Fermat, Huygens-Fresnel, plot structure, and roleplaying


You might recall from Ted Chiang’s beautiful story “Story of your Life”, or from the movie Arrival that was based on it, that one of the ways of formulating the laws of optics is Fermat’s Principle of Least Time, which states that the a beam of light gets where-ever it is going in the least¹ possible time, taking into account the speed of light at the different places it might go through. The protagonist of the story took it as a profound insight that for a photon to travel in the direct direction from the beginning of its course, the end-point of the course must be determined at the outset. The story also featured the most extreme version of the Sapphir-Whorf Hypothesis ever seen in the wild.

However, you might also recall from high school physics the Huygens-Fresnel Principle, which shows you how to derive all the laws of optics—the law of reflection, the law of refraction, and even the law that light travels in a straight line—simply by treating every point on the wavefront as a source of spherically-propagating wavelets that interfere with each other. One way to consider that is as a demonstration of the wave-particle duality of light. That is not the bomb. In my opinion the bomb is that Fresnel’s Principle of Least Time and the Huygens-Fresnel Principle are provably equivalent. They can never produce discrepant predictions. Indeed, you can prove that the Huygens-Fresnel Principle implies Fermat’s Principle. They are equivalent descriptions of the same physics, though one requires a photon to know its destination and every possible course through space, whereas the other only requires the photon to know, at and for each instant, its energy and the speed of light in each direction in its immediate vicinity.

I think that plotting an RPG is like that.

It is fashionable now, though perhaps not new, to take lessons for RPGs from literary criticism. Literary critics are used to judging a work in its post facto entirety: planned, drafted, revised. They admire the gracefully structured plot, complete and elegant. They disparage the signs of a writer making it up as he or she writes, when they recognise them². They recommend planning to avoid them and revising to eliminate them. The problem in applying their advice to role-playing, the reason that I think that a lot of modern GMing advice and game design is misguided, is that I think that improvisation in the moment is the essential heart of role-playing, and that to cut it out (in an attempt to emulate products in a fundamentally different form of story-telling) risks ruin.

Back in, umm, 1992 one of my players (@gisborne, it was) lent me a copy of James N. Frey’s How to Write a Damned Good Novel, from which I (a) figured out what my English teachers had been supposed to teach me ten years and more before, and (2) learned an incomplete but useful collection of rules for good storytelling that can be applied locally, without having to know what the plot is and what the conclusion will be. You can see that those would be useful in improvising stories.

Agreeing with Our Roger that there are forms and techniques for roleplaying that are different from those most suitable to planned and revised forms, I call for the Huygens-Fresnel version of the laws of good writing.

¹ If you learned about Fermat’s Principle in first year (freshman) physics class, as I did, you would know that that is bit of a simplification; the principle is that the beam of light gets wherever it ends up at in stationary time, which means that there are other courses not taken, very close to the course taken, which would have taken only a very tiny bit longer. The differential of time taken with respect to course is zero exactly at the course taken: which is the condition for a local minimum or a local maximum (or an inflexion, for that matter).

² When my father was an inmate of an expensive institution for unwanted children (as he described it) his English teacher told his class that they must plan their essays and other compositions, that all great writers write to a plan. It being one of Those schools one of the boys wrote to every living great English writer then recognised, to ask whether he wrote to a plan. Only Somerset Maugham answered, and he said that writing to a plan is excellent advice that his correspondent would do well to follow, but that to be frank he didn’t do it himself.


Defining the differences of the form is where I usually founder: I feel that going back and changing something that’s “happened” is an extreme measure and should be avoided if at all possible, while @MichaelCule regards it as rather more acceptable.


That’s kind of implicit in my theory of RPGs as a literary form, as hinted at in GURPS Adaptations. I think that we play until we reach a point of resolution, and then we look backward and see a story that emerged from a lot of thrashing around. And sometimes the emergence is the important step. RPGs just put the emergence up front, where the audience can see it because they’re taking part in it.


Back in the early nineties, on <rec.games.frp.advocacy>, my formulation used to be that RPGs differ from other forms variously as being

  • co-operative,
  • collaborative,
  • improvisatory, and
  • participative.

But now that we have Critical Role I suppose I’m proven wrong.


I think it is possible o do a little better than thrash around, and give yourself a chance for something that feels like a story while you are doing it.


What kind of timescale are you talking on here? Do you expect to see “resolution” in this sense several times a session, once a session, once in a number of sessions, or at the end of a campaign?

