#( one of his many silly things )

[paintedcrows]

Holiday Classics

Been thinking about Ford watching the 70s Animated Lord of the Rings Movies... (companion comic to this post!)

[crabsnpersimmons]

"Hair dyes or perms or just a quick snip, you can always count on your ol' pal Clip!"

it's about time i officially shared my design for Clip from my hairdresser au! here's the silly boi himself!

a.k.a. the most complicated character i've ever designed...

close ups and additional comments under the cut!

that's my boi, despite his crazy design, i love him. his silly top knot hat, the horn-like points around his faceplate, his speckled colours, his four arms, and his funky pants. he's just soooooo fun.

Clip likes to play games and knit! he even made the patchwork pants he wears (he made Sun and Moon a pair too, but they're too precious for them to wear... also a little gaudy to wear in public—doesn't stop Clip tho!). He actually makes everything the boys wear, since there's not a lot of things in their size/shape.

instead of resting at night, he can be found in their living room, playing Kirby 64 for the nth time and/or knitting something. he's just too restless to stay still, he's always gotta be doing something and if it isn't gaming, knitting, or hairdressing, then he's up to No GoodTM.

Clip... likes popping balloons. he says "Goodnight!" with each popped balloon and once he's done, he tosses up the scraps like confetti all while giggling joyfully.

needless to say, he is not fun at parties. Sun and Moon don't let him near balloons for this reason.

and yes, he has sewing needles on hand at all times. for fashion emergencies... and for unsuspecting balloons.

Clip's not allowed to have a phone (just imagine all the in-app purchases Sun and Moon would have to deal with), but he likes to keep up with his customers and their games, even if he doesn't get their fixation over bluenets he'll never openly admit it but he prefers curly-haired blond hunks that look sweet in soft pastels but could also squash him like the spider he is

also, he's great at microbraiding! though i imagine if Sun and Moon are free, they'd come help to shorten the wait but also to compete and see who braids the most (Clip always wins of course—make anything into a game, and he's winning)

aaaaand there's this! i wanted to make sure Clip would be able to freely rotate his waist so his arms could have their full range of motion, and this was the solution i came up with: a crop top on top and a wrap around his waist. and Clip here is being a sneaky little scamp about it.

[lbhslefttiddie]

despite his initial rough impression, lqg gets a "fun" rating on the gege scale

[physicallyimprobable]

what's the 3-dimensional number thing?

Well I'm glad you asked! For those confused, this is referring to my claim that "my favorite multiplication equation is 3 × 5 = 15 because it's the reason you can't make a three-dimensional number system" from back in this post. Now, this is gonna be a bit of a journey, so buckle up.

Part One: Numbers in Space

First of all, what do I mean by a three-dimensional number system? We say that the complex numbers are two-dimensional, and that the quaternions are four-dimensional, but what do we mean by these things? There's a few potential answers to this question, but for our purposes we'll take the following narrative:

Complex numbers can be written in the form (a+bi), where a and b are real numbers. For the variable-averse, this just means we have things like (3+6i) and (5-2i) and (-8+3i). Some amount of "units" (that is, ones), and some amount of i's.

Most people are happy to stop here and say "well, there's two numbers that you're using, so that's two dimensions, ho hum". I think that's underselling it, though, since there's something nontrivial and super cool happening here. See, each complex number has an "absolute value", which is its distance from zero. If you imagine "3+6i" to mean "three meters East and six meters North", then the distance to that point will be 6.708 meters. We say the absolute value of (3+6i), which is written like |3+6i|, is equal to 6.708. Similarly, interpreting "5-2i" to mean "five meters East and two meters South" we get that |5-2i| = 5.385.

The neat thing about this is that absolute values multiply really nicely. For example, the two numbers above multiply to give (3+6i) × (5-2i) = (27+24i) which has a length of 36.124. What's impressive is that this length is the product of our original lengths: 36.124 = 6.708 × 5.385. (Okay technically this is not true due to rounding but for the full values it is true.)

This is what we're going to say is necessary to for a number system to accurately represent a space. You need the numbers to have lengths corresponding to actual lengths in space, and you need those lengths to be "multiplicative", which just means it does the thing we just saw. (That is, when you multiply two numbers, their lengths are multiplied as well.)

There's still of course the question of what "actual lengths in space" means, but we can just use the usual Euclidean method of measurement. So, |3+6i| = √(3²+6²) and |5-2i| = √(5²+2²). This extends directly to the quaternions, which are written as (a+bi+cj+dk) for real numbers a, b, c, d. (Don't worry about what j and k mean if you don't know; it turns out not to really matter here.) The length of the quaternion 4+3i-7j+4k can be calculated like |4+3i-7j+4k| = √(4²+3²+7²+4²) = 9.486 and similarly for other points in "four-dimensional space". These are the kinds of number systems we're looking for.

