The Daemonic Number System
"The Daemonic number system, known simply as 'kumin ad atoku', or mind-counting, is a base-13 counting system. Why it is Base-13, instead of the standard Human Base-10, is a simple explanation: it was made in honor of the Great Zimraka. 8 fingers, 4 talons, and 2 half-talons, total to 13. The ancestral Daemon had an unusual digit count."
---Ke'tlan explaining the number system to his human friend, Brandi
Writing System
The numeric script follows a similar structure to The Daemonic Language, where its shapes are made with sharp, straight lines; what makes these different, however, is that they feature no diagonal lines-- instead, opting for vertical and horizontal lines. There are some overlaps with the alphabet: namely, in 1 [S] and C/12 [T].
Numbers are also grouped into three categories of four, where shapes 2 and 3 add onto their preceding shape, and shape 1 and 4 being "flipped" versions of the other. Γ F E L are 1, 2, 3, and 4; ⼗ ⼲ 王 ⼯ are 5, 6, 7, 8; and, interestingly, 9, A, B, and C are 1, 2, 3, and 4 rotated 90 degrees.
Going into the double digits, however, slightly complicates things. More or less, the 10s digit slowly makes a "box" around the 1s digit. Like the ones places, each 10s place is grouped into three categories of four. Instead of each member of a group adding to the shape, however, each group adds to the shape, and each member of a group rotates around the 1s place.丨[10] 冖 [20]亅 [30] __ [40] 厂 [60] 匚 [90] 冂 [A0] 凵 [C0] 囗 [100, informal].
Some Daemon have opted towards a more modern version of the number glyph system, using the symbols typically assigned to the ones place in each digit location, and using the 0 in the Universal Human Tongue in place of "zero" spots. This sometimes leads to some confusion, due to Human number systems being mostly Base-10, especially since many Daemon, in fact, end up learning both counting systems.
To counteract the confusion, digit-by-digit numbers written in Base-10 become surrounded by modified brackets: either guillements [« »] or standard Daemonic quotation marks [「 」].Syntax
Syntax is incredibly important in Daemonic counting. Without the proper syntax, one could accidentally say a thousand [zimra'be] instead of a hundred [zimra'chal], or eight [tchal] when they meant 700 [ta'chal].
The Daemonic number system is directly inspired by the Tzotzil number system, though instead of the Tzotzil's base-20, Daemonic opts for base-13. This is because 13 is integrated into not only Daemonic culture, but Solaris' date [13 months per year] and time [26 hours per day] systems.
Both Tzotzil and Daemonic number systems' syntax incorporate a bit of built-in multiplication and exponents: the largest numbers are exponents, which are multiplied by singular digits, and then added by multiplied [and singular] digits. To help visualize this concept, here's an example:
"2021" in Base-X Number Systems | ||
|---|---|---|
| Base-10 | Base-13 [Daemonic] | Base-20 [Tzotzil] |
two-thousand twenty-one | chez'ka-chal sal-ezimra'zir | vo' - bok' jun xcha'-vinik |
2 x 103 + 20 + 1 | 11 x 132 + 6 object of the 13th 13 | 5 x 202 + 1 object of the 2nd 20 |
Vocabulary
The basic vocabulary within the Daemonic number system is broken up into three categories: singular digits [the groundwork], compound digits [multiplicative language], and exponential digits [large numerical values]. Just like Tzotzil, the singular digits become modified as the numbers get larger, and there is tangential reference of larger numbers when you get to the "ones" place starting in double-digit numbers.
| 1 | ul | ulla | 1 object |
| 2 | chel | chela | 2 object |
| 3 | tel | tela | 3 object |
| 4 | vel | vela | 4 object |
A-Vowel Numbers
These numbers, just like in the symbol example near the top of this page, are grouped in a singular category, known as the "A-vowel" numbers.
This is because their alternate spellings all end with the vowel "A". Sometimes, they are known as U-to-A Numbers, for better clarification.
