In short, then, the problem is that knowledge of knowledge has no "subject matter." Further, since this absence is what defines knowledge of knowledge, it is unclear how such a definition could ever be linked to subject matter without compromising itself. One intriguing way in which this abstract problem is made clearer is through Socrates's description of the ideal city-state that wisdom or temperance would supposedly rule (if it existed). Such a state would be perfect in every detail, since, with knowledge of both knowledge and ignorance at the top of the hierarchy, no one beneath it would ever act without knowing exactly what they were doing.
Socrates uses the absurd perfection of such a state to suggest that this pure ideal of reflexive knowledge is just as much of a pipe dream—the unreality of this ideal state shows how firmly entrenched the "knowledge of knowledge" definition is in unreachable idealism. Such a move is illustrative, and does not logically prove the impossibility of such knowledge. Nonetheless the point is well taken. It is curious, however, that the ideal state, governed by wisdom, should here be used as an example of impossibility, since Plato will later write the entirety of the Republic on just that idealized entity.
This consideration of idealism leads to the only semi-viable solution to the intractable separation of ideal self-knowledge from actual, practical beneficial knowledge: Socrates suggests that wisdom is really something that, even while defined by a kind of abstract knowledge about knowledge, has its effects in the facilitation of practical inquiry. This seems intuitively right, even though the exact mechanism may be a little unclear. In particular, such a model seems to match up quite well with the Socratic method itself, allowing for the pursuit of concrete knowledge to be guided by a set of meta-rules about how that pursuit should proceed (in Socrates's case, such a process is the elenchus).