Pair programming with two computers
I've been pair programming on laptops recently. Not the ideal situation by any means; the screens are too small and you can't pass the keyboard to your pair without turning the screen so far away from you that it becomes hard to read.
On the other hand, my pairing partner and I both have laptops, the codebase is huge, and neither of us is familiar with it. "Perhaps we could work faster by using both machines at the same time," we thought: one of us could use one to search for information in the codebase while the other coded or we could both search for information at the same time.
It turned out to be a bad idea. We found that we often each drifted away from our common task as we followed separate trains of thought. We also learned different things and couldn't easily share what we had learned with one another, the very opposite of pair programming's intended effect.
The value of pairing comes not from "parallel processing" but from two people thinking about different aspects of the same problem and constantly communicating with one another to keep their understanding of the problem in sync. The constraint of using one computer forces the pair to work in a way that produces the benefits of pair programming.