Define attentiveness. It may be easier to consider its opposites:
What we experience when we go into a chain drug store
Our reaction to the rhythms of overheard anonymous iPods

The most vivid example of attentiveness that I recall is a three-month-old listening for the first time to a small bell.

Consider that bell: Clearly the sound starts when the bell is struck. But when does it end? Does it ever end?

The possibility of endless vibration keeps us listening even to silence when the bell is no longer actually sounding.