When most people world build fantasy tales, they try to follow in the footsteps of Tolkien, Le Guin, and other great world-builders. They invent landmasses, history, languages, and art.
Meanwhile, there's me. My dragons have math.
All math starts with a counting system. In the real world, this comes from by counting fingers on the hand. We have sets of five, ten, and twenty (for when you add toes). From there you develop digit symbols - 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. Through out history, humans have favored ten-digit systems. It appeals on an instinctual level.
An elf or even a centaur has the same
hand as a human does. They likely use a similar system with different
symbols. Meanwhile, dragons are decided not human or human
adjacent.
To complicate things, there are multiple types of
dragons in Mundus. One of my draft notebooks has a scribble that
dragon in Mundus treat gravity and other natural laws as
'suggestions.' Celabramar is a a massive quadruped with wings. Madam
Vircroc is biped like a velociraptor with vestigial wings. At the end
of the story, yet another dragon uses the knuckles of their wings and
short hind legs to walk like a bat.
All this biodiversity means that there isn't a standard set of twenty digits on a dragon. A dragon with wings and two back legs would only have digits on their feet. That number of digits could also vary from dragon to dragon.
If the feet are built like a bird's for grabbed and perching, there would be three forward and one pointing back. (There could also be just three or just two.) If they are more like a dinosaurs, say a sauropode, there will be five. Some dragons don't even have feet. The dragons of Mundus need a counting system that works for them, not for humans.
My solution was to have them use a base-five system. Four-toed dragons count your claws – 1,2,3,4. Most other dragons will count the longest four fangs. If you have more than four toes, the short extra acts like the zero when you write ten '10.' Short fangs also fill this round. Two long and one short means one group of four plus two, our six. (Base-five, the quinary number system, is a real thing. It used in Astralian First Nation languages like Gumatj.)
The biggest difference is that dragons won't name all the numbers that humans name in a ten digit counting system. For example in English, we have unique names for the first twenty numbers and then name the groups of ten up to hundred – thirty, forty and so on.
My dragons name their numbers up to sixteen and then name groups of eight digits. Numbers five through nine don't have special digit symbols just like our eleven is written as '11.'
So what does this mean from a storytelling angle? Well, in Mundus, it means that some people foolishly think that dragons are stupid because they 'don't know what twenty it.' However, it's really a translation error. Dragons have math, advanced math even. It's a necessity when you are a nation of large carnivores managing wild food sources. Averages, perimeters, rate of change, and probabilities- these aren't just things in a textbook for dragons. Dragons are scary good at math.
In my W.I.P., Celabramar converts volume from square feet to bushels without a reference table or calculator. He also converts pounds of silver to the market price of sheep. He also reads and corrects Leon's math, which was written in human numbers. Celabramar lives in a cave, can't hold a pencil, and can do algebra in his head.
Leon is a Wizard. He's basically the guy who went to college and finished a Master's Degree. That doesn't stop him from making mistakes because he is tired or focusing on the wrong things.
I did this on purpose. It's been in my notes for years. I wanted the reminder that technology and culture isn't a sure indicator of education and intellegent. If you judge only the surface level, you miss so much of the world.
On a lighter not, the story has yet another dragon math Easter-egg. Through out the story, Celabramar uses several techniques to mange his temper – deep breaths, shredding a tree, and self-talk. Celabramar stops himself from yelling at a bigot by counting in his head.
He counts to eight, not ten.
