Traditional Counting System in The Age of Embers | World Anvil
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Traditional Counting System

While the vast majority of the world uses a standard number system, those who still pride themselves in divine work use a more traditional, and much more complicated number system. Unlike the standard system which is base-10, this traditional system is base-11, meaning an extra digit is needed to count numbers.  

The Digits

A base-10 system has only ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This base-11 system adds an additional digit after 9 representing what would be 10 in the standard system. This unit is written X. So what would be 11 in the standard system is written as 10 and the following numbers are treated thuslywise:
Standard (base-10) Traditional (base-11)
9 9
10 X
11 10
12 11
19 17
20 18
21 19
22 20
100 91
121 100
1,000 82X
1,331 1000
10,000 7571
14,641 1,0000
In the traditional system, there are four digits between commas as opposed to the three in the standard base-10 system.  

Spoken Numbers

Unlike the standard system that has simple names for each number, multiple of 10, and so on, the traditional system has a complex methodology of naming numbers in regards to the digits, what position they occur, whether or not they repeat, and what power of 1,0000 they are:
Number Alone Prefix Infix Repetition Infix Suffix God
1 Unos Pe(r)- -ku(n)- -un Perkwunos
2 Lan Wel- -el- -la(n)-* -an Weland
3 Sos Au(s)- -as- -so(s)-** -so Hausos
4 Tya Wes- -es- -ya Westya
5 Ras Mi(m)- -im- -ra Mimras
6 Eith Se(y)- -ei/ey- -ith Seith
7 Yos Ko(l)- -ol- -lo Kolyos
8 Nos Gu-/Gw- -we(n)- -no Gwenos
9 Not Me(n)- -en- -ne Menot
X Unras Thu(r)- -un- -na Thunras
10 Wos De(y)- -e(v)- -vos Deiwos
*When an infix repeats twice, the second one is replaced with this infix.   **When an infix repeats thrice, the second and third are both replaced by this infix.   There are some linguistic changes that occur when certain sounds become adjacent to one another:
  • s + v = zv Wes- + -vos = Wezvos (40)
  • s + y = sh Seyes- + ya = Seyesha (644)
  • s + s = z Wes- + -so = Wezo (43)
  • l + l = ld Wel- + -lo = Weldo (27)
  • n + n = nd Thurun- + -na = Thurunda (XXX)
1,0000 is “myriad” and is spoken as the suffix -or or, more rarely as the word Stor. Each segment of four digits is a single word therefore restarting the prefix-infix-suffix cycle.
  • 8,0000 > Gwor
  • 8,2450 > Gwor Welesimvos
  • 873X,2450 > Gwolasunor Welesimvos
  • 8XXX,0000 > Gwunsosor (here can be seen the use of the -so(s)- repetition infix removing the multiple -un- suffixes)

Optional Zero Abbreviations

These are only written in ledgers or if speed is required. They do not affect pronunciation and do NOT spread across commas.
0 remains unchanged 50 remains 302 remains
00 > C 500 > 5C 3002 > 3C2
000 > M 5000 > 5M 3,0002 > 3M2
0000 > D 5,0000 > 5D 30,0002 > 30,M2 (not 3D2)

Larger Numbers

Grander numbers are based on powers of Stor (1,0000) and are either given a set name or a suffix.
Alone Suffix
Myriad 1,0000 Stor -or
Myriad2 1,0000,0000 Storan -sel
Myriad3 1,0000,0000,0000 Stoso -saus
Myriad4 1,0000,0000,0000,0000 Stoya -ses
Myriad5 1,0000,0000,0000,0000,0000 Stora -zmim
Myriad6 1,0000,0000,0000,0000,0000,0000 Storith -sey
Myriad7 1,0000,0000,0000,0000,0000,0000,0000 Stolo -skol
Myriad8 1,0000,0000,0000,0000,0000,0000,0000,0000 Stono -zgu
Myriad9 1,0000,0000,0000,0000,0000,0000,0000,0000,0000 Stonë -zmen
MyriadX 1,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000 Stona -sur
Myriad10 1,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000 Stovos -zdey
Stovos converted into the standard decimal system equals: 6,626,407,607,736,641,103,900,260,617,069,258,125,403,649,041   Other Suffixes:
  • Ordinal: -eth (Weleth “second”)
  • Adverbial: -es (Auses “thrice” or “three times”)
  • Multiplier: -polt (Depolt “elevenfold”)
  • Reciprocal: -ath (Welath “one-half”)

Reciprocal Digits

Since a base-11 number system possesses difficult ratio expansions, those who attempt to do division with this system must use new digits to represent the complex numbers.
Word Digit Expansion
Welath "one-half" C 0.555...
Ausath "one-third" Ʃ 0.3737...
Wesath "one-fourth" J 0.2828...
Mimath "one-fifth" Ɔ 0.222...
Seyath "one-sixth" d 0.1919...
Kolath "one-seventh" V 0.163163...
Gwath "one-eighth" Ø 0.1414...
Menath "one-ninth" P 0.124986 124986...
Thurath "one-tenth" T 0.111...
Deyath "one-eleventh" þ 0.1

Times Tables

*1 *2 *3 *4 *5 *6 *7 *8 *9 *X *10
1 1 2 3 4 5 6 7 8 9 X 10
2 2 4 6 8 X 11 13 15 17 19 20
3 3 6 9 11 14 17 1X 22 25 28 30
4 4 8 11 15 19 22 26 2X 33 37 40
5 5 X 14 19 23 28 32 37 41 46 50
6 6 11 17 22 28 33 39 44 4X 55 60
7 7 13 1X 26 32 29 45 51 58 64 70
8 8 15 22 2X 37 44 51 59 66 73 80
9 9 17 25 33 41 4X 58 66 74 82 90
X X 19 28 37 46 55 64 73 82 91 X0
10 10 20 30 40 50 60 70 80 90 X0 100

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