[To be explicit, for those who know the words: What we are looking for is a vector algebra over the real numbers with a prescribed basis under which the Euclidean norm is multiplicative and the integer lattice forms a subring.]

Part Two: Sums of Squares

Now for something completely different. Have you ever thought about which numbers are the sum of two perfect squares? Thirteen works, for example, since 13 = 3² + 2². So does thirty-two, since 32 = 4² + 4². The squares themselves also work, since zero exists: 49 = 7² + 0². But there are some numbers, like three and six, which can't be written as a sum of two squares no matter how hard you try. (It's pretty easy to check this yourself; there aren't too many possibilities.)

Are there any patterns to which numbers are a sum of two squares and which are not? Yeah, loads. We're going to look at a particularly interesting one: Let's say a number is "S2" if it's a sum of two squares. (This thing where you just kinda invent new terminology for your situation is common in math. "S2" should be thought of as an adjective, like "orange" or "alphabetical".) Then here's the neat thing: If two numbers are S2 then their product is S2 as well.

Let's see a few small examples. We have 2 = 1² + 1², so we say that 2 is S2. Similarly 4 = 2² + 0² is S2. Then 2 × 4, that is to say, 8, should be S2 as well. Indeed, 8 = 2² + 2².

Another, slightly less trivial example. We've seen that 13 and 32 are both S2. Then their product, 416, should also be S2. Lo and behold, 416 = 20² + 4², so indeed it is S2.

How do we know this will always work? The simplest way, as long as you've already internalized the bit from Part 1 about absolute values, is to think about the norms of complex numbers. A norm is, quite simply, the square of the corresponding distance. (Okay yes it can also mean different things in other contexts, but for our purposes that's what a norm is.) The norm is written with double bars, so ‖3+6i‖ = 45 and ‖5-2i‖ = 29 and ‖4+3i-7j+4k‖ = 90.

One thing to notice is that if your starting numbers are whole numbers then the norm will also be a whole number. In fact, because of how we've defined lengths, the norm is just the sum of the squares of the real-number bits. So, any S2 number can be turned into a norm of a complex number: 13 can be written as ‖3+2i‖, 32 can be written as ‖4+4i‖, and 49 can be written as ‖7+0i‖.

The other thing to notice is that, since the absolute value is multiplicative, the norm is also multiplicative. That is to say, for example, ‖(3+6i) × (5-2i)‖ = ‖3+6i‖ × ‖5-2i‖. It's pretty simple to prove that this will work with any numbers you choose.

But lo, gaze upon what happens when we combine these two facts together! Consider the two S2 values 13 and 32 from before. Because of the first fact, we can write the product 13 × 32 in terms of norms: 13 × 32 = ‖3+2i‖ × ‖4+4i‖. So far so good. Then, using the second fact, we can pull the product into the norms: ‖3+2i‖ × ‖4+4i‖ = ‖(3+2i) × (4+4i)‖. Huzzah! Now, if we write out the multiplication as (3+2i) × (4+4i) = (4+20i), we can get a more natural looking norm equation: ‖3+2i‖ × ‖4+4i‖ = ‖4+20i‖ and finally, all we need to do is evaluate the norms to get our product! (3² + 2²) × (4² + 4²) = (4² + 20²)

The cool thing is that this works no matter what your starting numbers are. 218 = 13² + 7² and 292 = 16² + 6², so we can follow the chain to get 218 × 292 = ‖13+7i‖ × ‖16+6i‖ = ‖(13+7i) × (16+6i)‖ = ‖166+190i‖ = 166² + 190² and indeed you can check that both extremes are equal to 63,656. No matter which two S2 numbers you start with, if you know the squares that make them up, you can use this process to find squares that add to their product. That is to say, the product of two S2 numbers is S2.

Part Four: Why do we skip three?

Now we have all the ingredients we need for our cute little proof soup! First, let's hop to the quaternions and their norm. As you should hopefully remember, quaternions have four terms (some number of units, some number of i's, some number of j's, and some number of k's), so a quaternion norm will be a sum of four squares. For example, ‖4+3i-7j+4k‖ = 90 means 90 = 4² + 3² + 7² + 4².

Since we referred to sums of two squares as S2, let's say the sums of four squares are S4. 90 is S4 because it can be written as we did above. Similarly, 7 is S4 because 7 = 2² + 1² + 1² + 1², and 22 is S4 because 22 = 4² + 2² + 1² + 1². We are of course still allowed to use zeros; 6 = 2² + 1² + 1² + 0² is S4, as is our friend 13 = 3² + 2² + 0² + 0².

