Uexküll (3.4) Theoretical Biology, “The Mark-Signs”, summary

 

by Corry Shores

 

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[The following is summary. All boldface and bracketed commentary is my own. Proofreading is incomplete, so please forgive my typos. Page citations refer to the 1928 German edition first and to the 1926 English edition second.]

 

 

 

 

Summary of

 

Jakob von Uexküll

 

Theoretical Biology

[Theoretische Biologie]

 

Ch.3 The Content-Qualities

[Die Inhaltsqualitäten]

 

3.4 The Mark-Signs

[Die Merkzeichen]

 

 

 

Brief summary:

Each threshold in our awareness of variation presents a “mark-sign”. The ability to discern mark signs varies for the person or creature, depending on their level of sensitivity to that sort of qualitative variation. There are two kinds of mark-signs. {1} Qualitative  mark-signs: these distinguish qualitatively-different things, and they are represented by angles in our diagrams. {2} Intensive mark-signs: these are found along a continuum of variation; they are determined by thresholds of variation-awareness; and they are represented in our diagrams by the lines between the qualitative mark-sign angles.

 

 

 

Summary

 

§383

[A “mark-sign” corresponds to a threshold in our attention. So a mark-sign is found at each of the smallest discernible objective changes in a stimulus. (It is an “alteration in the content that is just perceptible to the attention”.)]

 

[In the prior section we discussed a method of determining thresholds, based on Weber’s technique. The idea is that a continuously varying objective intensity in a stimulus is perceived in steps. The objective stimulus can increase continuously without our sensing it, but when it crosses a certain threshold in our awareness, we notice a change. We can think of these thresholds as moments when our attention changes or “turns”. Uexküll will now define his notion of the mark-sign in terms of these thresholds where our attention changes.] “By employing the method of determination of threshold, and developing the same principle, we arrive at the concept of the mark-sign” (65 / 76). [Uexküll describes a method for finding the thresholds or mark-signs in a color continuum. It seems the procedure finds the smallest objective variations that we can discern as distinguishable. Apparently, we keep magnifying the constituent parts of the continuum until we find a part where we are unable to discern a difference. The number of all the smallest discernible parts is the number of mark-signs in the continuum.]

We divide up the whole colour-band between two turning-points into tiny segments lying alongside one another, and make them so small that at least two adjacent parts, considered by themselves, are indistinguishable by the eye. Now let us magnify the individual parts until every two adjacent ones become just distinguishable from one another. Then the number of individual parts gives the number of mark-signs that the colour-band holds for us. Interpreted in this way, the mark-sign means the alteration in the content that is just perceptible to the attention.

(65-66 / 76)

 

 

§384

[The capacitiy to discern mark-signs varies with abilities and handicaps, like between a trained musician and a tone-deaf person.]

 

Certain people are more sensitive to color variations, and thus they experience more mark-signs in the same color continuum. “The number of mark-signs for colour increases with the skill of the individual observer in distinguishing colours; it gives us a clue to the amount of colour in his appearance-world [Erscheinungswelt]” (66 / 76, bracketed insertion mine). Color-blind people have fewer color mark-signs. While those with normal sight can think of the color-blind person’s appearance world by subtracting colors, the color-blind person is unable to imagine what it is like to have those color mark-signs. The same holds for those with tone-deafness (66 / 76).

 

§385

[There are two kinds of mark-signs: {1} qualitative  mark-signs, which distinguish qualitatively-different things and which are represented by angles in our diagrams, and {2} intensive mark-signs, which are found along a continuum, are determined by thresholds of variation-awareness, and are represented in our diagrams by the lines between the qualitative mark-sign angles.]

 

Uexküll then distinguishes two sorts of mark-signs: {1} mark-signs of qualitative difference, and {2} mark-signs of intensive difference. Qualitative differences are always ones involving definite qualities, and we represented them using angles in our spatial diagrams. But other less qualitatively definite qualities appear as intensive variations between definite qualities. They are distinguished by the thresholds.  [Recall the color example from section 3.2.

Here we see the two different sorts of mark-signs. Red, yellow, green, and blue are qualitative mark-signs, and the variations between them contain a series of intensive mark-signs.] When assessing intensive mark-signs, it is arbitrary where we start and which direction we go (66 / 76-77).

 

 

 

 

 

Works cited (in this order):

 

Uexküll, Jakob von. 1928. Theoretische Biologie, 2. gänzlich neu bearbeitete Auflage. Berlin: Springer.

 

Uexküll, Jakob von. 1926. Theoretical Biology. Translated by Doris Livingston MacKinnon. London: Kegan Paul, Trench, Trubner & Co. / New York: Harcourt, Brace & Company. PDF available at:

http://www.archive.org/details/theoreticalbiolo00uexk

 

 

.

Somers-Hall, (Ch.5), Deleuze’s Difference and Repetition, ‘Chapter 5. The Asymmetrical Synthesis of the Sensible’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Chapter 5. The Asymmetrical Synthesis of the Sensible

 

Very brief summary:

In Chapter 5, Deleuze examines how intensive difference is found in the extensive world and is at work in the productions of extensive properties and qualities. The Idea colludes with fields of intensity in the world so to explicate actualizable paths of development implicated in the Idea. On account of intensity’s “depth”, it cannot be represented, and also, it is a wellspring that continually injects difference, variety, and energy into the world by constantly generating differential relations. This depth is also at work in individuation, which is the fundamental process that produces the structures that secondarily come to be our subjectivity, ego, I, etc.  In efforts to represent intensity’s depth, we posit an Other as the grounds of representation, but it is an erroneous concept.

Brief summary: 
Intensive difference is at work in the generation of extensive properties and other qualities.  In thermodynamics, intensive differences in heat explain the work that is done in such thermodynamic systems as engines, for example. But more needs to be said, because we still need to know what makes intensive differences come about and regenerate. Since instead of succumbing to entropy which equalizes intensive differences and reduces the world to a homogenized disorder, we instead have living forms that increase intensive difference and tend toward heterogeneous order. These intensive differences that are spatially distributed come about on account of a deeper sort of intensity of some kind which generates also the extensive space and qualities within it, and as well it is responsible for the continual renewal of intensive difference in the world. One way to distinguish intensive from extensive multiplicities is what happens when you divide them: divisions of extensity produce homogeneous parts, while divisions of intensity produce heterogeneous ones. Intensities interact with Ideas when explicating into extensive actualizations. The Idea provides a network of actualizable outcomes, and the intensive circumstances of the world help channel the unfolding of those actualizations. For example, the DNA of the embryo is like the Idea, and it instructs the cell to divide, but the differential relations in the given chemical make-up of the embryo encourage certain divisions of the cell rather than others. Thus this development is dramatized. There is also a developmental process underlying who we are. It is our individuation, which is not our self, subject, or ego, but it is responsible for them. Since it is unrepresentable, our faculties fail to recognize it. They instead see as the grounds for representation a supposed Other which is the omni-perspectival view on the world that guarantees the wholeness of its parts. But in fact it is representable. Also, since philosophical thinking takes us to the pre-subjective structures of the world and ourselves, it is a solitary and solipsistic exercise.

