For some time now I have evoked the concept of attractors and points in phase space to describe the structure of objects. Since these are somewhat foreign concepts in philosophy and I am using them, I suspect, in idiosyncratic ways, it would be worthwhile to clarify just what I have in mind and, more importantly, clarify what problem these concepts are designed to respond to. In a nutshell, the concepts of attractor and phase space are designed to account for the relation between what I call the local manifestation of objects and objects in their proper being. Attractors and phase spaces belong to the proper being of objects and are virtual, while points in phase space belong to the local manifestations of objects and are actual.

To understand these concepts it is necessary to understand the problem to which they respond. So why am I evoking these concepts? What philosophical work do they do? Objects are substances. Before Continentalists coming out of a Nietzschean and process oriented tradition begin to twitch, it is necessary to understand that the question of what a substance is is very much open. There is no a priori reason, for example, to suppose that substances can’t be processes or events. I won’t get into the details of this point here, but in my view process metaphysics critiques of substance are way overblown. They are right to critique the concept of substance as a bare substratum, but nothing about this critique suggests that we should throw out the concept of substance altogether. It only entails that one proposal as to the nature of substance is mistaken or wrongheaded.

Setting all this aside, it will be recalled that one way in which Aristotle defines substance is as that which is capable of sustaining contrary qualities at different points in time. One and the same substance, say a piece of paper, can have the quality of being smooth at one point in time and wrinkled at another point in time. Being-wrinkled or being-smooth are what I call local manifestations of an object. They are manifestations of an object because they are actualizations of the power of a substance. In other words, they are actualizations of what a substance can do.

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In evoking the concept of manifestation it is necessary to carefully decouple or de-suture this concept from anything belong to the phenomenological or empiricist tradition of philosophy. Partially following Badiou in Logics of Worlds, manifestation is first and foremost manifestation to a world, not a subject, perceiver, or body. Were all sentient beings to be wiped from cosmos, manifestation would still take place. As a consequence, manifestation is not equivalent to givenness as it functions in the epistemo-metaphysical tradition we’ve inherited from Hume and Kant. Manifestation refers not to phenomenality or givenness to a subject, but to actualization within a world regardless of whether or not there is any sentient being present to receive this manifestation. If manifestation is local, then this is because it is a state of substance at a local time and place. To be sure, the manifestation can have a duration and it can be spread out in space. Nonetheless, the manifestation is still spatio-temporally localized in a world and for this substance.

Thus we have two terms: Substance or the proper being of objects, and local manifestation or the actualization of an object in the world. Likewise, local manifestations can be contraries in one and the same object. The key point not to be missed is that objects or substances are not their local manifestations. Were this the case, then it would be impossible for substances to be substances while taking on contrary qualities or properties in their local manifestations. For this reason I have made the strong claim, following Graham, that no one has ever perceived an object and that no object has ever encountered another object. Objects only ever encounter other objects as local manifestations, never as substances. As Harman repeatedly puts it, objects are not bundles of qualities. It is for this reason that I refer to the proper being of objects as virtual, carefully distinguishing the proper being of objects from their actualizations or local manifestations. Local manifestations are always effects of objects, never objects themselves.

Yet if this is the case, we need a set of concepts distinct from those pertaining to local manifestation to describe the substantiality or proper being of objects. The concept of attractor and phase space is designed to do this work. In holding that substances are that which can possess contrary qualities (or local manifestations) at different points in time, it is also being claimed that substances are variations. Objects differ from themselves. They differ from their local manifestations and they differ across their local manifestations. If this identity in difference is to be accounted for, metaphysically we require concepts that capture the principle of this variation. And since the local manifestations of any substance are simultaneously infinite in principle or at least indefinite (there’s no limit to the local manifestations possible for an object) and constrained (not every sort of local manifestation is possible for every sort of object, e.g. sound-waves can’t be colored), we need a set of concepts that both captures the object as an open set or unlimited multiplicity at the level of local manifestations, but also the manner in which this open set is constrained (we can thank Cantor for giving us the resources to think constrained infinities).

Returning to the bare substratum problem critiqued so compellingly by Locke, we need a metaphysical machinery that allows us to be concede the point that objects are not their qualities or local manifestations, but that also does not lead to the conclusion that the substantiality of objects is a bare, structureless substratum (the absolute chaos of the white sheet). If the idea of a bare substratum is so problematic for metaphysics, then this is because it undermines the individuation of objects. By Leibniz’s principle of indiscernibles, if all substances were bare substratums then they would be identical. But this is absurd. Therefore substance must have a structure that is other than its local manifestations and that is not chaos or undifferentiated.

