This week my students and I jumped in to Manuel DeLanda’s Intensive Science and Virtual Philosophy. Back in graduate school I remember the horror I experienced when I first read this book. At the time Difference and Givenness was under review. I was already obsessed with DeLanda’s earlier work in the form of his articles and A Thousand Years of Non-Linear Philosophy, but these works were largely concrete analyses of the world. Intensive Science, by contrast, articulated DeLanda’s generalized Deleuzian ontology in terms of chaos and complexity theory, developing a general ontological account of morphogenesis and individuation. This was the book I had wanted to someday write. As a consequence, I immediately hated it even as I loved it. To this day I find that I am every bit as much a DeLandian as I am a Harmanian.
At any rate, as we plunge into Intensive Science, I increasingly find myself asking “do attractors do anything?” Before I get to this, first a brief explanation of what an attractor or a singularity is, drawing on wikipedia. As the wiki article on attractors explains them,
An attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed.
Take a very simple and rather uninteresting fixed point attractor like that that belongs to a system composed of a bowl and a marble. To begin with, our marble sits on the edge of the bowl. We flick the marble setting it in motion. The marble now slides up and down the sides of the bowl until it finally settles at the bottom of the bowl and ceases moving. The singularity or attractor of this system is that point of rest at the bottom of the bowl. This is the fixed point towards which the system composed of the bowl and marble evolves over time.
read on!
So, returning to the question, do attractors do anything? Let’s articulate the question this way: There are two ways of approaching attractors. One way of approaching the concept of attractors is to treat them as descriptive elements of a (scientist’s) model of a dynamic system. Another way is to suggest that attractors themselves contribute something to dynamical systems themselves, regardless of whether they’re modeled by any investigator.
These two claims are entirely different. If we take the first route, attractors don’t contribute anything at all to dynamic systems. If we take the second route, attractors are literally “doing” something within dynamical systems. DeLanda’s position, if I understand him correctly, is that attractors contribute something to dynamical systems. But I have difficulty seeing how this is so. Clearly there are singularities (attractors) of various sorts towards which dynamic systems evolve or tend, but it’s hard to see how these attractors are doing anything. The marble comes to rest at the bottom of the bowl not because an attractor is influencing that marble in any way, but because of the force of gravity and the way it functions in this particular system. Talk of this system’s attractor seems not to refer to anything ontological, but rather to an aspect of the scientist’s model of the system’s behavior. While I don’t at all doubt or reject the value of identifying attractors or various points towards which systems tend, I’m unclear as to why I should expand my ontological commitments to introduce additional entities beyond the objects themselves to account for the points towards which these systems tend. Yet this seems to be exactly the move that DeLanda is making. What I can’t figure out is why I need anything besides objects and gravity to account for the behavior of these systems. Am I missing something?
This issue is particularly interesting for me due to the debate Graham and I have had over the years over the issue of potentiality. As I go back through DeLanda, I find myself that in many respects I’m much closer to Graham and Latour’s positions regarding actualism (not to mention Michael’s) than I am to DeLanda’s. While attractors have figured heavily in my onticology, they have never been elements of objects that do something. With Graham and Latour, objects have to go through all the translations and transformations to get from one object to another. In other words, for me acorns do not virtually contain oak trees. Rather all sorts of translations have to take place to get from acorns to oak trees, and the oak tree that evolves from the acorn is a genuine and novel creation in the universe. There’s nothing that is pulling the acorn to the oak tree. Potentiality or virtuality are important dimensions of objects for me (and here I guess Graham and I still diverge), but when I think of virtuality/potentiality, I don’t have something like the acorn containing an oak tree in mind, but rather something more like the potential energy contained within a tautly drawn spring or rubber band. The translations still need to take place. Virtuality also just means that something must be susceptible to affecting and being affected by other things for interactions to take place. This is DeLanda’s first definition of virtuality in a recent talk at EGS (which my students and I watched this week. He’s a very funny lecturer, though he likes violent examples). Thus, for example, I am unable to be affected by ultraviolet light because my eyes just aren’t put together that way. Ultraviolet affects are withdrawn for me. Likewise, a knife cannot cut a neutrino because the neutral charge of neutrinos prevents it from affected and being affected by the sort of matter that composes a knife. This capacity to affect and be affected is what I mean by the virtual. Yet again, all sorts of translations at the level of the actual take place here.
