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| == Proto == | | # ℕ – Natural Numbers – 1,2,3,… |
| {| class="bluetable"
| | #: Numbers used for counting discrete objects. Equality is determined by direct inspection. |
| |+ Consonants of the Proto
| | # 𝕎 – Whole Numbers – 0,1,2,3,… |
| ! !! Labial !! Dental !! Alveolar !! Dorsal
| | #: Adds zero, the additive identity. Useful when “none” must be distinguished from “does not exist”. |
| |-
| | # ℤ – Integers (German ''Zahlen'') – …,−3,−2,−1,0,1,2,3,… |
| ! Nasal
| | #: Numbers closed under subtraction. Every number has an additive inverse. Often interpreted as magnitude with direction. |
| | m || n || || N
| | # ℚ – Rational Numbers (quotients) |
| |-
| | #: Numbers of the form <math>\frac{a}{b}</math> with <math>a,b\in\mathbb{Z}</math> and <math>b\neq0</math>. |
| ! Stop
| | #: Equality has a finite certificate: <math>\frac{a}{b}=\frac{c}{d} \iff ad=bc</math>. |
| | p b || t d || k g || q ʔ
| | #: Most quantities in the world cannot actually be divided into arbitrary rational parts. |
| |-
| | #: <hr> |
| ! Sibilant
| | # 𝕂 – Constructible Numbers (German ''Konstruierbare'') |
| | f || s z || || x
| | #: Lengths constructible with compass and straightedge. Equivalent to starting from 0 and 1 and allowing <math>+,-,\times,\div</math> and square roots. |
| |-
| | #: They cannot be exhaustively exhibited as decimals or directly compared. |
| ! Fricative
| | # 𝕆 – Origami Numbers |
| | þ || ł ɮ || || h
| | #: Lengths constructible with origami folds or neusis (marked ruler). Equivalent to extending the constructible toolkit to include cube roots. |
| |-
| | #: <hr> |
| ! Rhotic
| | # 𝕊 – Shifting Root Numbers |
| | || r ɻ || ||
| | #: Numbers whose digits can be generated sequentially by classical digit-extraction root algorithms. Each digit is determined exactly and never later revised. |
| |-
| | # ℙ – Polynomial Numbers |
| ! Approximant
| | #: Roots of finite polynomials <math>a_nx^n+\dots+a_1x+a_0=0</math>. |
| | || j || w
| | #: They can be approximated to arbitrary precision by iterative methods such as Newton’s method. Earlier digits may occasionally require revision during computation. |
| |}
| | # 𝔾 – Geometric Numbers |
| | #: Numbers arising from geometric quantities that are visually meaningful but difficult to access numerically. Examples include <math>\pi</math>, <math>\ln 2</math>, and <math>\sin(1)</math>. |
| | #: The new additions at this stage are transcendental. |
| | # Σ – Series-defined Numbers |
| | #: Numbers defined by infinite sums <math>\sum_{n=0}^{\infty} a_n</math>. |
| | #: Stopping after finitely many terms yields a predictable approximation. |
| | # 𝕃 – Limit-defined Numbers |
| | #: Numbers defined as limits of sequences <math>\lim_{n\to\infty} a_n</math>. |
| | #: Each stage recomputes the value from a finite rule. |
| | # 𝔸 – Arbitrary Algorithmic Numbers |
| | #: Numbers defined by any explicit algorithm generating digits or approximations, even if they have no particular geometric or analytic meaning. |
| | # 𝕌 – Uncomputable Numbers |
| | #: Quantities that can be defined logically but whose digits cannot be generated by any algorithm. |
| | #: <hr> |
| | # 𝔇 – Divergent Numbers |
| | #: Values assigned to divergent series by summation methods such as Cesàro, Abel, Hölder, or Borel. |
| | #: Example: <math>1-1+1-1+\dots =_{\text{Cesàro}} \tfrac12</math>. |
| | # ζ – Zeta Numbers |
| | #: Values assigned to divergent sums using analytic continuation, especially through the Riemann zeta function. |
| | #: Example: <math>1+2+3+4+\dots =_{\zeta} -\tfrac{1}{12}</math>. |
| | #: Ramanujan is the most famous advocate of this interpretation. |
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|
| | | * ℕ–ℚ exhibitable |
| {| class="bluetable"
| | * 𝕂–𝕆 geometric |
| |+ Vowels of the Proto
| | * 𝕊–𝕃 algorithmic approximation |
| ! !! Front !! !! Back
| | * 𝔸–𝕌 algorithm / logic |
| |-
| | * 𝔇–ζ regularization |
| ! High
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| | i ī || || u ū
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| |-
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| ! Mid
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| | || ǝ ||
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| |-
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| ! Low
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| | || a ā ||
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| |}
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| no vowel hiatus
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| was SOV
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| == Now ==
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| Super-fusional=polysynthetic
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| * z --> ʃ | |
| * ɮ --> č | |
| * ɻ --> ɚ | |
| * ? --> ø | |
| <pre>
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| m n ŋ ܡo ܢo ܥ MNŊ
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| p b t d k g q ʔ ܦoܒo ܛoܖo ܟoܓo ܩo ܐ. PBTDKGQ
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| ɸ~β s~z ʃ~ʒ χ~ʁ ܧo ܣo ܙo ܚo (FV)(SZ)(ŠŽ)(XĦ)
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| θ̼ ɬ t͡ʃ h ܬo ܫo ܨo ܗo þ Ł Č H
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| r l ݍo ܠo R L
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| j w ܝo ܘo Y W
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| </pre>
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| <pre>
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| i=j u=w ܐܺorܐܻ x ܐܽorܐܾ
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| e=h o=ħ ܐܶorܐܷ x ܐܳorܐܴ
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| ɚ=r a=ʔ ǝ=ø ܐ݅orܐ݆ x ܐܰorܐܱ x ܐ݃orܐ݄
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| </pre>
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| ==== Diphthongs ====
