University of Virginia Library

II. PHYSICAL SCIENCE

The nineteenth century created the great doctrines
of molecular chemistry, thermodynamics, and statis-
tical mechanics, all of which take full cognizance of
the fact that physical matter consists of discrete parti-
cles. Yet, in an overall sense, “Physical Science” of the
nineteenth century gave decisive preference to “field”
theory over “particle” theory, that is to continuity over
discreteness.

Thus, in the beginning of the nineteenth century,
Thomas Young and A. Fresnel rendered a decision,
which was then long adhered to, that light is composed
of waves and not of corpuscles. Secondly, D. S. Poisson,
C. F. Gauss, and G. Green created field conceptions
of “potential,” with parallel mathematical properties,
for electrostatics, magnetostatics, and gravitation.
Thirdly, Maxwell's electrodynamics, as corroborated by
Heinrich Hertz, was a field theory, and it is frequently
viewed as the representative field theory of the cen-
tury. Fourthly, mathematical physicists from Cauchy
to Kirchhoff created and standardized the theory of
mechanics of continuous media, which assumes that
mechanical matter is distributed continuously, with a
finite density point-by-point. This mathematical as-
sumption runs counter to the indisputable hypothesis
of basic physics and chemistry that matter is atomistic,
or molecular; but, operationally, the theory of contin-
uous media has been overwhelmingly successful and
it is simply indispensable for many contexts. Finally,
in statistical phenomena and theories, nineteenth-
century physics was led to operate almost exclusively
with the Gaussian law of probability, and this law
represents continuous distribution par excellence.

Furthermore, within fluid mechanics, which is a part
of the theory of continuous media, Helmholtz created
a major theory of vortices. Lord Kelvin, his contem-
porary, was so impressed with it, that he hastily dashed
off a theory of “vortex-atoms,” in which individual
atoms, even in their singleness, were made into contin-
uously spread-out vortices à la Helmholtz. This attempt
of Kelvin was so ill-advised that present-day physics
has all but “suppressed” the memory of it (R. H. Silli-
man). Lastly, Helmholtz fully shared the general pre-
sumption that acoustics is a theory of waves, that is,
a field theory, although it was he who pioneered in
the discovery (for which he is justly famous), that,
physiologically, there are discrete “tone atoms,” that
is tones which the ear cannot “resolve” by physically
subdividing them.

Physics of the twentieth century changed all this.
It did not give up nineteenth-century insights but it
refocused them. All field-like constructs of the preced-
ing century were fully retained, and even enlarged and
added to; but they were all balanced or complemented
by the introduction of appropriate particle-like con-
structs of a dual kind. Thus, electric fields were bal-
anced by electrons, light waves by photons, sound
waves by phonons, and even gravitational fields were
balanced by would-be duals which are hopefully called
gravitons; conversely, and most importantly, all ele-
mentary particles of matter were balanced by undula-
tory counterparts, the so-called de Broglie waves. In
the final outcome, the nineteenth-century link between
physics and continuity was nowise weakened, but it
was balanced by an equally viable link between physics
and discreteness, and the whole structure of physics
has been brought to rest on a duality between the
continuous and the discrete. Except for sporadic and
disjointed anticipations in philosophy of science (M.
Jammer, p. 241), general philosophy of the late Victo-
rian and even Edwardian era was unprepared and ill-
equipped to cope with the novel postures in basic
physics, and only very slowly is general philosophy
accommodating itself to the stubborn fact that the
duality principle in physics is here to stay.

A peculiar adumbration of our present-day duality
between the continuous and the discrete may be dis-
cerned in the outlooks of the first atomists Leucippus
and Democritus (fifth century B.C.). They recognized
from the first that an atomic hypothesis does not only
assert that physical matter is “granulated,” that is, built
up of particles which in a suitable sense are indecom-
posable, but also that these particles “interact” with
each other across the “void” that separates them from
one another. They interact unceasingly, and for the
most part “invisibly.” It is the mode and manner of
these interactions which constitute the structure of
matter, mainly in its microscopic properties, but also
in its macroscopic attributes. Democritus saw this more
clearly than most participants in the seventeenth-
century “Revival of Atomism” (R. H. Kargon, 1966),
and even chemists of the nineteenth century may have
been lagging behind Democritus in this crucial insight.
Democritus may have also known, in thought patterns
of his, that even if an atomic theory intends to be
“philosophical” rather than “physical” (van Melsen),
it still has to establish its “legitimacy” by offering a
context of physical explanations of some degree of
novelty. Giordano Bruno, for instance, did not know
this at all. He offered various atomistic and monad-

ological statements, but they served no purpose in
physics (K. Lasswitz, I, 391-92).

Aristotle, who lived about a life span after Democ-
ritus, was much concerned with the first atomists and
their doctrine. He was opposed to atomism, but not
because it assumed that matter consists of minimal
constituents. In this assumption, Aristotle might have
acquiesced. He was a biologist, and a very great one
too, and as such he had it in his thinking that an organic
tissue (like flesh, skin, bone, etc.) consists of “minimal”
parts; just as in modern biology a tissue is composed
of cells, which are ultimate units of life. What Aristotle
could not accept for himself was the crucial assertion
of atomism that, ordinarily, any two atoms are sepa-
rated from each other by a spatial vacuity, which
surrounds each of the atoms and extends between any
two of them. Aristotle simply “abhorred” a vacuum,
any vacuum, and he could do so with metaphysical
justification. Firstly, even in present-day biology, cells
are adjoined wall to wall, without biological interstices;
and secondly, in physics proper, Aristotle was a
thermodynamicist, and it is a fact of present-day phys-
ics, which Aristotle anticipated, that in a purely
thermodynamical system an absolute vacuum is not
allowed for. It is true that since the nineteenth century
this kind of thermodynamics has been deemed com-
patible with an atomic, or rather molecular structure
of the substances which compose the system (Bochner,
p. 160). However, this reconciliation of apparent op-
posites has been brought about by statistical mechanics;
but the basic attitudes of this doctrine were far beyond
the reach of Aristotle, and of antiquity in general.

In spite of his opposition to atomism, Aristotle had
a masterful grasp of the achievements of the Atomists,
as evidenced, for instance, by the following passage.

(Meta-
physica, 985b 4-10; trans. Kirk and Raven, pp. 406-07).

This remarkable statement could serve as a motto
for the polarity between particle and field and even
for the de Broglie duality between corpuscle and wave.
It is notable that Aristotle even “apologizes” for the
Atomists for expressing the polarity between full and
void in the quaint, and possibly misleading Parmenid-
ean contrast between “Being” and “Non-Being,” and
Aristotle is reassuring the reader that the “Non” in
“Non-Being” is only a façon de parler without any
negative intent or force. And Aristotle's casual obser
vation that “the two together are the material causes
of existing things” is an oracle for the ages, for our
age of physics, at any rate.