Hadokai Tubatonona — Numeric System
The Two Systems
The Tubatonona operate with two distinct numeric registers, culturally separated:
Common/Practical (base-10): Used by craftsmen, traders, and everyday people. Derived from finger-touching counting — thumb to each finger on each hand. This is the system documented below.
Cosmic/Religious (base-8): Used for sacred and philosophical calculation. Derived from the spaces between fingers — four spaces per hand, eight total. Counting intervals rather than endpoints. This system reflects the cultural philosophy of Balance: you are not counting what is, you are counting what separates what is. The formal morphology for base-8 is not yet written — it is the next design phase.
The Philosophical Ceiling
Before the numbers themselves, the Tubatonona relationship to large quantities must be understood.
Numbers are for arrows, stones, days, and lengths of rope. They are practical instruments. Beyond the countable lies magomakva — the ever-receding horizon. Not infinity as an abstract mathematical concept, but the horizon as a lived physical truth: real, visible, always exactly one step further than you can reach. The Tubatonona did not need to invent a word for infinity. They already had one. It was the horizon.
ʃatototo— one billion — exists as a word. It lives almost entirely outside of practical use, and beyond it is not just a larger number. Beyond it is magomakva, a representation of the unreachable or “the infinite”.
The Digit Stems
Every digit is two syllables in the script, always CVC-bounded by the null consonant ungʌ. What appears as a vowel pair in the Latin word column is always two complete syllable blocks in the script.
Counting is taught through thumb touching, where the thumb will touch each finger in succession as the numbers increase, pinky, ring, middle, and index represent kai, kae, kao, kau. The thumb standing alone represents the hand unit, ka, indicating both the left hand and five. Contextually, word order makes mistaking the physical object for the numeric indicator impossible.
Similarly, ʃai, ʃae, ʃao, ʃau, and ʃa behave and follow the same pattern, counting the numbers six through ten in order. ʃa indicates both ten and the right hand.
| Word | Script | Syllables | IPA | Numeric |
|---|---|---|---|---|
| kai | ka=i= | ka.ee | /ka.i/ | 1 |
| kae | ka=e= | ka.e | /ka.ɛ/ | 2 |
| kao | ka=o= | ka.o | /ka.o/ | 3 |
| kau | ka=u= | ka.oo | /ka.u/ | 4 |
| ka | ka= | ka | /ka/ | 5 |
| ʃai | ʃa=i= | ʃa.ee | /ʃa.i/ | 6 |
| ʃae | ʃa=e= | ʃa.e | /ʃa.ɛ/ | 7 |
| ʃao | ʃa=o= | ʃa.o | /ʃa.o/ | 8 |
| ʃau | ʃa=u= | ʃa.oo | /ʃa.u/ | 9 |
| ʃa | ʃa= | ʃa | /ʃa/ | 10 |
The left hand (ka-) covers 1–5. The right hand (ʃa-) covers 6–10. ka alone is five — the thumb standing alone. ʃa alone is ten — the right thumb standing alone.
The Scale Suffixes
The scale suffixes are not invented for mathematics. They are the existing HT size modifier stack — ti (small/lesser), ta (medium/average), to (large/greater) — applied to the digit stems. The numeric scale fell out of existing morphology. This is not a coincidence. It is the language being consistent with itself.
| Suffix | Scale | Morphological root |
|---|---|---|
| -ti | ×10 | ti — small, lesser degree |
| -ta | ×100 | ta — medium, average |
| -to | ×1,000 | to — large, greater degree |
| -toto | ×1,000,000 | to+to — much larger |
| -tototo | ×1,000,000,000 | to+to+to — immense |
The Tens (×10)
| Word | Meaning |
|---|---|
| kaeti | 20 |
| kaoti | 30 |
| kauti | 40 |
| kati | 50 |
| ʃaiti | 60 |
| ʃaeti | 70 |
| ʃaoti | 80 |
| ʃauti | 90 |
| ʃati | 100 |
The Hundreds (×100)
| Word | Meaning |
|---|---|
| kaeta | 200 |
| kaota | 300 |
| kauta | 400 |
| kata | 500 |
| ʃaita | 600 |
| ʃaeta | 700 |
| ʃaota | 800 |
| ʃauta | 900 |
| ʃata | 1000 |
The Thousands (×1,000)
| Word | Meaning |
|---|---|
| kaeto | 2,000 |
| kaoto | 3,000 |
| kauto | 4,000 |
| kato | 5,000 |
| ʃaito | 6,000 |
| ʃaeto | 7,000 |
| ʃaoto | 8,000 |
| ʃauto | 9,000 |
| ʃato | 10,000 |
The Parser Rule
One rule. Consistent at every scale.
[digit stem] + [scale suffix] = that many of that scale. State terms largest to smallest. Add all terms.
This mirrors OSV logic: the largest, most significant value is established first. The sentence — numeric or grammatical — begins with what matters most.
Example: 61,543
ʃaitito ʃata kata kauti kao
| Term | Parse | Value |
|---|---|---|
| ʃaitito | ʃai(6) + ti(x10) +to(x1000) | 60,000 |
| ʃata | ʃa(10) + ta(×100) | 1,000 |
| kata | ka(5) + ta(×100) | 500 |
| kauti | kau(4) + ti(×10) | 40 |
| kao | kao | 3 |
Referential vs. Quantitative
The suffix du distinguishes a number as a concept from a number as a quantity.
| Form | Example | Meaning |
|---|---|---|
| Bare/suffixed | kai, ʃati, ʃaitito ʃata kata kauti kao | the quantity — counting, measuring |
| +du | kaidu | the number one — abstract, referential |
When a Tubatonona counts arrows, they use the quantity form. When they discuss the number system itself, teach mathematics, or reason about numeric relationships, they use du. The distinction between the symbol and what it counts is grammatically mandatory, not optional.
The Infinite
magomakva — the ever-receding horizon.
Not a number. Not a mathematical symbol. A word that was already in the language for a completely different purpose, which turned out to also be the only word needed for what lies beyond counting. The Tubatonona did not decide that infinity equals the horizon. The language decided, and they agreed.
Open Items for review and expansion
The base-8 cosmic/religious system shares the same digit stems but requires its own scale suffix morphology and a formal written parser. The philosophical framework is complete — intervals rather than endpoints, four spaces per hand, counting what separates rather than what exists. The formal morphology is the next phase of development. The concept of base-8 is one of symmetry and is predicated on