DanielFilan comments on Unrolling social metacognition: Three levels of meta are not enough.

[DanielFilan]

See this paper arguing that humans have the ability to solve tasks that require up to seven levels of recursive metacognition, especially when those tasks are ecologically valid (i.e. the prompts are films of interactions, and the question is to pick which sentence one of the participants is more likely to say). Abstract:

Recursive mindreading is the ability to embed mental representations inside other mental representations e.g. to hold beliefs about beliefs about beliefs. An advanced ability to entertain recursively embedded mental states is consistent with evolutionary perspectives that emphasise the importance of sociality and social cognition in human evolution: high levels of recursive mindreading are argued to be involved in several distinctive human behaviours and institutions, such as communication, religion, and story-telling. However, despite a wealth of research on first-level mindreading under the term Theory of Mind, the human ability for recursive mindreading is relatively understudied, and existing research on the topic has significant methodological flaws. Here we show experimentally that human recursive mindreading abilities are far more advanced than has previously been shown. Specifically, we show that humans are able to mindread to at least seven levels of embedding, both explicitly, through linguistic description, and implicitly, through observing social interactions. However, our data suggest that mindreading may be easier when stimuli are presented implicitly rather than explicitly. We argue that advanced mindreading abilities are to be expected in an extremely social species such as our own, where the ability to reason about others’ mental states is an essential, ubiquitous and adaptive component of everyday life.

[ETA: the paper was actually brought to my attention by the author of the OP]