Because I’m expecting all of those, in a nested manner. The multiple-per-session resolutions are individual activities: in my current campaign, usually a conversation, an agreement, or a fight. One-a-session is an attempt to end the session on a resolution, or in a place where a resolution is forthcoming, but giving the players a chance to think more about it looks worthwhile. A resolution to a set of sessions is a plot arc, and the end of the campaign may be some vast final accomplishment, or it may be simply the feeling that “we’d like to play something else now.”


I’m with you, although I may later realise that an event was more significant than it seemed at the time. But characters also do that.


That varies from campaign to campaign. Some of my campaigns are structured like classic Star Trek, with each episode standing on its own (though “episode” may be longer than one session). Some are structured like novels, with a continuing development from start to end. There are also intermediate cases.


On one hand, yes. But on the other hand, it’s nearly impossible for a campaign to be as tightly plotted as a novel or a movie can be. The primary writer doesn’t know what the co-writers are going to come up with. “No plan of battle survives contact with the enemy.”


It’s nearly impossible for a campaign to be as tightly plotted as a novel or a movie can be. But its quite possible to be perceptibly well plotted, and a few times I have run sessions that were more tightly plotted than typical mass-market hackwork.

Right, but having a plan of battle is the Fermat-Principle approach to plotting. A Huygens-Fresnel GM deals in conflict, situation, steadily rising tension, steadfast characters, and half-premise instead of step-sheet and finished premise. He makes his plans of rope and when anything breaks he ties a knot. He lowers his spyglass and shouts "By God! I think that will do!"¹

¹ Sir John Monash was a great general, but so was the Duke of Wellington.


Certainly – I’ll name names here, because I’ve said it before in public – I think that the Robin Laws’ approach exemplified in Hamlet’s Hit Points (which, I’ve recently realised, was done before by Mike Pondsmith in Dream Park) is misguided for the sort of RPGs I like.

What it will produce is RPGs that work like other forms of storytelling, in the sense that you get the story shapes which occur there. If I were designing an RPG for Firefly or Star Wars or anything else reasonably well-known, I might well include something like that, because people are presumably picking up that RPG because they like the original, and it will get you the sort of story that occurs in the original.

(Side note: to what extent is “we all go down a dungeon, get hurt and rich, then spend the money on magic and ale and do it again next week” now a defined story shape that people expect to happen in a dungeon-bash game?)

But my version of @Agemegos’ original question is: what is a story shape that is native to RPGs?

I think @JGD’s nested resolutions may be a part of it. It certainly involves focus on the small; a game may pull back from boring bits like uneventful travel, but a fantasy novel will rarely describe each sword blow in minor battles, and even a film will generally not show you whether each shot hits or misses. (Some games do pull back, but nobody will be surprised if it doesn’t.) Playing the mechanics to stay alive in a fight is an enjoyable activity in itself, while not being the only thing one wants to do or (for me) even the main thing; one might regard it as the equivalent of a mini-game.

RPGs typically have a band of heroes, but in other story forms almost always there are one or two leads. There are exceptions, but they’re noteworthy. The 2003 remake of The Italian Job (which, yes, absolutely didn’t need to be remade, but was quite enjoyable even so) managed this by employing the rather dull (if pretty to look at) Mark Wahlberg in the lead, under-writing both his and Charlize Theron’s parts, and getting much more interesting actors in the secondary roles. But consider something like Leverage, which is a great deal more like RPGs than most linear media: it very definitely has two leads and three supporters. The supporters get their own storylines and important moments, sure, but the focus is on the leader. Similarly, Mission Impossible (another show conceptually close to the sort of RPG I like) has the guy in charge and the people working for him. Some games have characters who end up being more interesting than others, but that’s certainly not something that one sets out to do.

(In my 1960s psionics game, the telepath and clairvoyant ended up having much more to do than the others, in part because my usual style of game is largely about information-gathering.)


It is possible, of course, to run an RPG with one player and one protagonist. I’ve done it a few times, though not any time lately. But I agree that that’s not the center of gravity of RPGs as a literary form.


Sure. But my standard of comparison isn’t mass market forgettable entertainment; it’s skilled work in a given form.

I think that’s what I mean by “thrashing around.”

