#although... not exactly?

[cepheusgalaxy]

Me when child soldier Shinya is canonic :D

[kairithemang0]

Ella and Tadius from Cinderella's Castle give very similar energy to Curt and Tatiana from Spies Are Forever. Both not interested in each other romantically but are absolutely best friends and probably kiss each other on the cheek when they meet up and everyone sorta thinks they're together and they never deny it but they know they're not together and never will be

[cubbihue]

Would the Hazel puppet we see in a few of the shows episodes be a kind of very basic changeling? Its obviously made out of way less unwishes than Chimmy but the similarities are too striking to be ignored.

YES! YES IT ISS.

Hazel's puppet is a very basic changeling. So basic, that it's only purpose is to complete one specific set of actions. When those actions are done, it disappears! It's quite literally and physically a sock puppet.

The differences between Hazel's changeling and Timmy's changeling is that their lifespans and construction is different. They serve different purposes.

Bitties Series: [Start] > [Previous] > [Next]

More information about changelings that's ultimately just world building ramblings. Lotsa paragraphs.

Hazel's changeling is short lived, low on unwishes, and more specific to the job.

Her changeling is a one-and-done tool. It only has to do one thing. "Distract the Teacher." "Distract the Mother." So it doesn't need a lot of unwishes, it just needs enough to do its job! As a result, it is made of low quality cloth, it can't verbalize, and it doesn't make its own actions.

Hazel's changeling favors Perceptional Magic. This is why Mr. Guzman doesn't recognize that Hazel's changeling isn't Hazel. He can't see that it's made of felt and sticks. It's constantly pooling out perception magic to warp how its being viewed.

For this reason, the changeling doesn't actually need as much connections as Timmy's does. It can exist by itself, or with Hazel, so long as it has just enough Unwishes to keep it alive. Maybe not stable, but, alive.

By contrast, Timmy' changeling is on the opposite end of this spectrum.

Timmy's changeling is a continuous tool. It must persist and adapt and grow. "Go to school" "Get a job" "Find a partner". It needs many unwishes to face many situations and scenarios. So the changeling has a more difficult build.

The magic it favors is different. Timmy's changeling requires Environmental Magic. People see it for how it looks. It has human skin and can speak the human tongue. But what it requires is a suitable environment. Otherwise, people will know it for what it is. Wooden and hollow.

The more developed and high-tech the Changeling is, the less it's recommended for it to see it's real counterpart. The bigger the amount of Unwishes, the more you want it to be stable and calm. Especially when that changeling's job is "Be Human".

[wild-until-we-are-free]

let it be known that i had a dream the other day that jimmy and joel joined hermitcraft 10, refused to create bases or interact with the rest of the hermits, went to live in a lush cave with nothing but a crafting table and furnace, one singular blue bed, and a 15x15 nether portal, and every time either of them went through the portal or did a transition in their videos they displayed this screen advertising their new tumblr accounts.

[liam-summers]

3.10 | 6.22 ⤷ Bangel + Dying, being brought back to life because they have a calling, and being disillusioned because of it.

[brawngp2009]

THE PRINCE OF THAILAND: galex Crazy Rich Asians AU.

When Alex asks George if he wants to go with him to Thailand for his cousin's wedding, he immediately agrees. But there are reasons why a humble vet with bleach-fried hair keeps the distance from his huge, noisy and nosy family. And George is about to experience it first-hand.

@hypersoft-fest week 5: romantic comedy.

[read a little bit of lore below the cut]

George, an aspiring event-planner/art enthusiast, meets Alex, a vet, when he takes his parents' dog to the clinic. Alex gives George his phone number, and George assumes that he wants to ask him out, but turns out Alex has a bad habit of caring too much and he gives away his personal phone number almost to every client. However the misunderstanding leads to the first date, which leads to many more.

Eventually George meets Alex's friends: Yuki, a business-school dropout turned chef; Zhou, a young and talented fashion designer and influencer; and Lando, a travelling sports photographer specializing on Formula One. Alex, Yuki and Zhou went to a posh International School together and know each other for a very long time. Alex and Lando met when they were both in the university looking for a roommate.

After dropping out of business school Yuki opens a restaurant "Toro Rosso" with Pierre Gasly, who oversees administrative side and staff, while Yuki is in charge of the kitchen. The restaurant becomes very popular, booked and busy. Alex takes George there for one of their first dates to impress him, and it works.

Lando has a bit going on with Oscar Piastri, a Formula One driver and WDC contender, where he posts only extremely bad and blurry pictures of Oscar on his F1 photography instagram to which Oscar always replies with dead-pan "Thank you very much. The best photos ever👍🏼". Other drivers' pictures are normal, good even.

