I'm drawing a comic about a new conscious and sapient species,
that appeared on Earth after humans, and their path from campfires
to atomic energetics. It's going to be a long journey!
It would never happen in the story of my comic (since humans were extinct there long before the packers emerged), but I just wanted to draw them side by side, haha.
I've developed mathematics for a non-human mind, for my comic "The book written by tiny paws"
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.
A few million years after the last human died on Earth, conscious mind reappears. This is a story about two individuals of a new species at
wanted to try my hand at this binary system - tricky to get used to but the result looks remarkably similar to typical binary!
it feels similar too - the way it interacts with powers of two, and how the "final digit" indicates even/odd. kind of interesting given how different the process is - it almost surprises me how similar it is since its so difficult to conceptualize in a way that binary isnt (to me anyway). youll also note that i ended (started?) every number with a . even though multiplying by 1 is redundant. partially bc thats what you did with 11 in your example, but i also like the consistency - it helps make a distinction between the symbols as numbers vs operations if you always start with 1 and apply operations from there. not sure if this is canon lol it just made sense to me
i also wanted to try converting a bigger number - its surprisingly easy!
although i would imagine this process is more difficult if you conceptualize big numbers as nested shapes - its easier for me to show my work with the shorthand of 60 than needing to imagine a 60-sided shape. although perhaps..... okay hang on.
now THIS was fun. i wrote out the full (2n+1) form of 37 in step 3 to make it easier to visualize, since i had to do dot isolation twice and im still learning this number system - naturally someone more familiar with it wouldnt need to write it all out. it really does force you to think in factors though - dot isolation is especially difficult if you get a prime number as a result, because to even write down your result you need to either do it again in your head or write a 37-sided shape. maybe theres a better way to break down the numbers for this kind of calculation, rather than just brute forcing it. since its already broken down into its prime factors...... hmm. lots to play with here!
anyway this is a really cool concept!! im soooo curious about how they would develop things like addition or division from here...... and the comic itself is very cute <3
I've developed mathematics for a non-human mind, for my comic "The book written by tiny paws"
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.
A few million years after the last human died on Earth, conscious mind reappears. This is a story about two individuals of a new species at
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