05 June 2006

Intensity and the Genesis of Extensities

My work with Deleuze has largely been organized around trying to make sense of a single claim he makes in chapter 5 of Difference and Repetition. There Deleuze writes, "Difference is not diversity. Diversity is given, but difference is that by which the given is given, that by which the given is given as diverse. Difference is not phenomenon but the noumenon closest to the phenomenon... Every phenomenon refers to an inequality by which it is conditioned. Every diversity and every change refers to a difference which is its sufficient reason. Everything which happens and everything which appears is correlated with orders of differences: differences of level, temperature, pressure, tension, potential, difference of intensity" (DR, 222). If I find these remarks so fascinating and enigmatic, then it is because they stand so squarely opposed to traditional empiricism, yet Deleuze describes his ontology as empiricist. That is, empiricist begins with the premise that all knowledge originates in experience. Yet experience is precisely the given, the phenomenon, diversity. And indeed, I do not think it would be mistaken to suggest that a good deal of the secondary literature on Deleuze has often taken him as a traditional sort of empiricist. Thus in Patrick Hayden's book, we find Hayden emphasizing the first synthesis of repetition in chapter 2 of DR, despite the fact that there are two additional syntheses and that Deleuze refers to the synthesis of habit as the ground of good and common sense upon which the image of thought is based. Massumi fairs a bit better, but it's clear that habitus also enjoys a privilege in his reading of Deleuze. Yet if we take Deleuze at his word, the qualitative world of impressions is an effect of this world of intensities. As Deleuze will argue throughout chapter five of DR, intensive difference is cancelled and covered over by extensive difference, such that we must distinguish between a brute repetition (found in extensity such as the ticks of a clock) and a clothed and hidden repetition found in intensity.

Deleuze's understanding of the manner in which intensive difference generates extensities or actualized forms can be drawn from the examples he provides in the passage above. The difference between an extensive difference and an intensive difference is that where the former remains the same when divided, the latter changes in kind when divided. Thus, for instance, if I divide a piece of wood in two, I'm left with two pieces of wood. Moreover, if I combine two teaspoons of paprika together I'm given two teaspoons of paprika. However, I cannot divide or add to something like a temperature or pressure without producing an increase in kind. According to Deleuze, these intensive differences are generative of qualities, forms, and parts. Thus, for example, an increase in temperature with regard to water produces a phase transition generating steam. Similarly, a soap bubble forms itself by equalizing surface tension among the component elements of which it's composed, so as to cancel the difference by reaching a minimal state of tension. In doing so it produces the form of the soap bubble. If we begin with the actualized entity (the soap bubble) we miss the intensive difference of which it is an effect insofar as these differences tend to minimize or cancel themselves.

In light of these concepts, it can be said that transcendental empiricism unfolds the real conditions for the individuation of entities. These conditions (intensive difference, multiplicity, singularity), disappear in the actualized form, and in this regard Deleuze diverges from classical empiricism that begins and ends with the given. If such a position is transcendental, then this is because these intensive differences are the genetic conditions under which entities emerge. If this position is "empirical", then this is because these intensive differences must be discovered, because they can't be anticipated in advance, and because the effects that they produce are indeterminate and aleatory depending on the chance relations in which they're brought together. As such, transcendental empiricism is not an epistemological position (as in the case of Hume or Locke, or Kant with respect to transcendental idealism), but an ontological thesis pertaining to how beings come to be. It is because the world is composed of inequalities (intensive differences) that diversity comes to be produced as an effect.

A good deal of excellent work has been done exploring the implications of this idea of intensive differences that cancel themselves in extensities in the secondary literature. Thus, in his brilliant Intensive Science and Virtual Philosophy, Delanda shows the relevance of this idea in the biosciences, chemistry, and physics. These points are followed up nicely by Beistegui in Truth and Genesis. Massumi's Reader's Guide to Capitalism and Schizophrenia is highly suggestive as to a number of directions in which these concepts might taken. However, just as each field of actualities has its corresponding virtual field in Ideas or multiplicities composed of differential relations and singularities, all of which have their own calculus, so too does each individuated being have its intensive differences drawn out in extensity through which it is actualized.

