In writing the previous post I felt the need to spend a few moments explaining how those characteristics of the virtual make it different in kind from the possible. I have often used the two as synonyms in an effort to avoid relying on technical terms, but for Deleuze there is a crucial distinction. In fact, this distinction in kind between the possible -- conceived as just a negated copy of the actual -- and the virtual -- conceived as positive potential different from the actual -- is the core motor of Deleuze's philosophy. You might almost say that this distinction is difference in-itself. We've touched on this idea before when we discussed Being and Non-Being (?-Being) in the Sophist, especially at the end when we pushed back against Quine's ontological 'urban renewal' (aka slum clearance). It's so important that its literally the last words Deleuze ever wrote.
There is a big difference between the virtuals that define the immanence of the transcendental field and the possible forms that actualize them and transform them into something transcendent.
So I'm sure we'll come back to this distinction many times. I pause to address it again now because the image of the two mirrors facing one another I used as inspiration for our discussion of virtual objects cast this difference in a slightly new light for me.
Possibility space is intuitively familiar to us -- its all of the things that might happen. But how can we define an open-ended entity like that? Well, in physics, they define it as phase space. It's just a space constructed from all the possible values that the various variables that describe the system (the degrees of freedom, like position and momentum) can take on. Any of the points in this space would describe an actual system at a given time, and the system is always currently at one or another of these points.
A virtual space is subtly different because it does not take from granted that we already know which are the right variables to use in describing the system. In other words, it doesn't take for granted that we know what the right question to ask will be. For purpose P, we might want to describe the system using variables (x,y,z) but for purpose Q we better use (a,b,c). Once it's established as a discipline, physics can skip over this question and just assume that things like position and momentum describe everything. But this choice of variables was anything but obvious as the discipline got established. Trying to define a virtual space takes us back towards figuring out what question we were trying to ask to begin with, and for what purpose. Which makes it more like constructing a space of possible possibility spaces. We want to investigate the different ways of describing a system and how these ways might be related.
This seems to be a fairly straightforward generalization of constructing a phase space until you realize that this time you are unable to take for granted and bracket your purpose in choosing one set of variables instead of another. All possible descriptions for all possible purposes doesn't seem like a well formed concept. So its doesn't seem like you can lay out this whole space once and for all the beginning as we did with classical phase space. All you can really do is bootstrap your way towards this space of total possibility, or possibility raised to another power (it's not clear quite how to describe this entity -- in some sense it's like describing the world as chaos). You begin with a particular purpose in mind and characterize the variables that describe the possible behavior of the object relevant to this purpose. Consider that if the behavior of the object were pushed into some interesting corner of that phase space, it might start to do something surprising, might begin to function in a new way that you had not expected. It might now lend itself to a different purpose, or at least make you wonder about other aspects of its behavior that you had neglected in your first description.
[To add a concrete example here, consider the way a tropical chimp would describe water. It rains. It forms ponds and rivers, etc ... It behaves in a certain well defined way, does certain well characterized things relevant to tropical chimp life. Then the chimp goes on a ski vacation. Or climate change brings the chalet to the chimp. Now, water can also be ice, which has a whole different set of relevant properties and behaviors. In fact, tropical chimp probably thinks of it as a completely different thing for a while. Of course, physics reassembles this all as a single phase diagram of water. But that only happens with the benefit of hindsight]
In short, you might discover a new experience of the object that leads you from examining one space of possible behaviors into examining a completely different one. The virtual is meant to describe the way you move through this space of possible spaces that cannot be completely defined in advance. The possible, by contrast, is always defined in advance and limited by an initial question that is supposed to define everything relevant about the object. The possible contains no sense of progressive specification or qualitative change. Everything is laid out at the start, and all the points in the phase space are equivalent aside from the empirical fact that the system happens to be in just one of them right now. The possible also removes the observer from the problem of describing the system. It assumes in advance the availability of a complete description, valid for every observer looking at this system in any way.
I'm trying to very abstractly describe how the virtual entails some sort of shuttling back and forth between the object in question and the subject interacting with it. And even more than just going back and forth between two fixed points, it enables the construction or progressive unfolding of the possibilities of those two sides. The virtual is always a transcendental synthesis that goes beyond the subject and object and from which they emerge. This idea of emergence from a transcendental field is at the heart of everything Deleuze wrote. The requirements this idea imposes allows you to understand all the other concepts -- the need for multiplicity, for there always being more, for affirmation, etc ... Right now, I'm finding that our discussion of the partiality and 'missing-ness' of virtual objects, they way they are in-process, in motion between subject and object, trapped between two mirrors, illuminates a new aspect of what we mean by a transcendental field.
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