Much of the meeting was centered on orientation when moving in 3-space. What is the internal representation and what happens at the “South Pole.”
This has been the topic of research for a long time, and the “hairy ball” problem applies here.
See this post for related information about 3D representation in movement:
Does this look familiar?
Then see this paper in particular regarding turning in 3-space.
By the way, the head direction update rules I use in this model are based on: https://www.physiology.org/doi/abs/10.1152/jn.00501.2017 (The video above was an addendum to the previous meeting, https://www.youtube.com/watch?v=AfszqPfX314, where I started by mentioning this paper.) It’s from the same authors as the paper that @Bitking linked to, but more recent.
Another note: Toward the end of this video I showed the paths that result from following a single head direction cell like a compass. All paths lead into the south pole, and I showed that most paths get stuck there, but this is actually an artifact of the fact that I approximated the path rather than solving it analytically. I think the actual path will make a figure-8 with its crossing point at the south pole.
The author points out that nature has arranged so that the cowlick/singularity is parked in a space where the critter is not likely to encounter in normal behavior.