So, one way of solving the recursion problem would be for Hugh to never use the machine as a first resort for answering a question Q. Instead, Hugh must resolve to ask the machine only for answers to questions that are “smaller” than Q in some well-ordered sense, and do the rest of the work himself.
But unless the machine is faster at simulating Hugh than Hugh is at being Hugh, it is not clear what is gained. Even if it is, all you get is the same answer that unaided Hugh would have got, but faster.
So, one way of solving the recursion problem would be for Hugh to never use the machine as a first resort for answering a question Q. Instead, Hugh must resolve to ask the machine only for answers to questions that are “smaller” than Q in some well-ordered sense, and do the rest of the work himself.
But unless the machine is faster at simulating Hugh than Hugh is at being Hugh, it is not clear what is gained. Even if it is, all you get is the same answer that unaided Hugh would have got, but faster.