But a function is a temporal (within time) mapping/relation that brings us back to hierarchies and trees. A function is a directional mapping from source to target that sets them apart as binary dichotomies, in two different domains. Asking questions about functions is a human endeavor that occurs within the time continuum. A book itself is a little purposeless machine.

Since a machine, at least in western science, has a specific operational pre-conditions, and a predefined goal. Machines are tools. They are designed by Engineers… In this sense Purposeful machine are functions, that brings us back to hierarchies and trees. If we want to operate within the consistency plateau, we must argue that books/assemblages are ultra-temporal purposeless machines. But reading and writing activities are performed within time, aren't they?

1 and 2. Principles of connection and heterogeneity: any point of a rhizome can be connected to anything other in a fuzzy relation and must be. This is very different from the tree or root, which plots a point, fixes and defuzzified to a binary order.

In this sense, is rhizome has any meaning, it must be a undefuzzified fuzzy machine.

The linguistic tree on the Chomsky model still begins at a point S and proceeds by dichotomy. On the contrary, not every trait in a rhizome is necessarily linked to a linguistic feature ONLY by a binary SYNTACTICAL/GRAMMATICAL relation. Semiotic chains of every nature are connected to very diverse modes of coding (biological, political, economic, etc.) (In a fuzzy relation which allows the introduction of MEANING/SEMANTICS into the model) that bring into play not only different regimes of signs but also states of things of different status (read: different meaning). Rhizomatic RAPTURE is a fuzzy relation that connects between two seemingly parallel plateaus or grammatical systems. Our criticism of these linguistic models is not that they are too abstract but, on the contrary, that they are not abstract and not meaningful enough, that they do not reach the abstract meaningful purposeless machine that connects a language to the semantic and pragmatic contents of statements, to collective assemblages of enunciation, to a whole micropolitics of the social field.

A Rhizome is therefore both a neurofuzzy system (each relation between node is a fuzzy relation) AND a fuzzyneuro system (training is done through fuzzy decision making that take meaning and heterogeneous fields into consideration) that folds around itself, so it’s inputs are also it’s outputs.

There is always something genealogical about a tree. It is not a method for the people. A method of the rhizome type, on the contrary, can analyze language only by decentering it onto other dimensions and other registers. A rhizome, from a graph theory point of view is a directed non-rooted fuzzy weighted graph. If we want to be precise then we need to observe that a rooted tree can also contain multi-dimensional fuzzy links and that any rooted tree can be re-rooted or un-rooted to a directed graph. A re-rootable tree with cross-dimensional relations and nodes can be Rhizomatic in nature. A distinction between the quality of the links and the rootedness quality of a graph must be made. What’s important is the quality of the graph links and not whether or not it is rooted or not; there are many ways to map a rhizome structure. It seems that every critical activity or charting process (if it is happening within time and space) must begin from one of the Rhizome’s n-dimensional vector, and so it functions as a temporal root; as a temporary autonomous zone. In principle, any Rhizome vector can perform as a root of a surveying operation. Each survey crosses different dimensions and highlights different system qualities.

This observation is reinforced by Principle 3: multiplicity: it is only when the multiple is effectively treated as a substantive, “multiplicity,” that it ceases to have any relation to the One as subject and object, natural or spiritual reality, image and world… …There is no unity to serve as a pivot (root) in the object… …A multiplicity has neither subject nor object, only determinations, magnitudes, and dimensions that can not increase in number without multiplicity changing in nature. So multiplicity is really nothing but an exact many to many fuzzy relation. Each vector is a member of a fuzzy set to a certain magnitude. Each fuzzy set can exists in different dimension/plateau since it describes qualities and not just quantities. … the Actor’s nerve fibers in turn form a weave. And they fall through the gray matter, the grid, into the undifferentiated… since the gray matter is a neuron/fuzzy network.

4. A rhizome may be broken, shattered at a given spot, but it will start up again on one of its old lines. This is in the heart of distributed systems such as neural networks where MEMORY is not stored in a component that is distinguishable from the Central Processing Unit logic that operates on it. You can break specific lines but the network will recover since no pinpointable location contains knowledge, logic or code that the system require to operate.

The Rhizome is a high fault tolerance distributed system that acts more as a community then Von-Neumannian aggregate of crisp components.

