Present-day Dualities. In bilateral symmetry, how-
ever much it might deviate towards asymmetry, the
parts that are “symmetrically” opposed are expected
to be, at least in a recognizable approximation, equal
and conformable, by congruence or other modes of
equality. In a duality however—or in a polarity, which
is an intensified duality—the entities that are opposed
are expected to be different, and even contrary, by
contrast, or otherwise. Usually, a duality contraposes
two contrasting aspects of the same whole, and an
asymmetry contraposes two complementary parts of
a whole larger than either part. But this criterion is
sometimes not easy to apply, and, altogether, sym-
metries, asymmetries, and dualities overlap in impor-
tant ways.
Thus, Plato's dichotomy, which is meant to be a
logical procedure for arriving at a definition of any-
thing definable (Sophist 218D-231B) proceeds by
exhibiting a succession of dyads; and it cannot be
readily made out whether in Plato's construction the
two elements in a dyad are symmetric, asymmetric,
or dual. Leaping ahead from Plato's procedure by an
ingenuous dichotomy to a present-day procedure by
an intricate computer, in which so-called “informa-
tion” is coded, produced, and transmitted by a succes-
sion of dyadic yes-or-no signals, it is again not easy
to decide whether the two possibilities “yes” and “no”
are symmetric, asymmetric, or dual.
But there are significant contemporary cases in
which there are no such doubts. For instance, the
opposition between corpuscles and de Broglie waves
in particle physics is a pronounced duality, because
the selfsame particle is sometimes a corpuscle and
sometimes a wave, depending on the context. That is,
an elementary particle exhibits properties that can be
best explained by endowing the particle with features
of both a corpuscle and a wave. In an ontological
interpretation of the entire theory, corpuscle and wave
may perhaps be viewed as complementary parts of a
unit larger than either, but in the prevalent inter-
pretation in working physics they are different but
coextensive aspects of the same whole. Furthermore,
in its purely mathematical apparatus, this duality is
but an instance of an extremely comprehensive duality,
the only one of its kind, which is spread through all
parts of mathematical analysis, and in which the
two magnitudes which are contraposed are distinctly
heterogeneous.
Yet, there is another case from particle physics, a
baffling one, which again belongs to the doubtful cate-
gory, namely the opposition between matter and anti-
matter. The transformation which creates the opposi-
tion is “charge conjugation” that is the replacement
of electrons by positrons (=anti-electrons) and of
positrons by electrons throughout a physical system in
its entirety. It would be a case of symmetry rather than
of asymmetry, except for the fact that in our part of
the universe, at any rate, the anti-particles are much
less stable than the particles. Furthermore, the unstable
“free” positron becomes very stable when bound with
a neutron to form a proton. And the resulting pair
composed of electron and proton is in a sense only
a duality, because by its mass the proton is quite
unequal to the electron, being about 1835 times larger.
