The cube appears in the depth-psychology corpus along two principal axes, each carrying considerable symbolic and epistemological weight. The first and most archaic axis is Platonic-cosmological: in the Timaeus, Plato assigns the cubic form to earth on account of its maximal stability, grounding a tradition in which the hexahedron signifies material fixity, ponderous impassivity, and the foundational stratum of elemental existence. Cornford’s commentary elaborates the constructive geometry behind this assignment — isosceles triangles generating square faces, the cube distinguished from the three remaining regular solids by its exclusive alliance with the terrestrial element — while also noting the ontological consequence that earth alone cannot be transformed into the other elements. The second axis is phenomenological: Merleau-Ponty returns repeatedly to the cube as a limit-case for theories of perception and embodied cognition. For him, the cube crystallises the inadequacy of both empiricist associationism and intellectualist formalism: neither the accumulation of perspectival appearances nor the discursive definition (six equal faces, twelve equal edges) exhausts or even initiates the perceptual act. Only the lived, motile body — taking up a position in space — renders ‘enclosed’ and ‘between’ intelligible. A minor but notable register appears in cognitive-neurological literature, where the Necker cube functions as a standard instrument for measuring directed attention. Across these registers the cube serves as a touchstone for some of the most fundamental tensions in the library: form versus matter, concept versus percept, definition versus experience.
The cube is the most stable of them because resting on a quadrangular plane surface, and composed of isosceles triangles. To the earth then, which is the most stable of bodies and the most easily modelled of them, may be assigned the form of a cube
Plato’s Timaeus establishes the definitive cosmological thesis: the cube is earth’s proper form by virtue of its structural stability and its composition from isosceles (half-square) triangles.
, Timaeus, -360thesis
One can bring together discursively the notion of the number six, the notion of ‘side’ and that of equality, and link them together in a formula which is the definition of the cube. But this definition rather puts a question to us than offers us something to conceive.
Merleau-Ponty uses the cube to demonstrate that conceptual definition is insufficient for genuine perception: the cube can be conceived only through the positional commitment of an embodied subject in space.
, Phenomenology of Perception, 1962thesis
It is, according to intellectualism, the thought of the cube as a solid made up of six equal faces and twelve equal lines at right angles to each other—and depth is nothing but the co-existence of the faces and the equal lines. But here again we are being given as a definition of depth what is no more than a consequence of it.
Merleau-Ponty argues that intellectualism’s reduction of the cube to a formal definition of depth inverts the explanatory order: depth is the condition of the cube’s co-existing faces, not derivable from them.
, Phenomenology of Perception, 1962thesis
To earth let us assign the cubical figure; for of the four kinds earth is the most immobile and the most plastic of bodies. The figure whose bases are the most stable must best answer that
Cornford’s commentary confirms and contextualises Plato’s assignment of the cube to earth, linking its six stable square bases to earth’s immobility and plasticity among the four primary bodies.
, Plato’s cosmology the Timaeus of Plato, 1997thesis
The second elementary triangle, the half-square, is now used to construct the square face of the cube. Here again Plato uses more elements than are necessary—four instead of two.
Cornford details the geometric construction of the cube’s square faces from half-square elementary triangles, noting Plato’s deliberate use of surplus elements as part of a broader theoretical strategy.
, Plato’s cosmology the Timaeus of Plato, 1997supporting
he could have built his pyramids, cubes, and the rest just as well. Moreover, if there were only one grade of solids, all the transformations described could occur between them.
Cornford explains why Plato builds multiple grades of regular solids — including cubes — arguing that this structural plurality enables the full range of elemental transformations described in the Timaeus.
, Plato’s cosmology the Timaeus of Plato, 1997supporting
Why are the half-square and the half-equilateral better than any possible alternatives? A third question, about which nothing is said here, is the size of the elementary triangles.
Cornford raises the foundational question of why Plato’s two elementary triangles — including the half-square used to construct the cube — are preferred over all geometric alternatives.
, Plato’s cosmology the Timaeus of Plato, 1997supporting
The resulting cubes will be much closer together in size than on the alternative plan.
Cornford’s reconstruction of Plato’s graded solid theory shows that the chosen method of building cubes from elementary triangles produces a more proportionate range of solid sizes than alternative constructions.
, Plato’s cosmology the Timaeus of Plato, 1997supporting
The square has the power of ‘swelling itself out’ (oYKoiia8a,) into the cube — the first body reached in the above progressions.
Cornford traces the Pythagorean arithmetical-geometrical lineage in which the square ‘swells’ into the cube, situating the solid within a generative numerical sequence foundational to Platonic cosmology.
, Plato’s cosmology the Timaeus of Plato, 1997supporting
Necker cube pattern control tests … Necker cube (Orbach et al.123)
In cognitive-attentional research, the Necker cube appears as a standard psychometric tool for assessing directed attention and concentration within the Attention Restoration Theory framework.
, The impacts of nature experience on human cognitive function and mental health, 2012aside
has learned to discriminate a cube from a sphere by touch, and is either given sight or, following Evans’s suggestion, is subject to direct cortical stimulation.
In the context of the Molyneux problem, Gallagher uses the cube-sphere discrimination as the standard haptic-to-visual transfer case for examining cross-modal perception and body-schema formation.
, How the Body Shapes the Mind, 2005aside