The Axiom-Scope

The Axiom-Scope is a graduated brass instrument, 1.4 metres in length, issued to each floor's Assay Office for the purpose of determining how far a given axiom extends before it is superseded by another. It consists of a fixed sighting rule, a sliding cross-bar carrying forty graded apertures, and a spirit level whose bubble was replaced in 3011 with a sealed glass bead of the Tower's own manufacture. The Axiom-Scope does not measure truth; by Fifth Concordance, Annex 2, it measures only the distance at which a proposition stops being binding, which the Librarians have always held to be the more useful figure.

Function and reading

An axiom is laid on the assessment rail and sighted through successive apertures until the cross-bar ceases to admit it. The aperture at which the proposition ceases to admit light is recorded as its scope, in units of one gradus (approximately 38 centimetres). Scopes are entered on the floor's Axiom Register and are considered binding on all subordinate offices until the next general resurvey, customarily conducted in the winter quarter when traffic on the Spiral Theta is light.

The instrument's great advantage over the older method — reading axioms aloud to a stairwell and noting where the echo changes — is reproducibility. Two clerks with two Axiom-Scopes of the same issue will return figures within three gradus of one another, provided both have been kept out of the damp. The Axiom of Recursive Validation cannot be scoped by instrument at all, since it re-enters the aperture as soon as it has passed through, and its register entry consists of a single undated dash.

History

The Axiom-Scope was devised in 2988 by Clerk-Ordinary Mavel Orrun, an instrument-maker of the Scriptorium of Minor Weights, who had grown exasperated with a dispute between the Division of Subjunctive Scope and the Ventilation Division over the reach of the Axiom of Documented Intent. Orrun's initial model carried only twelve apertures and a pine body; the brass model and the forty-aperture plate date from the second recension of 3002, following an incident in which a pine Scope warped overnight and scoped the Axiom of Administrative Containment at a figure eleven times its usual value, briefly bringing the whole of the north-east quadrant to a halt.

Distribution was slow. The Tenth Concordance did not so much authorise the instrument as notice it, and the third clause of that document, which had been intended to clarify the jurisdictional scope of the Scriptorium, was read for three decades as giving the Instrumentarium a general licence to survey anything that would hold still. This reading was eventually reversed by Determination 44, which held that the Scope may be applied to any proposition except a custodial one, on the ground that custodial propositions return a scope equal to the length of the room they are kept in.

The graduated dispute

The central scholarly disagreement concerns the graduation itself. The Seventh Concordance asserts that the apertures are "arbitrary in width but fixed in sequence, and the sequence is the whole of the law" (Seventh Concordance, Annex 9), while the Ninth Concordance holds in its second recension that the apertures are "equal and divisible, being forty in a rule of forty," and that any apparent inequality is a defect of the plate and not of the doctrine. The two annexes have never been reconciled.

Survey Directive 9.12.7, which primarily governs Survey Scope Delimitation, quietly adopts the equal-division reading in its schedules but cites the Seventh Concordance in its preamble. Clerks have learned to check which document a returning surveyor was trained under before reading the surveyor's figures, a practice known informally as "asking the plate." The dispute turns, in the end, on whether a twelve-aperture plate held in the Scriptorium's reserve collection is a Scope at all. The Instrumentarium declines to rule on the question and has twice declined to lend the plate out.

Care, and the prohibition on double-scoping

Axiom-Scopes are inspected quarterly. The spirit bead is wiped, the sliding cross-bar is run to full extension and back twice, and the assessment rail is dressed with a drop of lamp oil, no more. A Scope that has been dropped must be re-collimated before its next use; a Scope that has been dropped on a custodial floor must be re-collimated and re-sworn, as the oath is considered compromised by association.

Double-scoping — laying an axiom in the rail and sighting it a second time within the same working day — is prohibited outright under Precedential Hierarchy, as the second reading is invariably lower than the first and the difference cannot be attributed with confidence to the axiom. Clerks found double-scoping surrender the instrument to the Instrumentarium for a period of one month and receive a note on their file. The rule is unpopular, and the file notes are numerous.

Known anomalies

Three classes of axiom are known to resist scoping altogether. Axioms touching appetite give figures that vary between clerks. Axioms that name the Tower itself return a scope of zero, which the Axiom of Inexhaustibility is held to explain and which no one has been able to demonstrate. And the Variable Axiom, by its nature, refuses to settle in the rail; the standard remedy is to scope it in the morning, before it has had time to become something else, and to accept the record as provisional. The Axiom of Material Coherence and the Axiom of Catalogued Existence frequently fail to admit light at any aperture whatsoever, a condition the Instrumentarium records plainly as "no reading" and about which it does not speculate.

The Axiom-Scope is not to be used as a pointer during lectures, and the record of 3014, in which an entire floor's register was re-scoped by an instrument borrowed from a neighbour, remains a caution on the subject of lending.