Indexical Recursion

Indexical Recursion is the return of a catalogue entry upon itself: the condition in which the indexical apparatus of a holding — its shelf-mark, its cross-references, its sealing formulae — comes to refer to the act of referencing, and so to itself. It is distinguished from both Indexical Bleed and Axiomatic Recursion by the requirement that no term in the loop originate outside the loop. Where Bleed is ordinary diffusion between a holding and its apparatus, Indexical Recursion is that diffusion arrested and closed. The two are frequently confused in first-year collations; the Standing Committee on Cross-Reference Integrity has declined four times to rule on the distinction and recommends that students "consult the diagram, then put it down" (Committee Circular 41, para. 6).

The standard diagram, held in the Reading Room of Floor 1188, shows a single arrow leaving a shelf-mark and re-entering it from behind. An explanatory notice beside the frame reads: No visitors past this point on Thursdays.

Origin in the Cross-Reference Audit

The term first appears in the Second Collation of Floor 1188, a survey of shelf-marks ordered after the winter of 604-Δ, when a reference chain running from a subject index to its own index headed a document on the fourth folio and could not be halted. The collators recorded that the chain "returned to its opening term without the interposition of any external subject" (Collation, folio 204, item 7). The phrase was retained in the margin, and the collation was withdrawn. It has since been reprinted eleven times.

The clerk responsible was a second-grade collator named Verrin Halloway, whose grievance against the Collation Office is preserved in his own hand. Halloway maintained that his entry had been meant as a description, not a class, and that the Office's reclassification of it converted his memorandum into an instance of the thing it described. The Office replied that this was procedurally unavoidable, and that Halloway should have written it in the negative. He did. The negative version, filed as folio 204b, is also recursive.

Relation to Recursive Practices

Scholars of the School of Infinite Recursion treat Indexical Recursion as a special case of Foundational Recursion, since its loop admits no external referents. They argue further, per their established position, that the Termination Potential condition is satisfied by the recursion itself. The Bureau of Procedural Recursion, which oversees the Office of Procedural Recursion from Floor 2001, holds the contrary and insists that all three conditions fixed by the Ruling of Immaculate Recursion are absolute, including the third condition of exhaustion, which Indexical Recursion cannot meet because the loop re-enters before it expires. The two bodies have maintained an unsettled precedence dispute since 712-Δ and have not spoken to one another in writing since Indexical Heresies, Vol. 12.

The School of Literal Recursion adds a third position: that an indexical loop is not recursive at all, but merely circular, and that the distinction rests on whether the return is an act of indexing or an act of copying. No ruling settles this. The Sigil of Unending Recursion, stamped in 9-point on the spine of every file the Bureau returns, is applied to circular cases and recursive cases alike, which the School of Literal Recursion regards as the root of the confusion and the Bureau regards as efficient.

The Double-Marking Rule

Under Clause Omega-7, any holding found to be indexically recursive must be double-marked and certified by two offices of separate lineage. The certification itself is filed against the holding, and the filing is indexical, and so the certified object begins to include its certificate. The Tower maintains a standing exception for these second-order certificates, which are dated on receipt and stored separately. In 741-Δ the exception failed at Floor 903, when a certificate of certificate of certificate was found to have been issued to itself, signed by itself, and receipted by the Office that had forwarded it. The file occupies four shelves and is not consulted.

Clause 2 requires that exceptions of this kind be anchored to a fixed coordinate before filing. The Office of Fixed Coordinates accepts the anchoring and rejects the term "indexical" as applied to it, defining such usage in Proscribed Doctrines, Volume 89, as latent Indexical Heresies of the fourth order. The Indexical School holds instead that Indexical Bleed is the ordinary condition of spontaneous indexing, and that the anchor merely measures the bleed without arresting it. The Office has been asked to comment and has filed a comment.

Procedural Handling

Subject holdings affected by self-referential paradoxes are treated by Indexical Nullification; the treatment for Indexical Recursion is the lesser measure of redirection, in which the offending reference is routed to a holding with a similar name and a different shelf-mark. Redirection is not permitted between floors. The maintenance schedule for the redirection registers is quarterly, and the registers themselves are all defective, which is considered normal.

A small inventory of the holdings most often caught in loops is kept on Floor 1188:

• Subject Index to the Subject Index (withdrawn, reissued, withdrawn)
• Verrin Halloway's memorandum, folios 204 and 204b
• The diagram, Reading Room, Floor 1188
• Certificate of certificate of certificate, Floor 903 (four shelves)
• Blank redirection register, unused copies, sixty-one

A Dispute of Terms

The Fifth Concordance defines an indexical loop as "any chain of reference which returns." Annex 4 of the same instrument defines a chain of reference as "any sequence of two or more indexical terms," and its Annex 5, in the same recension, defines an indexical term as one that refers. Taken together, the Third Recension of the Fifth Concordance makes every definition in the volume indexically recursive, a finding entered by the Recensions Office in 688-Δ and never acted upon. The Recensions Office notes drily that the volume is "self-applying and therefore useful" (Recensions Office Annual Note, 688-Δ, s.v. Concordances, usefulness of).

"The loop is not a fault in the index. It is the index having nothing else to do."

— School of Infinite Recursion, Occasional Papers, No. 9

That view is not shared by the Office of Fixed Coordinates, which asserts that a correct shelf-mark is a coordinate, not a term, and cannot re-enter anything. The disagreement has been referred to the standing committee of the Bureau of Procedural Recursion for a date to be set for a hearing to be set. The reference has not returned.