Larval Subjects . 
October 27, 2011 at 12:51 am
Assuming your characterization of DeLanda is correct, then you’re right and he’s wrong about attractors. They don’t do anything. As you say, they’re elements in mathematical descriptions. The term is unfortunate in that it DOES suggest that attractors, well, attract.
October 27, 2011 at 1:07 am
I find this line of thought somewhat persuasive, but it seems like without some work it might prove too much. The metaphysicians who pose a similar argument as the “downward causation” objection to treating dynamical systems’ attractors and other emergent properties as ontologically real (rather than epiphenomenal) often intend to attack a much larger class of claimed ontologically emergent entities. For example, some dynamical-systems theorists and philosophers of mind argue that things like “anger” and “friendship” are just models of dynamical-system behavior, attractors or system-oscillation patterns that describe how the human-system functions but aren’t themselves real.
October 27, 2011 at 1:57 am
Mark,
Can you expand on that? I’m not sure I understand.
October 27, 2011 at 1:58 am
Kubla,
You’re right about the unfortunate nature of the term. I dislike it intensely. I don’t think either DeLanda nor the mathematicians think there’s anything teleological here, yet I’m still trying to understand (within DeLanda’s account if I understand it correctly) why we should introduce attractors into our ontology as doing anything. With you I’m inclined to see them as elements of a description, not elements in being.
October 27, 2011 at 3:03 am
Levi, have you ever made a cup of tea? And incorporated the expectation of water boiling (singularity, transduction) into your practice of making a cup of tea? Is this expectation not ‘real’, does it not define the reality of making a cup of tea?
Or framed in Whiteheadian terms, part of the dynamical system of ‘thirsty Levi’ involving the appetition of ‘thirst’ that can be satisfied by the cup of tea and hence involving the act of boiling water.
October 27, 2011 at 3:17 am
Hey Glen,
Of course the expectation is real, but this is not about our anticipation of events ornpsychology, but about what we include in our ontologies, ie, what what be an actor whether or not cogniciant beings existed. Do we need some additional ontological factors to explain the processes in that tea, or are the interactions themselves enough. Addmitedly, no matter how much I love him, Whitehead is an enemy here as I reject any cosmological purposiveness or teleology in the universe. I suspect DeLanda would be similarly hostile to such teleology.
October 27, 2011 at 3:58 am
this is really interesting, Levi, as one of your most ardent critics ;) and it seems this is a major point of difference from those interpreting Deleuze, Whitehead and others in a way congruent with, for example, Massumi’s work.
Aren’t you worried about leaving out massive parts of reality, i.e. what actually happens in the world, from your ontology then? This has been my central criticism since reading Harman’s book on Latour.
An ‘attractor’ (or I prefer ‘singularity’, usually mutiple singularities) characterises a threshold within a system, such as the system of OOO that is based on naming a composition of singualrities/events as objects or actors because they pass a certain threshold of non-human coherency/consistency in their object-based eventhood. You actualise that OOO-threshold singularity differently to the way I do, for example.
There is an excess here that is not accounted for by only focusing on actors without incorporating a ‘sense’ of the acts, where an ‘act’ is only one possible dimension/slice/configuration of a singular event. (Does it even make sense to talk about act-less actors? Then there are all kinds of problems around what the ‘act’ is.)
I like Ian Bogost’s keynote diagra address from a few years ago where he breaks down a game into a ‘mess’ of constituent potentialities characterised by the object relations (code-for-hardware, etc.) for engaging with a different, but related state of affairs.
With the tea boiling example we couldn’t possibly exhaust the different dimensions of the event, but it is irrelevant as these different dimensions (different POV, ways of incorporating it into wildly divergent perceptual apparatuses ‘insect media’ etc) are still arranged by the singularities.