Summary

(5.1 Introduction) We move now from the Idea to the role of intensive difference in space. (5.2 Thermodynamics and Transcendental Illusion) For Deleuze, difference is a difference in intensity. In thermodynamics, a system performs more work when there is a greater differential between input and environmental temperatures. In other words, an intensive difference is what changes the functioning of the system. But thermodynamics also has the idea of entropy, which implies that heat differentials in systems over time tend to equalize as the system enters into a state of homogenized order. Deleuze thinks thermodynamics is missing the element of the creation of differentials. Thermodynamics cannot for example explain the generation of life forms, where there is a movement toward more and greater differentials as the organisms becomes increasingly heterogeneous and organized rather than homogeneously disordered. (5.3 Merleau-Ponty and Depth) Deleuze has three spatial syntheses that are parallel to the temporal ones. 1) Intensive differences become spatially localized by being distributed into various spatial locations. From there they may exchange locations on the basis of how they relate, like how heat moves toward cold. 2) Intensive depth somehow generates the extensive space that intensities explicate into along with the qualities that are obtained. 3) The distributions of intensive differences along with their extensive properties and other qualities remains fresh and dynamic, because the intensive depth responsible for them returns eternally. In this way, newness and variety are continually injected into systems, which counteracts the tendencies toward entropy. (5.4 The Three Characteristics of Intensity) Intensity is of the realm of the spatium, and extensity of the extensum. Intensity explicates into extensity, thus intensity is more fundamental. The extensum is a homogenously divisible multiplicity, since its divisions produce parts of the same nature. This is what happens when we divide measures of space for example. The spatium is a heterogeneously divisible multiplicity, since each division produces parts that differ in nature. For example, were we to divide our consciousness of a melody between what it was like many moments before and what it is like now, we will find that the experiences are qualitatively different. Intensity has three important features, it includes the unequal in itself, since it does not divide into equal parts, it affirms difference, since its differential relations are not negational, and it is an implicated, enveloped, or embryonized quantity, since it explicates into extensities. (5.5 Individuation) Differential potentials in the physical world, like the electrical ones that create lightening, are intensive differences that explicate into extensive ones. There are actualizable outcomes implicated in the intensive relations that become explicit and manifest in the extensive world. For explication to happen, there is firstly the Idea, which is the structure of actualizable instantiations which in the Idea are a network of complicatedly implicated differential relations. The Idea establishes the sorts of solutions that can be taken. But the Idea interacts with the fields of intensities in the world which co-determine which actualization will explicate. For example, the embryo has a DNA code which can be thought of as the Idea. But this has to do with how it interacts with the intensive situation of the embryos and not because it is a fixed code. Certain intensive differences like in the chemical composition of the embryo help determine how the embryo develops. Thus the development is dramatized, since it is not entirely predetermined by the DNA. (5.6 The Other) For Deleuze, the individual is not the same as the ego, subject, I, etc. Rather, the individual has more to do with the generative processes that allow these other subjective structures to arise. Our faculties cannot recognize this generative process within us, since it is sub-representational. They have a solution for this, but it does not succeed. They need a non-representational basis for representation. They note how our perspectival limitations only give us fragments of the world and never complete objects. We seem however to posit an unlimited omni-perspectival view that guarantees the wholeness and unity of the parts of the world. But this omni-perspectival view is not possible for any subjectivity, and is thus seen as the Other. Because it creates a common constituted world for all of our judgments to agree about, the Other is the basis for representation. But such an Other is not really unrepresentable, but is only so for human which are perspectivally limited. But to really be the basis for representation, it needs to be un-representable. Deleuze also thinks that since philosophical thinking takes the thinker to the pre-subjective structures of reality, including those within oneself, it is a solitary and solipsistic exercise.

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

 

 

 

 

Somers-Hall, (5.5), Deleuze’s Difference and Repetition, ‘5.5 Individuation (244–56/305–19)’, summary

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 5. The Asymmetrical Synthesis of the Sensiblence

 

5.5 Individuation (244–56/305–19)

 

 

Brief summary: 

For Deleuze, we have a realm of extensity. It is our familiar world we experience, and it has spatial features and other determinate qualities. One view would say that the states of affairs in this realm of extensity are determined by other extensive factors in prior moments, in a mechanistic sort of model. Deleuze, however, thinks that something more is at work. For him, there is another layer  of reality couched within the extensive world. There are not just extensive relations, like one thing being beside another. There are also intensive ones, like the “potential differences” that physics studies. We might for example have an electrical charge in the clouds and another in the ground. We could talk about extensive relations and say that the sky sits above the ground, but this will not explain to us much about why and how the coming lightning bolt will shoot between them. The charges or “potentials” in each region are such only in their differential relation to one another. That difference itself, which is relationally “between” them but not spatially interposed between them, is an intensive difference. Many varieties of intensities are couched in the extensive world, and they help shape it. The intensive difference between the charges shapes the extensive world by sending a powerful and destructive lightning bolt through the intervening region between the clouds and the ground. This transformation of the extensive world by means of intensive difference is called “explication:” certain actualizable outcomes are implicit in the intensive situation, and they become explicit through explication, meaning that they manifest overtly in the extensive world. The way that intensive relations explicate has to do with their interactions with “Ideas.” An Idea is a network of pure differential relations that might find one actualization or another when they are explicated. Perhaps all vertebrate organisms now and going way back in evolution have skeletons that are isomorphic. One explanation is that there is a transcendental template that is merely a fixed set of relations which may manifest in a wide variety of ways in different organisms. So the template of relations is an Idea. Any of many various organisms expressing it is an explication. Now also, the physical intensive conditions surrounding the organism’s embryonic development are the “field of intensities,” which is a notion that is important when understanding how creatures develop uniquely from nearly identical embryos. In fact, the embryos are never identical, even if the DNA is. For, there are contingent features in the actual situation, like the chemical composition of the embryo’s cytoplasm. They cause one embryo to follow one path of division and another embryo to follow a different developmental course. What happens is the fixed DNA code colludes with the variable intensive relations of the actual situation, and thus the development is dramatized rather than mechanistically predictable.

Summary

SH says we may now pose two interrelated questions: 1) How does intensity explicate into extensity, when the two differ in kind? 2) What is the relationship between intensity and Ideas? (180)

2) What is the relationship between intensity and Ideas?
We begin with the second question, since it will help us answer the first one. Recall Geoffroy’s evolutionary anatomy from section 4.5 [there is a transcendental “template” of sorts for the relations that the parts of specific species may take. (Note, “template” is my term, not SH’s. It do not mean it too literally. Again see section 4.5 for the concept).  Thus a fish fin is analogous to a human leg, since each bears the same relative position with respect to the rest of its own body parts. The point here seems to be that the transcendental template is an intensive field of differential relations. It is not an extensive map or plan saying one part must reside in a particular spatial position and take on specific spatial dimensions and have specific qualities. The fin has very different properties from the human leg. Here we see how intensive differential relations explicate into particular extensive features. One danger is seeing DNA as that intensive template. The DNA implies one specific development of a certain individual, and so it is perhaps not deeply intensive like Geoffrey’s template, which implicates an infinite variety of actualizable developments.]

When we looked at the structure of the Idea in the previous chapter, we saw that one of the examples Deleuze gave was of Geoffroy’s unity of composition (4.5). Geoffroy’s intention in developing this structure was to provide a way of comparing different animals in terms of the way in which they actualised a universal set of relations between bones. Thus, the form of actual creatures differs depending on how the non-metric relationships between parts were given determinate magnitudes in extensive space. The anatomical structures of a giraffe and a bison can both be mapped onto the same unity of composition if we only consider the relationships between bones, and put to one side the sizes of the bones themselves as expressed in extensity. The Idea therefore is in some sense determinative of the structure of the organism. At this point, we encounter a potential danger in our account of the development of the form of the organism. If we see the unity of composition as determinative of the form of the organism, we risk merely reiterating the structure of the organism at a transcendental level. By doing so, we remove the essential characteristic of the Idea that it is different in kind from the structure it generates. Deleuze cites DNA as the modern formulation of the Idea of the organ- | ism, in that it presents a field of elements that are different in kind from the characteristics we find in the organism to which it relates. Despite the fact that DNA differs in structure from the structure of the organism, there is still a temptation to understand it in terms of those structures. Thus, as the biologist Susan Oyama writes, ‘though we all know that there are no hooves or noses in the genes, the accepted formulation is that the genes that are literally passed on make hooves and noses in ontogenesis’ (Oyama 2000: 43). Seeing a direct relationship between the Idea and the extensive form that it determines in fact rests on the same model of synthesis we saw in Kant’s philosophy. The Idea here would be akin to the active subject that manipulates passive extensive matter into form, and the differenciation of the Idea would be the simple expression of its structure. To turn to Oyama once again, we can see that this model of active synthesis is indeed widespread in genetic theory [the following up to citation is Oyama quotation]:

