This chapter is dedicated to an exploration of the connections between ignorance, possibility, and impossibility. While traditionally studies of ignorance have been firmly anchored in debates about knowledge (and the lack of knowledge), what I propose here is that this phenomenon is (also) essential for our engagement with the possible. The sociocultural theory of the possible claims that possibility emerges at the intersection between multiple perspectives that, in turn, build on differences of position within a shared social, material, cultural, and psychological space. Conversely, the impossible is concerned less with what cannot be actualized as much as with the singularity of perspectives and the negation of difference. The argument I develop is that ignorance plays a key role in both the dynamic of possibility and impossibility. More concretely, ignorance can keep us away from recognizing and embracing other perspectives, while it can also make us humble and curious about those perspectives and positions in the world that are inaccessible to us. I will take the case of the perspective of others, especially migrants and refugees, to illustrate a small typology including: default ignorance or the state of not being aware, on a daily basis, of perspectives different than our own; deliberate ignorance or the conscious decision not to engage with the perspective of specific others; masked ignorance or the assumption of understanding a perspective one has no understanding of; and wondrous ignorance or a state of complete openness to new perspective without the expectation of final or certain knowledge. In the end, the embodied and distributed nature of each of these forms of ignorance will be discussed in light of how they contribute to the (im)possibility of an authentic engagement with others and otherness.