7. Chora and Topos. In Plato's creation myth in the
Timaeus space-in-the-making, that is, space in its
cosmogonic nascency and formation, is called chora
(χω̃ρα), but after its creation has been completed it
is called topos. In general usage, chora and topos have
approximately the same range of meanings, but chora
is used more loosely and informally, and it is less
specific than topos. “A locus in mathematics, that is,
a figure which is determined by, or results from, specific
requirements, became topos, not chora. In the Meteor-
ologica, when Aristotle wishes to single out a geo-
graphic district in a country, chora usually stands for
country and topos for district” (Bochner [1966], p. 152).
In De caelo Aristotle adheres to Plato's distinction,
but since his account is less cosmogonic than Plato's
the occurrence of topos prevails. However, going be-
yond Plato, markedly so, Aristotle also uses the name
of topos for an entirely different space, namely for the
space of physics proper, that is, for the operational
space of “laboratory physics” of today. Nowadays it
is imperative that this space be kept distinct from the
space of cosmology, and Aristotle confused the two but
little (Bochner [1966], pp. 154-55).
Aristotle presents his “laboratory space” in the spe-
cial essay on topos in Physica 4, 1-5. His leading asser-
tion is that in a scientific study of a physical system,
space is not given as the spread across the system, as
the naive view has it, but is given by the total structural
behavior as determined by the boundary configuration
of the system; and Aristotle's first succinct definition
is: “topos is the inner boundary of what contains”
(ibid.). When attempting to elaborate this first defini-
tion into a detailed description, Aristotle encounters
complications which are intrinsic to the subject matter,
and he arrives at alternate descriptions which are
seemingly not quite consistent with each other. How-
ever, on closer analysis these inconsistencies can be
reconciled (Bochner [1966], pp. 172-75).
Furthermore, it is important to realize that in
present-day physics the conception of space is prag-
matically used in alternate versions which are not
identical and that no serious harm arises. Thus, (i) in
engineering mechanics as taught in engineering schools
all over the world, and in large parts of so-called
“classical” mechanics and physics, space continues to
be Newtonian, that is Euclidean, as in Newton's
Principia (i.e.,
Philosophiae naturalis principia mathe-
matica, London, 1687). But, (ii) the theory of single
electrons or other elementary particles—that is, the
so-called quantum field theory—operates in the space-
time of the
special theory of relativity which is differ-
ent from the space-time of Newton's mechanics. How-
ever, (iii) in the physics of our galaxy at large (the
so-called Milky Way) and beyond, space is subject to
the
general theory of relativity; and most “models” of
the universe presently under examination are different
from the two preceding ones. Finally, (iv) the “statis-
tical” space of quantum mechanics may be viewed as
being different from, and thus inconsistent with any
“non-statistical” space, Newtonian or relativistic
(Bochner [1966], p. 155).
Of course, in physics of today there is, as has always
been, a great quest for consistency, unity, and harmony.
But, in any one science, the volume of knowledge is
growing so fast and in so many subdivisions of the
science, and explanation is so far behind experi-
mentation that a detailed internal harmonization is not
attainable. In particular, the concept of space is so
ubiquitous, and is reached by so many avenues and
channels, that it would be stifling and sterile to force
upon it metaphysically a single logical schema, which,
even if acceptable today, might become unsuitable
tomorrow.
