"The Western tradition", as passe-partout, includes fringe figures, émigrés and migrants. Rather than looking to resources at the core of the Western tradition to overcome its own blindnesses, I am more interested in its gaps and peripheries, where other thoughts and renegade knowledges take hold. It is in the contact zones with strangers that glimpses of any culture's philosophical blindness become possible and changes towards a different understanding of knowledge can begin. In the context of education, I am above all interested in PhD candidates who wish to draw on the bodies and modes of knowledge they bring with them to the university. Some are not well represented: Indigenous and other non-Western traditions, non-English languages, and the renegade knowledges of marginalised groups. My context is that of creative practice-led PhD theses at AUT University, Auckland (Aotearoa/New Zealand) which have made me aware of the importance of cosmopolitics to understand education in the context of entangled histories of colonisation and domination; border-crossing interdependencies; new types of conflict and new ways of building communities. My study thus explores aspects of transculturation--involving not only ethnic cultures (often the default understanding of culture) but also different disciplinary knowledge cultures. The place that no-one owns in Western tradition, the place of fringe figures, émigrés and migrants, may offer a point from which non-traditional candidates' thoughts can lever off to build connections with their own stores of knowledge. (Non-traditional candidates belong to minorities in Western universities until about thirty years ago when traditional candidates were "male, from high-status social-economic backgrounds, members of majority ethnic and/or racial groups, and without disability".) This usually means for Western supervisors that they need to recognise their ignorance towards parts of their own traditions, as well as those of their candidates. The proposition I will explore is that the emergent research of non-traditional candidates can thrive on gaps and on the fringes--provided that both candidates and supervisors are able to be porous to the unknown and "troubled by the presumption of equality". The potential of the gap, the unknown, which simultaneously separates and connects candidates and supervisors, can be the beginning of generating a thing in common. This is a rich and creative place for new thought, which may open the academy to transcultural knowledge.