In a Fermat approach, you see the exact least-time path, and everything points at it. But in an H-F apprach, as I experience that in gaming, you have some guns on mantels that will never be fired. There’s kind of a statistical hunting round the final path, with tentative movements that will be abandoned, and negotiations over what the actual “story” is, all of which are visible to the audience because they’re participants in those negotiations. It’s as if you don’t see only the real photon but a haze of virtual photons.


I think these differences point to why game session recordings are a minority form of entertainment compared with other linear media. When I’m watching or listening to a recording I’m engaging my gaming skills: here’s how the GM is getting this effect, how the players are failing to spot that, how each side is reacting to the other’s hints about what they want, and so on. To a non-gamer I suspect it would feel like amateur drama.


Perhaps I err in that, for me, “thrashing around” suggests a person in a grand mal seizure.

I think have run at least four one-shot games and a least one adventure in a long campaign in which there were no guns not fired, no tentative movements. Perhaps it is the golden haze of memory, perhaps they all date from my most manipulative period as a GM. But I think improv can be deft and sure, and dare aspire. There are sometimes jams in which nobody fluffs. They are rare perhaps, but it’s worth trying each time not to fluff this time.


Ah, we have a terminology problem. “Thrashing around,” to me in an RPG context, implies something very disorderly, with different people trying to work on quite different stories, or none at all.


If we’re talking about single sessions, I’ve had those too. I remember, for example, my Buffyverse campaign where the Slayer of Alta California in 1810, her half-demon best friend, and the handsome army lieutenant both of them were interested in, making a journey back from San Francisco to Boca del Infierno, stayed overnight in a grove of trees where the Roman god Cupid had taken up residence, and all got zapped with his enchanted arrows. It was a brilliant comedic storyline, about 90% of which was due to the acting of the three players.

But I was thinking more in terms of lasting campaigns, and of some episodes in such campaigns being less perfect than others. When I ran the episode above, it was in one of the campaigns of my best cycle ever: Boca del Infierno (vampire slaying in Alta California, or “Buffy meets Zorro”), Manse (an isolated castle in the midst of a magically chaotic wilderness, controlled by five clans of aristocratic sorcerers), and Whispers (my first Transhuman Space campaign, focused on a private investigative firm). Seriously, looking back, I think that was the high point of my GMing. But all three campaigns had things that I would have edited out if I were turning them into a book or a television series. I don’t think that was because I was an inept GM; I think it was because RPGs are collaborative storytelling, and there are likely to be coordination problems.


Sure, but on the other hand TV series and even miniseries without dud episodes, comic series without dud issues, and so on are a lot rarer than movies and short stories without plot defects.

When I was at the top of my game as a GM¹ I used to reckon that I GMed at about one third the speed of AV storytelling. One of my 4–5 hour sessions was had just a little less happen in it than in a 90–110-minute movie in the same genre. And movies go at about a minute per page of text. So a 170-page Vance novel like City of the Chasch is about two sessions of play. The “Demon Princes” series is material for only a semester of weekly sessions.

I love The Three Musketeers. It is great, a classic. I love the “Sherlock Holmes” canon too. But you can bet your arse there are bits I’d take a blue pencil to.

¹ And, not to hog the credit, when I had a group of pretty damned good players.


I can’t lay hands on my copy of Frey’s How to Write a Damned Good Novel. I think I lent it to my niece when she was studying English for her higher school certificate, which was five years ago. Anyway, I don’t have it to hand to refresh my memory, so the following is going to be a bit incomplete and haphazard.

Frey used a formulation of theme (which he called “premise”) that it should be X + Y ⇒ Z, where usually X and Y are something about the protagonist and something about the situation, and Z is the resolution of the novel. For example, the theme of Romeo & Juliet might be expressed as “love + family feud ⇒ disaster”. Bits that show that there is love and that there is a family feud, and showing their combination leading to a disaster are part of the story an are in. Bits that don’t shoe them leading there are not part of the story and are out. Anything that shows something else other than love and family feud causing the disaster undermine the theme and are faults. Now, I don’t think you can start out having settled on such a theme in an extemporary collaborative participative form. You might put it over on an audience. But when the writers are the audience they have to feel that X + Y is not really ⇒ing to Z, it is being forced at the Doylist level and not happening naturally at the Watsonian level and the “proof” doesn’t feel convincing. But what you can do is play to find out what happens. Start with X + Y and_make sure that everything that happens follows from X + Y_. Z emerges from the improv, and you have a theme. A theme, that is, that you discovered during play as an audience discovers the theme of a play while watching, of a book while reading. I refer to “X+Y” as a “half-plot”, but there has got to be a better term.

