Well, the very first characteristic of a rhizome stopped me, and I had to start reading again. In what sense did Deleuze and Guattari mean that "any point of a rhizome can be connected to anything other, and must be" (Thousand Plateaus, 7)? I have a hint of an answer, and I'm working on some other answers, but keep in mind that I am not suggesting that what I say here is what DnG meant when they wrote the above comment. I don't know what they meant, and in some ways, their meaning is irrelevant to me. All I want to talk about—perhaps all I can talk about—is how I interpret what they say. Here's one way:
I think initially I was stymied by my assumption that DnG were saying any point of a rhizome can be directly and simultaneously connected to any other point without any intervening or intermediary points. My mechanistic view of physical reality balked at this, or in DnG's terms, I was trapped in arborescent thinking. In aborescent, or hierarchical, structures, each node occupies a fixed point in the overall structure and connects directly only to those nodes immediately above and below it. Its relation to all other nodes in the structure are mediated, and thus controlled, by the nodes through which it must pass in order to connect and communicate to those remote nodes. Moreover, two points cannot occupy the same space. Arborescent thinking has a very strict economy: one point, one space. A point can occupy only one space, and no two points can occupy the same space—a place for everything, and everything in its place. Any point is responsible for the points below it and responsible to the point above it.
Arborescent thinking, then, creates a rigidly delineated arrangement of any thing, physical or mental. Rhizome thinking is different, though it can incorporate arborescent thinking (Arborescent thinking does not include rhizomes, however). In a rhizome way of thinking, no given point is fixed in any given place. Rather, a point is a nexus of potential places, properties, trajectories, and speeds, a swelter of probabilities that emerge and shift as the point interacts with the field of other points. Moreover, all those points are exerting some influence, some connection, however small, on every other point in the field, all at the same time. And the field is ultimately very large: the entire Universe. Everything is, in fact, connected to every other thing.
Everything, then, is a shimmering potential of probability that emerges into our consciousness for an instant and then arcs on to some other expression. Nothing is static, nothing stays in its place. No place for anything, and nothing in its place.
This connection of any one point to all other points is easy to see in digital information, where any piece of data can easily be connected to any other piece of data. For instance, at Amazon readers are constantly applying new tags to books. Indeed, any book in Amazon can have as many tags, identifiers, as people wish to give it. Thus, Deleuze and Guattari's A Thousand Plateaus need no longer be filed in a hierarchical taxonomy under French philosophy, but can be filed as well under modern psychology, poststructuralism, friends of Michael Foucault, stuttering, and weed management. DnG can be connected to most any idea that any reader, however deranged or sane, can imagine.
These connections are hypertext, and they are magical. I'll let Michael Wesch's marvelous video say it for me again: