Vex-Marlow scale

The Vex-Marlow scale is the Tower's standard instrument for converting resonant frequencies into drift quanta, expressed in Standard Drift Units (SDUs). It is not a physical object in the way a balance or a plumb line is an object. It is a graduated agreement — a table of correspondences ratified jointly by the Vex and Marlow readings offices in Y203 SCE and amended eleven times since — and its authority rests almost entirely on the fact that no floor has been able to agree on a competing agreement long enough to displace it.

The scale runs in the negative by convention. A subject at rest on the scale reads 0.0; a subject whose language has begun to drift away from its own meaning reads below zero, and the numbers continue downward without a recorded floor. Field measurement of SDUs is conducted using the Vex-Marlow scale, and a subject's drift is considered within tolerance if it does not exceed -5.2 SDUs. That figure appears in so many ordinances that clerks refer to it simply as "the threshold," as though there were only one.

Origin and early readings

The scale takes its name from two offices rather than a single inventor, though the Vex Ledgers preserve the working papers of Arlo Vex and, in a rival hand, those of Elara Vex — neither of whom is mentioned in the ratification instrument at all. The Marlow readings were collected by the Uncertainties Desk on Floor 6,178 between Y197 and Y202, largely from visitors who had lost the ability to say where they were going and had begun to say where they had been instead. The Vex readings were collected from documents that had changed opinions while shelved.

The two sets did not agree. The ratification of Y203 was reached only after the Uncertainties Desk agreed to discard its upper register entirely, on the grounds that "a reading that requires a reader to be twice present is not a reading but a rumour" (Marlow Ratification, Preamble iii). The discarded register has never been recovered, and the Desk still lists it as pending.

Calibration and dual ratification

Vex-Marlow Calibration requires dual ratification by a senior Anomalist and a neutral observer from the Alexandrian Interpreters. The neutral observer is required to sign the calibration sheet and then to leave the room before the sheet is filed; the reason given in the standing order is that "an attested reading is one taken in the absence of its witness." Clerks have long observed that this arrangement makes the observer's neutrality difficult to review, and the Alexandrian Interpreters have declined three times to comment on the point, the fourth request having been lost in transit between Floors 412 and 413, which do not connect.

In Y231 a calibration performed on Floor 2,044 was ruled void because the senior Anomalist and the neutral observer were the same person wearing two coats. The ruling, Fourth Concordance, Annex 9, established that coats do not constitute separate offices. It has since been cited in at least forty unrelated disputes, most of them concerning seating.

The threshold dispute

Scholarly disagreement centres not on the value -5.2 but on what it measures. The Manual of Annotative Stability (Revised 12th Edition) establishes a threshold of -5.2 SDUs on the Vex-Marlow scale for footnotes to be considered "hypergravitic," and treats the figure as a property of the annotation. Fourth Concordance, Annex 2, holds instead that the figure is a property of the reader, and that a footnote is hypergravitic only when it depresses the reader sufficiently to pull the surrounding page down with it.

"The threshold is not in the note. The threshold is in whoever is holding the book. A note read by a rested scholar may sit comfortably at -4.0 and the same note at the same hour will read -6.1 in the hands of a scholar who has not eaten."

— Fourth Concordance, Annex 2, "On the Location of the Threshold"

The Manual's editors replied in the 12th Edition preface that Annex 2 "confuses the instrument with the hand that shakes it," and added that they did not propose to discuss the matter further. They have discussed it further twice.

Use in diagnosis

A drift alignment exceeding -5.2 SDUs on the Vex-Marlow scale is diagnostically significant for Retroactive Numeracy, a condition in which a subject's recollections of floor numbers revise themselves after the fact. The scale is not used to measure Linguistic Resonance directly; that is the province of the Vex Saturation Scale, and the two are frequently confused by junior staff, who are issued with a one-page sheet explaining the difference and a second sheet explaining why the first sheet is out of date.

Protocol Gamma-12 execution is mandated for subjects registering above 7.2 on the Vex Saturation Scale during preliminary audition, and a Vex-Marlow reading is taken first, before the saturation instrument is unsealed, so that the two records can be compared afterwards. Comparison is required. No comparison has ever been published.

Maintenance and known irregularities

The primary reference table is held on Floor 1,209 in a case with a broken latch; the case is not to be closed, as closing it alters the readings of any document stored inside, a note the Vex archival office has appended in red to every inventory since Y244. Field copies are transcribed by hand, and transcription error is the scale's most persistent problem. The Vex Protocols require a field copy to be checked against a second copy, which must itself be checked against a third, and the third against the primary table, which cannot be closed.

Between Y261 and Y263, a duplicated minus sign circulated through nineteen field copies on the eastern stairwells, producing readings that appeared to be within tolerance but were in fact enormous. The error was discovered by a clerk named Havren Soll, who noticed that every subject on his round was drifting upward at precisely the same rate and concluded, correctly, that the fault was in the paper. His report was accepted and his name was omitted from the errata sheet, for which he petitioned the office four times. The errata sheet still omits him.

The scale remains in force. Its eleventh amendment, ratified Y288, changed only the spacing of the tick marks and provoked a decade of correspondence.