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wedrifid comments on Compartmentalization as a passive phenomenon - Less Wrong
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GEB has a section on this.
In order to not compartmentalize, you need to test if your beliefs are all consistent with each other. If your beliefs are all statements in propositional logic, consistency checking becomes the Boolean Satisfiability Problem, which is NP-complete. If your beliefs are statements in predicate logic, then consistency checking becomes PSPACE-complete, which is even worse than NP-complete.
Not compartmentalizing isn't just difficult, it's basically impossible.
It took me several seconds to guess that GEB refers to Godel, Escher, Bach.
Sorry about that!