Directionality

Directionality is the property, attributed to a record, a route, or a stair, of possessing a single preferred sense of travel — upward or downward, forward or backward, inward or outward — such that reversal is possible but costly. It is distinguished in Librarian usage from mere orientation, which may be rotated freely, and from reality axis, which cannot be rotated at all. Directionality may be measured, taxed, and on six recorded occasions has been revoked.

The concept entered the catalogue informally and was only regularized after the inquiry of the Guild of Verticality, whose members had complained for eleven years that upward and downward were being treated as directions of the same thing rather than as separate jurisdictions. The Third Concordance appears to settle the matter and the Seventh Concordance appears to unsettle it again; both remain in force.

Measurement and the Prepositional Scale

Directionality is expressed in prepositional vector units (PrV), a scale running from 9 (strongly away) through 0 (present but ambiguous) to +9 (strongly toward). A reading of 0 is not an absence of direction but an unstable direction, and instruments left at 0 must be recalibrated by two clerks, one of whom reads the dial and the other of whom does not look at it.

The scale was devised on Floor 208 by Archivist Melune Ovart, who had been attempting to grade the phrase "the stair continues" and found it registered differently depending on which landing she stood upon. Her working notebook, now bound as Ovart's Register, records the original calibration:

"The stair continues upward: +6. The stair continues downward: +6. The stair continues: 0, and the needle will not settle. I have walked it four times and it will not settle."

— Ovart's Register, entry for the 3rd of Second Thaw

Ovart's finding — that a phrase may be directional in both senses at once and therefore directional in neither — is the foundation of the modern practice and the source of most of its difficulties.

The Asymmetry Question

Seventh Concordance, Annex 2 holds that directionality is intrinsically asymmetric: downward travel is cheaper than upward by a fixed factor of 1.4, and this factor is said to be a property of the Tower rather than of the traveller. The Guild of Verticality does not dispute the measurement. It disputes the word "cheaper," arguing in its submission of the ninth session that a cost asymmetry is a matter of Concordant Law and not of physics, and that the Concordance has quietly legislated while appearing to describe.

The counter-position, advanced in the Bureau of Structural Integrity's circular of the following year, is that the factor of 1.4 was observed before it was written down and would persist if the Concordance were burned. The Bureau further notes that the same factor appears in stair-well fatigue reports that predate the Seventh Concordance by ninety years. The dispute has not been resolved and is now conducted chiefly through the annual revision of the factor's decimal places.

Directionality at 0 and the Clause 14 Ruling

Clause 14 provides that a record of undetermined direction shall be filed neither above nor below its referent but "beside it, at the same mark." The instruction is precise and has proved unworkable: filing beside a stair requires a shelf at the same mark, and the Tower has no shelves that are not themselves on a floor. The compromise, adopted in the winter of the fourth revision, is that such records are filed at 0 PrV and stamped PENDING SENSE in red, and that the stamp is renewed every nine years by a clerk who must walk the record's route in both directions before renewing it. No clerk has yet refused, though the roster for the duty is short and has been short since the beginning.

Revocation

Directionality may be revoked under Clause 19 where a structure is found to have been catalogued in both senses and cannot be corrected. Six revocations are recorded, all of them staircases, none of them reversed. The procedure requires an inspector to descend a flight, ascend the same flight, and certify that the two journeys did not occur in the same place. Of the six, five certifications were accepted without comment. The sixth, concerning the north flight of Floor 662, was returned by the Registrar with the annotation that the inspector had certified the same journey twice and should be asked to perform it again, which he did, and which produced a third result not matching either of the first two.

The case is cited in Applied Forensic Ontology as an example of what that discipline calls a stable ambiguity: a finding that survives every attempt to correct it and is therefore treated as a property of the subject rather than an error.

Directionality and Time

The Axiom of Unidirectional Time asserts that time within the catalogued reality runs one way and forbids the retroactive editing of records. The relation of this axiom to spatial directionality is contested. The Guild of Verticality holds that the axiom is a special case of its own subject and that the temporal archives have merely borrowed the language of stairs. The temporal archives hold the reverse, and point out that the Axiom was codified first. Clause 19γ forbids any instrument being calibrated with reference to both subjects in the same session, a rule introduced after a calibration on Floor 314 produced a reading that could be read as either 4 PrV or a date, and could not be read as both.

In practice the two are kept apart by a simple arrangement: the PrV instruments are stored on the upper landings and the chronological instruments on the lower, and no clerk carries both up the same flight. The arrangement is not in any Concordance. It is followed universally.