The discovery of DNA and its confirmation of a gene theory that had long been in search of its material agent offered an enormously attractive apparent solution to the puzzle of the origin and perpetuation of living form. A material object housed in every part of the organism, the gene seemed to bridge the gap between inert matter and design; in fact, genetic information, by virtue of the meanings of in-formation as ‘shaping’ and as ‘animating,’ promised to supply just the cognitive and causal functions needed to make a heap of chemicals into a being. (Oyama 2000: 14)
(SH 180-181)

 

[The next concept to deal with is individuation, but I am not entirely sure I grasp what it is. In the last section, SH perhaps defined individuation as “the emergence of the subject from an a-subjective field of intensity”  (The full sentence was: “we will also have to deal with the problem of individuation, or the emergence of the subject from an a-subjective field of intensity”) (179). In the case of development from DNA, the subject I think would be the creature that develops, and the a-subjective field of intensity would be the transcendental template. Or (as we see later) maybe otherwise it is found in the actual physical conditions of the embryo’s development. So in the Geoffroy example, I am confused what is the Idea and what is the field of intensity. Judging from the material that follows, it might be like the following. The Idea is the template. But the field of intensity is found in the physical properties of a particular explication of that Idea. So under certain conditions in the intensive differences of the situation, it will explicate one way and under other conditions it will explicate another way. Let me quote.]

Deleuze himself notes that seeing Ideas as solely responsible for the constitution of the world is a potential misstep in the philosophy of difference that we are prone to [the following up to citation is Deleuze quotation]:

In fact any confusion between the two processes, any reduction of individuation to a limit or complication of differenciation, compromises the whole of the philosophy of difference. This would be to commit an error, this time in the actual, analogous to that made in confusing the virtual with the possible. Individuation does not presuppose any differenciation; it gives rise to it. (DR 248/308–9)

Instead of the structure of the organism being governed by the operation of Ideas on passive extensity, Deleuze instead argues that it is governed by the interplay between the Idea and the field of intensity: ‘Individuation is the act by which intensity determines differential relations to become actualised, along the lines of differenciation and within the qualities and extensities it creates’ (DR 246/308).
(SH 181)

[The important point seems to be that the Idea does not act on the extensive world like a cookie cutter and directly shape it. At this point I am still missing what the interplay is between the Idea and the field of intensity, which determines the organism’s structure. Perhaps it has something to do with the idea of the dice throw, but I am not sure. The material to follow might clarify this.]

1) How does intensity explicate into extensity, when the two differ in kind?
We now examine the process of intensity’s explication into extensity (181-182). The process has a fourfold structure:  differentiation-individuation-dramatization-differenciation. 1) Differentiation: one part of the structure are the calculus differentials of the Idea, which do not resemble anything in sensibility. [Since this moment has singularities (the differentials) that have not yet been actualized or explicated,] it is structured by “pre-individual singularities”. 2) Individuation: [For this part of the structure, we need to understand intensity as a difference between two potentials. In the thermodynamics example, there was a difference of potential between the heat regions. The greater that difference, the more work the system could perform. I am not familiar with this physics terminology where we would refer to two things as potentials. It might be like saying in the case of engines, there are two regions of different temperatures, and there is a potential difference between them, meaning that the difference can potentially cause a change in the states of the system. Or perhaps in the case of lightning, we could say that the electrical charges in the cloud and on the ground are of different values. And, this could potentially cause a discharge of electrical energy, if the potential difference between the regions crosses a certain threshold.] “The second moment is the moment of intensity. As we saw, intensity is understood as a difference between two potentials. It is this difference between potentials which allows work to be done in the thermodynamic model of intensive quantities” (182). [We then turn to the example of cellular anatomy. I do not follow this example so well, so let me quote it first:]  “To return to the example of the cell, we not only have the nucleus, which contains the genetic material, but also the cytoplasm, which appears to be a homogeneous field. Nonetheless, we find that the cytoplasm contains chemical gradients that determine differences between points within the egg” (182). [This might be referring to the discussion  in section 4.12. One thing I note here is that we have two terms, the cell and the egg, and I think they refer to the same thing, the embryo, but perhaps I am mistaken. Another thing that I am not sure about is the developmental process that is being referred to. Perhaps the idea is the following (but I am making a guess here). This cellular egg will divide further and further, each time perhaps differentiating into more distinct cells. (Perhaps with each differential repetition there is another “individuation,” but I am not sure). And perhaps also those divisions do not operate merely in accordance with the DNA’s instructions. Rather, each egg will divide partly on the basis of the chemical composition of the seemingly homogenous basic fluid that fills it. Thus it is not really homogeneous, since within it is a field of intensive differences which lead to different patterns of self-division. This field of intensive differences, then, is the field of individuation. I am not sure how this works. If I were to guess, perhaps there are something acting like fault-lines in the fluid or other structural sorts of irregularities that make the divisions open to contingent factors.]

To return to the example of the cell, we not only have the nucleus, which contains the genetic material, but also the cytoplasm, which appears to be a homogeneous field. Nonetheless, we find that the cytoplasm contains chemical gradients that determine differences between points within the egg. These differences set up potentials similar to the differences in temperature which allow the thermodynamic engine to function. This field of potentials is what Deleuze calls the ‘field of individuation’: ‘An intensity forming a wave of variation throughout the protoplasm distributes its difference along the axes and from one pole to another’ (DR 250/312).
(SH 181)

3) Dramatization: [The idea here is a bit hard for me to follow at a certain stage. The first point seems to be that one Idea can be actualized as one specific explication or as another. For example, the Idea of color can be actualized as red or as blue, etc. Whichever actualization it does take will of course exclude the other actualizations that could have found explication, even though they were there virtually in the Idea. Also, Geoffrey’s “unity of composition” (what I call the template) is an Idea that can actualize as this or that animal.]

The interaction of these two moments Deleuze calls ‘dramatisation’. If we return to the archetypal model of the Idea, colour, we can see that the Idea can be actualised in a variety of forms, each of which excludes the actualisation of other forms. If we actualise the Idea of colour, it will have to take the form of a particular colour. Similarly, if we actualise the Idea of the unity of composition, we will get a particular animal.
(182)

[I get lost, however, in the next sentences:]

It is the field of intensities which determines which form is actualised by determining the speed of development of various parts of the organism according to the distribution of intensities within the egg. Thus, the field of intensity determines how the relations between elements are determined in extensity.
(182)

[Let us stick first with the organism example. There is a field of intensities, which we said could be for example the differential relations in the cytoplasm. Somehow the field of intensities will change the speeds of development of various parts of the organism. I am not sure how that works. I can see how the in the case of the cytoplasm the heterogeneity of the composition creates potential fault lines of division, but I do not understand how they would modulate the speeds of division. There must be other factors, or I may have misunderstood what the field of intensity is (which is not unlikely). But how it is that the differences in developmental speeds between parts can determine the organism’s form is maybe something we can guess at. Perhaps for example, a giraffe egg at some point undergoes an acceleration in the division of the neck cells. And likewise, if we were to compare the development of different giraffes, some will have slightly faster speeds of division in the neck and thus result as a taller giraffe. (Although, later we learn that only secondarily would we say that they are both giraffes). Also, I do not know how this idea of the speeds of development would work with the example of the Idea of color. Perhaps it does not apply, and something else is at work in the explication of color. SH continues,] “As Deleuze noted in Chapter 4, this process of dramatisation relies on movements by the embryo that are topological – that is, understood in non-metric rather than metric terms” (182). [I do not remember if in the SH text here dramatisation was put in these terms, or if it is just that way in DR, but perhaps in SH’s text we might refer back to pages 164-165. Regarding topology, I suppose that the transcendental template (Geoffrey’s “unity of composition”) is understood topologically, since there are various deformations that preserve the relations of points of intersection of the parts. But I do not know. It reminds me of animations I have come across for “topological isomorphism”. This one is from wiki.

