I think there's a really different level of cognition between a bird and a human, general intelligence, and I have the intuition there's really the highest level of cognition an entity can achieve, models that model what the model is modeling (thinking) and can go on on nesting modeling indefinitely, the only limits are on memory, processing power (or time) and to an extent information gathering. If a superintelligence is developed or develops I don't think it will be "super" in the sense of a novel way to understand the universe, just better modeling.
But going back to the bird example, the bird doesn't know as well as a human what a monitor is, but the knowledge it gathers is enough, from experience to know it's harmless so why it should be alarmed? The difference with a human, the general intelligence part, is that the bird, as far as we know, doesn't model the intentions or inner workings of the monitor and it doesn't seem to model itself interacting with it in complex ways