Bergson, Time and Free Will, Chapter 2, §73 "Mechanics Deals with Equations, which Express Something Finished, and not Processes..."

by Corry Shores
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Henri Bergson

Essai sur les données immédiates de la conscience

Time and Free Will: An Essay on the Immediate Data of Consciousness

Chapter II, "The Multiplicity of Conscious States," "The Idea of Duration"

Part XXV: Velocity and Simultaneity

§73 "Mechanics Deals with Equations, which Express Something Finished, and not Processes, such as Duration and Motion"

Previously we discussed the way that physicists obtain knowledge of the positions for moving bodies. Their methods and results tell us about simultaneities and not movements over objective time. Bergson demonstrated that both the formulas for average velocity and for instantaneous velocity really only tell us about simultaneities of objects.

Bergson now does more to address the mathematical nature of these scientific methodologies. A scientist might object that the differential formula for instantaneous velocity allows us to find the velocity anywhere along the object's course of movement. That suggests there is a continuum of time, and our formula deals with one given point along that continuum. Because mathematics is dealing with incredibly small intervals of time, it would seem that we can be sure that time is a continuum that is infinitely divisible into such infinitely small durations.

Bergson notes that it is not the the interval itself that the differential formula quantifies. Rather, it wants to know the "extremity" or limit of an interval. Let's look again at the methodology we examined in the previous entry.

Here is MIT physics professor Walter Lewin explaining how the differential formula will look at the extremity or limit of the interval, and not the interval itself.

And here is Kelly Liakos' wonderful animation of the mathematics of the process. We see that we are moving our attention from one extremity of the interval to the other extremity.

Now, because we are dealing with an extremity or limit, we are really dealing with a simultaneity and not an interval. This we may better imagine by following Leibniz' triangle demonstration [also see this entry on the limit.] We note that this extremity does not extend in space. Hence it is a simultaneity and not a duration. Therefore, physics does not deal with a time that is extensive, objective, and continuous. It only makes quantitative determinations about simultaneities.

So Bergson writes that time intervals, duration, and motion are all left-out-of the differential equation itself. [And we also learned in the previous entry how time is excluded from average velocity equations as well.] He argues that this is because duration and motion are not extensive objects. Rather, they are "mental syntheses." (120a) So a moving body will occupy many points along a line of motion. But, the motion itself is really the simultaneities of those place-occupations with other object placements and with instants of our consciousness. So motion itself has nothing to do with lines. (120b)

When an object is at one point, that is a distinct location from when it is at another point. So these points that the object takes-up along its motion are external to one another. Or, one object can take the exact same place as where another one was. So these places may also be identical to one another. This makes them like numbers, which are discrete units different from or identical with one another. Yet they are all relative to each other, because they all fall within a homogeneous space.

We also learned from Bergson that consciousness is made-up of moments of duration. Each one is qualitatively different. There is no extensive temporal-space between one mental state and another. So our states of consciousness do not fall along a line, [like Husserl's temporal consciousness.] Nonetheless, because there is no space between mental acts, they interpermeate. This makes them continuous. It is a strange sort of continuum, because it is not continuous like an extensive line is continuous. [We will see that Deleuze describes it as a "contraction." For Husserl, what makes the continuum of consciousness possible is that there is always some likeness from one moment to the next. But this implies a linear continuum, because it means there are never discrete parts. But for Bergson the duration of consciousness is continuous because every part is discrete and different. That absolute discretion causes there to be nothing between each one. And with nothing in-between each state, that makes them all contract together, or "interpermeate" as he says. This subtle distinction will prove to make all the difference for Deleuze's anti-Husserlean theory of phenomena.]

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Images from the pages summarized above, in the English Translation [click on the image for an enlargement]:

Images from the pages summarized above, in the original French [click on the image for an enlargement]:

Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

Available online at:

http://www.archive.org/details/timeandfreewill00pogsgoog

French text from:

Bergson, Henri. Essai sur les données immédiates de la conscience. Originally published Paris: Les Presses universitaires de France, 1888.

Available online at:

http://www.archive.org/details/essaisurlesdonn00berguoft

Video from:

Lewin, Walter. 8.01 Physics I: Classical Mechanics. Fall 1999. Video Lecture 2. MITOpenCourseWare. Creative Commons Licence.

Moving Secant Line animation from Kelly Liakos

available online at:

http://calculus7.com/id1.html