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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.


30 Dec 2009

Through Three, Flows the Mind, of One. §76. 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 distinguished actual multiplicities (which are numerical and discontinuous) from virtual multiplicities (which are continuous and qualitative). Bergson thinks that Einstein's multiple time is an actual multiplicity, but real concrete lived duration for Bergson is a virtual multiplicity. Yet even though it is multiple, it is still single and universal.


§76 Through Three, Flows the Mind, of One

To understand how this is, we first recall Bergson explaining that we may be aware of two flows at once. We may be separately aware of each of them by dividing our attention between them. Or, we might think of them each in their uniqueness, but be conscious of them both in one act of awareness [see §40 of Duration and Simultaneity]. In this way, consciousness unites other contemporaneous flows. Bergson writes [underlined is Deleuze's quotation]:

When we are seated on the bank of a river, the flowing of the water, the gliding of a boat or the flight of a bird, the ceaseless murmur in our life's deeps are for us three separate things or only one, as we choose. We can interiorize the whole, dealing with a single perception that carries along the three flows, mingled, in its course; or we can leave the first two outside and then divide our attention between the inner and the outer; or, better yet, we can do both at one and the same time, our attention uniting and yet differentiating the three flows, thanks to its singular privilege of being one and several. Such is our primary idea of simultaneity. We therefore call two external flows that occupy the same duration 'simultaneous' because they both depend upon the duration of a like third, our own; this duration is ours only when our consciousness is concerned with us alone, but it becomes equally their when our attention embraces the three flows of a single indivisible act. (Bergson 36c.d)

So consciousness, which is duration, itself may unify duration. Bergson "endows duration with the power to encompass itself" (Deleuze 80c). If there were just two fluxes, the bird's flight and our consciousness for example, then we cannot say there are simultaneous fluxes. This is because a third flux is needed to bring the other two together.

The flowing of the water, the flight of the bird, the murmur of my life form three fluxes; but only because my duration is one of them, and also the element that contains the two others. Why not make do with two fluxes, my duration and the flight of the bird, for example? Because the two fluxes could never be said to be coexistent or simultaneous if they were not contained in a third one. The flight of the bird and my own duration are only simultaneous insofar as my own duration divides in two and is reflected in another that contains it at the same time as it contains the flight of the bird: There is therefore a fundamental triplicity of fluxes. (Deleuze 80c.d)

L'écoulement de l'eau, le vol de l'oiseau, le murmure de ma vie forment trois flux ; mais ils ne sont tels que parce que ma durée est l'un d'entre eux, et aussi l'élément qui contient les deux autres. Pourquoi ne pas se contenter de deux flux, ma durée et le vol de l'oiseau par exemple ? C'est que jamais deux flux ne pourraient être dits coexistants ou simultanés s'ils n'étaient contenus dans un même troisième. Le vol de l'oiseau et ma propre durée ne sont simultanés que dans la mesure où ma propre durée se dédouble et se réfléchit en une autre qui la contient en même temps qu'elle contient le vol de l'oiseau : il y a donc une triplicité fondamentale des flux. (80-81)

[In footnote 15, Deleuze cites part of Duration and Simultaneity (see §35) where Bergson discuss the fancied enlargement of our consciousness. We begin by considering our awareness of our immediate surroundings. Then we think of the space neighboring it on the outside. Then we continue to enlarge that halo until we are imagining the whole world, all anchored down in our consciousness. "Each of us is generally content with indefinitely enlarging, by a vague effort of imagination, his immediate physical environment, which, being perceived by him, participates in the duration of his consciousness. But as soon as this effort is precisely stated, as soon as we seek to justify it, we catch ourselves doubling and multiplying our consciousness, transporting it to the extreme limits of our outer experience, then, to the edge of the new field of experience that it has thus disclosed, and so on indefinitely - they are really multiple consciousnesses sprung from ours, similar to ours, which we entrust with forging a chain across the immensity of the universe and with attesting, through the identity of their inner durations and the contiguity of their outer experiences, the singleness of an impersonal time" / "Chacun de nous se contente en général d'élargir indéfiniment, par un vague effort d'imagination, son entourage matériel immédiat, lequel, étant perçu par lui, participe à la durée de sa conscience. Mais dès que cet effort se précise, dès que nous cherchons à le légitimer, nous nous surprenons dédoublant et multipliant notre conscience, la transportant aux confins extrêmes de notre expérience extérieure, puis au bout du champ d'expérience nouveau qu'elle s'est ainsi offert, et ainsi de suite indéfiniment : ce sont bien des consciences multiples issues de la notre, semblables à la nôtre, que nous chargeons de faire la chaîne à travers l'immensité de l'univers et d'attester, par l'identité de leurs durées internes et la contiguïté de leurs expériences extérieures, l'unité d'un Temps impersonnel" (Bergson 32c.d/59c-60). Deleuze says in the footnote that this (self-awareness of duration) is a reflexive act of duration which brings it close to the cogito. Also in this footnote, Deleuze refers also to §§34-35 of Duration and Simultaneity. Here Bergson speaks of a triplicity of continuities.
a) The flow of our internal life: "A melody to which we listen with our eyes closed, heeding it alone, comes close to coinciding with this time which is the very fluidity of our inner life" (Bergson 30c).
b) The flow of our voluntary movement; and,
c) The flow of movement in space: "To each moment of our inner life there thus corresponds a moment of our body and of all environing matter that is 'simultaneous' with it; this matter then seems to participate in our conscious duration. Gradually, we extend this duration to the whole physical world, because we see no reason to limit it to the immediate vicinity of our body" (Bergson 31a).]

