”Take an ordinary sheet of Russian paper with four corners. In the majority of cases you then squeeze on to it, ignoring the edges… a bored caryatid, a conceited Corinthian capital or a plaster…The Japanese do it the other way round. You have a branch of a cherry tree or a landscape from this whole the pupil cuts out compositional units: a square, a circle, a rectangle” (Eisenstein, p.146).
Eisenstein’s analogy of constructing a framed composition onto an orthogonal planar surface characterizes a common approach to design. We situate our buildings on planar surfaces cropped from the earth’s spherical geometry.
The human scale is unable to expose the earth’s curvature because the earth is approximately a sphere and a sphere is a Manifold.
Manifold: A topological space that locally resembles Euclidean space near each point. Examples: Sphere, Torus etc.
Manifold: many and of several different types.
The diagrams below show a remapping of the Steles from the four-corner site to the surfaces of two different manifolds. This is synonymous with substituting the circular thumbnails (figure 24.4) for the rectangular thumbnails (figure 24.3). As opposed to the site in Berlin, the surfaces of the sphere and the torus have no definite linear boundaries.
“Beyond the Shot.” Sergei Eisenstein, 1929. https://doi.org/10.5040/9780755699759.ch-024.
A field of Steles on a Sphere 
A field of Steles on a Torus
Shot Montage Rhythm: Spatial City
Shot: a structure
Montage: collection of structures of different sizes and shapes
Rhythm: the space frame which holds the structures; ensures occasional coincidence where necessary
The Spatial City