The same fact from the S2 numbers still applies here: since 7 is S4 and 6 is S4, we know that 42 (the product of 7 and 6) is S4. Indeed, after a bit of fiddling I've found that 42 = 6² + 4² + 1² + 1². I don't need to do that fiddling, however, if I happen to be able to calculate quaternions! All I need to do is follow the chain, just like before: 7 × 6 = ‖2+i+j+k‖ × ‖2+i+j‖ = ‖(2+i+j+k) × (2+i+j)‖ = ‖2+3i+5j+2k‖ = 2² + 3² + 5² + 2². This is a different solution than the one I found earlier, but that's fine! As long as there's even one solution, 42 will be S4. Using the same logic, it should be clear that the product of any two S4 numbers is an S4 number.

Now, what goes wrong with three dimensions? Well, as you might have guessed, it has to do with S3 numbers, that is, numbers which can be written as a sum of three squares. If we had any three-dimensional number system, we'd be able to use the strategy we're now familiar with to prove that any product of S3 numbers is an S3 number. This would be fine, except, well…

3 × 5 = 15.

Why is this bad? See, 3 = 1² + 1² + 1² and 5 = 2² + 1² + 0², so both 3 and 5 are S3. However, you can check without too much trouble that 15 is not S3; no matter how hard you try, you can't write 15 as a sum of three squares.

And, well, that's it. The bucket has been kicked, the nails are in the coffin. You cannot make a three-dimensional number system with the kind of nice norm that the complex numbers and quaternions have. Even if someone comes to you excitedly, claiming to have figured it out, you can just toss them through these steps: • First, ask what the basis is. Complex numbers use 1 and i; quaternions use 1, i, j, and k. Let's say they answer with p, q, and r. • Second, ask them to multiply (p+q+r) by (2p+q). • Finally, well. If their system works, the resulting number should give you three numbers whose squares add to 15. Since that can't happen, you've shown that the norm is not actually multiplicative; their system doesn't capture the geometry of three dimensions.

[oceanwithouthermoon]

yk when i think about it, especially when im watching the anime with people who havent read the manga, the reason a lot of people who only watch the anime and didnt read the manga misinterpreted saikis character so badly is definitely in part because of how damn fast paced the anime is 😭

like that little smile and eye shine frame is there for not even half a second in the anime, so its easier to miss it and assume that he really did only finish those workbooks to get coffee jelly ☠️ its much more clear if you get a good look at how he reacts here that hes just a silly little tsundere and a fucking liar

[yea-baiyi]

i keep thinking about the odyssey i am THINKING about wei wuxian as odysseus. you were dead. its been years since you’ve seen your family. the child you left behind is almost a man. you wear a face they don’t recognise, you sneak in through the back door. the dog gives your identity away. the world knows it’s you when you draw your weapon. the person you love recognises you by the original symbol of your love—a secret that no one else in the world knows about, still, because they kept it safe for all these years. you get the chance to go back and despite everything, you found home waiting for you; he kept your place and raised your son and he was still there waiting for you when you got back. tell me o muse, about a complicated man i am extremely not okay

[pkaykim]

Oofurixmas2022 for @meela-31

[cloudpalettes]

hey detectives 🔎‼️

[omaano]

"I bet it was the martini that blew your cover." "You can judge my drinking habits after you got me out of here, Djarin!"

I've seen one (1) James Bond movie my entire life back when 00Q was a whole thing on this hellsite, but I'm ready to die on the hill that Din would make a great Q who knows how to work in the field and can poke at gadgets just fine, but also gets very passive agressive when he has to work overtime - he asked for the office job because his kid is going to school and they are working on building a normal-adjacent nighttime routine, which is very difficult when the agent he's working with cannot stick to a plan.

For the Spies/Assassins square on my Bobadin AU bingo for @bobadinweek

(I've seen all the John Wick movies though, so if Boba's pose is familiar, that is why)

[luck-of-the-drawings]

OH ARTHUR BENNETT.. such a gorgeous and intriguing character. terribly burdened by a GRUESOME set of crimes, his light suffocated by a HEAVY century of GUILT. so tragic, so dark and broody, and yet PAINFULLY awkward in any social setting ever

[hecatialapis-lazuli]

i feel like I've talked about this before but I wish blazblue dipped more into the horror of the situation. Whether you wanna go cosmic or existential both kind of work, though I guess the theme is a bit more despair than horror? Those two feel like they marry together pretty well.

