Tuesday, May 25, 2021

Myst Nostalgia and the D'Ni Numerical System

 Myst came out when I was 7 years old, and Riven, its first sequel, came out four years later when I was 11. While I played the third game, it's these first two that had huge influences on my general aesthetic tastes. I loved the weird sort of "fantasy technological" style of it, where it wasn't really science fiction in any serious way, but there was still sort of futuristic technology amongst the broad 19th Century furnishings.

Anyway, in the second game, taking place in the "Age" (which might be thought of as a world or plane) of Riven primarily, one of the important things to discover is the workings of the D'ni numerical system. The D'ni are an ancient civilization that discovered or developed the magical art of Writing, which allows the creation of linking books that can take a person between Ages.

Anyway, using a creepy children's toy that has what looks like sacrifices being dropped toward a carnivorous fish or shark, you can work out the basics of five symbols that correspond to the numbers 1-5. Each is just a couple of lines drawn within a square, but it gets slightly more complex. The number system is kind of simultaneously a base 5 and base 25 system (our own number system is base ten, because once we hit 10, the "counter" resets and we add another place to the number - the digit to the left of the original one now indicates how many times the original counter has cycled through its 10 symbols, going 0123456789).

The Roman Numeral system ran into an issue when it got to certain amounts, due to the fact that it needed a new set of symbols for each multiple of ten, whereas the Indian/Arabic numerals can represent arbitrarily large numbers. The D'ni system can as well.

The reason I say the D'ni one is sort of both base 5 and base 25 is that there is a kind of reset every five numbers, but you only add a new digit to the number every 25 counts.

Every digit is represented as lines within a square. The "one" digit is a vertical line that cuts the square in half. The "five" digit is a horizontal line that cuts it in half, but the truth is that really what it is is the "one" rotated counterclockwise 90 degrees. Thus the "six" is a square cut into four segments by a vertical and horizontal line - representing effectively "five plus one." When you reach ten, you instead rotate the symbol for "two" counterclockwise 90 degrees, and overlay the other digits rightside up to say "ten plus X".

Eventually, when you get to 24, you have the symbol for 4 (a rectangle that covers the lower right corner of the square, a little taller than it is wide) along with itself rotated 90 degrees counterclockwise (hence representing "four-time-five plus four")

But when you hit 25, there's no more room for this - you can't just rotate another 90 degrees because your vertical line will just become vertical again, so now we finally move on to another digit - but the "digits," which, again, are all within squares, are now bound, sharing a "wall" to make it clear these are part of the same number. The first position, like in Arabic numerals, represents the highest order of magnitude, while the next represents the next lower. So 25 is thus just the "one" digit followed by an empty square, representing zero. In this sense, it's the equivalent of 10 (which is just a one followed by a zero) except that, being a base 25 system, it represents a value of 25.

Anyway, I just ran across a website that will convert Arabic numerals into D'ni ones, and I'm kind of delighted by it.

If you are running a TTRPG and want to play around with codes embedded in numerical systems, I'd recommend stealing this wholecloth. You could also take it as inspiration to make other systems - maybe a base 12 system or something else.

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