The Recursive School (or Fractal Continuists)

The Recursive School, known in its own seals as the Recursive School (or Fractal Continuists), is a body of the Librarians charged with the certification, adjudication, and — where certification fails — the containment of self-referring structures within the Tower. Its standing commentary on the administrative behaviour of Recursive Buffer Zones is received as authoritative by every office except the one that administers them. It issues Recursive Loop Certifications and formally certifies Recursive Anchoring under Ruling 88.45, a document it did not draft and has spent four centuries interpreting.

The parenthetical in the School's formal style is not decorative. It records the settlement of the Naming Concordance of 1109, by which the Continuist faction — those holding that a recursion is best understood as a shape repeated at diminishing scale — were permitted to retain their name inside the School's own name, on condition that they never use it in correspondence.

The Continuist Question

The School's internal history is largely the history of two readings of the same mandate. The Continuists hold that a recursion is a fractal: the same relation, at smaller scale, indefinitely. The Literalists hold that a recursion is a return, and that a thing which does not return to itself has merely been drawn twice. The two positions were held to be compatible until the winter of 1344, when an inspection of Floor 6118 (the Annex of Small Repetitions) found that the Continuist reading had permitted the cataloguing of a bracket that contained itself at nine scales of magnification. The bracket was certified, since the Continuists were in the majority that year. It was then found to be uncertifiable, since the Literalists chaired the review. Both findings stand in the record and neither has been struck.

Senior Indexer Elira cites the episode in the fifth of the Elira Theses, where it is offered as evidence that "a body which certifies what it has itself described will always find the description adequate" (Elira, Thesis V, clause 3). The School has not answered the Theses directly.

Certification and Its Failure

A Recursive Loop Certification is a short instrument, rarely longer than a page, attesting that a given structure's references to itself are finite, enumerable, and closed. The School issues between forty and sixty a year. Most are routine. The forms are held at the Registry of Loops and Returns on Floor 4402, which is reached by the west stair only; the east stair arrives at Floor 4402 as well, but at a different Floor 4402, and the Registry does not accept documents filed from it.

Certification has failed conspicuously twice. The first failure, in 1401, was procedural: a certification was issued to a structure that had already been certified under a different name, and the two certificates, cross-referenced, generated a third structure requiring certification. The second, in 1612, was substantive and is treated by the School as a founding embarrassment. The structure concerned had been certified as closed on a Thursday and was found on the Friday to be open by one reference, which pointed to the certificate itself. The School's response was to issue a certification for the certificate, a decision later regularised under The Recursive Certification Loop.

"Where the instrument of closure is itself within the field it closes, the instrument shall be certified separately, and the certifying officer shall not be the officer who signed the original."

— Ruling 88.45, Annex 2, clause 7

Relations with Other Offices

The School's relations with the Office of the Fractal Indexer are correct and cold. The Office, established by Ordinance 88124 to enforce catalog termination, regards the School's tolerance of small repetitions as an invitation to the very indices the Ordinance was written to end. The School regards the Office's termination orders as premature, and has said so in nine standing commentaries, the most recent in 1788. The quarrel descends through the fourth field of the Elira Theses, which both bodies claim to interpret and neither will amend.

Day-to-day oversight of the School falls to the Bureau of Recursive Affairs, which handles its correspondence, its seals, and its complaints, and which has twice been asked to arbitrate between the Continuists and the Literalists and has twice declined on the ground that the matter is doctrinal.

Inventory of the School's Instruments

The School's working holdings, as returned at the last general inventory, are as follows.

• Certificates of Recursive Loop, in force: 1,204.
• Certificates of Recursive Loop, withdrawn: 119, of which 61 were withdrawn and later reinstated.
• Standing commentaries on the Recursive Buffer Zones: 9.
• Seals: 3 (the Loop, the Return, and the Small Repetition). The third is used only by the Continuists and is not recognised in correspondence.
• Chairs: 14, of which 2 are held jointly and 1 is held by a structure.

Visitors to the School's chamber on Floor 3971 are asked not to count the shelves aloud, as the count is itself a return and must be certified before it may be spoken.