This aphorism piques my interest because it touches on Nietzsche's idea that the awakening to knowledge should be experienced as pleasure (i.e. "the gay science")--as "cheerful," not "serious."
How much that we hear, listen to, even memorize fails to awaken us to knowledge? How much that we hear, listen to, even memorize, even accept as "the truth," is like dreamless sleep?
The awakening to knowledge that delights us is that which corresponds to our inner selves, our passion, that inchoate innerness that we are constantly in the process of discovering--if we bother to--like (to use Nietzsche's analogy in the preface to On the Genealogy of Morals) bees ("honey-gatherers of the spirit") always on the lookout for something to bring back home to the hive.
And there's Whitman's metaphor: the spider who launches filament after filament into empty space, waiting for the connection that will form the basis of its home, its web, its network of sensibility (its soul).
"Awake ... in an interesting manner"--this involves the moments, the dreams, the insights we do remember because that forever-under-construction, never-finished sense of self finds something there with which to connect, thus discovering and defining a part of oneself ... for oneself.
To live interestingly is to remain, as much as possible, in a state of wanting to "find out"--also an interesting phrase because it suggests that knowledge, wisdom, meaning, whatever, is to be "found," pulled in from the "outside" and then, perhaps, turned into honey.
To be awake uninterestingly is, perhaps, not to be awake at all?