Wittgenstein's lion
How do we know? Play a game with the computer, and see who wins.
There's no reason why we can't apply the same logic elsewhere. Set up a testable scenario, see who wins.
The error here is thinking that dogs understand anything.
With dogs it’s less a question of intelligence but communication something more intelligent AI is unlikely to have a problem with.
What would our being baffled by a super-intelligence look like? Maybe some effect like dark matter. It would make less sense the more we found out about it, and because it's on a level beyond our comprehension, it would never add up. And the lack of apparent relevance to a super-intelligence's doings would be expected, because it's beyond our comprehension.
But this is silly and resembles apologies for God based on his being ineffable. So there's a way to avoid difficult questions like "what is his motivation" and "does he feel like he needs praise" because you can't eff him, not even a little. Then anything incomprehensible becomes evidence for God, or super-intelligence. We'd have to be pretty damn frustrated with things we don't understand before this looks true.
But that still doesn't work, because we're not supposed to be able to even suspect it exists. So even that much interaction with us is too much. In fact this "what if" question undermines itself from the start, because it represents the start of comprehension of the incomprehensible thing it posits.
It’s a form of communication. You can learn to distinguish different kinds of barking a healthy dog is making, but that doesn’t mean you’re going to care nearly as much about a large animal showing up.
A dog will walk around the house, look at everything, smell everything, and touch many things. It makes things like finding slippers much easier.
I'm not sure we'd enjoy a robot doing the same, randomly wandering around the house and poking at stuff for some unspecified and uncommanded purpose.
Our perceptions are shaped by our cognitive limitations. A dog doesn't know what the Internet is, and completely lacks the cognitive capacity to understand it.
An ASI would almost certainly develop some analogous technology or ability, and it would be completely beyond us.
That does NOT mean we would notice we were being affected by that technology.
Advertising and manufactured addictions make people believe external manipulations are personal choices. An ASI would probably find similar manipulations trivial.
But it might well be capable of more complex covert manipulations we literally can't imagine.
The reason I mentioned my dog is because, even though dogs have limited intelligence compared to humans, my dog thinks he's better at playing ball than me. What he doesn't know is that I let him win because it makes him feel in control.