Wouldn’t that mean that singualrities have a radical importance for OOO in that without them you couldn’t characterise an object as an object without them, as the qualities of an object are qualities-for-a-subject, but the singularities are empirically transcendental. The singularities of a object (transductive threshold of water boiling) come to characterise an event (making tea) by modifying the behaviour of the system (Levi + kitchen + colleague’s dirty teaspoons (i.e. further series of singular points) + etc).
‘Attractor’ already involves a space-time fold of the cosmos into a subject (human or otherwise), so I’d imagine it would be rejected by OOO. Surely Delanda use of the term is drawing on a particular terminology to make a point about singularities.
October 27, 2011 at 4:26 am
Glen,
Teleology means theology and design for me. I resolutely follow Darwin in advocating a post-teleological cosmology. Entities can set goals, but there’s no cosmic design or purposes. Are you advocating such theology and design theory? I part ways there and think Whitehead betrayed all that was interesting in his thought in his postulation of god and thesis that entities have subjective aims. This is why Deleuze, a Darwinian, is much more interesting than Whitehead.
October 27, 2011 at 4:39 am
And why would you be an ardent critic? I like assemblages, events and processes. My objects or substances are dynamic systems. I find it odd that folks coming from the creativity/becoming camp wish to police vocab and becoming. There’s stasis and essentialism here, but I don’t think it’s on my end.
October 27, 2011 at 5:15 am
I have not read all of the above comments, but I think the description at the end of the post about the acorn containing a tree is something that DeLanda want’s to develop an alternative of in _Intensive Science_ he gives an analogous example with an egg which comes close to Latour/Harman position as described in the post:
“While in essentialist interpretations of embryogenesis tissues and organs are supposed to be already given in the egg (preformed, as it were, and hence having a clear and distinct nature) most biologists today have given up preformism and accepted the idea that differentiated structures emerge progressively as the egg develops. The egg is not, of course, an undifferentiated mass: it possesses an obscure yet distinct structure defined by zones of biochemical concentration and by polarities established by the asymmetrical position of the yolk (or nucleus). But even though it does possess the necessary biochemical materials and genetic information, these materials and information do not contain a clear and distinct blueprint of the final organism.”(17)
October 27, 2011 at 5:23 am
Interesting, I see the point your making re teleology.
A singularity as attractor has already accumulated some ‘sense’ — a fold of the cosmos giving the singularity consistency.
Events are as much about the distribution of causality as they a distribution of subject-object relations; causality is not predetermined or ‘designed’. This is apparent in the way various thinkers have engaged with events and those elements of events that can be thought as elements of the current event but are not apparent in the current ‘pulsing’ of reality, Foucault’s eventalisation, Derrida’s to-come, etc.
For example, the singularity at play in the marble-bowl system actualised as an attractor in a system involving gravity, is actualised as a different kind of attractor when it is picked up and put to a wall so as to harness the faint sound waves in its parabolic form and concentrate them in such way as to be intelligible to the human auditory system. The way you suggest there are no attractors is the same way I would suggest that there are no objects; an object is an element of an event that has gathered some consistency as an immanent part of the event.
Critic? Well, mainly because I do not see the world as an aggregate of objects, there is an excess to objects (but present in events/process/happening of the cosmos) that is not accounted for by an object oriented ontology.
I posted my first notes on the first part (only the first several pages really) to Massumi’s Semblance and Event, which addresses these points: http://eventmechanics.net.au/deleuze/event-semblance-reading-notes-1/
October 27, 2011 at 9:00 am
Following on Eli Rosenthal (#10), one thing about the acorn, it won’t become an oak unless it’s in the right environment under the right circumstances. So we’ve got to think about the interaction within the acorn/environment couple, where the acorn, of course, plays a different role in that interaction.
October 27, 2011 at 9:39 am
A really enjoyable post, Levi. I think you broach the problem most elegantly. I’m on a brief coffee break from marking hell so, I’ll be brief. You’re right that it seems strange to treat singularities as causes and that one could adopt a nominalist position here and just treat them as features of the models with which we employ to describe dynamical systems. However, Delanda does have arguments for being ontologically committed to singularities:
1) the argument from mechanism-independence. Systems composed of different kinds of entities or stuff can exhibit a common attractor profile. This is what makes computer simulation of phenomena like hurricanes or learning cortical maps possible. The fact that one dynamical system (a computer) can simulate a system with entirely different components may be explained by positing possibility spaces or attractors common to the simulator and the simulated.
