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NOTES TO PP. 481-493 D 573

 

which the variable reacts upon its antecedents: Modeles math'ematiques de la morphogenese 

(Paris: 10/18, 1974), pp. 218-219.

 

14.  On Riemann's and Helmholtz's presentations of multiplicity, see Jules Vuillemin, 

Philosophie de I'algebre (Paris: PUF, 1962), pp. 409ff. 

15.  See Bertrand Russell, The Principles ofMathematics (New York: Norton, 1964), chapter 

31. The following discussion does not conform to Russell's theory. An excellent analysis of the 

notions of distance and magnitude according to Meinong and Russell may be found in 

Albert Spaier, La pensee et la quantite (Paris: Alcan, 1927). 

16.  Beginning in chapter 2 of Time and Free Will: An Essay on the Immediate Data of 

Consciousness, trans.F. L. Pogson (New York: Macmillan, 1958), Bergson repeatedly uses the 

noun "multiplicity," under conditions that should attract the attention of commentators; that 

there is an implicit reference to Riemann seems beyond doubt. Later, in Matter and Memory, 

trans. Nancy Margaret Paul and W. Scott Palmer (New York: Humanities Press, 1978), he 

explains that Achilles' stride can be divided perfectly into "submultiples" that differ in 

nature, however, from that which they divide; the same goes for the tortoise's stride; and the 

submultiples, "in both cases," themselves differ in nature. 

17.  See Bergson, Time and Free Will, p. 82: if a multiplicity "implies the possibility of 

treating any number whatever as a provisional unit which can be added to itself, inversely the 

units in their turn are true numbers which are as big as we like, but are regarded as provision-

ally indivisible for the purpose of compounding them with one another." 

18.  Albert Lautman, Les schemas de structure (Paris: Hermann, 1938), pp. 23, 34-35. 

19.  On this properly Euclidean conjunction (which is very different from the process of 

accumulation), see Lautman, ibid., pp. 45-48. 

20.  Benoit Mandelbrot, Fractals: Form, Chance, and Dimension (San Francisco: W. H. 

Freeman, 1977). 

21.  On these two kinds of space, see Jean-Pierre Vernant, Mythe et pensee chez les Grecs, 

vol. 1 (Paris: Maspero, 1971-1974), pp. 174-175. 

22.  Michel Serres, La naissance de la physique dans le texte de Lucrece. Fleuves et turbu-

lences (Paris: Minuit, 1977): "Physics is based much more on a vectorial space than on a met-

ric space" (p. 79). On the hydraulic problem, see pp. 104-107. 

23.  Serres, La naissance de la physique, pp. 35, 135ff. 

24.  Anne Querrien has clearly demonstrated the importance of the Ecole des Ponts et 

Chaussees (School of Bridges and Roadways) in this elaboration of the concept of work. For 

example, Navier, an engineer and professor of mechanics, wrote in 1819: "We must establish a 

mechanical currency with which to estimate the quantities of work used to accomplish every 

kind of fabrication." 

25.  It is a commonplace of missionaries' narratives that there is nothing corresponding to 

the category of work, even in transhumant agriculture, with its laborious ground-clearing 

activities. Marshall Sahlins is not content to remark the briefness of the time devoted to the 

labor necessary for maintenance and reproduction, but goes on to stress qualitative factors: 

the continuous variation that regulates activity, and the mobility or freeness of movement, 

which excludes stockpiling and is measured in terms of the "convenience of transporting the 

object." "La premiere societe d'abondance," Les temps modernes, no. 268 (October 1968), 

pp. 654-656, 662-663, 672-673. 

26.  The principal texts are Alois Riegl, Die Sp'dtromische Kunstindustrie (Vienna: 

Staatdruckerei, 1927); Wilhelm Worringer, Abstraction and Empathy; A Contribution to the 

Psychology of Style, trans. Michael Bullock (New York: International Universities Press, 

1963); Henri Maldiney, Regard, parole, espace (Lausanne: L'Age d'homme, 1973), especially 

"L'art et le pouvoir du fond," and Maldiney's discussion of Cezanne. 

