by Hervé Musseau
Thyatian System
Description: I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII... (with prefixing substractions, written left to right).
Variants: Milenian System: I, II, III, IIII, V, VI, VII, VIII, VIIII, X, XI, XII... (without prefixing substractions, written left to right).
Sindhi/Hulean/Hin Systems: I, II, IIV, IV, V, VI, VII, IIX, IX, X, XI, XII, XIIV, XIV, XV, XVI, XVII, IIT, IT, T, TI... (similar to Thyatian, but with a 5/10/20 base instead of 5/10).
Sindhi/Hulean Systems: I, II, III, IIII, IIIII, IIIIX, IIIX, IIX... (base 10/20).
Karimari System: I, II, III, IIII, V, VI, VII, VIII, VIIII, X, XI, XII, XIII, XIIII, XV, XVI, XVII, XVIII, XVIIII, T, TI, TII...
Used in: Thyatis, Karameikos, Darokin, Glantri, Ierendi, Five Shires, Sind, Hule and neighbors, Milenia, Traldar, the Savage Baronies, and many other places.
History: The Traldar, when they lost most of the advances and knowledge of the Nithians, had to devise a way of keeping track of cattle and other goods, and like most primitive cultures counted on their fingers. The Milenians later improved this into written symbols which are still used today. The system was brought from Milenia by the fleeing Thytian tribes and refined to include substractions through prefixing [e.g., "IV" for 4, rather than "IIII" - Ed.]. The Thyatian system has been adopted throughout the empire and wherever the Thyatians have settled lands. Many cultures use a variant of that system, either adapted from other cultures' or developed independently, generally with other symbols but the same base.
Usage: Easy to count, it becomes cumbersome to represent large numbers (less so with prefixing). Operations are difficult, even more with the Thyatian representation.
Nithian System (a.k.a. Ylari Numerals)
Description: 1, 2, 3, 4, 5, 6, 7, 8, 9, 01, 11, 21... (decimal, written from right to left).
Variants: Blackmoorian System: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10... (hexadecimal written from left to right; the exact symbols are lost to time).
Used in: Nithia, Ylaruam, Thothia, Darokin, Minrothad, some others.
History: The hexadecimal system was one of the many advances the Blackmoorians salvaged from the Beagle. It quickly became the system of the scientists, and as technomancy became widespread it replaced the native Thyatian-like system. The system would likely have been lost after the Great Rain of Fire were it not for the fact that the Nithian tribe, who was to become the next largest human civilization, had picked it up and adapted to a more natural decimal base. Because of the Spell of Oblivion, the system is only known as the Ylari Numerals in the Old World.
Usage: Very practical to represent large numbers and for financial calculations, it is used mostly by traders to keep records of large sums of money (Darokinian CLOCs are labeled in Ylari numerals).
Alphatian System
Description: 24-base Nithian-like system using the 24 symbols of the Alphatian alphabet (alpha, beta, ..., omega), written left to right.
Used in: Alphatia and its dominions.
History: The Alphatian system is very much integrated into the Alphatian language. In Alphatian, alpha is both the first symbol of the alphabet, the number one, as well as the first, the one, and many other variations that aren't distinguished in Alphatian.
Usage: Used by mundaners only for counting, Alphatian numbers can be tapped by spellcasters for their intrinsic magical power and thus appear in magical incantations as well. [See the author's Alphatian Language article, in this issue, for more information about the Alphatian linguistic system. -Ed.]
Herathian System
Description: To each of the 21 first letters (aleph, beth, ..., sin) of the Herathian alphabet is assigned a value: 1, 2, 3, 4, 5, 6, 7, 8, 16, 24, 32, 40, 48, 56, 64, 128, 192, 256, 320, 384, 448. Numbers up to 511 can thus be represented (octal base, written right to left), with higher numbers being composed by adding more triplets separated by the 22th letter, taw.
Variants: None.
Used in: Herath.
