Volume IV: Language — Chapter 9: Senary Numeral System
"Six is the foundation of everything. 6 limbs, 6 letters of the genetic code, 6 digits in our system. Six is the number of harmony." — Mathematical Treatise, +2 000 Y.E.
Related sections: → see [Volume IV, Ch.03, "Grammar: Overview"], → see [Volume I, Ch.34, "Measurement Systems of Théxar"]
Introduction
The language and mathematics of the Xha'Ruun are based on the senary numeral system. The choice of base 6 is motivated by biology (six limbs) and genetics (a six-letter code). The senary system is not only a way of writing numbers but also a cultural constant, reflected in the calendar, in measurements, and in architecture.
9.1 The Digits
| Digit | Symbol (Unicode) | Name |
|---|---|---|
| 0 | U+E000 | mor (void) |
| 1 | U+E001 | ven (one) |
| 2 | U+E002 | sha (two) |
| 3 | U+E003 | tor (three) |
| 4 | U+E004 | vex (four) |
| 5 | U+E005 | rass (five) |
The names of the digits coincide with the basic roots (→ see [Volume IV, Ch.08, "Lexicon and Word Formation"]): ven (truth), sha (language), tor (strength), vex (home), rass (accord) — numbers are conceptually connected with cultural meanings.
9.2 Examples of Counting
| Decimal | Senary | Xha'Ruun |
|---|---|---|
| 0 | 0 | mor |
| 1 | 1 | ven |
| 6 | 10 | ven-mor |
| 12 | 20 | sha-mor |
| 36 | 100 | ven-mor-mor |
| 216 | 1000 | ven-mor-mor-mor |
Place values are powers of six: ven-mor = 1×6 + 0, and ven-mor-mor = 1×36 + 0×6 + 0. Mor names the zero digit; it is not a suffix appended to every place.
9.3 Senary Mathematics
The senary system defines the mathematical culture:
- Fractions — positional, in powers of 6;
- Calendar — six months of 29 days and four Days of Renewal; every fifth year adds one day (→ see Volume II, Chapter 17).
- Measurements use defined unit ratios; the base used to write a number does not require all these ratios to be powers of six (→ see Volume I, Chapter 34).
9.4 Cultural Significance
The number 6 is a cultural constant: 6 limbs, 6 letters of the code, 6 digits, four spatial cases are not adjusted to fit this number; 6 laws of the canon. Senary harmony pervades language, science, and religion.
Chapter Summary
- The senary system: digits 0–5, places in powers of 6.
- The names of the digits coincide with the basic roots.
- Reading a positional number preserves its zero places, mor.
- Senary notation does not make all calendar and measurement ratios multiples of six.
- Six is a cultural constant of the civilization.