The concept of multiplicity has two fates in the Twentieth Century: Bergsonism and phenomenology (Deleuze, 1991, pp. 115–118). In phenomenology, the multiplicity of phenomena is always related to a unified consciousness. In contrast, in Bergsonism, “the immediate data of consciousness” (les données immédiates de la conscience) are a multiplicity. Here, two prepositions, “to” and “of,” indicate perhaps the most basic difference between Bergsonism and phenomenology. Of course, this phrase is the title of Bergson's first work, Essai sur les données immédiates de la conscience. The standard English title of this work is Time and Free Will: An Essay on the Immediate Data of Consciousness. It is the text that Sartre claimed attracted him to philosophy.

Time and Free Will has to be seen as an attack on Kant, for whom freedom belongs to a realm outside of space and time. Bergson thinks that Kant has confused space and time in a mixture, with the result that we must conceive human action as determined by natural causality. Bergson offers a twofold response. On the one hand, in order to define consciousness and therefore freedom, Bergson proposes to differentiate between time and space, “to un-mix” them, we might say. On the other hand, through the differentiation, he defines the immediate data of consciousness as being temporal, in other words, as the duration (la durée). In the duration, there is no juxtaposition of events; therefore there is no mechanistic causality. It is in the duration that we can speak of the experience of freedom.

For Bergson, we must understand the duration as a qualitative multiplicity — as opposed to a quantitative multiplicity. In Time and Free Will, we find several examples of a quantitative multiplicity; the example of a flock of sheep is perhaps the easiest to grasp (Time and Free Will, pp. 76–77). When we look at a flock of sheep, what we notice is that they all look alike. Thus a quantitative multiplicity is always homogeneous. But also, we notice that we can enumerate the sheep, despite their homogeneity. We are able to enumerate them because each sheep is spatially separated from or juxtaposed to the others; in other words, each occupies a discernable spatial location. Therefore, quantitative multiplicities are homogeneous and spatial. Moreover, because a quantitative multiplicity is homogeneous, we can represent it with a symbol, for instance, a sum:  “25.”  In contrast, qualitative multiplicities are heterogeneous and temporal; this is a difficult idea, since we would normally think that if there is heterogeneity, there is juxtaposition. But, in the duration, heterogeneity does not imply juxtaposition (or it implies juxtaposition only retrospectively). Again, Bergson gives us many examples; but perhaps the easiest example to grasp is the feeling of sympathy, a moral feeling (Time and Free Will, pp. 18–19). Sympathy is not only the easiest to grasp, it is also significant, as we shall see. Our experience of sympathy begins, according to Bergson, with our putting ourselves in the place of others, feeling their pain. But, if this were all, the feeling would inspire in us abhorrence of others, and we would want to avoid them, not help them. Bergson concedes that the feeling of horror may be at the root of sympathy. But then, we realize that if we do not help this poor wretch, it is going to turn out that, when we need help, no one will come to our aide. There is a “need” to help the suffering. For Bergson, these two phases are “inferior forms of pity.”  In contrast, true pity involves not so much fearing pain as desiring it. It is as if “nature” has committed a great injustice and what we want is to be seen as not complicit with it. As Bergson says, “The essence of pity is thus a need for self-abasement, an aspiration downward” into pain. But, this painful aspiration develops into a sense of being superior. We realize that we can do without certain sensuous goods; we are superior to them since we have managed to dissociate ourselves from them. In the end, one feels humility, humble since we are now stripped of these sensuous goods. Now, Bergson calls this feeling “a qualitative progress.” It consists in a “transition from repugnance to fear, from fear to sympathy, and from sympathy itself to humility.”  The genius of Bergson's description is that there is a heterogeneity of feelings here, and yet no one would be able to juxtapose them or say that one negates the other. There is no negation in the duration. We shall return to this important point concerning negation when discussing “Creative Evolution.”  In any case, the feelings are continuous with one another; they interpenetrate one another, and there is even an opposition between inferior needs and superior needs. A qualitative multiplicity is therefore heterogeneous (or singularized), continuous (or interpenetrating), oppositional (or dualistic) at the extremes, and progressive (or temporal, an irreversible flow, which is not given all at once). Because a qualitative multiplicity is heterogeneous and yet interpenetrating, it cannot be adequately represented by a symbol; indeed, for Bergson, a qualitative multiplicity is inexpressible. Bergson also calls the last characteristic of temporal progress mobility. For Bergson — and perhaps this is his greatest insight — freedom is mobility. Because Bergson connects duration with mobility, in the second half of the Twentieth Century (in Deleuze and Foucault, in particular), the Bergsonian concept of qualitative multiplicity will be dissociated from time and associated with space (Deleuze 1986).

