Draft 7: Yet more typos and copy-paste errors I introduced while trying to fix the text. Added the /z/ law L10a.

Draft 6: More typos. Said anθtka for humankind instead of anθka in the lexicon. Added the -st coda.

Draft 5: Added two sentences at the end of the accusative overlay paragraph explaining how the “source” is conceived of in Laulai. Thanks to bradrn on the ZBB for suggesting the term “metalinguistic”.

Draft 4: Explaining the -am.

Draft 3: Mentioned the accusative overlay style. Death and typos.

Draft 2: Typos. Corrected one grammatical description.

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0. Introduction

0.1 The language and its speakers

Laulai [lau.ˈlai] (exonym: Neo-Arcadian) is spoken by some eight million people whose ancestors left the Earth in the sixth century AD and have been living ever since in armored holds strung from Mercury to the middle system. They are descended from an Arcadian hill people and from the brotherhood that came up into their valley out of Kroton carrying the Pythagorean doctrine.

The Laulai will tell you their name means lau “wave” + lai “beginning”: the first wave, those of the first rising, the Vanguard. It probably does not. Laulai is a substrate word, opaque in and older than Auloic. The brotherhood used it for the hill people they settled among. The Laulai think they are the master race of the solar system, but they continue to use the old name.

The brotherhood came out of Magna Graecia believing that number governs the world. In the highlands, they proved there is a small set of intervals, the serk or true intervals, such that a physical system brought into alignment with one does mechanical work. Provided that a mind is present proving the theorem, a hull built to the proportion of a serk in the appropriate units accelerates, and a resonator tuned to one turns a dynamo. This force is called vril †, a word that comes from late Latin. A people who were farming goats in 500 BC reached the moon in a thousand years propelled by this power.

The ratios are complicated. They are not the ratios the historical Pythagoreans wrote down: 2:1, 3:2 and 4:3. Finding a new one is the work of multiple lifetimes. Each guild knows a handful and keeps them secret.

The mathematics has to be done by a mind in real time. A serk on a plate doesn’t generate power by itself. A person (a loaded term in Laulai) has to understand the math and prove the theorem. Conducting the proof is physical work performed by a nervous system that makes it effective. The Laulai word for this capacity is sorm, the reach. The Laulai word for developing this ability is xamn, the waking. See §0.3 below.

0.2 The ksost

The ksost are planetary-scale globules of exotic matter. They come from beyond the firmament, singly and at shortening intervals. In the nursery, every Laulai child hears them coming when the sirens blare.

What is wrong with them. A ksost is mam, crooked. Everything within the firmament is built on proportions that resolve. Reduce a rib, a resonator, a hull or a moon, and the reduction terminates. A ksost does not. Its proportions keep running past every terminating algorithm the guilds know of, each one in a different direction.

They have no single size. Range it twice and you get two numbers that will not reconcile, though the target has not moved. Its extent is an interval rather than a quantity, so a rangefinder returns a kolt (bracket): between eleven and nineteen thousand. Everything downstream of the measurement inherits that bracket. Gunnery against a ksost therefore means filling a volume rather than hitting a point. The seventh guild would prefer to board the target.

Their insides are bigger than their outsides. The technical word is kolp, the fold. A boarding party can walk for four days inside a body that could easily be towed. The corridors are the same corridor appearing repeatedly, marked by nars (an open seam) a join where two surfaces meet at an angle that does not add up. The eye sees it as a shadow. When measured, you feel an edge that’s not there. Companies rope themselves together and pay the rope out behind them. That rope is the only environmental factor that can be trusted to have a fixed length.

They sound. Anything with proportions corresponds to a pitch. A ksost‘s proportions slide rather than settling, which the sixth guild’s instruments read as a sarn (a wandering tone). Broadcast through space along an etheric medium, it comes up through the deck before it can be heard. Crews describe it as a chattering of the teeth and a vibration in the bridge of the nose.

They damage their observers. Prolonged observation of a non-terminating figure affects the nervous system. The sixth guild calls it mamn (the crooking). The effect is contagious. First the inner ear stops agreeing with the eye, then the hands stop going where intended, then a person cannot visualize a proportion at all, a career-ending calamity. Hunters work off instruments and go by the sarn.

They shed. Behind a ksost there is a wake of rimp, crooked matter. It is cold, it can be picked up, but it will not stack, will not tessellate and will not sit still in a hold. Most of what the guilds know about the serk they learned by competing to get their hands on rimp. This makes it expensive. Storing it is an issue because crookedness is contagious.

They have purpose. They are not alive in any sense that can be classified using the syzygies. Nevertheless, they are purposive. Most of them go for a target: the sun, the moon, one of the outer holds, and often enough the Earth. One went for nothing anybody could identify. It is still floating in space at a point relative to other objects in the solar system.

The kinds. No two are alike, but hunters have field names for behaviors they keep encountering. The names are class VII.

θalm the plate: flat, tens of kilometres across, no thickness anybody has measured. Edge-on it is not there. It comes in slowly and it cuts anything it encounters.
šarn the singer: heard for eleven days before it was seen. Named on the sarn with the inner holds’ sibilant (§8.3, L9).
mnok the jesters: several thousand small, identical bodies sharing a single figure. Destroying any number of them has no effect: There is only one object, and none of its components are that object.
xasp the mouth: an opening. Things go in; rimp comes out.
kolp the fold: small outside, enormous inside. The only kind that has ever been mapped, differently each time.
arke the still one: entered, stopped, and has done nothing since. One is still out there. The seventh guild will not approach it and does not say why.

How they are fought. By proof. A hunting company goes out carrying the mathematics describing the limiting case of a serk and closes the gap: the prover holds the ksost‘s figure, states the construction and runs the algorithm. If the last step lands, the body is stitched to a resolving proportion, and the contagion halts. The verb is rakt, to close. A hunter does not say he killed it. He says it was closed. The language of the proof must satisfy some arithmological properties that will be discussed later.

What is left afterwards is a rakt-rim, a closed body: finite, measurable and cold. It now has a fixed size. Research halls will pay a fortune to get their hands on it if you can deliver it to them without succumbing to the contagion.

If the chain does not land, the ksost is remains itself and the prover is destroyed. He has put a great deal of vril through a ratio that did not resolve, with himself in the middle of it. What returns is a corpse or an imn-anθ (§0.3).

0.3 The child lords and the creatures of ash

The sorm (the reach), which lets a person hold a figure and put force through it, is at its strongest at about the age of seven and gone by about fifteen. This is because of secret ratios at work in the construction of the human body.

Laulai armies are commanded by children. A sen-mis, a child lord, goes to the war-shrine at four, is woken at six or seven. By eleven can hold a construction of forty steps while under fire and close it. The shrine trains them in occult mathematics and military sciences. An experienced sen-mis of thirteen with a good company behind her is a force to be reckoned with.

When adolescence arrives, the reach goes away. What remains is an imn-anθ, an ash-person: a former lord who cannot hold a conversation, and spends the rest of a long life muttering in a gallery. The Laulai keep them fed and warm and near the shrines because every so often an imn-anθ stops muttering and speaks one clean sentence: a θamn, an axiom, something seen entire and without proof. About one in nine of those turns out to be true and important. The rest are noise. An amanuensis sits with each of them and writes down their words.

A minority of lords return to their senses. This is an irk-anθ, one turned back. Most irk-anθ want to sell books or coffee in quiet shop somewhere on a low gallery away from crowds and attention. Some do other things. A mne-mis is a war-lord, a burnt child grown into a general who now sends other children in their place. A teu-anθ works at proofs in a hall. An orn-anθ sings esoteric songs with frightening words but an irresistible lilt. The general population fear and revere such people.

0.4 Earth

The Order says the earth is not defended by its inhabitants and would not survive one ksost on its own. That’s what is used to justify the way the earth’s population is treated.

A hold runs on valves, ducting, hull-plate, boring and waste. This work is done by abducted mortals and bred slave populations. Mortals are brot †, class V, the class of seed, fire, livestock and grain (§4.2). The bred lines include the kauzes (diggers), the sipzes (hammerers), the nalzes (cooks), the pmizes (hunters), and the falzes (lovers), bred to lure hapless mortals into Laulai congregations on earth.

The congregations (brot-launt) are societies the Order plants on Earth through falzes intermediaries. The congregation often owns things like a pedigree book, a ritual space and a liturgy. The oldest are Anglo-German in the nineteenth-century. They were organized around two interests, heredity and psychic powers, both of which were brought in by the mortals themselves. Through the congregations, the Laulai influences Earth’s supremacist movements and most of its governments. This approach is cheap, congenial and self-recruiting. The congregation is also a bulk source of slaves. Members who vanish are written up as casualties of violent clashes with rival extremists. They are in fact in an off-world hold, tightening bolts.

A congregation is also used as an instrument. The ninth guild sends down a serk: a ratio, instructing the congregation’s inner circle to hold its tones, in unison, at a fixed hour, as long as the meeting lasts. Several hundred nervous systems in phase constitute a powerful resonator that can be used from space.

When quality matters more than numbers, the press-gang is conducted. A pmizes crew, coordinating with a congregation’s intel, abducts the targeted individuals directly at night, off roads and out of beds. The taken are called xrešt, a noun in class X. Accordingly, they are carried as cargo.

To meet mortals directly, the eighth guild runs a showing (kišt) with an ongzes, a seeing-engine. Mortals call the Laulai Nordic aliens despite most of them having a visibly Mediterranean appearance, not unlike that of olive-skinned Greeks. The small grey incurious ones are kauzes or pmizes.

The eighth guild also handed Earth’s occultists the word vril, which the Laulai got from the Romans (§9.3).

0.5 The Auloic family

Auloic is a small family of agglutinative languages once spoken around the Peloponnese, in the highlands and the karst. It was pushed out of the lowlands by Greek before the classical period. Auloic is partly reconstructible from Laulai, from scattered Arcadian and Messenian glosses, from a few hundred place-names, and from two inscriptions nobody fully understands.

Branch	Range	State
Arcadian	the central highlands; the largest branch, and the only one with internal diversity	one daughter survives: Laulai
Triphylian	the western foothills and the coast north of Pylos	extinct by the third century BC
Kynourian	the eastern seaboard between Argolis and Laconia	extinct; two inscriptions, undeciphered
Aigialic	the north coast of the Peloponnese	extinct; place-names only

Laulai survives because its speakers left the planet. Every other Auloic variety was absorbed into Greek in the ordinary way. The hill dialects that stayed on the surface were Greek by the second century AD and gone by the fourth. Laulai has been called Neo-Arcadian in some comparative literature.

Typologically Auloic looks like the other pre-Greek languages of the eastern Mediterranean and the Caucasus rim: agglutinating, suffixing on the noun with a long chain, prefixing on the verb with a field of directional preverbs and class markers, a small vowel system, class agreement, case stacking on dependents, relativization that reaches only the argument that stands, subordination done with non-finite chains and with case endings on the verb rather than with conjunctions. Almost all of that is still there in Laulai, some in fossilized form (§8).

The Laulai describe themselves as plask †, the noble Pelasgians mentioned by Homer, the aboriginals of Greece who were said to be older than the moon. Arcadian antiquarians did claim that. There were ancient writers of fiction who mentioned that the moon’s own people were an Arcadian tribe. The Laulai read these as prophecy and claim to have fulfilled it when they settled the moon in the sixth century.

0.6 The history, in brief

The Imposition (θalt, “the casting-over”), from about 500 BC. The brotherhood replaced fifty-seven words: the numbers above four, the elements, the lights, the nearest kin, four parts of the body, and the objects of religion. Father and mother went. Daughter and elbow stayed. Fire, water and air went; the earth stayed. God, soul and world went, while the altar, the oath and the libation are Arcadian to this day. There is no Greek word in Laulai for a valve, a bearing or a seam.

The vowel-loss, within three generations, and unrelated to the above. The unstressed vowels dropped, first medially and then finally. A language of polysyllabic stems with long suffix chains became a language in which three stems in four have one syllable (§8.3).

The reinterpretation, from about 300 BC. The brotherhood, now several generations in and speaking the language natively, looked at the evolved speech and had a revelation. They saw a language where no noun can be mentioned without a number on it, where nouns fall into opposed pairs, where every act is marked for direction. To this they added by decree a tenth noun class, at least two case endings, a polarity system, and the arithmetic of §7. Each addition sits in a subsystem that does not quite fit.

The descent, from about 200 BC, into the karst under the home valley. The surface holdings were kept for six centuries and then gradually let go.

The Withdrawal (tnošt, “the clearing-out”), completed in the sixth century AD. The moon was taken during this time. The outer holds were founded six centuries later.

The limit, found about 1100 AD and confirmed by the loss of nine hulls over the following five centuries. The psnai-lont, the firmament, is an invisible wall around the solar system that has prevented organic life from passing through so far. The Order only offers metaphysical reasons as to why it exists. The Laulai are a cosmic aristocracy that cannot leave its own house.

The incursions, older than the official chronicles, arriving at shortening intervals for three hundred years.

0.7 The registers

There are three registers. Everybody uses at least two of them daily.

Laulai proper, the nursery-speech, medr-lok (mother-word). Everything in this grammar is true of this register unless noted otherwise. It is what the shops, the galleys and the gun-decks use.

Tkalok [tka.ˈlok], tka “ten” + lok “word, ratio, account”: the register that mathematics is done in. Tkalok is Laulai with the Hellenic stratum obligatory even when the vernacular has an Arcadian synonym, with tone written (§1.6), with the class prefix obligatory on the verb (§5.3), with the direction of every act stated (§5.2), and with the balance of §7.2 in force. Every proof, every construction, oaths, official correspondence, and orders that must be carried out to the letter are in tkalok. Children learn it in the trial-hall from ages nine to fourteen. The second guild’s war-shrine takes children at four and teaches this register from the nursery, because a sen-mis has to compose it in real time while contagion might be entering through the hull.

Fot-lok, slave-speech. Reduced Laulai spoken by the bred lines and the taken as a common language: no concord, no preverbs, no converbs, three cases, no balance. It is an offence for a person to speak it except downward. It has an ordinary plural, which the standard grammar does not allow (§4.1 ii), but which is nevertheless spreading upward from the lower galleries.

0.8 Pythagorean interpretation of the grammar

Subsystem	Inherited from Proto-Auloic	Interpretation
Numeral suffixes on nouns (§4.1)	obligatory enumeration	qualitative number: every mention states a thing’s arithmological state
Noun classes with concord (§4.2)	nine semantic classes	the Table of Ten Opposites: a tenth class decreed to make the count
Class agreement on the verb (§5.3)	polypersonal prefix field	the act is stamped with the kind of thing it applies to
Directional preverbs (§5.2)	four orientational, plus a growing locational set	the decad of directions, and the ladder of descent and ascent
Postpositions (§4.3)	seven, no case morphology	ten emanation cases, two of them Greek, sorted into a tetraktys
Case stacking (§4.4)	dependents agree in case	the emanation runs down the whole phrase
Converb chains (§5.6)	clause-chaining, non-finite	the proof
The joints (§5.6)	a verbal noun taking the postpositions	ten of them, sorted into a second tetraktys: the emanation runs through the act
The relative prefix (§6.6)	a second slot in the agreement field	nothing: the ninth guild doesn’t like that it seats a doer in the case of what stands
Rest / motion aspect (§5.1)	stative vs. dynamic verb classes	being over becoming
Pitch accent (§1.6)	three registers	the fourth and the fifth sounded in every sentence
Monosyllabic root canon (§1.3)	an accident of vowel-loss	the triad as the shape of what exists
—	nothing	polarity: peratic and apeiric (§4.2)
—	nothing	the decad-balance on an effective step (§7.2)
—	nothing	the ten guilds read as the ten syzygies (§4.2)

The rows with “nothing” in the middle column are where the brotherhood constructed rather than interpreting the grammar. The other components were already there and were given a better story.

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1. Phonology

1.1 The consonants

The primary decad. Ten consonants in a triad, a triad and a tetrad. The doctrine has found a way to count them that comes out at ten, which took some doing.

Rank	Name	Members	Manner
1	Limit triad (lont)	/p t k/	voiceless stops
2	Breath triad (psnai)	/f θ s/	voiceless fricatives
3	Mediating tetrad (arm)	/m n l r/	nasals and liquids

A word may also begin with its own nucleus (a “head”, ir “lip”, ont “to be”). The zero onset is not written and is not counted, being the silence out of which the ten proceed.

Proto-Auloic had ten consonants, p t k s m n l r and two glides w and j. The glides went (§8.3, L1) and /f/ and /θ/ rose to take their places in the count. The decad has always existed, but it has not consisted of the same consonants in the past.

The ogdoad of descent. Eight further consonants occur, none of them primary. Each arose from the decad by a law that has since stopped operating, and each is now partly independent.

Segment	Arose by (§8.3)	In the corpus	Status
š	*s beside a dental, and initially in the inner holds	20 stems	admitted to the standard
č	*k before a front nucleus	21 stems	phonemic; the law has stopped
x	*k aspirated, word-initially	35 stems	phonemic
z	*s voiced between nuclei	34 stems	phonemic
d	voicing of *t	42 stems	phonemic
g	voicing of *k	20 stems	phonemic
b	voicing of *p	15 stems	rare; the labial resists
ð	Greek d spirantised, in the oldest loans only	3 stems	fossil

The akousmata hold that the labial, being the mouth’s boundary, will not be made to sound. The /b/ is duly rare, and is considered uncouth among higher circles. /ð/ survives in ðaur † “water” and oðas † “path,” both Greek from the first century of the Imposition. This makes them older than the law that would otherwise have caught them.

Two segments occur in one word each. /ž/ in džait “to live,” which has a commoner variant zait with no difference in sense. /v/ in vril † “motive force, the work a true interval does,” which is Latin and came in late enough to miss the sound laws (§9.3).

1.2 The nuclei: the tetrad and the yoked triad

The four simple nuclei are /a e i o/. The language has four roots consisting of a single simple nucleus, and each is also a word.

a “head” • e “brother” • i “bird” • o “long”

The tradition calls these the four monads. A great deal of commentary rests on them. Proto-Auloic had five vowels. The fifth was lost by an ordinary sound change (§8.3, L11). Languages in the region tend to have a four-vowel system.

The three yoked nuclei are the diphthongs ai au eu, each counting as one nucleus and one syllable. Four simple and three yoked make seven, “the number without mother or offspring.” The doctrine says that’s why the voice can be counted but not generated. They are the residue of the lost glides (§8.3, L1).

Hiatus is licit in one sequence only. Two nuclei may stand together if and only if they are i + o: xio “north,” plio “dissonance,” θio “rumor,” tio “shoe,” nio “to refuse,” pio “delight” and io “echo”. Every other apparent vowel sequence in the corpus is one of the three diphthongs. A diphthong, being two morae already, never stands beside another nucleus. A suffix that would break the rule either takes its consonant-lean ally, or it’s swallowed (§1.5, laws 4–5).

/u/ is not a vowel. It occurs as the closing element of au and eu, and otherwise in one word: nukt † “night,” which L11 reached too late.

Length is not phonemic and is not written.

1.3 Word shape

Laulai is a monosyllabic-root language: 787 of the 1,106 distinct stems in the lexicon have exactly one nucleus. The property is twenty-three centuries old and falls straight out of §8.3 L3–L4.

The triliteral canon. The lawful root is a triad of segments, usually onset–nucleus–coda: lok, met, θom, xer, paur, tas, nam, pok. 531 stems have exactly three segments and 364 of those are CVC. The doctrine reads this as the phonological form of the teaching that whatever exists has a beginning, a middle and an end.

Shape	Count	Name	Reading
1 segment	7	the monads and the yoked	prior to the triad, not deficient
2 segments	122	unfinished (nesrak)	a root that has not closed
3 segments	531	canonical	the triad
4 segments	204	burdened	a triad carrying a fourth
5+ segments	242	compound	two roots, or a root and a suffix

The seven single-segment roots are exactly the seven nuclei, each standing alone as a word: a “head,” e “brother,” i “bird,” o “long,” and the yoked ai “to run,” au “brown,” eu “ancestor.”

The tetrad cap. No phonological word exceeds four syllables, suffixes included. Longer grammatical words break into two phonological words at a juncture, written –. Every count starts again on the far side of it. A hunter’s rank, a hull’s name and a forty-step construction are correspondingly full of hyphens.

1.4 Sonority: onsets, codas, and what may cross a boundary

Ranked: stops and the affricate /p t k b d g č/ = 1; fricatives /f θ s š x z ð/ = 2; nasals /m n/ = 3; liquids /l r/ = 4.

