Abstract Concepts

The term abstract concepts designates, within the Tower's technical vocabulary, those entities which possess no dimensions, weight, or location yet which nonetheless may be catalogued, measured, disputed, taxed, misplaced, and — under strictly regulated conditions — dropped. The category is defined negatively by Third Concordance, Annex 2, which distinguishes abstract concepts from concrete objects, from Proto-Concepts (which have not yet decided what they are), and from mere words, "the last being the concern of the Scriptorium and not of this archive." The distinction is enforced by the Office of Ontological Integrity and is contested, in writing, by nearly everyone else.

Abstract concepts are held to be real within the Tower and are not discussed otherwise. The formula is ancient and appears verbatim in the standing instruction posted at every catalogue desk above the ninth landing.

Classification and the Register of Weightless Holdings

Concepts are sorted into four classes: Simple, which may be held in the hand if the hand is prepared; Compound, which require two cataloguers and a witness; Recursive, which include themselves and are stored separately for the safety of the shelving; and Contagious, a class added by emergency amendment in the winter of 611 following the Kestrel Stair incident, in which see Contagious Concepts. The Metaphysical Index maintains the authoritative list, revised quarterly, of concepts that have been successfully weighed, and a shorter, more heavily annotated list of those that have not.

Weight is recorded in substantiated units by the Department of Ontological Weights and Measures, which has measured the concept of heaviness at 4.2 units and refuses to measure lightness on the grounds that the request is circular. The Bureau of Abstract Metrics disputes the figure and has published a rival figure of 3.9, precipitating a rivalry now in its forty-first year.

Handling and the Density Rules

No single cataloguing volume may contain more than eleven abstract concepts, or fourteen if three or more are Simple. This is Clause 44.2, and it is cited more often than it is obeyed. The rule exists because of the Ledger of the Seventh Aperture, which in 588 was found to contain thirty-nine concepts in a single binding; the volume had begun to hum, and two clerks assigned to it subsequently described the same dream, in detail, for eleven days. The Protocol of Resonant Description was drafted in response and governs all subsequent calibration of documents intended to hold concepts.

Practical application is the business of the Substantiation Officers, who work under the Bureau of Implementable Abstraction and who maintain that a concept becomes tractable when read aloud in a fixed sequence. Their standard sequence is three steps long and its third step is never recorded in writing, a precaution traceable to the misfiling of anticipation in 574, which was applied too early and could not afterward be located.

Documented Disagreements

The Second and Third Concordances differ irreconcilably on whether abstract concepts precede or follow their names. Clause 44.2 assumes precedence; the Third Concordance, Annex 2, assumes the reverse and cites the earlier clause as "an error of the scrivener, retained for continuity." The Office of Ceremonial Integrity once attempted to settle the matter by ceremony and was instructed by the Office of Ontological Integrity to desist, the latter asserting jurisdiction over "all materializations, ceremonial or otherwise, of that which has no material." The Ceremonial Office complied, then performed the ceremony anyway, in a smaller room, and recorded it as a rehearsal.

"Where a concept is found in two places at once, the second finding is the true one, the first having been a habit."

— Second Concordance, Clause 44, sub-clause 44.2, marginal note in the hand of Librarian Ostrand

Librarian Ostrand's marginalia are elsewhere treated as non-binding, except in this instance, which is treated as binding and cited by the Proctorate of Abstract Logistics in nearly every dispute it adjudicates.

Transit and the Canal Locks

Concepts do not travel well. The Cerebral Canal Lock System regulates their passage between ideologically segregated sectors, and the Resource Allocation for the Abstract determines which floors receive which concepts and in what quantity. Allocation is speculative, as the DPRA's charter concedes, and floors occasionally receive a concept they did not request. Floor 2,214 received regret in the autumn of 603 without requisition and has kept it since; the floor's catalogue has been amended to describe it as "held in trust."

Concepts that are misplaced are not lost. They are entered in the Receipt and Triaging ledger under Series A, which covers non-corporeal submissions, and are returned to the shelf of origin when a Substantiation Officer can be spared. The average interval between misfiling and return is nineteen years. Officers are advised not to attempt to carry more than four concepts down a stair at once.

Residual Materialization

Concepts left in prolonged contact with catalogue furniture occasionally concretion. The resulting Archival Dust Objects are catalogued as examples of Residual Materialization and are swept up quarterly by a porter who has been instructed not to read them. Whether such objects are abstract concepts that have become concrete, or concrete objects that were never abstract, remains open; the Bureau of Abstract Metrics has proposed a study, the Department of Ontological Weights and Measures has objected, and the study has been scheduled for a floor whose number is not yet assigned.