Recognition by sight

Use in the book

The technique initially seems to contradict §12, where every figure appears as a straight line. Section 6234 resolves most of the difficulty by distinguishing outline from variations within it. Fog makes more distant portions dimmer. When the observer faces a vertex symmetrically, the rates at which its two sides fade disclose how sharply they recede. A Triangle and a Pentagon can therefore be distinguished without either becoming visible from above.

The explanation is a lesson in mediated knowledge. Observers do not need direct access to a complete object in order to reason reliably about it. They do, however, require conditions, practice and assumptions. Regularity allows one angle to stand for the rest; a suitable orientation makes the elementary construction possible; experience handles cases where neither object nor observer stays still. The method is powerful because these conditions can often be met, not because sight has become omniscient.

Social life makes the skill harder and more consequential than the diagram. A crowd contains figures rotating, advancing and retreating together. The observer must calculate while also avoiding collisions and showing due deference. Etiquette forbids the Square to touch his betters, so the easier method cannot settle his uncertainty. Those betters possess a practical understanding of his movements that he cannot reciprocate. The art distributes safety and embarrassment unequally.

Training then turns this inequality into apparent character. Wealthy children take years to acquire the privileged faculty; poor children cannot defer useful work for so long. When the trained noble later surpasses the precocious tradesman, the narrator describes a nearly regenerative transformation. The educational investment recedes behind the spectacle of superiority it has produced.

There is a further limitation in the very aim of recognition. Identifying a person's number of sides tells the observer how to behave towards his rank. It does not disclose intentions, generosity or truthfulness. The society continually treats success in the first kind of reading as authority in the second. Abbott's lucid optical account makes it possible to admire the faculty while questioning the excessive social and moral claims attached to it.

Places to read

1. §6234“recognize one another by the sense of sight”
2. §6234“infer with great exactness the configuration of the object observed”
3. §6234“my view will lie as it were evenly between his two sides”
4. §6234“after a very long training supplemented by constant experience”
5. §6234“know all about your movements”
6. §6234“an unattainable luxury”

In this edition

Note 64 records a genuine fault in the narrator's retrospective quotation: §523 does not state the earlier qualification exactly as §6234 claims. Note 67 explains the bisected-angle diagram. It is important to preserve both observations: a sound illustrative construction does not make the surrounding narrator infallible.

Conversazione

An evening social gathering devoted to conversation, often with intellectual or artistic associations. In Flatland its moving company of distinguished Polygons becomes a demanding practical examination in reading rank from shifting patches of brightness. Printed form: conversazione (§ 6234). See Recognition by sight.

Foreland

A headland or projecting stretch of coast. In the comparison with a sailor’s distant view, such projections disappear into a single apparent line: the example explains how a visible outline can conceal the shape that produces it. Printed form: forelands (§ 12). See Recognition by sight.

Kinetic

Concerned with motion. Wentbridge’s Kinetic Geometry addresses the changing appearances of figures that move and rotate, giving an imposing academic title to the practical art of navigating elite company. Printed form: Kinetic (§ 6234). See Recognition by sight.

Pasteboard

Stiff card made from layers of paper, proposed as material for the reader’s model figures. The familiar schoolroom material turns an abstract claim about vision into an experiment: lower the eye to the table and the model’s distinct outline becomes a line. Printed form: pasteboard (§ 12). See Recognition by sight.

Retirement

Recesses or parts that draw back, here indentations of a coastline rather than withdrawal from employment. Contrasted with projections, the word names relief that ordinary light and shadow may reveal but Flatland’s uniformly luminous world cannot display. Printed form: retirements (§ 12). See Recognition by sight.

Sagacity

Practical shrewdness and sound judgment. Even the sagacity of an educated Square is taxed by a crowd, a difficulty the narrator enlarges into an argument that bodies outside predictable forms would destroy social order. Printed form: sagacity (§ 723). See Recognition by sight.

Static

Concerned with figures at rest, as one branch of the Geometry taught at Wentbridge. Paired with Kinetic, it makes the academic distinction directly relevant to the everyday challenge of recognising stationary or moving people. Printed form: Static (§ 6234). See Recognition by sight.

Perfect propriety in Polygonal society (contextual phrase)

“to comport oneself with perfect propriety in Polygonal society” (§ 6234)

The alliterative phrase joins respectable conduct to a particular bodily and social class. Comport oneself means behave or carry oneself; propriety requires knowing how to move among high-ranking figures without collisions or unwelcome requests to touch them. The Square concludes that one should ideally be a Polygon oneself. This is more than a joke about snobbery: prolonged schooling and habitual practice give the rich an informational advantage over a visitor who cannot interpret their changing outlines. The apparently effortless grace of superior breeding has expensive conditions. The narrator’s own difficulty is useful evidence, since he possesses education and respectability yet still feels outmatched. Membership in the fashionable circle depends on embodied training that formal knowledge alone cannot supply. See Recognition by sight, Polygon, and Education and schools.