In a dramatic novel, Frey advises, it is best to establish the status quo before introducing the initiating incident. That’s so that the audience know the protagonist, know who this is happening to. This can be rather different in RPG. If character-players are going to develop-in-play then you need a bit of prefatory adventure-like material for those players to start knowing their characters, which is a form of Frey’s “establish the status quo”. If they do develop-at-start but each independently, I think you need a bit of such material for each player to present his or her character to the others. If your group does extensive “session zero” communication and collaboration on character design then I think that develops the status quo and the actual play ought to start with the initiating incident. Emulating the parts of work in another form in which the status quo is established in the eyes of the audience is not called for.

Like the characters of a dramatic (or procedural) novel, protagonists and antagonists need a strong core of consistency. If a character is inconsistent, and an unexplained aberration of behaviour determines the outcome of a scene, then the causal chain through the plot is broken at that point. Things happening afterwards are not caused by things happening before.

Now, a dramatic character will change at some point. That will be the crisis of the drama, and the change will be the “character development” that my English teachers wittered about without explaining it properly. Anyway, that change in behaviour will not be unexplained. It will be explained by the events of the plot and the pressure that the character is put under, and it will lead to the resolution of the conflict. It is not evidence against the need for a strong core of consistency.

Frey’s book is about writing dramatic novels, not procedurals. He was describing dynamic characters, not iconic characters. Procedurals are less acceptable to literary snobs, and perhaps the analysis wasn’t available then. Anyway, the strong core of consistency for an iconic character is his or her heroic ethos, or schtick. Unlike the dynamic character in a dramatic story, the iconic character in a procedural story doesn’t resolve the conflict by developing. She or he resolves it by demonstrating the power of her or his schtick to mend disorders in the universe.

Players have to know whether to expect drama or procedure. They have to generate characters with the appropriate core of consistency. And then they have to stick to it right up to breaking point.

Characters — meaning player characters and significant NPCs — have to avoid two opposite faults: anticlimax and jumping conflict. The conflict should rise steadily until it forces a resolution, in each scene, in each arc, in the plot overall. Jumping conflict is obviously an unmotivated action that breaks the continuity of cause. Anticlimax is less obviously so, but it is the chief cause in RPG of plots wavering and seeming loose and limp. Part of the craft of a collaborative improv storyteller is to keep upping the conflict until it forces a change in the situation. One of Robin Laws’ dramatic scenes may end with the whatsit granting the petition, refusing the petition, or setting a condition for granting the petition, but it never ends in indecision with someone walking away.

One of the important things that prevents characters from just walking away from teh conflict is what Frey calls a “crucible”. The GM has to make sure there is one.

So a few of the techniques that I recommend for generating plot without planning are:

  • generate a character with a strong core of consistency
  • establish an expectation amongst the audience other players about what this character will do
  • react to the situation as is justified by the circumstances, the level of tension, and your character’s appropriate maximum capacity
  • until the conflict in a scene/arc/plot gets resolved, step the tension up, not down, but don’t jump. If you feel that you can’t go higher, break off in a way that resolves the conflict
  • stay consistent to your core of consistency; if in a drama until character development will resolve the conflict.


I’ve heard the core novel plot described roughly as “something bad happens to a good person; they do something about it”.

I think there’s been a shift in role-playing style over the decades. A lot of players who got into it in the early days (which just about includes me) have a tendency to think of the GM as the enemy: any sign of weakness will be pounced on. Oh, your character likes kittens? There’s a kitten over there. You go to pick it up? Har har har five hundred ton weight.

Or the first example in John Wick’s Play Dirty: the superhero character had got points for having an aged grandmother, so the GM set things up to expose her dirty secret in front of said grandmother, who promptly had a heart attack and died. Har har.

So the tendency is to smooth off anything distinctive about the character, to avoid having vulnerabilities; if “nobody could have survived that” then you can shout at the GM, but if you were caught by something specific that counts as a fair kill, or something. But as one makes the transition to the GM and players as storytelling partners, that shifts: as far as I’m concerned, many disadvantages are useful as a tool for explaining PC motivation and adding some sort of personal stake in the adventure, whether that’s because of your Dependent, your Duty, your Hunted, or simply your Greed; they’re hooks by which I can involve the character in the plot, and I’m going to use them to do that, not simply to make your character less fun to play.