I am not sure if this illustrates a relevant concept, but I could imagine all the different vertebrate animal species being deformations from one another, while all maintaining the same relative connections of the parts. So using the animation as an analogy, just as the mug and the donut are topologically isomorphic without maintain metrical relations between the parts, so too is the dolphin and the human topologically isomorphic, and that is because both of our skeletons are explications of the same set of differential relations. Regarding the notion of dramatization, I am not sure if I understood it correctly to begin with. The idea might be that the developmental speed variations are not predictable, and they are complicated by the different “actors” or parts serving as variables in the development. The next example SH found is excellent and fascinating. It seems that frog DNA has, in a sense, “learned”  basic dynamic properties of fluids. Not all the information for how the organism develops is contained in the DNA. Rather, it seems that the DNA exploits the physical properties of fluids and lets those dynamics help shape the forms. So here there is an interplay between the DNA and the contingencies of the physical world. It also seems that SH’s point is that for this reason, DNA can in fact act like an Idea, on account of the dramatization of its explication into the physical world of specific extensive properties and qualities.]

As Deleuze noted in Chapter 4, this process of dramatisation relies on movements by the embryo that are topological – that is, understood in non-metric rather than metric terms. While these movements are possible within the intensive field of constitution, they are not possible within the constituted field of extensity: ‘Embryology already displays the truth that there are systematic vital movements, torsions and drifts, that only the embryo can sustain: an adult would be torn apart by them’ (DR 118/145). While it might be claimed that DNA differs from the unity of composition, in that it specifies one particular form or species, in fact, we | can note that here too, the milieu in which the genetic material expresses itself is fundamental to the form generated [the following up to citation quotes Stewart and Cohen]: Development seems to involve dynamics as well as chemical computation. When the developing frog embryo turns itself inside out during gastrulation, it looks just like a viscous fluid, flowing in an entirely natural manner. Some of the information required to make this process work may be specified by the laws of fluids, not by DNA. Brian Goodwin sees development as a combination of natural free-flow dynamics and DNA-programmed intervention to stabilize a particular dynamic form. Why should nature waste effort programming the shape of the organism into DNA if the laws of physics will produce it free of charge? It’s like programming into DNA the fact that salt crystals must be cubical. For example, the eye – a shape that puzzled both Darwin and his detractors – is dynamically very natural. Rudimentary eyes can occur naturally without any special DNA coding. Natural selection can then refine the rudimentary eye into something more sophisticated, but it is the dynamics that gives selection a head start. (Stewart and Cohen 2000: 294)
(SH 182-183)

[Recall the discussions on differenciation in section 4.8, section 4.11, and section 4.12. I might be mistaken, but differenciation seems to be the process (or result of a process) of explication whereby what is actualized has determinate features.] 
4) Differentiation: “The process of dramatisation gives us the final moment: differenciation. The result of the process of dramatisation is the extensive form. We should note, however, that the intensive does not become extensive, but rather gives rise to it. To that extent, dramatisation is concomitant with differenciation” (183). [The last point seems crucial, but I may not have gotten it well. Explication does not exhaust the intensive it seems. Or maybe we should say, what is explicated is something parallel to its intensive origins which remain intensive even while being explicated in extensity. Perhaps then the idea is that the “unity of composition” (the template of actualizable relations) is for the most part left unaltered regardless of its actual explications, which are infinite in their variety.]

SH then notes the two senses of Deleuze’s claim that the world is an egg. 1) “The first is that the milieu of individuation is not circumscribed by the boundary of the egg. In fact, we can note that the spatium (the complete field of intensity) is not made up of discrete elements. As such, the field as a whole is responsible for the differenciation of each entity, although most moments of intensity will have a negligible effect in each case” (SH 183). [I did not grasp what the idea was there. Maybe the basic idea is that the way a particular egg develops depends not just on what is contained within it but also on external factors, like with the frog egg example, and so the whole world is somehow involved in the development of any one egg. Probably it means something else, but I am missing it.] 2)  The second sense is that all phenomena can be understood on the model of the egg. [Perhaps the basic idea is that Deleuze thinks all phenomena result from this fourfold structure of explication, and thus all the world is an egg in that sense. SH then discusses the example of lightning, and I think here he is potentially bringing a lot of clarity to these ideas. But I am not sure I follow it well enough yet. 1) Individuation: A potential difference comes about in the electrical charges. There are now a multiplicity of ways the situation can develop. 2) Differentiation: this is supposed to have something to do with calculus differentials. In this example, perhaps the idea is that nature “calculates” the solutions to the problem of the differentially related charges. 3) Dramatization: the lightning takes the path of least resistance, but this is based perhaps on contingent and unpredictable factors.  4) Differenciation: the lightning takes one (branching) path and not another, and the lightning takes on all its physical properties.]

The second sense is that all phenomena can be understood on the model of the egg. If we return to the opening of Chapter 1, for instance, we find the example of lightning: ‘Lightning . . . distinguishes itself from the black sky but must also trail it behind, as though it were distinguishing itself from that which does not distinguish itself from it. It is as if the ground rose to the surface, without ceasing to be ground’ (DR 28/36). Here, a difference in electrical potential between the cloud and the ground (individuation) leads to a process of equalisation of charge (differentiation) along a path of least resistance (dramatisation), leading to the visible phenomenon (differenciation). Intensity expresses itself as extensity without itself | ceasing to be intensity. There are of course differences in the process of differenciation of biological, physical and social Ideas, but in each case, it is by being brought into relation with a field of intensity that the Idea becomes actualised.
(183-184)

SH says we now can interpret Deleuze’s claim that “‘‘it is not the individual which is an illusion in relation to the genius of the species, but the species which is an illusion – inevitable and well founded, it is true – in relation to the play of the individual and individuation’ (DR 250/311)” (SH 184). [The material here is a bit complicated. I am not sure, but perhaps the ideas are the following. We might think that individuation is like taking a “cookie cutter”, as DNA might be thought of being, and stamping it onto the world to give it living forms. However, we have seen that it is not so simple, as the frog egg example illustrated. In that case, there was a dynamic and cooperative interaction between the DNA’s patterns for development and the physical world of contingent factors that play vital roles in how the organism develops. Now, this means that each development is individual in the sense that it is a variation that was not pre-planned specifically. However, we might be tempted to say that for example all frogs are of a particular species, despite the particular variations of each individual. Were we to make this mistake, we would also think that perhaps the features of the species are set in advance, perhaps encoded in the DNA, and result like cutting a cookie. But this is an error in Deleuze’s view, since we are dealing with those properties after they have been explicated. We are not dealing with the dynamic factors of their origination, which do not follow a rigid plan. Instead, 1) we are looking at the differentiated properties that we predicate to an individual as a subject, and thus we are dealing with representations, and 2) on the basis of those representations, we say that a number of similar individuals are instances of the same species. I will quote, because I think I do not have it exactly right:]

As we saw in Chapter 1, species are defined by the addition of differences to an indeterminate subject. By progressively specifying the properties of an individual, we gradually limit the logical possibilities of what something can be, determining the nature of man, for instance, by addition of the properties material, animate, sensitive and rational, to substance. Given that different individuals clearly do belong to different species, we might be tempted to claim that this hierarchy of terms is what determines the nature of the individual. Thus, we saw that even though DNA differs in kind in structural terms from the organism to which it relates, there was a strong temptation to see it as straightforwardly encoding the kinds of properties Porphyry’s tree relied upon: ‘there is a tendency to believe that individuation is a continuation of the determination of species, albeit of a different kind and proceeding by different means’ (DR 247/308). Once we recognise that individuation does not simply operate on homogeneous, or at best, recalcitrant, matter, but relies on the particular potentialities within the egg, then we can no longer see it as a process of active synthesis relying on the attribution of universal qualities to a particular subject. Rather, differences are always individual, to the extent that they are determined by the reciprocal interplay of Ideas and intensity. They only give rise to these generalised properties once we draw together these individual differences according to their resemblances within the structure of representation.
(184)