Onsets ascend, with three allowances. A word-initial cluster must rise (pl, pr, tr, kl, kr, kn, pn, tn, gn, dn, br, dr, gl, gr, ml, mr, nl, nr), and two nasals may stand level (mn-, nm-). To this the language adds:

1. The breath allowance. A voiceless fricative may be followed by anything: θp-, θm-, θk-, θs-, sp-, st-, sk-, sn-, sm-, šn-, štr-, xt-, xp-, xk-, xm-, xn-, xl-, xr-, fn-, fs-.
2. The sigmatic onsets. ps-, ks-, ts- and č- behave as single segments and may be followed by anything.
3. The dental onsets. pt- and kt-.

Everything else is unlawful initially. In particular a sonorant before an obstruent (*lnθ-, *rmp-, *nd-) and a stop before a stop (*tk-, *tp-). Nevertheless, the lexicon contains one such stem, the numeral tka † “ten” (§9.3).

Codas descend or hold level: -rt, -mp, -nt, -rn, -mn, -ls, -sp, -rm, -kt, -rk, -nk, -ns, -lt, -ln, -nd, -st, -št, -ng, -rs, -rp, -ms, -lm, -mt, -lk. Sixteen stems had rising codas. Eleven were repaired and five protected: dendr † “tree,” kosm † “world,” makr † “great,” medr † “mother,” petr † “stone.”

The sigmatic codas -ps, -ks, -ts are allowed as the mirror of the sigmatic onsets: ops “eye,” aps “from,” eks “six,” lits “gold,” niks “vibration,” saits “you (pl).”

Inside a word, the coda’s rank must be at least the following onset’s, or the following consonants must themselves form a lawful onset. The second escape does most of the work: mnis-met syllabifies mni-smet, because sm- is lawful under the breath allowance.

What the law allows and forbids. *km-, *θt- and *-tp are all lawful by the rules, but they are unattested.

1.5 Sandhi: the five contraction laws

1. Like nuclei fuse (the unison): a + a → a. The fused vowel is long. Length is not written and the syllable counts once.
2. Like consonants fuse: lok + kat → lokat; met + tel → metel.
3. Unlawful boundaries take the linking -a-: tešt + kne → teštakne.
4. Hiatus resolves to the one licit sequence. Where suffixation would put two nuclei together and the result is not i + o, the suffix appears in its consonant-lean ally: accusative -am ~ -m, ablative -aps ~ -ps. Three nuclei in a row are forbidden.
5. The absorption law. Before an aspect suffix a stem-final nucleus is absorbed, diphthongs included: pli + ai → plai “is reckoning,” sni + om → snom “is built,” θko + ai → θkai “is condemning,” nau + ai → nai “is charging.” The same absorption applies to a name taking an arithmological suffix in the call (§5.9): Arna + ek → Arnek. The homophonies this produces, such as nai “is charging” beside nai “yarn,” are tolerated.

1.6 Tone

There are three tone-registers, standing in the ratios 4:3 and 3:2, so that a well-formed sentence sounds the fourth and the fifth. They are named after the words that describe them:

• θor (low, “the resting”): stasis-aspect verbs, monadic and decadic nouns, verbs in fo-.
• ske (mid, “the middle”): kinesis-aspect verbs, apeiric-pole nouns.
• θis (high, “the raised”): peratic-pole nouns, verbs in la- (§5.2).

Like languages in the region, Proto-Auloic had a three-way lexical pitch accent. Pitch that once distinguished words was reinterpreted by the brotherhood to distinguish grammatical categories. The assignment was rigged to occur in the two consonant intervals, which sounded pleasing to adepts trained in Pythagorean musical practices.

The working orthography does not write tone. Tkalok writes it wherever polarity would otherwise be ambiguous. In 1846, a company of twelve took a peratic reading off an apeiric noun in a chain spoken aloud on a gun-deck. They closed it, but eleven of the twelve died doing it. Nobody has since been able to reconstruct what they actually proved.

1.7 Compliments

These two words carry considerable social weight.

rošt “calibrated” is said of a word, a phrase, a hand, a gait or a face that has been brought to a standard and can be checked against it. tilt “tuned” is said of something that stands in a ratio to something else. The first is a property of a thing along with a standard. The second is a property of a relation, and is the higher compliment. A root of exactly three segments is rošt. A sentence whose tone-contour actually sounds the fourth and the fifth is tilt.

To be called mern-rak, equal to the sum of one’s own parts, is the highest compliment one Laulai pays to another.

Speakers of fot-lok are not described as rošt or tilt.

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2. Numerals, ratio and measure

The numerals are described early in this grammar because everything else is built out of them. Nine of the following ten numbers are the obligatory number suffixes on every noun (§4.1). The same nine supply the values of the balance (§7.2). Two of them are the two perfections. One occurs in the name the Order gives its own register.

1 en, 2 di, 3 tre (combining tri-), 4 tra, 5 pent †,
6 eks †, 7 sept †, 8 okt †, 9 nop †, 10 tka †

All ten are borrowed, in two layers. Five to ten came in with the brotherhood at the Imposition and are Greek except for two (§9.3). One to four arrived a great deal earlier from an Indo-European neighbor in the lowlands, possibly an early Greek dialect or something else spoken there. They were already old and native-feeling by the time the brotherhood arrived. tra “four” is the Greek combining form τετρα- with its first syllable gone, an effect of the sound change §8.3 L2. tre cannot be primitive at all, because Proto-Auloic had no initial clusters (§8.2). See §8.7.

šal “thousand” is the only numeral with no source in Greek, in Italic, or anywhere else, and is the best candidate for a pre-IE Auloic number.

Above ten, there is a reversion: 11 tkakaten (tka-kat-en). 100 ektan, 1000 šal, 10 000 tkašal, the perfect myriad. Long figures are recited positionally, digit by digit, with tas “empty” for zero: 3047 is tre tas tra sept.

Ordinals take the essive: enkne “first,” dikne “second,” trikne “third,” trakne “fourth.” Because the tetrad is the sworn number, trakne means both “the fourth” and “warranted, foursquare, good”.

Units are interval-derived. Lengths are string-ratios of the standard monochord, the lir. Pressure is counted in ditensi steps, each twice the last, making it a logarithmic scale. Pitch and frequency are given in tritensi and tratensi degrees. A declared allowance is a rant.

2.1 The serk

A serk is a true interval: one of the ratios that physically affect the world. There are known to be at least forty. The guilds publicly admit to knowing thirty-one among themselves.

A serk is not a ratio that’s easy to comprehend. The ratios the historical Pythagoreans wrote down (2:1, 3:2, 4:3) build scales but were otherwise physically ineffective. The brotherhood spent its first two centuries in the highlands discovering serk that were long, ugly and irrational. Each has to be held to a tolerance that is beyond human understanding (i.e. the reach) under ordinary circumstances. When a mind reaches one as the outcome of a proof, vril is produced. The hulls are powered by vril.

It is openly taught how to search for a serk, how to prove a candidate, how to write it, how to run a construction on it and how to fail safely. But the values of the effective ratios are guild secrets.

2.2 The two perfections

A number equal to the sum of its own parts, itself excepted, is mern-rak, “part-whole.” The guilds know two:

eks †: 6 = 1 + 2 + 3
septakt †: 28 = 1 + 2 + 4 + 7 + 14

They have been looking for a third for two thousand years.

Six governs things. The hexadic (§4.1) means in healthy running balance. This could refer to resonant qualities in parts of a machine.

Twenty-eight governs sayings. 28 is the triangle of seven as 10 is the triangle of four. If the decad is the tetrakt † then twenty-eight is the septakt †, the heptaktys. Seven is the number of the nuclei, the wandering lights and the metals, “the number without mother or offspring.” Sworn speech balances at 28 (§7.3).

The Laulai use a lunar calendar. All their temporal cycles reset at 28: the watch is 28 hours, the month 28 days, the turn of duty on the firmament 28 watches, and the oath of descent is sworn in the 28th year of life.

The ordinal of 28 is septaktakne, with the linking -a- of §1.5 law 3: “twenty-eighth; sworn, perfected, unimprovable.” The seventh guild calls hunters who return by that title.

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3. Morphological overview

Laulai is agglutinative. It suffixes on the noun and both prefixes and suffixes on the verb. The verbal prefix field is the last surviving piece of a much larger scheme (§8.4). Morpheme order is unchanged from Proto-Auloic. The doctrine reads it as emanation: the most inherent categories nearest the root, the most relational farthest out.

Noun template:

ROOT – (DERIVATION) – ARITHMOLOGICAL NUMBER – (POLARITY) – CASE – (STACKED CASE)

Verb template:

(PREVERB) – (CLASS or RELATIVE) – ROOT – (VERSION) – ASPECT or JOINT – (NUMBER)

Noun class is inherent, but unmarked on the noun. It surfaces as a prefix on agreeing words and the verb (§5.3). Polarity is carried by tone or written with -lon / -pol where tone is unavailable.

The agreement slot takes the class prefix or the relative če- (§6.6). The aspect slot takes an aspect or one of the ten joints (§5.6).

Because roots are monosyllabic and the cap is four syllables, a fully loaded verb of preverb, class, root and aspect is full. Anything further breaks at a juncture, and speakers feel the constraint. A sen-mis under fire talks in short bursts with audible hyphens.

3.1 The templates by register

Slot	nursery-speech	tkalok	fot-lok
arithmological number	obligatory	obligatory	normally obligatory, but dropped in some contexts
polarity	tone only	tone; written -lon / -pol where tone will not carry it	absent
case	obligatory	obligatory	archic, accusative, locative; the rest absent
stacked case on dependents (§4.4)	usual	obligatory	absent
class concord on adjectives	obligatory	obligatory	absent: adjectives stand bare
class prefix on the verb (§5.3)	optional	obligatory	absent
aspect	obligatory	obligatory	obligatory
preverb (§5.2)	optional	obligatory	absent
the joints (§5.6)	all ten	the seven old ones; -aps, -am, -os avoided	the bare joint only
chaining	usual	obligatory in proof	absent: clauses are juxtaposed
the bound form (§6.6)	usual	absent: it cannot be checked	absent
the noun of the act (§6.7)	usual	avoided; it costs a number	absent
verbal number	optional	obligatory	absent
the balance (§7.2)	not in force	in force	not in force

Slave-speech has no preverbs and no converbs. A fot-lok verb is root and aspect and stops. A narrative in this register is a string of short sentences laid end to end. It is the only variety in which a bare uncounted plural is attested.

The arithmological number is obligatory in all three. Everyone in the holds, person or slave or cargo, normally states the arithmological state of everything they mention. However, fot-lok sometimes drops them. There is an example in the texts.

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4. The noun

4.1 Arithmological number: the ten inflections

Every noun obligatorily inflects for one of ten numbers, each carrying a quantity and a qualitative association. There is no number-neutral noun. Every mention of a thing is a claim about its arithmological state.

The suffixes are the numerals in their combining grade. Proto-Auloic had obligatory enumeration. Vowel-loss welded on the suffixes on. The brotherhood supplied post-hoc justifications.

The paradigm, on elm “engine” (class VI):

#	Number	Suffix	Form	Quantity	Doctrinal and technical sense
1	Monadic	-∅	elm	one	the engine as unique original: the master-pattern, the thing others are struck from
2	Dyadic	-di	elmdi	two	two engines coupled in opposition; also “some engine or other”: the indefinite, the unvetted, the mass-produced
3	Triadic	-tri	elmtri	three	engines in mediated concert; a balanced triple installation
4	Tetradic	-tra	elmtra	four	the engine as installed, founded, warranted; the number used in deeds
5	Pentadic	-pen	elmpen	five	the engine as generative and live, married to its source
6	Hexadic	-ek	elmek	six	the engine in healthy running balance; the well-tempered plant
7	Heptadic	-sep	elmsep	seven	the solitary engine; a one-off, an experiment, a thing with no fellow
8	Ogdoadic	-ok	elmok	eight	massive material completion: heavy plant, the built solid, and dead plant
9	Ennadic	-nop	elmnop	nine	the engine at the limit: end of service, redline, the horizon of failure
10	Decadic	-ka	elmka	ten / all	all engines; the engine-park as perfected totality; engine-kind

Notes.

(i) The decadic is -ka, not -tka: the numeral sheds its stop in suffixation. The doctrine interprets this as the decad, having arrived, lays down what it carried. Phonologically, tk- is unlawful inside a word.

(ii) The decadic does the work of a plural. There is no separate stem for “humankind” or “everyone”: both are anθka, the decadic of anθ “person.” A bare uncounted plural, a multitude that has not been numbered, cannot be said in the standard language. The doctrine is delighted about this. The Order congratulates itself on having created a language where talk of collective punishment is difficult. This is questionable, if for no other reason than that the verb does have a collective suffix.

As a consequence of the above, every available form either singles out or completes. The monadic brot is the unique original, the pattern others are struck from. The dyadic brotdi is some mortal or other, and a hull’s orders carry the dyadic. The decadic brotka is mortal-kind, complete, finished, needing nothing, and is of the same order as engine-kind. Between the specimen and the finished kind there is no definite multitude of unknown size, such as the several thousand million people now alive on a planet, uncounted and unfinished.

Fot-lok has a plain plural and speaks of mortals with -s. The standard grammar calls this a corruption.

(iii) Quantities above ten obey reversion: eleven engines are elmka elm, “all-and-one-more.”

(iv) The qualitative readings are taught and examined in the halls. The difference between the ogdoadic and the ennadic is the difference between a hull that is heavy and one that is about to stop being a hull.

(v) Number on persons. The paradigm is the same on a person as on an engine. A Laulai speaks of himself in the monadic, of a colleague in the monadic, of a guild in session in the decadic, of a bred line in the decadic (falzeska, “the whole of that line”), and of an individual slave in the dyadic, the number of “some object or other.” A slave in the tetradic has been inspected and warranted, which happens to breeding stock. A slave in the ogdoadic is dead. The one number no slave may take is the monadic.

(vi) Example with a ksost. The Watch signs at the ennadic, ksostnop, which could mean either, “at the limit” or “the ninth of the tally” depending on context. A hunting company that has seen it could report at the heptadic, ksostsep, “the one with no fellow”. Seers come back saying the ogdoadic, ksostok, a great built solid. On its own, the number system gets no nearer to a description than this. §4.2a explains the adjectives.

The pentadic would assert that the thing has a source inside the limit. The tetradic would say it was installed on purpose. These are unattested.

4.2 The ten syzygies: class and polarity

Every noun belongs inherently to one of ten syzygies, yoked pairs of opposites. In any clause, a noun stands at one pole: peratic (limit column, θis tone, suffix -lon, from lont “bound”) or apeiric (unlimited column, ske tone, suffix -pol, from pol “many”).

Class says what a thing is. Polarity says what state it is in right now. Handedness, on and off, live and dead, true and warped are grammatical.

Syzygy	Opposition	Concord	From	Typical membership	Peratic	Apeiric
I	limit / unlimited	me-	met “measure”	measures, media, fields, fluids, times	bounded, metered	unbounded, raw flow
II	odd / even	pa-	pas “number”	number, data, proof, record	odd, prime, indivisible	even, splittable
III	one / many	an-	anθ “person”	persons, bodies, aggregates, parts	the individual	the aggregate, the crowd
IV	right / left	xe-	xes “wheel”	thread, gearing, rotation, cordage	right-handed, clockwise	left-handed, widdershins
V	generative	sa-	saz “animal”	sources, couplings, seed, fire, the bred	emitting, source, plug	receiving, sink, socket
VI	rest / motion	el-	elm “engine”	engines, mechanisms, resonance, sound	at rest, cold, parked	running, live, hot
VII	straight / curved	θo-	θom “straight”	rod, plate, edge, structure, extension, and the ksost	straight, true, closed	curved, crooked, open
VIII	light / dark	fa-	faut “light”	lamps, rays, images, color, the waking	radiant, visible	occluded, occult
IX	good / bad	so-	son “good”	evaluation, temper, obligation, the sacred	benign, sound, owed	malign, awry, forfeit
X	square / oblong	ne-	anbe “square”	form, jig, casing, vessel, building, stuff	true, calibrated	warped, out-of-true

Nine of the classes are inherited, unlike the ninth class. Nine are recoverable as Proto-Auloic noun classes with straightforward semantic cores, though the meanings have changed over time. Class IX has no core meaning, holds a quarter of all nouns, and cannot be rigorously defined. The brotherhood needed ten because the Table of Opposites has ten rows. Whatever would not fit in the other nine went into IX, which was glossed good and bad. It will accept anything.

Polarity was mostly the brotherhood’s. Proto-Auloic had a definite/indefinite distinction on the noun, of the kind the languages of the region generally had. The Order reinterpreted this as limited and unlimited, which is why the two suffixes come from the words for “bound” and “many”. This subsystem may only be four hundred years old, if that.

Agreement. An adjective takes the concord prefix of its noun’s syzygy and the noun’s polarity as a suffix.

• ðaur merilon: “the water, cold-and-bounded”: in the tank, measured, or possibly for you to drink
• ðaur meripol: “the water, cold-and-running”: on the deck, in the gallery, possibly someone’s problem
• elm elsonlon: “the engine, sound-and-at-rest”: cold, parked, well
• elm elkankpol: “the engine, malign-and-running”: live and misbehaving, one of the first phrases an apprentice learns
• snip xeθomlon: “a true right-hand thread”, against snip xeθompol “a true left-hand thread”

Using a suffix instead of a clause as in other languages helps with brevity.

The ten guilds are read as the ten syzygies. Each guild owns the vocabulary of one class, examines in it, and takes its name as the decadic of its own emblem. The guild is, in this reading, the perfected totality of a craft. A child enters one at nine and is thereafter that guild in dress, in vocabulary and in what it is licensed to work on. A guild is a path. People can and do leave.

Class	Guild	Name	Emblem	What it is for
I	first	mniska	mnis “gauge, judgment”	measurement, chronometry, and the Watch on the firmament
II	second	xepka	xep “ledger”	number, proof, reckoning: its inner shrine is the mneka, “the War,” the child lords
III	third	nomka	nom “law”	persons, pedigree, judgment between Laulai
IV	fourth	kertka	kert “gear”	transmission, mechanism, the fabric of the holds
V	fifth	θauka	θau “seed”	the Seed: gene-lines, the bred races, the stock of the Earth
VI	sixth	armka	arm “harmony”	resonance, sound, medicine, maintains the largest collection of serk tables and proofs
VII	seventh	relka	rel “blade”	edge and structure: its inner shrine is the hunt
VIII	eighth	ongka	ong “vision”	the waking, the seeing-engines, and the showings
IX	ninth	manska	mans “hierophant”	the Order itself: rite, oath, obligation, the sacred
X	tenth	oðaska	oðas † “path”	hulls, holds, cargo: therefore the press-gang, responsible for abductions

The war-shrine. Mneka conducts its intake at four, before the trial-hall age, because a commander has to compose a construction in tkalok real time while contagion might be entering through the hull. The second guild concluded long ago that children who learn the register at nine will rarely do that well. The children it produces are sen-mis, child lords. (The compound is attested centuries before the shrine existed. Originally, it meant a lord who had not yet come of age, a young master.) They are taught arithmological games scored by balance. Secret ratios are used in awakening occult powers. A sen-mis of eleven can carry a chain of forty steps in her head and put the last step down while the deck is rotting away.

Where the races sit.

	Stem	Class	Concord	What follows
a Laulai	anθ † “person”	III	an-	the individual against the aggregate; may be monadic
a mortal of Earth	brot † “mortal”	V	sa-	the generative class: seed, fire, livestock, grain, the grown and the bred
a slave	fot “slave”	V	sa-	as above; dyadic by default
a bred line	falzes, kauzes, pmizes	V	sa-	named with the instrument suffix (§4.6)
one of the taken, in transit	xrešt	X	ne-	cargo: form, casing, vessel, stuff
a ksost	ksost	VII	θo-	straight/curved, and usually at the crooked pole (§4.2a)

brot is class V and anθ is class III, even though in Greek they were synonyms. Ἄνθρωπος and βροτός both meant a human being. In Laulai they had different classes. Twenty-five centuries later, anθ takes the person-class, the person-pronoun and the emanation cases in full while brot takes the class that also holds se “ox,” θi “sheep,” θau “seed” and tong “harvest.” In Laulai a mortal is not a bad kind of person. It is a crop.

Slave was class III until 1743. Every text before that date has fot in the person class with the concord an-, the expected treatment of an Arcadian word for a captive taken in a hill raid. Every text afterwards has class V. The shift is abrupt, and it began in the same decade as the first bred lines (§9.5).

4.2a The crooked class

The ksost is class VII, straight/curved, and does not usually take the peratic pole, ksostlon. However, a hunting company that has closed one (§7.1) can put -lon on a ksost.