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| First: ey, ai, ow, aw. Second: all long vowels (aa, ee, ii, oo, uu, ɚɚ).
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| Morae: (C)V = 1, CVV/CVC = 2, CVVC = 3. Stress is on the third from the end mora (or the first syllable – obviously – if its too short). This is easiest to remember in the writing without vowels: stress is on the third to last letter.
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| yes gemination
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| === Nouns ===
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| Genders: three big groups, with five in the last
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| # Eternal: these are all (attributes of) God, '''O Righteousness''', '''God of Love''', '''Geometry in the Mind of God'''
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| # Forms: these are the Forms as they existed embodied before the Fall, '''True Man=Adam''', '''table-ness''', some angels
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| # Natural: these are all here and now, after the Fall, maybe sinful, maybe not
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| ## People - man, woman, spiritual beings
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| ## Animals - domestic animals, occupations, highly-complex tools, faces, hands, families, cities
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| ## Beasts - non-domestic animals, moving things (water, fire), medium tools, body part*
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| ## Seeds - technically alive, inert tools, homes, regions/places,
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| ## Rocks - not alive, verbal nouns, mass nouns
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| Numbers: there are three
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| # Singulative - takes the place of definiteness, "THE ONE"
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| # Paucal - a few, some, a couple
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| # Collective - unmarked, quasi-plural
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| {| class="bluetable"
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| |+ '''Prefixes'''
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| ! !! Eternal !! Form !! Person !! Animal !! Beast !! Seed !! Rock
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| |-
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| ! S
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| | rowspan="3" | š(a)-
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| | ??
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| | ??
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| | ??
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| | ??
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| | ??
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| | rowspan="3" | ??
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| |-
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| ! P
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| <!-- Eternal //-->
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| | rowspan="2" | ?
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| | ?
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| | ?
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| | ?
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| | rowspan="2" | ?
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| |-
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| ! C
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| <!-- Eternal//-->
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| <!--Seed//-->
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| <!--Rock//-->
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| |}
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| Case: there are three -- '''suffixes'''
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| # Nominative: (also doubles as vocative) -ø
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| # Accusative: -(u)L
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| # Oblique: (mainly genitive and dative) -(w)o
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| Person: 3rd person always agrees with one of the 7 genders. There is 1S, 2S, 1PX, 1PI, 2P, 1C, 2C
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| Pronouns: As in Hebrew, they can be independent or affixed. Independent is only used in simple (copulative) sentences. The prefixes attach to postpositions (like Hebrew), they attach to nouns to mark possession, and the verbs to mark the accusative.
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| === Verbs ===
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| _ uses normal Nominative-Accusative morphosyntactic alignment. Verbs are marked for
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| # (if transitive) object person slot
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| # (optional) applicative slot
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| ## ''passive''
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| ## ''mediopassive''
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| ## benefactive
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| ## instrumental
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| ## locative
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| ## comitative
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| # (optional) noun-incorporation slot
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| # lexical verb, which inflects for
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| ## subject person
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| ##* there 12 of these!
