For diasporic African peoples, the transatlantic slave trade created a condition of “kinlessness,” a legal and social exclusion from recognized forms of family affiliation. This kinless condition, moreover, was transmitted through birth, making kinlessness a logical impossibility even while it remained a historical reality. Faced with the notion that African Americans had “no family tree,” some black writers responded with novels that located recognizable bloodlines for African American families. But an unpublished novel by W. E. B. Du Bois offers a strikingly different analysis of the notion of black kinlessness. In this narrative, a black Harvard undergraduate convinces his white classmate to undergo an operation that will temporarily make him a “Negro.” Once he undergoes the operation, however, the student discovers he has entered “the fourth dimension of color,” a new domain in time and space that is “outside the bounds of humanity.” At a time when ideas of black kinlessness still had potency in US law and society, Du Bois's strange representation of blackness as a fourth dimension in space is counterintuitive. Why forgo the conventional novelistic categories of family and kinship? Although Du Bois's narrative repeats an image of black kinlessness, it creates a catachrestic novel form through which to uncover the illogical historical logic of kinlessness. Only a catachrestic narrative space like Du Bois's fourth dimension can make kinlessness intelligible as a fully human condition and a historical reality.