural: the Joad Family comes into conflict with their environment because the environment changes: the Dust Bowl.  
  3. Setting, or Environment.  This is the world or milieu in which the story is set.  In some stories, the setting itself becomes a character, as does Middle Earth in The Lord of the Rings, or New York City in the Matthew Scudder stories of Lawrence Block.  But the setting is more than simply a) the physical setting(s).  It also includes the "social, moral, and cultural" interactions within each physical setting, which might be called b) the "generalized significance."  The world of Left Hand of Darkeness is more than just a planet certain characteristics; Middle Earth is chock full of different cultures and mores with which the collective protagonist must contend.  But the third aspect of Setting is c) the atmosphere, or emotional setting, what we might call "the mood."  The Shire is not just a place; neither is Mordor or Lothlorien. 
  4. Events, or Plot.  The plot is a sequence of causally related events, arranged in such a way as to give the story continuity, pace, and "thematic significance" (that is, signify the theme or idea behind the story).  There are two basic kinds of narratives: a) plot, properly speaking, which is a story about accomplishing (or failing to accomplish) a goal; and b) story line, which is a story in which the character of the protagonist is altered by the events of the plot.  This is not the same as #2, above, which is how well realized the characters are.  You may have vivid characters in a humdrum plot; or cardboard characters in a story line. 
For a story to really click, it should score high in all four categories.  Many years ago (in a typewritten letter, that's how many years ago) I showed Nancy Kress a Story Cube I had sketched in a moment of whimsy.  Because drawing a four-dimensional cube on a two-dimensional sheet is contra-indicated, I only drew three of the four.  But the basic idea is simple:

Imagine each dimension of the story as, well, a dimension. 
X. Character Axis.  Runs from stereotyped, cardboard characters up through fully realized 4-dimensional characters.  A character like Nero Wolfe would fall somewhat left of the middle, as he is "characterized" essentially by a set of odd and deliberately distinctive quirks. 
Y. Event/Plot Axis.  I'm not sure "dull" is the right word for the low end of the axis.  Perhaps "hackneyed would have been better; and "ingenious" rather than "page-turner." 
Let's pause.  Nancy Kress replied concerning a then best-seller that "the characters had all the depth of wallpaper, but I couldn't stop turning the pages."  Considering only the Characters and the Plot, it is certainly conceivable that a story could succeed with an engrossing plot while having merely adequate characters.  Similarly, a story could succeed with fascinating characters and only an adequate plot.  Fans of Sci-Fi often complain about literary fiction because "nothing happens."  Fans of Lit-Fi often complain about science fiction because the characters don't seem to develop.  But it's really that one genre is further out one axis and the other is further out a second axis.  A reader once complained to me that I spent too much time developing characters; he only wanted "the content," that is, a narrative of the plot events.  Just tell me what happens, not what sort of childhood the protagonist had. 
Z. Setting Axis.  At one end is the dreaded "white room," iow, a generic setting, not well described.  It is a world where a dog is only a dog and not a snarling Doberman; and a chair is only a chair and not an upholstered wing-back chair.  At the other end is a setting so well described that the reader thinks he is in it.  It is not simply the Doberman snarling in the wing-back chair, but the generalized significance and the emotional mood of the setting.  The homeowner indulges his dogs, and that is his chair, and he is warning you off.  Or the dogs have all gone mad and the Doberman has eaten the homeowner and has now taken his seat.  It could be a comic scene or a scene of terror.  Now we are at the far-end of the Setting axis. 

Idea/Theme Axis (not shown).  The continuum here runs from shallow to deep, or something of that sort.  Sometimes, we're only looking for light entertainment; other times for something that will grip us and make us think.  As with the other axes, a story may succeed with a pedestrian or repetitive idea - Sherlock solves yet another case - provided the events that accomplish this are ingeniously arranged, and Sherlock is a convincing character. 

The Pot-boiler Barrier.  Down in the corner is a quarter-sphere below which we have cardboard characters in a white room pursue a humdrum plot in pursuit of a fatuous idea.  These are sometimes called "best sellers."  (No!  Smack!  Bad Flynn!  Bad!)  Actually, they are called The DaVinci Code.  (Stop that!)  But the idea that you can pursue a fascinating plot with ordinary characters goes only so far down the scale of ordinariness.  There comes a point on the scale where the characters are so badly realized that no amount of plot excitement can save them.  And the same goes for the other Dimensions of Story.

