It’s Triangles all the way down.

I learned something incredibly fascinating today and I have to write about it.

I was in a conversation with one dear friend and several other people, mostly strangers or people I had interacted with minimally on Twitter but was very interested in (future friends‽) . The seed for the discussion was an episode of RadioLab called “Lost & Found in which various interesting stories about how humans and animals find their ways around in three dimensional space. In the episode, author Jonah Lehrer discusses the fascinating fact that humans and many other types of animals have a specialized type of neuron in their brains called a “grid cell” that “stores and integrates information about location, position, and direction” to help animals understand their position in space and navigate. They're called grid cells because they have periodically spaced triangular firing fields. Some sources say it they fire on a hexagonal grid, but a regular hexagon is just a six pack of equilateral triangles so it doesn't really matter for my purposes.

I have always been interested in “tiling problems” and I already knew that there are only five regular polygons that can tile the plane. This is why Hexagons are the shape of choice for so many board games. It made intuitive sense to me that the brain would use triangles to navigate because it is the simplest (fewest number of sides) regular polygon that can tile the plane. It makes sense to subdivide space around us into triangles and address each of them separately as to what's there.

This triggered a memory of an article that I read several years ago about why wild Foxes lead you to treasure in Skyrim. There had been a decade of speculation about this topic, and whether it was an intentional weird little mechanic or whether it even happened at all, and then in 2021 or so one of the developers came forward and clarified what was going on. It turns out that the world of SkyRim is covered in an invisible-to-the-player grid of triangles that the developers call “Navmesh”. This is used by NPCs to navigate the world and to choose how to react to you. Some areas of the map are essentially wide open spaces with not much going on, and so the triangles there are bigger. Some areas are dense with stuff, and so the triangles of the navmesh are smaller because NPCs need to be able to react to things on a more granular scale. In Skyrim, foxes run away from you and try to hide, and they run toward areas with tighter navmesh (more, smaller triangles) because there's more likely to be a place to hide there. Since treasure is also something to interact with, navmesh is also dense around treasure! Badabing, badaboom. Foxes lead you to treasure.

Did the developers at Bethesda explicitly know that this is how mammal brains navigate‽ Or did they just separately happen upon the most elegant solution for mapping creature navigation to a three dimensional space? I don't know. Maybe one of them will see this and tell me!

If you liked this, find me on twitter: @chasews

Sources/other stuff to read/watch:

https://kotaku.com/yes-skyrims-foxes-do-lead-you-to-treasure-sort-of-1847514070#:~:text=But none has ever being,if it ever got spooked

radiolab: https://m.youtube.com/watch?v=Ac6B7bFG8zs&utm_source=substack&utm_medium=email

grid cells: https://www.nature.com/articles/nrn3766