### Zeno & quarks: the Parable of the Racecourse

Zeno of
Elea was a Greek philosopher and metaphysician who studied under
Parmenides in the Fifth Century before Christ. Zeno postulated
arguments that attempted to defend Parmenides’ theory that all
Being is One, an idea known as “monism.” One of the attributes
of the monists’ theory is that since all Being is One, there can be
no motion within that which exists. Among his most famous arguments
to prove this concept is the parable of the racecourse. In this
parable, Zeno asks his listener to consider a runner in a racecourse.
In order to finish the race, the runner must travel the distance,

*D*, from the starting line to the finish line. Zeno states that in order to traverse*D*, however, the runner must traverse half the full distance,*A*(where*A = D/2*). The distance to this midpoint*A*also has a midpoint,*B*, which must be traversed before*A*can be reached. This second midpoint*B*has a further midpoint,*C*, and so on in an infinite halving of the distance that must be traversed. Zeno argues that the distance from the starting point to the finish line is described by an infinitely multiplying set of midpoints. Thus, the distance from the starting line to the finish line is an infinite distance. Since the runner must traverse the distance from the starting point to the finish line in a finite amount of time, it is impossible for the runner to actually traverse the distance; the runner is, therefore, immobile and unmoving. According to Zeno, this proves that motion is impossible, because every distance can be described with the racecourse as an infinite distance.
The
logic behind Zeno’s parable of the racecourse appears to be sound,
in that it contains no fallacies or syllogisms. The logic does
contain assumptions that are critical to its being able to prove the
hypothesis for which Zeno posits the parable in the first place. The
key assumptions are (1) that it is impossible for the runner to cover
an infinite amount of distance in a finite amount of time and (2)
that the distance the runner must cover is an infinite distance. The
argument also seems to rely upon the assumption that an infinite
regression of midpoints actually multiplies the distance over which
the runner must conduct his course in order to meet the finishing
line. For all the impressiveness of Zeno’s logic, it appears that
even granting his premise that the midpoints do infinitely regress,
the distance the runner must travel does not actually increase.
Instead, what is multiplying in an infinite manner is the measurement
of what point in space the midpoint exists.

In order
for the runner to not reach the finish line, he must be committed to
reaching the midpoint as Zeno describes it. Zeno’s logic does not
address, however, whether the whole of the distance itself is a
half-distance. What if

*D*is really the midpoint of some other distance,*Y*, where*D = Y/2*? It could also be that*D*is a further division of the midpoint of an even greater distance,*Z*, where*D = Z/16*.*Of course, the theory of infinite regression that Zeno relies upon to make the distance an infinite distance would insist upon determining upon a midpoint,**D/2*, which would then lead into the problem posited by the original parable. This difficulty could be overcome, however, if one could conceive that there existed a fundamental unit of measuring distance or some fundamental building block of matter of which there could be no further division. As an example, suppose that a quark, which is the particle that makes up protons, neutrons, and electrons, truly is, as contemporary physics suggests, the smallest particle in matter and existence. As such, it could not be halved and maintain its state as matter; it would dissipate into energy and cease to exist if halving were attempted. If this is true, it could be argued that the length of a quark is the fundamental distance of the universe, and that in order to traverse any distance, one must cover the distance as measured by quark-lengths. In other words, contrary to Zeno’s theory, the distance from the starting line to the finish line would not be an infinite value as determined by a regression of halving, but rather some finite distance described by quark-lengths from the starting line to the finish line.
If the
distance from the starting line to the finish line can be described
in finite measurement, as has just been suggested, then one of the
fundamental assumptions behind Zeno’s parable—that an infinite
regression of halves defines the distance—is defeated, and the
logic underlying the parable collapses. Instead of the runner being
unable to cover the so-called infinite distance in the finite amount
of time available, there is rather a finite distance that can be
covered in a finite period of time. This solution to the question of
how the runner can complete the racecourse has the added virtue of
also describing the observable fact that if Zeno had gone to a
racecourse in Elea, he would have seen many runners completing the
racecourse instead of standing immobile in the Oneness of Being.
While the theoretical logic behind Zeno’s parable is both alluring
and simple, its very simplicity suggests its weakness: it is too
simple to describe demonstrated reality.

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