#math! wild

[kooldewd123]

wild life episode one: wow, six lives seems kinda excessive. how deadly do they expect these wild cards to be?

wild life episode two: oh.

wild life episode three: OH.

[8pxl]

14 yrs ago i started playing magic the gathering as a kid, and i had the dream to do art for them

3 yrs ago i tweeted about those dreams:

today i’ve released 11 official magic the gathering cards, and it’s honestly so surreal and insane to me! i did that!! i fulfilled a childhood dream, and i honestly couldn’t be more proud 🥹

[more-mara]

This video is constantly on my mind

[newquestion]

misinterpreted networked wild

of course there's one more image! here you go!

[inkskinned]

love when men cry about body hair bc "it's hygiene" and yet 15% of cis men leave the bathroom without washing their hands at all and an additional 35% only just wet their hands without using soap. that is nearly half of all men. that means statistically you have probably shaken hands with or been in direct contact with one of these people.

love when men say that women "only want money" when it turns out that even in equal-earning homes, women are actually adding caregiver burdens and housework from previous years, whereas men have been expanding leisure time and hobbies. in equal-earning households, men spend an average of 3.5 hours extra in leisure time per week, which is 182 hours per year - a little over a week of paid vacation time that the other partner does not receive. kinda sounds like he wants her money.

love that men have decided women are frail and weak and annoying when we scream in surprise but it turns out it's actually women who are more reliable in an emergency because men need to be convinced to actually take action and respond to the threat. like, actually, for-real: men experience such a strong sense of pride about their pre-supposed abilities that it gets them and their families killed. they are so used to dismissing women that it literally kills them.

love it. told my father this and he said there's lies, damned lies, and statistics. a year ago i tried to get him to evacuate the house during a flash flood. he ignored me and got injured. he has told me, laughing, that he never washes his hands. he has said in the last week that women are just happier when we're cooking or cleaning.

maybe i'm overly nostalgic. but it didn't used to feel so fucking bleak. it used to feel like at least a little shameful to consider women to be sheep. it just feels like the earth is round and we are still having conversations about it being flat - except these conversations are about the most obvious forms of patriarchy. like, we know about this stuff. we've known since well before the 50's.

recently andrew tate tried to justify cheating on his partner as being the "male prerogative." i don't know what the prerogative for the rest of us would be. just sitting at home, watching the slow erosion of our humanity.

[cosmetichorror]

Lu au where everyone is the age of their game

Wild is 7

Warriors is 10

Sky is 13

Twilight is 18

Four is 20

Wind is 22

Time is 26

Legend is 33

Hyrule is 37

Warriors and Wild are LITERALLY child soldiers, Sky is in middle school (and is more than happy to travel as it means he has less homework to do…)

Twilight is a fresh adult and doesn’t know what he’s doing with his life

Four is still as short as he is in the comic. Also much to Sky’s dismay Four basically becomes his teacher so he doesn’t fall behind in his studies.

Wind finally can legally drink…. He’s the wine aunt. He’s a nut case. The kids love him. He and Time were babysitting Warriors during the WAR and they’re both still mad they put a like, 9 year old into a war.

Time is freshly married…. He’s as bad (if not worse) then Sky ever could be when it comes to being lovey dovey.

Legend is mad he has to go on another adventure after he’s been comfortably retired for a decade. He becomes the new old man, despite Rulie being older…. And btw Hyrule is still his little brother.

Hyrule is aging wonderfully much to everyone’s surprise. He looks 25. He still can’t read btw but he has mastered life in the wilderness. He is like a mountain lion, he can hide behind anything and sneak anywhere now. Give him a leaf and he’ll find a way to hide behind it and you’ll never see him….

They would’ve never found Hyrule if they didn’t have Warriors and Wild with them, and even then them finding Hyrule was more so Hyrule allowing them to find him so he could check on the kids.

