For historical reasons, several numeric bases is used in Taruven, namely binary, base 5, base 8 (octal) and base 24.
Few know or care about the binary system, which is mostly included for completeness, though patterns of zeros and ones have a sort of pronounced shorthand that is used to describe binary patterns of all sorts, like for instance a chessboard. In the summary, this is the column for "colloquial binary".
Prior to the first grammar of Taruven, there were two competing systems in use; base 5 was used for monetary matters and measurements of everyday quantities while base 24 was used by scientist and for fractions and extremely large quantities. Base 8 was the winning compromise though there are still localities that use base 12 or base 16.
aìle 0 þa 1
Base 2 | Pattern | Base 10 | Name |
---|---|---|---|
24 (nibble) | 100 | 16 | thallen |
01010101 | 85 | hatalen | |
10101010 | 170 | taladen | |
28 (byte) | 100000000 | 256 | areì |
0: aìl
01: aìda
10: þaìl
11: þada
00: halaì
01: haìda
000: halelaì
001: halata
010: hatalaì
011: hatade
100: þalaìle
101: þaìleda
110: þadaìle
111: þatada
These days, base 5 is used as the base for some forms of computing instead of binary, and for the lower denominations of the old monetary system. These days, the highest number possible in base 5 is 1562410, that is 444445: kaìr-šīra kaìr-kanta kaìr-vynta kaìr-arta kaìr-kaìr.
Unique for base 5: nnta 5. nnta is used instead of the word for zero in compound numbers of base 5: 1010 (2×5) is ran-nnta and not *ran-aìren.
Octal adds šu for 5, gaò for 6, di for 7 and hreì for 8. As with nnta for base 5, hreì is used for zero in compound octal numbers: 3210 (4×8) is kaìr-hreì and not kaìr-aìren
The word for 16, thallen, is from the binary pattern 10002. The word for 24, jaryan, is likewise from the base 24 system. In some dialects, nnta from the base 5 system is used for 5 instead of šu.
Base 24 adds hūš 9, myn 10, vru 11, allin 12, adren 13, arran 14, avryn 15, thallen 16, agrun 17, aỳra 18, ašora 19, ařan 20, avalle 21, atira 22, amara 23 and jaryan 24. While nnta and hreì is used for compound numbers like n×5 in base 5 and n×8 in octal respectively, jaryan is only used when the compound number is between 24 and 47, inclusive. If not, the much shorter yar is used instead: jaryan hreì 3210 (24+8), but ran-yar hreì 5610 (2×24+8). Furthermore, instead of *šu-yar the word šyar is used.
Binary | Colloquial Binary[*] | Base 5 | Base 8 | Base 24 | ||
---|---|---|---|---|---|---|
0 | aìle | aìle | aìren | aìren | aìren | |
1 | þa | þa | þa | þa | þa | |
2 | 21 | þa-aìle | þaìl(e) | ran | ran | ran |
3 | þa-þa | þada | hvenn | hvenn | hvenn | |
4 | þa-aìle-aìle | þalaìl(e) | kaìr | kaìr | kaìr | |
5 | 51 | þa-aìle-þa | þaìleda | nnta | šu | šu |
6 | þa-þa-aìle | þadaìl(e) | þa-þa | gaò | gaò | |
7 | þa-þa-þa | þatada | þa-ran | di | di | |
8 | 81 | þa-aìle-aìle-aìle | þalaìle-aìle | þa-hvenn | hreì | hreì |
9 | þa-aìle-aìle-þa | þalaìle-þa | þa-kaìr | hreì-þa | hùš | |
10 | þa-aìle-þa-aìle | þaìleda-aìle | ran-nnta | hreì-ran | myn | |
11 | þa-aìle-þa-þa | þaìleda-þa | ran-þa | hreì-hvenn | vru | |
12 | þa-þa-aìle-aìle | þadaìle-aìle | ran-ran | hreì-kaìr | allin | |
13 | þa-þa-aìle-þa | þadaìle-þa | ran-hvenn | hreì-šu | adren | |
14 | þa-þa-þa-aìle | þatada-aìle | ran-kaìr | hreì-gaò | arran | |
15 | þa-þa-þa-þa | þadata-þa | hvenn-nnta | hreì-di | avryn | |
16 | 24, 2×8 | … | thallen | hvenn-þa | thallen | thallen |
17 | … | þalaìle-haìda | hvenn-ran | thallen-þa | agrun | |
18 | … | þalaìle-þaìle | hvenn-hvenn | thallen-ran | aỳra | |
19 | … | þalaìle-þada | hvenn-kaìr | thallen-hvenn | ašora | |
20 | … | þaìleda-halaì | kaìr-nnta | thallen-kaìr | ařan | |
21 | … | þaìleda-haìda | kaìr-þa | thallen-šu | avalle | |