27.  All of these points already relate to Riemannian space, with its essential relation to 

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NOTES TO PP. 493-498

 

"monads" (as opposed to the unitary Subject of Euclidean space): see Gilles Chatelet, "Sur 

une petite phrase de Riemann," Analytiques, no. 3 (May 1979). Although the "monads" are no 

longer thought to be closed upon themselves, and are postulated to entertain direct, 

step-by-step local relations, the purely monadological point of view proves inadequate and 

should be superseded by a "nomadology" (the ideality of striated space versus the realism 

of smooth space).

 

28.  See Edmund Carpenter's description in Eskimo of ice space, and of the igloo: "There 

is no middle distance, no perpecti ve, no outline, nothing the eye can cling to except thousands 

of smokey plumes of snow... a land without bottom or edge ... a labyrinth alive with the 

movements of crowded people. No flat static walls arrest the ear or eye ... and the eye can 

glance through here, past there" (no pagination). 

29.  These two aspects, the Encompassing Element and the Center, figure in Jean-Pierre 

Vernant's analysis of space in Anaximander; Mythe et penseee chez les Grecs (Paris: Maspero, 

1971-1974), vol. 1, part 3. From another perspective, the entire history of the desert concerns 

the possibility of its becoming the encompassing element, and also of being repelled, rejected 

by the center, as though in an inversion of movement. In a phenomenology of religion like that 

of Van der Leeuw, the nomos itself does indeed appear as the encompassing-limit or ground, 

and also as that which is repelled, excluded, in a centrifugal movement. 

30.  Whatever interactions there may be, the "art of the steppes" had a specificity that was 

communicated to the migrating Germans; in spite of his many reservations about nomad cul-

ture, Rene Grousset makes this point in The Empire of the Steppes, trans. Naomi Walford 

(New Brunswick, N. J.: Rutgers University Press, 1970). pp. 11 -25. He notes the irreducibility 

of Scythian art to Assyrian art, Sarmatian art to Persian art, and Hunnic art to Chinese art. He 

even points out that the art of the steppes influenced more than it borrowed (see in particular 

the question of Ordos art and its relations to China). 

31.  On this question of light and color, in particular in Byzantine art, see Henri Maldiney, 

Regard, parole, espace, pp. 203ff., 239ff. 

32.  The correlation, "haptic-close-abstract," was already suggested by Riegl. But it 

was Worringer who developed the theme of the abstract line. Although he conceives of it 

essentially in its Egyptian form, he describes a second form in which the abstract assumes 

an intense life and an expressionist value, all the while remaining inorganic: Abstraction 

and Empathy, chapter 5, and especially Form in Gothic (London: Putnam's and Sons, 

1927), pp. 38-55. 

33.  Andre Leroi-Gourhan, Legesteet la parole (Paris: Albin Michel, 1964-1965), vol. 1, 

Technique et langage, pp. 263ff.; vol. 2, La m'emoire et les rythmes, pp. 219ff. ("Rhythmic 

marks are anterior to explicit figures.") Worringer's position is very ambiguous; thinking that 

prehistoric art is fundamentally figurative, he excludes it from Art, on the same grounds as he 

excludes the "scribblings of a child" (Abstraction and Empathy, pp. 51-55). Then he advances 

the hypothesis that the cave dwellers were the "ultimate result" of a series he says began with 

the abstract (p. 130). But would not such a hypothesis force Worringer to revise his conception 

of the abstract, and to cease identifying it with Egyptian geometricism? 

34.  Worringer establishes an opposition between the power of repetition, which is 

mechanical, multiplying, and without fixed orientation, and the force of symmetry, which is 

organic, additive, oriented, and centered. He sees this as the fundamental difference between 

Gothic ornamentation and Greek or classical ornamentation: Form in Gothic, pp. 53-55 

("The Ceaseless Melody of the Northern Line"). In a fine book, Esthetiques d'Orient et 

d'Occident (Paris: E. Leroux, 1937), Laura Morgenstern develops a particular example, dis-

tinguishing the "symmetrical antithetism" of Sassanid Persian art from the "disjointed 

antithetism" of the art of the prdto-Iranian nomads (Sarmatians). Many authors, however, 

have stressed the centered and symmetrical motifs in barbarian or nomad art. Worringer 

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