That's a fun read.
The computer would have to be outside of the universe being computed.
No computer could ever compute the universe it resides in.
How does this thought experiment deal with black holes?
Could this be the way the computer deals with incalculable regions? Density becomes to high, to difficult for compute, so the computer protects itself from infinity creating the event horizon and slowly pulls the information back into the system through hawking radiation at a manageable rate?
Also a curious coincidence, a black hole with the mass of our universe would be the size of the current universe... So, computers computing computers