Octal Arithmetic is the Na'vi system of counting, based on the number eight, developed because the Na'vi have only four digits on each hand. Na'vi use the octal arithmetic in daily life for supply of foodstuffs, materials and hunting.
Human Number System[]
Humans today use a base-10 (decimal) number system, composed of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A second column added to the left uses the same digits to indicate values ten times greater. Digits in a third column have a value a hundred (10 × 10) times greater, and so on. E.g., 2,475 = (2 × 1000) + (4 × 100) + (7 × 10) + (5 × 1) = 2,000 + 400 + 70 + 5 = 2,475.
In ancient times some people used other systems. The ancient Romans used a quintal system; African and Nepalese civilization used a dozenal system.
Na'vi Number System[]
Na'vi use a base-8 (octal) number system, composed of eight digits: 0, 1, 2, 3, 4, 5, 6 and 7. A second column added to the left uses these same digits to indicate values eight times greater. Digits in a third column have a value sixty-four (8 × 8) times greater, and so on. E.g., 2,4758= (2 × 51210) + (4 × 6410) + (7 × 810) + (5 × 1) = 1,02410 + 25610 + 5610 + 510 = 1,34110
Early in the history of their language, the Na'vi had no words for numbers higher than mevol (1610), the sum of all fingers and toes on their body. Anything more was simply called pxay (many).
Note that octal numbers are often confused with decimal numbers. Unless a numeral "8" or "9" is present or the base system is indicated (2,4758 = 1,34110), there is no way to tell them apart.
Expressing numbers in the Na'vi language[]
Small numbers[]
- ’aw
- mune
- pxey
- tsìng
- mrr
- pukap
- kinä
- vol
- volaw (8+1)
- vomun (8+2)
- vopey (8+3)
- vosìng (8+4)
- vomrr (8+5)
- vofu (8+6)
- vohin (8+7)
- mevol (2 × 8 = 16)
- mevolaw (16 + 1)
- mevomun (16 + 2)
The pattern of accenting and combination continues in this manner.
- pxevol (3 × 8 = 24)
- tsìvol (4 × 8 = 32)
- mrrvol (5 × 8 = 40)
- puvol (6 × 8 = 48)
- kivol (7 × 8 = 56)
- zam = 64 (100 octal)
- vozam = 512 (1000 octal)
- zazam = 4096 (10000 octal)
Larger numbers[]
The following tables help in the construction of numbers. This table contains all 1 and 2-digit octal numbers. Columns represent the left digit, rows represent the right digit of an octal number:
| 0 (0+x) | 1 (8+x) | 2 (16+x) | 3 (24+x) | 4 (32+x) | 5 (40+x) | 6 (48+x) | 7 (56+x) | |
| 0 | vol | mevol | pxevol | tsìvol | mrrvol | puvol | kivol | |
| 1 | ’aw | volaw | mevolaw | pxevolaw | tsìvolaw | mrrvolaw | puvolaw | kivolaw |
| 2 | mune | vomun | mevomun | pxevomun | tsìvomun | mrrvomun | puvomun | kivomun |
| 3 | pxey | vopey | mevopey | pxevopey | tsìvopey | mrrvopey | puvopey | kivopey |
| 4 | tsìng | vosìng | mevosìng | pxevosìng | tsìvosìng | mrrvosìng | puvosìng | kivosìng |
| 5 | mrr | vomrr | mevomrr | pxevomrr | tsìvomrr | mrrvomrr | puvomrr | kivomrr |
| 6 | pukap | vofu | mevofu | pxevofu | tsìvofu | mrrvofu | puvofu | kivofu |
| 7 | kinä | vohin | mevohin | pxevohin | tsìvohin | mrrvohin | puvohin | kivohin |
Sometimes you may want to express numbers bigger than 77 (63 in decimal). With the following table you can construct octal number of up to five digits by simply putting the fragments together from left to right.
Notes:
- The -l of vol is dropped when the last digit is not 1 or 0.
- If you get a double m, you may drop one of them.
- The ×1 column can only be used for 1-digit numbers.
| ×4096 (10000) | ×512 (1000) | ×64 (100) | ×8 (10) | combining | ×1 | |
| 1 | zazam | vozam | zam | vol | -aw | ’aw |
| 2 | mezazam | mevozam | mezam | mevol | -mun | mune |
| 3 | pxezazam | pxevozam | pxezam | pxevol | -pey | pxey |
| 4 | tsìzazam | tsìvozam | tsìzam | tsìvol | -sìng | tsìng |
| 5 | mrrzazam | mrrvozam | mrrzam | mrrvol | -mrr | mrr |
| 6 | puzazam | puvozam | puzam | puvol | -fu | pukap |
| 7 | kizazam | kivozam | kizam | kivol | -hin | kinä |
Examples:
- 2010 = 3×512 + 7×64 + 3×8 + 2 = 3732 (octal) = 3 vozam + 7 zam + 3 vol + 2 → pxevozamkizampxevomun
- 10000 = 2×4096 + 3×512 + 4×64 + 2×8 + 0 = 23420 (octal) = 2 zazam + 3 vozam + 4 zam + 2 vol → mezazampxevozamtsìzamevol
Tip: If you are familiar with the binary system, you may find it easier to convert decimal numbers to octal numbers by first converting them to the binary system. If you have a number in the binary system you can divide it into blocks of 3 digits and convert each block back to get the number in the octal system.
- Example: 2010 = 1*1024 + 1*512 + 1*256 + 1*128 + 1*64 + 0*32 + 1*16 + 1*8 + 0*4 + 1*2 + 0*1 = 11 111 011 010 = 3732
Ordinal numbers[]
Ordinal numbers take the (unstressed) suffix -ve. However, the forms are somewhat irregular; they are generally based on the short/combining forms of the numerals, but "third" and "eighth" are based on the long/final forms.
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The series continues with mevolawve "seventeenth (21st)", etc. *Zamve (*zave ?) is not attested. As these are adjectives, they take a when modifying nouns directly: a'awve / ’awvea, etc.
Derivations of numbers[]
Numerals form various derivatives, such as ’awpo "an individual", nì’awve "first(ly)" (as in, "I was here first"), ’awsiteng "together" (one-make-same), kawtu "no-one" (not-one-person), kawkrr "never" (not-one-time), nì’aw "only" (one-ly), and nì’awtu "alone" (one-person-ly), all from ’aw "one"; also nìmun "again" (second-ly) and perhaps muntxa "mated" from mune "two".
There are two words for "once", ’awlie and ’awlo, the difference of which is not clear. "Twice" is melo.
Notes[]
- The Na'vi have a version of "This Little Piggy", the game in which Earth children have their toes grabbed one by one as a poem is recited. The Na'vi version has only four lines and refers to a viperwolf cub, not a pig.
- Old School House: RDA educational center for Na'vi sited in jungle clearing 2.25 kilometers northeast of Hell's Gate. Focus on English language for Na'vi children. Accessed by armored vehicles, Samsons, or avatars on foot.
Sources[]
- James Cameron's Avatar: An Activist Survival Guide pgs. 32-33, by Maria Wilhelm & Dirk Mathison
- http://wiki.learnnavi.org/index.php/Numerals
- Na'vi Numbers on wikibooks.org