In their dialogues and collaborations, Gilles Deleuze and Félix Guattari enquire of the nature of borders. They summon principles of inclusion and exclusion associated with borderlines. They eschew expressions built on the polarities of ‘either … or’ and in their own diction replace binary constructions with the conjunctive ‘and’. Furthermore, in ‘Rhizome,’ the introduction to A Thousand Plateaus, they argue for rhizomatic connections – fostered in language by ‘and … and … and’ – to replace what they call the arborescent model of the ubiquitous Western tree (Deleuze and Guattari 1987). In constant movement, the tissues and tendrils of rhizomes call attention to the horizontal surfaces of the world in which they proliferate. They bring to their observer a new sense of space that is seen not as a background but a shape that, with the rhizome, moves and forever changes. In the field of play Deleuze and Guattari often produce hybrid, even viral connections and downplay the presence of genealogies conveyed in the figure of the tree bearing a stock-like trunk. Rhizomatic connections form open territories that are not constricted by the enclosing frame of a rigid borderline.

In the same breath the two philosophers argue for ‘smooth’ spaces of circulation. They take a critical view of ‘striated’ spaces, replete with barriers and borders that are part of an ‘arborescent’ mentality. Striated spaces cross-hatched by psychic or real borderlines drawn by the state (social class, race, ethnicities) or by institutions (family, school), prevent the emergence of new ways of thinking.