Something about plot in general, and one work in particular;

An episode is one configuration of the variables that define a plot.

These variables are:

• Subject – let’s call it S. Its coefficient, which we’ll call α, has two values:

+ indicating that the subject of the episode is the Hero, - that the subject is (an)other

• Transitivity – T. Its coeffieient, which we’ll call β, also has two values:

+ indicating that the action of the episode is Affect, - that it is Effect

• Cost – C. Its coefficient, γ, has two values:

+ indicating that the cost of the action is borne by the Hero, - that it is borne by (an)other

If α_n, β_n and γ_n are the values of these three variables in episode n, then α_n+1 is defined as -α_n, β_n+1 is defined as -α_nβ_n, while if α_n = β_n,  γ_n+1 = -βγ_n and γ_n otherwise.

This gives us eight ordered configurations of the three variables, which are set out below, beginning for convenience with the configuration in which all variables have the value - (the ninth configuration in order would be the same as the first, the tenth the same as the second, and so on, so any starting point will produce the same eight possibilities in the same cyclically repeating order).

α	β	γ	(Lacanian equivalent)	My names for these episodes
-	-	-	$	the wilderness
+	-	-	—	the easy task
-	+	-	S1	the city
+	+	-	→	the easy journey
-	-	+	S2	the new place
+	-	+	—	the difficult task
-	+	+	a	the garden
+	+	+	←	the difficult journey

I’m not going to discuss the homology of this schema with Lacan’s Discourse of the Master here, but simply introduce his terms, which can be a convenient shorthand for stages in the narrative.

Let me explicate how this applies on the ground. In the first episode the Subject of the action is Propp's Donor. The effective action is the conferring of power on the Hero (a magical agent, a helper, etc). This power comes from the Donor’s own bounty, and so the Donor bears the cost. We will assume that an episode has a fixed cost, which must fall one way or the other.

In the second episode the Hero as Subject effects a task. The task is easy, or at least facilitated, and so comes as it were cheap to the Hero. The cost must therefore be borne elsewhere.

In the third episode the Subject is Propp’s Villain. The Villain is affected by contest with the Hero, the brunt of which falls on the Villain. Therefore the Villain bears the cost of the encounter.

In the fourth episode the Hero has an easy (or facilitated) journey, so again the cost falls elsewhere. Note that affect for the Hero typically involves a journey, while effect typically involves a task: the Hero’s journeys are often passive or facilitated. Where a journey is on the initiative of the Hero it may count as effect.

In the fifth episode, the King, as Subject, gives information, not power, to the Hero – cheap to the giver and hence the cost is borne by the Hero.

The sixth episode requires the Hero to perform a difficult task: the cost is borne by the Hero.

In the seventh episode the Princess subject is affected, but not overpowered, so the cost belongs to the Hero once again.

Finally, in the eighth episode, the difficult journey is made at the Hero’s cost.

Some obvious equivalences: costly/taxing/burdensome/unwelcome. Cost places demands on the Hero’s resources, means a lot to the Hero, so cost also = meaning.

Easy/facilitated/pleasant, etc. The Princess’s experience in the garden is pleasant for her, meaningful to the Hero.

The episode as sign: it seems to me that we may see S as a rheme, T as a dicent, C as an argument, and the chain of episodes as a chain of semiosis. Accordingly, there is no point in prolonging the chain beyond the eighth term – to do so is to start another narrative. Equally, the audience can be relied on to supply the missing terms of any narrative that is truncated, because the chain is self-generating.

Suppose we apply this to an example: here I’ve chosen The Twins at St Clare’s (Enid Blyton 1941).

We begin with episode 8 – the difficult journey. Pat and Isabel O’Sullivan are dispatched much against their will to a new school (affect/undergoing). when they arrive they face hostility/criticism from some of their schoolfellows (Janet) and teachers (Mam’zelle).

The next episode is three times repeated: Kathleen volunteers to show Isabel how to clean the boots of the Sports Captain, Belinda Towers, Mam’zelle volunteers to give the twins extra coaching in French, Belinda selects Pat for the lacrosse team even though Pat has broken bounds by pretending to be her twin.

The easy task is overtly fulfilled by Isabel's success in cleaning boots and lighting Belinda’s fire and impliedly by the facilitation of the twins’ French studies and Pat’s play in the team.

The episode of the city is also three-branched. Here the first form, to which the twins belong, is initially the Villain, playing tricks on the ineffectual Miss Kennedy. Pat and Isabel (who have not directly instigated the pranks) nevertheless lead the class in owning up (thus conquering themselves as it were). Later they organise a mass apology to Miss Kennedy when they find she is teaching to support her ailing mother. In between these two instances of general self-reproof is Kathleen’s confession that she is a thief, and her acceptance by her classmates (the poor girl was driven to it by not having enough pocket money). In each case we see the cost of righteousness exacted from the transgressor.

Pat, Isabel, Janet and Kathleen sneak out to the circus – this is the easy journey. The cost is borne by the others, who have been unjustly gated in punishment for a broken window.

Then we have a quarrel between Janet and Sheila, a girl desperate to conceal her humble origins. These are revealed to the twins by Winifred, the Head Girl – information they are burdened with, because it behoves them to be understanding. But the unmasking is not confined to Sheila: Janet is revealed to be magnanimous (getting Sheila the job of prompter in the class production which leads her to inherit the main part when the girl playing it falls ill) and Kathleen is revealed as an animal-lover, rescuing an injured dog that the girls find when on a walk.

This episode is clearly parallel to the 'makeover' episode of reality shows, which have an analogous episodic structure.

Then we have the difficult task: Isabel accidentally sees the geography paper the night before the exam. What is she to do? She resolves to fail deliberately, but is reprieved when it turns out that the paper she saw was intended for the second form.

And then finally, the garden. The school concert is a success, the end of term arrives, the twins sing the praises of St Clare’s. Which is, of course, the Princess, and now means everything to the girls.

It’s a romance, in short, and one that very well exemplifies how a plot begins at one place and develops to a conclusion just short of its starting point (which is where we will pick up in The O’Sullivan Twins, the next book in the series. And that, as they say, is another story.