[cloudycloudsminusclouds]

i'd like to think that when mumbo died jimmy's ear wing-feathers became loose.. he gets to keep his back wings because wings are cool but if jimmy continues to manage to not die at some point the wings on his ears might vanish entirely

[kurohe]

tangotek the man you are

[witchofthemidlands]

Me watching Midnight for the first time aged 8:

Me watching Wild Blue Yonder for the first time aged 24:

[portraitofalinkonfyre]

Oh my God I'm such a twilight girlie you write him so good!!! Like I'm a blushing mess here giggling kicking feet the whole nine yards. Also making him thic is such a accurate power move 🤭🤤 one of these days I'd love to hear all your thoughts on the different 🍆 sizes for the links I just know it'd be glorious until then I shall devour all your writing repeatedly while imagining hot blondes (your four rut one is my absolute favorite I must confess)

Anon you flatter me!!

Hyrule: 4.9 inches. Now, before you come at me in the comments for making our fairy prince smaller than Four, hear me out: like I've said before, and continue to say, penis size is heavily affected by both genes and external factors, and even a slight discrepancy in either one can had mixed outcomes. 'But Fyre, we came here for sin, not a biology lesson!!', some of you may gripe, but I promise there's method to this madness. Ever since starting his first adventure at the ripe age of 9 or 10, Hyrule has been on constant alert because of 1) the literal cult trying to steal his blood to reincarnate a giant pig man and 2) the fact that his world is quite literally a wasteland with minimal food/tainted water/and all sorts of other nasty things. I can't even imagine the stress he was under during those frankly crucial developmental years, so it's highly likely that his body just... didn't fully develop due to a combination of him not getting enough to eat/drink and being on the run for most of his life (i.e lots of stress + probably a horrific sleep schedule). Moreover, both of these factors are what's known as endocrine disruptors, which can heavily affect mental and physical growth.

But now onto the dick-cannons: while he may not be the largest or thickest, I like to think Hyrule has a pretty good handle on what he's doing regardless*. Definitely not circumcised, considering his background (someone please tell him how to wash).

*(I once saw a headcannon that Hyrule probably used sex as a form of payment when things got tough, which I think is very underrated and absolutely true.)

Four: 5.5 inches. So I DEFINITELY did too much research on Four's, but I think y'all need to hear this. While I love the headcannon about Four's dick being 4 inches because his name is quite literally 'Four', I'm not sure anyone has tried to tackle this conundrum with his heritage in mind. Typically, penis size is influenced by parental genes, the person's own unique genes, and a combination of other external factors. For Four, we know for certain that he has Hylian parents, BUT he's also part Minish because of the events of Minish Cap. The Minish are typically described as anthropomorphic mouse people, so we can comfortably use mice as the basis for this genetic addition. Now, mice typically have a penis size of 10% of their body length (tip of nose to base of tail), which would concurrently put Four at 0.458333333 in feet, or 5.5 inches.

Dick-canons: probably circumcised. He's got the vibe of being pretty unassuming, but then he whips it out and everything suddenly makes sense. Balls* are on the bigger side (BREED), but no one's complaining.

*(Have you seen mice balls?? They're fucking [tee hee] massive. View at your own risk, but I couldn't have stopped the idea of Four like this if I tried. Yes yes I know this is a rat, but close enough!)

Wild: 5.6 inches. This one was probably the most difficult, because Wild's just... an average guy*. He doesn't have any non-Hylian transformations or crazy evolution history under his belt (tee tee), so all that really leaves is his height–which isn't a truly reliable measure of penile length, BUT we take what we can get in this blog–and background. It's somewhat implied that his father was a knight/someone who worked for the kingdom, which means he and Warriors were likely raised in very similar situations, though Wild's likely was a bit more stressful. For one, he pulled the Master Sword from its pedestal at the ripe old age of 12, and was immediately shipped off to guard Princess Zelda while she attempted to awaken her powers. While not as extreme as Hyrule's backstory, this is still a great deal of pressure for a child who arguably had a very peaceful life before finding the Master Sword, but I don't think he suffered any developmental conditions; even with the stress of finding out you're the Hero of Hyrule before you even finish puberty, it's reasonable to assume that Wild was physically cared for by the royal family, if only for the fact that his destiny was to defeat Ganon. Not just that, but there's the whole other issue of being stuck in a shrine for 100 years after dying; I'm no doctor, but that doesn't sound like favorable conditions for anyone. Obviously, the shrine heals him, but is that all it does? It's a well-known fact that water isn't good for skin**, especially considering he laid in it without moving for a century, so it's hard to imagine how his dick looked after the bath to end all baths.