Somewhere Deleuze remarks that these intensive differences as differences presiding over individuation must be surveyed in every field. There has been a good deal of success in thematizing these differences in the biosciences, chemistry, and physics, but what are the intensive differences presiding over the genesis of extensities in other fields such as art, the clinical setting, social relations, economics, political transformations, and so on? For instance, does part of the efficacy of analysis lie precisely in the fact that in the manner in which the analyst conducts himself as dead or the "dummy hand", certain intensive relations are subtracted from social interaction that are normally present in other social relations? Suppose, for instance, we have an individual who is convinced that others wish to denegrate and reject him because he is short, Jewish, and is doing graduate work at the wrong university. Whenever he encounters someone new he anticipates these rejections and therefore pre-emptively responds to their remarks in a mocking and combattive fashion, producing the very thing that he fears and justifying his belief about the Other; albeit without realizing it. In entering analysis the analyst doesn't respond to any of these strategies. He doesn't take offense at being mocked or prickled. He simply nods and punctuates speech. He doesn't even ask that the analysand speak about anything in particular. Does not this subtraction of a certain field of interactions introduce a new set of intensities into the analysand's social interaction that minimizes itself in a different way? Doesn't the absence of response become generative of new emergent ways of thinking, feeling, and acting? That is, over and above any "interpretations" given, there is already an intensive field in analysis that differs markedly from those we find in ordinary day to day life. What light would the investigation of this field of intensities shed on how the unconscious comes to actualize itself in the speech of the analysand. What other intensive differences are operative in the analytic setting. What counts as an intensity with respect to social change? Are there intensities that are conducive to the rise of fascist passions? Are there intensive social differences conducive to revolution? What are the relevant extensities that compose these fields? How can these concepts be put to work in other domains of experience in a non-metaphorical way that would allow us to avoid the reductive tendency to analogize everything to biology, physics, or chemistry, and truly speak of the conditions of real being rather than reducing one order of being to another order of being from which it differs in kind?


Blogger Drury said...

Dear Sinthome,

Wisely, you warn against the tendency to reduce Ideas that operate in the fields of society and art, for instance, to biology, chemistry or physics. However, I'm curious why you do not warn against reducing these fields to mathematics (the calculus, Reimannian geometry, topology). You note that each field of actualities has a calculus. Do you mean to imply a non-mathematical notion of calculus here (Delueze himself speaks of relations of speed and slowness in ATP. Perhaps he does this in order to discuss intensive differences in a language that would not reduce the phenomenon to maths) OR is the reduction of fields of actualities to maths an appropriate way of surveying the intensities or genetic conditions of these fields? Are you suggesting that math somehow draws us closer to the being of beings?

Thanks for any thoughts you might have

June 05, 2006 6:14 PM  
Blogger Sinthome said...

I don't take it that these things are being reduced to mathematics. Rather, mathematics just gives us a way of thinking certain interdependent relations. All that's really being said here is that the elements have no being apart from their relations. Thus, taking the example of the phoneme b/p in English (an example of which Deleuze is fond), this differential only has value according to its relation (in the sound spectrum, perhaps a sort of body without organs, "b" is literally nothing by itself, nor is "p" anything along). b/p takes on value in reciprocal determination because a substitution of "b" for "p" can produce a difference at the level of the actual in terms of meaning ("bat", "pat", "hat"). My remarks about differential calculus, Reimannian spaces, topology, etc., aren't intended to literally mean that language or chemistry are maths, but just to think about the local organization of these different Ideas or multiplicities. As Deleuze says, each Idea or multiplicity has its own calculus.

June 05, 2006 7:20 PM  
Blogger Drury said...

Thanks for the response Sinthome, it helps me grasp your meaning. But, is it the case that mathematics, in your estimation, gives us the best model for thinking certain interdependent relations? If no, might it be the case that there be no best model since the pertinent model, whatever it be, would depend on the actual objects or field of being? If this is the case, then how do we avoid the situation wherein our determinations are a result of tracing the transcendental from the empirical that we had hoped to explain in the first place? If there is a best model for thinking inderdependent relations, what then would you take it to be. Haven't the great philosophical transformations been touched off by philosophers attentive to mathematics or logic (perhaps we might choose to call logic the best model for thinking interdependent relations)?

June 05, 2006 7:40 PM  
Blogger Sinthome said...

I'm not quite sure I understand the question. I take it that the criticism of tracing the transcendental from the empirical lies in conceiving the transcendental in terms of an idealized resemblance to the empirical which then serves as a model of the empirical (such as a greek statue serving as a model of what the human *ought* to be). It's worthwhile to remember what calculus is: the mathematics of objects undergoing continuous variation. Take the example of a car accelerating. At each instant the velocity increases such that the difference in velocity from one instant to another approaches the infinitely small. This increase or decrease in velocity doesn't resemble the actualized motion. Of course, the relations involved in each instance of actualization will differ. Thus the relevant differences in velocity differ from the relevant differences in the slope of the curve of a circle or oval. And the relevant differences in the case of sound or images would differ yet again. Just as the relevant differences in a chemical process would be different yet again. And so on. In each of these cases, what is actual does not resemble the differentials that virtually underly it.

No doubt the future will bring other forms of mathematics that will be part and parcel of new ontological discoveries.

June 06, 2006 7:00 AM  
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