On Deleuze and Guattari and 'indiscernibility'

It is not as if one transformed itself into the other, but as if something passed from one to the other. This something can only be called a 'sensation'. It is a zone of indetermination, of indiscernibility, as if beasts and people respectively had reached that point always ad infinitum that immediately precedes their natural differentiation. This is what we call an affect.

Art itself survives in these zones of indetermination, as soon as the material passes into the sensation ... These are blocs. Painting needs something different from the ability of the painter to trace resemblance between the animal and the human form showing us their transformation: we need the potency of a background which can dissolve forms and impose the existence of a zone where we do not know anymore what is animal and what is human, and where the triumph or the monument of their indistinction delineates itself...

Thought
Whichever its affective tone, the primary characteristic of what is encountered is that it can only be sensed, and therefore it is opposed to recognition. "It is therefore in a certain sense the imperceptible ... It is imperceptible precisely from the point of view of recognition." Contingent imperceptibility of the too small or too far for the empirical exercise of the senses, is different from the essentially imperceptible, that which can only be sensed from the point of view of a transcendental exercise of sensibility. Not a simple sensible being, but "free or untamed states of difference in itself; not qualitative opposition within the sensible, but an element which is in itself difference, and creates at once both the quality in the sensible and the transcendent exercise within sensibility. This element is intensity, understood as pure difference in itself, as that which is at once both imperceptible for empirical sensibility which grasps intensity only already covered or mediated by the quality to which it gives rise, and at the same time that which can be perceived only from the point of view of a transcendental sensibility which apprehends it immediately in the encounter."
That which can only be thought is an aleatory point enveloping differentials of thought, designating the highest power of thought, i.e. the unthinkable, or the inability to think empirically. All begins with sensibility: it is always through an intensity that thought comes to us. A violence is communicated from one faculty to another, an Idea: "an impulse, a compulsion to think which passes through all sorts of bifurcations, spreading from the nerves and being communicated to the soul in order to arrive at thought."

Inflection
Exfoliation happens through forlds, or curves. In order for exfoliations and curvatures to become perceptible, the surface has to be de-squamated.
For Deleuze, the ideal genetic element of the variable curvature, or fold, is the inflection. Inflection is the true atom, the elastic point, the (metaphysical) point where the radius 'jumps' from inside to outside. In other words, a line is the path of a point that changes direction at an inlfection (or folding) point. For Deleuze, this is the eternal return of difference, or the differential of thought: the idea.

In The Fold, Deleuze tells us how Paul Klee defined inflection as the genetic element of the active line, showing his affinity with the Baroque and Leibniz, and his opposition to Kandinsky, who was closer to Descartes and based his painting on an idea of rigid angles, rigid points that can only be moved by an external force.
Klee's point is a point of inflection, where the tangent touches and crosses the curve: the point-fold.
Bernard Cache defined this point of inflection as an intrinsic singularity which is not related to a development of coordinates (as extrinsic singularities, maximums and minimums do), and is not high nor low, at the right or the left, in progression or regression, because it is in absence of gravity. It is the pure event of a line or a point, virtuality, ideality to be actualised from the coordinate axes. In itself, it is not in the world yet: for Klee, it was the locus of 'cosmogenesis' (cha-os-mosis), a non-dimensional point between dimensions, an event waiting for an event to happen (point of indiscernibility, Idea?).

Cache classified three possible transformations of inflection:
-the serpentine line, depending on the morphogenetic field underlying the inflection point and on minimal outside influences by other lines: vectorial or symmetric transformations operating according to logical laws, and transforming inflection into a point of regression, or a cuspidal point (twofold, ogiva, circle). Each of these lines are to be considered in the third dimension as sections of planes, or surfaces (From Campbell, The Masks of God: Occidental Mythology: "The wonderful ability of the serpent to slough its skin and so renew its youth has earned for it throughout the world the character of the master of the mystery of rebirth ... Dwelling in the earth, among the root of trees, frequenting springs, marshes, and water courses, it glides with the motion of waves..")
-projective transformations expressing the projection, on an external space, of internal spaces defined by hidden parameters and variables of potential allowing for infinite variations. This is the type also described by D'Arcy Thompson and Renè Thom, and we can see it in nature as membranes like cells, shells, horns and all surfaces of minimal tension
-lines or planes with infinite variations, or infinitely variable curvatures, fluctutations from fold to fold: a curve crosses an infinite number of angular points and does not have any tangent, enveloping a spongy, cavernous world, more than a line and less than a surface (Mandelbrot's fractals, as non-dimensions). More than a question of determining now a point in-between two points, it is now a matter of always adding a new deviation, transforming every interval into the locus of a new curvature. From fold to fold (rather than from point to point), with contours dissolving and liberating the formal potentials of a material in transformation. The transformation of inflection does not admit symmetry anymore but becomes vortical: "the line effectively folds itself into a spiral differing the inflection in a movement suspended between heaven and earth, that distances or approaches a center of curvature indefinitely, and, any instant "takes its flight or risks to crash upon us."
Turbulences, in this suspended inflection, generate other turbulences, and the spiral follows a fractal model: dissolving its contour, turbulence ends in foam. Inflection becomes vortical, and its variation becomes fluctuating. It is the locus of vortices, sponges, mazes, meanders and labyrinths.

The art animated by these inflections is not anymore an art of structures but of textures, or 'cont-textures' (example of Bernini and his twenty different marbles). Art can thus be said to always follow a Baroque principle, that of a total art, or a unity of the arts, by extension. Every artistic expression tends in this sense to prolong itself, and to realise itself in the successive one, which surpasses it, in a mosaic where each different panel is surpassed by a matter that crosses it. Artistic forms touch and con-fuse themselves at points of indiscernibility, or inflection points, where the form is not yet realised.