• It takes concord. θo- like any other class VII noun. An adjective modifies it in the ordinary way: ksost θomampol, “the ksost, crooked and open.”
• Descriptive vocabulary is geometric:

Adjective	With concord	What it says
mam	θomampol	crooked; out of true in the general way
θoln	θoθolnpol	unclosing: the reduction does not terminate
kolt	θokoltpol	bracketed: it has no single measure, only a range
tirn	θotirnpol	doubled: the same part occurs more than once in one body
nirn	θonirnpol	over-hollow: the inside is larger than the outside
saun	θosaunpol	sounding: it is giving off a sarn

A specimen sighting, off the firmament, with two adjectives on it:

ksostok θokoltpol θosaunpol psnai-lontdips tiθošainai.
ksost-ok | θo-kolt-pol | θo-saun-pol | psnai-lont-di-ps | ti-θo-šain-ai
ksost-OGD(8)-ARCH | VII-bracketed-APEI | VII-sounding-APEI | firmament-DY(2)-ABL | HITH-VII-come-KIN
A ksost, a great built solid, bracketed and sounding, is coming this way, in across the firmament, from which station I know not.
Balance: 8 + 2 = 10 → 1. rak.

The dyadic on the firmament says some station or other (§4.1) because the range is too uncertain for the current instrument. The ogdoadic on the ksost says it is a great built solid. θokoltpol says the gunners will be given a bracket and not a range. θosaunpol says the resonance galleries heard it first. It may have been coming for some days.

4.3 The emanation cases

There are ten cases, arranged as the tetraktys: one source, two relational, three mediating, four worldly. The archic is the bare stem and has no source. Two are Greek endings imposed on the language. Five of the remaining seven have close Greek look-alikes: met beside μετά, es beside εἰς, aps beside ἀπό, kat beside κατά, tel beside τέλος. Only mon and kne are native beyond argument. If the five are loans, then seven of the ten cases postdate the Imposition. This means the case system in its current form is not inherited at all. It is unknown whether it evolved naturally like a creole through the use of Greek technical vocabulary.

Row	Case	Suffix	From	Function
1	Archic	-∅	—	the thing as it stands: source, and undergoer (§6.2); citation form
2	Dative	-mon	mon “to, for”	recipient, goal, the other
2	Ablative	-aps ~ -ps	aps “from, than”	separation, origin, comparison; and the ground of a saying
3	Locative	-es	es “in, at”	in, amid, at the middle of
3	Instrumental	-met	met “with, by”	means; and the doer of a kinesis verb (§6.2)
3	Comitative	-kat	kat “and”	accompaniment: together with
4	Accusative	-am ~ -m †	Greek	the affected patient, when it is definite and matters
4	Genitive	-os †	Greek	of, made of, belonging to
4	Essive	-kne	kne “likeness”	in the role of, in the form of
4	Terminative	-tel	tel “end, death”	unto, back to, culminating in

A note on -am. The accusative is unusual among the Greek borrowings. Attic and every dialect the brotherhood could plausibly have carried out of Magna Graecia mark the accusative singular in -ν, not -μ. However, word-final -ν regularly assimilates to -μ before a following labial-initial word, a phenomenon attested even in Greek epigraphy, where τὸν is occasionally spelled τὸμ ahead of πατέρα. The brotherhood is thought to have taken the ending not from the grammatical paradigm but from continuous speech, possibly a set liturgical phrase heard over and over ahead of a labial-initial noun. What was borrowed was the allomorph. This is not unlike what happened to tra “four” (§2), another Greek fragment where the assimilated form was kept rather than its dictionary entry.

The paradigm, on psnai “aether, sky, breath” (I) and lok “word, ratio, account” (IX):

Case	psnai	lok
Archic	psnai	lok
Dative	psnaimon	lokmon
Ablative	psnaips	lokaps
Locative	psnaies	lokes
Instrumental	psnaimet	lokmet
Comitative	psnaikat	lokat
Accusative	psnaim	lokam
Genitive	psnaios	lokos
Essive	psnaikne	lokne
Terminative	psnaitel	loktel

Number precedes case: psnaios “of the aether,” elmkatel “unto all engines,” elmtram “the installed engine as patient.”

Regarding the terminative note that both the end of a process and the end of a life are the same word. This lets a company order, ksostkatel, “unto all the crooked ones”.

The four monads decline badly. a “head,” e “brother,” i “bird,” o “long” are single nuclei and every vowel-initial ending collides with them. The accusative of i “bird” is im, homophonous with im “darkness”. The akousmatists have written voluminous commentaries on this.

4.4 Case stacking

A dependent noun takes its own case followed by the case of the thing it depends on. This is an inherited, areal feature of Auloic’s neighbors.

The commonest instance is the genitive. rel “blade,” pmišt “hunter”:

pmištos rel “the hunter’s blade” (archic head, no stacking)
pmištosam relam “the hunter’s blade, as patient”, genitive, then the head’s accusative
pmištostel reltel “unto the hunter’s blade”, genitive, then the head’s terminative

The same happens with the other cases, though it is rarer:

kotesam ksostam “the ksost that is in the hold as patient”, locative kotes, then accusative

Number stacks too. The dependent keeps its own arithmological number and takes the head’s case, so a single phrase can carry two values. Both of them count in the balance (§7.2). relka “all the blades” inside an accusative phrase is relkaosam, worth ten by itself. A proof-step with a stacked genitive in it changes the count by a lot. A sen-mis composing while under attack could restructure the whole clause to avoid one.

Slave-speech has none of this. A fot-lok genitive is a bare stem in front of its head.

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4.5 Pronouns

	singular	inherited plural
1	men “I”	mens “we”
2	sait “thou”	saits “you”
3 animate	ken “he, she”	kens “they”
3 inanimate	ton “it, the aforesaid”	—

ton is the anaphor of schematics: “the aforesaid gate.” It is also the pronoun of mortals and of slaves, ken being reserved for class III, the Laulai. A brot, a fot and a xrešt are ton along with gates and bearings. A slave being addressed takes the second person sait.

A ksost is ton. It’s class VII, and class VII is rods and plates.

The plural in -s is Arcadian. It is the last surviving fragment of the plural L4 destroyed. It survived because pronouns are short, frequent and stressed. It coexists awkwardly with arithmological numbers, which pronouns also take: menka “we-all, the guild in session,” kendi “the two aforesaid, in opposition,” kentri “the three aforesaid, in concert.” Careful speakers use menka for the guild and mens for the people in the room.

4.6 Derivation

Addition (-kat-, from kat “and”) sums concepts and their numbers: lirkatplas “string-and-plate,” a sounding-board assembly.

Multiplication (-di-, from di “two”) is the dyad’s act of doubling: merndimern “part-by-part,” a lattice or a matrix.

Ratio derivation is done on tensi “ratio” with the numeral combining forms: ditensi “the octave-ratio, 2:1,” tritensi “the fifth, 3:2,” tratensi “the fourth, 4:3.” A kert tritensikne is a gear in the form of the fifth: a 3:2 reduction.

The frozen suffixes. -an ~ -nan (quality), -zes (instrument), -št (assessed), -ne, -in (diminutives) were Proto-Auloic inflection and are now derivation (§8.4). Three are still productive:

• rap “strong” → rapan “strength”, pem “weak” → peman, plio “dissonance” → plionan “dissonant”, krad → kradan “harmonic”, kert “gear” → kertan “geared”, aun “rite” → aunan “ritual.” The suffix is -an after a consonant and -nan after a nucleus. sen “novice” → sennan “youth” avoids the correct allomorph because regular senan would collide with senan “to teach.”
• plige “to gauge” → pligezes “a gauge”, mozes “resonator”, nazes “bushing.” This is the shops’ way of naming a new tool. It is productive.
• -št forms the thing once it has been graded: nešt “watch,” sišt “inspection,” xrešt “one of the taken” from xre “to take,” θaušt “graded gene-stock” from θau “seed,” and sništ “construction, a figure once it has been built” from sni “to build.”

The rest are opaque. θonan “cruel,” tenan “ignorance,” konan “product” have no recoverable bases and are learned as is.

The bred lines are called by the instrument suffix:

kauzes (< kau “to dig”): the digging line: hull-boring, waste, ducting.
sipzes (< sip “to hammer out”), the striking line: plate, rivet, repair.
nalzes (< nal “to cook”): the feeding line: galley, hydroponics, recovery.
pmizes (< pmi “to hunt”): the tracking line: bred for the Watch and the press-gang. It’s the only line permitted to use a weapon.
falzes (< fal “to love”): the handling line: bred for symmetry, loyalty and appetite. They are placed in the congregations on Earth as handlers.

A falzes is morphologically a device for loving in the sense in which a pligezes is a device for gauging. The suffix carries no class of its own: mozes “resonator” is VI, nazes “bushing” is IV, tsmizes “moon” is VIII. The bred lines are class V.

Words for the burnt:

imn-anθ “ash-person”: a sen-mis whose reach is gone. imn is ash and also wine.
irk-anθ “turned-back person”: one who lost the reach while keeping their senses.
mne-mis “war-lord”: an irk-anθ who commands.
teu-anθ “proof-person”: one who works at proofs in a hall.
orn-anθ “chant-person”: an esoteric singer, on the same stem as orn “to forge.”
pmišt “hunter”: from pmi “to hunt,” with the assessive: one who has been tested.

5. The verb

5.1 Aspect: stasis and kinesis

The primary verbal category is the rest-motion opposition, not tense. This is Arcadian and typical of the region.

• Stasis -om (θor tone), from om “to stand”: states, finished configurations, the way a thing is now. metom “it has been measured.”
• Kinesis -ai (ske tone), from ai “to run”: processes, running, becoming. nai “it charges,” from nau “to push, to charge,” its diphthong absorbed before the suffix (§1.5, law 5).

If necessary, tense is indicated by particles and used adverbially: nak “long ago,” kra “yesterday,” nain “now,” tom “tomorrow,” alme “then.” Proto-Auloic had no tense either.

The opposition is more than aspectual: stative and dynamic are two classes of verbs as much as two forms of one. Many roots occur in one only. Roots that occur in both often differ by more than aspect. tos is “there is” in stasis and “sets down” in kinesis. nil is “holds” and “takes hold of”. ont “to be” has no kinesis at all. rakt is “is closed” and “is being closed”.

5.2 The ten preverbs

The verb takes a prefix from a closed set of ten marking the direction of the event with respect to the speaker. The set is inherited, it sits at the left edge where the vowel-loss never reached (§8.4). No larger piece of Proto-Auloic morphology survives intact anywhere else.

The four orientational preverbs are ancient and opaque:

	Preverb	Direction	From
1	ti-	hither: toward the speaker, onto the speaker’s own ground	*ti “this side”
2	na-	thither: away from the speaker, outward, onward	*na “that side”
3	la-	upward: up, out, into the open	*la, still free as the adverb la “upward”
4	fo-	downward: down, in, onto from above	*fo, still free as the adverb fo “downward”

The six locational preverbs are younger, transparent, and still stand free as adverbs. Whether three of them have finished becoming preverbs is a dialectal difference between the inner and outer holds:

ane- in, into • ni- out, out of • at- across, through •
ok- around, about • irk- back, backward • ets- forward, on

Four and six make ten, which the doctrine interprets as the decad of directions. It is set beside the ten cases and the ten syzygies.

Form. The orientational four are open syllables and attach without adjustment: ti-metom → timetom, fo-θkom → foθkom. Before a vowel-initial root the preverb loses its own nucleus: na-ontom → nontom, la-ontom → lontom, the latter being homophonous with lont “bound.” The one preverb that does not elide is ti- before o-, since i + o is a licit hiatus: ti-ontom → tiontom “it is here, it is at hand”.

The locational six end in consonants as often as not. Where the juncture would be unlawful they take the juncture rather than the linking vowel: at-šainai “flows across,” not *atašainai.

The direction is beginning to do things besides indicating direction. Because the preverb says which way an event moved with respect to the speaker, it says by implication how the speaker comes to be talking about it. This makes the preverb field the beginnings of an evidential system.

Preverb	Literal	Implication
ti-	it came here, to me	I was present; I underwent it; first hand
na-	it goes from here, outward	I am passing it on; it reached me from another
la-	it came up, into the open	it was brought out, worked through, shown
fo-	it came down, onto	it descended; the waking, the seizure, the thing that arrives unasked

A verb with no preverb implies nothing about evidence is the everyday norm. Tkalok always fills the slot.

The contrast between la- and fo- is important. A thing that came up was brought up by somebody and can be brought up again by somebody else. A thing that came down arrived, and the person it arrived on is the only witness there will ever be, meaning they were seized by an insight. The eighth guild works almost entirely in fo-.

The two old factions of the Order take their names from the same distinction without using preverbs: sesnan “the hearers,” from ses “to hear,” and teunan “the provers,” from teu “proof.” The hearers are the fo- party and the provers the la- party.

5.2a Manner

Laulai has no interrogative meaning “how.” The corpus only has tis, kes, ond and pols. This gap is ancient. A speaker who wants to know where something came from asks about the direction with the polar particle mar:

mar ti? “Were you there?” • mar na? “Are you passing it on?” •
mar la? “Did you bring it up?” • mar fo? “Did it come down on you?”

mar fo asks whether somebody is claiming a seizure.

The gap is smaller than it looks because manner is not a nominal in Laulai. It is a verb form: the instrumental joint of §5.6 says by doing thus. A speaker who wants to know a manner asks for the joint, not for a word: mar met?, “by doing what?”. This is how a deck would ask how something was managed. An interrogative for manner wouldn’t be doing anything thing that the joint wasn’t already doing.

5.3 The class prefix

Between the preverb and the root, the verb carries the concord prefix of its absolutive argument, the thing that undergoes. This is the single argument of a one-argument verb and the undergoer of a two-argument one, regardless of aspect (§6.2). The prefixes are the same ten as on the adjective (§4.2).

θorakt- close a ksost, a rod, a plate (VII) • parakt- close a theorem (II) • anmelai “looks at a person” • nemelai “looks at a hull” • elmelai “looks at an engine”

This is the last survivor of a much larger system. Proto-Auloic cross-referenced several arguments in the prefix field at once, in the manner of the languages north and east of it. Vowel-loss came at the word from the other end and never reached them (§8.4). One slot is left, but two things use it: the class prefix, and the relative če- of §6.6. A verb has one or the other, not both.

Where it appears. It is obligatory in tkalok, where it functions as a secondary failsafe mechanism. A listener who mishears the noun can recover its class from the verb. A prover who has lost track of which of two objects he is working on will hear himself say the wrong prefix before he finishes. It is optional in the nursery-speech. The rule of thumb is that it goes in when the absolutive noun is not in the clause and stays out when it is. This is how an agreement marker that is halfway back to becoming a pronoun would be expected to work. The akousmata (§11.1) have none, being archaic speech.

The class prefix and the preverb stack in that order, preverb outside: la- + θo- + rakt-om → laθoraktom “it is closed, and the working is out where you can see it.”

The prefix is the first casualty of the four-syllable cap. Where preverb, prefix, root and aspect will not fit in four (§1.3), the prefix is dropped. Polysyllabic roots almost never carry one. Ordinary speakers are coming to think of class agreement as something that happens in tkalok and formal speech rather than as part of the verb.

5.4 Version: causative, potential, involuntative, necessitive

Four suffixes stand between the root and the aspect. Three are archaic, frozen Proto-Auloic derivational endings. They are typical of the region. The fourth might be some two hundred years old, and the join is visible to philologists.

	Suffix	From	Sense
Causative	-sen	senan “to teach”	make, have, cause to
Potential	-rap	rap “strong”	can, is able to, has the reach for
Involuntative	-in	the old diminutive	it happened; I did not do it
Necessitive	-al ~ -nal	al “debt”	it falls to be done; it is owed

tosai “sets it down” → tosenai “has it set down”
metom “it has been measured” → metrapom “it can be measured”
melai “looks” → melinai “finds himself looking”
θpai “carries” → θpinalai “has to be carried”

An imn-anθ feeling a weak stream of insight might be tempted to say it with fo- and -in: it came down, and I did not do it. The amanuensis records the claim, to be tested later by a guild.

The potential could be used to describe a child lord: θoraktrapai, “she can close it”.

The necessitive is the newest morphology in the language. -al is al “debt,” which is still a free noun in class IX meaning a debt. It takes -nal after a nucleus on the model of -an ~ -nan (§4.6). Some say the Order ratified it because it brought the version markers to four. It doesn’t say that a thing ought to be done but rather that the doing is owed. Orders are therefore not given in it. An order takes the jussive (§5.5). Hunters use it: raktalom, “it needs must be closed”.

5.5 Verbal number and the jussive

After the aspect: -∅ singular, -di dual, -ka collective, the same three formatives as the noun, with the same readings. A collective on a verb of motion means the company moved as one thing.

Directives take the preposed jussive pen (from penan “command”) with kinesis. They conventionally take na- since one commands outward: pen naklosai “close it.”

A directive in ti- is an order from somebody standing where the thing is happening. This is why the war-shrine drills its children in ti-. A standing order in the confederation is that a ti- order from a qualified child is to be obeyed first and questioned later. Giving such an order without cause is a grave charge against a sen-mis.

5.6 The ten joints

Laulai does not subordinate with conjunctions. It puts a case on the verb. A dependent act takes, in the slot where its aspect would stand, one of the ten case endings (§4.3), and that ending says how the dependent act stands to the act it hangs off. The form is called a rin, a joint, a word used in a gearing shop. The set of them is rinka, the ten joints. The doctrine sets it beside the ten cases, the ten syzygies and the ten directions.

Two of the ten that a proof uses are sometimes described as converbs. The other eight are called as adverbs.

Row	Case	Joint	What it says	On mel “look”
1	Archic	-∅	one act and then the next, with nothing said about how they stand	mel
2	Dative	-mon	purpose: in order to, so as to	melmon
2	Ablative	-aps ~ -ps	cause: because, since, seeing that	melaps
3	Locative	-es	simultaneous: while, in the doing of	meles
3	Instrumental	-met	manner and means: by doing, by way of	melmet
3	Comitative	-kat	sequential: having done, and then	melkat
4	Accusative	-am ~ -m	complement: that, the fact that (§6.7)	melam
4	Genitive	-os	attributive: which, that (§6.6)	melos
4	Essive	-kne	conditional: if, in the event that	melkne
4	Terminative	-tel	limitative: until, up to the point where	meltel

A jointed clause has its own arguments and its own class prefix. It takes its subject from the finite verb at the end unless a new one is stated. The chain is right-headed: everything hangs off the last verb, which alone carries aspect and number.

The concessive is two joints. even if is the conditional with the clitic -kat on it: melknekat, “even if he looks”, a stacked joint on the model of the stacked cases of §4.4. There is no eleventh ending. This fits the doctrine.

Where they came from. Proto-Auloic subordinated by putting a postposition on a verbal noun, which is how most of the region did it (§8.2). L3 and L4 took the verbal noun’s vowel. The postposition survived because it was outside it, exactly how the case suffixes on the noun survived (§8.4). What is left is a case ending sitting on a bare root with nothing in between. This means a joint carries no aspect, no number and no polarity. There is nothing there to carry them. The doctrine interprets this as the emanation running through the act as it runs through the thing.

Three of the ten are unstable. They are the three that begin with a nucleus (§9.4 ix). They are also because, that and which.

Eight worked examples, in the order of the table. The complement joint and the attributive joint have sections of their own (§6.7, §6.6).

sen ompam nalmon, kemtel tišainai.
sen | omp-am | nal-mon | kem-tel | ti-šain-ai
child-MON(1)-ARCH | bread-MON(1)-ACC | cook-CVB.PURP | hearth-MON(1)-TERM | HITH-go-KIN
The child is going over to the hearth to cook bread.

kre xefosaps, xap ni-šainai.
kre | xe-fos-aps | xap | ni-šain-ai
rope-MON(1)-ARCH | IV-break-CVB.CAUS | NEV | OUT-go-KIN
Because the rope has gone, nobody goes outside.

ksostam θonges, sen-mismet θoraktai.
ksost-am | θo-ong-es | sen-mis-met | θo-rakt-ai
ksost-MON(1)-ACC | VII-see-CVB.SIM | child.lord-MON(1)-INS | VII-close-KIN
While the ksost is in view, the child lord is closing it.

snipam xermet xpemet, tikipom.
snip-am | xer-met | xpe-met | ti-kip-om
thread-MON(1)-ACC | hand-MON(1)-INS | touch-CVB.MAN | HITH-discover-STAT
I found the wire by feeling for it with my hand.

Note: xermet and xpemet have the same ending, once on a noun and once on a verb.

relam nilkat, ni-šainai.
rel-am | nil-kat | ni-šain-ai
blade-MON(1)-ACC | take.hold-CVB | OUT-go-KIN
Having taken up the blade, he goes out.

sopam melkne, pen načelai.
sop-am | mel-kne | pen | na-čel-ai
blood-MON(1)-ACC | look-CVB.COND | JUSS | THITH-call-KIN
If you see blood, call it.

xap kre xemetel, ane-šainai.
xap | kre | xe-met-tel | ane-šain-ai
NEV | rope-MON(1)-ARCH | IV-measure-CVB.LIM | IN-go-KIN
Never go in until the rope has been measured.

