Upward and Northward

Use in the book

The difficulty is prepared in Lineland. The King translates left and right into north and south, the only two opposed directions he knows. The Square grows impatient with this mistranslation before committing its exact counterpart when the Sphere addresses him. What looks from outside like a foolish refusal is, from within, the almost irresistible assimilation of unfamiliar language to a known spatial system.

The Sphere's explanation in §162345 is more exact than the eventual slogan. Moving a Square northward makes some of its points pass through positions previously occupied by other points. Moving it out of the plane would give every point its own new path. This describes the relevant independence of the new direction without actually enabling the Flatlander to perform the movement. The pupil's repeated demand for an indication exposes the gap between a structural account and an available gesture.

For a time bodily experience closes that gap. In Spaceland the Square sees cards laid on one another rather than northward of one another, and learns the construction of a Cube. After returning, he tries to preserve the discovery by repeating words. In §202 the several forms of the phrase become a charm, mechanically recited before sleep. Its survival in language initially feels like a guarantee that the experience can be recovered.

The phrase then fails as a teaching instrument. The grandson ridicules it after hearing the Council's proclamation, and the Square shakes a moveable Square purposelessly, unable to enact the direction. The comic awkwardness matters: a teacher possessing true testimony can still fail to give a pupil either intelligible language or a reproducible demonstration. The formula is not worthless, but its brevity hides the practical knowledge it was intended to recall.

At trial it becomes the President's first question. In prison it becomes a Sphinx-like riddle that threatens rather than guides. The movement of the phrase from explanation through mnemonic charm to torment gives the narrative a verbal history of diminishing command. The words have not changed their reference; the narrator's capacity to inhabit their meaning has altered. Abbott makes a compact expression carry the difference between remembering that something is true and still knowing how to think it.

Places to read

1. §162345“No, not Northward; upward; out of Flatland altogether” — The original correction is spatially explicit
2. §192345“not, as you supposed, Northward of the other, but on the other” — Construction supplies practical clarification
3. §202“mechanically repeating, like a charm” — Explanation contracts into a mnemonic
4. §212“I move it somewhere” — The attempted demonstration loses its direction
5. §2223“like a soul-devouring Sphinx” — The clue becomes a riddle that consumes its keeper

In this edition

The notes connect the phrase to Flatland's southward attraction and retain its varying formulations rather than standardizing every occurrence. That variation distinguishes the original lesson, the sleeper's repetition and the final catch-phrase.

Catch-phrase

A compact, readily repeated formula. The narrator recognizes that the words about upward movement cannot alone carry the understanding he wants to communicate. Printed form: catch-phrase (§ 2223). See Upward and Northward.

Charm

A formula repeated as though it had a securing or magical power. The Square uses the words about upward movement to retain an experience he is already finding difficult to reconstruct. Printed form: charm (§ 202). See Upward and Northward.

Inane

Empty, pointless or lacking intelligible content. The Square's broken explanation ends in an inane gesture because he cannot enact the direction he is trying to teach. Printed form: inane (§ 212). See Upward and Northward.

Soul-devouring Sphinx

The narrator's image for the once-helpful precept about upward movement. Its unanswered riddle now threatens his mind, reversing the phrase's earlier function as a guide. Printed form: soul-devouring Sphinx (§ 2223). See Upward and Northward.

The soul devouring Sphinx (contextual phrase)

§ 2223: “a soul-devouring Sphinx”. The remembered instruction Upward, not Northward has become a riddle the narrator cannot solve in practice. The named monster transforms a successful clue into a torment. The Square still has the words, and knows that their distinction mattered, but cannot consistently recover the direction or mental image they once opened. The failure is therefore neither ordinary forgetfulness of a formula nor proof that the formula was always meaningless. It is a broken relation between language and a once-available conception. By setting this image beside the fluctuating Cube, the ending makes the price of revelation a problem of continued intelligibility as well as of punishment. See Memory and forgetting and Upward and Northward.