what Aristophanes had called “deep Dark’s bottomless wombs”—the womb of Tiamat’s generativity as well as the womb of chōra’s agitated motion—come to yield order, a distinctively mathematical order at that.
If creation is to work, it must bring together—must literally articulate—the most advanced state achievable by the Receptacle “even before the Heaven came into being” (52d) with the most elementary form of mathematical ordering. As Cornford comments, “from the abyss of bodily ‘powers’ in complete abstraction from the works of Reason, we now ascend to the lowest level at which the element of order and design contributed by the Demiurge can be discerned in the turbulent welter of fire, air, water, and earth.”74 To depict this situation graphically, we can imagine two triangles touching at their respective tips. The bottom triangle (“N” for Necessity) represents the “abyss” and “turbulent welter” of the Receptacle—recalling the abyss of Apsu and the tumult of Tiamat—and the upper triangle (“R” for Reason) the “order and design” of mathematical rationality.
The point of overlap (“d”)—that is, where the two factors of Necessity and Reason touch at their tips—is “depth” (bathos), which Merleau-Ponty has termed “the dimension of dimensions.”75 For depth is a dimension of every spatial span and spread, no matter how such a stretch may be determined or measured. It is even an important dimension of motion, including that primal motion by which, in the Receptacle, like seeks like and unlike drifts away from unlike.
Depth is also a feature of every surface, and it is by virtue of depth-of-surface, even more than by depth-of-motion, that the fateful step is taken from the realm of sheer sensible qualities (the proper constituents of the Receptacle) to the material bodies whose stereometric shapes are supplied by the Demiurge in his first and most definitive world-creative act. Depth is at once the mediatrix between sensible quality and body and that which enables the application of geometry to material body itself.
In the first place, then, it is of course obvious to anyone that fire, earth, water, and air are bodies; and all body has depth. Depth, moreover, must be bounded by surface; and every surface that is rectilinear is composed of triangles.76
It is from the combination of two such triangles—the right-angled isosceles and the half-equilateral—that all four of the solid geometrical figures of the primary bodies are constructed. For the pyramid (fire), octahedron (air), icosahedron (water), and cube (earth) are each three-dimensional figures whose surfaces are constituted from these triangles (the surfaces of a cube from the isosceles; those of the other figures from the half-equilateral). What matters in such applied mathematics is less its intrinsic plausibility—for which a convincing case can in fact be made77—than its earnest effort to mathematize what in the original state of the Receptacle remains rudely rough in character. It is this effort that is the proper work (ergon), the sole creative task, of the Demiurge (construed literally as a “working for the people”).78 It is the mathematizing of the Receptacle that counts, for here alone Reason is able to win over Necessity to its own aims.79
V
We witness in Plato’s “likely story” a general movement from a space that is radically heterogeneous to a space that is on its way to becoming homogeneous. In Eliade’s terms, this is a movement from a “sacred space” of discontinuity and difference (e.g., between a temple and the profane space outside it) to a “secular space” of homogenized and all-too-predictable equiformity.80 On Heidegger’s assessment, it is an adumbration of a distinctly modern conception of space.81 In the language of the Timaeus itself, it is a movement from the erratic (and rectilinear) motions of sensible qualities to the regular (and circular) trajectories of geometrized physical bodies that imitate the motions of the heavenly bodies. But likely or not, prophetic or not, where does this story leave us with regard to the question of place? What does the Timaean cosmogenesis have to say about topogenesis?
What it has to say is that place itself—topos—is a derivative and comparatively late moment in a sequence of three stages whose first two moments are concerned with chōra.
Space: a matrix for particular places that is ingredient in and coextensive with the Receptacle as a whole; to be placed herein is to be placed in Space (chōra), that is, to be placed somewhere (but at no specific place or region) in the Receptacle regarded as a massive spatial sphere, beyond which there is Nothing, not even the Void. Thus Space “signifies total implacement”82—but only in the most nascent state.
Primal Regions: areas within the Receptacle constituted by the changing clusterings of like sensible qualities—areas that never attain strict homogeneity; were they to do so, motion would cease: “Motion will never exist in a state of homogeneity” (57e); such stasis is in any case precluded by the continual transformation of one primary body into another.83
Particular Places within Primal Regions: the discrete topoi that fully formed sensible bodies occupy. Each such place is thus a locus within a primal region composed of similar bodies; the locus itself is not stationary but is in effect the traced trajectory of the movement of these bodies as they change place from moment to moment.
The Timaean tale is thus a story of increasing implacement. The first two stages both preexist and succeed the intervention of the Demiurge: choric spatiality and regionality remain throughout. The last stage is not so much created by the craftsman-god as fashioned by him out of the material supplied by the first two. For the shape-bestowing geometrism of the Demiurge affects only the form of sensible bodies—not their quality, power, depth, matter, or motion. In endowing these bodies with stereometric form, the Demiurge is more of a micro-manager than a creator-god. His efforts are restricted to forming the exact fit required by any particular topos, since the shape and size of a material body situated in a given place cannot be incompatible with the surfaces of surrounding bodies. The Demiurgic action is mainly a matter of the configuration and covariation of an already (and always) existing choric Necessity.
The pertinacity of chōra illustrates a quite general point. In the Timaeus we find—in keeping with a classical Greek concern for maintaining well-ordered equilibria, usually in the form of means between extremes—a delicate but firm balance between such polar terms as Reason and Necessity, homogeneity and heterogeneity, the disorderly and the mathematized. This balance is most saliently seen in the complementarity that exists between the irregularity of aberrant bodily motions before the Demiurge intervenes and the regularity of geometric shapes grafted onto the erratically moving bodies. As Albert Rivaud remarks,
The theory of elementary figures is destined to explain how order is introduced into the moving chaos of qualities. By their definite and invariable properties, these figures infuse a certain fixity into Becoming. But they do not form its substance, which remains constituted by changing qualities.84
It is not so much that the initially wild motions are “subordinated”85 by the Demiurge—such a term would be more suitable in describing the martial confrontation between Marduk and Tiamat—as that errancy and regularity cooperate in the constitution of a world that is a conjoint product, a literal bi-product, of their disparate tendencies. For this reason, it is difficult to say whether the Demiurge imposes order on the Receptacle or draws out what is already immanent in its pregiven necessities. Perhaps, as Alfred North Whitehead suggests, both claims are true.
Plato in the Timaeus affords an early instance of wavering between the two doctrines of Law, [i.e. between] Immanence and Imposition. In the first place, Plato’s cosmology includes an ultimate creator, shadowy and undefined, imposing his design upon the Universe. [But] secondly, the action and reaction of the internal constituents is—for Plato—the self-sufficient explanation of the flux
