Angle

Use in the book

The work transmitted under Archytas’s name lists rule, plumb line, and right angle as measures of uprightness and straightness. It then compares such standards with perception and intellect as measures of their objects. Geometry supplies an analogy for discrimination, not a claim that thinking literally uses a carpenter’s tool.

Places to read

1. I.48.6.1The right angle participates in an analogy between measuring instruments and cognition.

Translation in this edition

“Right angle” should preserve orthos as well as the headword; “angle” alone would weaken the measuring example.

Use in the book

The opening taxonomy makes a reader learn two scales together. The Isosceles soldier's narrow angle makes him dangerous, whereas a many-sided nobleman's broad angles advertise refinement. These are not independent attributes accidentally bundled together. The narrator presents their connection as an arrangement that prevents intelligent popular leaders from possessing the physical power necessary to overthrow their rulers. The measured angle becomes a political explanation pretending to be an innocent description of anatomy.

The consequences reach into language. In §523, the near-equilateral ancestor has an “angle or brain” of 59° 30′. The conjunction makes measurement and mentality interchangeable without argument. A degree and a half lost after his disastrous collision can describe bodily inheritance, diminished family honour and the consequences of punishment at once. Numbers lend precision to a history whose causal assumptions remain fantastic. They do not eliminate prejudice; they furnish it with a register.

Angles also make people readable. If the citizen is regular, one corner can disclose the whole figure and therefore the rank appropriate to him. The single inspected part stands for the person, replacing any enquiry into character. The danger of touching that corner gives this social shorthand its apparent urgency. Courtesy, caution and hierarchy consequently share an instrument.

Yet the use of angles is not simply exposed as nonsense. The mathematical difference between a Triangle and a Pentagon genuinely supports the optical demonstration in §6234. Abbott lets sound geometrical inference and unsound moral inference use the same confident explanatory manner. A reader must distinguish what the angle establishes from what the society wishes it to establish. The distinction matters throughout the romance: being able to calculate a shape is not being entitled to calculate a person's worth.

Places to read

1. §323“a very sharp and formidable angle”
2. §323“their acute angle (which makes them physically terrible)”
3. §523“an angle or brain of 59° 30′”
4. §523“the family brain was registered at only 58°”
5. §6234“task the angularity of the most intellectual”

In this edition

The Diotimos notes supply numerical checks for the geometry at notes 34, 57 and 5923, and discuss phrenological measurement at note 59. Those historical explanations are modern annotation, not terms Abbott inserts into the narrative. The “angle or brain” identification itself belongs to the main text and needs no editorial paraphrase to reveal its violence.

Family brain

The registered angle treated as the hereditary measure of a family’s intelligence. Recording it in degrees gives a spurious precision to the account of how punishment and moral shock retard descendants’ ascent through the class system. Printed form: family brain (§ 523). See Angle.

Vertex

The corners at which a triangle’s sides meet, especially the acute point opposite the short base of an Isosceles. In the social account this mathematical feature becomes a weapon, a measure of intelligence, and an index of rank. Printed form: vertices (§ 323). See Angle.

Feel and be felt by (contextual phrase)

“feel and be felt by” (§ 523)

The older formula of introduction2345 spells out reciprocal action: each stranger will inspect the other’s angle and submit to the same examination. Its balanced active and passive verbs make equality within the encounter audible, even though the purpose is to discover unequal rank. Successive urban shortenings omit the explicit passive half and eventually make feel mean introduce. The narrator complains of linguistic degeneration, but the transformation also shows how a bodily procedure can become conventional social shorthand. A courteous introduction2345 grants access to information that cannot be read directly from an apparent outline. Because an unexpected movement may kill the examiner, the formal words are backed by an exacting discipline of stillness. Etiquette here manages physical exposure as well as reputation. See Feeling and touch, Angle, and Language and gender.