Eye and the visible line

Use in the book

The first demonstration requires the reader to move an eye. Looking down at a penny permits a circular appearance; bringing the eye exactly to table level produces a line. Nothing has happened to the object, but its appearance has changed with the observer's position. The lesson trains readers to distinguish a limitation of access from a deficiency in the thing observed. The coin is not becoming a line in itself.

Flatland's inhabitants cannot repeat the movement which gives the Spaceland reader this advantage. Their perceptual restriction is therefore a condition of existence rather than an error a little greater attentiveness can cure. The narrator's later expertise in interpreting brightness works within that condition. It does not amount to seeing from above. This difference between inference and direct disclosure remains essential to the romance's experiments with other dimensions.

The body also makes looking a social act. A Woman's eye and mouth occupy the same end; presented frontally, she becomes a bright point, while the less luminous rear can be almost invisible. Domestic custom requires women of rank to keep the bright, speaking end towards husbands and their male friends. The same orientation that secures men's safety also subjects them to continuous speech and observation, provoking the narrator's complaint. The attempt to control one danger creates a different intimacy he cannot wholly master.

The position of the eye can likewise explain a lower-class triangle's inability to monitor its own dangerous vertex. Here the narrative turns a bodily limitation into evidence of coarseness, although it has already required readers to understand their own seeing as position-dependent. The implicit comparison is pointed: a sympathetic account of perception for “us” becomes a judgement of nature when applied to “them.”

The Preface23 complicates visibility further by discussing unrecognised thickness and the tendency to name it brightness. It does not supply a complete anatomy of the organ. The important issue is conceptual: evidence can be present without an observer possessing the category needed to interpret it. The eye supplies evidence; an interpretation makes that evidence a world.

Places to read

1. §12“gradually lower your eye”
2. §12“nothing but a straight line”
3. §423“these two organs are identical”
4. §523“the eye is situated so far from their vertex”
5. §6234“by the visual organ”

In this edition

Notes 22, 25 and 6723 explain the plane, the coin experiment and the geometry of sight recognition. The Preface23's thickness argument is Abbott's second-edition material; the Diotimos discussion at notes 9–12234 is modern apparatus. The distinction between perceptual evidence and dimensional interpretation belongs to the fiction’s argument.

Cognizance

Awareness or perceptual notice. Because the low Isosceles eye lies far from his sharp vertex, he may scarcely take cognizance of contact there, making bodily arrangement part of the narrator’s explanation of recognition accidents. Printed form: cognizance (§ 523). See Eye and the visible line.

Luminous

Giving out light, as the edges of Flatland’s inhabitants do. Their visibility is built into their bodies rather than supplied by a sun; differences of brightness will therefore carry information about living bodies and their positions. Printed form: luminous (§ 12). See Eye and the visible line.

Sub-lustrous

Only faintly luminous. A Woman’s rear end is sub-lustrous enough to approach the dimness of an inanimate object, a physical condition that permits near-invisibility and supplies the professed rationale for intrusive safety regulations. Printed form: sub-lustrous (§ 423). See Eye and the visible line.