I'd also wager that "I don't know Timmy" is more thematically related. I feel most of the discussion in this thread glosses over what is most unsettling about Permutation City. It isn't just a book about what it could be like to be a simulated mind, it's most deeply about exploring the disquieting metaphysical consequences of computable minds. I can't think of a story that has as thoroughly scattered my basic grasp of reality as this one. Only Blindsight even begins to comes close.
In "I don't know Timmy" there's a sequence that goes:
"Well, we can't exactly turn it off."
"Why not?" asked Tim, halfway to the door, then stopped mid-stride and stood still, realising.
"Oh."
But you can turn it off without consequence and Permutation City explores the disturbing implications of why thoroughly (with a deus ex machina ending to save causal physics, as expected of an Egan story, physics is what has plot armor).