[The next idea seems to be the following. We seem to have ruled out that a species pre-exists in the DNA. Rather, the individual organism comes about through the dramatized interaction of the DNA with its intensive field of differential relations in its particular physical context of development. And only secondarily by means of representations do we recognize a species, which is really an illusion, since it was never involved in the generation of the individual. But maybe we can say in the frog example for instance, that there is still a species which is the calculable combination of  the DNA’s instructions and the laws of physics, chemistry, and other factors that determine the intensive relations within and around the embryo. So in other words, perhaps we might say that we have this particular species of frog because it is built into the system of development which makes use both of genetic instructions and the intensive field of differential relations within and surrounding the physical egg. However, we are not supposed to think this way. Instead, we should think that no intensive field is identical, and thus there is no species built into any of them. I am not sure, but maybe the idea would also be like the following. Consider two genetically identical cloned animals. We will still find differences in their physiology, small ones perhaps, which resulted from them having different intensive fields in their development. So perhaps one egg had a different distribution of chemicals in its cytoplasm, which caused its divisions to take a slightly different route than its twin. Then, maybe a scientist would say that were we to control all the intensive variables which factor into the development, that we would get a matured twin who is absolutely identical even on the cellular level. Deleuze’s claim might be that this is impossible, since no intensive field is identical to another.  Perhaps the reasoning is found in the final sentences of the paragraph. I am not sure I get this, but let me make a guess using this clone example, and afterward I will quote. The intensive spatium of course does not map extensively over the extensive world. However, perhaps each point in the extensive world somehow corresponds to a place or relation in the spatium. This might be analogous to how each part of an vertebrate animal’s skeleton corresponds to the transcendental template, which does not have extensive spatial features like the resulting organisms do. But, this also means for example that even if we have eggs with identical DNA, we could not also make their intensive fields identical, since those fields correspond to different parts of the spatium.]

Now, one final point to consider is that if the individuality of the intensive field is responsible for differences being individual, then it cannot be the case that the same intensive field exists in different eggs. If that were the case, then we could talk about there being a real existence to species, although this would derive from the intensive field, rather than the Idea. It therefore has to be the case that each egg possesses a different set of intensive potentials [the following up to citation is Deleuze quotation]:

The form of the field must be necessarily and in itself filled with individual differences. This plenitude must be immediate, thoroughly precocious and not | delayed in the egg, to such a degree that the principle of indiscernibles would indeed have the formula given it by Lucretius: no two eggs or grains of wheat are identical. These conditions, we believe, are fully satisfied in the order of implication of intensities. (DR 252/314)

This condition is met by the fact that intensity is not constructed from pre-existing equal units, as extensity is. Rather, Deleuze’s claim that ‘the world is an egg’ makes explicit that the entire spatium is implicated in the potentialities of each individual egg, although different aspects of it are implicated to different degrees. As each occupies a different position in the spatium, each expresses the spatium differently.
(184-185)

SH will now discuss the fundamental differences between Ideas and intensity. [This as well gets complicated. We first recall from section 4.8 Leibniz’s pairings of clear-distinct and obscure-confused. We note that phenomenal experiences, like the perception of the roar of the ocean, are made of component perceptions, which synthesize into the organic whole. The division of component perceptions goes all the way to the infinitely small. When we hear the ocean’s roar, we are also hearing each tiny wavelet’s sound in tiny perceptions. All those tiny perceptions then add up to the whole roar. Now, the roar as a whole sound, even though it is white noise, is clear to us, because it is distinct from other composite sounds, like maybe music or traffic noise. But do we hear it distinctly? We do not hear all its distinct component parts when we hear the composite whole. Were we to do so, we would somehow hear those sounds individually, but we would lose the clarity of the whole that the little sounds compose. Perhaps that is because we lose the organic unity of differentially related tiny sounds. Maybe we can look at it this way. Consider the ocean’s white noise and the traffic noise. They are clearly different sound experiences. Now consider instead if in each case we heard each tiny component in its distinction. We would be so focused on the parts that we would lose “sight” of the whole, and thus the clarity of the experience is lost, since we would not be able to differentiate the experience of the ocean roar’s tiny parts from the experience of the traffic’s tiny parts. So thus we have the other pairing, the distinct-obscure. Now we will apply these concepts to Ideas and intensive fields. The Idea is a set of differential relations. All of them are distinct. But, the Idea could actualize as one thing or as another. It is not clear which. So the Idea is distinct but it is obscure in how it relates to its explications. Yet, when we look at its actualized explications, it expresses some relations in the idea clearly, but others it also expresses in a less obvious way, and thus these other expressions get confused with the obvious ones. For that reason, from the side of explication, it is clear but confused. Let us consider a possible way of seeing this. Recall from section 4.5 the diagram we looked at.

“Fig. 3. Limb skeletons of extinct and living animals, showing the homologous bones: 1, salamander; 2, frog; 3, turtle; 4, Aetosaurus; 5, Pleisiosaurus; 6, Ichthyosaurus; 7, Mesosaurus; 8, duck. (After Jordan and Kellogg.)” (Morgan p.8)

Now consider for example numbers 1 and 6. Perhaps we might clearly see that the “f” bones are both expressions of a differential relation in the transcendental “template”. However, in 6, we have a very different distribution and shape to the other bones. So while particular relations to the Idea are clear, on the whole, very many of the relations are confused with one another.]

At this point, we can note the fundamental difference between Ideas and intensity. When we looked at Descartes’ method at the opening to Chapter 3, we saw that Descartes based his method on clear and distinct ideas. The lack of separation between these two terms is, for Deleuze, a fundamental failing of representation [the following up to citation is Deleuze quotation]:

the weakness of the theory of representation, from the point of view of the logic of knowledge, was to have established a direct proportion between the clear and the distinct, at the expense of the inverse proportion which relates these two logical values: the entire image of thought was compromised as a result. (DR 253/315)

Now, as we saw in the previous chapter (4.8), the terms clear and distinct do not need to be associated with one another. If we consider the noise of the sea, we can conceive of it clearly, in that we can recognise it. Nonetheless, we do not perceive the differences which make it up (the noise of the individual drops of water that make it up and are below our threshold of perception). In this case, our perception of the noise of the sea is both clear and confused. If we instead focus on the noise of the individual waves, we can conceive of these distinctly, even though we cannot form a clear idea of them as they are too small to perceive. Thus, in this case, we either focus on the waves, which are distinct, but obscure, or the sea, which we perceive clearly but confusedly. Similarly, the pure Idea, is distinct, in that it is completely determined. Nonetheless, in so far as it is only in relation to a field of intensity that it can determine how it relates to an actual organism (whether it will instantiate a bison or a giraffe), it is obscure. Conversely, intensity expresses some relations clearly only at the expense of other aspects of the Idea which, while still present in the organism, are only present confusedly, on the basis | of the domination of certain intensive potentialities. Thus, the process of differenciation can be seen as the movement from a distinct-obscure Idea to a clear-confused field of intensity.
(185-186)

[The next idea I do not grasp so well. I apologize, but I have to quote it, since I will botch any attempt to interpret it.]

Likewise, the thinker, as an individual, is an intensive field. The thought he expresses, however, is the distinct-obscure of the Idea. What gives unity to the thinker is this intensive nature. Just as we cannot divide an intensity without changing its nature, a thinker cannot give up their unity without ceasing to be the particular thinker that they are. Nonetheless, as we saw in Chapter 2, everything thinks. Thus, the death of the thinker is not the end of thought, but merely a change in thinking’s nature.
(168)

[I want somehow to take something away from this. I get the impression that there is an Idea or a network of Ideas that all thinkers are expressing some part of. But also it seems maybe that each thinker is somehow shaping that Idea or network of Ideas. Also somehow thinking itself in this or in some other more general sense is like an intensive multiplicity, such that were we to divide it or subtract from it, we change the nature of the whole. Thus, when a thinker dies, thinking itself keeps going, perhaps in the minds of other thinkers, but the overall Idea or network of Ideas has somehow changed. And maybe this spills over into how each particular thinker thinks. So perhaps we could say that when Derrida died, something in the way all of us did our thinking has changed somehow, since Derrida himself no longer was shaping the overall Idea or network of Ideas that we all express parts of and also help to shape.]