Your Challenge. 
I divided each dimension in the Story Cube into "low" and "high" halves.  This makes eight "rooms" in Story Cube Hotel.  The room numbers are (character, event, setting) and are either 0 (low) or 1 (high).  Don't be confused: it's like a cube plot of a 2^4 factorial experimental design.  (That was supposed to clarify.  The sort of mind that would create the story cube is the sort of mind who would think that would clarify diddly-squat.)  Anyhow, Room 000 is where the Potboiler Barrier is; but let us allow than some books or stories in this octant would not be quite that bad.  Room 010 is the room where characterization is low, plot is high, and setting is low.  And so on. 

Your mission, if you choose to accept it, is to suggest stories to go into various quadrants, SF or otherwise.  What would you put in Room 111 (characterization is high, plot is high, and setting is high)?  What were outstanding on two axes, but only so-so on another? 


( 23 comments — Leave a comment )
Jul. 16th, 2011 09:50 pm (UTC)
I think its form has to start with the medium in which it is told. Even in ancient times there were plays as well as epic poems.
Jul. 16th, 2011 10:32 pm (UTC)
"It is a world where a dog is only a dog and not a snarling Doberman; and a chair is only a chair and not an upholstered wing-back chair."

As a reader, I have the opposite problem quite often; the author insists on larding in details that I just don't care about. It happens mostly when talking about guns (I know nothing about them) and makes me eyes glaze over; after a page and a half of fervent description of exactly how big a hole the thing can blow in you how fast, often and many, I come away with just the general notion that Character A Has A Big Gun.

But it drives me wild when describing clothing; I don't care about labels or fashion, so I really am not interested if "Mark wore a vintage Galliano button-down twill side-vented 396 thread-count south-facing terrace grown Egyptian cotton full-jacket shirt in the Spring Pine Forest shade from the limited edition Milan collection of Fall 93" - I go "Mark was wearing a green cotton shirt. You couldn't have said that?" Okay, if it's an important plot point (e.g. Mark works on the bin lorries, how the hell can he afford couture), then I will stand it, but nine times out of ten it's extraneous detail that is just showing off the author's knowledge of (insert subject from wine to stamps) and has no relevance.

Sometimes I just like my dogs to be mongrels, yes?
Jul. 16th, 2011 10:46 pm (UTC)
And there's often the little question of whether the POV character would notice the detail.
Jul. 20th, 2011 03:09 am (UTC)
Tolkien deliberately tried to make his descriptions generic so that we would each see, for example, our own favorite hill or our own beloved forest.
Jul. 20th, 2011 04:03 am (UTC)
Did Tolkien say so? That sounds like something Lewis might have done in Narnia.

It's traditional for folktales to describe people and castles etc simply as "beautiful" so we can each make our own details. Baum did that at great length in Oz, and istr the same sort of thing ("spoor" etc) in Tarzan.

But there are many hills in LOTR and they all seem different to me.
Jul. 16th, 2011 10:36 pm (UTC)
What coordinates would you give ALICE IN WONDERLAND and GULLIVER'S TRAVELS? Lewis said they both needed very commonplace main characters, because an odd person in an odd place would be an oddity too many.
Jul. 16th, 2011 10:51 pm (UTC)
Is character development measured by the oddity of the characters?
Jul. 17th, 2011 06:47 am (UTC)
Even with the ordinary Alice and Gulliver, too much attention to the details of their character would be a distraction from Wonderland or Lilliput. As, imo, the details of movie Dorothy's family problem was a distraction from Oz.

Of course there's the genre where the odd place is just a sort of projection of the character's, er, character and problems (movie Oz, and Sendak, and probably Donaldson).
Jul. 20th, 2011 03:05 am (UTC)
Animal Farm
Good point! And in a satire like Animal Farm, the characters MUST be flat and static; otherwise, the allegory is overshadowed by irrelevant character development.
Jul. 20th, 2011 03:07 am (UTC)
Re: Animal Farm
So it comes down to the "kind" or genre and the elements proper to the genre in which the author is working.
Jul. 20th, 2011 09:18 am (UTC)
Re: Animal Farm
For that matter, going deeper into the characters in LOTR would have detracted from the larger picture.
Jul. 16th, 2011 10:43 pm (UTC)
I would say that To Kill A Mockingbird was a bildungsroman about learning how to appropriate treat other people.
Jul. 17th, 2011 01:44 am (UTC)
I would put Tim Powers' Declare in Room 111.
Jul. 17th, 2011 08:55 am (UTC)
000 -- zilch character, plot, setting: Da Vinci Code
100 -- mostly character: Godstalk. (The setting gets much more interesting in the later books)
010 -- mostly plot: typical Agatha Christie mystery
001 -- mostly setting: Ringworld. Rendezvous with Rama
101 -- zilch plot: The Dervish House; Look Homeward Angel
110 -- zilch setting: ... still thinking...
011 -- zilch character: the best of books set in a TV/movie franchise; the main characters can't change
111 -- good all: Lord of the Rings
Jul. 17th, 2011 08:34 am (UTC)
The Mathematics of Fiction - The Story Cube
Jul. 17th, 2011 05:48 pm (UTC)
It has come to me that I suddenly, desperately, want to read Moby Dick written in the style of James Thurber.

