#math posting

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.

Are you an aspiring math major, but don't know what your field of study should be? Consider using this flow chart to help determine what you should focus on!

but that's not just it, you can also add { }s

and it functions just the same as adding 2 1s

but therein lies the funniest part, that you can perform almost any function on it, from minus

to exponents

to even factorials!

and lists too!!!

you can even compare solutions of { }s in { }s

there's almost no restrictions, if you can do it with numbers, you can do it with { }

and this leads me to what I've seen a lot of people calling "desmosfuck" after the infamous programming language brainfuck, and it restricts you by not allowing any letters and no numbers, that includes sin, log, x, y and all the others. The only thing you can make out of { }s are points and numbers though, but thankfully that's usually enough to make a bunch of stuff.

like, if you need π, just use (-0.5)!^2

you need e? you already have π and i, just use e^(iπ)=-1 and rearrange it to e=-1^(1/(iπ)) and get -1^((π^-1)(i^-1))

want phi? sure, just use it's surd representation of (1+sqrt(5))/2

okay, but what if you really wanna do functions? well, if you're desperate, you can sorta do that, you just gotta use a concentration of points.

cos(x) and sin(x)? use the identities

cos seems easier

and x just has to be a dense list of numbers

now that we have x, let us... REWRITE!

that's dense... buuuut, it does the job as soon as we add the x part to the x coordinate!

absolute insanity

you can also get sin by subtracting x by half of pi

awesome

here's tan, btw

1615: two neighbouring numbers are together!

505: palindromic number!

678: FUCKING ASCENDING NEIGHBOURING NUMBER!!!