The concept of attractor and phase space, I think, goes a long way towards solving this problem. Attractors, which can be thought of as synonyms for powers or capacities of an object are both the metaphysical condition for properties, qualities, or states of an object, but are never identical to qualities of an object. Rather, an attractor defines both the condition and constraints on the infinite being of local manifestations of an object. Thus, closely connected to the concept of an attractor is that of a phase space. Phase spaces are found nowhere in geometrical space, but rather are a field of potential states that can be locally manifested. By way of metaphor, recall your algebra classes. To the right of this paragraph you see the graph of an equation for a line. In principle that line is infinite. Again, by way of metaphor, the equation corresponding to the line is the attractor for this system, the graph is phase space for this attractor (the infinity of states the substance can occupy), and any point on that line in the space of the world would be a local manifestation of a point in the phase space of this attractor.

Now the phase space and attractor can be anything we might like. It can be the acceleration of a zebra running. It can be variations in color of one and the same substance or object. Thus, for example, with the blue coffee cup I’m always talking about, it would be a mistake to say that the coffee cup is blue. No. Throughout the course of the day the coffee cup is a multiplicity of shades ranging from black (in the darkness of night) to brilliant blue (in the noon day sun) to a variety of shades in between. This infinite number of shades and variations is a phase space. The power to make color is an attractor. The attractor itself is never blue or any other shade of color (these are all local manifestations of substance at the level of the actual), but is the power that has the capacity to give blue. Consequently, we ought not say that the cup is blue, or that the cup has blue as a quality, but rather that the cup makes blue. Among the many virtualities that inhabit the cup, among its many powers, is the power of blue-making. And this attractor that presides over this power is itself colorless. It is not the color itself, but the condition of that color. Thus objects themselves, in their virtual proper being are never manifested and when objects interact with one another they never encounter the attractors of the object, but always only the local manifestations of the object or its qualitative actualizations.

Alternatively, we might think of a soap bubble floating through the air. The soap bubble is not a sphere– though occasionally it is in its local manifestations –but is rather an undulating variation across time.

For a moment it is a sphere, then it is ovaloid, then it is an irregular “s-shaped tube” and so on. It is clear that we can distinguish two different dimensions of the shape of any object. On the one hand, there is shape as local manifestation (at the moment it is a sphere). On the other hand, there is virtual shape or those attractors presiding over the phase space of the soap bubble’s shape, defining an identity-in-variation of the object across these undulations and local actualizations of points in this phase space. This virtual space of the object is an odd shapeless shape that functions as a condition for any local manifestation of the object. It is the power of shape defining a field, not any particular shape itself.

A couple of points should be made here. First, it is clear that at the level of actuality or local manifestation, objects are highly relational. Points in the phase space of the attractor of my coffee cup are actualized as particular shades of blue because of an interaction with other objects: photons of light. The soap bubble undulates as it weaves its adventure through manifestational space because of its encounter with wind. Consequently, we will have two ways in which the powers of objects can be manifested. On the one hand, there will be passive actualizations where the manifestation of a point in phase space is brought about through being acted upon by another object (the wind mutating the soap bubble). Likewise, on the other hand, there will be active actualizations where manifestation results not from being acted upon by another object, but rather from the internal power of the object itself. Thus, with Badiou, I agree that in many instances manifestation is relational, while rejecting the thesis that local manifestation is the object. All sorts of intricate questions remain to be asked about how this transition between virtual substantiality and local manifestation takes place.

Here there are two important points to be made. First, insofar as the virtual or substantial being is a constellation of attractors (my appropriation on Harman’s treatment of objects as “systems of notes” in Tool-Being) 1) it follows that in inter-ontic or inter-object interactions certain attractors can remain dormant or asleep while other attractors are actualized, and 2) the attractors themselves form relations within the endo-consistency of the object such that they can actualize themselves in ways that they would not be actualized were they isolated from one another. Second, not all objects can inter-relate at the level of local manifestation. In effect, some objects are invisible to one another. Neutrinos, if they do in fact exist, fall straight through the earth. This entails that there is nothing about the local manifestations of neutrinos that evoke local manifestations in other objects.

Third, if the concept of objects as split between local manifestation and substantiality is so important, then this is because– much like book-keeping in a ledger –it trains us not to confuse the proper being of objects with their local manifestations. The confusion of the proper being of an object with its phase space is what Bhaskar refers to as “actualism”. Here the idea is that objects are nothing but their manifestation. Actualism generates a whole host of philosophical problems ultimately leading to correlationism. However, in addition to this, actualism or the confusion of the proper being of objects with their local manifestation leads us to ignore the excess of objects over any of their local manifestation, reducing objects to a state of passivity or their relations to other objects at the level of local manifestation. What is lost here, as Harman has compellingly argued, is the possibility of accounting for how change within networks or assemblages of relations might be possible because there’s no longer anything other than the manifest relations from whence change might come. Additionally, actualism leads to a fatalistic and pessimistic view by virtue of reducing entities to their local manifestations, leading us to become apologists for the states of situations and their necessity by preventing us from discerning how objects always contain an excess over any manifestation the functions as the condition under which other states are possible.