In The Fold, Deleuze mentioned the unfamiliar name of Bernard Cache several times. Upon investigation, it turns out Cache's Earth Moves: The Furnishing of Territories (written in 1983 but never published) was a significant influence on Deleuze's Leibniz book (published in 1988). Of course, Cache was heavily influenced by attending Deleuze's seminars, to the point where Earth Moves' dedication is: "For Gilles Deleuze". So by reading this just in advance of our re-reading of The Fold, we'll be able to follow a full cycle of the intellectual feedback loop.
Cache's book is also very interesting in its own right, as I know of no other example of someone actually attempting to use Deleuze's ideas to analyze a subject that the master himself hadn't broached. Cache is an architect and furniture designer, and you could consider Earth Moves a sort of Deleuzian theory of architecture. This description, however, doesn't really do it justice. Even though Deleuze's style is recognizable regardless of what subject he approaches -- whether it's Spinoza or Nietzsche, painting or film -- he never created a system that one could simply apply to a given subject matter. So while Cache's approach to architecture definitely has a Deleuzian 'way of seeing', and occasionally a bit much of the master's allusive writing style, it's not immediately clear how his theory qualifies as 'Deleuzian'. In fact, in the main text, Cache never mentions Deleuze at all, and the idea of the singularity is the only concept we can point to that is borrowed directly. Instead, Cache accomplishes something much more subtle than a mere application -- it's as if he tried to rebuild Deleuze's non-dual philosophy from scratch in a new setting. This change of terms, together with the fact that the setting has an inherent connection to concrete images, makes the book particularly useful for our individuation project. Here, I'll try to approach it in the same loose interpretation style that Cache uses rather than going through it chapter by chapter; we may come back to some of the details when we return to The Fold.
Imagine that the surface of the earth is just one great big piece of cloth. In this flat and depopulated world, there is nothing but the cloth. No animals, no people, no buildings, just the topographic undulations of the surface. But the cloth is remarkably flexible, and it can deform at infinite variety of scales, both spatially and temporally. It can plunge down to create valleys and push up to form mountains. It can fold back over on itself to create the appearance of volumes. And any of these structures can surge or ripple across it, the way a tsunami travels the breath of the ocean even though the water just moves up and down. We should think of it by analogy to Mandlebrot's space filling fractals -- a topologically two dimensional object whose constantly varying curvature seems to conjure a third dimension from nowhere. Everywhere we look, we discover that solid objects turn out to be the nested folds of this surface. We too are nothing but these folds, and our looking itself nothing but a loose stitch that temporarily pins the fabric to itself.
Folding provides another interesting metaphor for the non-dual, and perhaps a particularly useful one since it immediately makes clear how emptiness and non-duality relate. All the solid and separate volumes that appear to populate the surface are hollow. They are perfectly real, perfectly differentiated structures, but if we were to pull the whole fabric taut again, we would find they disappear without a trace of essence. But Cache's analysis goes much further than this lovely metaphor. He breaks the fold down into three components -- the inflection, the vector, and the frame. Nominally, each of these refers to a specific aspect of a real construction site; the whole classification is inspired by an interesting meditation on the history and topography of Lausanne (it turns out that the whole book was inspired by Godard's short film about Lausanne). While the concepts have a wider applicability, the simplest way to understand them is still to think of the architecture and urban planning context that Cache begins with. Consider these diagrams that refer to the topography of Lausanne (pg. 13).
Before anyone shows up, the earth around the future site of the city has a shape (this would actually be diagram zero, with no arrows at all). Overall it rises from the level of the lake on the left, to the plains on the right, though not in a straight line. Usually, we are immediately drawn to see the landscape in terms of the various high and low points in this diagram. So we might say that the city is characterized by a couple of distinct hills separated by a prominent valley. Instead, Cache encourages us to think of this diagram more abstractly. In fact, the surface in itself doesn't have high and low points. If we rotate the diagram at an angle, these extrema would change position. Maximum and minimum are not inherent properties of the curve itself, but depend on the axes, the vectors, we impose on it. Of course, when we are talking about the earth and architecture, gravity is the default vector we are always forced to deal with. But it's important to see that this vector comes later, as a function of how we intend to use the surface. If we look at just the curve itself, independent of axis or orientation, it's not the minima or maxima that jump out at us, but the simple fact that it varies -- first it bends one way and then it bends another. No amount of rotation or translation or even scaling erases these bends, which are defined by the fact that the curve is convex here and concave there. The labels convex and concave are purely nominal and depend on which way we approach it, but their difference, and the inflection that leads us from one to the other is not. Inflection is an inherent part of the curve, what cache calls the atom of a curve or surface. So, interestingly enough, it's these inflection points that we usually associate with the second 'derivative' of the curve that actually provide its original description. After inflection comes the vector which orients the surface, and then finally there is the frame, which holds together both the extrema and the inflections which separate them as part of a single landscape. In the case of Lausanne, this frame is dramatized by a combination bridge and tunnel that draws together distinct parts of the city that would otherwise be separated by hills and valleys. Folding always involves these three moments: 1) inflection 2) vector 3) frame.
For Cache, architecture is the art of framing. Our buildings frame the activities of living and working. Our windows frame a connection between the interior of these spaces and their surrounding. Even our very bodies are frames for our biological life, hollow spaces created by a fold that lets us ingest the outside and digest it on the inside. And of course, we put frames around our art. Cache discusses how all of these shapes serve to create a relatively stable and protected space that is meant to allow something to happen inside. Normally, we might see the shape of the frame as something we simply impose on the world for our own purposes. But following the metaphor of folding, Cache has a more immanent explanation of the origin of the frame. It's more like a crystallization of an amorphous and constantly varying landscape into a fixed shape.
