Cube

Use in the book

The report says that earth comes from the cube and assigns other regular solids to the other elements. The statement concerns a proposed geometrical constitution, not an observation that every lump of earth visibly has a cubic outline. Its role should be read with the rest of the scheme.

Places to read

1. I.21.6c.2Earth is associated with the cube among the five solids.

Translation in this edition

“Cube” is direct; avoid replacing the figure with the broader word “solid,” which would erase the classification.

Use in the book

Before the name is learned, the grandson anticipates a Something else that a moving Square might produce. The Sphere subsequently names it through a comically prolonged compound, whose cumbersome form enacts the difficulty of attaching a familiar noun to an unfamiliar conception. A count of eight terminal points and six sides does not make it imaginable to the Square. The word arrives before the knowledge it is supposed to convey.

Actual acquaintance occurs in §192345. The Sphere stacks square cards, then supplies the practical instruction that the first lesson lacked. The Square initially sees an irregular plane figure and associates its outline with criminality. His mistake is neither pure stupidity nor a mathematical error: he lacks the learned interpretation of light, shade and perspective required to recognize depth. The reassuringly regular Cube looks socially disreputable when read through Flatland's classificatory habits.

Touch is decisive. Feeling verifies that the object is a Solid, after which changing the positions of objects and lights teaches the pupil to recognize it visually. A sense associated in Part I with women and lower-status figures becomes indispensable to the accomplished male geometer. The Cube is therefore an experiment in retraining perception, not simply an emblem whose meaning can be delivered in a sentence.

Its construction also excites a genealogical pleasure. The Square imagines himself as the progenitor of a being far more illustrious than himself because his motion could generate it. The analogy both resembles and exceeds Flatland's social inheritance, in which a son gains a side. Here generation adds a dimension. That imaginative pleasure soon prompts the more dangerous question of what a Cube might itself produce.

After the return, the Cube becomes the measure of memory's failure. About eleven months later the narrator cannot call it up with his eye closed. Later success never entirely restores his confidence that his mental picture matches the original. At the trial he cannot provide a diagram or description satisfactory to the President. In prison he still names it precisely while doubting his grasp of its shape. The familiar object of the reader's world thus becomes the romance's most painful example of knowledge that cannot be securely kept or transmitted.

Places to read

1. §152“Something else” — The child predicts an unnamed spatial result
2. §192345“a multitude of Squares parallel to one another” — The Cube is constructed by stacking
3. §192345“as you shall learn by the sense of Feeling” — Touch corrects a misleading appearance
4. §2223“I tried to see a Cube with my eye closed, but failed” — Recollection breaks down
5. §2223“the once-seen, oft-regretted Cube” — An ordinary solid becomes the object of loss

In this edition

The note to §192345 distinguishes the six square faces from the eight solid angles, and explains why a perspective image could look like an Irregular to the visitor. Its account of the diagram complements the narrative without making the Square's recovered mental image more certain than he says it is.

Cube

A three-dimensional solid with six square faces and eight corners. The narrator encounters it by construction, touch and trained sight, then gradually loses confidence in his ability to recall its exact shape. Printed form: Cube (§ 192345). See Cube.

Environed

Surrounded or bounded. The theoretical figure environed with six Squares is a cautiously described Cube in the narrator's attempted treatise. Printed form: environed (§ 2223). See Cube.

Perspective

The visual relations through which depth and spatial position are inferred. The newly arrived Square must learn it, along with light and shade, before he can recognize Solids reliably. Printed form: perspective (§ 192345). See Cube.

Progenitor

An ancestor or originating parent. The Square imagines himself progenitor of a Cube because a Square's movement through a new direction can generate it. Printed form: Progenitor (§ 192345). See Cube.

Solid angles

The corners where the Cube's faces meet. There are eight; they are not the six plane faces that bound the body. Printed form: solid angles (§ 192345). See Cube.

The Progenitor of so illustrious an offspring (contextual phrase)

§192345. “the Progenitor of so illustrious an offspring”

The Square's pleasure at encountering the Cube borrows the language of family advancement. His own movement through a new direction could generate this more complex being; he therefore imagines himself as an ancestor who might be proud of a superior descendant. The analogy resonates with Flatland's hereditary increase in sides, but the geometrical operation is different: it adds a dimension, not merely a side. This distinction matters to the next turn. If a Square can generate a Cube, the pupil asks, why should a Cube not generate a further figure? A flattering account of his place in the new order becomes a means of refusing that order's finality.

See also. Cube · Analogy