•dizzyscene •

"I aim to misbehave."

[michaelnordeman]

Buff-tailed bumblebee/Bombus terrestris/mörk jordhumla visiting a Blue globe thistle/Echinops bannaticus/blå bolltistel. Värmland, Sweden (27 July 2021).

[calware]

i really love this genre of image

[lunarthesugarglider]

[villaqueen]

The best part of that video is that the owner found the ORIGINAL plush later on the beach and took another video with it after their grandmother stitched it back up

[i-am-a-lonely-nerd]

I love the death grip after the toy was fixed up. Lessons were learned. Try to steal it this time you fucking bird. I dare you.

[girlnephew]

[ryanthedemiguy]

I don't think this is possible????

[physicallyimprobable]

Hello Ryan I am here to help. So the first step is pretty easy: Three cheeseburgers are worth 18, so each one is worth 6. If these are dollars, that's a steal!

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:

The possible values of cup are the intersections between the red, green, and purple. There are infinitely many of these which have an angle of around -π/3, and there are two weirdos: One which is a complex number very close to -2.98, and one which is somewhere around -25. The possible values for cup are all of these infinitely many solutions, and also all of their complex conjugates.

[sharkgirldick]

They were right, 99% of people can't solve it.

[peelerofpotatoes]

i've actually been working on some formulae to give all possible solutions to complex exponentiation problems recently, so here's my take on this:

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)

in effect, all this changes is the restriction on the domain of theta to be between -pi and pi, so you can just ignore that constraint.

[inthefallofasparrow]

[noporovi]

everyone get more empathetic and care about climate change & decolonization NOW

[inimoose]

Do you have any skeletons in your closet?

[teashoesandhair]

I'm in a little local cafe and the women behind the counter started griping to each other, "Oh Christ, Stephen's back again," "It's him, is it? I thought he'd stopped coming," "It's definitely him, look, it's bloody Stephen on a Thursday morning," "Do you want me to get rid of him or are you going to do it?" and so I was peering outside, trying to spot this nightmare customer, this pestilence of a person, this pox upon the cafe trade, and then one of the women from behind the counter ran outside, clapping two trays together loudly and yelling "GET OUT OF IT, STEPHEN!" and it turns out that Stephen is an absolutely gigantic fuck-off seagull who hangs around outside, menacing people for crumbs

[stonerparty]

[haverst]

[thememedaddy]

[kingpin-of-steel-act3]

[ihatenearlyeverything]

its ok theyre Gods lil helpers

[oatmealbrain]

And boy are they clumsy

[hydrangeafae]

Hi, these bees are babies! They’re not clumsy at all, this is what is called orientation flights. After birth and before beginning their careers as foragers (as all Honey bees cycle through all the jobs in the Hive throughout their lifespan), Honey bees take short flights back and forth, to and from the Hive, to orient themselves with their wings and their home so they can learn its location and how to get back home after foraging! Everyone has to learn, these are just smol little baby turkeys. Bees use the angle of the sun for location so adults have a better and more direct sense of location than any human

[polar-solstice]

IM SO PLEASED TO LEARN THIS!!!

They are just!!! Student drivers!!! 😭

[sindri42]

BONK!

[tahthetrickster]

just so we’re clear if you’ve never actually seen a cybertruck in person and have only seen photos of them i cannot stress enough how much worse they look in real life. like i honestly don’t know how it’s possible. most things look basically the same in pictures and in real life. but as stupid and ugly as cybertrucks look in photos, every person i’ve spoken to who has seen one in real life agrees that they somehow look even worse in person. and i know you’re thinking to yourself “tah they already look so bad in photos, how can they possibly look even worse in person?” I DONT KNOW. the first time i saw one on the road i was on a phone call and i literally cut myself off in the middle of a sentence just to be like “oh my GOD.” just an incredibly, laughably, unbelievably bad vehicle. i’ve never experienced anything like it. they’re just so bad

[dizzyscene]

I saw one in downtown Toronto and automatically said "ew" cause it looked so clunky. looked awkward trying to turn onto a narrow street.

[viktor-sbor]

In the 1830s, such books were very popular, as they showed the reader amazing 3D projections.

[frozenwolftemplar]

Honestly, this impresses me infinitely more than the snazziest 3D CGI imagery Hollywood can come up with.

[doctornerdington]

I was just trying to look up a score for the Mendelssohn recit but thanks for the info, Google. 🙄🙄🙄

[olowan-waphiya]

Tata'nka I'yota'nke (Sitting Bull)'s name and reputation are among the best known of Indigenous leaders in American history. He is often described as the 'chief' of the Lakota people, but he was, in fact, a spiritual leader, a medicine person of great stature for his integrity and courage. In 1890, one of the two main sites of the Ghost Dance in the Dakotas was on his land. He encouraged his people to take up the dance as a way to appeal to the Great Spirit to bring justice to the oppressed.

By December of that year, the American authorities were sufficiently afraid of the dance to plan the arrest of Sitting Bull. A number of 'indian police', backed up by a company of American troops, descended on Sitting Bull's home to make the arrest. As so often happens in volatile situations like this, things got out of control. Members of Sitting Bull's family protested. Some of the women ran forward to protect him. A shoving match began and then gunfire.

Sitting Bull was killed on December 15, 1890, at about fifty-six years of age. He died because of the Ghost Dance, which he understood to be a sacred liturgy of hope and reconciliation, but which his killers took to be a war dance by 'Indian Hostiles'. Ignoring the Constitution, the American government proclaimed the Ghost Dance religion to be outlawed. Without ever seeing or understanding it, they simply made it illegal. This level of paranoia on the part of the dominant culture led, a short time later, to the infamous massacre at Wounded Knee on the Pine Ridge reservation. So great was the Americans' fear that even a small band of starving people were seen as dangerous--so dangerous they had to be wiped out.

The massacre of unarmed dancers, the women and children left in the snow, had a chilling effect on all the nations that had taken up the dance. Among most of them there were ghost shirts or trances. The dances were the simple but dignified invocations of a people facing an apocalypse.

The level of brutality associated with Wounded Knee shocked the Indigenous nations and caused them to take the dance underground. To spare the lives of the innocent, Wovoka called on people to stop dancing in 1892. But the danced continued in secret for many years.

--We Survived the End Of The World: Lessons from Native America on Apocalypse and Hope by Steven Charleston

[continent-of-wild-endeavor]

[zagreus]

[metamelonisle]

the world should be a better place for indigenous north americans

[metamelonisle]

it really isn’t right now. but it could be! with your 🫵 help!

[metamelonisle]

this post was originally about north american indigenous people because i wanted to focus on them in particular (primarily bc this post, which wasn't expected to be spread to the degree that it is, was just about my friends, who are indigenous north americans, as well as the indigenous peoples of the continent that this account operates from). however, everyone making the addendum of "all indigenous people" are 100% correct, and i thank you for your input.

the world should be a better place for all indigenous peoples, no matter who or where they are. it really isn't right now, but it could be.

and as always, that better world can be a reality! with your 🫵help!

[uncahier]