This is explicitly meant to recall Simondon's theory of individuation as crystallization. Before the frame, we have only something like an amourphous milieu, filled with fluctuations of energy (inflection), and various polarizations (vectors) that will enable the medium to crystallize, but we don't have any concrete individuals. In Cache's terms this is the sort of intrinsic dis-orientation of the surface where it dissolves into nothing but completely chance fluctuations that don't even rise to the level of inflections (I'm not sure whether to think of this as the limit of a perfectly flat surface or an infinitely randomly crumpled one, a sort of white noise surface). It's pretty hard to even talk about this ungraspable sea of difference. But somehow it has the potential to become every solid crystalline object we find. In Simondon's scheme, it does this through the intervention of a seed. Some asymmetry appears in the surface, an inflection which instills it with what Cache calls a tendency. This isn't a full polarization of the medium which would correspond to a vector orienting the surface from the 'outside' and defining minima and maxima. Instead, these tendencies are vectors that point perpendicular to the tangents of the surface, and converge towards some center of curvature. We might call them the intrinsic vectors of the surface, and they appear in conjoined convex/concave pairs on opposite sides of the inflection point. They provide a sort of seed polarization that enables a fold to crystallize on the surface. In short, Cache considers Simondon's scheme less as a kind of splitting into phases than a kind of folding, and he maps the three components of a process of individuation -- amorphous pre-individual medium, seed, and crystal -- onto the three components of folding -- inflection, vector, and frame.
This is already an interesting change of metaphor that elucidates certain troublesome aspects of Simondon's theory. First, it gives it an even stronger non-dual flavor because it immediately explains the apparent duality of a splitting or phase transition as simply the folding of a single surface. Second, it goes a long way to help us understand Simondon's insistence that 'higher' individuations like the biological, psychic, and social, are not constructed on top of a completed physical individuation, but are inserted within it. The levels don't form a pyramid, but create a sort of hierarchy of neoteny, as if they were a nested set of detours on the way to complete crystallization. Thus, biological life, for example, is all the more successful in being a 'defective' aperiodic crystal that doesn't completely solidify the environment once and for all but crystallize metastable forms. Here Cache gives us the great image of fold within folds. We can imagine that the surface being folded never actually returns to touch itself and create a completely closed form. Instead, within each fold of fabric there remains enough slack to create another fold, and so on ... The surface folds up again and again, just like Mandlebot's fractal constructions. The same process of inflection, vector, fold is applied at a infinite variety of scales, such that new individuals are produced within the frame of the original. This model makes it much easier to understand how Simondon's physical individual is still bathing in the amorphous energy of the pre-individual, and how this leads it through further individuations towards the trans-individual. The single surface never closes and is never exhausted, it simply continues to fold.
Though the idea of a fractal folding appears quite late in the book, it is central to understanding Cache's overall point. Because while he presented the series inflection → vector → frame in its logical order, he thinks that in terms of activity this series runs in reverse. That is, vectors only start to exert force on a surface after passing through a frame that selects and stabilizes them, almost as if they needed a ground to push against in order to have an effect. Likewise inflections only appear to us as transitions between extremes defined by these vectors. In other words, every new fold happens within a previous fold, ad infinitum ... Every new individuation is an extension or deepening or differentiation of one that was already underway. Or conversely, every frame implies a larger out-of-frame, some unfolded exterior context or milieu in which it arises, but one which is nevertheless itself a folded frame at a larger scale. Obviously, this perspective fits perfectly with the way Simondon's theory posits an always incomplete individualization that maintains itself in a state of metastable feedback. A bit of the formed crystal becomes the seed that polarizes the medium and allows for the crystal to grow by sucking in new material. If this feedback loop works too well, however, the crystal grows to consume the entire medium, converting everything into copies of a single geometric frame and completely sealing the fold. All the interesting living forms we find somehow avoid this extreme. They are formed inside a frame that is not completely closed and actually introduce new centers and new variations in the partially enclosed surface that prevent it from sealing shut as a finished crystal. No life is possible at the pole of the amorphous pre-individual milieu. But a crystal is equally dead. Cache attempts to illustrate how life is a process of folding that always happens within the hollow space opened by another fold with a diagram of the surface of the earth (pg. 117).
Finally, the same concept of fractal folding can carry us into the mystery of what is always philosophy's most difficult question -- how can we, by hypothesis just a tiny fold within a fold within a fold of this great surface, imagine that we see its whole structure stretched out before us? If his theory is correct, how can Cache come up with it? Wouldn't this sort of all encompassing perspective only be available at the level of the first fold, the largest frame? More generally, if each fold or frame forms a subject at the center of its curvature, wouldn't this subject be almost closed on itself, able to perceive only further folds that happen within itself? I think both of these objections would hold if the surface only curved in one direction. But I think the type of infinite space-filling curve we're talking about precludes this possibility. Instead, our image of the surface should be something more like the infinite spiraling complexity of the border of the Mandelbrot set (minus its topological closure as curve). It quickly becomes almost impossible to tell whether a point is on one side of the curve or another. Thus there are centers of curvature and nearly closed frames that constitute subjective forms on both sides, and one side's infolding becomes the other's unfolding. If we label one side the soul and the other the body, we can start to understand how these are completely distinct, and yet both inseparable and even entangled hollows created by the process of crenulation. So which side are we on? Are we looking in or out? Or to bring it back to the architectural question Cache (almost) explicitly asks (pg. 72) -- which way does a house face?
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