Discontiguities, Vol. XII

Discontiguities, Vol. XII is the twelfth and, by the Librarians' own count, the only surviving volume of a projected forty-volume register of spatial inconsistencies observed within the Tower. Compiled under the direction of Archivist M. Kael and bound in the Tower's standard grey buckram at the Scriptorium of the Lower Sept, it was entered into the catalogue on 14-Θ-088 and has been amended in manuscript at least sixty times since. The volume's purpose is narrow and, its compilers concede, philosophically embarrassing: to record places that are not where they are.

The work is best known for Kael's paper On Discontiguities, printed as the volume's opening essay, though the bulk of the volume consists of survey returns, corridor measurements, and the dissenting opinions of a dozen offices that did not agree the survey should have been conducted at all.

Scope and method

The volume defines a discontiguity as any arrangement in which two locations are joined by a continuous path yet remain, by measurement, adjacent; or are adjacent yet require a journey to pass between. Kael's preliminary classification recognises four grades, of which the fourth — "unresolved, and not to be resolved by this office" — accounts for two-thirds of the entries. Surveyors worked in pairs, one walking and one recording, and the pairs were forbidden to exchange roles midway through a survey. The reason given in the volume's front matter is procedural rather than mathematical: the two roles used different inks.

Most entries are short. A representative return, from the corridor survey of 03-Ψ-101, reads in full: "Landing 6 and Landing 6a: forty-one paces apart when walked eastward, nine when walked westward, and the same landing when neither is walked." The surveyor, whose name the volume gives only as Second Recorder Anselm, added beneath this: "I have walked it eleven times. I do not propose to walk it a twelfth."

Relation to the Petalline Survey

Roughly a third of the volume is given over to arguments, largely by Kael, concerning the Petalline Survey — the great floral-metric traverse of the middle floors, whose returns were found to vary with the direction of the surveyor's approach in a manner the Survey's own directors declined to call an error. Kael's contention, set out across four annexes, is that the Petalline returns were never anomalous; they were simply taken in a Tower that had not yet been asked whether it was contiguous, and the question had not been put because no one wished to hear the answer. The Department of Florid Anomalies, constituted after the incident recorded in the Annals of Structural Anomalies Vol. XII, objected in a minority note that the Petalline Survey had been conducted on floors the Department did not administer and that Kael's reading of its returns was "energetic."

"The Survey did not fail. It measured what was there. What was there was not the same on both sides of the instrument."

— M. Kael, On Discontiguities, Discontiguities, Vol. XII, Annex 2

The Support dispute

A substantial appendix collects dissenting opinions on the Support apparatus — the load-bearing assemblies whose relationship to the floors they support has never been settled in writing. The volume's position, again Kael's, is that a discontiguity occurring beneath a Support is not a fault in the Support but a property of the space the Support is obliged to hold up, and that the Supports should therefore be catalogued as evidence rather than repaired. The Bureau of Ambivalent Geometry dissented at length, holding that a Support which holds up two places at once is holding up neither, and that the distinction mattered to the people standing on it. The volume prints the Bureau's dissent in full and does not answer it.

Readers consulting the appendix are asked to sign the volume out at the desk rather than at the shelf. The desk is on Floor 404 and the shelf is not.

Contradictions and later recensions

The volume's authority rests uneasily on the Seventh Concordance, whose guidelines for phenomenological cataloguing incorporated classificatory schemas from the Register of Ratifications, Vol. XII that had themselves been drawn from Vocalisations of Abstract Entities, Vol. XII. Kael's four grades do not map onto the schemas of the Vocalisations, and two later recensions of the Discontiguities attempt the mapping in opposite directions. The first, prepared in 12-Δ-093, treats the fourth grade as a residual class; the second, of 12-Δ-097, treats it as the primary class and the first three as its special cases. Both recensions carry the Librarians' seal. Neither has been withdrawn.

The Reality Cartographers' Guild has cited the volume in support of its long-standing claim that its headquarters are "simultaneously adjacent to and conceptually prior to all codified space," a claim the Guild supports by reference to Annals of Jurisprudence, Vol. XII. Kael's own view, recorded in a marginal note reproduced in facsimile, was that the Guild's headquarters were adjacent to the volume's subject matter but not to the volume, and that this was the more interesting fact.

The volume also records, in its final annex, the first formal classification of recursive citation loops, a matter more fully treated in the Cartographic Conservatory, Vol. XII. The two works cite one another; the Conservatory's editors have ruled that this is not a loop but a corroboration, and the ruling is printed in both.

Textual history and use

Only the twelfth volume survives. Volumes I through XI were listed in the Inventory of Minor Furnishings, Vol. 44 as shelving, and the discrepancy has never been reconciled; the Quarterly Registry Reconciliation Schedule records the matter as open, and has recorded it as open in every quarter since 12-Θ-104. Volume XII itself exists in three states — the original, the first recension, and a corrected printing whose corrections were never listed — and the Manual of Transcription Standards, Vol. III, §7.22 requires that citations specify which. Most do not.

The Log of Unfixed Coordinates, Vol. XII cites the Discontiguities in connection with the intersection of Spiral T-54 with the primary shaft of Spiral 40, an elevation the Log places between Sub-levels 7 and 12. Kael's surveyors placed it between Sub-levels 9 and 10. Both citations are considered correct.

The volume is consulted chiefly by parties to disputes over corridor jurisdiction, who are directed to it by Librarian-Scribe Valerius's Commentaries on Adjudicatory Precedence, Vol. XII and who generally leave unsatisfied. Kael's essay closes with a remark that has been read as a warning and, by the Bureau, as a concession: "A register of discontiguities cannot be complete. It can only be accurate, and accuracy in this matter requires that the register itself be entered in the register." The entry was duly made on 02-Σ-089. Its grade is not recorded.