I am in the middle of A Thousand Plateaus and considering the relationship between rhizome and body without organs.
One thought I had is that they both take part in the constitution of relationships between ideas, society, groups; but neither are treated as closed.
Some investigation on the internet turned up the following:
Therefore, “desire-‐machine” appears as a manifestation against the idea that desire is a lack. BwO as the body of rhizome-‐philosophy constitutes desire as the essence of production. When the body reconstruct the property relations over itself and waive the idea of being an “individual”, it would truly be free and on the way of becoming BwO. Different from being an individual, this type of becoming means “individuation” or “haecceity” as called by Deleuze and Guattari. Intermezzo fits this concern and perfectly represents the body of rhizome-‐philosophy. It re-‐constructs its body again and again within an endless improvisation. It acts between the acts and composes the rhythm of intervals. This position is characterized by the concept of “nomad” in the rhizome-‐ philosophy. Nomad/BwO/Desire Machine, whatever we all, is the body of rhizome-‐philosophy and represents the face of collective body. This body, similarly with the “collective body” of Walter Benjamin, is a manifestation against the capitalist mode of production. (source)
But the smooth space of the rhizome is always under constant threat of hierarchization and stratification while the tree can proliferate into a-centered systems given changes in local conditions, thresholds of intensity, coefficients of transversality, etc. Hence both the tree and the rhizome face the strata and the body without organs (4). Yet it is precisely their relation to these two sides which simultaneously indicates the mode of their processes of crossing between the actual and the virtual. Although the two authors do not speak of these two registers, this “dualism” seems completely necessary in order to confront all the principles which they stipulate for understanding the rhizome—in effect, its connectivity, heterogeneity, multiplicity, cartography and decalcomania. (source)
But I'm still having trouble characterizing the two concepts' relationship to one another.
What is (a concise explanation of) the relationship between the body without organs and the rhizome?