Dick-canons: it glows– assuming he actually does have a penis, it's fairly average looking. Probably circumcised for military/cleanliness reasons, but he does have a very lovely vein running up the side of the shaft that always looks like it's about to pulse out of his dick. He should probably get that check out. Average sized balls, maybe a bit on the small side due to 100 years of cold water exposure.

*(I'm just going to come out and say this: all the Links are, at their core, average guys. Twilight was a goat herder. Time may or may not have been birthed by a tree and raised by tree people. Hyrule is just a simple traveler. Wind wasn't even chosen, he just wanted to save his sister. That's why they're so likable... they're not born special, or heroic, or anything. They're just dudes. Regular, selfless, boring, amazing dudes. Anyways enjoy the rest of my insanity.)

**(Is it wrinkly? Dried up? Completely and totally detached?? Laying in water for even a few days can cause severe medical complications, such as open sores, loss of skin elasticity, bacterial and fungal infections, and tissue decomposition. Cold water can temporarily slow the effects of decomposition because of adipocere formation, which is a phenomenon in which a waxy substance forms over the skin as a byproduct of fat decomposition, but not for 100 years. By this logic, Wild shouldn't be on this list because he shouldn't have a dick.)

Legend: 6 inches. Y'all already know where this is going. Unlike his successor, Legend didn't begin his first adventure until the age of 12, and lived a fairly stable life before hand thanks to his Uncle. This means that there likely wouldn't be too many developmental factors to worry about in determining the dick-cannons, so now we must turn to his rabbit-ifying encounter from his first adventure. I'm going to use the eastern cottontail rabbit (Sylvilagus floridanus) for this example because they're one of the most widely studied/available rabbit species. Now, cottontails typically reach 14-19 inches in length, but I'm going to go with 20 inches for Legend because he is CHONK, and also 20 is a lot easier to do math with. Keeping this in mind, WikiVet has informed me that rabbit penises can range from 20 to 45 mm in length. I'm going with 45 mm (4.5 inches) because he's a big boy and I also want him to have a big dick, so, when paired with the 20 inch body length, you'll find that approximately 8.86% of a rabbit's length is dick. Now that we know dick-to-body ratio, all that needs to be done is put that against Legend's height of 5'6", which leaves us with 5.8476 inches, but I added an extra 2 in to account for the fact that he is also hylian. It just feels right.

Dick-canons: Definitely a good choice if you're not sure what you want; bunny boy has many talents. Definitely has some breeder balls*, and I firmly believe he's curved just right for maximum pleasure. Probably circumcised because of his uncle, but he's secretly glad because it means he doesn't have to clean it like he would if he wasn't.

*(Yup, we're doing this again. Scientifically, rabbits have some of the highest sex drives of any animal, and are capable of breeding six hours after giving birth [WTF], which means this absolutely applies to Legend. He is never not down for a fuck.)

Sky: 6.3 inches. Prepare yourself because this one is very speculative. So, Sky was born on Skyloft, a set of islands in the sky. He was trained as a knight for most of his life and had a generally very peaceful life, so no endocrine disruptors or developmental discrepancies to worry about. Moreover, we know he started his journey at seventeen, which means he's at the tail-end of development. Now, instead of turning to some type of animal encounter, I'll turn to his Hylian heritage to answer this conundrum. I doubt there's anything out there with Skyloft's exact elevation, but it does appear to be a decent few thousand feet above the cloud barrier, which I've discovered are most likely altocumulus clouds, which typically form at an elevation between 6,000 to 20,000 feet. To calculate this, I watched a Skyward Sword gameplay video and determined that, in-game, it takes approximately 1:02.87 to reach the surface, and, assuming Sky/Link, is going at terminal velocity (the fastest an object can go while in motion, which happens to be 120 mph for belly-to-earth skydiving), this would put Skyloft at a roughly 7,544.4 foot elevation, which aligns with the altocumulus cloud prediction. There are only so many places on Earth that match such a high elevation, but I'm going to choose the Himalayas (which are inhabited by the Tibetan people, which are already known to have more capillaries and a more specialized hemoglobin function due to living in higher altitudes) as our comparer-region. Using this information, we can safely assume that Skyloftians, though fictional, who evolved in a very similar environment, may exhibit some similar traits to the modern-day Tibetan people.

