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Counting in Ithkuil

Language overview

Forty-two in Ithkuil Ithkuil (Iţkuîl) is an experimental constructed language created by the Californian John Quijada (1978-2016), published on the web from 2004, a cross between an a priori philosophical and a logical language. Ithkuil has its own logogramic writing system, named Içtaîl, a morpho-phonemic script.

Ithkuil numbers list

  • 1 – llal
  • 2 – ksal
  • 3 – ţkal
  • 4 – pxal
  • 5 – sţal
  • 6 – cqal
  • 7 – nsal
  • 8 – fyal
  • 9 – xmal
  • 10 – mřal
  • 11 – llalik
  • 12 – ksalik
  • 13 – ţkalik
  • 14 – pxalik
  • 15 – sţalik
  • 16 – cqalik
  • 17 – nsalik
  • 18 – fyalik
  • 19 – xmalik
  • 20 – mřalik
  • 21 – llalök
  • 22 – ksalök
  • 23 – ţkalök
  • 24 – pxalök
  • 25 – sţalök
  • 26 – cqalök
  • 27 – nsalök
  • 28 – fyalök
  • 29 – xmalök
  • 30 – mřalök
  • 31 – llalek
  • 32 – ksalek
  • 33 – ţkalek
  • 34 – pxalek
  • 35 – sţalek
  • 36 – cqalek
  • 37 – nsalek
  • 38 – fyalek
  • 39 – xmalek
  • 40 – mřalek
  • 41 – llalîk
  • 42 – ksalîk
  • 43 – ţkalîk
  • 44 – pxalîk
  • 45 – sţalîk
  • 46 – cqalîk
  • 47 – nsalîk
  • 48 – fyalîk
  • 49 – xmalîk
  • 50 – mřalîk
  • 51 – llalak
  • 52 – ksalak
  • 53 – ţkalak
  • 54 – pxalak
  • 55 – sţalak
  • 56 – cqalak
  • 57 – nsalak
  • 58 – fyalak
  • 59 – xmalak
  • 60 – mřalak
  • 61 – llalûk
  • 62 – ksalûk
  • 63 – ţkalûk
  • 64 – pxalûk
  • 65 – sţalûk
  • 66 – cqalûk
  • 67 – nsalûk
  • 68 – fyalûk
  • 69 – xmalûk
  • 70 – mřalûk
  • 71 – llalok
  • 72 – ksalok
  • 73 – ţkalok
  • 74 – pxalok
  • 75 – sţalok
  • 76 – cqalok
  • 77 – nsalok
  • 78 – fyalok
  • 79 – xmalok
  • 80 – mřalok
  • 81 – llalük
  • 82 – ksalük
  • 83 – ţkalük
  • 84 – pxalük
  • 85 – sţalük
  • 86 – cqalük
  • 87 – nsalük
  • 88 – fyalük
  • 89 – xmalük
  • 90 – mřalük
  • 91 – llaluk
  • 92 – ksaluk
  • 93 – ţkaluk
  • 94 – pxaluk
  • 95 – sţaluk
  • 96 – cqaluk
  • 97 – nsaluk
  • 98 – fyaluk
  • 99 – xmaluk
  • 100 – ňal

The centesimal base or base 100

The Ithkuil numbers follow a centesimal numeral system, of base 100. To better understand this numeral system, let’s start with a more familiar one: the decimal system. In the decimal system (or base-10), we have ten digits, from zero to nine. When we add 1 (one) to 9 (nine), we get 10 (ten), or the unit 1 (one) followed by 0 (zero). This system is positional (the digits represent the units, and their rank the matching power of ten). Thus, 132 decomposes in 100 + 30 + 2 = 1*102 + 3 *101 + 2 *100. This system is also known as a positional decimal numeral system.
The base 100 uses “digits” from 1 to 99 (zero has no equivalent in Ithkuil). Its first ten is 100 in decimal (10010 = 10100), the base is noted in subscript. The decomposition of a base-100 number (in a positional system) is the same as the one of a decimal number, only the base changes: (132)100 = 1*1002 + 3*1001 + 2*100. If we carry it out, we get the matching decimal number, here 10,302.