The limitative on a t-final root fuses (§1.5, law 2), which is where met + tel → metel in that section comes from. It is a joint, not a case.

kre xefosknekat, xap irk melai.
kre | xe-fos-kne-kat | xap | irk | mel-ai
rope-MON(1)-ARCH | IV-break-CVB.COND-CONC | NEV | backward | look-KIN
Even if the rope goes, do not look back.

The sequential is used in proof (§7.1) and in instructions.

A joint carries no number. A chain of forty joints counts as one clause for the balance and one sentence for the grammar (§7.2). This is the reason the confederation’s mathematics is written in chains instead of embedded clauses. The register that has to count to ten cannot afford to nominalize.

Chains are long. Forty joints before a finite verb is not a forbidden construction. A fot-lok speaker, having only the bare joint, expresses the same content in forty short sentences.

5.6a Chaining a long text

Three things a chain does that a single joint does not:

(i) The class prefix says when the subject has changed. §5.3 gives the rule of thumb: the prefix goes in when the absolutive noun is not in the clause. A link whose absolutive is the same as the link before it carries no prefix. A link that changes the absolutive carries it whether or not the new noun is stated.

krem nilkat, θositkat, ni-šainai.
kre-m | nil-kat | θo-sit-kat | ni-šain-ai
rope-MON(1)-ACC | take.hold-CVB | VII-cut-CVB | OUT-go-KIN
He took up the rope, cut the plate, and went out.

Nobody has mentioned the plate. The θo- on the second link is what says the sentence has stopped being about the rope. A listener forty links into a construction hears the prefix and knows to look for something new. The war-shrine drills this in practice sessions.

(ii) The back-joint. In long recitations, the finite verb of one sentence comes back as the first joint of the next: … ni-šainai. šainkat, …, “… he went out. Having gone out, …”. The device is called irk-rin, the back-joint. It is used by the nenan (§11.8). A hundred and eleven lines of Sarndi are strung together with it.

(iii) A link that did not happen. nes stands in front of the joint it denies, denying that link only (§5.8). A chain can carry a step that was not taken, which is the ordinary way of saying without:

xap krem nes melkat, ni-šainai.
xap | kre-m | nes | mel-kat | ni-šain-ai
NEV | rope-MON(1)-ACC | NEG | look-CVB | OUT-go-KIN
Never go out without looking at the rope.

5.7 Example conjugation: sit “to cut”

Conjugation of an ordinary transitive root. sit is what a knife does to a rope.

Form	Analysis	Meaning
sitom	sit-om	“it is cut”
sitai	sit-ai	“it is being cut”
θositai	θo-sit-ai	“the plate is being cut” (VII)
tisitai	ti-sit-ai	“it is being cut here, at my hand, under my eye”
nasitai	na-sit-ai	“it is being cut out there, so I am told”
lasitom	la-sit-om	“it is cut open, and the cut is where you can see it”
fositom	fo-sit-om	“it is cut, and the thing came down on me doing it”
sitrapai	sit-rap-ai	“it can be cut”
sitalai	sit-al-ai	“it has to be cut”
sitinom	sit-in-om	“it turns out to be cut; nobody meant to”
sitsenai	sit-sen-ai	“he has it cut”
sitkat	sit-kat	“having cut” (joint)
sites	sit-es	“while cutting” (joint)
sitmon	sit-mon	“in order to cut” (joint)
sitos	sit-os	“that cuts, that was cut” (joint)
tisitaidi	ti-sit-ai-di	“the two of them are being cut here”
lasitomka	la-sit-om-ka	“they are all cut open, and you can see it”
pen nasitai	JUSS na-sit-ai	“cut it!”
xap fositai	NEV fo-sit-ai	“never cut with the thing above you”

A verb carrying a preverb, a class prefix, a root and an aspect comes to four syllables and can take nothing more (§1.3). Further additions break at a juncture. The fully specified forms of tkalok are full of hyphens.

Vowel-final stems are absorbed (§1.5, law 5): pli “reckon” → laplai “is reckoned out”; θko “condemn” → laθkom “is struck off, in front of everybody.”

5.8 Negation and its scope

nes negates, and its position says what is being negated:

menmet enam nes knausai. “I do not know it to be one.” (before the verb: the proposition is denied)
menmet enam knausai nes. “I know it to be one, and I will not say how.” (after the verb: the direction is denied)

xap is the prohibitive, “never”. It is the particle used in the akousmata. (See the texts.)

5.9 The call

A čelan is a complete utterance consisting of a noun in an arithmological inflection and nothing else: no verb, therefore no aspect, no preverb, no direction, and no information about where anything came from. Alarms in the hold take this form. It is also used in the context where a name carries an arithmological suffix, a call about a thing’s state:

Arnatra. (4) “Arna installed.” → Arnek. (6) “Arna in running balance.”
→ Arnanop. (9) “Arna at the limit.” → Arnaka. (10) “Arna gone decadic.”

ksostnop, said down a gallery, is a call to take up stations.

5.10 The ground, and the axiom

The ground is an oblique in the ablative, the case of origin, standing before the verb and saying what a statement proceeds from:

peraps “out of trial” • teuaps “out of proof” • nomaps “out of custom” • nanaps “out of the raving” • titlokaps “out of the old speech”

Ground and preverb are independent and are routinely combined because they answer different questions: the preverb says which way the thing moved, the ground says what it moved out of. peraps lametom is “it has been worked out in the open, and it was the bench that did it.”

θamn is an oracular axiom: something seen entire, without proof and without a route to one. It takes no ground, because it came out of nothing. If it takes a preverb at all, it’s fo-. Such oracular utterances are often produced by imn-anθ. The ninth guild’s scribes write them down verbatim, in the involuntative, with nanaps against them in the margin. The sixth guild spends a great deal of money trying to validate them afterwards. About one in nine are solid.

5.11 The apprehensive

tsa + kinesis: lest, for fear that.

tsa reu-alnθaun našainai.
tsa | reu-alnθaun | na-šain-ai
APPR | cascade-MON(1)-ARCH | THITH-run-KIN
Lest the cascade run.

Elliptical in maxims, after the manner of the old symbola. The apprehensive is the only construction in Laulai that speaks of a future. The doctrine insists that it makes no claim about time but about tendency, the apeiric pole. That leaves §5.1 intact.

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6. Syntax

6.1 Emanation order

The unmarked clause is verb-final. The language is postpositional throughout, as are the cases (§4.3). The order is Archic – obliques – Terminative – Verb: from the source, through the means, unto the end, and followed by the act. The doctrine reads this as the deed being the terminus of the emanation. The Arcadians were always verb-final like their neighbors.

ðaur θerkmet kotel fošainai.
ðaur | θerk-met | kot-tel | fo-šain-ai
water-MON(1)-ARCH | crack-INS | room-TERM | DOWN-flow-KIN
Water is coming down through the crack into the room, and I am standing in it.

Nursery-speech, so the verb carries no class prefix.

Converb chains stack in front of the whole thing (§5.6), each with its own arguments. A long sentence in Laulai is a left-branching ramp with one verb at the bottom.

In front of everything there is a topic slot. A bare archic nominal may stand at the head of a sentence, outside its case frame, stating what the sentence is about.

omp, senmet saspom. “The bread: the child has eaten it.”

The verb of that carries sa- because the bread is not in the clause. The topic is outside the case frame and does not count as an argument, so the class prefix does a recovery (§5.3).

A topic is not a core nominal and does not count in the arithmological balance.

6.2 What stands and what acts

The archic is the case of the source that emanates. It takes the single argument of any verb that has only one, whether stasis or kinesis, and it takes the undergoer of any verb that has two. It never takes a doer standing over something else: an agent with a patient under it goes in the instrumental (§4.3) regardless of aspect.

kre xefosom. “The rope has broken.” (one argument; the rope is the thing it happened to)
mo šainai. “The dog is running.” (one argument, and motion; still the archic)
relmet krem xesitai. “He is cutting the rope with the blade.” (two; the blade is the means, the rope is what the cutting is done to)
relmet kre xesitom. “The rope has been cut, with the blade.” (two, and at rest; the case does not move)
ksost tišainai. “The ksost is coming this way.”
relmet ksostam θoraktai. “The blade is closing the ksost.”

Note how the last two put ksost in different cases. Historically they’d be in the same case, once as the thing arriving and once as the thing being closed. The doctrine says that only the source originates and everything else is an instrument of the emanation. In contemporary earth linguistics, we’d say Auloic languages were ergative.

The accusative is an overlay and is gaining ground. -am is Greek in usage (§4.3), marking an undergoer that is definite. ksost θoraktai is “a ksost is being closed,” ksostam θoraktai is “the ksost is being closed, the one we came for.” Twenty-five centuries later, it has spread far enough that in the inner holds, a definite undergoer is nearly always accusative and the bare archic reads as vague. The trial-halls still teach the older forms, which sound less snappy nowadays.

When Laulai was in more of a mixed state, a number of prestigious texts were composed that used the archic case as the agent and the accusative as the patient. The accusative overlay style sounds fancy, analogous to English thoroughly infused with French, but ordinary people never speak this way. Natively, any noun in the archic case is called the “source”, a metalinguistically meaningless term.

In Laulai, the “source” is an object in the world of ideas that emanates an action through the chain of links that forms the sentence, the action being the verb at the end. The patient is usually regarded as the source because it’s the furthest removed from activity.

A stasis verb can still name an agent, in the instrumental. Every report of a completed action is phrased this way: pmištrimet … θoraktomka, “closed, by the three hunters” (§7.1). Laulai doesn’t need a separate passive.

6.3 Agreement as consonance

Adjectives take their noun’s syzygy prefix, its polarity suffix and match its arithmological number where countability is at issue. The verb takes the syzygy prefix of its absolutive (§5.3). Dependents take the case of their heads (§4.4). All of it together is called arm, harmony.

Deliberate mismatch is plio (dissonance), a productive rhetorical device. A decadic adjective on a dyadic noun is a standard marker of lament. A class prefix that does not match the noun it agrees with can be an insult based on the associations of the dissonant class.

6.4 Coordination

Noun phrases coordinate with the clitic -kat. This is the comitative postposition doing a second job: the same morpheme, that makes the sequential converb (§5.6), used again. It attaches to the second member: rel snipkat “blade and filament.”

Clauses do not coordinate. They chain (§5.6). A Laulai who wants to say “and then” says a converb. A Laulai who wants to say “but” says two sentences and lets the tone do the job.

6.5 Questions

Polar questions take the preposed particle mar (§5.2a). Content questions use the interrogative in situ (tis “who,” kes “what,” ond “where,” pols “how many”) with no fronting or change of order, as is typical of verb-final languages. There is no word for “how”. A speaker who wants one asks about the direction, or about the manner joint (§5.6), instead.

6.6 Relative clauses

Laulai relativizes twice, once in the oldest morphology it has and once in some of the youngest. The two do not cover the same ground.

The bound form. The prefix če- stands in the agreement slot (§5.3) and fills the place of the argument that the clause is about. The clause then goes in front of its head like all modifiers (§6.1). The seventh guild calls the form a čelok, the prefix plus the word for “word”.

češainai ksost “the ksost that is coming”
nes čontom nars “a seam that is not there” (če- + ontom, elided in the manner of a preverb, §5.2)
relmet čeraktom ksostsep “the one with no fellow that was closed with the blade”

This reaches one argument. The slot it occupies cross-references the absolutive. This means a čelok can only be built on the thing that undergoes: the single argument of a one-argument verb, the undergoer of a two-argument one (§6.2). The doer is out of reach. There is no way at all to say the hunter who closed it with a če-.

What they do instead is turn the sentence round. If the patient goes into the essive, the doer comes out of the instrumental and stands in the archic, then če- can then reach it:

ksostkne čeraktom pmišt “the hunter who closes ksost”

The seventh guild calls it the way round. This seats a doer in the case of the thing that undergoes (§6.2 is doctrine). Note that ksostkne by itself is an insult (§11.5 ii). The construction itself is not confusing since one of them has a verb after it.

The attributive joint. The other road is the genitive joint of §5.6: the verb takes -os and goes in front of its head like an adjective.

ksostam θoraktos pmišt “the hunter that closed the ksost”

This has no restriction, so it’s more common and growing in popularity. However, it says nothing about which argument is being relativized, which is why tkalok can’t use it. An -os clause is interpreted in terms of what makes sense. If it’s ambiguous, somebody asks. It also stacks: Being a genitive, it takes the case of its head like any other dependent (§4.4). θoraktosam ksostam, “the ksost that was closed, as patient,” carries the head’s accusative on a verb.

Why proof has neither. A čelok has no class prefix, because če- is standing where the class prefix would be, and the class prefix is the secondary failsafe mechanism (§5.3). An -os clause does not say what it is hanging from. Neither is licensed in tkalok. A construction that has to pick one ksost out of two picks it with a number instead (§4.1). This costs a company a great deal of arithmological reconstruction work while under attack.

6.7 Complements, quotation, and the noun of the act

Three ways of putting an act inside a clause, of very different age:

The complement joint is -am, the accusative (§5.6) on the verb of the act being reported. It goes under seeing, hearing, knowing and saying, carrying its own arguments.

sen-mis snipes ontam nes tiknausom.
sen-mis | snip-es | ont-am | nes | ti-knaus-om
child.lord-MON(1)-ARCH | thread-MON(1)-LOC | be-CVB.COMP | NEG | HITH-know-STAT
I did not know the child lord was still on the wire.

lekt is the older approach and less popular. §9.1 leaves it half-finished: the complementiser is the word for “say”. A form that is still visibly a verb can be a confusing conjunction. It survives in the trial-halls and in writing. On deck, it has gone to the other end of the sentence and turned into an enclitic closing a quotation:

“pols kre”-lek tičelai.
“How much rope,” she called.

Quoted speech keeps its own deixis and its own preverbs. A tale recited in na- from end to end may claim nothing (§11.8). If it’s that person’s line, a reciter may put ti- in it.

The noun of the act. The suffix -št makes a noun out of a verb: sni “build” → sništ “a construction”, pmi “hunt” → pmišt “a hunter, one who has been out”, xre “take” → xrešt “one of the taken”, tno “clear out” → tnošt “the Withdrawal”, θau “seed” → θaušt “graded stock.” §4.6 calls these derivations. There, the suffix is called an assessive. This was the Proto-Auloic verbal noun, the same morpheme the ten joints are the residue of (§8.4).

It only goes on an open stem. Every -št noun in the corpus is built on a root ending in a nucleus without exception. That’s what is left of a suffix whose own vowel L4 removed. A consonant-final root has nowhere to put it. Three roots in four are consonant-final (§1.3), so the productive verbal noun of Proto-Auloic survives on a quarter of the lexicon. New ones are still coined and are still coined on open stems: the shops created plišt, “a piece of arithmetic once it has been done,” within living memory. There is no -št noun anywhere from met, mel, rakt or sit.

A noun of the act bears arithmological costs. The act is a noun. It takes an arithmological number and a case like any other noun, so it counts in the balance (§7.2). If it carries a dependent, the dependent counts too (§4.4). A joint costs nothing and a nominalisation costs at least one and usually three. This is why the confederation’s mathematics is written in chains, not because of elegance or doctrine.

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7. Proof

The numbers welded to every noun, the classes stamped on every verb, the chains… All of this must be used to state the proof correctly under conditions of chaos and a shortage of time.

7.1 What a proof is and what it does

A theorem is teukt. A construction, the figure you build in order to prove one, is a sništ. The act of finishing is rakt, “to close.”

A proof in Laulai is one sentence. The steps are not limited (§5.6). Each step is a converb, hung off the one at its right. The whole chain runs into a single finite verb at the end, which is where the proof concludes. Laulai has no conjunction that will link two finite clauses into an argument. A chain that stops without a finite verb has not concluded anything yet.

ksostsepam θomelkat, serkdim meplikat, teukt paraktom.
ksost-sep-am | θo-mel-kat | serk-di-m | me-pli-kat | teukt | pa-rakt-om
ksost-HEP(7)-ACC | VII-look-CVB | serk-DY(2)-ACC | I-reckon-CVB | theorem-MON(1)-ARCH | II-close-STAT
Having looked on the ksost that has no fellow, having reckoned the two intervals — the theorem is closed.
Balance: 7 + 2 + 1 = 10 → 1. rak.

This is a sentence of three steps. A hunting construction runs to thirty or forty, spoken flat and fast, all of it grammatically one sentence. This is what the war-shrine drills in.

What the proof does. The main work is done by a mind with sorm carrying a serk while the chain runs. The chain is how the mind keeps its grip. Each step is a place to advance the figure another step without forgetting details. Even without a sentence, a very good prover can still be effective on simple problems. A sen-mis is reduced to that when the deck noise gets bad enough that she cannot hear herself. However, the arithmological count matters. More on that in the next section.

Against a ksost, the chain has a target. How it is trying to resolve a geometric puzzle is explained in §0.2.

pmištrimet ksostseplonam θoraktomka.
pmišt-tri-met | ksost-sep-lon-am | θo-rakt-om-ka
hunter-TRI(3)-INS | ksost-HEP(7)-PER-ACC | VII-close-STAT-COLL
The three hunters have closed the ksost that had no fellow, and it is bounded now.
Balance: 3 + 7 = 10 → 1. rak.

7.2 The decad-balance

A clause is rak (“whole”) when the arithmological values of its core nominals sum to ten exactly, or to a number whose digit-reduction passes through the decad to the monad, as 28 → 2+8 = 10 → 1. Sums that reduce past ten without touching it (25 → 7) are nesrak. Sums that never reach ten are not reducible at all. A step worth nine has no effect. There is a name for one worth nine: nopkne nesrak, unwhole at the ninth. One short, and useless.

What counts. Core nominals count, the verb does not, an attributive adjective does not (it carries a number for concord and is not a nominal), a topic or vocative standing outside the case frame does not (§6.1), a stacked dependent counts at its own number as well as the head’s (§4.4), an unknown counts at whatever number it carries (§7.4), a joint costs nothing (§5.6), and a noun of the act costs its arithmological value (§6.7).

A nominal in the instrumental counts. The instrumental is the agent case (§6.2). It is also the case of a plain tool, the language does not distinguish them, and neither does the balance. The practical effect is that saying how you did something costs a number. A prover who is short reaches for the tool and a prover who is over leaves it out.

The balance is taken over the whole sentence. A chain of forty converbs and a close (§5.6) is one sentence with one balance. The total has to reduce through the decad. The last link of a construction is chosen partly for its value, being the last place a prover can still move the number.

What it is for. A step that balances is effective. A listener who cannot follow the mathematics at all can still hear whether each step comes to ten. That is the job of the signals rating who stands at a nine-year-old’s shoulder while she runs a construction over his head. When a step does not balance, something has been dropped, misheard or mis-said, the listener says so. The chain is stopped before it wastes a serk.

A nesrak step is not false. It may be perfectly true and often is. It’s just ineffective at channeling occult power, so Laulai battle-provers must restate everything until it comes to ten. The habit has spread well past mathematics. Laulai verse scans the way it does because of this.

Everyday speech is not rak and is not meant to be. A person who starts balancing in the middle of an ordinary conversation has changed the conversation. Even if his sentences prove nothing, it might frighten his interlocutor.

sen-mistrimet ksostsepam θoraktai.
sen-mis-tri-met | ksost-sep-am | θo-rakt-ai
child.lord-TRI(3)-INS | ksost-HEP(7)-ACC | VII-close-KIN
The three child lords are closing the ksost that has no fellow.
Balance: 3 + 7 = 10 → 1. rak.

elmtramet ampdim konantratel laminanom.
elm-tra-met | amp-di-m | konan-tra-tel | la-minan-om
engine-TET(4)-INS | vapour-DY(2)-ACC | yield-TET(4)-TERM | UP-transmute-STAT
The installed engine turns unruly vapour into founded yield.
Balance: 4 + 2 + 4 = 10 → 1. rak.

The verb of that last sentence carries no class prefix, because preverb, prefix, root and aspect would come to five syllables and the cap is four (§5.3).

7.3 The heptaktys-balance

Above the decad stands a stricter grade. A clause is mern-rak, part-whole, when its core nominals sum to 28: the second perfect number, the triangle of seven, and a figure that reduces 2+8 → 10 → 1 into the bargain, so a mern-rak clause is rak as well.

Twenty-eight is a legal grade rather than a mathematical one. An oath sworn at ten can be released by the person who took it. An oath sworn at twenty-eight cannot be released under ordinary circumstances.

What it costs. No noun exceeds ten, so a mern-rak clause needs at least three core nominals where a rak clause can be built on two. It needs high values, commonly the decadic twice over. Speech at twenty-eight is therefore speech about totalities, and swearing about specific things is not easy. A speaker who needs twenty-eight reaches for the guild entire, the line entire, mortal-kind. This has shaped Laulai law in unforeseen ways.

relkamet čilkat psaisepam anθkatel lasonandom.
rel-ka-met | čil-kat | psai-sep-am | anθ-ka-tel | la-so-nand-om
Blades-DEC(10)-INS | oath-MON(1)-COM | soul-HEP(7)-ACC | person-DEC(10)-TERM | UP-IX-bind-STAT
The Blades entire, with the oath, bind the solitary soul unto all persons.
Balance: 10 + 1 + 7 + 10 = 28. mern-rak.