 

 

 


Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Oyama, Susan (2000), The Ontogeny of Information: Developmental Systems and Evolution, Durham, NC: Duke University Press.

Stewart, Ian, and Jack Cohen (2000), The Collapse of Chaos: Discovering Simplicity in a Complex World, London: Penguin Books.

 

Morgan, Thomas Hunt. A Critique of the Theory of Evolution. Princeton/London: Princeton University Press / Humphrey Milford Oxford University Press, 1916.
Available at the Internet Archive:
<https://archive.org/details/critiqueoftheory00morgrich>

Mug topological isomorphism animation:
https://en.wikipedia.org/wiki/Homeomorphism

 

 

 

 

 

 

Somers-Hall, (5.4), Deleuze’s Difference and Repetition, ‘5.4 The Three Characteristics of Intensity (232–40/291–300)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 5. The Asymmetrical Synthesis of the Sensiblence

 

5.4 The Three Characteristics of Intensity (232–40/291–300)

 

 

Brief summary: 

Extensity, which is of the realm of the extensum, is fundamentally different from intensity, which is of the realm of the spatium. The most important difference is that intensity is more fundamental than extensity, since extensity takes on its features as a result of intensity explicating into certain extensive expressions. The main distinguishing feature is their divisibility: The extensum, as it is extensive, is a multiplicity that is homogeneously divisible, meaning that each division produces parts that are of the same nature. Two meters (of something) can be divided into two equal (and identical) parts. The spatium, as it is intensive, is a multiplicity that is heterogeneously divisible, meaning that each division produces parts that are of a different nature. Each moment, our consciousness synthesizes the past with the present into a whole mental state. But each successive moment of consciousness is qualitatively different from prior ones. For example, with each new note of a melody, the character of that melody as a whole changes. Were we to divide our consciousness between the way it once was when we heard a prior note with the way it is now, having heard more notes that have altered the melody’s character, we would have two parts of consciousness that differ qualitatively. Thus, they differ in nature. Deleuze emphasizes three important features of intensity: 1) because it is not metrically homogeneous like extensity, it does not divide into equal parts, and thus intensity includes the unequal in itself; 2) since an intensive difference does not involve one thing being the negation or denial of another, but rather is a matter of pure differential relations, intensity affirms differences; and 3) because it explicates into extensities, intensity is an implicated, enveloped, or embryonized quantity.

 

Summary

SH now asks, “what are the characteristics we find in intensity? We first note important differences between intensity and extensity. When you combine two extensive magnitudes, like two spatial distances, you get one whose value is the numerical total of the two. That is not how intensive magnitudes work, however. For example, if you combine fluids of different temperatures, the new temperature is not the addition but rather the average of the two. “intensity understood prior to its location in extensity will have different characteristics to extensity itself” (174). So for Deleuze, the “nature of | the extensum and the spatium as a whole are radically different,” but he also focuses on the differences between intensive and extensive elements and also the differences in the ways each kind of element relates to others of its own type (174-175). Deleuze’s account discusses cardinal and ordinal numbers, while all the while in the background is Bergson’s account of two multiplicities. [SH discusses Bergson’s multiplicities in his Hegel, Deleuze… book, Pt2.Ch3.Sb4]. For Deleuze, intensity has three characteristics: 1) it includes the unequal in itself, 2) it affirms differences, and 3) it is an implicated, enveloped, or embryonized quantity (SH 175).

1) Intensity includes the unequal in itself.
SH will follow Delanda’s analysis in his Intensive Science and Virtual Philosophy. Extensive quantities, we noted, maintain their nature when added, [and perhaps intensive quantities do not. If intensive quantities change their nature when added, I am not entirely sure how the prior example of combining fluids with different temperature applies, since I would think they keep the same nature even if they average. For, they would form a fluid with its own temperature that could be added to yet another, repeating the same process.] Extensive quantities “can be measured numerically, and […] these measurements are comparable (or commensurate) with one another” (175). [The next ideas are slightly complicated, but they are straightforward. It seems we need to establish different orders of ordinal numbers, since within each order certain values are suggested or desired, but that order cannot express them. Another order is then posited which can express those other values. So we begin with natural numbers, which do not have decimal values between them. So among the natural numbers, we have 2, 7, and 8, for example. We can divide 8 by 2 and get 4, which is also a natural number. But if we divide 7 by 2, we get something greater than 3 but less than 4. So we need to turn to another order of numbers, fractions, which would give us seven halves, in this example. But fractions do not allow all quantities to be expressed, since for example there is the value of pi, for which there is no exact ratio of integers that could express it. So we need another order of numbers, the real numbers (which will include both rational numbers, that is, those that can be expressed in fractional form, as well as irrational numbers, which cannot be expressed fractionally). So again, within each order, there is an incommensurability that cannot be expressed within that order and which thus calls for another order to express it.]

As Deleuze notes, this difference reflects one of the key features of extensive magnitudes: that they can be measured numerically, and that these measurements are comparable (or commensurate) with one another. Now, if we look just at the natural numbers (0, 1, 2, 3 . . .), we find that frequently we come across magnitudes that cannot be expressed in these terms. For instance, provided we remain with the natural numbers, we cannot divide 7 by 2, as the result is not itself a natural number. The obvious solution to this difficulty is to introduce another order of numbers that does allow us to relate these two quantities to each other, in this case, fractions. Similarly, we will discover that fractions do not allow all quantities to be related to one another, leading to the instigation of a new order of numbers: real numbers (such as √2 or π). In each case, we have an incommensurability between quantities that cannot be cancelled within the order of numbers themselves, but only by instigating a new order of numbers.
(SH 175)

[So we note that fractions proceeded from natural numbers, and reals from fractions.] Now we ask, from what order of numbers do natural numbers proceed ? (175). We turn now to the difference between ordinal and cardinal numbers. Cardinal numbers can have identities in the sense of forming equivalents and compositions. So the difference in value from one to three is the same as from two to four (175). Ordinal numbers, however, “just give us a sequence without requiring that the difference between the elements is the same in each case (thus, the difference between first and third does not have to be the same as the difference between second and fourth)” (SH 175). [Cardinal numbers can be said to have a metrical distance. For example, the “distance” between one and three is the same “distance” as between two and four. (That of course sounds right, but I wonder if numerical differences obtained through subtraction imply a geometrical sort of distance like on a number line. I guess the idea is that so long as the differences between units are standardized, that this creates a sort of metric.)] Ordinal numbers can also be thought of as having distances, but it is not metrically consistent or measurable like with cardinal numbers [so first is more distant from third as it is from second, but that does not mean we can say there is the same distance from first to second as there is from second to third.]

Since ordinal numbers do not operate on the basis of metrical units spanning between their values, “the kinds of operations we can perform with cardinal, natural numbers cannot be performed, meaning that we cannot produce equalities within this domain. Rather, it is only by the addition of a common measure between numbers (and thus the conversion of ordinal numbers to cardinal numbers) that we can begin to talk about equalising quantities” (176); [we then turn to a Deleuze quote. It seems we first need to understand the spatium as having distances enveloped in it, which might be like how the syntheses of space somehow explicate extensive space from an intensive spatium. What is happening here is a bit vague in my mind. The next thing is that when ordinals are converted to cardinals, it involves such an explication of the spatium.] “ ‘In fact, ordinal number becomes cardinal only by extension, to the extent that the distances enveloped in the spatium are explicated, or developed and equalised in an extensity established by natural number’ (DR 233/292)” (SH 176). SH continues:

We can note that, in these cases, we have a model that parallels the account of intensity we have seen so far. An uncancellable difference (intensity) gives rise to a new domain (extensity) within which that difference is cancelled. ‘Here, however, we rediscover only the duality between explication and the implicit, between extensity and the intensive: for if a type of number cancels its difference, it does so only by explicating it within the extension that it installs. Nevertheless, it maintains this difference in itself in the implicated order by which it is grounded’ (DR 232/292).
(SH 176)

