Representation versus cartography in Deleuze and Guattari?

Question

Can someone help me contextualize and concretize the theme of representation (what they sometimes call "tracing") versus cartography ("mapping," "diagramming," even "meta-modeling", etc.) in Deleuze and Guattari?

There are a lot of drawings and diagrams in both the mutually-authored works and Guattari's own work -- it seems like this diagrammatic sort of "thinking" is doing productive work. Consider this diagram/drawing of the signifier from A Thousand Plateaus:

I am not looking for an explanation of this or any particular diagram -- after all, we could multiply examples endlessly. At this point I am just looking for some help establishing the role of this theme in their work, in particular helping shed some light on this opposition between representation and cartography that seems at work all over the place. For instance, and if only to show this is not only in ATP, from Guattari's Machinic Unconscious (172, 'Trees and Tracings, Maps and Rhizomes'):

Tracings constitute some of the essential elements of diagrammatic semiotization. They do not have the function of harnessing redundancies of resonance, of representing stratified realities, but of directly jumpstarting mutational signs-particles. Within tracings, figures of expression are treated as the primary matters of an experimentation bearing upon abstract machines. Maps themselves are like laboratories where experimentations on tracings are set in interaction. Thus, here the map is opposed to the structure; it can open itself in all its dimensions; it can also be ripped apart; it can be adapted to all kinds of assemblies.

Answer 1

Watson's Guattari's Diagrammatic Thought addresses this directly, and in particular goes over the evolution of this concept in some detail (from p. 12):

The concept of the diagram appears in A Thousand Plateaus (ATP 141-144, 531 n. 41 / 176-180, 177 n. 38) but the details of its development are found in Guattari's writings of the 1970s. The notion was adapted from Charles Sanders Peirce, who includes the diagram among the icons in his index-icon-symbol model of the sign. Peirce identifies three types of icon: image, metaphor, and diagram. For him, the icon operates through a relation of resemblance between the sign and its referent. Guattari would agree that the image and the metaphor signify through resemblance, which is to say representation, but his version of the diagram functions differently because as he defines it, the diagram does not signify; it is "a-signifying"... Examples of the diagram at work include the algorithms of logic, algebra and topology; as well processes of recording, data storage, and computer processing; all of which are used in mathematics, science, technology and polyphonic music. Neither mathematics nor musical notation are languages -- rather, both bypass signification altogether...

Already in his notes for Anti-Oedipus, Guattari senses that Peirce's diagram is somehow special, that it unleashes "deterritorialized polyvocity," that it must be understood as distinct from the image because the diagram is a site of production (AOP 72, 214, 243-255/97, 308, 346-349). He continues reflecting on the powerful, productive diagram in Revolution moleculaire [Molecular Revolution] and L'inconscient Machinique [The Machinic Unconscious], concluding that diagrams "are no longer, strictly speaking, semiotic entities." Their "purpose is not to denote or to image the morphemes of an already-constituted referent, but to produce them" (IM 223, 224). In other words, diagrams do not represent thought; rather, they generate thought. Diagrams abound in experimental science, he says, because it is "a sphere where signs have a direct effect on things," involving "both material technology and a complex manipulation of sign machines" (MR 166/RM 303). The diagrammatic consists precisely in this conjunction between deterritorialized signs and deterritorialized objects.

Watson proceeds to demonstrate how Guattari on several occasions illuminates the notion of the diagram with the example of theoretical physics. The takeaway for me here was how the diagram functions 'outside of' language but nevertheless 'makes use' of signs. Watson formulates this point as follows (p. 13): 'This "diagrammatic process" makes use of signs, but not language, and therefore uses neither signifiers nor signification.'

Finally, with regard to the drawings, Watson also notes that

Guattari never claims that the drawings which illustrate his books are "diagrams," according to his concept, but his drawings do figure heavily in his analytical writing. His drawings work like diagrams in the sense that they seem at times to generate ideas, as if they were operating on their own, like little machines.

Watson also sheds some light on the relationship between schizoanalysis and cartography, and helps place it within a larger cultural-theoretical context:

[Guattari] characterizes schizoanalysis not only as metamodeling, but also as map-making, a process of building "a map of the unconscious--with its strata, lines of deterritorialization, and black holes." Guattari's emphasis on cartography (as for example in the title Cartographies schizoanalytiques) can be placed within a larger poststructuralist vogue of mapping which presupposes "the unremitting deconstruction of representational thinking" and therefore "excludes a metaphysical definition of mapping the classical mimetic sense." Recognizing this rejection of representation and mimesis is crucial to understanding how Guatarri defines modeling, mapping and the diagram... Metamodeling can be understood as a very special form of map-making. It consists in making maps that are not content to merely illustrate, but which also create and produce.

Answer 2

First, I find this a most teasing set of insights. Second, there may be a link here with Bernard Lonergan and his sense of what's going on when one works from within a schematic framework, and an unfolding way in which there is a movement toward the Unknown. It's like a drawing in perspective, the vantage point is off the page, as is the expanding frame off the page in the opposite position from the vantage point. Third, It may be appropriate to understand the significations of 5 and 6 as “The Cross” || Resurrection, “beginning again as if for the first time.” I would understand awaking on the morning of Feb. 5, 1959 and seeing on the pad “Y-E-S” as the point of “beginning again as if for the first time!” In that sense, and most significantly “the Seventh Day” remains hidden or is present in the silence of the “Unknown/Known.”
Fourth, these last several years I've been reading and reflecting on the life work of Maximos the Confessor. His work is fraught with implied schematics within an unfolding open orientation aimed toward a sense of the integration of all on a concrete cosmic scale. The Council of Chalcedon and the "Two Natures" Controversy, A.D. 381 was an attempt to describe the unity of the human and the divine in the phrase "distinctions without loss of confusion or relation." This was a key insight for Maximos as well as for Samuel Taylor Coleridge and John Henry Newman, Thomas Merton, and Bede Griffths, to name a few who have reflected on this passage from the Council over the centuries following within and beyond the Christian religion. Ron Whitmer, Gonzales, LA