Recursive Vanishing Point Placement

Recursive Vanishing Point Placement (R.V.P.P.) is the procedure by which a Point of Entry is itself assigned a Point of Entry, and that second Point of Entry a third, to a depth fixed by the attending clerk and recorded on the Spiral Register at the time of filing. It is distinguished from ordinary placement by the requirement that every stage of the chain remain independently verifiable; a chain whose links cannot each be produced on demand is not a Placement but a supposition, and is struck from the Register without hearing. The procedure is governed jointly by Concordance 37 and Annex 9 of the Third Concordance, which disagree on almost every point of substance and have done so since 878 T.R.

Origin and the Winter Recension

The practice emerged from the repairs to the Retrograde Steps undertaken in the winter of 874 T.R. A party of four clerks, working upward from the landing at the Chamber's outer door, found that scaffolding erected against the north face had acquired a second set of fittings beneath the first, and beneath those a third, faint but legible under lamplight. The junior of the party, Clerk Amarine Vesk, proposed that the fittings be logged not as a defect but as a hierarchy, and that the hierarchy be treated as the record of how the scaffolding had come to be there. The Winter Recension of the Steps adopted her proposal in full. Within a decade the method had been extended from scaffolding to documents, then to holdings generally.

The first complete chain on record — nine links, terminating at a nail — is preserved in the Annex of Minor Terminals and may be consulted by written application. The nail has its own catalogue card.

The Two Accounts of Termination

The central disagreement concerns how a chain ends. Concordance 37, clause 12, holds that a chain terminates when a link cannot be further reduced, and that such a link constitutes a "sufficient floor" for the entire structure: "What rests upon the irreducible rests, and need not be asked after again" (Concordance 37, clause 12). The Third Concordance, Annex 9, denies that any link is irreducible and requires instead that every chain close upon itself, returning to its first term before the Placement may be entered in the Register.

"A chain that does not return has merely stopped, and a thing that has merely stopped is not placed, but abandoned."

— Third Concordance, Annex 9, marginal gloss in the hand of the Recensor of the Ninth

Both instruments are in force. Clerks resolve the matter by filing under one and citing the other, a compromise formalised in the Memorandum of Alternating Compliance (891 T.R.), which permits the practice but requires that the discrepancy be noted in the margin in red.

The Vesk Objection

In 883 T.R. Clerk Amarine Vesk — by then Senior Registrar of the Office of Terminal Admissions — raised what she termed the objection of infinite regress: if the Placement of a Point of Entry requires a prior Point of Entry, then no Placement can be completed without a first term that is not itself placed, and the procedure is therefore either circular or unbeginning. Her objection was heard over four sessions and answered by the Determination of the Unplaced First (884 T.R.), which held that the first term is not unplaced but pre-placed, and that pre-placement is a condition rather than a record, and therefore not subject to documentation. Vesk accepted the ruling and appended a note reading, in its entirety, "The condition is doing a great deal of work here." The note was retained in the recension and is frequently quoted.

Relation to the Vanishing Principle

Recursive Vanishing Point Placement intersects uneasily with the Vanishing Principle. A holding whose chain of placements cannot be produced in full is, under the Principle, administratively treated as never having entered the Tower — and yet the chain itself may be a holding, requiring its own Placement, which may in turn be unproducible. The Chamber of Vanishing Precedents addressed the difficulty in the Vanishing Stairwell Determination of 901 T.R., concluding that the Vanishing Stairwell between Floors 209 and 210 was not a component but a conditional event, and that its Placement was therefore to be recorded at depth one only. Whether that reasoning extends to ordinary holdings remains unsettled; the Bureau of Conditional Architecture maintains that it does not, while the Office of Terminal Admissions has applied it twice, both times on a Friday.

Depth Schedules and Known Failures

Depth is set by the attending clerk and entered on the Spiral Register before work begins. Standard depths run from three to seven; depths beyond eleven require the countersignature of a Librarian and are rarely granted. The deepest chain on record, filed by Clerk Ossian Brade in 896 T.R., reached sixty-one links before terminating at a Recursive Aperture of the fourth grade, which the Register accepted as a valid closure without further inquiry. Brade's filing was challenged in 898 and upheld, on the ground that the Aperture, being self-referential by nature, satisfied Annex 9 without the need for a return.

The procedure has failed publicly twice. In 887 T.R. a chain lodged against Floor 412 was found on audit to contain the same link twice under two spellings; the Placement was voided and the clerk reassigned to the Scriptorium of Second Copies, where he remained until retirement and is remembered for the tidiness of his hand. In 903 T.R. a chain was filed at depth fourteen without countersignature; the error was discovered only when the countersigning Librarian declined to sign a document he had already signed, on the ground that he had no memory of it, and the Chamber ruled that his denial was itself evidence of depth but not of authorisation.

Chains are filed in duplicate. The second copy is not retained. Clerks are reminded that the Sigil Placement Box is for sigils only, and that the practice of using it to hold spare links, while widespread, has never been authorised and is not to be described as customary in any filing.

See also

• Recursive Loopbacks
• Aperture of Recursive Radiance
• Sanctity of Placement
• Deposits of Amnesiac Sediment