We saw how heat was cancelled in its own domain of energy and temperature [but this is not a case of intensities in the intensive spatium, but rather of intensities explicated into the extensive physical world of energy transfers.] Yet, intensity is not equalized in its own domain of intensity. It can only be equalized after being explicated into the constituted realm of extensities. “Whereas in the thermodynamic model, difference is cancelled within its own domain, leading to the idea of the heat death of the universe, for Deleuze difference can only be equalised in a constituted realm, leaving it unequalised in its original domain” (176). Cardinal numbers, as we have gathered, presuppose extensive space. [I am not sure I get the next point about time and ordinal numbers. The Bergson quote seems to be saying that a succession of increasing numbers needs a spatial structure, since without it, each successive number would displace the prior and we would never have more than just one thing at a time. Then it seems SH is saying that Deleuze follows Bergson’s claim that a) cardinal number requires space, and also that b) there is a temporality to ordinal numbers, perhaps since they are understood only in terms of their succession, but I am not sure I follow correctly, and c) this temporal succession requires space. The final point that quotes from the Deleuze lecture, in the SH quotation below, I do not grasp so well. Time arises in an ordinal series. But it arises secondarily as a spatialized time. Perhaps the idea is that is that the pure form of time is somehow intensive, and in some way it is ordinal succession, and out of it somehow arises an extensive time of cardinal succession. I probably have that wrong, and even so, I do now grasp how that works. Let me quote:]

As cardinal numbers are constituted from elements that are absolutely identical with one another, they presuppose an extensive space. Bergson makes the point as follows [the following up to citation is Bergson quotation, and bracketed text within it and within the next Deleuze quotation is SH’s]:

And yet [numbers] must be somehow distinct from one another, since otherwise they would merge into a single unit. Let us assume that all the sheep in the flock are identical; they differ at least by the position which they occupy in space, otherwise they would not form a flock. But now let us even set aside the fifty sheep themselves and retain only the idea of them. Either we include them all in the same image, and it follows as a necessary consequence that we place them side by side in an ideal space, or else we repeat fifty times in succession the image of a single one, and in that case it does seem, indeed, that the series lies in duration rather than in space. But we shall soon find out that it cannot be so. For if we picture to ourselves each of the sheep in the flock in succession and separately, we shall never have to do with more than a single sheep. In order | that the number should go on increasing in proportion as we advance, we must retain the successive images and set them alongside each of the new units which we picture to ourselves: now, it is in space that such a juxtaposition takes place and not in pure duration. (Bergson 1910: 77)

Thus, Deleuze follows what he takes to be Bergson’s claim that ‘space [is] a condition of number, even if only an ideal space, the time that arises in the ordinal series arising only secondarily, and as spatialized time, that is to say as space of succession’ (L 00/00/70).
(SH 176-177)

[All this material was to explain how intensity includes the unequal in itself, but I am not sure how to sum up how that is so. I suppose that it contains the unequal within itself, because equalization is only possible when intensity is explicated and thus when it is not within itself. Therefore, it seems, within intensity is only unequality somehow. The ordinals for example do not have a standarized metric, so in a sense their differences are unequal, perhaps.]

2) Intensity affirms difference.
The first claim “aimed to show that intensity couldn’t be understood in terms of extensity” (177). The second claim is that intensity “also cannot be understood as a quality” (177). Deleuze supports this claim with another one: qualities are understood  in terms of negation, but intensity, when characterized by difference, is not understood in terms of negation. Recall how for Aristotle’s notion of definition, the difference between species involves a negation. [see again for example section 1.6, and before that section 1.2. As we noted, in Aristotle’s system of division, things are differentiated on the basis of clear defining limits that determine what is special and proper to each thing. These limits serve to define what makes one thing what it is and what makes something else not that thing but rather something different entirely, and thus Aristotle’s system makes use of negation.]

As we saw in Chapter 1, within the Aristotelian notion of definition, a difference presupposes negation. That is, when we wanted to talk about the essence of man, we did so by attributing a property to him called a difference. This difference allowed us to divide the genus into two opposed classes: the rational and the non-rational. Negation was thus fundamental to the process of definition, and to the specification of properties. We can sum up this characterisation of difference with the claim that if x differs from y, x is not y.
(177)

[For the next point, recall from section 1.4 how for Scotus, there is a difference in quantitative intensity between God’s infinite perfection and the finite perfection of our world. So also, our finite (im)perfection is not to be understood as a negation of God’s infinite perfection. Rather, we are different degrees on the same scale of the intensive variation of being. We also saw, again from section 1.6, how the negation-based models involve a notion of extensive space, since if one thing is not another, they cannot occupy the same place, whether that by physical space or a sort of “conceptual space” you might say. But intensive differences never involve one being a negation of another. I am not entirely sure I understand how to conceive intensities, unlike extensities, which I can picture in my mind more readily. I wonder if the idea is something like this: say you have two intensive magnitudes of heat, with one being greater than the other. What makes one have its own value is understood only by its relation to the other, or to some third value, perhaps zero (or becoming-zero or infinitesimally-away-from zero or something like that). Since each of the intensive values is such only in relation to the other, what defines each of them is not that one is the negation of the other, (that it is “not the other”), but instead that together they differentially relate, and it is that relation itself which defines them jointly. Perhaps one problem with this heat example I used is that differences in heat are not intensive in the way we mean it here, since they have been explicated in such a way that they may be assigned numerical values which themselves are extensive. At any rate, the next idea I think comes from a possible objection, which is that an intensity can diminish to zero, thus intensities can be negated. But Deleuze notes that when it comes to physical intensities, there is no zero value. I am not sure, but perhaps the idea is that intensities can get smaller and smaller to the infinitely small, but never to zero, and when we say ‘zero’ for some intensive value, we really mean infinitely little. I am not entirely sure why this is. Maybe it is because intensities are always the difference between values, but total zero has no value and thus it cannot enter into a differential relation with other intensities.]

As we saw in Chapter 1, this constraint on the concept of difference was not inherent to difference itself, but only difference thought in terms of extensity. Scotus’ intensive conception of difference avoided the need to define it in terms of negation. We can, in effect, note that the introduction of negation into difference rests on the need to see contrary properties as not inhering in the same object, or occupying the same ‘space’. Since intensity is prior to the emergence of both objects and (extensive) space, these restrictions do not apply to it. As Deleuze points out, even if we do look at intensity as it occurs within extensive space, we do not find the strict absence of intensity: ‘It is said that in general there are no reports of null frequencies, no effectively null potentials, no absolutely null pressure, as though on a line with logarithmic graduations where zero lies at the end of an infinite series of smaller and smaller fractions’ (DR 234/294).
(SH 177)

[The next idea is that negation can be applied to properties, but not to intensities. From the Plato example, one instance of a property seems to be ‘equal to’ or at least just physical size. But I am not sure what would be other properties. They would not for example I guess be the ones mentioned above, like frequency and pressure. They would be extensive sorts of things I suppose like spatial dimensions, and perhaps physical distributions of component parts (or maybe not, if density is an intensity). But I wonder if these properties includes color, which can be understood quantitatively (and perhaps intensively) in terms of light wave frequency or qualitatively, with each basic color being different in kind from the others (blue is not more or less of something than red is, in how it appears). At any rate, for the next idea, recall how for Plato, contrary properties, like objects that under certain conditions appear equal, and under others appear unequal, shock us to think more about the Ideas we use. Deleuze also thinks that contrary qualities have this power. Yet, Plato thinks that the shock turns our mind toward timeless Ideas. Deleuze, however, thinks that the contrary properties arise because their source is (somehow) intensive difference. Thus, these shocking moments are an invitation to think more directly about the intensive basis of thought.]