That is a hunter’s oath, sworn at the shrine door at the age of twenty-eight, or at whatever age a hunter reaches his twenty-eighth time out, whichever comes first. This oath cannot be released.

The two perfections disagree about people. Six is perfect and the hexadic means in healthy running balance. Twenty-eight is perfect and governs what cannot be undone. The seventh guild swears its hunters at twenty-eight and reports them at six. The ninth guild’s position is that six is a number for machines. The seventh guild says that a hunter takes an oath to live as an organic machine.

7.4 The unknown

The saik ⟨—⟩ is the unknown, the quantity a construction is solving for. It fills a nominal slot, takes case, takes number, and counts in the balance. An absence would do none of those. A saik is a stated unknown.

In speech it is pronounced. A saik is a silence one mora long carrying the polarity the prover expects to find (§1.6), θis if he expects the peratic, ske if he expects the apeiric. A listener therefore hears that there is an unknown and which way the prover is betting. The polarity can be pronounced as a syllable to be safe, but some esoteric singers can sing silence with a tone. This saves a split second. Skeptics say that in reality, the beginning and end of the tone are perceived on the preceding and following syllables.

The number on the unknown says what kind of thing is being looked for, using the ordinary readings of §4.1. This is a descriptive apparatus ten items long:

Value	What the prover has said he is looking for
1 monadic	a unique original: a first case, a pattern others will be struck from
2 dyadic	an indefinite: any member at all, the prover does not care which
3 triadic	three terms in concert; the standard shape of a mediating step
4 tetradic	an installed, warranted value: a constant, once found, to be filed
5 pentadic	a live source; the thing the effect is coming out of
6 hexadic	a value that puts the system into running balance
7 heptadic	a one-off with no fellow, and the value most often set against a ksost
8 ogdoadic	a great built solid: a bound, a mass, a ceiling
9 ennadic	a limit value, a redline, an asymptote
10 decadic	the whole kind at once: a general solution rather than a particular one

—sep serkdiaps θometkat, ksost θoraktom.
—sep | serk-di-aps | θo-met-kat | ksost | θo-rakt-om
UNK-HEP(7) | serk-DY(2)-ABL | VII-measure-CVB | ksost-MON(1)-ARCH | VII-close-STAT
Having measured the unknown, the one with no fellow, off the two intervals — the ksost is closed.
Balance: 7 + 2 + 1 = 10 → 1. rak.

The class prefix on the verb is the bet stated a second time. A verb whose absolutive is a saik has no class to agree with, so it takes the class the prover expects to find (§5.3), θo- above, because he is betting the unknown turns out to be a fact about the thing’s geometry.

Solving for a polarity is the one case where the saik is spoken with no tone at all, the prover by definition not knowing which way it goes. Nothing else in the language is untoned. Everyone who has heard it done live describes a beat of flat silence in the middle of a fast chain.

Three limits. A saik cannot be the verb, because it takes nominal morphology and there is no silent aspect. A saik standing alone with a number and no verb is not a clause but a čelan, a call (§5.9). The accusative of a saik is written —am and said —m, with nothing to choose between the allomorphs of §1.5 law 4 because there is no segment to choose from. This is the one morphological question in the language that is not just unsettled but undecidable.

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8. Historical phonology

8.1 The two strata

Every stem belongs to one of two layers and the layer can usually be identified from its shape.

The Arcadian stratum is the bulk of the language: nine stems in ten, effectively the whole of the technical, agricultural, domestic and mechanical vocabulary. Its stems obey §1.4 without exception.

The Hellenic stratum is what the Imposition brought: fifty-seven stems, one in nineteen of the lexicon. Kinship (ptir † “father,” medr † “mother,” brot † “mortal,” anθ † “person”), the body (ops † “eye,” os † “mouth,” an † “tooth,” aštin † “skeleton”), the elements (ðaur † “water,” paur † “fire,” psnai † “air,” petr † “stone,” dendr † “tree”), the lights (el † “sun,” aštir † “star,” laump † “lamp, star,” skot † “dark,” emer † “day”), the numbers above four, the sacred and the abstract (θeu † “god,” psai † “soul,” kosm † “world,” nom † “law,” arm † “harmony,” tetrakt †, kspenan † “wisdom”). Six sit outside those fields: mikran † “small,” mern † “share,” paln † “again,” ols † “all,” pol † “many,” per † “trial.”

Seven of the fifty-seven break a law of §1.4 because they were sacred and resistant to certain changes. Greek πέτρος lost its ending like everything else and came out as petr, ending in a rising cluster that no native word is allowed to end in.

The Greeks get the worst of it. A people whose whole apparatus is Greek in its vocabulary and Greek in its arithmology is not fond of Greeks. The standing view in the holds is that Greece heard the doctrine first, from the brotherhood’s own mouths, and rejected it. A Greek taken in the press-gang is worked harder than anybody else. Having been taught sacred history, the sixth guild’s drill-songs are still rude about Kroton twenty-five centuries later.

A Greek who accepts the Pythagorean doctrine is a different matter. Such a person is called by the title prot-fot (first-slave): the one who came to it before. There are perhaps forty in the system. They are exempt from the press-gang by statute, their descendants are entered in the or-tlaim. Everybody is slightly uncomfortable around them.

The two strata are also the two registers seen from a lexical angle. Tkalok requires the Hellenic form wherever one exists: ðaur and not a ra-compound for water, anθ and not sen for a person. A Laulai child learns the Arcadian stratum first, finding out at nine that the words its mother used are the low ones. The trial-halls have a word for the psychological effect on a nine-year-old: penen, shame. This shame persists and fuels the pride and duty they are taught afterwards.

8.2 Proto-Auloic

The reconstructed common ancestor, Proto-Auloic in Greek and titlok in Laulai, had, as far as we can tell:

• Ten consonants: p t k s m n l r w j.
• Five vowels: a e i o u.
• Syllables of the shape (C)V(C), no initial clusters.
• Stems of two or three syllables ending in a vowel, because they were built to carry suffixes.
• Initial stress, fixed, with a minority class stressed on the second syllable.
• A verbal complex of the type found all round the eastern rim: a prefix field carrying orientation and the class agreement of more than one argument, then the root, then a suffix chain carrying version, aspect, enumeration and a postposition, each element separable and each with its own vowel.
• Ten orientational and locational preverbs at the head of that prefix field, of which four form the ancient core.
• Case stacking: dependents carried their own case and then the case of their heads (§4.4).
• Clause chaining by non-finite verb forms, with no coordinating conjunction for clauses (§5.6).
• A verbal noun, which took the postpositions like any other noun, and is the source of the ten joints (§5.6) and of the -št nouns (§6.7).
• A relative prefix in the agreement field, filling the slot of whichever argument the clause was about (§6.6).

Very little of that survived intact, as §8.3 explains.

8.3 The sound changes

	Law	Effect	Example
L1	Glide loss. *w and *j drop between nuclei; the hiatus contracts	source of all three diphthongs, and of the open CV stems	*kewa > keu; *teje > te
L2	Pretonic syncope. In the second-stress stem class, the first vowel drops	source of the CCV stems, of the CCVC stems, and where the cluster was unsayable and L13 repaired it, of the a-initial stems	*tepe > θpe “awl”; *mede > *mde > amde “sharp”
L3	Post-tonic syncope. Non-initial vowels drop where what they leave can be said	the CVCC stems	*kerat > kert “gear”
L4	Apocope. The final vowel drops after a lawful coda	the event: 787 monosyllables out of 1,106, and the death of the suffix chain	*mela > mel “look”; *irno > irn “earth”
L5	Palatalisation. *k > č before a front nucleus, in onset	21 stems	*kile > čil “oath”
L6	Aspiration. *k > x word-initially	35 stems	*keras > xer “hand”
L7	Lenition. *p > f word-initially before a vowel	the only native source of /f/	*pemi > fem “speak”
L8	Spirantisation. *t > θ initially, and before a sonorant or stop	the commonest law; 7% of all segments	*toma > θom “straight”
L9	Sibilant shift. *s > š beside a dental; initially in the inner holds	20 stems, and the -št of the assessives	*testa > tešt “scales”
L10	Voicing. A single stop between nuclei voices: *t most readily, *k less, *p least	d 42 stems, g 20, b 15	*meta > med-, and “the reluctance of the labial”
L10a	Sibilant voicing. *s voices to z between nuclei, the fricative counterpart of L10	34 stems	*amse > amze “well”
L11	*u > o outside the diphthongs	the vowel tetrad of §1.2	*turu > tor “stew”
L12	Degemination. Like consonants and like nuclei fuse	§1.5 laws 1–2	*tettu > tet “guild”
L13	Prothesis. A word left with an unsayable onset takes a-	the a-initial stems, one in twelve of the lexicon	*mdi > amdi “sea”
L14	Epenthesis. An unsayable cluster takes a supporting vowel	the second half of the repair wave; it ran to completion in the Arcadian stratum	*krnaus > kernaus “kernel”

L13 and L14 are the repair wave. They applied to the Arcadian stratum and not to the Hellenic, so amdi “sea” was repaired and petr “stone” was not. Between them they touched over a hundred stems. Anything that arrived after they stopped was never repaired at all. That is how vril † comes to have a /v/ in it when nothing else in the language does (§9.3).

8.4 What the laws did to the morphology

L4 did more than shorten words. It destroyed a morphological system and left traces all over.

The suffix chain became stem-final consonantism. Proto-Auloic *root + version + aspect + enum + case was five separable morphemes with five vowels. After L3 and L4 the enumerative suffix survived because the case suffix outside it was in the way. The case suffix survived where it began with a consonant. The version markers survived as the three of §5.4 and lost the rest. Everything else was crushed into the coda. This is why the modern language still has a clean agglutinative number–polarity–case template with almost no polysyllabic stems. The outer morphology was saved by being on the outside.

The derivational suffixes are the casualties. -an ~ -nan, -zes, -št, -ne, -in were productive Proto-Auloic morphemes: a quality marker, an instrument marker, an assessive, two diminutives. L4 welded them to their stems. What had been inflection became derivation, most of it opaque. The stems with no recoverable base at §4.6 are the residue. This often happens to an agglutinative language that loses its vowels. It is an argument for the reconstruction in §8.2, explaining why a language with a rigid suffixing template has a hundred and twenty frozen suffixed stems and no living suffixation to match.

The suffix chain also produced the subordination. Proto-Auloic subordinated by putting a postposition on a verbal noun, common enough in its region of origin. L3 and L4 took the verbal noun’s vowel and left the postposition standing on a bare root. The ten joints of §5.6 are what that looks like twenty-three centuries later: ten case endings on a verb, with no noun between them, nothing to carry number or polarity, because there is nothing is left to carry it. The same event turned the verbal noun’s unsuffixed form into the -št nouns of §6.7. That’s why they only occur on stems that end in a vowel.

The prefix field was saved by being a prefix field. L2–L4 attacked the right edge and never reached the left. The two classes of prefix still standing there are the most conservative morphology in the language: the ten concord markers of §4.2, which have barely changed in twenty-five centuries, and the ten preverbs of §5.2, of which the ancient four have not changed at all. What is missing from the field is everything except one agreement slot: Proto-Auloic had two or three arguments there, and Laulai has one slot (§5.3).

The relative če- of §6.6 is the only piece of the second agreement slot that came through. It came through because it indicated something unique. It’s *ke- with L5 on it. ken “he, she” is the same old deictic without L5, which puts the prefix on the far side of a sound change that stopped before the reinterpretation.

A language that lost a whole suffix chain and kept most of a prefix field was never suffixing on principle. Its morphology sat on both sides of the root, which eroded from one side. What is left looks lopsided.

8.5 What the doctrine could not have invented

The ten arithmological numbers are the ten numerals, in their combining grade, in the order a child counts. Five of the seven postpositions are homographs of Greek prepositions. The comitative and the instrumental sit in the mediating row with the locative, where they belong doctrinally, while the ablative, a separation and mediating if anything is, sits in the relational row with the dative because there had to be two there.

The syzygies come in a set of nine that is semantically coherent and a tenth that is a bag. Nobody has ever managed to rigorously define class IX (§4.2). The brotherhood needed a tenth and took left over nouns.

Case stacking, the converb chain, the class prefix on the verb and the ergative use of the instrumental are all things the doctrine has an elaborate reading of and could not conceivably have made up, because all four are shared with neighboring languages.

Relativization only reaches the undergoer (§6.6), common enough in a language whose agreement runs like this one’s. It’s also shared with the neighboring languages. The seventh guild’s way round it seats a doer in the archic, which is a flat contradiction of §6.2 and of everything the doctrine says the archic is for. Nevertheless, it has been in continuous use for as long as there have been records.

8.6 The dating

Event	Date	Evidence
the Imposition (θalt)	c. 500 BC	the Hellenic stratum is Attic-Ionic of that century, ending and all
the vowel-loss (L2–L4)	c. 450–350 BC	it catches the Hellenic stratum, so it postdates the Imposition
the repair wave (L13–L14)	c. 350–250 BC	applies to the Arcadian stratum only, i.e. after the strata were distinguishable
the reinterpretation	c. 300 BC	the first arithmological glosses in the akousmata
the descent	from c. 200 BC	vocabulary of the karst; lan, lans, tip “cave” become structural terms
the Withdrawal (tnošt)	to c. 550 AD	the last loanwords of the surface centuries are late Latin
the taking of the moon	during the Withdrawal	the 28-day month and 28-hour watch are fixed from here
the limit found	c. 1100 AD	nine hulls lost
polarity; the balance made statutory	17th–18th c. AD	statute, dated, signed
the heptaktys grade	1809	statute, and the first mern-rak oath is two years later
the necessitive (§5.4) ratified	1814	statute; the form is a century older in the shops

The top of this table and the bottom of it are defensible. The middle rests on the Order’s own chronicles, which is a devotional genre.

8.7 The low numerals

The Order believes that numbers from one to four are Arcadian, five and above were imposed, and that this is the evidence that the tetrad was found among the hill people rather than brought to them. The first half cannot be true:

Laulai	Gloss	Greek	Indo-European	Difficulty
en	one	ἕν	*sem- / *Hoi-no-	none
di	two	δύο	*dwoh₁	none; it is also the multiplicative morpheme of §4.6
tre, tri-	three	τρεῖς, τρι-	*treyes	none, and the combining grade matches the Greek combining grade exactly
tra	four	τέτταρες, τετρα-	*kʷetwores	it is the Greek combining form with the first syllable gone, which is what L2 does to a word

These are more than comparable. They are Indo-European. The internal evidence agrees: Proto-Auloic had no initial clusters at all (§8.2), so a primitive tre is impossible, and nothing else in the numeral system has that shape.

They are also not the Imposition’s. They are phonologically integrated in a way the Hellenic stratum is not, they are in the substrate’s own place-names, and they were already old when the brotherhood arrived. The account that fits everything is a much earlier borrowing: a Bronze Age loan from whatever Indo-European was being spoken in the lowlands, quite possibly an early dialect of Greek itself, at a date when Auloic still had the shape §8.2 reconstructs and the loans had time to be integrated into it.

šal “thousand” has no obvious source in Greek, in Italic, or anywhere else. This makes it the only numeral in the language with a good claim to being pre-IE.

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9. Irregularities

9.1 Homophony

Seventeen sets survive:

al debt / deer • asp chimney / to eat • elm engine / fear •
imn ash / wine • irn earth / rite • lekt to say / that (COMP) •
lil brave / flour • men I / island • menan magister / youth •
met measure / with • mni axle / leather • nan joy / prophecy •
nasp archon / silver • orn chant / to forge • pen leaf / the
jussive / the pentadic suffix • rel blade / to ferment • čirt quotient
/ housing

Most are ordinary collisions. Five have additional significance:

met and lekt are grammaticalizations caught in the middle of the process: the instrumental case is the word for measure, and the complementiser is the word for say. Neither is an accident.

nasp “archon, silver” is treated as an akousma rather than a collision: the ruler and the coin have one name. nan “joy, prophecy” likewise: the seizure is named for a word that also means delight.

imn “ash, wine” is the one that gets used. An imn-anθ is an ash-person and possibly a wine-person.

elm means “engine, fear”. There is a second word for fear, xosan, used when the difference matters, but the collision is old. Three others are like this: irn “earth, rite” beside aunan “ritual”, menan “magister, youth” beside sennan “youth”, čirt “quotient, housing” beside kot-marn “housing.” In each pair the short word is old and ambiguous, while the long one is younger and exact. Speakers use the short one until they are being careful.

al “debt, deer” has quietly acquired a third member, the necessitive of §5.4: raktalai “it falls to be closed”.

A commoner kind of collision arises between a stem and an inflected form: nai “yarn” against nai “is charging” (nau + -ai), and lont “bound” against lontom “it is out in the open” (la- + ontom). The quotative enclitic -lek (§6.7) is a newer one, sitting on lek “taste”, setting up hosts for a pun between speech and flavoring. These are collisions between different orders of thing. There are a great many of them.

9.2 The Hellenic stratum

Fifty-seven stems are marked † as belonging to the stratum the Imposition brought. The mark indicates the word came in with the brotherhood.

an tooth • anθ person • aps from • arm harmony • aštin
skeleton • aštir star • brot mortal • dendr tree • dom house •
eks six • ektan hundred • el sun • emer day • es in •
ims half • kat and • kosm world • krau crystal • kspenan
wisdom • laump lamp, star • lekt say • makr great • medr mother •
mern share • met with • mikran small • nom law • nop nine •
nukt night • okt eight • ols all • ops eye • os mouth •
oðas path • paln again • paur fire • pent five • per trial •
petr stone • plas sheet • plask Pelasgian • pol many •
prot first • psai soul • psnai air, breath • ptir father •
sept seven • septakt the heptaktys • skot dark • tel end •
templau temple • tensi ratio • tetrakt the tetraktys • tka
ten • zait live • ðaur water • θeu god

Seven of the fifty-seven break a law of §1: dendr, kosm, makr, medr, nukt, petr, tka. Those are the ones the vowel-loss mangled and the repair wave didn’t touch because they were holy. From these, the stratum is visible from the shape of the word. The other fifty are phonologically integrated and are known to be loans only by their etymologies: nom beside νόμος, skot beside σκότος, el beside ἥλιος, emer beside ἡμέρα, arm beside ἁρμονία. Nothing in the sound gives them away, and a speaker who has not been taught which is which cannot tell.

Four stems carry the dagger without belonging to this stratum: štrat † “street,” az † “coin,” laus † “hymn” and vril † “motive force,” all four late Latin and discussed in §9.3. The dagger means not Arcadian.

Notes on harder cases.

• mikran “small” ← μικρός stands beside makr † “great” ← μακρός and has never looked like a loan, for the reason given below.
• mern “share, portion” ← μερῶν, the genitive plural of μέρος, of the parts. The stratum came in as whole inflected forms. This is one of them, fossilised in an oblique case and carrying an -n that no nominative would have. It is the first element of mern-rak. The Greek definition of a perfect number is a number equal to the sum of its own μέρη. The highest phrase in the language is a compound with both Greek and Arcadian components.
• paln “again” ← πάλιν, which gives psai-paln “the return of souls”: παλιγγενεσία reassembled out of its own parts by people who no longer noticed or cared that whether half was Greek.
• ols “all” ← ὅλος. A quantifier the language does not need since the decadic does the work of a totality. It is correspondingly rare and survives because it is in the liturgy.
• per “trial, ordeal” ← πεῖρα. The ground-formula peraps “out of trial” (§5.10) is ἐκ πείρας.

Why mikran hid. A bare *mikr is unsayable in Laulai, ending in a rising cluster just as makr does. makr survived in Greek shape because it was protected: it stands in the teaching. The seven law-breakers are the seven that resisted some of the changes. Smallness is not in the teaching, so μικρός was left to the ordinary machinery. Instead of prothesis (L13) or epenthesis (L14) the word took the native quality suffix -an, which supplied a nucleus and closed the syllable. No other stem was known to have been repaired by derivation. Having been repaired that way, it looked derived. A word that looked derived was thought to be native.

Regarding pol. The apeiric suffix -pol is taken from pol “many,” and its opposite -lon from lont “bound.” Polarity is the brotherhood’s own construction and is the clearest case in the language of doctrine building grammar. If pol is πολύς then the two poles of that construction are not a native pair. The limit is named in Arcadian and the unlimited in Greek, which is πέρας and ἄπειρον with one of them translated and the other not. The commission that standardized suffixes included a Greek word for the unbounded pole and either did not notice or did not mind.

What was replaced, and what was not.

