To surprise and inform

In information overload regimes, it is necessary for messages to not only provide information but also to attract attention in the first place. Bayesian surprise is an information-theoretic functional that has been experimentally shown to measure the attraction of human attention. This paper studies the limits of reliable communication under a constraint on surprise so as to limit distraction: surprise-constrained capacity. It also considers attention-seeking capacity, where the goal is to maximize both information rate and surprise to attract attention. Properties of these functions are proven. There are no nontrivial tradeoffs for surprise-constrained capacity, but an interesting tradeoff arises for attention-seeking capacity; reversing the direction of constraint does not yield essentially equivalent problems.