Knowledge and wisdom often operate at cross-purposes. In particular, wisdom means turning towards the world, paying attention to the things we find there, while with knowledge we turn our backs on them. Knowledge thrives on certainty and predictability. But in a certain world, where everything is joined up, nothing could live or grow. If a world of life is necessarily uncertain, it also opens up to pure possibility. To arrive at such possibility, however, we have to rethink the relation between doing and undergoing, or between intentional and attentional models of action. I show how attention cuts a road longitudinally through the transverse connections between intentions and their objects. Where intention is predictive, attention is anticipatory. And if the other side of prediction is the failure of ignorance, the other side of anticipation is the possibility of not knowing. The idea that predictive knowledge demands explication perpetuates the equation of not-knowing with ignorance. Education, science and the state are powerful machines for the production of ignorance. I argue, however, that ignorance and not-knowing are entirely different things. In a world of life, not-knowing betokens not ignorance but the wisdom that lies in attending to things.