Isosceles

Use in the book

The category is introduced through exact-looking dimensions, but the description immediately becomes evaluative. A small base belongs to a “degraded type,” and the sharpest bodies approach the appearance of Women. Geometry establishes a continuum of shapes; the narrator turns the continuum into a descent towards reduced humanity. The technical name helps this judgement pass as classification rather than hostility.

The Isosceles also exposes an inconsistency in the account of natural equality. In §323, inequality of all three sides is a reason to doubt whether the worker deserves to be called a human Figure. In §723, having two equal sides satisfies the class-specific standard of regularity. The standard is therefore not a single geometrical requirement applied impartially. It varies to preserve the recognised categories, while the language of universal nature disguises that variation.

The sharp body contains a political dilemma for the rulers. Soldiers can penetrate and destroy the blunter figures who govern them. The supposed law of compensation resolves this dilemma by making increased intelligence widen the angle and reduce its offensive power. The Isosceles may become cleverer only by becoming less dangerous. Where this natural management fails, the state recruits some members, purchases the allegiance of leaders and sets the rest against one another.

The gap between the lowest and near-equilateral members is enormous. Some possess an angle of half a degree and become disposable school apparatus; the Square's ancestor has nearly reached sixty degrees and a recognised claim to respectability. A single class-name collapses these differences when convenient, then subdivides them when labour, warfare, discipline or instruction requires it. Classification serves administration as much as description.

Kinship unsettles the narrator's distance from the group. His grandfather belonged to it, and the story of earlier family misfortune invites sympathy for a worker caught in an accident. He can recognise a full human history within his own ancestry while dismissing the class collectively. The inconsistency makes Isosceles a key term for reading how prejudice survives knowledge rather than merely resulting from its absence.

Places to read

1. §323“Triangles with two equal sides”
2. §323“they can hardly be distinguished from Straight Lines or Women”
3. §323“the wretched rabble of the Isosceles”
4. §523“one of the least irregular of his unhappy Isosceles class”
5. §523“half a degree, or thirty minutes”
6. §723“an Artisan or Soldier must have two of his sides equal”

In this edition

Note 35 supplies the Greek derivation; notes 34 and 602 check the narrow-angle geometry. Note 75 explicitly identifies the shifting meaning of regularity. These explanations help separate a mathematical triangle from the particular body-type and social category for which Abbott uses its name.