5. Is it not the essence of the map to be traceable? The tracing should always be put on the map. The tracing has already translated the map into an image. But can we even imagine concepts that have no image, that are imaginable? How can we image the Rhizome but through it’s tracing? One must not be lazy to trace, overlay the trace back on the Rhizome and retrace a different chart that may lead to dead-ends and pitfalls. But most people are lazy in the sense they try to be efficient by listening to Occam’s principle of reason that they must have been trained at trained in academic institutions. To put the tracing back on the map also means to re-open tough to deal with questions and dilemmas, to question one’s personal/social history and values.

It’s the Nietzschean attempt to overcome oneself.

…the brain is not rooted or ramified matter. … the brain is a multiplicity immersed in it plane of consistency or neuralgia, a whole uncertain, probabilistic possiblisitic/fuzzy system (“the uncertain nervous system”). The is important since scientists kidnapped probabilistic systems by probability theory. Probability is not uncertainty. Probability theory works with binary logic to predict future occurrences of random events in nature. Possibility theory and fuzzy sets theory deals with the possible and with meaning by comparing an event to an ideal prototype set that has no-crisp boundaries. In a probabilistic system, all probable possibilities sum up to form 100% of occurrence. In an uncertain system we may have up to x% of uncertainty that is taken into account. We may use fuzziness to make predictions that narrow this unknown dark matter percentage.

Arborescent systems are hierarchical systems with centers of significance and subjectification, central automata like organized memories. In the corresponding models, an element only receives a subjective affection along pre-established paths. This is evident in current problems in information science and computer science, which still cling to the oldest models of thought in that they grant all power to a memory or a central organ….

This must relate to the Von-Neumann model that separates the computer = state automata into distinct components – control logic and central memory. To these centered systems, the authors (Pierre Rosentiehl and Jean Peition), contrast a-centered systems, finite networks of automata in which communication runs from any neighbor to any other (At least in theory, before training) and all individual are interchangeable, defined only by their state at a given moment – such that the local operations are coordinated and the final, global result synchronized without a central agency. This is the neural networks model. This opened the floodgate for large sponsoring of neural networks research and development. In neural networks in which there are no distinct components – The memory/knowledge is distributed throughout the system. There is no separation between the reasoning process and the system’s knowledge. There is no knowledge dictator/root structure that is external to the system. …”There is no reason for the graph to be a tree…” (we have been calling this kind of graph a map) so the rhizome is a neural network after all: a mechanical network of finite automata (a Rhizome).

Take psychoanalysis as an example again… psychoanalyses cannot change its method in this regard: it bases its own directional power upon a dictatorial conception of the unconscious. But don’t all other Western scientific disciplines follow the knowledge tree model? It is odd how the tree has dominated Western reality and all of Western thought, from botany to biology and anatomy, but also gnsiology, theology, ontology, all of philosophy…: the root-foundation. Science start with axioms, authority, funds and assumptions as soiled plateau in which they root a theoretical forest of systems, paradigms, algorithms and explanations. To think Rhizomatic is to put back the charting done since Plato and his Binary logic, back on The Map and to start again form the pre-Socratic DJs – just as Nietzsche proposed.

So the Rhizome may have been just Greece in disguise. One possible route of investigation would be to continue the Nietzschean undertaking of uncovering “Greece”. But the rhizome is an antigenealogy so what is it? The rhizome is precisely this production of the unconscious – The rhizome is more than a neural network after all – It is a 1:1 map of the human brain produced by artificial organic/mechanical/computerized simulation of a neural network.

We must observe that by some estimations, an untrained human neural network (A newborn infant) contains about 1000 billion neurons. Each neuron has output paths and a synaptic junction (Axons) to roughly 1000 other neurons.

Let us summarize the principal characteristics of a rhizome: unlike tress or their roots, the rhizome connects any point to any other point, in a fuzzy relation, and its traits are not necessarily linked to traits of the same nature, but they may be linked to fuzzy sets of meaning. It brings into play very different regimes of signs, and even nonsign states (neurons). The rhizome is reducible neither to the One nor the multiple since reduction is a well-defined analytical/mathematical tool based on binary logic. It is composed not of units but of dimensions, or rather directions in motion. It has neither beginning nor end, but always middle (milieu) from which it grows and which it over-spills. Regarding assemblages and mulieu... ...To me, assembly is the invisible language of our time and DJing, is the forefront art form of the late twentieth Century... ...  In the electronic milieu that we all move in today, the DJ is a custodian of aural history. In the mix, creator and re-mixer are woven together in the syncretic space of the text of samples and other sonic material to create a seamless fabric of sound that in a strange way mirrors the modern macrocosm of cyberspace where different voices and visions constantly collide and cross fertilize one another.