If the singularity mind was bigger than us, but of the same nature, we would be able to compute it with pencil and paper, or in a computer, and to analyze it to see how it works (very slowly, as a Turing machine).
My impression is that we couldn't, just like we couldn't decode an audio file that stream forever without real-time decoding. Once we "compute it" "very slowly," the AI will already have improved twice, tenfold, a thousandfold. It will be fruitless.
Not to mention, even if the AI is simply a Von Neumann machine with really impressive specs, what makes you think we'd be able to decode it? If you gave me a RAM chip, I wouldn't know what to do with it without an EE book. Now imagine a technology a thousand times more advanced.
What I mean: given enough time, we'd be able to analyze a specific computation (not all real-time computations of such mind). However, our patience, lives and our universe too is finite, so it could set practical limits to our task. Say: decoding X signal would only take me more time than the universe to end, so, that's anyway an impossible task. But we should be able, in principle and with infinite time, to analyze any computation. (Well, we should first set a meaning for "analyze" in this context)
My impression is that we couldn't, just like we couldn't decode an audio file that stream forever without real-time decoding. Once we "compute it" "very slowly," the AI will already have improved twice, tenfold, a thousandfold. It will be fruitless.
Not to mention, even if the AI is simply a Von Neumann machine with really impressive specs, what makes you think we'd be able to decode it? If you gave me a RAM chip, I wouldn't know what to do with it without an EE book. Now imagine a technology a thousand times more advanced.