Previously Bergson explained what really scientists do when they measure velocities. They are not calculating the continuous correspondence between time and distance changes. For, time is not a continuum. Rather, we have discrete states of consciousness, and motion occurs in discrete units. So both Achilles and the tortoise take the same number of "steps" or actions. Achilles' steps are longer than the Tortoise's. So Achilles overtakes his opponent.
We also learned that there is nothing homogeneous in duration or motion. Whenever we conceive of duration or motion as being homogeneous, we are really translating them into space. For this reason, we now learn, science must eliminate the "essential and qualitative element" of time and motion before it may deal with them. Bergson finds this evident in astronomy and mechanics.
If the sciences were to define duration itself, then they might become mired in metaphysical technicalities with no methodological value. So mechanics for instance does not define duration itself. Rather it gives the conditions for the equality of two durations, and they base it on identical motions. We will see how this strips movement of any duration.
So we consider two objects with identical physical properties. They begin under the same physical conditions. And they are moved by the same physical causes. We see already that we should expect that it will take the same amount of time for either to go a certain distance. So their durations are equal if their distances-traveled are equal.
Now, in order to complete this observations, we need to:
a) note the exact moment when the motion begins. This is an external change. And it coincides with one of our internal psychic states. So it is a simultaneity of a discrete internal state with an external change. Then we need to
b) note the moment that the motion ends. This is a simultaneity of the same sort. Lastly, we need to
c) measure the distance the body traveled. Of all the above observations, this is the only one that may involve real (extensive) measurements.
These conditions only deal with space and simulteneities. So duration never factors-in. We only are saying that at the end of time t, there is a series of simultaneities leading up to it. [Consider how Walter Lewin of MIT describes the time-points that we observe:]
So between now and then, the object moves. Along its course, we pinpoint places where we note the simultaneity between our consciousness states and the object's location. But the phrase "between now and then" cannot refer to some real temporal extension that spans continuously between the time points. For, the interval of duration we experience in the mean times only exists for us on account of the interpenetration of our conscious states. Outside us, there is only space, and not time. Hence in the exterior world, there is nothing but simultaneities. Their successive nature is possible only by means of our mind comparing the present with the past. But because this is a subjective procedure, we cannot say that the succession of simultaneities in the world around us is objectively successive.
To further impress this point, Bergson will now have us consider the rate that the simultaneities succeed each other. We first have to build from what he previously proved about time. Time is made up of discrete units. These are the simultaneities we are here dealing with.
So let's consider an object that moves from one place to another. And perhaps it does so through 10 simultaneities. If objectively these simultaneities succeeded each other at a faster rate, the object would still need to move through 10 simultaneities. In this case we would experience the succession differently, so its duration would be qualitatively different. But, there is no extension of time that contains these simultaneities. So we cannot say that their succession is objectively faster.
We will later see how astronomers contract very distant simultaneities. For example, one astronomer could predict eclipses that will occur throughout the next centuries. In this way, he determines a succession of simultaneities that will involve many generations of minds who experience the durations between them. But because there is not objective time between these simultaneities, the astronomer may in just a matter of seconds run through them all in his mind when making his predictions.
[Directory of other entries in this series.]
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.
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