There's also a lot of analogising of this to visual/spatial reasoning, even to the point of talking about "visual illusions", when its clearly a counting task as the title says.

It makes it tedious to figure out what they actually did (which sounds interesting) when it's couched in such terms and presented in such an LLMified style.

They study it because it already has a known solution.

The point is to see how LLMs implement algorithms internally, starting with this simple easily understood algorithm.

The analogy stems from the notion that neural nets are "grown" rather than "engineered". Chris Olah has an old, but good post with some specific examples: https://colah.github.io/notes/bio-analogies/

In this case the analogy is quite insightful. If you dig into it, those "boundary cells" are indeed very similar to their feature neurons, and particularly so as a self-emerging feature in the model. As such, they can shortcut the feature or replace it with a more efficient algorithm artificially or otherwise train those neurons in isolation to achieve a more crystallised or "clear-headed" version of the model much like people brains can improve cell specialisation with learning and reinforcement.