In Anathem, two of the characters have a discussion about how a person can “make” facts from their observations of the universe. In the course of their discussion, one makes the point that whenever we see the world and begin predicting behavior, we are in essence creating a series of counterfactual universes and discarding them as they don’t “fit the facts”.

This reminded me of my favorite method of proof – proof by contradiction. For some reason, I sometimes found thinking about alternate math systems more interesting than solving regular problems. Proof by contradiction let me do both: I could set up the alternate system in which the rules were different somehow, and then discover the flaws with respect to the “real world” and generate the proof.

Do we set up counterfactual universes in our heads? And if we do, could we apply a more rigorous method of proof to discarding them “by contradiction” than pattern matching?