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| ## aspect --- like Hebrew perfect vs imperfect
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| ### continuous
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| ### aorist (perfective)
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| ### future (irrealis)
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| ## evidentiality --- like Qal vs Piel vs Hiphil
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| ### direct
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| ### hearsay
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| ### inferential
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| ### ''imperative/cohortative/optative''
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| # (optional) auxiliary slot --- these are old "to be equal (是)", "to be at/exist (在)", and "to have (有)". These three times the three aspects make nine conjugations
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| ## <pre> : Continuous Aorist Irrealis</pre>
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| ## <pre>Not one : present. past. subjunctive.</pre>
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| ## <pre>ye old be: pres. cont past cont. conditional</pre>
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| ## <pre>ye old at: imperfect past. impf. fut. imperf.</pre>
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| ## <pre>old have : perfect. plurperf. fut. perf.</pre>
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| # (optional) indirect object person slot
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| # (optional) negation slot
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| Participles and infinitives are handled completely separately, like other stems (a la Hebrew)
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| === Syntax ===
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| Word order is totally free, but it used to be SOV, so there is some tendency for the verb to come at the end.
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| === Derivation ===
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| _ is a triconsonantal language, like Hebrew or Akkadian. It is largely spell-able without the vowels, once you know the language.
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| There are very regular patterns for noun and verb creation, which we will document with the very regular word BáLrM, ''to hate''. The lexical form is BóLeM. Where there are two in a slot, the top is exclusive and the bottom is inclusive
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| ==== Direct ====
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| <!-- The direct aorist is basically o-e+suffix, call it the Poel //-->
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| <!-- The direct continuous is basically prefix+i-e //->
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| <!-- The direct subjunctive is basically o-infix-a //-->
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| {| class="bluetable"
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| |+ BóLeM
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| !
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| ! colspan="3" | Aorist
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| ! colspan="3" | Continuous
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| ! colspan="3" | Subjunctive
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| |-
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| ! !! sg !! pauc !! collect !! sg !! pauc !! collect
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| |-
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| ! rowspan="2" | 1
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| | rowspan="2" | '''B'''ó'''LM'''oÞ
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| | '''B'''ó'''LM'''iQ || '''B'''ó'''LM'''iM
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| |-
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| | '''B'''ó'''LM'''oS || '''B'''ó'''LM'''oŊe
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| |-
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| ! 2
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| | '''B'''o'''L'''éY'''M''' || '''B'''o'''L'''é'''M'''rĦ || '''B'''ó'''LM'''iN
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| |-
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| ! 3E
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| | colspan="3" style="text-align:center;" | '''B'''ó'''L'''e'''M'''
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| |-
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| ! 3F
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| | '''B'''o'''LM'''ŕPoŠ
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| | colspan="2" style="text-align: center;" | '''B'''ó'''LM'''aŠe
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| |-
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| ! 3P
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| | '''B'''ó'''LM'''iŁ || '''B'''o'''L'''é'''M'''ŁeY || '''B'''o'''L'''Łé'''M'''uW
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| |-
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| ! 3A
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| | '''B'''o'''L'''e'''M'''KoŊ || '''B'''o'''L'''ŕŊ'''M'''o || '''B'''o'''LM'''oŊ
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| |-
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| ! 3B
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| | '''B'''o'''L'''e'''M'''ČeT || '''B'''o'''LM'''eTu || '''B'''o'''LM'''rÇ
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| |-
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| ! 3S
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| | '''B'''o'''L'''é'''M'''ZrŽ
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| | colspan="2" style="text-align:center;" | '''B'''ó'''LM'''rŽ
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| |-
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| ! 3R
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| | colspan="3" style="text-align:center;" | '''B'''o'''L'''í'''M'''ÞiM
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| |}
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| ==== Hearsay ====
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| <!-- The hearsay aorist is basically þ+i-u+suffix //-->
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| <!-- The hearsay continuous is basically prefix+þ+i-r //->
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| <!-- The hearsay subjunctive is basically þa+infix-u //-->
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| ==== Inferential ====
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| <!-- The inferential aorist is basically :a-e-suffix //-->
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| <!-- The inferential continuous is basically prefixr:-e //->
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| <!-- The inferential subjunctive is basically :a-infix-r //-->
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| ==== Imperative ====
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| <!-- The imperative aorist is basically aorist direct pared down//-->
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| <!-- The imperative continuous is basically continuous direct pared down//->
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| === Nouns ===
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| Base noun form: aBLuM
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