The D'ni used a unique base-25 counting system, rather than the decimal (or base-10) system used by many human societies. They also used numerals unlike any encountered on the surface. Their system had unique symbols for the numbers zero to four and all other numbers are constructed by various arrangements of these.

## Writing D'ni Numerals

The decimal system has ten digits (0 to 9), and the place value is always a power of ten. This means that the number **37** means *3 sets of 10 with 7 sets of one *((10^{1}*3) + (10^{0}*7)). The number **105**, means *1 set of 100 plus 0 sets of 10 plus 5 sets of one *((10^{2}*1) + (10^{1}*0) + (10^{0}*5)).

The D'ni used a base-25 system, meaning their place value was based on powers of twenty-five. There are two logics used when writing D'ni numerals, the first is for recording numbers from 0 to 24, the second is for numbers 25 and higher.

### Writing up to 25

To write numbers up to 25, the D'ni used 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 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 five); 3 becomes 15 (3 sets of five), and 4 becomes 20 (4 sets of five).

The two sets of glyphs, 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 higher

The quintary system described above 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 the decimal number of 10, the first symbol is 1 and the second symbol is zero. So, using a place value of 25 (5^{2}), 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-Five

The number 25 can be an exception to the system detailed above, as it has been written both as a special single digit and as two separate digits.

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

However, in rare cases, it has been represented as a unique symbol:^{[1]}

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

## Trivia

Gehn's timepiece in Riven shows the number 25 depicted as a square with a diagonal slash: [/]. Richard A. Watson explained that it was an error in the original font made during the production of the game, and was used by mistake. Some fans wrongly mistook this as the symbol 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 simultaneously the zeroth for the next day, as the cyclical number sequence wraps around itself on watches^{[1]} (similar to the fact that 00:00 = 24:00 on a 24 hour clock).

## References

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