Like. Think of CS. You have Noel, becoming what she always was, something inhuman. Literally screaming and crying after having the truth of the world and the PFDs revealed to her. You have Ragna, also learning the truth, and that he has tried so, so many times and failed every single time. You have Terumi, relishing in the hopelessness that should cause, yet being just as stuck as everyone else, and painfully aware that if he wants out of this hell, he has to claw his way out.

Idk, I just think there's a lot of stuff in blazblue that lends really well to horror. There's already themes about loss of autonomy, just play a little more into that, emphasize the helplessness before the Master Unit, and then the satisfaction of finally being free.

Hell, the Master Unit/Origin still is sympathetic in this interpretation. She's suffering, she's not doing anything out of malice, she just wants to be a person. Not even the Origin is immune to the horror of being a thing, strung up to watch and desperately try for another ending this time. This time, it'll work.

[tennessoui]

au where jedi healers take a vow not unlike jedi temple guards, but instead of wearing a mask and becoming anonymous, they give up their sight and wear blindfolds to allow the Force to guide their every action. it’s also supposed to blind them to their patients’ differences, which used to be symbolic but since the war between the jedi and the sith broke out, has become much less so

because jedi healers are supposed to heal regardless of if their patient is a jedi or a sith, when they’re deployed on battlefields after the fighting is over, they use the Force to heal every injured person they come upon.

anakin skywalker, who was chosen from the creche and agreed to follow the Healing path at the age of 9, thinks it’s sort of stupid that they have to wait until after the fighting is over to begin to help because he can feel people dying in the Force, he can feel their pain--

young general kenobi, who remembers his old creche-mate anakin skywalker and how blue his eyes once were, thinks it’s beyond foolhardy that this healer is stealing out across an active battlefield, blindfold over his eyes and bending down to heal karking darth maul and single-handedly diverting all of obi-wan’s attention away from the droids and sith legion because now he has to make sure he’s ok he can’t just leave him to the whims of the Force, he’s unprotected and he’s going to get himself killed----

it’s a headache and a half for everyone involved because general kenobi keeps abandoning his battle strategy and sometimes even position to ensure healer skywalker’s safety and healer skywalker keeps dropping everything and everyone the moment he feels obi-wan kenobi get hurt in the Force to rush to his side, Force Vow of Healing Equality be damned.

but......the Council keeps deploying them to the same battlefield because healer skywalker is never more effective as when he knows he must heal fifty mortal wounds before he can rid general kenobi of a headache, and general kenobi is never as ruthless as when skywalker is on the field close to him, in potential harm’s way

despite how much they insist they hate each other 

[beanghostprincess]

hear me out: modern au, zolu

zoro is born into a rich family, but he doesn't give a fuck about their business, has no clue about what he wants in life, and is feeling more and more lost by the day.

enter thief luffy, who chooses Zoro's house as the next target. zoro only catches a glimpse just before he escapes out of the window, flashing him a grin and changing his life forever.

but luffy has to come back because he forgot something and nami's super mad about it. zoro's waiting for him this time with the very thing he needs, planning to catch him but of course this ends with them being friends because well it's luffy. and he secretly likes the idea of his family freaking out over the stolen goods.

they hang out and zoro discovers that luffy's somehow both a clumsy idiot and somehow silent and nimble when it comes to thievery at the same time(how? luffy makes him go with him for one of the heists and doesn't tell him that till they are there and zoro goes through a dozen heart attacks while luffy follows his reckless plans) it's the most fun zoro has had in his life. of course, it ends with luffy asking him to join him.

anyway, band of thieves romance dawn trio au. ace and sabo are also pretty well known thieves, having their own gangs and all.

do you think this idea will work for a fic? it just popped into my head lol

Thinking about Zoro being born into a rich family is honestly so funny but it makes sense because. You know. Mihawk. Tbh, in this AU I see Zoro also obsessed with swords and wanting to be a swordsman but, everybody knows him because of his father so he has this personal thing in which he wants to win a fight against him to take over the dojo. Or something like that. It's surprising how accurate you can make Modern AUs sometimes- But also, Mihawk wants him to keep studying too, and hell if he knows what to do with his life. He's lost mentally and physically 24/7. Perona teasing him about it doesn't help.

And,, Luffy and Nami being thieves together is actually so cute 😭 Robin Hood type of thieves except that they also keep a lot of the money since, y'know, "It's a job like any other! And I need to pay the rent somehow-" Nami says. Ace is a thief because it's kinda fun and thrilling but Sabo does it mostly for the poor-- Great team, honestly.

