In her post Questions about rhizomatic learning, Jenny Mackness ponders the arrangement of space in Deleuze and Guattari's rhizome. She quotes D and G: "Nomad space is ‘smooth’, or open-ended. One can rise up at any point and move to any other" and "A rhizome has no beginning or end; it is always in the middle, between things, interbeing, intermezzo." She then notes the difficulty envisioning such a space, saying that her "past experience has suggested that there are always boundaries that we come up against". I share her difficulty, and I think that it's the boundaries that cause the problem for both of us and for most others.
I start with boundaries as Paul Cilliers uses them in his article Why We Cannot Know Complex Things Completely (2007), where he argues that knowledge is not representational but relational: "a result of the dynamic interaction between all the meaningful components in the system" (85). This leads to a problem because any system, even the most trivial garden slug, has an approximately infinite number of dynamic relations that could be considered at any one time. We use context and boundaries to limit the number of considerations that we must make at any given time in order to form some useful understanding of whatever bit of reality we happen to be engaging, the garden slug for instance. We must limit and differentiate. As Cilliers says, "For meaning or knowledge to exist at all, there have to be limits" (87), or boundaries.
We learn these boundaries from parturition, when we are first separated from the mother and relationship and dynamic interaction become unavoidable. Perhaps we develop some sense of boundaries earlier, but I really have no expertise or even much idea about that. I am certain, however, that one of the first tasks after birth is for babies to differentiate themselves from their mothers. That may be the biggest bit of learning we ever do, and I suspect that everything else we learn follows from that first striation in the rhizome. After we form me and you, we form here/there, up/down, wet/dry, hungry/full, and all the rest. We start slicing and dicing our world, the rhizome, and we form our boundaries within the context of our social groups: mother/child dyad, family, clan, and larger.
These differentiations are always an act of power, and we learn to use our own idiosyncratic powers as well as the power of our groups to form our world. We do it so often and so automatically, that it comes to feel natural, and we are often shocked when we learn that others don't see the same things that we see, don't have the same meaning about the Eiffel Tower as we do.
The point that I think Deleuze and Guattari and others such as Serres are making is that reality is not striated naturally. All of the boundaries and structures that we trace onto the rhizome to make it meaningful and useable are acts of power, individual and group. We say, "up" or "down", and the rhizome says, "Whatever." The rhizome is "always in the middle, between things, interbeing, intermezzo", and up and down really depend totally on our point of view and the way we have sliced and diced things. Moreover, something in the rhizome resists our marking and differentiating, or is indifferent to our meaning-making, and flees our naming and knowing through lines of flight, deterritorializing here and reterritorializing in the most unexpected places, as when a grape deterritorializes in Argentina only to reterritorialize in me as a nice Merlot. We make the mistake of thinking that our naming and knowing, our differentializations, are permanent markers on reality. The rhizome teaches us otherwise.
This is, of course, very eastern in its feel—not quite buddhist, but damn near it. It is also very much a part of complexity theory. From what I read, modern physics says that everything in the Universe is interconnected to everything else (gravity, for instance, extends totally across the Universe), and the boundaries we make between this and that are mostly a matter of convention and convenience, not a matter of absolute truth. New laws and new boundaries are constantly emerging, which means that our knowledge should be constantly emerging, should be constantly renewed. This pleases me greatly, as I will never run out of things to learn, even if I should prove to be eternal as the fundamentalists insist. Can you imagine an eternity with nothing new to learn? God spare us.