Being-at-home in a particular, determined, world is dangerous for thinking. For thinking to be thinking/becoming, one should not get too comfortable. For thinking is to not arrive back home, in the same place one begins. But how to escape the world that has created who you are, gave you purpose and a past? How to make sure the future is not a repetition of the Same? How to break away from something that you need? In this article, my aim is not to give one more solution to this fundamental problem that is in essence an ethical problem. For providing a refuge, a new theory, a new methodology, would be providing a new island for those who realise that a flood is endangering their own island. My aim is to exercise the craft of exilic thinking as a way to deal with the contradiction already pointed out by Heraclitus and Parmenides – “We both step and do not step in the same rivers. We are and are not.” Exilic thinking as a craft of fragilising the self establishes a matrixial borderspace through which the impossible becomes possible.