the titular rose-colored boy from that paramore song

elves are frequently white-coded. they are often written as seeing other "races" as lesser, and use the language of real life racism- 'savage', 'children', etc. the narrative often justifies this by giving them a grand, ancient history, innate talents, art, culture, etc that other peoples are shown to lack or simply have less of or are "inferior". they are also usually visually coded with features common to peoples of northern europe; pale skin, long bony faces, downward pointing noses, blonde hair, tall, etc.

thus, some people you find hating on elves are expressing hatred towards white supremacy and a rejection of the idea that there is an Objectively Better race. i think those people are correct in their values and justified in expressing that in a jokey way that engages with the modern fantasy genre.

on the other hand, elves are almost always also coded as feminine. they are naturalists as opposed to industrialists, artisans and intellectuals as opposed to laborers. they are thin, with long head hair and no facial hair. they are emotional, capricious, and impractical. you will often, historically and in modern conservative spaces, straight up see transmisogynistic slurs like "sissy" levied at elves. this almost always goes hand in hand with contrast to dwarves, who are codified as hairy muscular industrialist practical laborers. you even see this in elven wine vs dwarven beer.

i deeply resent when elves are used this way and have a kneejerk reaction whenever i see someone larping as a dwarf who hates elves.

this also touches on the way in which misogyny is used as a shorthand for the bourgeoise! the rugged manly rural farmer in jeans vs the sissy foppish intellectual sex pervert! the way many transmisogynists imagine all trans women as privileged white rich intellectuals that they can Punch Up!

You see these delectable motherflippers? These are called STATES. You stupid foreigners might not be able to wrap your head around this, but basically they're administrative subdivisions of the country.

And here's the thing: They are totally heckin' different from each other! For instance, New York:

Looks TOTALLY DIFFERENT from Kansas:

And they both look TOTALLY different from California!

as if she had some meaningful ownership over the concept of letting people spin a little wheel at your booth. and i would be infringing upon her business venture by doing so myself three states away the next time around.

From the second equation we get that cheeseburger plus fries-squared is five. Subtracting cheeseburger, which is six, from both sides, we get that fries-squared is negative-one. Math fans will know that there are two solutions to this; either fries are the "imaginary unit" 𝒾 or they are its negative, -𝒾. We'll do the rest of the problem with 𝒾, keeping in mind that at the end we should also take the complex conjugates as solutions.

Finally, we have that cup to the power of fries, minus cup, equals three. Replacing fries with 𝒾, and moving a cup to the other side, we get that cup-to-the-𝒾 is equal to cup-plus-three.

Now, the weird part about this is the cup-to-the-i. The problem with this is that complex exponentiation is technically not a thing. That is to say, there is no one function which is mathematically equal to "input-to-the-power-of-𝒾". In fact, there are infinitely many such functions.

Fortunately, due to reasons that take about six pages to explain (trust me I've done it), there is one particular function that many people have agreed is "the most reasonable one". This is not a mathematical notion, but a human preference. Seeing as this question was presumably written by a human, I am comfortable with using this function.

So, what function is this? Well, given a complex number r∠θ written in polar form (if you don't know what that means don't worry), where -π < θ ≤ π, then (r∠θ)^𝒾 = e^(-θ)∠ln(r).

Applying this to our problem a value r∠θ will be a possible solution for cup if e^(-θ)∠ln(r) = r∠θ + 3. Splitting this into real and imaginary parts, we get two equations: e^(-θ) cos(ln(r)) = r cos(θ) + 3 and e^(-θ) sin(ln(r)) = r sin(θ). We can graph these equations on Desmos:

let the value of the glass = z, for z ∈ ℂ:

z^(±i) = 3+z

let z = r·e^(iθ) for r,θ ∈ ℝ, -π < θ ≤ π

∴ z = r·e^i(θ+2πn) for all n ∈ ℤ

∴ (r·e^i(θ+2πn))^(±i) = 3+r·e^i(θ+2πn)

distribute powers (apologies for the use of ∓):

r^(±i)·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

convert to the same base:

e^i(±ln(r))·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

split into real and imaginary components:

re: cos(±ln(r))·e^(∓(θ+2πn)) = 3+r·cos(θ)

im: sin(±ln(r))·e^(∓(θ+2πn)) = r·sin(θ)

So are we noticing a pattern yet

So are we noticing a pattern yet

So are we noticing a pattern yet