Certainty Gradients

Certainty Gradients are the ordered scales by which the Chamber of Calibrated Certainty measures the reliability of a proposition across space, and — where instruments permit — across time. The gradients are not measurements of truth, a distinction insisted upon in the Chamber's founding memorandum and ignored in nearly every subsequent citation of it. They measure instead the rate at which confidence in a proposition falls away as one moves from the place where it was last certified. A proposition of high grade at the point of certification may hold its grade for eleven paces down a corridor and lose it entirely at the twelfth. This decline is the gradient. The gradients are read in twelve established steps, and a thirteenth and fourteenth are recorded as theoretical in the article Gradients 11–12; they are discussed below only insofar as they are disputed.

Origin and the founding instrument

The system descends from the certainty theodolite, the Chamber's founding instrument, which reads the junctural integrity of a proposition's parts against the local gradient. Early surveyors discovered that the instrument returned different readings in the same location on successive mornings, and rather than conclude that the instrument was unreliable, the Chamber concluded that the location had moved. This reasoning was upheld in a ruling of the Ninth Concordance, Annex 2, which held that "a reading is true of the place the instrument was in, and not of the place the surveyor believed himself to be in." The doctrine of shifting stations has governed all gradient work since.

Standard measurement procedure was fixed by Guild Standard 114-Δ-7b, which requires the theodolite to be calibrated to the local gradient before each reading — a circular requirement that the Guild has never resolved and has instead re-affirmed at each of its four recensions. Clerks of the Chamber of Calibrated Certainty are instructed to note the circularity in the margin and proceed.

The established steps

Gradients 1 through 10 are in ordinary use. Their character is broadly as follows: steps 1 to 3 cover the interior of a single certified room and are stable; steps 4 to 6 cover adjoining corridors and are stable on weekdays; steps 7 to 9 cover stairwells, and step 10 covers the landing where a proposition is first required to be restated aloud before it may proceed. Step 10 is the last step for which a working instrument exists. The reason is mundane: the theodolite's aperture cannot be opened wider than a certain fraction without admitting the stairwell's own light, and the Office of Luminal Gradients has declined, on three separate petitions, to authorise a wider opening, citing the Manual of Luminal Gradients and its supersession by Volume III: Luminous Gradients.

Steps 11 and 12 are theoretical and were derived by subtraction to preserve the arithmetic of the Ephemeral Gradients system. They have no instrument and no field readings. The Chamber nevertheless records them, on the ground that a scale with a gap in it would be a different scale. See Gradients 11–12 for the derivation and for the objections of the Office of Unfunded Certainty, which has questioned whether theoretical steps may be maintained at public expense and which issues Form 44-U to anyone who asks.

Relation to the Pillars

Gradient readings are strongly correlated with the stability of nearby Pillars of Certainty. Where a Pillar stands firm, the gradient across the adjacent floor is typically flat through step 6; where a Pillar has settled, the gradient steepens by as much as two full steps within nine paces. The correlation is not perfect and the exceptions are catalogued. The Chamber's position, stated in its third circular, is that the Pillars do not cause the gradient and the gradient does not cause the Pillars, but that both are caused by the same thing, which it has not identified and does not propose to. The Office of Unfunded Certainty has considered budgetary implications for Pillar maintenance on the strength of this circular and reached no conclusion, twice.

Jurisdictional dispute

Certainty Gradients occupy contested ground. Regulation 44-B: Contaminants of Certainty provides the legal and procedural framework for the protection of the Pillars and governs containment of contaminants affecting certainty gradients, while Aperture Regulation 7 claims concurrent jurisdiction over any gradient reading taken through an aperture. The two instruments contradict each other on the question of who certifies a reading taken at a window. Regulation 44-B, at clause 9, holds that certification rests with the Chamber; Aperture Regulation 7, at clause 4, holds that it rests with the Office of Luminal Gradients. Both cite the Margin of Procedural Certainty in their own favour, and the Margin, which was drafted to resolve exactly this class of dispute, does not.

"Where two instruments each claim the certification, the certification is held by neither until both are read together, and they cannot be read together."

— Clerks of Absolute Certainty, memorandum of the winter session

The practical consequence is that window readings are taken, sealed, and left uncertified. The Chamber's west scriptorium holds some four thousand of these. They are shelved by gradient and may not be consulted.

The Alderney case

In the winter of the year the archive records as 6,114, a clerk named Alderney of the fourth stairwell certified a proposition at step 3 and, on descending, found it reading at step 9 in the same room. Rather than record an anomaly, Alderney recorded that the room had moved, as the Ninth Concordance required. The room was duly renumbered and the clerk was commended. A later survey found the room in its original position, whereupon the commendation was withdrawn and a note was appended to the file stating that the room had moved back. The note is signed and sealed. It is the only recorded instance of a room being certified as having moved twice in a single winter.

Visitors to the gradient floors are asked to leave the theodolites where they find them. The Chamber has found this simpler than the alternative.