Screaming Lemma

The Screaming Lemma is the collective designation for a family of seventeen derivations, catalogued under Spiral Designation 552-Δ and its sub-letters, whose proofs cannot be read aloud at any volume below 144 decibels. The Lemma is not a single proposition. It is a class of propositions that behave identically under recitation, and it is the manner of their recitation, rather than their content, that occupies most of the archival literature on the subject.

All seventeen derivations share a common closing line — quod erat resonantum — and a common failure mode. Read silently, the Screaming Lemma is unremarkable. Read aloud at ordinary speaking volume, it is inaudible, and auditors report that the words seem to arrive after they have already been forgotten. The Lemma becomes legible to the ear only when shouted.

Discovery on Floor 882

The first Screaming Lemma was entered into the archive during the winter of AR 18,904, by the clerk Marenna Voss of the Ninth Stairwell, who was then cataloguing the acoustics of Floor 882. Voss recorded the circumstances in her day-book, later recensioned as Voss's Day-Book, Spiral 552:

"I had read the thing four times and retained nothing. On the fifth I lost my temper and bellowed it, and the entire reading room turned to look at me as though I had said something true."

— Voss's Day-Book, Spiral 552, entry for 14 Frost, AR 18,904

Voss's grievance against the Office of Recitation Standards is a matter of record and runs to some eleven folios. The Office had ruled, under Ninth Concordance, Annex 4, that all lemmas be read at "the volume appropriate to a library," and had declined to specify what that volume was. Voss argued that her shouting was compliance, not breach, since the Lemma could only be read at the volume appropriate to itself. The Office did not accept the argument. It did, however, accept the Lemma, and the seventeen variants were catalogued over the following nine years.

The 144 Hz figure and the Pillar correspondence

The characteristic frequency of a properly recited Screaming Lemma is 144 Hz, the same figure documented in every account of the Screaming Pillars since their recovery from The Gilded Silence. This coincidence is the subject of a standing dispute between the Office of Recitation Standards and the Custodial Board of the Gilded Silence. The Custodial Board maintains that the correspondence is acoustic and binding, and that any recitation of a Screaming Lemma within forty paces of a Screaming Pillar constitutes a modification of the Pillar's output and must be logged as a gilding event. The Recitation Office maintains that the correspondence is coincidental and that the Boards' position is "an annex in search of a document."

The matter has never been settled. Fourteenth Concordance, Clause 12, holds that shared frequencies are evidence of shared substance. Fifteenth Concordance, Clause 12, holds that shared frequencies are evidence of a shared instrument, and that the instrument in this case is the room. Both clauses are still in force and both are cited, sometimes in the same paragraph, by clerks who have not read the other one.

The Crisis and after

The Screaming Lemma is generally treated as a forerunner of the Crisis of the Fractured Lemma of AR 19,715, though not a cause of it. The Crisis was precipitated by the submission of Lemma 552-Δ-7, and the resemblance in designation has caused confusion in the indexes for four hundred years. The distinction, stated plainly in Index Corrections, Volume 40, is that the Fractured Lemma asserted two incompatible derivations at once, while the Screaming Lemma asserts one derivation at a volume no one can ignore. The first fractures the archive. The second merely disturbs it.

Nonetheless, the Lemma-Birds were inscribed with copies of Lemma 552-Δ-7 between AR 19,714 and AR 19,716, and certain of those copies were found, on examination, to have been overwritten in a hand that the Ornithographic Office has declined to identify. The feathered copies remain of uncertain ratification status, a phrase that appears in eleven separate Concordances and clarifies nothing.

Inventory of the seventeen derivations

The sub-letters are held in the East Annex of Recitation, cabinet 552, and are counted each year by the Office of the Standing Count. The Count's return for AR 19,802 records the following dispositions: four derivations classified as audible and intact; nine classified as audible and fragmentary; two classified as inaudible and intact, which the Count notes is "a contradiction in the object and not an error in the count"; and two classified as missing, with a marginal note in the Count's hand reading "ask Voss." Voss has been dead since AR 19,041.

A visiting researcher of AR 19,866, one Halloran of the Twelfth Aperture, requested permission to read the Screaming Lemma in its entirety in a single session. The request was granted on condition that he bring his own water.

Reading practice and current standing

Current practice requires that the Screaming Lemma be recited by two clerks alternately, so that neither is required to shout for more than a minute at a time, and that the recitation take place in a room with a door. The Screaming Pillars themselves are held under containment on Floor 1022, and the Echo Theory for Screaming Pillars has been applied, without success, to the Lemma's more fragmentary sub-letters.

The Lemma remains in active use in the teaching of acoustics, and appears in the Seven Refutations of the Unyielding Lemma as a cautionary example of what the Refutations call "an argument that will not be whispered." Readers wishing to consult the Lemma are advised to do so in the morning. The reading rooms are quieter then, and the clerks who staff them have not yet been shouted at.