2) A related reason why we might commit to possibility spaces is that some phenomena seem to exhibit macro-stability with respect to small micro differences in their components. This is another side to the substrate independence noted in 1.
If neither condition held, then it would be hard to explain why there are higher level laws which can be applied without a complete knowledge of the micro-components of the relevant systems. For example, we don’t need folk neuroscience to do folk psychology!
I’ve got some parallel reflections over here;
http://enemyindustry.net/blog/?p=1475
David
October 27, 2011 at 2:54 pm
Levi,
It’s a bit difficult to tell if I’m mistranslating debates (some of the stuff I remember comes up in chaos theory, and some of it in analytical metaphysics, and I’m a bit rusty on both). But what I had in mind was something like: one argument for how “middle-level” entities emerge ontologically is a dynamical-systems-emergence argument that sounds vaguely like DeLanda here (but maybe the similarity is superficial).
Something like: yes, the brain is a network of neurons, and flowing water is moving molecules, but the dynamic properties of these systems, macro-states like “whirlpools” and “anger”, can’t be reduced, in the eliminative-materialist way, to being “just” epiphenomenal descriptions of the dynamics of the “real” lower-level system.
One of the common counter-arguments sounds, at least superficially, like your argument against attractors being real here. More or less: these middle-level entities can’t be ontologically real, because they don’t themselves have any effects that aren’t entirely captured by the lower-level dynamics— i.e. there’s no “downward causation”, because whirlpools are just a description of a particular steady state in fluid dynamics, not something with causal powers separate from the causal powers implied by fluid dynamics.
October 27, 2011 at 5:45 pm
I agree that potentiality remains an important concept. I agree with Latour that the acorn does not contain an oak tree, and ought not be reduced to the oak tree, but the fact is, an acorn cannot become a maple tree (without significant modification). I see the point about the translations and transformations that must be done to make the acorn into the oak (and also that the acorn can fail to become an oak), but I think there is something significant to the fact that the acorn – given the right conditions – will tend to become an oak and not a maple tree, or a cat, or Popeye.
Question: if I put my finger or another object in the bowl with the marble, which prevents it from coming to rest in the original attractor point, does that new resting position then become the attractor or is the marble just kept from it’s original attractor? Also, can there be more than one competing attractor? It sounds as if the concept of attractor is, as you say, just descriptive, and kind of an “after-the-fact” descriptor too. In a truly complex, dynamic system how would you be able to predict ahead of time what the attractor was?
October 27, 2011 at 7:07 pm
Question: if I put my finger or another object in the bowl with the marble, which prevents it from coming to rest in the original attractor point, does that new resting position then become the attractor or is the marble just kept from it’s original attractor?
By sticking your finger or other object in the bowl you’ve changed the system. It will have a new attractor or, possibly, attractors.
Also, can there be more than one competing attractor?
Sure, if that’s how the system is. Dynamicists will talk of an attractor landscape, meaning a structure of multiple attractors. For example, Berkeley’s Walter Freeman uses complex dynamics to model the mammalian olfactory system. Each odorant will have its own ‘signature’ and its own basin (attractor) in the attractor landscape. When the rat learns to recognize a new odorant, not only will a new basin be added to the landscape, but the entire landscape will change, just a bit.
It sounds as if the concept of attractor is, as you say, just descriptive, and kind of an “after-the-fact” descriptor too. In a truly complex, dynamic system how would you be able to predict ahead of time what the attractor was?
You can’t. That’s the point of modeling using complex dynamics. The only way to predict future states of such a system is to run a simulation from some initial starting point.
October 27, 2011 at 8:24 pm
@kubla, Thanks for the answers! This adds a new aspect to my interest in modeling.
Levi, how does (or doesn’t) the concept of “attractor” relate to your concept of “regimes of attraction”? Are they synonymous, or are there differences? Is the regime like the “attractor landscapes” kubla describes above?
