https://en.wikipedia.org/wiki/Good_regulator_theorem

every good regulator must contain or have access to a model of the system it regulates.

the mapping they construct is only a homomorphism, meaning the model can lose information about the entity that is modeled. So, while the system that is regulated is a pattern of behavior in the world, it is not necessarily the only pattern of behavior observable in a regulated entity.

The principal point that the authors present with this figure is that regulation requires of the regulator to conceive of all variables as it regards the set