"drawing closer to God" (prayer phrase)

1. We (start and) end the weekly Bible Study with prayer and among the phrases that sometimes arise is "...may we draw closer to God."
So I asked what does this mean if real life: exactly how far CAN a person draw close to God without actually being God?
Put another way: What does it look like when a person is close to God or in daily and hourly relationship with God?
Is this quantity (number of minutes per day when one's mind is filled with such things) or quality (depth, breadth, flavor); or maybe both?
 
Answer emerging from that conversation: much like the difference between "knowing" (in your head) about a matter versus knowing the same thing (by dint of experience, not just book knowledge), so too the God community is not just distinctions, connections, terminology but has to involve experience; knowing in this second, bodily way.
Drawing ever closer to God means, then, to identify in His world; His kingdom; His works and tasks for we His hands and His feet. And yet how seldom we actually glimpse our own identities at a given moment, let along over the process of growth and change. Self-awareness of identity sticks out when one is out of the taken for granted routines and comfortable, convenient environment. Identity is shaped by experience, not by head-knowledge alone; adversity and responding to it is another influence (adversity tests one's true character; "a friend in need is a friend indeed").
 
2. I reflect on the parable channel of Jesus' teaching and the rabbinic mode of Midrash (overstate a case in order to see it more clearly as it truly is).
Although the stories are persuasive by logic and emotion and example/deeds, still the message exceeds our finite minds. So it is sort of ironic that syntax and words and teaching is conveyed by logic and yet the subject of Faith by its essential character is without boundaries, definition or fixed shape and patterns of logic. It is a matter of the heart - sort of like the story, "The Little Prince" [Le Petit Prince by Antoine St. Exupery]: "It is only with the heart that one can truly see" [or ...that one can see truth].