Thanks,
Jeremy
October 27, 2011 at 11:01 pm
Hi Jeremy,
There’s a slight difference between the attractor landscapes Kubla is referring to and my regimes of attraction. Attractor landscapes consists of the singularities towards which a dynamic system evolve. In the example of the bowl, the attractor landscape consists of singularity: the bottom of the bowl. For the system modeler, these attractors or signularities are mathematically interesting because the dynamic system can reach one and the attractor from many different vectors or trajectories. For example, you can place the marble anywhere on the lip of the bowl but it will still setting in this particular basin of attraction.
Regimes of attraction are the relationships one object shares to other objects. In the case of the dynamical system consisting of the bowl and marble, the marble’s regime of attraction would consist of the bowl, the planet earth, air density, humidity, etc. Regimes of attraction play a role in how objects behave as well as in how they actualize themselves. Think of your skin. When you walk into the cold, your skin tightens, gets goose bumps, hair prickles up, etc. These are local manifestations or actualizations. These local manifestations or actualizations take place because of the regime of attraction you’re in. Here the regime of attraction would consist of things like the relative position of the earth to the sun creating cold weather, your clothing or lack thereof, etc. In a lot of ways the concept of regimes of attraction captures both the ecological dimension of the world and refers to what we often call “environments”. I try to avoid using the word “environment” because we tend to think of environments and rather fixed ones at that. Regimes of attraction are not a container but are relations to a variety of different objects (which is really what an environment is anyway). They’re dynamic, changing, unfolding, interactive, and can never be pinned down once and for all.
October 28, 2011 at 10:26 am
A point of information about attractors. They can be of several types (see, e.g. the Wikipedia article). The attractor for the marble-basin system is a point attractor. The image Levi has put at the top of the original post shows a so-called strange attractor. The whole thing is the attractor, not just some one point within it.
October 28, 2011 at 1:00 pm
Great, Levi! One other important difference (or is it?) I think, is the capacity of the objects within a system to alter the regime of attraction. In the case of the bowl – what if the marble could alter the shape of the bowl as it moved, thus creating a new attractor in each moment? Then, what if there were several marbles, each altering the shape of the bowl in it’s own way? Then, what if the bowl was continually reconfiguring itself in response to the marble’s movements and reconfigurations?
This concept is fun! :)
October 28, 2011 at 1:08 pm
Yep! Many regimes of attraction, but not all, are bilateral with the objects affecting and being affected by each other. Let’s god back to Foucault’s discussion of docile bodies in Discipline and Punish. Foucault speaks as if the human bodies being formed by a disciplinary regime– say Napoleon’s new form of military discipline –are just passive matters that have the form of discipline stamped on them. But the bodies through their responses and actions modify that regime as well. We might think here of the Christian experiments during the middle ages where they attempted to separate from all earthly things. There was nonetheless a “return of the repressed” that generated problems (in the Deleuzian sense) leading to an evolution of laws and practices in response.
October 28, 2011 at 7:02 pm
I posted a piece here using the marble/bowl metaphor to describe different approaches to social theory.
October 30, 2011 at 1:10 am
There may be no downwards causation, but there is also no upwards causation:
The very fact that network of forces seem to be identical with attractors suggests that what we have is two competing descriptions of reality, but we do not actually have a neat path from one to another:
Can we construct the attractor for arbitrary forces and relationships? No, not at the moment. We can map the forces and relationships, we can run it and see the attractor, we can’t always get one from the other.
If the situation appears where we can, then the status of attractors will become very different; if it is the case that we can derive one from the other and not vice versa, we will probably favour that approach. If it is the case that both can be derived equally from the other, then it becomes a matter of preference.
If we prove situations in which they are mututally independent? All hell will probably break loose!
October 31, 2011 at 6:06 pm
I’ve been having a think about why one might want to work in attractors vs force networks:
Force networks are inherently spatial, which is fine, but it means that there are certain patterns that it is easy to miss:
Imagine a ball in a bowl, that moves so fast as to hop out of the bowl, into a nearby one. After swinging around in that bowl it hops back over the side into the original bowl.
What is happening here? Well in one sense the ball is leaving it’s relationship to one of the bowls and exchanging it with another. It’s moving from one regime of attraction to another.
Or you might say it is undergoing a phase transition, then undoing it.
