Showing posts with label chemistry. Show all posts
Showing posts with label chemistry. Show all posts

9 Jan 2013

Pt3.Ch8.Sb2 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The Philosophy of Nature.’ summary


by
Corry Shores
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[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Hegel, Deleuze, and the Critique of Representation, Entry Directory]


[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]


 

Henry Somers-Hall

 

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

 

Part 3: Responses to Representation



Chapter 7: Hegel, Deleuze, and the Structure of the Organism



Subdivision 2: The Philosophy of Nature





Brief Summary:

For Hegel, the Idea is The One Totality and it is self-determining reason. This totality is nature, but it becomes other to itself as externality and multiplicity. Nature is rational. The movement in nature involves the identity of difference and identity. So while there are multiplicities of bodies, they form whole systems. In physics bodies form indifferent relations to one another. In chemistry chemicals combine and transform, but their processes are not self-perpetuation. They are however in organic life. Here we have unity and difference in the form of the unity of the organism being constituted through the differences of its organs, and its processes are self-perpetuated.




Summary


For Hegel, the idea is self-determining reason.

More than this, through the recognition that the Idea relates to itself, much as the moments of infinity did in the doctrine of being, we come to realize that the Idea itself is "the One Totality" (EL, §242). That is, it forms a self-referential whole. (212)

The totality is nature, but it is an immediacy, which makes it a one-sided determination of nature. The Idea as totality then becomes other to itself as multiplicity or externality.

We can note, however, that Hegel argues that while this idea of a unified totality is already nature, as a strict unity, it represents an immediacy and is therefore a one-sided determination of nature. In order to counteract this one-sidedness, the Idea "resolves to release out of itself into freedom the moment of its particularity or of the initial determining and otherness, [that is,] the immediate Idea as its reflexion, or itself as nature" (EL, § 244). In order to thus become determinate, the Idea therefore becomes the other of itself as immediate unity. Nature is thus first presented as multiplicity, or pure externality. (212)


Even thought the Idea becomes other to itself, nature is not governed by reason; rather, it become reason that is expressed otherwise than as self-determining idea. So [1] nature is immanently rational, it is a moment of reason and not a creation of it. [2] Yet reason is not in the form of reason in nature.

however, reason is not present in the form of reason in nature . In fact, it is other than itself. Because of this, we will encounter in nature moments of contingency, where there is an incommensurability between the particular forms of nature and their rational Notion. (213)


Nature is a system of stages. The movement between states is governed by reason, which is the movement of the inner Idea of nature. The Idea’s governing principle is the unity of identity and difference. The moment of difference is what first predominates in nature. Nature we said is externality in its opposition to the pure idea. This externality we find described in Philosophy of Nature, where it is discussed in terms of matter. Because matter is infinitely divisible, this implies the parts’ indifference to each other, which would be their externality. But externality is one side of the Idea and unity is the other, so matter contains the idea of unity. So while the planets seem indifferent to one another, in fact they form one system of “bodies in reciprocal relations to one another”. (213)


The Philosophy of Nature describes an immanent movement with there “arising of more and more explicitly unified systems of diverse parts, culminating in the animal organism.” (213) Space, as externality, is the first moment. It gives rise to time and matter. The physics of matter gives us a universal system that allows us to relate all material bodies to one another. but because it is universal, it is too abstract to capture the particularity of the world. (213)  This makes the determinate content become isolated and detached from one another, lacking any necessary connection. So in physics, bodies enter into relations of movement, but in chemistry, different bodies can enter into transformative relations, and this will mean that chemistry does more to develop the moment of unity in difference. For example, acids and bases combine to form salts, which are chemicals with properties different to both acids and bases. [Different salts can mix in water. But chemistry does not completely tell us about the identity of difference and identity.]

While salts are neutral , by combining certain salts, mediated by another substance such as water, we can, in special circumstances, get them to exchange their respective salts. In the chemical sphere, we therefore have a concrete unity between the different elements. Salts and acids, for instance, appear to be inherently relational. While this is the case, chemical interactions do not give us the complete idea of the identity of identity and difference that we are looking for, however. (214)


Various chemicals can be separated and unified. These processes repeat, making them conceivable as part of one greater unified process. If the produces of these chemical processes spontaneously renewed the processes of combination and separation, then they would be life. So it is in the organism where Hegel locates the unity of difference in nature. An organism is a whole but it is made of separate organ parts. And unlike bare chemical processes, it can perpetuate its own processes rather than have them perpetuated by means of external intervention. Because it is about organs and organisms, it refers to the problem of the one and the many. (214)


Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

8 Mar 2010

Forks & Dice: Bifurcation in Prigogine & Stengers, Order out of Chaos: Man's New Dialogue with Nature

by Corry Shores
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Forks & Dice:
Bifurcation in Prigogine & Stengers,
Order out of Chaos: Man's New Dialogue with Nature
La Nouvelle Alliance: Métamorphose de la science



In the second section of the third chapter in Cinema 2, Deleuze describes a kind of forking where a path of development skews-off wildly at unstable points:

And it is not just the circuits forking between themselves, it is each circuit forking within itself, like a split hair. [...] its repetitions are not accumulations, its manifestation refuse to be aligned, or to reconstitute a destiny, but constantly split up any state of equilibrium and each time impose anew 'meander', a new break in causality, which itself forks from the previous one, in a collection of non-linear relations. [footnote 8: On this notion of forking, cf. Prigogine and Stengers, Order out of Chaos: man's new dialogue with nature, London: Heinemann, 1984, pp. 189-90.] [Deleuze 47bc; 47c; 280a]