Ithkuil numerals

1
1100
2
2100
3
3100
4
4100
5
5100
6
6100
7
7100
8
8100
9
9100
10
10100
100
100100
10000
10,000100
100000000
108100
10000000000000000
1016100

Ithkuil numbering rules

  • The roots of numbers one to ten are the following: -ll- [1], -ks- [2], -ţk- [3], -px- [4], -sţ- [5], -cq- [6], -ns- [7], -fy- [8], -xm- [9], and -mř- [10].
  • From these roots, we can form the digits in base 100 by adding to them -a-, the affix marking the oblique case of the word (the standard case found in dictionaries), and the affix -l-, the Ca., or the synthetic affix, which marks here we are describing an object.
  • From one to ten, nothing else is needed, so we get: llal [1], ksal [2], ţkal [3], pxal [4], sţal [5], cqal [6], nsal [7], fyal [8], xmal [9], and mřal [10].
  • To form higher numbers, we suffix those first ten numbers to express the addition: -ik (+ 10), -ök (+ 20), -ek (+ 30), -îk/-uëk (+ 40), -ak (+ 50), -ûk/-iëk (+ 60), -ok (+ 70), -ük/-akk (+ 80), and -uk (+ 90). These suffixes are actually made of two affixes: the first one being marking the case, and the second one, -k, describing an “unbounded” set.
  • With the affixes -i- and -k, we obtain: llalik [11], ksalik [12], ţkalik [13], pxalik [14], sţalik [15], cqalik [16], nsalik [17], fyalik [18], xmalik [19], and mřalik [20].
  • With the affixes -ö- and -k, we obtain: llalök [21], ksalök [22], ţkalök [23], pxalök [24], sţalök [25], cqalök [26], nsalök [27], fyalök [28], xmalök [29], and mřalök [30].
  • With the affixes -e- and -k, we obtain: llalek [31], ksalek [32], ţkalek [33], pxalek [34], sţalek [35], cqalek [36], nsalek [37], fyalek [38], xmalek [39], and mřalek [40].
  • With the affixes -î- and -k, we obtain: llalîk [41], ksalîk [42], ţkalîk [43], pxalîk [44], sţalîk [45], cqalîk [46], nsalîk [47], fyalîk [48], xmalîk [49], and mřalîk [50].
  • With the affixes -a- and -k, we obtain: llalak [51], ksalak [52], ţkalak [53], pxalak [54], sţalak [55], cqalak [56], nsalak [57], fyalak [58], xmalak [59], and mřalak [60].
  • With the affixes -û- and -k, we obtain: llalûk [61], ksalûk [62], ţkalûk [63], pxalûk [64], sţalûk [65], cqalûk [66], nsalûk [67], fyalûk [68], xmalûk [69], and mřalûk [70].
  • With the affixes -o- and -k, we obtain: llalok [71], ksalok [72], ţkalok [73], pxalok [74], sţalok [75], cqalok [76], nsalok [77], fyalok [78], xmalok [79], and mřalok [80].
  • With the affixes -ü- and -k, we obtain: llalük [81], ksalük [82], ţkalük [83], pxalük [84], sţalük [85], cqalük [86], nsalük [87], fyalük [88], xmalük [89], and mřalük [90].
  • With the affixes -u- and -k, we obtain: llaluk [91], ksaluk [92], ţkaluk [93], pxaluk [94], sţaluk [95], cqaluk [96], nsaluk [97], fyaluk [98], and xmaluk [99].
  • The root of the word for hundred is -ň-. From it, we form the word ňal [100]. The compound numbers from 10010 to 10 00010 (i.e. from 10100 to 100100) are formed stating the “ten” (in base 100), the word for hundred in the partitive case (ňial) and the “unit” (in base 100). Beyond 199100, ňial can be omitted. We can thus write ksalîk (ňial) xmalök [4229100] (literaly “42 hundreds 29”).
  • The scale numbers, or powers of 100, have the following roots: -zm- for tens of thousands (1002), -pstw- hundreds of millions (1004), and -čkh- for tens of quadrillions (1008). From them, we can form the words zmal [10,000], pstwal [one hundred millions, or 108], and čkhal [10 quadrillions, or 1016].
  • For the names of big numbers, their partitive case is used (respectively zmial, pstwial, and čkhial). If the scale name (the term of the base unit) is in the partitive case (which expresses the part of a whole), the lower scale names are in the comitative case(which expresses the accompaniment), and the coordinative suffix -iň is also used.
  • We can thus write the following numbers: cqalök zmial nseuluk (ňial) cqalûk [269,766100] (literaly “26 ten-thousands, 97 hundreds and 66”), llalök ňial zmual [21,000,000100] (literaly “21 hundreds of ten-thousands”), ksalok ňial xmalokiň apstwial ţkeul ňial ţkalakiň zmual pxeulek mřalûk [727,903,533,460100] (literaly “72 hundreds andt 79 hundreds of millions and 3 hundreds andt 53 ten-thousands and 3460”).

Books

A Grammar of the Ithkuil LanguageA Grammar of the Ithkuil Language
by , editors John Quijada (2012)
[Amazon.com Amazon.com]

Sources

Other artistic languages

Atlantean, Atrian, Azazilúŝ, Barsoomian, Dovahzul, D’ni, Giak, Hylian, Ithkuil, Itláni, Kēlen, Kiitra, Láadan, Na’vi, Shiväisith, Trigedasleng, Va Ehenív, and Wardwesân.

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