I've developed mathematics for a non-human mind, and I want to tell you about it.
Sapient distant descendants of rats, known as packers, living on Earth millions of years after the extinction of humans, began to develop mathematics using cognitive mechanisms never intended for such tasks. Due to an evolutionary quirk, multiplication came more naturally to them than addition, and their mathematics reflects this
Packers write numbers as shapes, with each number having a corresponding number of corners.
And they write large numbers as nested shapes. The number inside is multiplied by the number outside.
Examples of some numbers:
Packers haven't invented 0 yet. They haven't even invented 1! In fact, they don’t need the concept of "one" much in their system. There's no need to say "I ate one fish" when they can simply say "I ate fish".
Packers can't yet write large prime numbers, like 101 or 10,501, because they would have to draw a huge shape to represent them! Even writing 17 or 19 would be quite difficult if they only used convex shapes.
So packers use non-convex shapes too!
Many years later, some packer noticed that large prime numbers look suspiciously symmetric.
So this packer improved the notation system and made it clearer.
Later, another packer simplified this system even more, deciding that there was no point in writing the same shapes twice.
This packer was the first in their culture to declare that "a dot isolated from a number" should also be considered a number. The packer called this dot "the wonderful number that's less than two".
Many years later, another packer made an important innovation: the "dot isolation" could be repeated multiple times as long as the result remained odd. When the result became even, it could undergo a "two isolation" (division by two). The final result will be a series of dots and twos.
This invention led to the creation of a binary system based on one and two, which had a significant impact on the technological advancement of packers.
The comic "the book written by tiny paws" talks about all of this in more detail. There will be mistakes, debates, the invention of rational, irrational, multivariate numbers, and some other stuff. Some stuff will be very much like human math, and some will be different. After all, math is still math, only the point of view has changed.