("Moral: The one that got away just keeps getting bigger.")
Jul. 18th, 2011 12:19 pm (UTC)
Scene: Bedroom of inn, where Queequeg and Ishmael are sharing a bed

"All right, have it your way - you heard a white whale!"
Jul. 17th, 2011 05:53 pm (UTC)
After thinking about this, I think I'm fairly stingy about what I'd count as genuinely 111; it's really Jane Austen and Charles Dickens territory. In classic science fiction, I think Jules Verne's very best works perhaps make it to 111, as does Shelley's Frankenstein; possibly Stapledon's Sirius, and maybe Miller's A Canticle for Leibowitz. Perhaps a tiny handful of others. But most of the best science fiction seems to me to fall simply into a box with 1 somewhere in it, and mostly into 001 and 011. Which is still good, of course; the difficulties of getting out of Room 000 at all are not to be underestimated. Most authorial geniuses are so simply because they can consistently guarantee a 1 along one of the axes. Jules Verne's awesomeness was the ability to write consistent 011 (the richness of his settings is usually muted in the older English translations; in the French they are often almost overwhelming -- lush and colorful, with extraordinarily intricate detail).

It's tricky though. Someone who is really good at setting can give the illusion of deep characterization, for instance. Put a flat character against the right sort of rich background and you'll get the illusion of depth. Frank Herbert and James Blish come to mind; the most striking things about their most striking characters are all just things inherited from the scenery, but the scenery's so splendid you often don't really notice how much of the characterization really is just vague association with sandworms or flying cities. And so it is with others: if you are really good at one, there's a kind of spill-over effect for readers (these characters must be cool to be in such an awesome story; or, this character is so amazing that a story about him reading the phonebook would seem gripping).
Jul. 17th, 2011 08:01 pm (UTC)
Now that got me thinking about the use of projective geometry in fiction; but alas, that is one of the textbooks I failed to keep.
Andrew Brew
Jul. 18th, 2011 11:33 pm (UTC)
I commented in the wrong place, didn't I?
I responded on Blogspot, but it's lonely over there...

This is what I said

In room 111, LOTR, obviously. I don't need to explain why, do I?
Also in this room:
Ursula Le Guin's Earthsea (first three only - the later books I would score differently)
C.S. Lewis Until We Have Faces

As for others, and free-associating as I go along...
011 John c. Wright, Golden Age (I have read the first two - still have to get the third)
001 Olaf Stapledon, Starmaker
Whoops - Free-association dead end. Start again
010 Rider Haggard, King Solomon's Mines
101 Nikolai Gogol, Taras Bulba
100 Barry Longyear, Enemy Mine
110 Fascinating characters, compelling plot, dull wallpaper. Dunno
000 I wont say I don't go there, but there are a million of them.

For the purpose of the exercise, I am shoehorning the Theme/Idea axis in as parallel with the setting axis - Starmaker, for example, has a setting only remarkable for its gradiosity, but since it is expressing an idea equally grandiose - albeit to me repugnant- I give the combination a high score on that axis.
Jul. 19th, 2011 02:59 am (UTC)
Re: I commented in the wrong place, didn't I?
It does seem to get less traffic than this place. Don't know why. Some of the same people are on both places.
Jul. 19th, 2011 12:18 pm (UTC)
I don't mean it as an unfair or negative comparison, but the first thing I thought of when I saw your story cube was the "diagramming" of poetry from Dead Poets Society.
Jul. 20th, 2011 02:24 pm (UTC)
I enter the coveted corner of the Writer’s Hypercube!
( 23 comments — Leave a comment )


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