Field	Hellenic	Arcadian
kinship	father, mother, mortal, person	son, daughter, sister, brother, wife, husband, widow, kin, ancestor, twin, household, child, heir, orphan
the body	eye, mouth, tooth, skeleton	arm, elbow, ear, jaw, shoulder, brain, finger, claw, heel, neck, face, fist, nose, leg, belly, throat, hair, sinew, foot, skin, hip, palm, knee, breast, liver, hand, vein, brow, flesh, bone, tongue
the elements	water, fire, air, stone, tree	earth
the numbers	five, six, seven, eight, nine, ten, hundred, half	one, two, three, four, thousand, but see §8.7
the sacred	god, soul, world, law, harmony, the two counts, wisdom	rite, oath, holy, scripture, altar, prayer, shrine, invocation, offering, libation, witness-oath

What was replaced is what appears in the teaching. Father and mother are the cosmic parents and went; daughter and elbow are not doctrine and stayed. The earth, a thing the hill people stood on rather than a term of art, remained. The numbers used in arithmology went, while the numbers a child counts stayed. The apparatus of religion, altar and libation and oath and shrine, is Arcadian, while the objects of religion are Greek. The brotherhood replaced what it argued about and left the people to go on worshipping in their own vocabulary.

Two words for star. Both ἀστήρ and λαμπάς came in, which is unusual, since the Imposition normally replaced a word rather than doubling it. aštir † is the star as a point in a pattern: catalogued, standing in a pemn “constellation,” the one the first guild takes am interest in. laump † is the star as a burning thing: a luminary, anything that shines whether or not it remains fixed in place, so it is equally the lamp a person carries. The seven wandering lights are laump and never aštir, so the metals are taught with one word and the navigation tables written with the other. laump has meant “star” for as long as it has meant “lamp”: laump-klars is a star-chart, and amntems-laump “corpse-light” and krau-laump “crystal-lamp” hold the other sense open beside it.

Two of the doctrine’s own class-names are loans. The three consonant classes of §1.1 are lont, psnai and arm. lont is Arcadian. psnai and arm are Greek. The names given to the native sound-system are, two times in three, imposed vocabulary.

The model for prothesis. aštir “star” and aštin “skeleton” were long shown as type-specimens of L13. They are ἀστήρ and ὀστέον, their a- is Greek and was there before the brotherhood arrived. The Hellenic stratum was never touched by the repair wave, so a loan cannot show prothesis. The real examples are amdi “sea” from *mdi, amde “sharp,” alnθaun “flood,” along with some eighty more in the lexicon below.

9.2a Loans that didn’t change form

The dagger marks a word whose shape came from outside. It doesn’t indicate words whose shape is Arcadian and whose sense is not. A brotherhood that needed a term and found the hill people already had a word in the neighbourhood did not always import a Greek one. Sometimes it widened what was there, and the result is invisible to the tests in §9.2.

• lok “word, reason, account”: Arcadian in form and λόγος in every one of its uses. This is possibly an early Greek corruption. Auloic-shaped stems rarely carry a range like that: utterance, ratio, reckoning and the account a thing gives of itself are one word in Greek because of a particular argument that Greeks were having.
• saik “stillness”: an ordinary word for quiet, now the technical term for the unknown (§7.4). The brotherhood arrived with a five-year rule of silence. The Arcadian word was used to name it. The abstract sense came later and is now the common meaning.
• kernaus “kernel, essence”: a farming word for the inside of a nut. Possibly a Germanic corruption. The standard rendering of οὐσία, kernaus-met “assay” is etymologically essence-measure. Historically, the essence of a thing was the edible part.
• rak “whole”: native, and its technical sense is τέλειος, complete in the sense in which a number is complete. nesrak is then an Arcadian negation of a Greek idea on an Arcadian pattern.
• nan “joy; raving, prophecy”: probably the residue of a translation. μανία is divine madness, not necessarily a bad thing. A word for delight was the nearest the language had.

Argued and not accepted. Three forms have been proposed for the stratum proper and are not daggered here, on the ground that a plausible etymology is not a demonstration. These are possible corruptions, but they could also be a coincidence.

• mans “hierophant” ← μάντις. The sense is close. The difficulty is the dental, since μάντις should give *mant and the loss of the stop before the sibilant is not regular. mans gives manska, which is the ninth guild, the Order itself. If this etymology holds, the Order’s name for itself is Greek for the seers, while the native word for what a seer actually undergoes is nan, which also means joy.
• faut “light” ← φάος. It would make a third syzygy exemplar a loan after met † and anθ †. The vowel is not straightforward.
• io “echo, memory” ← ἠχώ. Attractive, and blocked by §1.2. io is the specimen of the one licit hiatus. Would a language import its own type-specimens, or were those conceived of after this was already imported?

A stratum defined by shape is a lower bound. Fifty-seven stems are identifiable. An unknown and probably larger number were incorporated, leaving no hard evidence.

9.3 Marginal segments

• /ð/ occurs in two independent words, ðaur † “water” and oðas † “path,” both from the first century of the Imposition and older than the law that would have caught them.
• /ž/ occurs in one word, džait “to live,” beside a commoner variant zait. The inner holds prefer the second and the akousmata use the first.
• bare /u/ occurs in one word, nukt † “night,” which L11 reached too late.
• /v/ occurs in one word, vril † “motive force,” on which see below.
• the onset tk- occurs in two common words: tka † “ten,” and the thing named after it, tkalok, the Order’s register, along with a number of specialized compounds. The doctrinal gloss is that the decad is where number completes itself and passes out of the lawful. It is fitting that the name of the ten and the name of the speech of the ten should be the only words in the language that break the law of beginnings.

Three words are Italic and not Greek: souvenirs of the brotherhood’s century in Magna Graecia, carried out of Kroton before the flight.

• sept † “seven” ← septem. Every other Attic numeral is regular and this one is not. It is also the base of septakt.
• nop † “nine” ← novem, by the plain treatment of *w (L1), which turns it to p: *nowem > *nopem > nop. ἐννέα will not give this form by any route.
• templau † “temple, trial-hall” ← templum, the marked-out ground an augur works in. The ending is unexplained.

Four words are late Latin, from the last three centuries the Laulai spent on the surface. This is the surviving vocabulary of that period: a road, a coin, a hymn and the force that powers civilization.

• štrat † “street, road” ← strāta, the paved way. Class X, with the built things.
• az † “coin” ← as, assis. The Arcadian words in the same field are mas “silver-coin,” ami “price” and ize “trade”. The borrowed one is a unit, which a people is expected to borrow when they are being paid in somebody else’s money.
• laus † “hymn” ← laus, laudis. It sits in class VI with the resonance vocabulary rather than in class IX with the rites.
• vril † “motive force; the work a true interval does” ← virīlis, “of a man, having a man’s strength,” from vir and beside vīs, vīrēs “force.” The derivation is the language’s own: pretonic syncope (L2) takes vi-RĪ-lis to *vrīlis, apocope (L4) takes the ending off, and vril is what is left. It arrived late enough that the repair wave was over and nothing came back to fix the onset, and late enough that Latin v was no longer a glide, so Laulai has a /v/ only in one word.

One word is neither. kaf “coffee” came up from the surface some two hundred years ago with a shipment of taken and has been in every gallery in the system within a generation. It is rare for loans to be accepted like this since the Withdrawal.

Vril is the most important noun in the confederation, known to be a Roman adjective for manly. The eighth guild handed the word to a circle of Earth occultists in the 1860s during a run of showings. One of them put it in a novel, and it has been going round the surface ever since attached to a fictional underground master race.

9.4 Living variation

(i) The palatal law has stopped. k became č before a front nucleus and then ceased, stranding čal “town,” čai “back,” čse “amount” and čme “praise” with č before nuclei that never conditioned it. These four have to be learned.

(ii) The triadic and tetradic suffixes nearly collide. -tri and -tra differ in one vowel and in fast speech they may not differ at all. Since a mis-said suffix changes what a step is worth, and a step worth the wrong thing is ineffective, the practice in tkalok is to say the numeral out in full: elm tre for elmtri. A free numeral carries its value into the balance exactly as the suffix does.

(iii) Class IX is a residue. A quarter of all nouns are class IX, many for no better reason than that no other class claimed them. The inner holds assign mikran “small” to IX and the outer holds to II. This is a dialectal difference that places where someone is from.

(iv) The pronominal plural in -s (mens, saits, kens) is the only non-numeral inflection left. It competes with the decadic on the same words. The lower galleries have quietly rebuilt a plural out of it that the standard language does not have.

(v) Three of the six locational preverbs are not yet preverbs. ane-, ni- and ok- attach directly in the inner holds (okmelai “looks about him”) and are written with a juncture in the outer, ok-melai, where they are still felt as adverbs standing in front of the verb. at-, irk- and ets- take the juncture everywhere. The orientational four take none anywhere, their transformation being complete.

(vi) The class prefix is going. It is obligatory in tkalok and optional in the nursery-speech. In the fast speech of the outer holds, it survives mainly on class III and class VII: on persons, and on the ksost.

(vii) Case stacking is contracting. The full stack of §4.4 is universal in tkalok and in writing. In speech, the inner holds stack only the genitive. A stacked locative is now a mark of an old, formal or careful speaker.

(viii) The accusative is spreading at the expense of the archic on definite undergoers (§6.2). This is the largest ongoing change in the language, led by the gun-decks.

(ix) Three of the ten joints are not settled. -aps, -am and -os (§5.6) are the three that begin with a nucleus. A nucleus-initial ending on a root whose final vowel is gone has nothing to lean on. They have been worn off and rebuilt from the noun paradigm more than once. They differ between the inner and outer holds in irregular ways. These are the words for because, that and which.

(x) The way round is spreading. The construction that lets a doer be relativized (§6.6) is universal in the seventh guild and common on the decks. It goes against the doctrinal interpretation of the grammar, so it’s forbidden in formal writing.

9.5 Two changes with dates

The class of fot. fot “slave” stood in class III with the persons in every text before 1743. It’s in class V with the grown and the bred in every text afterwards. Nothing in the sense of the word changed and no sound law is involved. The break is clean, and it falls in the decade of the first bred lines. A slave stopped taking the person-concord an-, stopped taking the person-pronoun ken, and began taking ton “it.”

The older state is still visible in the akousmata, which cannot be revised:

xap fotmon femai.
xap | fot-mon | fem-ai
NEV | slave-MON(1)-DAT | speak-KIN
Speak not to the slave.

The case is the dative, of the recipient and the other. Class V nouns are not addressed; one does not speak to seed, fire, grain or an ox. A maxim forbidding speech to a slave presupposes a slave one could speak to, and prohibitions are not ordinarily issued against the impossible.

The naming of the bred lines. The -zes pattern is attested from the same decade: kauzes, sipzes, nalzes, pmizes, falzes. It was productive within a generation.

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10. The Lexicon

The whole of the attested vocabulary: 1128 entries covering 1106 distinct stems, arranged by syzygy for nouns and by part of speech otherwise. The figure in brackets after a noun is its default arithmological number (§4.1): the inflection it takes when nothing in the context calls for another. Nouns without a figure are attested in too few contexts to give one.

† marks a stem that is not Arcadian: the fifty-seven of the Hellenic stratum (§8.1) and the four late-Latin loans of §9.3.

Class assignment is inherent and never marked on the noun itself. It surfaces on agreeing words and on the verb (§5.3), through the concord prefix given in each heading. Three assignments are not where a reader may expect them. brot † “mortal” and fot “slave” stand in V, the generative, the class of seed, fire, livestock and grain. ksost stands in VII, with rod, plate and everything else that is either straight or not (§4.2a).

I – limit / unlimited (me-): measures, media, fields, fluids, times (44)

alnθaun (2) flood, waterfall; alnθaun-fals (2) flood-gate, sluice; amdi sea; amp (2) smoke; amze (4) well; emer † day; idai scale (trade); in (2) snow; irn (4) earth; kar (4) time, season; knau (2) half-part; lau (2) wave; lit year; lom (3) weight; mamil month; mik (1) moment, instant; milne week; mlen (4) lake, hoard; mnis (3) judgment, measure; morb (2) cloud, mist; nang (1) horizon; nen shore; ner stream; not spring; nukt † night; on wind; op (2) ice; pin river; pok (4) ground; psnai † (1) sky, air, breath; psnai-alnθaun sky-flood, deluge; psnai-lont (4) firmament; ra rain; rarm (1) nadir; tešt (3) scales, judging; top place; ðaur † (2) water; čilp hour; θimp (1) zenith; rant (4) tolerance, declared allowance; el-kosm (10) the system, everything inside the limit; tsmizes-kar (4) the moon-month of twenty-eight days; serk (7) true interval, one of the ratios that does work on the world; taus (2) the outside, the hard cold past a hull

II – odd / even (pa-): number, data, reckoning, record (53)

ansol (2) fraction; karn (3) proportion; kelerp (10) number (number); kernaus-met essence-measure, assay; kor-pas (2) digit; lazen (3) mean-average; lok-tlaim (4) lexicon, word-list; lort (3) series; mik-tlaim (4) clock, moment-tally; mnis-knaus (10) sum; mnis-tešt (4) judgment-scales; omn (1) name; pas (10) number (quality); pedalkau figure; pemn (3) constellation; ramt (10) order-measure, canon; sašti (10) zodiac; sinb (3) sequence; solp (1) meridian; tadai (2) remainder; tauk (2) difference (number); tensi † (3) ratio; tetrakt † (10) the sacred count (fossil); teu (1) proof, evident truth; teu-klars (4) diagram, proof-drawing; teu-tešt (4) proof-scales, test-balance; tlaim (4) tally, list; tork (3) progression; tren conjunction; trini (7) cipher; xep (4) ledger; xol difference (quality); ðaur-mik (4) water-clock; čirt (2) quotient; čse amount; titlok (10) the old speech, the substrate tongue; tkalok (10) the decad-speech, the register of proof (§0.7); nesrak unwhole, ineffective (§7.2); medr-lok (1) nursery-speech, mother-tongue (§0.7); septakt † (10) the heptaktys, twenty-eight; mern-rak (10) a perfect number, and of an utterance the sworn grade; or-tlaim (4) pedigree, kin-tally; fot-lok (10) slave-speech (§0.7); nešt-tlaim (4) the roll of the Watch (§11.3 v); tnošt-tlaim (4) the roll of the Withdrawal; mne-tlaim (4) war-tally, engagement record; teukt (1) theorem; kno (3) lemma, a step granted; sništ (4) construction, a figure once it is built; teu-snip (1) proof-thread, a chain of steps; plio-teu (2) counter-proof; plišt (2) a reckoning, a piece of arithmetic once it is done (§6.7); čelok (1) the bound form, a clause tied by če- (§6.6)

III – one / many (an-): persons, bodies, aggregates, parts (139)

a head; abi market; ade daughter; ain twin; ak clan; aln arm; an † tooth; anθ † (1) person (one of the Laulai); anθka (10) all persons, the people entire; as tongue; de household; dne king; e brother; emp elbow; eu ancestor; fi ear; fik jaw; ge shoulder; ile son; kamp novice-of-guild; kel flock; klak (3) wright; klaz (1) initiate; kol neighbour; kom brain; kon chief; kop herd (animal); kor finger; kretmis captain of industry; kri claw; lap soldier; lars (1) adept; launt (10) congregation, gathering; le husband; ler heel; li neck; lirai (1) guild-master; lo face; lop army; lor tail; mans (1) hierophant; mau fist; medr † mother; melg great one, elder; menan (1) magister; mis (1) lord, teacher; mor swarm; mos (3) elder-council; nam (10) assembly; nasp (4) archon; ne nose; nelmi (3) engineer; nip leg; nit caravan; no throat; nok belly; onan judge; ops † eye; or kin; os † mouth; par horn; pet queen; pi hair; pme village; pond steward; ponen precentor; pslaus singer, poet; pso servant; ptir † father; rai (2) journeyman; raut censor; razau cantor; ris sinew; rit wing; ro sister; rom foot; ron toe; sal stranger; sam guest; sap lung; sen (2) child, novice; sennan youth; sen-mis (1) child-lord, boy-master; sil (2) apprentice; sim skin; sir enemy; sop blood; sos (3) council; sot hip; spai proctor; tai hoof; tal watchman; tan palm; teng warden; tepe freeman; tet (10) guild; tetka (10) the confederation; til knee; tim friend; tli trade-guild; to wife; tol breast; xen liver; xer hand; xik guard (society); ze orphan; čai back; čal town; čik city; čin heir; θe widow; θek vein; θil brow; θmi flesh; θon master-craftsman; laulai (1) a Laulai, one of the people; laulaika the race entire; plask † (1) Pelasgian, of the first descent; kosm-nasp (10) the archon-race, the cosmic aristocracy; mniska (10) first guild, the Measure; xepka (10) second, the Ledgers; mneka (10) the War (shrine of the second); nomka (10) third, the Law; kertka (10) fourth, the Gearing; θauka (10) fifth, the Seed; armka (10) sixth, the Harmony; relka (10) seventh, the Blades; ongka (10) eighth, the Visions; manska (10) ninth, the Order; plagka (10) the Invocation (shrine of the ninth); oðaska (10) tenth, the Paths; menan youth; pmišt (1) hunter, one who has been out; imn-anθ (2) ash-person, a burnt child lord; irk-anθ (1) turned-back person, one who recovered; mne-mis (1) war-lord, general; teu-anθ (1) proof-person, scholar; orn-anθ (1) chant-person, singer; prot-fot (1) first-slave, a Greek who took the doctrine unforced (§8.1)

IV – right / left (xe-): thread, gearing, rotation, transmission (32)

aldi weave (cloth); ani loom; emi thread-spun; emt (6) orbit; kert (3) cog, fate-wheel; kre rope; krot (4) stator; lir (1) cord, lineage; malk (3) shaft; mni (3) axle; nai yarn; nand-lir (2) bind-cord, restraint; nazes (4) bushing; pamp (5) rotor; psai-snip (1) soul-thread; reu-lir (3) song-cord, instrument string; rin (3) joint, and a joint of speech (§5.6); sals (3) spindle; sirn (6) epicycle; snip (2) thread, nerve; snip-θilt (2) knot-thread, tangled circuit; sošt (6) flywheel; tins (4) bearing; tirt (2) cunning, a twist; tni (3) lever; xes (6) wheel; čairt (6) wheel-work; šisne (4) mounting; θok-čairt fate-wheel, horoscope; lans (4) gantry, catwalk; noln (2) yoke, harness-beam; irk-rin (1) back-joint, the link a reciter comes back on (§5.6a)

V – generative (sa-): sources, couplings, seed, fire, the grown and bred (93)

al deer; alntinan wheat; dendr † (4) tree; enen cheese; enerk (5) power, anger; eni meat; ep pig; fai bean; fak (5) kiln; fap pepper; fas wood; fe mouse; fek pot-herb; gi rat; i bird; ikt barley; imn wine; is wolf; izai fat; kan ant; kem (5) hearth, furnace; ker nest; keu milk (food); ki bear; klo egg; kro butter; lel broth; lil flour; map feast; mat berry; min branch; mo dog; mok scale (animal); na horse; nap meal; nek grass; nol moss; non worm; nri (5) root; omp bread; pa hare; pam fur; pan dough; pap soup; paur † (2) fire; pebau (5) growth; pen leaf; pis fly (animal); pom crumb; pro hunger; pte flower; rapan strength; ren beer; rene moth; rip apple; rir spider; ros root-crop; saink (5) heartbeat, thrust; san honey; saz animal; sazip (5) birth; se ox; sel snake; sntasp fish (animal); som feather; tek spice; termanki grain; tong harvest, all-fruit; xe (1) lightning; xok fruit; xot nut; či goat; čip herb; čis onion; θau (5) seed; θes bee; θi sheep; θin oil; θki (5) yeast; θo beast; brot † (2) mortal, one of Earth; brotka (10) mortal-kind; fot (2) slave (class III until 1743); fotka (10) a slave-race; θaušt (4) gene-stock, graded seed; θau-kot (4) seed-chamber, breeding house; kauzes (2) the digging line; sipzes (2) the striking line; nalzes (2) the feeding line; pmizes (2) the tracking line; falzes (2) the handling line; brot-launt (2) a congregation on Earth (§0.4); nalne (2) mouthful, a bite of something cooked

VI – rest / motion (el-): engines, mechanisms, resonance, sound (38)

alnin (3) antinode; ams (4) apparatus; ank riddle-song; det echo-of-voice; elm (4) engine; eun (4) mechanism; fals (2) gate, threshold; io (2) echo, memory; klide (3) timbre; krad harmonic; laus † hymn; lidit (3) pitch (resonance); mirne (2) beat-tone; mozes (6) resonator; nais (3) standing-wave; nalte (3) consonance; narn (1) fundamental; neln litany; niks (2) vibration; orn chant; plap (3) interval; plio (2) dissonance; rem (4) mill; rern (2) storm, chaos; rern-θaun (2) storm-bell, alarm; reu-alnθaun (2) song-flood, resonance cascade; reu (3) song, spirit-voice; rezas (3) resonance; sarmi (2) overtone; tort (3) node; tson (3) tone-quality; vril † (7) motive force, the work a true interval does; xem (1) heart, driving-core; xem-kert (1) heart-engine, prime mover; θaun (3) bell, summons; θaun-templau (4) bell-tower, campanile; θomp transmuter, change-engine; sarn (2) wandering tone, a pitch that will not sit

