mango's no.1 fan

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)

I will admit I REALLY like the recent improvements they've added to tumblr's search (you can exclude terms now!! you can search multiple tags!! and time frames!!) so it's not like they're incapable of adding useful features. it might be mutually beneficial for us as users if we were more vocal about things we want and don't want. Some features I'd like to see added:

spoilerable text

spoilerable images

the return of hover text!! remember when we had that?

ability to embed videos in reblogs

ANIMATED GIF ICONS!!!!!!!!!!!!

the ability to turn off other people's animated gif icons

the ability to filter original posts on a user's ENTIRE blog, not just a tag/search

more html support, like what if we could build tables

adding reactions to replies! I'm glad we can like them more but it'd be nice if we could take this further

embeddable tiktoks?? I don't even use tiktok but I remember trying to embed one in like 2020 and I'm surprised we still can't! even vines were able to be embedded

being able to search in your DMs. not being able to do this is why I tend to redirect mutuals to discord

MUTING USERS POSTS/COMMENTS WITHOUT BLOCKING THEM! just cause I don't want to see someone's posts doesn't mean I don't want us to never interact ever

a mutual-only dashboard feed

a feed for the blogs you're subscribed to

get rid of tumblr tv lmao I've literally never used it

"mark as read" button for communities without opening them

please dear god no AI shit unless it's a way for me to filter/block it easier

In 2021, Swarovski (the company that makes the very sparkly crystals you see in certain jewelry, on figure-skaters' twinkliest outfits, on red carpet dresses), decided they didn't want the grubby fingers of small-time jewelers, clothing designers and costumers and crafters on their shiny beads and rhinestones anymore. They decided to limit their sales to "luxury" and couture creators, not girls who sell stuff on Etsy. The tenor of their press release on the subject was snide and insulting. Resellers (like your favorite bead shop) would no longer be allowed to carry their product; the average Jane on the street would not be able to purchase them. You could only get them if you had an authorized business agreement that bound you to very strict brand behavior. And those of us who still had good stock of the crystals would no longer be "permitted" to use the brand's name in our listings for sale.

Every bead shop and craft supply place and many, many small clothing makers--wedding shops, prom and dancing dress suppliers, the sort of salt of the Earth mom and pop time machines of shops that are the backbone of the field--scrambled to find something that could replace them. The last of the stock dwindled quickly, all of us grabbing what we could get while there was any chance of it, and then it was gone and we no longer had any access.

I was Big Pissed about it at the time. It was just so goddamn stuck-up, when wholesalers and indie jewelers had made them so much money, when some people I knew--when *I!*--had been brand-loyal for decades. But with no recourse, everyone pivoted fairly quickly, most of us to Preciosa Crystals. Those are Czech, quite sparkly, and considerably less expensive than Swarovski. The faceting method they use is different, but not worse; any differences are hardly noticeable when you're seeing them as a hundred pinpoints of light.

Well, out of nowhere, Swarovski just dropped this: https://www.harmanbeads.com/swarovski-brand-policy-update

"Effective June 1, 2026, Swarovski updated the distribution and brand usage policies introduced in 2021. Businesses may now purchase Swarovski Crystals without signing a Brand Control Agreement, and Authorized Distribution Partners may once again sell Swarovski Crystals to resellers, including bead stores and online retailers. Businesses may also use the Swarovski brand name when following Swarovski’s Proper Use Guidelines. Designers, manufacturers, artists, brands, retailers, and resellers are now eligible to purchase Swarovski Crystals through authorized distribution channels."

They want us back. A lot of the companies who could have kept a brand relationship with them also have swapped to Preciosa, over the last half-decade, in solidarity with indie creators and out of a sour awareness that it could be them, next. And it doesn't hurt that Preciosa was able to expand their line quite a bit now that everyone who wanted sparkle had no choice but to go to them.

And I'm not seeing nearly anyone who intends to return. The feeling is, "Y'all told us to fuck off! Off we fucked! And now, that's what you can do, too!" I'm seeing a lot of "How many of us did you stab in the back?" comments from the people whose money they're hoping to attract.

the authors have developed a "phubbing scale" and demonstrated that it has strong correlation with the existing "maladaptive technology use" scale. from this, they conclude the "phubbing scale" is a valid and useful metric.

the "maladaptive technology use" scale, if you go and read that paper, has shown strong correlation with the "problematic smartphone application use" construct.

have you caught the problem yet? nowhere has it been proven that scoring high on any of this is actually bad for you.

> express annoyance with a common failing of academic writing in your field

asked students to volunteer to take a "screen-free challenge" where they didn't use electronic devices in class for a semester

recorded students' views on the challenge at the end of the course, and found that most of the students who participated had positive views while most of the students who didn't participate had negative views

completely ignored that this might just mean "people who thought something was a bad idea didn't do it", and instead concluded "the screen-free challenge leads to more positive views on the learning experience"

not true

rude actually

minimizing a disability

"everyone's a little weird"

true

human brains are very different

not diagnosing random people

Hey everybody! I have a story in this anthology! You know that Caleb guy I talk about every now and then? Well he's aroace, and I wrote a little story from his past.