## 31 Dec 2009

### The Flux of Two in the Time of One. §77. Ch.4.One or Many Durations? Bergsonism. Deleuze

[The following summarizes parts of Deleuze's Bergsonism. My commentary is in brackets. Paragraph subheadings are my own.]

Gilles Deleuze

Le bergsonisme
Bergsonism

Ch.4.
Une ou plusieurs durées ?
One or Many Durations?

Previously Deleuze discusses what he calls Bergson's triplicity of fluxes. The flow of the bird's flight along with the flow of a river will only be simultaneous if another flow brings them together. A flowing consciousness which is aware of these other fluxes draws them into itself and in that way unites them, even while being aware of their qualitative differences. Conscious durations envelop other durations and themselves. We might imagine the whole of all durations as being enveloped together in one encompassing act of conscious duration. In this way, there is one single flow of duration that is made up of a multiplicity of fluxes.

§77 The Flux of Two in the Time of One

Bergson considers duration to be a virtual multiplicity [see §75] as well as a continuous multiplicity [see this entry on Riemann's and Bergson's notion of a continuous multiplicity].

When we divide duration, we obtain elements that are different in kind. [Now, recall that Bergson distinguishes numerical and non-numerical multiplicities. (See §33 of Deleuze's Bergsonism). A numerical multiplicity, like any number in general, may be divided without changing its nature. However a non-numerical multiplicity, like conscious duration, changes with each division. Yet, we may still extract numerical values from conscious states in a secondary and qualitative way. Bergson's example is the bell tolling the hour while he is engrossed in his writing. While taking a pause, he tries to recall the number of tolls. He did not originally set-out an image of each one in ideal space as they rung. However, by the final toll, the group has a certain feel to it. If for example there were four tolls, he would know so, because hearing four tolls feels a certain way, and hearing three or five tolls each feel their own unique ways. In this sense, numerical values begin as qualities. Only afterward may they be given a quantitative value. Numbers however already imply their divisions, because any quantity is divisible in any variety of ways. A numerical unit is already a multiplicity of fractions already combined to form the given value. Space itself is like this too. But conscious duration does not come pre-packed with its divisions. Bergson needed to commit an additional mental action to convert his feeling of four tolls into the numerical quantity four.] Deleuze parenthetically references Matter and Memory (reference to be added later) to explain how conscious duration requires an act of consciousness in order for it to be divided [underlined is Deleuze's quotation]:

Abstract space is, indeed, at bottom, nothing but the mental diagram of infinite divisibility. But with duration it is quite otherwise. The parts of our duration are one with the successive moments of the act which divides it; if we distinguish in it so many instants, so many parts it indeed possesses; and if our consciousness can only distinguish in a given interval a definite number of elementary acts, if it terminates the division at a given point, there also terminates the divisibility. (Bergson 273-274)
L'espace n'est d'ailleurs, au fond, que le schème de la divisibilité indéfinie. Mais il en est tout autrement delà durée. Les parties de notre durée coïncident avec les moments successifs de l'acte qui la divise ; autant nous y fixons d'instants, autant elle a de parties; et si notre conscience ne peut démêler dans un intervalle qu'un nombre déterminé d'actes élémentaires, si elle arrête quelque part la division, là s'arrête aussi la divisibilité. (230)

Hence Deleuze notes that the parts we divide from duration "only actually exist insofar as the division itself is effectively carried out" (Deleuze 81). [Also recall from §75 that duration is a continuous and non-numerical multiplicity. It is made-up of its qualitative multiplicity. But the numerical discreteness of these multiple elements only exists secondarily or potentially, after an act of consciousness divides them. So they are virtual multiplicities]. Before we divide the virtual multiplicity of duration, there would of course only be one single time (81c). [Now also recall Bergson's use of the Achilles and Tortoise paradox to explain the indivisibility of motion and hence also duration (see §70 of Time and Free Will). Achilles' movement involves longer steps than the tortoise's. And the movement and consciousness of each runner is qualitatively different from the other.] Deleuze notes that in Bergson's Achilles & tortoise illustration, we are decomposing one flowing event into two separate fluxes, the motions of Achilles and of the tortoise, each of which is qualitatively different from the other. [Deleuze now turns to a point Bergson makes in Duration and Simultaneity. In Chapter 3, §50, Bergson first defines duration as being something that is consciously experienceable. A temporality that cannot possibly be experienced is not one that exists. But if there are two conscious observers, that means neither one's time is less real. We would obtain imaginary time however if one observer were to use Lorentz' formulae to calculate what from his own perspective would be the temporality of the other person. Yet, as Bergson showed, this calculated temporality is not the one the other person experiences. Rather, they both experience the same flow of duration. See §§59 & 60, §§64-71, §§72-79, §§80-82, §§87-116, and §§121-125 in Bergson's Duration and Simultaneity.]

We might consider then Achilles and the tortoise as being observers moving relative to each other. Let's first take Achilles' perspective. He experiences a concrete flow of conscious duration while running. But from his point-of-view, he might calculate some figure that determines what from his perspective the temporality must be like for the tortoise. Physicists perform such calculations in order to be sure that no matter the reference-point, all figures can come into accord despite the problems light causes for their mathematics. [See §74 of Deleuze's Bergsonism for a brief overview of Einstein's relativity. Or see Chapter 1 of Duration and Simultaneity, or see this simplification of the theory]. Yet Bergson notes that for their scientific purposes, physicists always must arbitrarily take one point-of-view instead of any other one, even though they know it could have been some other one just as well. So in other words, to obtain the fruits of relativity theory, the absolute relativity of moving bodies must be suspended temporarily. But, says Bergson, philosophers are not interested in producing accordant calculations for cosmic computations. They are concerned rather with reality, in this case, the reality of time and also space. Bergson meticulously accounts for why both Achilles and the tortoise, for example, experience the same flow of duration. Their different movements might create the appearance of time distortions in the other flux, but in reality there is none. In a sense, Bergson is saying that scientists imagine fantasy times for mathematical purposes, and then confuse them with the real times that actual consciousnesses would experience.

Hence in regard to divergent fluxes, Deleuze notes that Bergson's "whole thesis consists in demonstrating that they can only be livable or lived in the perspective of a single time" (81d). If we want to say in the first place there are two time flows for different consciousnesses, we "are forced to introduce a strange factor: the image that A has of B, while nevertheless knowing that B cannot live in this way. This factor is completely 'symbolic'; in other words, it opposes and excludes the lived experience" (82a). Hence Bergson concludes that there is only one Time, no matter if we divide it into component fluxes or if we consider them all together at once. (82a)

Bergson, Henri. Duration and Simultaneity. Ed. Robin Durie. Transl. Mark Lewis and Robin Durie. Manchester: Clinamen Press, 1999.

Bergson, Henri. Durée et simultanéité: A propos de la théorie d'Einstein. Paris: Librairie Félix Alcan, 1923. Available online at:http://www.archive.org/details/dureetsimultan00berguoft

Bergson, Henri. Matière et mémoire: Essai sur la relation du corps à l'esprit. Ed. Félix Alcan. Paris: Ancienne Librairie Germer Bailliere et Cie, 1903. Available online at:http://www.archive.org/details/matireetmmoiree01berggoog

Bergson, Henri. Matter and Memory. Transl. Nancy Margaret Paul & W. Scott Palmer. Mineola, New York: Dover Publications, Inc., 2004; originally published by George Allen & Co., Ltd., London, 1912. Available online at:http://www.archive.org/details/mattermemory00berg

Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Deleuze, Gilles. Le bergsonisme. Paris : Presses Universitaires de France, 1966.