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Aqua Utopia|海の底で記憶を紡ぐ

@theartofmadeline
taylor price
PUT YOUR BEARD IN MY MOUTH
The Stonewall Inn

Product Placement
Not today Justin

shark vs the universe

pixel skylines

tannertan36

PR's Tumblrdome
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"I'm Dorothy Gale from Kansas"
EXPECTATIONS
wallacepolsom
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Today's Document
will byers stan first human second

Discoholic 🪩

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@attractthecrows
new fav video just dropped
I don't think this is possible????
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.
They were right, 99% of people can't solve it.
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.
kurtis conner video: This Conservative Influencer is Crazy
drew gooden video: The us governments obsession with integrating ai into every facet of our daily lives is going to bring about the collapse of society if we don’t get of our ass and start taking action
danny gonzalez video: Buying Food on Ebay
eddy burback video: I did the russian sleep experiment for a month
tasting history with max miller video: Hardtack [WHACK WHACK]
I see a lot of folks defending their vitriolic repugnance towards toddlers with cries of "but my sensory needs!" as if children are not also in possession of sensory needs. As if you, an adult here on Tumblr.com, do not have the capability and resources to learn the skills or acquire aids for coping with competing access needs. Or, y'know, just the option to leave, the way children most often do not.
You're holding an actual child to higher standards than you hold yourself, but it's the child that should be removed from public and community spaces. For your comfort.
Go fuck yourselves.
if you go looking for doom and gloom all you will see is doom and gloom. if you go looking for reduced items at the grocery store you may find a littol treat
hehehehehe * sudden moment of clarity that straightens my spine * what is this. who am I. * the clarity fades * hehehehehehe
This ad was part of a road safety campaign in 1967.
Sounds hot
theres a whole album of song titles you can make just from the words of this tweet
check out my next stoner metal ep, featuring such classics as:
Marijuanification
Complete Derangement
Stoned Sex Drive
Derangement Manifests a Literal Sex Demon
Monstrum Incarnate
Narcotic Parody of Sex
this makes smoking weed sound so much cooler than it is
The post going around about how people's parents met has, of course, got me wondering about more fictional variants. So if you feel so inclined, tell the story of how your Shepard's parents met in the tags. Or, for Earthborn Shepards, perhaps the story of how/why they ended up on the streets?
Gonna step outside my usual programming a bit because that light pollution take and a lot of the responses to it aggravated me so much.
No, wanting to see the night sky isn't a twee retvrn to ghibli-ass take. It's not a matter of some anprim impulse to dismantle industrial society for ~nature aesthetics~, it's an extremely visible symptom of environmental degradation that gets downplayed because the externality seems trivial to most people: "Oh no, the night sky, what ever will we do without it."
But it actively disrupts light-sensitive circadian rhythms in plants and wildlife, which disrupts foraging patterns, reproductive and hibernation cycles, and contributes to wildlife population declines. It's not the major contributor to those declines, but it's an additional point of stress in an ecosystem already stressed by climate change and other forms of industrial pollution. And so much of it is wholly unnecessary.
I don't think people realize how far-reaching the problem is, either. That light isn't just confined to the places people use. You don't escape it by just taking the bus to the edge of town. That light carries, in some cases for hundreds of kilometers. Death Valley has some of the darkest skies in the US, and yet, the dome of light above Las Vegas is visible on the horizon over 250 km away! Anywhere within 50 km of a major urban center, just about anywhere in the world, never gets darker than a night under a full moon.
And this is very much a recent problem too. Before the switchover to LEDs, it was relatively expensive to light places. That meant actually accounting for the energy use and making sure it was being used where it was needed. That light was also warm-colored, so it didn't travel as far. With the decreased cost of lighting, it became standard to light places like daytime whenever they might be needed. Lighting didn't get safer, it just got more thoughtless.
The reason you see astronomy-types sounding the alarm most loudly is because they're the ones who have been seeing the full effects of light pollution and its encroachment on dark skies. It's a hobby for me too, but it's partly because I am a night owl who grew up in a small town with nothing else to do. I used to be able to clearly see the Milky Way horizon to horizon when I grew up in the mid-00s. The last time I visited about five years ago, I could only see it overhead. The population has fallen by like 10%, but the skies are brighter. I can tell when the college decided to leave the football stadium lights overnight. I can tell where the car dealerships that added overnight display lights are. I can even see when trucks with the fuckass LED light bars are coming over a hill from 5 km away.
I'm all for well-lit, safe, and accessible spaces for people to work and play at night. But there is an impact from lighting, and it can and should be regulated like any other point source pollution. It's a pretty straightforward and materialist assessment. But go off about the big scary anprims are coming for your society so people can see the stars I guess, that's not at all a reactionary response to hearing about a problem
#also a lot of the time the solution to light pollution is so stupidly easy it should be a no brainer to do it#like using more directional shades on streetlights#or different color lights instead of bright white#like#you do not actually have to live in the dark all the time to mitigate this problem!!#this is easier than fixing the ozone and we did that!
Okay, but that's an important point! Don't leave the important point in tags!
Tja
Found here 🦋
Depending on context:
* well then.
* ain't nothing you can do about it.
* well how about that then.
* you brought that upon yourself dude.
* it is what it is.
* that was completely to be expected.
* told you so.
Je nach Kontext:
* tja.
* tja.
* tja.
* tja.
* tja.
* tja.
* tja.
There was a lighthearted (at least, to me) discourse about surviving without AC in the UK heat. And Fredo had a good point that I concur with- the Deep South heat something evil so y'all can try to say we wouldn't hack it if you want 😭
a kitty is like a stuffed animal that is so heavy and it bite you and she loves you so much and you're best friends
Needs the last part
@heatandapathy you forgot the best part
you are never living this down
godawful post i made when i was 14. let me escape it please god
Never!
NOT EVEN IN DEATH