new age retro punk

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)

“It’s tempting to assume”: someone’s assumption is about to be criticized

Also AfD: Let's organize our 2026 Party Conference on the same day and in the same area as the NSDAP did theirs in 1926, 100 years later haha!

AfD voter type 1: Oh, that's just a coincidence, you're just trying to discredit them!!!! *conveniently forgets the party chairman in that state is a history teacher*

there’s sixteen Colorado counties that their most searched was “wolf furry”, plus thirty-odd counties (not counting either Arapahoe or any of the ones marked here as “Insufficient Data”) which may well have had plenty of searches for “wolf furry”, just fewer than for whatever they’re labeled here

and “skunk furry” searches in Arapahoe County outnumbered “wolf furry” searches in the entire state of Colorado

GIRL THE EGG COLUMN IS NOT A GOOD IDEA. YOU DO NOT NEED CONVINCING YOU NEED CONVICTION.

IS REASON ENOUGH. BE A

GIRL TODAY RIGHT NOW

Some have called "they pay me in woims" Sluggo's catch phrase. It's not. He said it once, and folks on Bluesky loved it so much they say it all the time, especially in response to the Nancy Comics by Ernie Bushmiller account. Here's the original "they pay me in woims" from February 22, 1978:

And, another mention of woims from September 13, 1949:

And the Woims Wednesday (aka Woimsday) image that gets posted almost every week because of the popularity of the word:

It started with someone listing "places with uncanny energy," like gas stations on a road trip, empty movie theaters, etc.

Then someone reblogged it and said those are called "liminal spaces," defining liminal as in-between, neither one thing nor another.

Tomorrow (July 4th, 2026) is the 10 year anniversary of the-crepes-of-wrath's comment, which:

Predates the 2020 spike in interest by four years

Predates the original backrooms post, and the the creation of r/liminalspaces by three years

Predates the earliest mention that KnowYourMeme attributes to Twitter by two years

I'm pretty sure this is the moment the term "liminal spaces" was attached to this sort of imagery, and it's TEN YEARS OLD TOMORROW!