Theiling Online    Sitemap    Conlang Mailing List HQ

# The numerical system of Chasma"o"cho

From: Christophe Grandsire Tuesday, September 7, 1999, 9:48
```Hi everybody,

This time I won't bother you with grammatical features in my New
Personal Language, but with the numerical system I find really neat, and
disturbing as the rest of the language, but yet usable. This system is
derived from the calendar system I made, and that I won't present here
(it's more an issue for conculture) except if you want me to present it.

The principal thing to know is that there is two numerical systems, not
only one. There is the so-called scientific system, very straitforward
and expandable, used mainly for scientific purposes or big numbers, and
the so-called common system, more complicated and related to the
calendar, and used in everyday life for numbers not too big (less the 1
million I mean). The scientific system is octal and only octal. The
common system is octal, but mixed with a duodecimal system. I'll present
first the scientific system, because it's the easiest one.

THE SCIENTIFIC SYSTEM:

The scientific system is relatively simple and straightforward. It has
roots for numbers from zero to seven and roots for the powers of eight.
To make numbers, just compound those roots in the same way than the
regular system of Esperanto. The different roots are:
0: 0: chiu /dJ'Ew/
1: 1: ye /j'e/
2: 2: pan /p'an/
3: 3: uh /'ytS/
4: 4: thig /T'ig/
5: 5: vol /B'Ol/
6: 6: ceuz /g'9z/
7: 7: bzom /bz'Om/
10: 8: joe /dZ'Oj/
100: 64: japa /dZap'a/
1000: 512: jaocho /dZawtS'o/
1 0000: 4096: jathi /dZaT'i/
1 0000 0000: 16 777 216: jasejo /dZas@dZ'o/

As you can see, the digits are grouped by four, not by three. To make
stems from these roots, just compound them. Suffixation means addition
and prefixation means multiplication as usual, except for the unity
which is added by the prefix e-. So 9 (11 in octal) is ejoe /edZ'Oj/,
whereas 10 (12 in octal) is jopan /dZop'an/ (joe become jo- when
followed by another number. 16 (20 in octal) is simply panjoe
/pandZ'Oj/. Also, uh is suffixed as -h and prefixed as u-). This prefix
e- is never put inside a number, so 73 (111 in octal) is ejapajoe
/edZap@dZ'Oj/, not *japa'ejoe. When this can lead to ambiguities (does
ejojathi mean 10 0001 or 11 0000?) the suffix -ye can be used to
disambiguate, so ejojathi /edZodZ@T'i/ is 11 0000 and 10 0001 is
jojathiye /dZodZaT@j'e/.

The compound formed by this way is always regularly stressed (primary
stress on the last syllable and secondary stress on the second-to-last
syllable).

THE COMMON SYSTEM:

The common system is more complex as it mixes base 8 and base 12 and
has non-straightforward derivations. It uses the same roots from 0 to 8
than the scientific system, but then it uses other roots for the rest.
The roots used are:
0: 0: chiu /dJ'Ew/
1: 1: ye /j'e/
2: 2: pan /p'an/
3: 3: uh /'ytS/
4: 4: thig /T'ig/
5: 5: vol /B'Ol/
6: 6: ceuz /g'9z/
7: 7: bzom /bz'Om/
10: 8: joe /dZ'Oj/
11: 9: yej /j'EdZ/
13: 11: uj /'ydZ/
14: 12: gama /gam'a/
20: 16: pinchuu /pindZ'u/
30: 24: uchuu /ydZ'u/
40: 32: thechuu /TedZ'u/
50: 40: vochuu /BodZ'u/
60: 48: thegma /TEgm'a/
140: 96: jogma /dZOgm'a/
5552: 2922: jorqui /dZORk'9j/

The reason for the use of such roots for such numbers relies on the
calendar system. The composition is generally additive (with the prefix
e- for the unity, replaced by the suffix -ye for disambiguation like for
the scientific system) and multiplicative like the scientific one,
except for some things like:
- the numbers from 13 to 15 (15 to 17 in octal) are formed by
substraction:
15: 13: upinchuu /yp@ndZ'u/ (16-3)
16: 14: panpinchuu /panp@ndZ'u/ (16-2)
17: 15: yepinchuu /jep@ndZ'u/ (16-1)
20: 16: pinchuu /pindZ'u/
21: 17: epinchuu /ep@ndZuu/ (16+1)
22: 18: pinchuupan /pindZ@wp'an/ (16+2)

- thegma can never be multiplied (but jogma and jorqui can) (NOTE:
thegma and jogma are used like French 'quatre-vingt, quatre-vingt-dix',
so 56 (70 in octal) is thegmajoe /TEgm@dZ'Oj/) and 64 (100 in octal) is
thegmapinchuu /TEgmap@ndZ'u/).

The stress rule of those stems is still regular.

THE USE OF THE NUMERIC STEMS:

Those stems cannot be used as they are. They must be used as adjectives
(which can be nominalized) to make cardinal or ordinal numbers (nothing
very strange, but I already told you that I wanted a disturbing language
but not mandatorily an original one).

To make cardinal numbers, the stems must be turned into AR- adjectives
(which agree with the noun in animation -gender-) and so must be
prefixed by AR- when used with an animate noun (this prefixation is
generally regular, except with 1: ye whose animate form is er /'ER/, and
the numbers prefixed by e-, whose animate form is prefixed instead by
er-).

To make ordinal numbers, the stems must be turned into -EUTH adjectives
(which agree with the noun in construction) and so must be suffixed by
-EUTH in normal state (this suffixation often leads to modifications of
the stem or irregularities, like 1: ye whose ordinal form is euth,
a"e"vi /'9T,'ajv@/: first or 2: pan whose ordinal form is panth, pa"nvi
/p'anT, p'anv@/: second).

Okay, so much for the numeric system of Chasma"o"cho. And as usual, I
calendar system I made, just tell me (I'll answer you off-list I think,
as this topic is not very relevant for the conlang-list and I'm not on
the conculture-list with this e-mail address).

--
Christophe Grandsire

Philips Research Laboratories --  Building WB 145
Prof. Holstlaan 4
5656 AA Eindhoven
The Netherlands

Phone:  +31-40-27-45006
E-mail: grandsir@natlab.research.philips.com
```