Different peoples have different ways of counting.

Base 10 is used by the Clanfolk and by people who learned accounting from them: Klindrel and Lashrefites.

Base 6 is used by peoples who speak Knowledge’s language: the Children of Knowledge, Justice, Beauty, and Sun.

Worker people use base 12.

Some reports claim that the Daughters of the Moon use base 9, but that is too impractical to be believable.

Why Use Base 10?

The base 10 numbering system is natural because people have 10 fingers (in our world and in Edgewhen). Your fingers let you count to 10, and then to go higher, you count 10s of 10s, 10s of 10s of 10s, and so on.

If that’s so natural, then …

Why Use Base 6?

Ten is divisible by 5 and 2, but not by 3. That’s why you can write one-half as 0.5 and one-fifth as 0.2, but one-third is 0.33333333… In Edgewhen, where the number of elements, deities, demons, days in a month, months in a year, and lithics in a day are all divisible by 3, the inability to neatly divide by 3 is a serious flaw.

Six is divisible by 2 and 3. It’s not divisible by 4 or 5, but no number can be divisible by a number greater than one-half of itself. So in that respect, six is divisible by everything possible.

Here’s a quick conversion table:

in base 10 … in base 6
1 1
5 5
6 10
7 11
8 12
9 13
10 14
11 15
12 20
35 55
36 100

Here are some fractions:
one sixth: 0.1
one third: 0.2
one half: 0.3
two thirds: 0.4
five sixths: 0.5

Those look nice. Furthermore:
one quarter = 0.13
one eighth = 0.043

Finger Counting in Base 6

Knowledge taught people a special way of counting on their fingers:

Hold out your right fist. Starting with your thumb, stick out one finger at a time and count 1, 2, 3, 4, 5. You’ve used up all the fingers on that hand.

Make a fist again and hold up your left thumb. That’s 6. (Write it as 10 in base 6.)

Now count with your right hand again: 11, 12, 13, 14, 15. Make a fist and add another finger on the left: 20.

You can count up to thirty-five (55 in base 6) this way.

When Children of Knowledge show numbers bigger than five, they hold the hand of sixes higher. That was the left hand in the example above, but you can swap their roles if you want. Just hold the sixes hand higher when you are showing the number to Children of Knowledge. Otherwise they might get confused.

Numbers in the Novels

I don’t want readers to spend time converting from base 6 to base 10, so I give all figures in base 10, even if the character is thinking of them in base 6.

If a Child of Knowledge sees a herd of twenty deer, he’s actually thinking he saw about eighteen. If he mentions that something hasn’t happened for over two hundred years, he really means 216 years. Anything that lasts a “week” is really lasting only 6 days.

Sometimes the inaccuracy annoys me and I give the figure in “dozens”. If a company has 3 dozen soldiers, that means it has six sixes, which is a nice round number in their number system: 100.