So, our durational consciousness may envelop other fluxes (and itself included) and bring them together in one flowing act of consciousness. Hence your and my durations each have the power "to disclose other durations, to encompass the others, and to encompass itself ad infinitum" (80d).

This triplicity of flux then illustrates two essential characteristics of duration:

1) Duration is in one sense multiple, because it is made of a multiplicity of fluxes. Yet in another sense, it is single, because these multiple fluxes obtain their simultaneity from being unified in another duration. So we would not say that duration is indivisible. However it is not divisible like Einstein's multiple times. So it is divisible only in this special way.

2) Duration involves a succession. But it is more than just that. For, the successions are simultaneous coexisting fluxes.

Deleuze ends by citing two parts of Duration and Simultaneity. The first elaborates on the triplicity, and we provided it above in the quotation with the boat and bird fluxes [Deleuze quotes: Such is our primary idea of simultaneity. We therefore call two external flows that occupy the same duration 'simultaneous' because they both depend upon the duration of a like third, our own .... (Bergson 36d).] The second half of the quotation comes from §49. Bergson explains that science begins with real duration, then abstracts the conscious experience out of it, which produces a homogeneous extensive time. So if physical bodies exhibit a motion, science will think of it as having transpired across a certain number of simultaneities. But these would be like points on a line (it is a 'time-line'). And all the points on a line are simultaneous with each other, and not temporally successive. The only thing that makes this representation temporal and not spatial is the fact that we can trace it back to a consciousness that experiences the duration that unfolded during the movement. Bergson writes [underlined is Deleuze's quotation]:

this is time only because we can look back at what we have done. From the simultaneities staking out the continuity of motions, we are always prepared to reascend the motions themselves and, through them, the inner duration that is contemporaneous with them, thus replacing a series of simultaneities of the instant, which we count but which are no longer time, by the simultaneity of flows that leads us back to inner, real duration. (Bergson, Duration and Simultaneity 42c)

Hence at the heart of Bergson's multiplicity of fluxes is a concrete, internal conscious experience of duration.



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


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.


Einstein's Time is Actual but not Durational §75. Ch.4.One or Many Durations? Bergsonism. DeleuzeBergsonism. 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 reviewed Bergson's account of Einstein's relativity. For Einstein, relativity implies a multiplicity of times. But for Bergson, the assumptions of relativity should lead us to conclude that there is but one duration, and not a fractured multiplicity of them. Nonetheless, duration itself is still a multiplicity of sorts, for Bergson.



§75 Einstein's Time is Actual but not Durational

So now Deleuze wonders, what sort of multiplicity is duration, for Bergson? Deleuze has us recall Bergson's two sorts of multiplicities [See §32 and §33 for this prior treatment]:

1) Actual multiplicities. These are numerical and discontinuous.

2) Virtual multiplicities. These are continuous and qualitative.

Einstein posits there being a multiplicity of discretely different times, each depending on the position of the observer [For more, see Bergson's Duration and Simultaneity, particularly the first chapter]. Hence Einstein's time for Bergson is an actual multiplicity rather than a virtual one. According to Deleuze, Bergson criticizes Einstein for having confused these two sorts of multiplicities, which also resulted in Einstein confusing time with space [perhaps because time which can be stretched is an extensive and hence spatialized time]. Yet duration as we saw is still a multiplicity for Bergson. The question is, what kind of multiplicity is it? Deleuze says that Bergson's duration is "a single, universal and impersonal Time" (80ab).


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.