A summation of the numerical system in "The Elements of Friendship" · 4:05pm Jan 19th, 2015
For time immemorial, the Three Pony Tribes were divided by more than just racial prejudice. The Earth Chancellery and the Unicorn Kingdom held the commonality of using a quaternary numerical system, only knowing the numbers 0, 1, 2 and 3 (though the fact of the mattered remained that Earth Ponies saw the Unicorns as obnoxious and self-absorbed, and the Unicorns saw the Earth Ponies as uncultured and dirty), since they only had four limbs and no fingers. (Basically, our four would be written by them as '10'.) The Pegasus Empire, for their part, used a senary system, adding 4 and 5 on top of the quaternary system of the landlovers. (Our six is the Pegasi's '10'.) The union of the Three Pony Tribes as the United Tribes of Equestria did not change these numerical systems, at least at first, because a good number of mathematicians of all three subraces found a certain divide in how their formulae interacted. The loss of such information and the great collapse of society and technology because of the Age of Discord could have been a dramatic setback to their world. However, some bright minds emerged after the establishment of the Equestrian Diarchy, and a new numerical system was initiated that all Equestrian mathematics would abide by:
The dozenal system.
Because of the disparate number of limbs by which the Pegasi counted when compared to the other two subraces, it was decided that the lowest common multiple that 4 and 6 shared would be the basis by which ponies would count. 4, 8, 12... 6, 12...
Counting in the Dozenal System:
Compared to the senary system of the Pegasi, there are double the digits, adding 6 (six), 7 (seven) , 8 (eight), 9 (nine), X (ten) and E (eleven). The old number of '10' which was called 'four' by Earth Ponies and Unicorns and 'six' by Pegasi became known as 'dozen'. So in that manner, a pony who would have previously identified as being eleven-four-and-two years old (written as 112) (twenty-two (22) in a decimal system) would now call her or himself dozen-ten years old (written as 1X years old). Whereas ponies would previously count by twitching each leg or wing in turn, this method of "counting" was no longer suitable to the new counting system. A new means of counting emerged: fetlock and pastern, cannon and upper arm, shoulder and flank, left and right could count to dozen for Earth Ponies and Unicorns, and fetlock and pastern, cannon and upper arm, primaries and secondaries, left and right could count to dozen for Pegasi.
100, which was previously four-four to Earth Ponies and Unicorns, and six-six to Pegasi, became gross (one-forty-four in the decimal system). 1000 (seventeen-hundred-twenty-eight (1728) in decimal) became megagross.
The benefits of the dozenal system over the quaternary and senary systems of old proved especially helpful in multiplication and division, as dozen was divisible by more whole factors than four or six, allowing larger numbers to be expressed in smaller digits than was possible before.
There are other races that have since adopted the dozenal system, such as the Zebras of Pundamilia and the Hippalectryons of Stableroost. The Griffons of Orlalvov steadfastly maintain a duodozenal system (their 10 is equivalent to dozen-two (14) in the dozenal system), counting by the digits on their claws and paws.
So yeah. I've decided on inputting the dozenal/Base-12 system into The Elements of Friendship. This will be a gradual integration into Book One over the coming weeks, replacing the idea of a sixteen-hour day with a duodecimal counting system. Frankly, it makes more sense for a race which has either four or six limbs to use a dozenal counting system than for them to use a sixteen-hour day.
Happy reading, folks!
EDIT: I guess I forgot to detail the additional periods of years that exist in the ponies' dozenal system:
douzaide - a period of a dozen years.
grossentury - a period of a dozen-dozen years; a gross of years.
meggrossium - a period of a dozen-gross years; for us, that would be 1728 years. Plural: meggrossia.
giggrossiad - a period of a gross-gross years; that is, 20736 years.
Also, there are two words that should be known: megagross and gigagross. These are two words that I have coined to indicate, respectively, the numbers 1000 (1728) and 10000 (20736).
EDIT [12 Feb 2015]: Deer use the quaternary system, or Base-4.
They count as one, two, three, quart, quart-one, quart-two, quart-three, two-quart, etc. In numericals, that is written as 1, 2, 3, 10, 11, 12, 13, 20. For 100, which for us base-10 folks would be 16, they call it square. So, to say that somedeer is twenty years old in base-4, one would say square-and-one-quart years old. 1000 is "cube" to the Deer, and sixty-four in the decimal system. NightMare Moon's banishment, which is a dozen-gross (1000) years, a meggrossium, in the dozenal system, is written as 123000 to Deer, and pronounced "cube-cube-two-square-cubes-and-three-cube years".
Uhhm a little thing the number 0 is historically seen the youngest number in existence
(16th century there were still many who didnt know 0) it needs a specific mathematical understanding to acknowledge that you need this number for higher mathematics
just wanted to say that
2733288
I understand that. I have had the habit of writing out N as a Roman numeral for zero, when there is no indication that they used the letter N for anything of the sort. If anything, they just used the word nulla ("zero") to represent that value.
Something I thought some time ago: what about measurements? Because metric uses base 10, and British units are based on body parts the ponies lack...
So... does “duodozenal” mean base-16? I’m confused.
5234270
In octal? Yes.