Thus, whereas negation can be applied to properties, we never actually discover the negation of an intensity, but only its difference from other intensities. Deleuze here supports Plato’s insight that the fact that objects | can possess contrary properties presents a shock capable of leading to thinking. Rather than seeing these contrary properties as leading us to contemplation of a timeless realm of Ideas, Deleuze argues that they refer us to a field of intensive difference responsible for the change in qualities we find in the world around us. What makes the qualities in becoming contradictory is that they actualise an underlying intensive difference, and it is this difference that provides the real opening to thought.
(177-178)

3) Intensity is an implicated, enveloped, or embryonized quantity.
SH explains that this third characteristic of intensity is derived from the first two. [We now make a distinction between cardinal numbers and qualities. Cardinal numbers are divisible, but qualities are not. The reason we can divide cardinal numbers is because both their unity and their division are matters of mental actions. They are unified insofar as we mentally treat the value as a whole unit, but they are divided insofar as we regard them as a collection of smaller values. There is also discussion in the quote about continuity and discontinuity. I do not follow it readily, so I will just quote it and return to it if it factors in later. The next idea is that intensity can be divided, but not like extensities can be, since intensity is not metrically homogenous.  But I do not understand how it can be divided. What we know is that if you divide an intensity, it changes the nature of what was divided, with the example being Bergson’s notion of consciousness or duration. I am not exactly sure how you divide consciousness in the first place, and then how the result of the divisions would be different in kind. Perhaps we might check section Pt2.Ch3.Sb4 from his Hegel, Deleuze book. But it gets a bit clearer when we look at the Bergson example (I am just not sure how it works for intensive things other than consciousness). He notes how if we listen to a melody, each new note or moment changes the character of the melody as a whole, just as each new moment of consciousness more generally changes the whole of consciousness on the whole. It seems Bergson gives one way in this melody example how we might divide our consciousness. He says that we can dwell on one note, while the melody continues developing in the moving present, and when we do so, we notice a difference between how the melody sounded back when that note was playing with how it sounds now, after more development has taken place. It seems then we can “divide” consciousness temporally by considering different moments making up present consciousness. What we notice is that each is different qualitatively. (One moment of the melody is not more or less than another. They instead have different characters). I am not sure Bergson would consider consciousness an intensity, but perhaps it is meant to illustrate more the idea of a type of multiplicity, of which Deleuze includes intensities, which change in nature when divided. For, SH’s next point is that the two types of multiplicity (ones that when divided produce parts that are the same in nature and ones that when divided produce parts that are different in nature) “can be mapped onto the extensive and intensive in a relatively straightforward manner” (179)]

Finally, as a third characteristic, ‘intensity is an implicated, enveloped, “embryonised” quantity’ (DR 237/297). This third characteristic is derived from the previous two. We have seen that cardinal numbers are divisible. Deleuze makes the claim in a lecture on Bergson that this is because, since they are a collection of equal units, dividing them is simply an intellectual operation [the following up to citation is Deleuze quotation]:

The divisibility of the unit; for a number is a unity only by virtue of the cardinal colligation, that is to say the simple act of the intelligence that considers the collection as a whole; but not only does the colligation bear on a plurality of units, each of these units is one only by virtue of the simple act that grasps it, and on the contrary is multiple in itself by virtue of its subdivisions upon which the colligation bears. It’s in this sense that every number is a distinct multiplicity. And two essential consequences arise from this: at once that the one and the multiple belong to numerical multiplicities, and also the discontinuous and the continuous. The one or discontinuous qualifies the indivisible act by which one conceives one number, then another, the multiple or continuous qualifying on the contrary the (infinitely divisible) matter colligated by this act. (L 00/00/70)

Qualities, on the other hand, are not divisible. It makes no sense to talk of dividing rationality, or animality, for instance. Now, intensity is not like quality, in that it can be divided. It is not composed of equal elements, however, but is rather a sequence of asymmetrical relations, such as we find with the ordinal numbers (it is asymmetrical in that second is defined by being ‘in between’ first and third, but first and third are not ‘in between’ second). Thus, ‘a temperature is not composed of other temperatures, or a speed of other speeds’ (DR 237/297). If an intensive multiplicity is not simply constituted from pre-existing elements, then division is true division, leading to a change in the nature of what is divided. Here we can turn to Bergson’s alternative form of multiplicity. For Bergson (at least at this stage of his philosophical development), this alternative form of organisation is that which we find in our conscious | states, although for Deleuze this mode of organisation is not simply a feature of our perception of the world, but rather of the world itself. As we can see, Bergson’s account of the perception of a melody presents clearly the way in which dividing non-extensive multiplicities leads to a change in their nature [the following up to citation is Bergson quotation]:

Pure duration is the form which the succession of our conscious states assumes when our ego lets itself live, when it refrains from separating its present state from its former states. For this purpose it need not be entirely absorbed in the passing sensation or idea; for then, on the contrary, it would no longer endure. Nor need it forget its former states: it is enough that, in recalling these states, it does not set them alongside its actual state as one point alongside another, but forms both the past and the present states into an organic whole, as happens when we recall the notes of a tune, melting, so to speak, into one another. Might it not be said that, even if these notes succeed one another, yet we perceive them in one another, and that their totality may be compared to a living being whose parts, although distinct, permeate one another just because they are so closely connected? The proof is that, if we interrupt the rhythm by dwelling longer than is right on one note of the tune, it is not its exaggerated length, as length, which will warn us of our mistake, but the qualitative change thereby caused in the whole of the musical phrase. We can thus conceive of succession without distinction, and think of it as a mutual penetration, an interconnexion and organization of elements, each one of which represents the whole, and cannot be distinguished or isolated from it except by abstract thought. (Bergson 1910: 100–1)

The two different notions of multiplicity can be mapped onto the extensive and intensive in a relatively straightforward manner [the following up to citation is Deleuze quotation:]

Therefore there are two types of multiplicity: one is called multiplicity of juxtaposition, numerical multiplicity, distinct multiplicity, actual multiplicity, material multiplicity, and for predicates it has, we will see, the following: the one and the multiple at once. The other: multiplicity of penetration, qualitative multiplicity, confused multiplicity, virtual multiplicity, organized multiplicity, and it rejects the predicate of the one as well as that of the same. (L 00/00/70)

These two forms of multiplicity can be related to the extensum (extensity in general), and the spatium (the field of intensive difference as a whole).
(178-179)

[Recall the three spatial syntheses from section 5.3. Quoting from our brief summary: “1) Intensive differences are localized by being distributed into various spatial locations, and they move from place to place according to how they interrelate and interact (in thermodynamics, for example, heat moves from its location to where cold is located, normally). 2) The extensive space into which these intensities are distributed and the qualities belonging to those things in extensive space come about somehow by means of intensive depth. 3) These distributions of intensities and their explications into extensive properties and other qualities continues to remain fresh and in a perpetual state of renewal.”] “The three spatial syntheses show how these two multiplicities are related” (SH 179). [It seems the idea is that they are related by the process of explication. I think I grasp what the results of explication are (namely, explicated intensities in the extensive realm, perhaps in the form of numericalized intensive properties, extensive properties, and qualities) but as a process or activity, I still do not quite understand how explication works. I have questions like, where are the deeper intensive differences that become explicated? Are they in the same location as the explicated ones? How does the transition from one realm to the other transpire? Or is it that there are extensive givens, but acting on them somehow are forces of variability, and explication is the effects of the variation?] SH concludes this section by turning us to the next one: “The final question to be addressed is how the intensive multiplicity is | related to the Idea. In answering this question, we will also have to deal with the problem of individuation, or the emergence of the subject from an a-subjective field of intensity” (SH 179-180).

 

 

 


Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

L:

Deleuze, Gilles, lecture of date 00/00/70.
French:
http://www.webdeleuze.com/php/texte.php?cle=107&groupe=Conf%E9rences&langue=1
English: 
http://www.webdeleuze.com/php/texte.php?cle=111&groupe=Conf%E9rences&langue=2


Bergson, Henri (1910), Time and Free Will, trans. F. L. Pogson, London: Allen and Unwin.

DeLanda, Manuel (2002), Intensive Science and Virtual Philosophy, London: Continuum.