VII – straight / curved (θo-): rod, plate, edge, structure, extension (60)

ambe sail (trade); amn sphere-celestial; antri (4) wall; arme (2) wedge; armpalmaul (4) frame; edi (2) hammer; esp net; ez (2) saw; kam girdle; kim (4) plate; kin sickle; kla rib; kle patch; kli (4) bridge; lal (2) tool; lan (4) stair; lon hook; los (2) chisel; lot (2) needle; mak spoon; mes ladle; mim plough; mre sledge; nar seam; nis spine; pik (2) peg; pim hem; ping (4) chassis; plas † (4) plain, sheet; pne bone; ral boat; rel (2) blade; rep oar; ret scythe; sak spade; sat (2) file; sau ladder; sik (2) nail (tool); siz knife; sonk edge; tme nail (body); tnai censer; xar (5) bow, curve; θak cart; θem fence; θep ship; θir anchor; θmpe (2) axe; θpe (2) awl; pol-rel (7) the many-blade; θepka (10) the fleet, all ships; ksost (9) one of the crooked ones, one of the things that come in from outside the limit; θalm (9) the plate, a ksost that is all surface; šarn (9) the singer, a ksost heard before it is seen; mnok (9) the jesters, many bodies on one figure; xasp (9) the mouth, a ksost that is mostly an opening; kolp (9) the fold, a ksost larger inside than out; arke (9) the still one, a ksost that entered and stopped; nars (2) open seam, a join whose angles do not add up; kolt (2) bracket, the pair of numbers a rangefinder returns instead of a range

VIII – light / dark (fa-): lamps, rays, images, colour, the occult (29)

amntems (2) ghost, omen; amntems-laump (2) corpse-light, will-o-wisp; ampsai (1) shadow-soul, shade of the dead; anbis (2) meteor; aumn dream; aštir † (1) star; el † (1) sun; faut (1) light; im (2) darkness, shade; klor (4) glass, mirror; kne likeness; krau † (4) ice-stone, crystal; krau-klor (4) crystal-mirror, speculum; krau-laump (4) crystal-lamp; laump † (1) lamp, star; laump-klars (4) star-chart; nante (2) comet; ong (3) vision; psnai-petr (2) meteor, sky-stone; skot † (2) dark(ness); sonen (2) eclipse; tsmizes (1) moon; ongzes (4) seeing-engine; kišt (2) a showing; brot-ong (2) the reading of mortals; psai-paln (10) the return of souls; xamn (1) the waking, the opening of the reach; sorm (1) reach, what a waked mind can put through a ratio; xamn-kot (4) waking-chamber

IX – good / bad (so-): evaluation, temper, obligation, the sacred (179)

aken (10) liturgy; akrauzes folly; al debt; alde longing; almi tax; almpint duty; alni purpose; alnte idea; ami price; amk murder; amzi disgust; anki skill; anze argument; anθka humankind, the living; ardi thirst; ari promise (society); arm † (1) peace, order; arni profit; asp chimney; aum doubt (mind); aun (3) rite; aunan (3) ritual; dai attention; ebau grief; emn proverb; enz mind; ern rage; etke forgetting; fa thunder; far loneliness; fat blame (speech); fit jest; fsi affection; gli jealousy; gni loss; gri shout; int (2) sin, defect; ir lip; ird belief; irm sorrow; irs life; ize trade; kak treaty; kazasθi beauty; kepi unease; kernaus (1) essence, kernel; ket courage; kik intention; kinan wonder; klars (4) drawing, rune; knarpau poem; kok sentence; konan product; kos craft; kosm-arm (10) world-order, cosmic law; kosm-psai (10) world-soul; krage art; ksau (1) truth; kse part; kspenan † (10) wisdom; kti agreement; lai beginning; lak problem; laren despair; las tribute; lat goods; lazau libation; lek taste (food); len valley; lep whisper; lip curse; lis pit; lok word, reason; mamir pride; mart pity; masp opposition; mek sameness; mem contract; memau calm; mern † (2) share, portion; mimeu offering; mit prison; mne war; mot insult; nan (1) joy; nan (1) raving, prophecy; nararp thought; nel opinion; nelešti ugliness; nenan tale; net fine; nle warning; nols sacrifice; nom † (10) law, custom; nonan surprise; nre comfort (emotion); peman weakness; penan command; penen shame; pep insight; per † (3) trial, ordeal; pes mantle; pio delight; pip refusal; pla (2) mistake; plag invocation; pleg decay; por crime; pos mountain; psai † (7) soul, self; pske health; rak (10) whole (quality); ras wage; razis speech; reu-mern verse; rikni envy; saik (1) stillness; the unknown (§7.4); sek prayer; senin age; ser patience; sis punishment; ske middle; sol veil; talt lie (mind); tap stable; tat gratitude; teke theft; tel † end, death; tenan ignorance; tenli saltpetre; tes (1) witness-oath; tider desire; tok threat; tor stew; tot farewell; trize greeting; xak request; xarp hope (emotion); xat answer-given; xau (1) silence; xel riddle; xin rind; xme disorder; xne blessing; xos terror; xosan fear (emotion); čil (1) oath; čim knowledge; čme praise (speech); šik choice; šin debate; θai regret; θam boredom; θan loan; θap decision; θat truce; θazes sickness; θelk scripture, god-word; θet understanding; θeu † (1) god, spirit; θilt knot, spell; θim lady; θio rumor, hearsay, story; θit witness; θke question; θol (4) right (society); θot plan; θsi contempt; nešt (3) watch, vigil, night-keeping; θamn (1) axiom, what is seen entire and without proof; čelan (1) a call, a number-call; sišt (3) inspection, the assessing; θalt (10) the Imposition, the naming-over; tnošt (10) the Withdrawal, the clearing-out; or-nom (10) the law of descent; elm fear; irn rite; mamn (2) the crooking, the sickness of having looked (§0.2); tirnan (2) doubling, the state of a body whose parts come round twice

X – square / oblong (ne-): form, jig, casing, vessel, building, stuff (109)

aim smoke-hole; anbe (4) square; amdi-pal island; andai sanctuary; ange cellar; arde sandal; arne cloak; az † coin; azen window; aštin † body, skeleton; dom † (4) house; enan garment; enk hut; eps shirt; ert belt; fer hill; fes sash; fet courtyard; fim felt; fis box; fni harbour; id floor; iln home; imn ash; im-kot (4) dark-chamber, camera obscura; izas robe; kagi roof; kelme wool; kem-kot (4) furnace-chamber; kent (4) lead (material); kep door; kosm † (10) world, universe; kot (4) room, womb; kot-marn (4) housing; lam pot; lem chest (body); les forest; lik (4) workshop; lits (4) gold; lorm shrine; malθ incense; marn (4) casing; mas silver-coin; mip bowl; mni (3) leather; mol cargo; momp lime; nant (4) sulphur; narilt (4) iron; nark altar; nasp (4) silver (material); nem wares; neu granary; nir hide (cloth); oðas † path, road; pai barn; pal rock; pek glove; pel forge (dwelling); penke linen; petr † (4) stone; pil basket; pirk (4) mercury; ple bucket; prok temple-precinct; prom clay; ram coat; rek cup; renasθ (4) steel; reu-kot (4) sound-chamber; rim thing, matter; sai sand; saik-kot (4) silence-chamber, anechoic room; sanester (4) bronze; sep loft; sims (4) copper; tam (4) storehouse; templau † (4) temple, court; templau-fals (4) temple-gate; tik jar; tinan (4) tin; tio shoe; tip cave; tir chamber; tiθ dye; tne hood; tse cap; šis (4) seal; štrat † street, road; θar mud; θni boot; θok (4) stamp, fate; θos dust; θrmaunan (4) brass; θspe cloth; θerk (2) fissure, crack; pi-θerk (2) hairline crack; tirm (2) creep, slow drift out of true; korm (4) certificate, attested paper; kosm-kot (10) a hold, world-chamber; xrešt (2) one of the taken, cargo; xre-kot (4) press-hold; men island; čirt housing; loks (2) book, bound account; kaf (2) coffee, the black draught of the surface (§9.3); rimp (2) shed, the crooked matter in a ksost’s wake; rakt-rim (1) closed body, the carcass of a ksost once it has been closed; kimp (4) pressure-shell, hull-suit

Verbs (155)

ades forget; ai run; andi forbid; ant doubt (abstract v); ap wake; ar walk; arm-nau tune; asp eat; aus bite; daun give; ek sit; elau polish; elt come; emau chant; end prove; fal love; fem speak, tell; fen compare; fep listen; fom respect; fop choose; fos break; iks deny; ilk promise (abstract v); inan grind; inen understand; ins spin; ip speak, name; ire weld; isp believe; izes weave (action v); ka sleep; kap trust; kau dig; kelti despair-of; kip discover; kir dry-out; klos close, finish; knaus know; komp mix, blend, alloy; lar sharpen; laz have; lekt † say; lerau intend; lim brew; limn attune; lin drop; lol braid; mai thresh; mal reap; mel look; mep taste (basic v); mer shear; met † measure, law; mikam assay; minan transmute; mop guess (abstract v); mosk despise; nal cook; nand bind, oblige, tie; nat smoke-cure; nau push; nep tear (basic v); nil hold; nilke temper-metal; nio refuse; nme burn; nor dig-out; nos pull; om stand; ons drink; ont be (copula); opt see; orm remember; orn forge (action v); orp explain; pak fish (action v); pat agree; peu chew; plarpen carve; pli reckon; plige gauge-measure; plo wash; pmi hunt; pot cough; pra plait; prar resonate; pre lift; psa plant; pse salt-preserve; psri learn; rel (2) ferment; rik invent; riz dare; riθ measure-out; ronan oscillate; rope hope (abstract v); ror roast; rot bake; sair amplify; salki vibrate; sar put; sem herd (action v); senan teach; ses hear; set swallow; si lie (basic v); sip hammer-out; sit cut; sme winnow; sni build; sok dispute; spi decide; tar sew; tin breathe; tmau forge-weld; tomt quench; tos place, set, there-is; toz damp; tri catch; tro boil; xan throw; xonk calibrate; xpe touch; xre take; xse milk (action v); xte allow; zait † live; čir trap; čmpe be; šain flow, flee, go; šait anneal; šir betray; šit sow; θal cast; θant die; θel want; θen smell; θers do, make; θik obey; θle rub; θme imagine; θop change, transform; θpi carry; čel call out, cry the number; tno clear, empty out (a hall); θko condemn, strike from the roll; pert enter in the roll, register; tasp step over, cross; kis show, appear before mortals; rakt close, prove shut; klos close; xamn wake, open the reach; imnai go to ash, burn out; kerm scorch, sear; xirn tear open, rip

Adjectives (116)

adi wide; amde sharp; anan cowardly; arbi just; arge rare; au brown; aze white; bau profane; bi cool; em soft; er pale; erm ash-grey; fok common; gau tainted; gen free; ik grey; il hard; ime short; kank bad; kas full; ke green; kertan geared; kis open-known; klari wrought; kler corroded; konen hasty; kradan harmonic-adj; lašte honest; lenan clever; lil brave; lont bound; ma thin; makr † big, great; mam crooked, out of true, the standing adjective of the ksost (§4.2a); me silver (colour); meu greedy; mi blue; mikran † small; mil unjust; mir holy; mom FALSE; monan untuned; nanis gentle; nas clean; nim far; nin deep; nirθ humble; o long; ol yellow; opel sky-blue; panan tempered; pau TRUE; pe narrow; pem weak; pilte wise; pimn malleable; plionan dissonant; po warm; pop shallow; prabe generous; prad deceitful; pri strange; prot † first, foremost; psi slow; rap strong; rat careless; rau proud; razai harsh; rerm ductile; rezasan resonant; ri cold (basic adj); ril fast (basic adj); rošt calibrated; sanan careful; sas right (basic adj); siln cast-adj; sin dull; sinan foolish; sind brittle; siθ patient; sne pure; so heavy; son good; sor new; sti familiar; ta dark-red; tadi red; tas (1) empty, cup; te thick; tem dry; tempe kind; tep wrong; ter loud; ti golden; tilt tuned; tit old; trene black; xal near; xek stupid; xke wet; xlir mechanical; xom young; čit dirty; θa hot; θis high; θom straight; θonan cruel; θor low; plask † (1) Pelasgian; mern-rak (10) perfect; rošt-nes uncalibrated, unfit; θoln unclosing, that does not terminate; tirn doubled, occurring twice in one body; kolt bracketed, having no single measure; nirn over-hollow, larger within than without; saun sounding, giving off a sarn

Particles and adverbs (44)

alme then; alne soon; ame there; ane inside; at across; ebi below; et still, yet; ets forward; eč along; fo downward; fon meanwhile; irk backward; it here; iθ already; ko behind; kra yesterday; la upward; mals very; mar Q (polar particle); nain now; nak long-ago; nes not; ni outside; nik right (space time); ok around; paln † again; pir seldom; pon west; ran east; re before; rer late; rol early; sa between; tak always; tau south; ten often; tle left; tom tomorrow; tske above; xap never; xio north; pen jussive (§5.5); θas today; tsa apprehensive, “lest”

Numerals (13)

di two; eks † six; ektan † hundred; en one; ims † half; nop † nine; okt † eight; pent † five; sept † seven; tka † ten; tra four; tre three; šal thousand

Pronouns (7)

ken he/she (3sg anim); kens they (3pl anim); men I (1sg); mens we (1pl); sait you (2sg); saits you (2pl); ton it (3sg inan)

Postpositions (source of the cases) (4)

aps † from (ABL), than (compar.); es † in, at (LOC); met † with (COM/INSTR); mon to, for (DAT/ALL)

Conjunctions (5)

am if; dit because; kat † and; lekt † that (complementizer); res or

Interrogatives (4)

tis who; kes what; ond where; pols how many

Demonstratives (2)

ent that (dist); ot this (prox)

Quantifiers (2)

ols † all; pol † many, much

The seven metals are assigned to the seven wandering lights. The assignment is taught with the heptadic: lits to the sun, nasp to the moon, pirk to the swift one, and so on.

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11. Texts

This section presents nine bodies of material, in the following order: The akousmata, which are old, mostly Arcadian, and recited in the nursery-speech. The constructions, which are tkalok. The hunt, which is tkalok composed live by people in dangerous circumstances. Beside it one testimony, which is a man talking for a day. Earth, which is what the confederation says to a species it is farming. Then two sections with loose speech: gun-deck speech, where the living language is shown, and a specimen of fot-lok, which is considered corrupt. Then the ash. Then the tale.

11.1 Akousmata

The akousmata are old and deliberately obscure. They are recited to apprentices without explanation and glossed aloud by seniors on the floor, differently in different halls. Most are Arcadian in every word, which makes them the best evidence anybody has for the substrate’s syntax. Most turn on a homophony, which is how they survived a language that lost its vowels. None of them balance, being maxims rather than proofs, laws or binding in any sense. None of them carries a class prefix on the verb either. That absence is one reason they are held to be archaic (§5.3).

(i) xap liram taspai.
xap | lir-am | tasp-ai
NEV | cord-MON(1)-ACC | step.over-KIN
Step not over the cord.

lir is the monochord standard and it is also lineage. Never cross a cable run. Never stand over the measure you are about to take. In the third guild’s reading, never get issue outside the line, the or-tlaim that has been kept for twelve hundred years.

(ii) xap xemam aspai.
xap | xem-am | asp-ai
NEV | heart-MON(1)-ACC | eat-KIN
Eat not the heart.

xem is the heart and the driving-core. Do not consume yourself with grief. Do not run the core down. The seventh guild recites it at people who have come back from a hunt and will not stop talking about it.

(iii) xap sizmet kemam xpai.
xap | siz-met | kem-am | xpe-ai
NEV | knife-INS | furnace-MON(1)-ACC | touch-KIN
Touch not the furnace with a knife.

In metallurgy, this applies literally. Morally: do not answer heat with an edge. The hunting shrine reads it as tactical doctrine, meaning never take on a ksost with the weapon you happen to be holding.

(iv) xap faim aspai.
xap | fai-m | asp-ai
NEV | bean-MON(1)-ACC | eat-KIN
Abstain from the bean.

The oldest and the most argued over. fai is class V, the generative, so the received gloss is that one does not consume what generates: “Don’t kill the goose that lays the golden eggs.” The inner holds keep it as a dietary rule, while the outer holds keep it as a rule about seed stock. They eat beans.

The fifth guild’s reading is the operative one and is why the maxim is painted at the door of every θau-kot: no Laulai line may be used as stock. Mortal gene-lines are bought, taken, cut and recombined without limit. anθ material is not touched, on pain of erasure from the or-tlaim.

(v) xap falsaps irk melai.
xap | fals-aps | irk | mel-ai
NEV | gate-MON(1)-ABL | backward | look-KIN
Look not back from the gate.

Once a hall is cleared, do not go back into it, not for a tool and not for a coat. It is the plainest of the akousmata and the most often disobeyed. The records of the last century hold nine entries that begin with: he had gone back for…

(vi) pen anθam naprai; xap natosai.
pen | anθ-am | na-pre-ai | xap | na-tos-ai
JUSS | person-MON(1)-ACC | THITH-lift-KIN | NEV | THITH-set.down-KIN
Help a man to take up; never to lay down.

Both verbs take na-, outward: the help goes away from the speaker and never toward him. Drill-masters gloss it as a rule about not getting under a falling load. Everybody else glosses it as a rule about generosity. It says anθ. The obligation stops at class III and the third guild has been explicit about that since 1751.

(vii) xap im melai.
xap | i-m | mel-ai
NEV | bird-MON(1)-ACC | look-KIN
Look not at the bird. Or: look not at the dark.

im is the accusative of i “bird” and the citation form of im “darkness”. The gnomic style permits a bare stem as object, so the maxim is ambiguous and cannot be disambiguated. It is the standard example of what the akousmatists mean when they say a symbolon is not a sentence with a hidden meaning but a sentence with two meanings and no way to choose.

11.2 Constructions

Everything here is tkalok. A construction is one sentence: a chain of converbs and a conclusion (§7.1), balanced over the whole (§7.2).

i. A hunting construction, five links. This is the standard opening against a slow ksost that has already been ranged. It is taught at eight and everybody in the second guild can recite it in their sleep.

ksostnopam θomelkat, narnam elplikat, serktrim meriθkat, —penam θoxonkat, ksost θoraktom.
ksost-nop-am | θo-mel-kat | narn-am | el-pli-kat | serk-tri-m | me-riθ-kat | —pen-am | θo-xonk-kat | ksost | θo-rakt-om
ksost-ENN(9)-ACC | VII-look-CVB | fundamental-MON(1)-ACC | VI-reckon-CVB | serk-TRI(3)-ACC | I-measure.out-CVB | UNK-PENT(5)-ACC | VII-calibrate-CVB | ksost-MON(1)-ARCH | VII-close-STAT
Having looked on the ksost at the limit, having reckoned its fundamental, having measured out three intervals against it, having calibrated the unknown that is its live source — the ksost is closed.
Balance: 9 + 1 + 3 + 5 + 1 = 19 → 10 → 1. rak.

The unknown is pentadic because what the company is solving for is the thing the ksost is coming out of (§7.4). The construction is an argument that a crooked figure still has a source and that the source is inside the limit even when the figure is not.

Nineteen reduces to ten and ten to one, which is the only reason the last link is ksost and not ksostdi. A prover picks the closing nominal partly for its sense and partly for its value. The sum must count to a perfect number for occult power to be channeled.

ii. The same construction, said wrong. In 1904 a sen-mis of twelve, on her fourth time out, put the heptadic on the unknown instead of the pentadic, one suffix out of place.

ksostnopam θomelkat, narnam elplikat, serktrim meriθkat, —sepam θoxonkat, ksost θoraktom.
ksost-nop-am | θo-mel-kat | narn-am | el-pli-kat | serk-tri-m | me-riθ-kat | —sep-am | θo-xonk-kat | ksost | θo-rakt-om
ksost-ENN(9)-ACC | VII-look-CVB | fundamental-MON(1)-ACC | VI-reckon-CVB | serk-TRI(3)-ACC | I-measure.out-CVB | UNK-HEP(7)-ACC | VII-calibrate-CVB | ksost-MON(1)-ARCH | VII-close-STAT
Having looked on the ksost at the limit, having reckoned its fundamental, having measured out three intervals against it, having calibrated the unknown that has no fellow — the ksost is closed.
Balance: 9 + 1 + 3 + 7 + 1 = 21 → 3. nesrak.

