I was thinking about the risks of Oracle AI and it doesn't seem as safe to me as Bostrom et al. suggest. From my point of view, even an AGI that only answers questions could have a catastrophic impact. Thinking about it a little bit, I came up with this Proof:
Lemma
We are not safe even by giving the oracle the ability to only answer yes or no.
Proof
Let's say that our oracle must maximize an utility function $\phi$, there is a procedure that encodes the optimality of $\phi$. Since a procedure is, in fact, a set of instructions (an algorithm), each procedure can be encoded as a binary string, composed solely of 0 and 1, Therefore we will have $\phi \in {\{0,1\}^n}$, assuming that the optimal procedure has finite cardinality. Shannon's entropy tells us that every binary string can be guessed by answering only yes/no to questions like: is the first bit 0? and so on, therefore we can reconstruct any algorithm via binary answers (yes / no).
Is this reasoning correct and applicable to this type of AI?