24 Dec 2009

Bergson's Einstein §74. 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

Une ou plusieurs durées ?
One or Many Durations?

Previously Deleuze discussed Bergson's position on whether there is just one duration or many of them. Bergson often describes duration as a heterogeneous qualitative multiplicity. So we might expect him to say that there are many durations. Oddly, Bergson holds that there is just one duration. This is his monist hypothesis of time.

§74 Bergson's Einstein

Deleuze wonders how we might account for Bergson's surprising position. It is the product of Bergson's confrontation with Einstein's relativity theory. Both Einstein and Bergson draw their notion of multiplicity from Riemann. However, they come to opposing positions regarding whether there is a plurality or unity of time.

Deleuze will review Bergson's summary of Einstein's relativity theory. [It can be found in greater detail in the first chapter of Bergson's Duration and Simultaneity].

We in the first place conceive of bodies in motion. [Their movement is reciprocal. While in a steadily moving train, we walk around and feel as though we are on stable ground. But we might observe through the window a person along the track rapidly coming-and-going. For us on the train, the person is in motion. But for this same person observing the train from the ground, the locomotive is the moving body, while she remains immobilized, standing on firm ground. This can be explained using Newtonian physics. But when dealing with the speed of light, we encounter a problem. First consider a man walking on a boat. He feels himself travel at the speed of his gait. But a woman on the docks sees him travel not just his walking speed, but also she adds to that the speed of the boat. So the walking-man's speed depends on the perspective of reference. This is not so for light. It goes the same speed for the person on the boat as it does for the person observing from the dock. But this is strange, because for the man on the boat, the light goes a certain distance. But for the woman on the dock, it goes a different distance; for, the boat moves underneath the light, in a sense. To explain how the light goes the same speed for different distances, Einstein theorized that] time dilates and space contracts [on a moving body, from the perspective of the reference position, which is provisionally considered as immobile, so that accurate calculations are made that will accord with all other moving systems, which also must take this phenomenon into account. But as a result of the distortions in time, what seems simultaneous on the boat is really not so from the perspective of the woman on the dock. Hence] simultaneities in mobile systems are not so for fixed ones. Einstein also theorized that motion, rest, and acceleration are all relative. [So for the woman on the dock, the boat-man is moving and is wrong about his simultaneities. But for him, his own boat is stable, and the dock moves away from him. So for the boat observer, what seems to be simultaneities on the dock for the dock person are not simultaneities for the boat person. Thus,] "these contractions of extensity, these dilations of time, these ruptures of simultaneity become absolutely reciprocal" (Deleuze 79bc). [So we have one time for the boat person, which he thinks differs for the time on the dock. Yet the person on the dock has her own time, which likewise she thinks differs from the boat's time. Hence] "there would be a multiplicity of times, a plurality of times, with different speeds of flow, all real, each one peculiar to a system of reference" (79c).

Now, if we want to situate a point somewhere, we need to indicate both its spatial and temporal position. So the only unity of time is the fourth temporal dimension united with its spatial dimensions [see this entry on the Mankowski diagrams for this correlation between time and space]. But this unity does not hold universally throughout the cosmos. The relations between time and space for moving bodies depend upon the relative speed of the observer. So in this way "It is precisely this Space-Time block that actually divides up into space and into time in an infinity of ways, each one peculiar to a system" (79d). [All of this is Bergson's summary of Einstein's theory of relativity. Bergson builds from the same premises to conclude that there is only one duration, and not the plurality that Einstein posits].

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.

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