My ongoing project on caves and climate also makes use of different Deleuzian spaces as seen in the title of my book in preparation. The book’s title is a play with words pronounced like hole (that is the cave) but has different meanings. The focus for this entry is the second word, holey.
For Deleuze, a body or an assemblage is co-constituted with its space. The idea of space as a homogeneous whole where action takes place is a striated space. The arborescent/sedentary order (such as the State or the Church) relies on a striated space where everything is arranged and disciplined in closed systems (socially and physically). Striation occurs when technology reorders space and makes it measurable. A striated space is metric, extensive/actual and has lines of divide and demarcation that classify, measure and distributes space following politics or economy. This is also a segmented space that creates specific segments where certain rules occur. This striation comes from the overcoding, centralization, hierarchization, binarization, and segmentation of free movement.
Deleuze and Guattari sees nomadic thought as occupying a smooth space. This is a turbulant rhizomatic space where heterogeneity is distributed in an open manner. This space has not been disciplined. This space has more of affects and sensations than properties. Like a nomad, this space shifts with every movement, but the movements do not take place in space, it unfolds as the smooth space of the activity. A smooth space is intensive, boundless and oceanic. Like an ocean, it lacks distinction that privileges one place over other places and therefore it is non-disciplined. Smooth space cannot be controlled since it ceases to exist when it is overcoded by an arborescent order. The smooth space might be encircled and can turn static and become affected by the arborescent order. Smooth space lacks a long-term memory and can temporally emerge within a striated space.
However, these two forms of space only exist in mixture. The nomadic thought and the arborescent order are not dialectic opposites since they coexist in all social formations. Deleuze and Guattari focus on how forces striate space and also create forces that smooth spaces. There is always a constant interchange between smooth and striated space, so we can actually talk about smoothing and striating forces. The arborescent thought creates hierarchies and striations, but this tendency is prevented by nomadic thought that moves around and affects different striations of the arborescent order. However, if the nomadic thought gains access to the signification of certain nodes and therefore has to confront the arborescent order in a direct confrontation, it will become arborescent itself and striate space in order to maintain its obtained power.
There is also a third form of space that relates to the other two forms. A holey space is part of an underground space that connects with smooth space like a rhizome and is blocked by striated space. Holey space is the space of counter-action to striation. The cave is a holey space during periods when it is used as a hide out from the striating forces of the Catholic Church and Spanish State.