But what you might miss is that trajectory stitches back onto itself again (assume frictionless uneven bowls and no air to preserve the analogy) the ball repeats this pattern indefinitely.
If you stay there long enough to watch this you might notice, otherwise you may just throw your hands up at the realisation that the ball is not stable within the original regime of attraction, and decide you won’t be able to come to any definitive answer.
But the ball is not simply being passed from one set of relationships and forces to another, instead the portion of the cycle in the larger bowl is setting up the complementary part of the cycle in the smaller bowl so as to return it, and vice versa.
A human analogy might be a person who alternates between two areas, with distinct patterns of interaction in each, say work and home, but what he does in each area is dependant on what he did in the other.
In other words attractors allow you to create definite descriptions of behaviour not just in situations where there is a global network of forces, but also when there are multiple local networks, that other objects can move between. It is not just the effects, but the motions resulting from them.
It also provides a clear description of indirect communication between separated domains; if there is a “migrant” attractor that someone can take on, between two countries, then those countries can have a fairly stable pattern of interaction through this third object interacting with both of them, even if neither ever directly interact as nations.
But to abstract from the physical case, what do I mean by motion vs effect? Well all it needs to mean is:
Properties that objects can begin to manifest because of a network of forces, but then continue to manifest in other situations.
Properties that cause objects to change from one regime of attraction to another.
And properties that have meaning/dynamic significance in multiple different regimes of attraction.
The first can be considered decay or memory in objects, that they do not always instantly fully reconfigure when in different relationships from those that caused the previous configurations.
The second is that there are exit doors for patterns of relationships that lead to other patterns.
And the third has something to do with informational openness; that patterns of relationships can include significant features not created within that system but still meaningful in it’s terms.
Attractors may allow you to map the above, if you look for stable ones in migrant objects.
November 2, 2011 at 3:59 pm
I’m reading Delanda at the moment as well.
I’m stumped by this post
1) I haven’t read Delanda the same way, or am I misreading you? What you suggest with the oak and the acorn, that in Delanda’s reading the acorn necessarily presupposes the oak is precisely what Delanda is rejecting isn’t it? That there is no form of oak, that we get many ‘oaks’ from ‘acorns’ is due to a a multiplicity of attractors most of which are virtual, that forces do and can occur that will allow the path from the acorn to jump attractors? Thus there is no ideal form? The oak is not one giant attractor, but rather there is an attractor or rather there are several (just not an infinite amount?) that means these potentials exist within say first the germination process then the next process etc etc.
2) I’m confused by the need for attractors to ‘do’ anything. yes, attraction is a process, but if it is a dynamic process then the question is are they doing anything as you suggest. I get that. But so what? What is the importance of doing here?
Delanda states that attractors ‘confer on trajectories a certain degree of stability, called asymptotic stability’ (p-.29). So that is an acknowledged effect (is an effect a doing?).
But later he suggests ‘a space wth multiple attractors breaks the lnk between necessity and determinism, giving a system a ‘choice’ between different destinies…” (p.35). Which he suggests results in end state contingentaly affected by determinism and chance that ultimately is affected by the environment that allows the possibility of accidents and the jumping of attractors and a change of end state. This is how I understand his intepretation of morphogenesis with regards to attractors.
If as Delanda suggests ‘attractors are never actualised’ then the reason they don’t ‘do’ anything is that they never get the chance. That is why they exist in the virtual domain. As I understand Delanda’s explanation of the virtual so far (I’m only up to page 77), then the virtual is all potential, or where ptentiality exists. Surely things can only ‘do’ on actualisation, otherwise in the virtual they can only ever be ‘about to do’?
February 2, 2012 at 8:18 pm
Josh W. (24): the work/home analogy you’re describing is akin to a 2-stage periodic attractor.
The second thing is that, there are strange determinants; one topology with attractors is not alone, but generally coupled with other topologies with their own attractors. This is gone through in detail in his book, Philosophy and Simulation, which I highly recommend.
DeLanda doesn’t use the term, but what he’s arguing for is a form of structural realism (you make an ontological commitment to the real mathematical structures, of which the virtual and actual are subsets).