The heptadic is not a stupid value to put on a ksost‘s source. It is what half the seventh guild would have said. It is also two more than five, and twenty-one does not pass through ten. What it passes through is three, the number of balance. Fortunately, the company was able to back out of the engagement with everybody alive.

iii. An order. Composed in one breath, at the moment of contact, in ti-, which no adult present may contradict without having stood where she was standing (§5.5).

pen relmet —nopam tinandaika.
pen | rel-met | —nop-am | ti-nand-ai-ka
JUSS | blade-MON(1)-INS | UNK-ENN(9)-ACC | HITH-bind-KIN-COLL
Put the blade on the unknown at the limit — here, all of you, now.
Balance: 1 + 9 = 10 → 1. rak.

The unknown is ennadic and not ksost-anything, because at the moment of contact she does not yet know what she is looking at. Because of the collective on the verb, the company is to move as one object.

iv. The oath of descent, sworn by every Laulai in the twenty-eighth year of life, at twenty-eight, and not releasable under ordinary circumstances (§7.3).

anθkamet nomkat ksostkam mneseptel lanandomka.
anθ-ka-met | nom-kat | ksost-ka-m | mne-sep-tel | la-nand-om-ka
person-DEC(10)-INS | law-MON(1)-COM | ksost-DEC(10)-ACC | war-HEP(7)-TERM | UP-bind-STAT-COLL
All persons, with the law, bind the crooked ones entire unto the one war.
Balance: 10 + 1 + 10 + 7 = 28. mern-rak.

The heptadic on mne is significant: the war is a solitary war, ongoing since before the official chronicles. The seven also makes the sum effective.

11.3 The Watch and the hunt

Composed in the open, at speed, by someone with only a few seconds to respond.

i. A Watch report, off the firmament, sent down as one sentence.

psnai-lontam memeles, ksostnop tiθošainai.
psnai-lont-am | me-mel-es | ksost-nop | ti-θo-šain-ai
firmament-MON(1)-ACC | I-watch-CVB.SIM | ksost-ENN(9)-ARCH | HITH-VII-come-KIN
While the firmament is being watched: a ksost, at the limit and the ninth of the tally, is coming this way.
Balance: 1 + 9 = 10 → 1. rak.

The ennadic says two things at once and the meaning depends on context: at the limit, and the ninth of the tally. tiθošainai, in ti-, means she is not repeating anything.

ii. The closing report. Two hunters, coming in, on the ramp, before anybody has got their helmets off.

pmištdimet ksostoklonam θoraktomka.
pmišt-di-met | ksost-ok-lon-am | θo-rakt-om-ka
hunter-DY(2)-INS | ksost-OGD(8)-PER-ACC | VII-close-STAT-COLL
Two hunters have closed the great built solid, and it is bounded now.
Balance: 2 + 8 = 10 → 1. rak.

ksostoklonam is the point of the sentence. The ogdoadic says what they were looking at, a great built solid (§4.1 vi). The -lon says it has a straight pole now, which it did not have when they went out (§4.2a).

There is a dyadic on pmišt because six went out.

iii. The shortest report. A single word, called down a ramp. It is a complete utterance (§5.9):

ksostoklon.
The great built solid, at the limit.

iv. The alarm. The other single word:

ksostnop.
A ksost, at the limit.

Said down a gallery, it’s the call to take up stations.

v. The roll. The first guild’s list of what has come through, kept at the firmament and read aloud at the turn of the twenty-eighth watch. Each entry is a date, a kind and a line, written by people who had to be brief.

Roll	Date	Kind	What is on the file
the first	—	—	Older than the roll. The file is one line and a drawing, and the drawing is of a nars, so at least somebody was inside it
the second	1731	θalm	Came in edge-on and was therefore not there. Nobody saw it until it turned, and when it turned it was forty kilometres of plate. It was already across the sun. It took the surface works of a middle hold in eleven hours, cutting, and it cut on the way out as well. The roll was instituted the following year.
the third	1790	arke	Crossed the firmament, stopped, and has done nothing since. It is still there, ranged eleven thousand times. The bracket has never closed by so much as a kilometre. Two companies have been sent to it. Both were recalled by the seventh guild after the second day. The seventh guild has never said what the first day’s signals contained.
the fourth	1846	kolp	A body a tender could tow, and a party walked eleven days inside it without reaching anything. Declared closed by a company of twelve on a chain nobody has ever repeated. Eleven of the twelve died on the last link, and the twelfth was six (§1.6).
the fifth	1871	xasp	Went for the moon. It took the northern yards, three hulls on the ways and about nine hundred fot. Everything it took came back out over the following month as rimp, drifting in the shape of the yard it had been.
the sixth	1902	mnok	Somewhere above four thousand identical bodies, none larger than a cart, moving as one figure. The fleet destroyed nine hundred of them in a day and nothing changed. Closed in the end by two shrines working the same construction from opposite ends of the system without either being told the other was there.
the seventh	1938	šarn	Heard for eleven days before it was seen, through the hull before it was heard in the air. It is the only entry with a recording attached. The recording is four minutes long. It is kept in the sixth guild’s galleries. Apprentices are played thirty seconds of it once.
the eighth	1961	nirn	Was not seen crossing the firmament. Was found already inside it, in a hold, with people living around it (§11.8).
the ninth	2004	—	Still open. It is θokoltpol, it is θosaunpol. It has been inside the firmament since 2004. It’s still coming.

The ninth is the reason there is a sen-mis awake in every hold in the system at all hours.

vi. A field note from inside one. Signalled out of the fourth of the roll on the ninth day, by rope, one sentence at a time. The hunter who sent it did not come back.

kolpok θonirnpol θotirnpol narstrim θonges, tiθontom.
kolp-ok | θo-nirn-pol | θo-tirn-pol | nars-tri-m | θo-ong-es | ti-θo-ont-om
fold-OGD(8)-ARCH | VII-over.hollow-APEI | VII-doubled-APEI | open.seam-TRI(3)-ACC | VII-see-CVB.SIM | HITH-VII-be-STAT
The fold, a great built solid, over-hollow and doubled, while three open seams are in view, is here, around me.
Balance: 8 + 3 = 11 → 2. nesrak.

Balance is irrelevant because vril effects are not at play. He was nine days in. θotirnpol means doubled, the same part occurring twice in one body. He had walked down a corridor and arrived at its beginning without turning round. The three nars are why he stopped walking. The last word is in ti- (§5.2), on my own ground.

11.3a Testimony: the fold at Iort

In 1994 a hunter of the seventh guild named Maro sat in a gallery of a middle hold for most of a day and said what had happened to him. A scribe of the ninth wrote it down. It runs to about nine hundred lines. It does not balance as he is not proving anything. He is telling somebody what a place was like. He uses because, until, even if, the one that, and I did not know that. That is to say, he needs the three joints the trial-halls call irregular and both of the relative constructions tkalok will not license (§5.6, §6.6). This is intended to give an example of subordination.

The company had gone out to a kolp sitting in the ice of Iort, an abandoned moon at the edge of the middle system. Six went in. Four returned.

i. The tone. Nothing had been seen. The resonance galleries sensed it for six days first, which is normal. Often, this is the only warning anybody gets.

θopraraps, reu-kotes tisesomka.
θo-prar-aps | reu-kot-es | ti-ses-om-ka
VII-resonate-CVB.CAUS | sound.chamber-MON(1)-LOC | HITH-hear-STAT-COLL
Because the thing was sounding, we had it in the galleries before we had it anywhere.

The causal joint, which no proof uses and no account can do without. He gets a reason and an event into one clause.

ii. Going in. The seam is at the bottom of a shaft in the ice, and everything after this happens in the dark.

krem nilkat, θositkat, ane-šainaika.
kre-m | nil-kat | θo-sit-kat | ane-šain-ai-ka
rope-MON(1)-ACC | take.hold-CVB | VII-cut-CVB | IN-go-KIN-COLL
We took up the rope, cut the plate, and went in.

Nobody has mentioned the plate. The θo- on the second link is what says the sentence has stopped being about the rope (§5.6a i). The rope is the tender’s, it is eleven hundred cords. It is the only object in the surroundings that keeps a fixed length.

Maro chains for pages and comes back on the back-joint about every third sentence — … ane-šainaika. šainkat, …, “we went in. Having gone in, —”.

iii. What the corridors do.

nes čontom narstrim tiθongomka.
nes | če-ont-om | nars-tri-m | ti-θo-ong-om-ka
NEG | REL-be-STAT | open.seam-TRI(3)-ACC | HITH-VII-see-STAT-COLL
We saw three open seams that were not there.

A bound form under a negation, which describes a nars (§0.2): a join at an angle that does not add up, that the eye sees as a shadow. When you measure it, you feel an edge that is not there. To counter this, apprentices are taught the bound form before they are taught arithmological balance.

iv. Xame. Prolonged sight of a figure that will not close does something to a nervous system. It starts in the inner ear.

Xame nes anilrapkat, kenam irk-θpinalaika.
Xame | nes | an-nil-rap-kat | ken-am | irk-θpi-nal-ai-ka
Xame-MON(1)-ARCH | NEG | III-hold-POT-CVB | 3SG-ACC | BACK-carry-NEC-KIN-COLL
Xame could not keep his grip, and had to be carried back.

The necessitive (§5.4) says the carrying was owed.

v. Nothing in there has a fixed size.

nemetrapos rimkam nes tikipomka.
ne-met-rap-os | rim-ka-m | nes | ti-kip-om-ka
X-measure-POT-CVB.ATTR | thing-DEC(10)-ACC | NEG | HITH-find-STAT-COLL
We found nothing in there that could be measured.

The attributive joint (§6.6), where the bound form would have served perfectly well. Maro uses -os forty-one times and če- eleven.

vi. The rope.

kremet mikamet, tirnanam tikipom.
kre-met | mikam-met | tirnan-am | ti-kip-om
rope-MON(1)-INS | assay-CVB.MAN | doubling-MON(1)-ACC | HITH-discover-STAT
I found the doubling by assaying it against the rope.

He had walked a corridor for two hours paying the rope out behind him and had come back to his own knot without turning round. That is θotirnpol, doubled, the same part occurring twice in one body (§4.2a). The rope said four hundred cords and the walk said something else.

kremet and mikamet have the same ending, once on a noun and once on a verb (§5.6).

vii. On the wire. Tarla was twelve and on her ninth time out, at the top of the shaft with a wire running down into the ice. She asked a question:

“pols kre”-lek tičelai.
“How much rope,” she said.

The quotation is closed with the enclitic, so it keeps her deixis and not his (§6.7). What she said next was an order, in ti-, (§5.5):

pen kretram —ekam tinandaika.
pen | kre-tra-m | —ek-am | ti-nand-ai-ka
JUSS | rope-TET(4)-ACC | UNK-HEX(6)-ACC | HITH-bind-KIN-COLL
Put the warranted rope on the unknown that brings it into balance — here, all of you, now.
Balance: 4 + 6 = 10 → 1. rak.

The tetradic on the rope signifies installed, founded, warranted, the number used in deeds (§4.1). Everything else down that shaft was bracketed and the rope was not. The unknown is hexadic, a value that brings the system into running balance (§7.4).

viii. The chain.

kolpokam θomelkat, sarnam elplikat, kretram xeriθkat, —penam θoxonkat, kolp θoraktom.
kolp-ok-am | θo-mel-kat | sarn-am | el-pli-kat | kre-tra-m | xe-riθ-kat | —pen-am | θo-xonk-kat | kolp | θo-rakt-om
fold-OGD(8)-ACC | VII-look-CVB | wandering.tone-MON(1)-ACC | VI-reckon-CVB | rope-TET(4)-ACC | IV-measure.out-CVB | UNK-PENT(5)-ACC | VII-calibrate-CVB | fold-MON(1)-ARCH | VII-close-STAT
Having looked on the fold, a great built solid; having reckoned its wandering tone; having measured out the warranted rope against it; having calibrated the unknown that is its live source — the fold is closed.
Balance: 8 + 1 + 4 + 5 + 1 = 19 → 10 → 1. rak.

This is the construction of §11.2 i. with two words changed, and it is worth seeing them side by side. The taught opening takes a ksost at the ennadic, reckons its fundamental, and measures out three true intervals against it: nine, one, three, five, one. Tarla had no fundamental, because the thing’s tone would not sit. She did not have three intervals because nothing down there could be ranged. What she had was a rope and a sarn. She put the wandering tone where the fundamental goes and the rope where the intervals go. Because eight and four come to what nine and three come to, the total did not move. Nineteen either way.

The hexadic unknown of the order and the pentadic unknown of the chain are not the same hole. Thirty seconds apart, she asks first for whatever value will bring the thing into running balance and then settles for a source, which is a smaller and a harder claim. Provers change their bet in the middle of a chain (§7.4).

ix. The last link. Maro was on the rope forty cords below the seam and could hear her.

nes klosknekat, ni-šainalomka.
nes | klos-kne-kat | ni-šain-al-om-ka
NEG | finish-CVB.COND-CONC | OUT-go-NEC-STAT-COLL
Even if it did not finish, we were going out, and that was nobody’s decision.

The concessive and the necessitive in one clause: He is saying the way out was owed to them by then and that no one was going to be asked.

x. The silence. The sarn had been in the frame and in the teeth for six days and the bridge of every man’s nose. Then it was gone, and four people all noticed at once.

On the ramp, said down the shaft by a man who had been awake for two days:

ksostoklon.
The great built solid, at the limit.

xi. The measure. A salvage crew measures a rakt-rim out loud in front of everybody. That is the proof that the job was done.

rakt-rim tkakaten lirmet timetom.
rakt-rim | tka-kat-en | lir-met | ti-met-om
closed.body-MON(1)-ARCH | ten-and-one | cord-MON(1)-INS | HITH-measure-STAT
The closed body measures eleven cords. I watched them do it.

Eleven cords is about the length of a hand-cart. Six people had walked about inside it for nine days and two of them never left. The crew carried the whole of it up out of the ice in a crate on the back of a tender.

xii. Tarla went out eleven more times. The eleventh was in 1997, when she was fifteen. The file after that date holds one entry and it is a gallery number (§0.3).

At the end of the day, in the gallery, the scribe asked Maro what had become of the rope:

krem tilazom.
kre-m | ti-laz-om
rope-MON(1)-ACC | HITH-have-STAT
I still have the rope.

11.4 Earth

i. A showing. Spoken by an operator into an ongzes while the percipient imagined the room, the light and the weather from his own head (§0.4). It runs in fo- throughout, the direction of the thing that arrives unasked. It does not balance since this is not an arithmological operation.

xap xosai. mens laumpaps feltomka.
sait mensmet knausom. mens saitmet nes knausomka.
pen nakai. sait paln melai.

Be not afraid. We have come down from the star.
Thou art known to us. We are not known to thee.
Sleep. Thou shalt see again.

The figures are tall and pale and silent intended to frighten the percipient. Mediterranean features are easily apparent, but percipients tend to see their own preconceptions without any outside help.

ii. The instruction. What is said to the taken after a press-gang, in fot-lok, by a handler on the way in. It is a fot-lok rendering of the fifth akousma (§11.1 v). The tenth guild’s manuals call it the instruction.

sait falsaps nes melai. sait ame nes ontom.
sait it ontom. sait nain ontom.

You do not look back from the gate. You are not there.
You are here. You are now.

No preverbs, no converbs, no concord, three cases, four sentences where the original uses one (§3.1).

iii. What a congregation sings. To Earth, the Order sends down a serk: a ratio for several hundred nervous systems to resonate, in unison, at a fixed hour (§0.4). The ninth guild has for two centuries used, as the carrier speech, the oath of descent (§11.2 iv):

anθkamet nomkat ksostkam mneseptel lanandomka.

Its congregations sing it phonetically, from sheets, in halls in Bavaria and Buenos Aires and outside Peshawar, as ahn-tha-ka-MET nom-kat KOSS-ta-kam mne-SEP-tel la-NAN-dom-ka. They have variously been told it is Enochian, Hyperborean, the speech of the Ascended Masters, that of angels, that of Adam, Akashic, or some original language before Sanskrit. In reality, it’s a Laulai sentence swearing to defend the planet.

iv. A handler’s line. What a falzes says to a congregation’s inner circle at the moment of recruitment in Laulai:

saits mensos ontomka. mens saitsos nes ontomka.
You are ours. We are not yours.

They are taught it as a blessing. They repeat it back.

11.5 Gun-deck speech

Living speech, not carefully composed.

i. elmka! “all the engines,” and also, on the homophony of §9.1, “fear entire.” The standard oath of the lower decks. A wright says it when a mount shears.

ii. ksostkne “in the form of a ksost“. Being called a contagion is an insult. ksost is class VII and a person is class III. That would be the plio of §6.3.

iii. imn “ash,” and “wine.” Said of somebody whose reach is going: he has had a drink.

iv. tas “empty.” Of a proof step: worth nothing. Of a person: no reach, never had any, will not be missed.

v. pen tilontai, jussive, “be bound, here.” Said to a company going out.

vi. mar fo? “did it come down on you?” (§5.2a). Asked of a child who has just come off a chain and is shaking.

11.6 A specimen of fot-lok

A work-chant off a kauzes boring in the eleventh gallery:

fots kauai. fots kauai. pal fosai.
fots xre. fots xre. tir tos.
fots kauai.

Slaves dig. Slaves dig. The rock breaks.
Slaves take. Slaves take. There is a chamber.
Slaves dig.

fots is a bare plural in -s, built out of the pronominal plural (§9.4 iv). There is no arithmological number. There is no concord and no preverb. xres and laz are bare stems doing the work of finite verbs, which §5 doesn’t allow.

The Order’s position is that this is all corrupt speech.

11.7 The ash

When an imn-anθ speaks, an amanuensis writes it down. If the insight is weak, the form uses: fo-, the involuntative, no ground (§5.10), no class prefix on the verb, and the concord going early (§5.3). None of them balance. They come to nine, nopkne nesrak, one short.

(i)

tsmizes θepok fontinom.
tsmizes | θep-ok | fo-ont-in-om
moon-MON(1)-ARCH | ship-OGD(8)-ARCH | DOWN-be-INVOL-STAT
The moon turns out to be a great built ship, and I did not go looking.
Balance: 1 + 8 = 9. nopkne nesrak.

(ii)

—sepmet brotdim fomelinom.
—sep-met | brot-di-m | fo-mel-in-om
UNK-HEP(7)-INS | mortal-DY(2)-ACC | DOWN-look-INVOL-STAT
The unknown, the one with no fellow, is looking at some mortal or other, and it came down on me.
Balance: 7 + 2 = 9. nopkne nesrak.

(iii)

serkekmet ksostrim fonandinom.
serk-ek-met | ksost-tri-m | fo-nand-in-om
serk-HEX(6)-INS | ksost-TRI(3)-ACC | DOWN-bind-INVOL-STAT
An interval in running balance binds three crooked ones, and I did not do it.
Balance: 6 + 3 = 9. nopkne nesrak.

The third of those was said in 1899 by a boy who had commanded four companies and could not by then dress himself. The sixth guild spent eleven years on it and formed with a construction that closes three ksost in series from one interval, the only thing in two centuries that has ever closed more than one. About one in nine of these revelations are effective. The scribes sit with all of them and write everything down. The ash-people sit near the shrines and are not looked at directly.

11.8 A tale: Sarndi

Laulai has a narrative genre and it is governed by a rule about evidence. A nenan is a tale, recited in a gallery. Every verb in it takes na-, outward, passed on, it reached me from another (§5.2). A tale in ti- would be testimony.

Sarndi, “Two Tones,” runs to a hundred and eleven lines in the sixth guild’s recension. It is about the eighth of the roll, 1961, the one that was not seen crossing the firmament and was found already inside it. It is attributed to an orn-anθ writing within a generation of the events. What follows is the closing:

sarndi nasesomka.
kosm-kotes ton nontom.
sen-mis nasesai. sen-mis nes namelai.
relka neltomka. tas natosomka.
sen-mismet teukt naparaktom.
sarndi naklosom.
ksostseplon nontom.
imn nasarnai.

Two tones were heard, they say.
It was inside the hold, they say.
A child lord hears it. A child lord does not see it.
The Blades came, they say. They found nothing, they say.
By the child lord the theorem was closed, they say.
The two tones stopped, they say.
It stood at the limit, they say.
The ash wanders, they say.

nontom is na- plus ontom, elided (§5.2). neltomka is na- plus eltomka.

In line eight, sarn is a noun, a wandering tone, a pitch that will not sit. The line conjugates it, which is unusual. The last thing the tale says is that the ash is doing what a tone does when it will not settle. (imn is also wine (§9.1).)

Sometimes these songs end with a formulaic utterance:

men tisesom.
I heard it. I was there.

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