Either the alleged super-intelligence affects us in some way, directly or indirectly by altering things we can detect about the world/universe, in which case we can ultimately detect it, or else it doesn't, in which case it might as well belong to a separate universe, not only in terms of our perception but objectively too.
The error here is thinking that dogs understand anything.
Dogs certainly do understand things. Dogs and cats have a theory of mind and can successfully manipulate and trick their owners - and each other.
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.
Yes, dogs can think and make choices, learn from experience, solve problems (like opening doors or finding hidden treats), and adapt to new situations.
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.
OK, it might be a cultural thing. Do dogs probe the secrets of the world around them, with all that barking, even a little? Is it that they're in an early phase and will eventually advance to do more with stones than lick them sometimes?
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.
> Do dogs probe the secrets of the world around them, with all that barking, even a little?
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.
Legs are a small subset of the problem. “Where did I see that last?” involves mapping out and classifying the environment. There’s some really impressive demos of manipulating objects on a table etc, but random clutter throughout a house is still a problem.
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.