⑦ Enduring Dreams

ZENO’S PARADOX: MOVEMENT AND THE NATURALIST VIEW

The fact of this articulation points to another source in natural language. Language, in particular written language, gives the impression of there being a continuity underlying discontinuous discrete states of things. The letters don’t make sense without it. Then where does this sense, the sense of continuous movement come from?

Sense has the continuous movement of making sense that time has too. It is there in what may be called natural time. This naturalist view is what Zeno set out to challenge and inasmuch as he gives the sense there is a paradox here he succeeded.

All is movement according to this naturalism. All however is not in movement, otherwise there would be nothing solid to grab hold of, but, whether the movement is of sense or of water or of the particles it carries along, for this view, for the temporal continuity supposed to underlie stable appearances, movement is prescriptive. It is the way time is pegged to movement that produces paradox.

The all, of all is movement, can be divided at any point. Zeno supposes the realisation of this potential. Being broken at every point it can be brings about either the cessation or the breaking down into parts and more parts of movement and from these parts the whole can no longer be accomplished.

Time however does not cease its achievement. It carries on regardless as if movement itself were separable from time. While for science time is a function of points articulated in space, for the naturalist view these points articulate time. Stillness rules time for the scientific view, leading to the immovable chronogeodeterminism of the block universe. Movement rules time for the naturalist view, leading to the paradox of the points along it being time’s stopping points.

Bergson’s answer to Zeno’s challenge is similar to his answer to science. He answers science’s division of time into simultaneities by saying that no such division can occur without a change in what is taking place in time, without qualitative change. He answers Zeno by saying that movement is not an accumulation of movements and so cannot be composed and decomposed as if it were.

The flow of his writing gives the same sense as he ascribes to a melody in music. Were it to pause and draw out any one note there would be a qualitative change. This is so for the movement of a written thought, for a melody and for the movement of physical bodies. Movement happens at a single stroke. It is indivisible according to Bergson.

Divided, its quality changes. Achilles need only walk to prove it. What Zeno shows in his paradox, since the change in the quality of Achilles’ steps, is a race between two tortoises.

Bergson’s answer to Zeno’s challenge to the view of time being articulated by movement and therefore composed of the series of points moved through is to point back to the time that movement takes, stating that time is neither an accumulation of nor decomposable into points or discrete states. To subtract one state that is moved through changes the nature of the whole movement. It is not with quantities of time that Bergson answers Zeno but with its quality, the overall step of Achilles being unequal in its quality for the time it takes to that of the tortoise.

Russell however does not accept the terms on which either Zeno’s challenge to the naturalist view of time or Bergson’s answer to that challenge rests. Between 1922 and Bergson forming his ideas around time and his answer to Zeno a new analogue for time has come into being. It is in Russell’s answer to Zeno, the cinematograph and cinematic time.