One of my favorite blog reads comes from Ottmar Liebert - the jazz/flamenco musician and practicing Zen Buddhist.
Ottmar shares da Vinci's 7 Principles. Here are a couple:
Curiositá - An insatiably curious approach to life and an unrelenting quest for continuous learning.
Sfumato (Literally "Going up in smoke") - A willingness to embrace ambiguity, paradox, and uncertainty.
Check out all seven. I notice that my insatiable curious approach to life can get muted by being too busy and unfocused. It's not a direct correlation - sometimes when I am busy I am more engaged. It's the combination of busy and unfocused that does me in.
I think you can explore and focus at the same time - meandering and being curious is stimulating.
What gets in the way of your natural curiousity?