This paper will identify and analyse contemporary processes of border-making and border permeability through the sonification and identification of mathematical and cultural morphologies of border forms. The paper will explore the historical and mathematical paradoxes of borders, their role in today’s global environment and the ways in which sonification can help delineate and expose their origins, not only territorial, geographical, and political borders, but also cultural, metaphorical and geological borders. The author will present a range of re-mediations from geometry to sound, showing how ideologies and cultures overlap and compete through border construction. Above all, the logical impossibility of many borders will be laid bare.