O-Vowel Numbers
Also known as A-to-O numbers, they, in contrast to the A-Vowel Numbers, have their starting vowel as "A", and their ending letter as O.
Note the odd construction of the Daemonic word for 8: tchalo. This is because it references two hands, as the ancestral Daemon had eight fingers total.| 5 | fal | falo | 5 object |
| 6 | sal | salo | 6 object |
| 7 | tal | talo | 7 object |
| 8 | tchal | tchalo | 8 object |
| 9 | u'chal | (1+8) object |
| 10 | ube'chal | (2+8) object |
| 11 | chezi'chal | (3+8) object |
| 12 | chebe'chal | (4+8) object |
Compound Numbers
These numbers subvert the formula a bit. 'U'chal' fits, but 'ube' refers to one foot, which has two toes, and 'chebe' refers to two feet, or four toes.
This is where the Tzotzil mathematical influence starts to come in: the numbers become additive. The next number is the "10" of Base-13.The Exponentials
This will skip over a few numbers, which will be covered next. These exponentials are all built on top of Zimraka, the name of the Legendary Warrior.
After zimra'ka [13[1]], every square has a suffix based on a body part: respectively, the arm [13[2]], leg [13[3]], tail [13[4]], and head [13[5]].| 169 | zimra'chal | zimra'chala | 132 |
| 2197 | zimra'be | zimra'bedna | 133 |
| 28561 | zimra'kosh | zimra'kosa | 134 |
| 371293 | zimra'kuv | zimra'kuven | 135 |
| 13 | zimra'ka | 1 x 13 | 26 | che'zir | 2 x 13 |
| 39 | te'zir | 3 x 13 | 52 | ve'zir | 4 x 13 |
| 65 | fa'zir | 5 x 13 | 78 | sa'zir | 6 x 13 |
| 91 | ta'zir | 7 x 13 | 104 | tcha'zir | 8 x 13 |
| 117 | u'chal'zir | 9 x 13 | 130 | ube'chal'zir | 10 x 13 |
The Multiplicatives
Simply-said, these numbers are multiples of 13 that are slightly modified by the suffix zir, shorthand of "Zimra'ka". 90, A0, B0, and C0 are unaffected, due to them being compound numbers.
The next section will show how the "X object of the Yth 13" works. After that, you will be able to construct your own Daemonic numbers, up to over four million, using the Daemonic Alphabet note.X Object of the Nth 13
Simply put, it's a reference to the next number; this is another borrowed Tzotzil characteristic. Object of the 2nd 13 would reference 30, and object of the 13th 13 would reference 100, as an example.
The numbers that supplement X aren't modified like the multiplicatives; instead, the number following it is, just like the multiplicative forms. Whereas che'zir is 2 x 13 (26), chel-echa'zir is 2nd object of the 2nd 13 (15).| X1 | ul-x'zir | X2 | chel-x'zir | X3 | tel-x'zir |
| X4 | vel-x'zir | X5 | fal-x'zir | X6 | sal-x'zir |
| X7 | tal-x'zir | X8 | tchal-x'zir | X9 | u'chal-x'zir |
| XA | ube'chal- x'zir | XB | chezi'chal- x'zir | XC | chebe'chal- x'zir |
| x-echa'zir | x object of the 2nd 13 | x-eta'zir | x object of the 3rd 13 |
| x-eva'zir | x object of the 4th 13 | x-efa'zir | x object of the 5th 13 |
| x-eza'zir | x object of the 6th 13 | x-eto'zir | x object of the 7th 13 |
| x-e'cho'zir | x object of the 8th 13 | x-abe'cho'zir | x object of the 9th 13 |
| x-abe'cho'zir | x object of the 10th 13 | x-echaze'cho'zir | x object of the 11th 13 |
| x-echabe'zir | x object of the 12th 13 | x-ezimra'zir | x object of the 13th 13 |
Daemonic Numbers
Dictionary
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