In his “Introduction to Metaphysics,” Bergson gives us three images to help us think about the duration and therefore qualitative multiplicities (The Creative Mind, pp. 164–65). The first is that of two spools, with a tape running between them, one spool unwinding the tape, the other winding it up. (During his discussion of Bergson, Heidegger focuses on this image in his 1928 The Metaphysical Foundations of Logic.) Duration resembles this image, according to Bergson, because, as we grow older, our future grows smaller and our past larger. The benefit of this image is that it presents a continuity of experiences without juxtaposition. Yet, there is a drawback: because a tape moves between the two spools, the image presents the duration as being homogeneous, as if one could fold the tape back over its other parts, as if the tape were super-posable, implying that two moments in consciousness might be identical. Yet, as Bergson says, “no two moments are identical in a conscious being” (The Creative Mind, p. 164). Duration, for Bergson, is continuity of progress and heterogeneity; moreover, thanks to this image, we can also see that duration implies a conservation of the past. Indeed, for Bergson and this is the center of his truly novel idea of memory, memory conserves the past and this conservation does not imply that one experiences the same (re-cognition), but difference. One moment is added onto the old ones, and thus, when the next moment occurs, it is added onto all the other old ones plus the one that came immediately before. In comparison, therefore to the past collection of moments, it cannot be the same as the one immediately before, because the past is “larger” for the current moment than it was for the previous moment. Although Bergson does not say this, one might say that Tuesday is different from Monday because Monday only includes itself and Sunday, while Tuesday includes itself, Monday, and Sunday. This first image, therefore, implies that duration is memory: the prolongation of the past into the present. We shall return to the question of memory below.

The second image of qualitative multiplicity is the color spectrum. We saw in the first image of the spools that there is constant difference or heterogeneity. The color spectrum helps us understand this, since a color spectrum has a multiplicity of different shades or nuances of color. Here we have heterogeneity, but there is a drawback to this image as well. We lose the characteristic of continuity or unity since the spectrum has colors juxtaposed. As Bergson says, “pure duration excludes all idea of juxtaposition, reciprocal exteriority and extension” (The Creative Mind, p. 164).

Bergson's third image is an elastic band being stretched. Bergson tells us first to contract the band to a mathematical point, which represents “the now” of our experience. Then, draw it out to make a line growing progressively longer. He warns us not to focus on the line but on the action which traces it. If we can focus on the action of tracing, then we can see that the movement — which is duration — is not only continuous and differentiating or heterogeneous, but also indivisible. We can always insert breaks into the spatial line that represents the motion, but the motion itself is indivisible. For Bergson, there is always a priority of movement over the things that move; the thing that moves is an abstraction from the movement. Now, the elastic band being stretched is a more exact image of duration. But, the image of the elastic is still, according to Bergson, incomplete. Why ? Because, for him, no image can represent duration. An image is immobile, while duration is “pure mobility” (The Creative Mind, p. 165). Later, in Creative Evolution, Bergson will criticize the new art of cinema for presenting immobile images of movement. As Deleuze will show in his cinema books, however, Bergson does not recognize the novelty of this artform. Cinema does provide moving images. In any case, in “Introduction to Metaphysics,” Bergson compares all three images: “the unrolling of our duration [the spool] in certain aspects resembles the unity of a movement which progresses [the elastic], in others, a multiplicity of states spreading out [the color-spectrum].” Now we can see that duration really consists in two characteristics:  unity and multiplicity. This double characteristic brings us to Bergson's method of intuition.

http://plato.stanford.edu/entries/bergson/