Like all other things, the D'ni developed their own system for counting and with this, their own numeral system. Unlike our system, the D'ni do not use a base ten system but rather a base twenty-five. The symbols for zero through four are the only actual original numbers in the entire numeral set. These symbols are then used as *base symbols* for higher numbers.

## Writing D'ni NumeralsEdit

The number system used by us is called a decimal or base-10 system. This means that we have ten digits (0 to 9), and our place value is based on tens, or powers of ten. This means that our number **37** means *3 sets of 10 with 7 sets of one*. The number **105**, means *10 sets of 10 plus 5 sets of one*.

The D'ni use a base-25 system instead, meaning their place value is based on powers of twenty-five. There are two logics used when writing D'ni numerals. The system which involves writing the number twenty-five and higher requires mastery of the first.

### Writing up until 25Edit

To write numbers up to 25, the D'ni use a base-5 (quintary) system.

The first five symbols in the D'ni numeric system form the base for any number higher than four:

0 | 1 | 2 | 3 | 4 |

For writing numbers that are multiples of five (quintads), each of these symbols is rotated 90° counter-clockwise. Thus, the glyph for 1 forms the glyph for 5 (1 set of five), when rotated; the glyph for 2 becomes the glyph for 10 (2 sets of fives); 3 becomes 15 (3 sets of fives), and 4 becomes 20 (4 sets of fives).

The two sets of glyphs then, units (1 to 4) and quintads (5, 10, 15, 20) can be *combined* for all values inbetween. For example, the number seventeen (17), is a combination of the glyph for 15 plus the glyph for 2 (15 + 2 = 17).

The process to *convert* a decimal number to D'ni can be described as follows: First, we divide the number by five. By dividing 17 with 5 (17 = 5 × 3 + 2), we get the number **three** (3 quintads) and a remainder of **two** (2 units); in other words, the number is written as [3][2] in the quintary system. So, we rotate the symbol of **three** 90° counter-clockwise, thus giving us the symbol for fifteen, which is the base digit (**three** quintads). Next, we simply take the remainder, **two**, which is then written over the base symbol.

+ | → | |||

15 | 2 | 17 |

Here is a formal list of the numbers from 0 to 24:

+ | 0 | 1 | 2 | 3 | 4 |

0 | |||||

5 | |||||

10 | |||||

15 | |||||

20 |

It is believed that the D'ni Alphabet is simply composed of cursive versions of the unit and quintad symbols, which are combined in a similar manner. It is possible that the two systems had a common origin and then evolved independently, with the numbers being geometric, and the letters more calligraphic.

### Writing 25 and higherEdit

The quintary system is a subset system of the D'ni numerical system and is used only for numbers up to 24. However, the D'ni use a base-25 system, and they write the number 25 as following:

As with our decumal number of 10, the first symbol is 1 and the second symbol is zero. So, using a place value of 25, this symbol states that we have *1 set of 25 with zero sets of one*. Thusly, we have the number **25**.

Using this concept, we can determine how to write any higher number. Once again, division is used when determining the appropriate symbols. For example, let's take the number 209. Because we are now working in a base twenty-five system, we take the number 209 and divide it by 25. This gives us the number 8 and a remainder of 9. So, we take the symbol for 8, which we determine how to make using the earlier mentioned system above. The symbol for 8 goes in the first slot and the remainder of 9 goes in the second, as shown below:

What we see is **[8][9]**, which in D'ni means we have *8 sets of 25 along with 9 sets of one*, which gives us 200 plus 9 for a grand total of 209.

### The Number Twenty-FiveEdit

The number 25 is what the entire numeric system is based on, and can be written both as a special single digit, or as two digits.

The most common, and mathematical way was to write it according to the base-25 number system, therefore represented as 1-0:^{[1]}

However it could rarely be represented as a single symbol:^{[1]}

One of is usages was to write comparisons, which in D'ni language are expressed on a scale 1-25.^{[1]} Therefore the expression *b'fahsee* would be written with that symbol. Other than obvious practical and esthetic reasons, it is not known if the single symbol had any special usage, like formal or ceremonial.

## TriviaEdit

In the game Riven, on Gehn's timepiece, the number 25 is depicted as a square with a diagonal slash, like [/]. Richard A. Watson explained that it was an error in the original font they made during the production of the game, and was used by mistake. Some fans wrongly mistaked this symbol as the digit for zero.^{[1]}

Watson joked that the [/] symbol could be considered a combination of the zero (dot) and the 25 (X) symbols, signifying how the 25th *pahrtahvo* is also the zeroth for the next day simultaneously, as the cyclical number sequence wraps around itself on watches^{[1]} (similar to our 00:00 = 24:00).

## ReferencesEdit

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}^{1.4}Numbering and Math