Gilkesh language

Number suffixes: cardinal, ordinal, nominal.

The following suffixes are used with Gilkesh numbers:

cardinal: -ge
ordinal: -wi
nominal: -ko
general number delimiter: -yik

Cardinal (or counting) numbers indicate how many of something there are. The suffix -ge indicates cardinal numbers; in ordinary conversation, it may be omitted when the context is sufficiently clear:

eshge keshin - three women
esh keshin - three women

The suffix -ge is used only with positive integers and countable objects; for measurements involving other types of numbers, see below.

Ordinal numbers, denoting a place in a series, take the suffix -wi. These have the same meaning and usage as ordinals in English:

dilwi - first
minwi - second
eshwi - third
... etc.

The category of nominal numbers refers to things designated by an arbitrary numerical value. This includes things like address and telephone numbers, serial numbers, and in general anything referred to as "number such-and-such".

haran minom eshko dar - building #123 (decimal)
min-thon esh-haran tesom shumko shod - room #2395 (decimal)

In modern usage, times and dates use the nominal form. Older texts dating from before the standardization of timekeeping use the ordinal, just as older English usage refers to "the third hour".

eshko dan - three o'clock [The standard Gilkesh day is based on the 28.5-hour rotation period of Shakti. It is divided into 16 danin or "hours" of about 107 terrestrial minutes, each comprising 256 hilqin or "minutes" of 25 terrestrial seconds. Timekeeping was originally reckoned from nightfall and was calculated according to the sixteen constellations, or danin, of the Gilkesh "zodiac".]

Finally, an all-purpose number delimiter, -yik, finds frequent use in mathematical and scientific environments. It indicates the end of a numerical value, and may be attached to integers, fractions, irrationals, positive or negative values, and real or imaginary numbers.

min chiym shumyik sentimetri - 2.5 centimeters (terrestrial measure)

Note that -yik does not itself specify whether a value is exact or approximate. For this, the correlatives akaron (lit. "the same number") and egaron (lit. "a different number") are used with the sense of "exactly" and "approximately".

Fingers, and more fingers.

Is the thumb a finger?

In prehistoric times, two main dialects of Gilkesh evolved. One of the principal differences was the use of two different words for "finger": ishid, which included thumbs, and shus, which excluded thumbs. (Thumbs were called tus by these speakers.)

The development of numeration systems paralleled the naming of fingers. Tribes that used the thumb-inclusive ishid adopted the decimal system, while the tribes that called their fingers (but not their thumbs) shus used octal numbers. (As we've noted elsewhere, the octal system eventually prevailed, and evolved into the hexadecimal system used in modern times.) It's not clear whether the difference in numeration arose from the difference in nomenclature or vice versa, and it may be a chicken/egg question. But it is clear that some populations thought of all ten manual digits as the same entity, and named and counted them accordingly; while others, reckoning the thumb as a thing apart, counted only the fingers that shared a common name.

In Universal Standard Gilkesh, both terms are retained, with their original meanings, but the dialectal division has long since disappeared.

GK Factorials

Download GK-hex-factorial.pdf

The first 32 factorials, in hexadecimal GK notation.

GK Fibonacci Numbers

Download GK-hex-fibonacci.pdf

The first 64 Fibonacci numbers, in hexadecimal GK notation.

GK Prime Numbers

Download GK-hexprimes.pdf

The first 256 prime numbers, in hexadecimal GK notation.

Phi in Hexadecimal Notation

Phi (the Golden Ratio constant) to 256 hexadecimal mantissa places, in GK notation.

E in Hexadecimal Notation

E (Euler's constant) to 256 hexadecimal mantissa places, in GK notation.

Pi in Hexadecimal Notation

GK Hexadecimal Numbers

Numbers played an important role in the development of agriculture, accounting, and astronomy in early Gilkesh civilization. Although most archaeological records have been lost, the surviving information attests to a well-developed system of mathematics dating even from prehistoric times.

Hexadecimal numbers first evolved as a shorthand form of octal notation. It should be noted that conversion between octal and hexadecimal is not generally trivial for large numbers (since sixteen is not a power of eight) and requires conversion to binary as an intermediate step; however, for numbers of one or two digits it is not terribly complicated. Probably the notation passed through a transitional, mixed-base phase. In any event, the hexadecimal system retained all the advantages of octal and allowed for large numbers to be expressed more concisely.

The names of the numbers in the Gilkesh hexadecimal system are:

decimal hex GK name

0 0 run

1 1 dil

2 2 min

3 3 esh

4 4 lem

5 5 shum

6 6 seth

7 7 sab

8 8 astu

9 9 astil

10 A asmin

11 B astesh

12 C aslem

13 D astum

14 E assith

15 F astab

16 10 mist

32 20 minon

48 30 eshon

64 40 lemon

80 50 shumon

96 60 sethon

256 100 rab

512 200 min rab

4096 1000 rob

65536 10000 ribub

The use of large numbers is of great antiquity, and both exponential and mantissa numeration were introduced early. Large quantities may be denoted either with common numbers, as above, or with exponential numeration. The suffix -oi marks the exponent and may be roughly translated as, "times sixteen to the power of". Thus, rab=minoi, rob=eshoi, ribub=lemoi.

[exponent marker] -oi

16^2 10^2 minoi

16^3 10^3 eshoi

2*16^4 2*10^4 min lemoi

Additionally, the word 'diyul' serves as a mantissa marker (or hexadecimal equivalent of a "decimal point"). It can combine with the exponent marker to produce a form of "scientific notation".

[mantissa marker]---- diyul

3 + 4/16 3.4 esh diyul lem

5 + 7/256 5.07 shum diyul run sab

32976 8.D*10^5 astu diyul astum shumoi

The first sixteen prime numbers are:

min, esh, shum, sab, astesh, astum, mistil, mistesh, mist-sab, mist-astum, mist-astab, minon-shum, minon-astil, minon-astesh, minon-astab, eshon-shum.

The first sixteen Fibonacci numbers are:

dil, dil, min, esh, shum, astu, astum, mist-shum, minon-min, eshon-sab, shumon-astil, astilon, astithon-astil, rab sabon-astil, min rab sethon-min, esh rab astumon-astesh

The first eight factorials are:

dil, min, seth, mist-astu, sabon-astu, min rab astumon, rob esh rab asteshon, astil rob astum rab aston

Pi to eight hexadecimal mantissa places (rounded):

esh diyul min lem esh astab seth astin astu astil

E to eight places:

min diyul astesh sab astith dil shum dil seth esh

Phi to eight places:

dil diyul astil astith esh sab sab astil astesh astil

In hexadecimal rounding, mantissa digits less than 8 (astu) are truncated.

Numerical tables were generated with the aid of Mathematica.

Gilkesh Numerals - Hexadecimal