Changing minds in a changing world

I defend a general rule for updating beliefs that takes into account both the impact of new evidence and changes in the subject's location. The rule combines standard conditioning with a "shifting" operation that moves the center of each doxastic possibility forward to the next point where information arrives. I show that well-known arguments for conditioning lead to this combination when centered information is taken into account. I also discuss how my proposal relates to other recent proposals, what results it delivers for puzzles like the Sleeping Beauty problem, and whether there are diachronic constraints on rational belief at all.