22 | … | þaìleda-þaìle | kaìr-ran | thallen-gaò | atira | |
23 | … | þaìleda-þada | kaìr-hvenn | thallen-di | amara | |
24 | 241, 3×8 | … | þadaìle-halaì | kaìr-kaìr | jaryan | jaryan |
25 | 52 | … | þadaìle-haìda | arta | jaryan þa | jaryan þa |
32 | 4×8 | … | þalaìle-halelaì | arta þa-ran | kaìrre | jaryan hreì |
40 | 5×8 | … | … | arta hvenn-nnta | šurre | jaryan thallen |
48 | 6×8 | … | … | arta kaìr-hvenn | gerre | ran-yar |
56 | 7×8 | … | … | ran-arta þa-þa | dirre | ran-yar hreì |
64 | 82 | … | … | ran-arta ran-kaìr | harran | ran-yar thallen |
72 | … | … | ran-arta kaìr-ran | harran-hreì | hvenn-yar | |
96 | … | … | hvenn-arta kaìr-þa | harran-jaryan | kaìr-yar | |
120 | 5×24 | … | … | kaìr-arta kaìr-nnta | harran-dirre | šyar |
125 | 53 | … | … | vynta | harran dirre šu | šyar šu |
144 | 6×24 | … | … | vynta hvenn-kaìr | ran-harran thallen | gaò-yar |
256 | 28 | … | areì | ran-vynta þa-þa | areì, kaìr-harran | myn-yar thallen |
512 | 83 | … | … | kaìr-vynta ran-ran | virran | avalle-yar hreì |
576 | 242 | … | … | kaìr-vynta hvenn-arta þa | virran-harran, virarran, utarha | utarha |
600 | 24×25 | … | … | kaìr-vynta kaìr-arta | virran harran jaryan | utarha jaryan |
625 | 54 | … | … | kanta | virran harran gerre þa | utarha ran-yar þa |
3125 | 55 | … | … | šīra | gaò-virran harran-šu | šu-utarha myn-yar šu |
4096 | 84 | … | … | šīra kanta ran-vynta hvenn-arta kaìr-þa | keryan | di-utarha ran-yar thallen |
13824 | 243 | … | … | kaìr-šīra ran-vynta hvenn-arta kaìr-kaìr | … | veraìn |
15624 | 56- 1 | … | … | kaìr-šīra kaìr-kanta kaìr-vynta kaìr-arta kaìr-kaìr | … | veraìn hvenn-utarha hvenn-yar |
65536 | 216 | … | … | - | … | kaìr-veraìn agrun-utarha ařan-yar thallen |
331776 | 244 | … | … | - | … | keìrye |
7.96×106 | 245 | … | … | - | … | šinn |
1.68×107 | 224, 88 | … | … | - | raỳan | ran-šinn ran-keìrye adren-veraìn avryn-utarha ran-yar thallen |
1.91×108 | 246 | … | … | - | … | gevan |
6.87×1010 | 812 | … | … | - | leìan | |
2.81×1014 | 248, 816 | … | … | - | thuìlan | |
7.92×1028 | 296, 832 | … | rišarga | - | rišarga |
Number + =ax
kaìrax
kaìr -ax
4 -th
4th
In other languages, these are adverbs or adverbial expressions that tell how many times something is/was done. In Taruven this is done by a verbal suffix created by the ordinal prefixed with o-, as in example 1a) below.
tšahohvenn
tšah o- hvenn
see times 3
I looked thrice
tšahonn
tšah -onn
see many.times
I looked many times
-onn | many times |
---|---|
-oje | few times |
-oál | no times |
Fractions are constructed by prefixing vÿ(l)- to the denominator:
kaìr vÿdi
kaìr vÿl- di
4 FRC 6
four sixths
hvenn vÿlařan
hvenn vÿl- ařan
3 FRC 20
three eigthteenths
vÿmyn
vÿl- myn
FRC 10
one tenth
hvenn vÿrišarga
hvenn vÿ- rišarga
3 FRC 7.92×1028
three 7.92×10-28s
Multiples are constructed by prefixing ō(g)-:
ōran
ōg- ran
MUL 2
double, two times
ōgařan
ōg- ařan
MUL 20
twenty times
It is quite likely that the multiplicative ōg- and the adverbial -o- derive from the same source.
Negative numbers are constructed by prefixing aì-:
aìran
aì- ran
NEG 2
lacking two, minus two, two below zero
aìaỳra
aì- aỳra
NEG 18
lacking eighteen, minus eighteen, eighteen below zero
Symbol | Decimal | Name |
---|---|---|
φ | 1.61833… ((1+√5)/2) | šira |
2π | 2×3.1415… | dyan |
x yhux = xy
nnta hranhux
nnta hran -hux
5 2 …
552, 2510
nnta hranhux þa
nnta hran -hux þa
5 2 … 1
552 + 1, 2610
nnta te hran
nnta te hran
5 + 2
55 + 2, 710
nnta ōhran
nnta ō hran
5 × 2
55 × 2, 1010
šu vÿdi
šu vÿ -di
5 ÷ 6
58 ÷ 68, 510/610
There's both a system of logic based similar to the western logic (binary, true-false) and one with five values. The former is well described elsewhere, and due to space-considerations the latter is left as an excercise to the reader :)