Mandae numeral system

Mandae numeral system is a dozenal numeral system used on the Continent. It was developed some time during the first revolution and has gradually replaced base 6 and decimal numeral systems used throughout Ahldoraean history.

Just like the Mandae language, during the second revolution the Mandae numeral system became an elitarian numeral system, existing along side the Dantrian one. The latter wasn't even positional and was used by the common people for basic calculations. A specialized positional decimal system was used by architects and other professionals in Central and Western Dantria.

Mandae numeral system quickly found its way to the east through diplomatic channels. It took hold in Yammoe, which at that time already had a system of public education, and recognized a base 12 numeral system as a better tool to teach arithmetic. By the end of SR, its use spread to Gantolia and was later adopted by the Loodon Empire.

Land and Zamborana Zambonia (later Zambon) continued to use a positional decimal system of the sort used by experts in Western and Central Dantria up until the 3rd CTR.

The Dantrian calendar uses a decimal system, as the widespread adoption of the Mandae numeral system for calculation came much later. Therefore, the inhabitants of the Continent treat years as obeying a very special, somewhat alien numeric system, different from the usual arithmetic they use in everyday life. At the same time, the name of the ordinals, as well as the symbols, are in Mandae even for the decimal system of the Dantrian calendar.

Mathematical research is done in the Mandae system.

Basic notation

Mandae has twelve digits, from 1 to 12. They are traditionally broken down into four groups: somes, sundial, olds and bigs. Somes are 1, 2 and 3 and "somes" means "a little bit", "numbers that indicate just some". The sundial group refers to the way the symbols incrementally add elements in order to indicate growth: a 4 is a square, a five adds a dot to the square, the 6 adds a line, the 7 adds two and, finally, an 8 is a square within a square, which is a way of displaying two 4s. The olds are united by a similar incremental symbol, which takes the basic element of 2 and adds a dot and then two dots. Finally, the bigs are simply the two largest digits, 11 and 12.

The general incremental nature of the symbols can actually be observed in digits 1 through 8: 1 is a line, 2 is essentially two connected lines, 3 is three and four is a square, made up of 4 lines. Then elements are incrementally added up to 8.

While there are special symbols for 72, 144 and 1728, numbers up to 144 can be pretty comfortably written down, using the available twelve digits. One uses a vertical line called "staff" (a literal translation from Mandae) to sum the digits, thus producing a new digit. For instance, if one wishes to write down 14, one can write it as any combination of the two digits, be it 12+2 or 11+3 or 10+4. Different countries tend to adapt several common combinations, and the rule of thumb is two try to use the largest digit. So, in case of 14 it would be more common to represent it by doing 12+2. Typically, the smaller number is on top and the larger number is at the bottom. One can also simply put one number after the staff, which would mean that the number is summed by itself, thereby allowing to write down 14 as 7+7:

The number 14 represented in three different ways: 12+2, 7+7 and 4+10.