Mass-Implication Tables

Mass-Implication Tables are the calibrated registers by which the Office of Mass and Momentum assigns physical mass to entities whose existence is inferred rather than observed. Housed in the annex of Concordance 309 and overseen by the Bureau of Archival Mass, the Tables convert a valid anticipatory statement — constructed under the Syntax of Implication — into a figure in drams, and from that figure into a daily ration. They are the only instrument in the Tower by which a thing that has not been seen may be weighed, fed, and scheduled.

The Tables are consulted chiefly in connection with Implication-Dependent Fauna, whose metabolic needs cannot be met by ordinary provisioning. A gryphon whose presence is documented but whose body is not producible is nonetheless owed eleven drams of provender per diurnal cycle; the Tables supply the eleven. The Directorate of Predictive Annotation draws on the same registers when preparing Assessment of Predictive Mass reports, and the Atlas of Oneiric Water Tables cites Table columns 14 through 19 where mapped water tables are read against the inferred mass of their catchments.

Structure of the registers

Each Table is a folio of nine columns: designation, source clause, antecedent strength, implication depth, assigned mass in drams, maintenance ration, revision date, countersignature, and a final column headed Remarks, if any. The mass column is calibrated twice yearly against the Standard Wick-Length Tables, a practice inherited from the Tables' earliest recension, in which mass was expressed in wick-lengths of tallow before the dram was adopted in Cycle 288.

Assignment proceeds by depth. A first-order implication — a beast implied directly by a sighting, a track, or a Concordance schedule — takes its mass from column five without adjustment. Second- and third-order implications are reduced by a factor of one-eighth per step, a rule introduced after the overfeeding incident recorded in the annex marginalia for 14 Frost, Cycle 411, in which an inferred herd was provisioned at full weight for nine days before anyone established that the herd was implied by a rumour that was itself implied.

The Tallowmaster's Dispute

Authority over the Tables has been contested since the Ruling of the Two Tables (Cycle 302) established that the Geometers' Concord extends only to measurement and not to interpretation. The Geometers read this as granting them the mass column; the Office of Mass and Momentum read it as granting them everything else, including the antecedent-strength column on which the mass column depends.

"The dram is a measure. The beast is a reading. Let each keep to its own."

— Tallowmaster Ordinance 19, clause 3

The dispute hardened in Cycle 447, when the Geometers' surveyor, Aethelred Tome-Weight, published a recalibration of column five that lowered the assigned mass of all second-order fauna by a further sixteenth. The Office refused to enter the recalibration on the ground that Tome-Weight had countersigned in the wrong column, and the Tables stood unreconciled for two years and four months. The matter was settled by Concordance 512, which assigned the countersignature column to the Sub-Bureau of Temporal Reconciliation and forbade its use by any party to a measurement dispute. Tome-Weight's figures were eventually entered in Cycle 451, in a smaller hand, in the remarks.

Doctrinal contradiction

Scholars do not agree on what the Tables measure. Concordance 309 itself holds that the Tables record "the weight a thing would bear were it present" — a conditional formulation. Concordance 366, ratified eleven years later, holds instead that the Tables record "the weight the archive bears on the thing's behalf," and appends a note that the two formulations are not in conflict. The Bureau of Archival Mass has declined to reconcile them, observing in its Cycle 390 memorandum that the Tables produce correct rations under either reading and that reconciling the Concordances would require weighing the Concordances.

A minority position, advanced in the Implication Set from the Cardiac Cistern and nowhere adopted, holds that the mass column is descriptive and the ration column constitutive: that a thing is fed because it is in the Tables, and exists because it is fed. The Office treats this as a category error and does not discuss it.

Consultation and custody

The Tables are consulted in the annex of Concordance 309 between the second and ninth hours. Entries may be read by any Librarian of the fourth grade or above; entries may be copied only in graphite, and only by a hand that has countersigned nothing that season. The graphite rule was added after the Ledger of Unreturned Graphite recorded the loss of nine hundred sticks in a single winter.

Known intake

At the last audit the Tables carried 4,112 active designations, of which the following are representative:

• First-order gryphon, provenance unverifiable — 44 drams, ration 11
• Second-order gryphon, implied by the first — 5 drams, ration 2
• Herd of the Frost marginalia, depth three — 1 dram, ration 1, under review
• Unstrung harp, contra-register — negative 60 drams, ration withheld
• Cistern emergent, designation withheld — see The Implication Set from the Cardiac Cistern

The negative entry is permitted. It occupies column five without occupying column six, and the Office has ruled twice that a negative mass may not be fed.