Et ce ne sont pas seulement les circuits qui bifurquent entre eux, c' est chaque circuit qui bifurque avec soi-même, comme un cheveu four-chu. [...] ses répétitions ne sont pas des accumulations, ses manifestations ne se laissent pas aligner, ni reconstituer un destin, mais ne cessent de morceler tout état d'équilibre, et d'imposer chaque fois un nouveau « coude », une nouvelle rupture de causalité, qui bifurque elle-même avec la précédente, dans un ensemble de relations non-linéaires [note 7: Sur cette notion de bifurcation, cf. Prigogine et Stengers, La nouvelle alliance, Gallimard, p. 190]. [Deleuze 68d; 69a; 69d]


We will avoid most of what is difficult about bifurcation, even though it is essential for fully grasping the concept. We do so on account of your author's limitations. I probably know less than most readers, who are invited to make corrections and provide better explanations. But also it seems the basic ideas that we need to apply in the context of cinema can be presented in a highly simplified form. So that is what we hope to accomplish in the following.

We will first discuss the notions of linearity and non-linearity, drawing from this page at Mathematics Illuminated.

Consider first x = 2.


And x = 2y


We notice that there is one line that tends the same direction throughout.

The equation is "linear" because its graph (all the "x,y" points on the coordinate plane that satisfy the equation) is a straight line, and also because a small change in the value of x effects a proportional, constant change in y. ("Linear vs. Nonlinear Systems")

But now consider x-squared = 4





And now also x-squared = y


We notice two things about the diagram immediately above. The higher power caused there to be a bifurcation of values. And the lines they graph are not straight or 'linear'.

A nonlinear equation is something that doesn't have just a first power of the independent variable and consequently can't be graphed as a simple straight line. ("Linear vs. Nonlinear Systems")

Mathematics Illuminated then gives the example of pendulum motion to illustrate the difference between linear and non-linear systems.

These so-called nonlinear systems can exhibit some wild behaviors, behaviors that might be considered surprising, behaviors that don't fit so nicely into equations. For example, our simple pendulum behaves very smoothly and predictably as long as it doesn't swing too high.
For larger and larger angles, the range of possible behaviors is more varied than the simple cycling back and forth. For example, if the pendulum has sufficient momentum, it will swing past the horizontal line of the pivot and go all the way around, over the top. If it has a little less momentum than this, it might stall near the vertical position above the pivot, lose the tension of the string, and drop almost straight down under the influence of gravity. Both of these behaviors are examples of nonlinearities. ("Linear vs. Nonlinear Systems," emphasis mine)

(Image obtained gratefully from Mathematics Illuminated)

For the sake of illustration, we might imagine that the pendulum can reach a critical point where there are a number of outcomes, none of which can be predicted. We might then again for the sake of illustration regard there to be a bifurcation point where the development of the system can fork-off into very different directions. Perhaps the slightest infinitesimal fluctuation can cause profoundly different outcomes.

In Order out of Chaos: Man's New Dialogue with Nature (La Nouvelle Alliance: Métamorphose de la science), Prigogine & Stengers describe bifurcation in chemical reactions. Hopefully we can profoundly simplify their explanation without falsifying it too much. The system will be stable if the variables are kept within certain bounds. But when an independent variable is pushed to a critical chaotic point, the dependent variable can veer-off or fork-away into two possible directions of development. They write:

Consider the bifurcation diagram represented in Figure 11.


This differs from the previous diagram in that at the bifurcation point two new stable solutions emerge. Thus a new question: Where will the system go when we reach the bifurcation point? We have here a "choice" between two possibilities; they may represent either of the two nonuniform distributions of chemical X in space, as represented in Figures 12 and 13.


The two structures are mirror images of one another. In Figure 12 the concentration of X is larger at the left; in Figure 13 it is larger at the right. How will the system choose between left and right? There is an irreducible random element; the macroscopic equation cannot predict the path the system will take. Turning to a microscopic description will not help. There is also no distinction between left and right. We are faced with chance events very similar to the fall of dice. (162-163, emphasis mine)

They write a bit later:

If we consider Figure 17 [...] we see that the system already has a wealth of possible stable and unstable behaviors.


The "historical" path along which the system evolves as the control parameter grows is characterized by a succession of stable regions, where deterministic laws dominate, and of instable ones, near the bifurcation points, where the system can "choose" between or among more than one possible future. Both the deterministic character of the kinetic equations whereby the set of possible states and their respective stability can be calculated, and the random fluctuations "choosing" between or among the states around bifurcation points are inextricably connected. This mixture of necessity and chance constitutes the history of the system. (169-170, emphasis mine)

Soon we will discuss the bifurcations of Mankiewicz' movies. When we do so, we will see that we arrive at critical and unstable points in the narrative where a character forks or bifurcates unpredictably. Prigogine & Stengers' bifurcation diagrams will illuminate this concept.



Credits:
Pendulum image and direct quotations regarding linear and non-linear systems obtained gratefully from:

Linear and non-linear graphs made using the following freeware:
GIMP, and

The Prigogine & Stengers text citations and images from:

Prigogine, Ilya, and Isabelle Stengers. Order out of Chaos: Man's New Dialogue with Nature. London: Heinemann, 1984.

Also,
Prigogine, Ilya, and Isabelle Stengers. La Nouvelle Alliance: Métamorphose de la science. Paris: Éditions Gallimard, 1979.


Deleuze citations from:

Deleuze, Gilles. Cinema 2: The Time Image. Transl. Hugh Tomlinson and Robert Galeta. London & New York: 1989.

Deleuze, Gilles. Cinéma 2: L'image-temps. Paris: Les éditions de minuit, 1985.