If Deleuze is a materialist, it is because he brings materiality to its limit: the familiar materiality of bodies and their physical relations of force, matter as substantial and formed, at its limit, passes over into the bodiless, insubstantial realm of an unformed and non-formal matter-function. We have the physico-empirical plane of material bodies, of visibilities or sensibilities, which relate in the passage of forces from body to body in causal chains. A cue strikes the cue ball, which strikes another ball, et cetera, constituting a series of passages of force. The complication here is that the passage of force becomes autonomous, inscribed on a different plane than that of the bodies which act and react.
It is this autonomy of passage which Deleuze and Guattari name rhythm. Rhythm must be understood in terms of an alternation, a passage from one thing to the other; they say that rhythm is what happens between milieus, it is a transcoding, a "coordination of heterogeneous space-times." (ATP 313) Coding refers to what Deleuze, in Difference and Repetition, calls 'habit': a regular pattern, a series of relations that endures coherently, that repeats. A milieu or habitus is ultimately no more than a consistent set of habits/codings which endures. Rhythm, however, is not simply a habit, a regular pattern or 'meter', but refers to that which interrupts habits/codes, undermines them, and forces them to reorient.
Rhythm, as alternation, involves a passage from one coded milieu into another; yet this does not simply mean that two foreign milieus relate to each other, that one relates to the other as different from itself, composed of different codes. Rather, they together relate to the outside, to an alterity irreducible to some determinate other. It is this outside upon which the passage is inscribed, in which rhythms reverberate. Rhythms are basically the relation between disparate codes, series, or patterns, such that two different codes relate to the Disparate, to their divergence as such. It is across this disparity that a novel conjunction of the coded elements occurs, that a 'transcoding' is born.
Rhythm is that reorientation of codes or patterns that results when two milieus encounter, between each other, that paradoxical element which undermines their consistent conjunction; ultimately, this element is nothing but a pure distance - not the distance between them, but the distance of each from its threshold, the point after which coding breaks down and the consistency of the milieu is compromised, resulting in a change in nature. Every coding envelops this distance, this threshold of decoding, which is not simply the distance of one set of habits from another, but more like the distance of each coding from itself, its inability to extend itself infinitely, to perfectly coincide with itself. At this point, the being of the thing (milieu) becomes indistinguishable from its problematic status - the consistency of the milieu depends upon the problem of its relation to the limit beyond which it will decompose.
Rhythm as alternation is ultimately the incessant oscillation between the consistent encodings of a milieu, including the transcoding that preserves this consistency when foreign milieus must relate across their difference, and the decoding or loss of consistency which characterizes a passage to the limit. This is the passage which becomes autonomous, drawing a plane apart from that of the milieus and their codes. Passage to the limit is the way an arrangement composes itself as such: beyond the incidental conglomeration of the milieu, an arrangement organizes itself on the basis of a limit it must posit as such by extending its power that far, by occupying the whole distance between its borders, and thereby realizing the threshold beyond which its influence ceases. As Deleuze and Guattari say, the territory is a place of passage, or even the place of passage, the taking-place of passage. The territory is constituted precisely when the threshold of a milieu (or the vertiginous conjunction of several thresholds, converging on the paradoxical element of an encounter) becomes the vector of deterritorialization, thus retroactively positing the consistency drawn between milieus as their 'territorialization', as the becoming-expressive of the habitual functions, and the emergence of partial surfaces, membranes, which give body to limits.
This incorporeal transformation of milieu into territory occurs only when the threshold qua problematic point is treated not as some external threat to the consistency of the milieu, but rather as intrinsic and constitutive of that consistency, a 'positive principle of non-consistency'. If the milieu is defined by a warding off of problems - a denial of the consistency of the milieu itself as problematic and unstable, endlessly caught in a coming-to-itself (positing of its constitutive limit) coterminous with a leaving-itself or becoming-other (passage to the limit/confrontation with the threshold of consistency) - the territory is born of a simple 'change of emphasis': the problem is posited as constitutive/productive, the entire habitual field is reoriented in relation to this problematic status.
Insofar as the entirety of the encoding is mobilized in a passage to the limit, the passage itself, in the mode of a fleeing or escape, a passage across the threshold indistinguishable from the threshold itself posited as such, is endlessly displaced within the field, potentially appearing anywhere, amongst any conjunction of elements/functions. The problematization of the field thus involves a displacement of the paradoxical element (line of flight, aleatory point) within the field such that the elements and functions are subject to a continuous variation or redistribution. A materialism of the problem, therefore, should acknowledge the ontological status of the problem as the line of flight, the drawing of limits which territorializes or individuates the pure multiplicity of milieus by virtue of an incorporeal surface, a body without organs, tearing asunder coded elements and functions which are then arranged in relation to the problematic points (thresholds) which, by chance, present themselves in the passage to the limit.
The point here is that the vulgar, physical materialism in which all that exists is empirical (perceptible) phenomena enchained by causal determination does not go far enough. In this view, reality appears to us as incomplete, plagued by misunderstandings, errors, illusions, et cetera, only insofar as we possess finite, imperfect epistemological relations to it. So reality is an ontologically complete and consistent 'mechanism', everything can be explained immanently within the material world without reference to any divine or supernatural beyond; unfortunately, this view nonetheless presupposes a perfect, untainted intellect, unbound by finite epistemological limitations, which has total access to the complete chain of causes.
Even if we have no conceivable way of occupying such a position, or we deny that there is any (divine) observer occupying it, this vulgar materialism still presupposes that such a position exists in principle. In this sense, the incompletenesses of reality as we experience it, the problems which intervene and disturb the consistency of our world(s), are only epistemological, symptoms of our finitude and embeddedness, which can be progressively overcome through scientific rigor, increasingly approximating the 'ideal', untainted prerogative. Existence is posited as complete, consistent, only insofar as we rely on a constitutive exception by reference to which we can explain apparent inconsistencies (problems) as illusions resulting from a false identification with the exceptional point.
Deleuze's point, if we may put it in these terms, is precisely that this incompleteness is not epistemological, that there is no exceptional point of clarity from which all problems will be recognized as illusory. He is far more radical, asserting that materiality must be extended to the problems themselves, that the inconsistencies we confront must be included in materiality. This means that for Deleuze, the ontological itself is incomplete, inconsistent, problematic. There is no exceptional point unencumbered by the limitations of finitude. In this way, we do not reduce all problems to the central problem of the inadequacy of our knowledge; rather, problems attain a primary ontological status. This status is precisely that of the threshold posited in the passage to the limit constitutive of the consistency of any arrangement; it is the force of deterritorialization which retroactively territorializes the milieu from which it departs; it is the incorporeal transformation of the ordinary into the singular, of delimited coagulations of flows into the unlimited becoming of virtualities.
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