An arrangement for determining those optimal times to permit an important pop-up message to be displayed by way of garnering a user's attention, while permitting less important messages to be displayed at times when a user's attention is unlikely to be garnered. In accordance with a particularly preferred embodiment, an arrangement is provided to recognize whether a user is looking towards a computer monitor and, at such times, to determine whether a blink rate of the user's eyes corresponds to a degree of focus and concentration that would ensure a strong likelihood of the user seeing or “catching” a message that may then appear. If such likelihood is thus determined to be strong, then a critical message may preferably then be displayed.