On the Western Continent of Ysi

[Base six numerals in positional zero-system given in lime; base ten, uncoloured and in parentheses.]

The numerals and mathematical notation system used in most of the civilised parts of the Western Continent of Ysi is base six. To be sure, there are several other systems in parallel use, but this base six system is, in general, what is used by educated people for practical mathematics. Of course, different tribes of rogue Mathematicians have their own, secret methods and numbers, but even they use base six when in contact with civilisation.

Why base six? The answer must seem obvious to anyone who has investigated a human hand, and its fingers - there are five of them! And because there are five fingers on the human hand, it is natural that we should use base six, whose largest single digit is 5. Furthermore, in base six you can count up to a 100 (36), if you use the digits of both of your hands, the right for the ones, and the left for the sixes, as is commonly done. No other numeral base accomodates itself to finger-counting, with the possible exception of base twelve, where you can count knuckle-bones.

The numerals used in writing are based upon the same ancient Western Logographic Script that has given birth to all of our writing systems, and you might recognise some of the shapes.

These numerals are written with a semi-positional system. There are thirty separate glyphs, ranging from 1 (1) to 5 (5), 1½ (1.5)to 5½ (5.5), 10 (6)to 50 (30), 100 (36)to 500 (180) and finally 1000 (216)to 5000 (1080).

If you wish to write 1, you write:

**'1'**

If you wish to write 20 (12), you write:

** '20'**

And if you wish to write 21 (13), you write:

** '20' + '1'**

And to write 4325 (989):

**'4000' + '300' + '20' + '5'**

The system is further complicated - or possibly simplified, from a certain point-of-view - when you need numbers greater than 5555 (1295). Beyond this number, the system turns wholly positional, and a special sign called the Six is used to mark within a string when a digit has exceeded itself; this is called a bijective positional system. For the last four digits, the ordinary system is used.

A demonstration is in place. [For clarity, the ordinary numerals are represented here with lime, and positional numerals with tea.]:

The number 54 000 (7344) is written:

'5' + '4000'

5 4000

The number 454 000 (39744) is written:

'4' + '5' + '4000'

45 4000

The number** ****50**4 000 (39744) is written:

'4' + **'6'** + '4000'

**4A** 4000

And the number **1 00**4 000 (47520) is written:

'5' + '6' ' + '4000''

**5A** 4000

&c. &c.. It really is quite simple.

**10 00**4 000

'5' + '5' + '6' + 4000

**55A** 4000,

**10 0**14 000

'5' + '6' + '1' + 4000

**5A**1 4000