On the days, when the restaurant is closed Yuki invites Alex and Zhou in, he sets up a small table in the kitchen for his friends to try out his new recipes.

Zhou is on his way to a big breakthrough in the fashion industry, Alex and Yuki regularly wear his street-wear designs. Through Alex Zhou meets Lando and George and they plan Zhou's first solo fashion show together.

[kaiserouo]

should've done this since day 1

very significant fuck

[bijou-in-another-world]

Saw this on Facebook and just about collapsed from laughing so hard 🤣😭

[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.

[nocturneneko]

Old Man War Criminal Yaoi

creative freedom commission for RTCuno1 on twitter

[quixoticanarchy]

Just realizing it’s kind of strange how the published Silmarillion leaves out Sauron actually finding out Beren and Finrod’s names. Like I’ve seen posts wondering when Sauron might find out and what if it’s not til the Third Age, but in the poetic Lay of Leithian he finds out in Tol-in-Gaurhoth because Finrod and Beren use each other’s real names and he overhears them. It’s already funny that the Nereb-and-Dungalef tactic works on Sauron but even funnier that it finally fails not because Sauron figures it out but because they give themselves away

And moreover, Sauron knowing Finrod’s identity is key to Finrod’s whole death: Sauron’s reaction to learning their names is to say the outlaw mortal’s life is worthless and he can die now, but Finrod will be kept and tortured long beyond what a Man could endure, until Sauron learns the secret of their errand. He also threatens to ransom Finrod back to Nargothrond if his people care enough about him – or suggests perhaps Celegorm will just keep the treasure and not bother. The published Silmarillion just says “…Sauron purposed to keep Felagund to the last, for he perceived that he was a Noldo of great might and wisdom, and he deemed that in him lay the secret of their errand.”

Whereas the poetic Lay has:

“’’Twere little loss if he were dead, the outlaw mortal. But the king, the Elf undying, many a thing no man could suffer may endure. Perchance, when what these walls immure of dreadful anguish thy folk learn, their king to ransom they will yearn with gold and gem and high hearts cowed; or maybe Celegorm the proud will deem a rival’s prison cheap, and crown and gold himself will keep. Perchance, the errand I shall know, ere all is done, that ye did go.’”

And it’s right after this that he sends the wolf to kill Beren. So Finrod essentially is not just keeping his oath to protect Beren but also responding to this threat he’s just received that Beren will be killed and he himself will be tortured to death afterwards. And the irony of course is Sauron could get the secret of their mission from either Finrod or Beren, and it’s Beren, who he wants to kill immediately (and who in the poetic version even says at one point that he’s willing to confess everything to try to trade for Finrod’s life), that the secret actually most matters to. But Sauron immediately discounts the mortal in favor of torturing the elf. Finrod has no stake in completing the Silmaril quest once Beren is dead so it’s a moot point by the time Sauron would discover it. But in dying, he denies Sauron the satisfaction of torturing him and the indignity of ransoming/failing to ransom him. And Beren, whose errand it is, stays alive a little longer. Finrod’s death protects Beren but critically it also denies Sauron what he wants - especially if he thinks only Finrod knew the secret he wants - and avoids a Maedhros-esque fate for himself.

[peachyutdr]

i finished it, was kicked out of the game, and then spent the next 10 minutes drawing this. i will now go take a shower, most likely cry, and then go through the emotional turmoil of convincing myself to reset so i can do a geno run. i hate it here :D

[thechy-fychannel]

y'all ever think abt how it was julie having the affair and it is even said multiple times that she was the one who left him, yet wilson was still the one who left their home and moved in with house. like. he couldn't bear to stay in their home alone. he immediately ran to house and stayed on his couch for weeks. suffered through his pranks and his laziness and his manipulation. telling him he wants him gone while sabotaging his attempts to leave. and he only left once he got a girlfriend again.

[maculategiraffe]

I think I figured out why my mom starts resenting babies at age four. it's because that's the point at which they've surpassed her emotional maturity level and she's jealous

[bluegarners]

i like dick best when he's stylistically handsome and not just... a man who is handsome. does that make sense? i don't want the usuals that combine to make the average handsome man. i don't want the regular european niceties that create a man you'd pass on the street or see on tv and think handsome. dick should be stunningly normal guy handsome. there should be a certain style or fashion about him that makes you look back, take a second look. you should see him and recognize that there's something there, something eerily beautiful, but by the time your brain processes this, he's already turned the corner, or his face is looking a different way, or he's just out of sight. there should be something in his essence that does make you want to look but also something that's a bit hard to grasp in the second he's in your view. there should be something there that lingers in your brain, like some kind of hauntingly ethereal after image

[lesiasmadness]

Probably my second favorite bit of dialogue in these games