I have a few different recurrent images that I associate with Deleuze's ideas, and I think this is as good a time as any to add some pictures to the mix. This is a vector field.
That is, one example of the differential fields I mentioned last time. Each little arrow is "a" difference. Forgive the long-windedness if you're already familiar with the concept, but for other folks ... you see these vector fields in a variety of circumstances in physics, but probably the simplest interpretation would be as a description of a gravitational field. In that context, each vector tells you the magnitude (arrow length) and direction of the gravitational force acting on something. So together they are basically describing a sloping landscape, filled with hills and valleys, though what you're actually seeing is the derivative or differential (the slope) of the hill at any given point. We're just looking at a map of the changes.
Obviously, by calling it a "field", you are acknowledging that there are always a multitude of little arrows all over the place. There's actually a technical mathematical definition of the term field, as in "field of rational numbers", but so far I haven't seen anything in D&R that makes me think he's referencing that concept. Maybe later. At any rate, if we want an image of the transcendental field, or the multiplicity of difference, or univocal being, I think this picture points the intuition in the correct direction. This is a world of tiny little arrows completely without pre-established form.
Of course, we often see some patterns in the arrows, especially if we blur the line between one and the next to create a trajectory (for example, that an imaginary ball would be following as it rolls over a landscape under the influence of gravity, or that of a smoke particle caught in a turbulent current)
These field patterns can be neatly summarized as units, or things, or monads, by the singularities in the differential field. Look carefully at the vortices in that picture and you will discover that each "one" that pops out to your eye is structured by some point in the field that all the local arrows point to but where there's no arrow at that point. In other words, where the vector field is zero. Or infinity, as in the case of a black hole:
That is, one example of the differential fields I mentioned last time. Each little arrow is "a" difference. Forgive the long-windedness if you're already familiar with the concept, but for other folks ... you see these vector fields in a variety of circumstances in physics, but probably the simplest interpretation would be as a description of a gravitational field. In that context, each vector tells you the magnitude (arrow length) and direction of the gravitational force acting on something. So together they are basically describing a sloping landscape, filled with hills and valleys, though what you're actually seeing is the derivative or differential (the slope) of the hill at any given point. We're just looking at a map of the changes.
Obviously, by calling it a "field", you are acknowledging that there are always a multitude of little arrows all over the place. There's actually a technical mathematical definition of the term field, as in "field of rational numbers", but so far I haven't seen anything in D&R that makes me think he's referencing that concept. Maybe later. At any rate, if we want an image of the transcendental field, or the multiplicity of difference, or univocal being, I think this picture points the intuition in the correct direction. This is a world of tiny little arrows completely without pre-established form.
Of course, we often see some patterns in the arrows, especially if we blur the line between one and the next to create a trajectory (for example, that an imaginary ball would be following as it rolls over a landscape under the influence of gravity, or that of a smoke particle caught in a turbulent current)
These field patterns can be neatly summarized as units, or things, or monads, by the singularities in the differential field. Look carefully at the vortices in that picture and you will discover that each "one" that pops out to your eye is structured by some point in the field that all the local arrows point to but where there's no arrow at that point. In other words, where the vector field is zero. Or infinity, as in the case of a black hole:
In either case, the pattern is summarized by a singular point in the vector field. Each singularity looks like the "center" of something. But the quotes around "center" and "one" are to remind you that all we've really been given is a bunch of arrows, and that there's no hard and fast division between one singularity and another. As we move through the field, we go seamlessly from being influenced by the first to being in the vicinity of of the second, though of course there may be some sort of transitional boundary where our motion changes direction more abruptly. Singularities are thus not forms or individuals or identities. They are "pre-individual" as Deleuze repeatedly says. They are really composed entirely of difference.
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