My limited experience of pair programming suggests that the biggest gain comes from having one brain devoted to the higher-level modelling and design task, and

My limited experience of pair programming suggests that the biggest gain comes from having one brain devoted to the higher-level modelling and design task, and the other brain (with the hands attached) devoted to the lower-level intricacies of where to put the braces and semicolons, what headers to include to access which parts of the standard library, and so forth. Because each brain can stay on one level without having to jump up and down the abstraction stack interruptions are lessened. Of course, if the higher-level brain starts to wander too far from the task at hand, the lower-level brain can interrupt, and if the lower-level brain gets tired of doing grunt-work, they can switch places.