History: This system is as old as the aranean language. The numbers are associated with magical properties. (According to aranean myth, the incantation associated with the Night Spider's True Name was uttered by Her followers to summon Her to Mystara, where She still resides, and only uttering it backwards can banish Her.)
Usage: Like Alphatians, Herathians sometimes use numbers in their magical incantations. Unlike the Alphatians, they don't really use them for counting purposes, instead using their second persona's system.
Minrothaddan Tokens
Description: Images of various goods, called "tokens," are drawn to represent one unit of that good.
Variants: None.
Used in: Minrothad.
History: The elves have little use for numerals, and used to have no system to represent numbers. As the nation's Nithian followers of Minroth started extensive trading, they developed a system of tokens that represented the goods bought and sold. Each good had its own tokens which represented various standard quantities of that good, with several units being represented by repetition of the token. As it became increasingly complicated to keep record of vast quantities of goods by lining tokens, the system began incorporating the notion of numeral followed by only one token. The Nithian system was first used of course, and then the Alphatian system was used as well, but after the fall of Nithia the Nithian system was wiped off the traders' memory by the Immortals, and only the Alphatian system remained. It was later abandoned in favor of the Thyatian system as it spread throughout the Old World. Currently, Ylari numerals are used for large numbers.
Usage: This system is specially adapted for trade bookkeeping, and is as easy or difficult as the Thyatian or Ylari systems. A level of complexity is added by the fact that there are set conversions between the various tokens that represent quantities of a same goods.
Tanagoro Pairs
Description: I, II, II-I, II-II, II-II-I...
Variants: Wallara: I, +, +I, ++, ++I...
Yavdlom: I, II, III, IIII, IIII-I, IIII-II, IIII-III, IIII-IIII, IIII-IIII-I, IIII-IIII-II, IIII-IIII-III, +, +-I, +-II...
Used in: Tanagoro, Yavdlom, Wallara.
History: This is a primitive method based on counting sticks, not unlike he Thyatian system but with a binary base, or a 4 and 12 base.
Usage: Very cumbersome for large numbers.
Dwarven Cubes
Description: 
... A full n-cube is equal to 2n(n+1).
Variants: Gnomish Bee-cubes: made with hexagons. A full n-bee-cube is equal to 6SUM(i=n,2n-1,i).
Used in: Rockhome, Kogolor, Serraine, Oostdock, other dwarven and gnomish communities.
History: These systems are as old as the dwarven and gnomish languages.
Usage: Very hard to grasp for non-dwarves and non-gnomes. Large numbers are typically represented by cubes of cubes (multiplications and powers) called "blocks." Dwarves and gnomes claim that operations on cubes are easy to figure out, but given the complexity of the cubes themselves few have bothered to try and acknowledge (or disprove) the claim.
Elven Leaves
Description: 
...
Variants: Each clan use their own style of leaves, which can be further refined by each individual elf.
Used in: Alfheim, Wendar, Minrothad, Icevale, Schattenalfheim, Gentle Folk, other elven communities.
History: The elves have always used leaves.
Usage: Little used as the elves don't have much use for numbers, and never for large numbers. For large numbers, elves use phrases like as many as there are trees in a forest or as numerous as stars in the sky.
Shadowelf Stars
Description: The shadowelf system is very much like their calendar, which was interpreted from Rafiel's Refuge of Stone. Thus, they use a combination of numerals in the 1-24 range, which add up to the 14 verses' names (the 1-24 and 1-14 numbers each have a different symbols). The number following the 24th of Bounty (24*14=336) is called (and symbolized by) a star (often translated as year). Like the days, some numbers are fasti or ne fasti. An example would be 15th of Wanderer star and 3rd of Kings.
Variants: None.
Used in: Shadow Elves' Territories, Aengmor.
History: Invented by the shamans along with the calendar, from the Verses of the Refuge of Stone.
Usage: Relatively easy to use, except for the fact that it combines two bases (24 and 14), neither of which are natural.
Copyright (c) 2000, Hervé Musseau. Used by permission. All rights reserved.