Luffy and Zoro getting along right away is so funny because it's 100% canon. I think Zoro would freak out a little at first because, well, Luffy is chaotic in every universe. But then he realizes that this could give his family a heart attack and suddenly being friends with Luffy seems more fun. Also, the guy is cute and carefree and Zoro is very weak for him. Zoro joining them because it makes his life less boring and telling Mihawk he found a job at a random place would be so, so funny to me--

It would definitely work for a fic and I'd read it without hesitation 🙏🏻❤️ It's sooo good!!!!!!

[no27-autonation-honda]

congratulations to Mme. Pascale Leclerc, who has surely just experienced both the funniest and most unhinged weekend a mother could ever have. Dear fucking christ, I hope your middlest son brought you a bottle of champagne for yourself, ma'am.

[somegrumpynerd]

I'm sure it's already been done before but y'know what would be a cool idea for a collab? A UTMV colouring/ activity book

Like you could get a bunch of artists to draw stuff of their favourite au guys but just up to the lineart and then people could print them out and colour them in! You could also have little activity pages mixed in like wordsearches or mazes too but themed to utmv stuff, it could be a fun thing!

[fountainpenguin]

Things that happened in Martyn & Cleo Double Life canon:

Cleo hoping to find her soulmate and start a life with them

Cleo dumping Martyn without giving him a chance to explain his side of the story, but hearing him out when he comes to her later

Martyn watching Cleo through his spyglass and telling the audience she seems safe and happy even though he thinks it's weird she's outside at night

Martyn, after he's had time to consider how he wants to play this, spinning a story about trying to be a provider for her and Cleo explaining that she wanted him, not things

Cleo not being remotely impressed by the "I was providing" sob story, lol

Martyn calling Cleo selfish for choosing to be with Scott because she's supposed to be HIS soulmate and he wants a partner

Cleo willing to forgive Martyn if he meets them halfway

Martyn refusing to meet them halfway because he doesn't think he did anything wrong

Martyn screaming about how Cleo's building bridges with Scott but "When will she think about mending our bridges???"

Martyn explaining to Cleo that he doesn't understand why his Session 1 actions bothered them

Martyn centering his character arc and roleplay on trying to win Cleo back without actually apologizing

Cleo giving Martyn a flower and stating that if he loses it, she'll be real cross with him

Cleo chasing Martyn out of her yard because he tried to put an HOA sign on her base and she wanted to make it clear that she wasn't associated with them and their hate for his base (even though she does think his heart base is strange)

Martyn attacking Cleo after she said attacking is a form of affection to her

Cleo setting boundaries with Martyn and explaining what he can do to get her back

Cleo sighing when Scar set her up on a date with Martyn, but taking the chance to talk to him instead of walking out

Cleo genuinely wanting Martyn in her alliance

Martyn and Cleo giggling constantly when they chat

Scar asking if Martyn wanted him to play a romantic music disc for him and Cleo (and Martyn getting excited and saying yes)

Martyn offering to take Cleo's armor and weapons to the deep dark so he can enchant them and bring them back while she stays safe

Cleo gifting Martyn diamonds, expecting nothing in return but not wanting him to die from lack of a good sword

Martyn and Cleo forming a secret alliance that allows Cleo to live with Scott while being on good terms with Martyn

Martyn expressing frustration that Cleo wants to keep this alliance secret because he wants them to be public allies; Cleo softly shushes him when people approach and might overhear

Martyn telling Cleo that she's putting out a lot of mixed signals because she keeps reeling him in and then pushing him away, claiming he is very confused about where he stands with her

Martyn teasing Cleo by punching her off a cliff and accidentally killing her and feeling so bad about it that he apologizes profusely despite roleplaying as someone who refused to apologize for Session 1

Martyn and Cleo immediately threatening Bdubs together when he said hi to them while they were hanging out, sdkfj

Martyn genuinely apologizing to Pearl for dumping her after Session 1

Martyn hiding under Cleo's bed while she defends him from an enderman attack

Cleo offering to let Martyn move into her house after Etho and Joel grief his base; Martyn saying he might take her up on that

Cleo and Martyn agreeing to move out and base together at Box

Cleo trusting Martyn with the location and resources of her red life base

Martyn rushing to Cleo's aid in the deep dark and trying to turn everyone against him instead

Cleo responding to Martyn's panicked shouts for her to eat by opening her inventory to get food (and drowning because she forgot she was in water)

Cleo hanging back and letting Martyn attack Scott while she does nothing to stop him from doing so, implying as much as she likes Scott, she won't kill Martyn (and herself) for him (and/or she trusted Scott to handle himself even though he ran away while Martyn was shooting at him)

Things that did not happen:

Cleo unwilling to forgive Martyn or consider being his friend and partner

Martyn and Cleo hating each other

Thank you for coming to my TED Talk