Ok, maybe I’m exaggerating a little, but hear me out for the brief as possible math lesson-
Joseph Fourier developed a method of solving a type of math problem called partial differential equation. The key insight is that any functional form can be approximated by a sum of sines and cosines of every possible frequency of various amplitudes. The answer comes from applying some boundary conditions and sort of seeing what forms could possibly comply to the boundary. Fourier Analysis and the Fast Fourier Transform algorithm are pieces of math that practically allow the rapid communication the modern world relies on.
I’ve been using Sly Flourish’s eight steps from return of the lazy dungeon master for a few years with many different RPG systems- DnD 5e, Shadowdark, OSE, Delta Green, Death in Space, and others. It just struck me yesterday though that the eight steps are similar to solving a boundary value problem.
Step one is to review the characters- this is the boundary condition. The players and the established fiction provide the boundary that the preparation must fit to.
The rest of the steps are the elements needed to improvise a game that extends that fiction and grows the world. NPCs, Treasure, Rumors/ Secrets (the most important bit), scenes, locations- these are all the “frequency space”. By having these pieces prepped, we shape the wave form, the shape, of the next session of our games.
This is mostly a silly analogy, but it does highlight that the steps, the elements we prep for the game, are tunable. Different input from the GM’s side will turn into different output on the table side. We can lean into the prep work that the players interact with the most, and we can use the elements to guide the campaign in certain directions without committing the cardinal sin of GMing- railroading.
I pulled the image for this article from a blog called visualizing math and physics.
Stuff Cam Wrote 