While researching, I also discovered an incredibly interesting phenomenon called "airplane boners", which is a scientific occurrence where changes in pressure can cause erections (i.e. flying on a place), and decided that this would be perfect fuel for my scholarly degeneracy, which leads me to my next point: Sky has a big dick as an evolutionary response to what is colloquially known as the 'airplane boner'. Not convinced? Let me explain. When a penis is erect, arteries in the pelvic/penile region dilate to allow for greater blood flow, which thus increases the size of the penis itself. Now, imagine being at a high elevation for your whole life, surrounded by people whose ancestors have never lived anywhere else. I firmly believe that Skyloftians are well-endowed as an evolutionary response that allows the sustainment of larger blood vessels as a sort-of defense against high air pressure. Natural selection favors these traits because they ultimately lead to reproduction, which is the single-most important characteristic of evolution. 6.3 inches was a bit of an educated guess, but I believe that because the people of Skyloft evolved in a closed high-altitude ecosystem, it's entirely reasonable for Sky to be THICC because his body has a adapted to handle a greater hemoglobin factor and increased vascular capacity, likely in the penile region.

Dick-canons: due to the blood-vessel evolution, Sky's dick is likely thicker than average, with some very visible veins running up the sides; so many that it likely makes his dick appear incredibly flushed when erect. Contrary to what some of you may think, I don't think he has large balls, because it is likely more advantageous to have a smaller scrotum to combat the elements/conserve heat. So no breeder balls for him, but that doesn't mean he can't breed you just as good ;)

Twilight: 6.8 inches. I feel like this goes without saying, but he's a country boy. He's hung. Twilight grew up in Ordon, a close-knit community where everyone takes care of everyone, which means he most definitely had a very good childhood. Like some of the others, I see no reason to bring up developmental challenges due to being chased by a cult or some similar bullshit, so we're going to skip right to his transformation of a wolf at the beginning of his journey. Contrary to Legend and Four, I do not believe that this transformation affected him significantly in terms of penis appearance/size. Twilight was 17 when his adventure began, which means he already is at the end of physical development from a biological standpoint, and, in Linked Universe, his tattoos appear to be the only true physical mark on his hylian body, so it's safe to assume that we don't need to take this into consideration. Now, some of you may say: "Fyre, but your theories were so crazy for the other ones and now you're saying Twilight's hung because he's country??" Yes. Yes, I am saying that.

BUT.

There's a pretty solid theory running around that Twilight is a very small part Gerudo, due to Talon (Malon's father) having married/banged a Gerudo woman in secret. In LOZ, it's fairly obvious that the Gerudo are supposed to emulate modern-day Middle Eastern culture, which a study by the National Institute of Health states have an average penis length of 14.34, or 5.6 inches. Obviously, this is nowhere near 6.8, but this is also a race of mythical female warriors, so everything's a little skewed. However, in every iteration we see of the Gerudo, they're always tall, somewhat aggressive, and visibly muscled, which are all indicators of above-average levels of testosterone. This is highly important because, in addition to being required to build muscle mass, testosterone is heavily responsible for penis growth during puberty, meaning that Twilight could very well be the way he is because of this naturally-increased testosterone production (i.e why he's so visibly muscled compared to the other Links), plus an assumed more efficient vascular system due to his heritage. Adding on to this, Twilight likely already has booming levels of testosterone due to his very physical, very labor-intensive occupation as a rancher, plus the fact that he's in the prime of his life. In short, he's doing everything right: he eats well, works out, and has fairly decent emotional and mental health, all of which can be correlated with optimal penile development.

Dick-canons: Breeder balls to the MAX. All that extra testosterone has got to go somewhere, and it ain't his head. Fairly girthy, so prep is a necessity. Has one big vein right under the head that honest-to-god throbs when he's turned-on. Probably not circumcised because Ordon is fairly closed-off and I can't see them as being sticklers for that.

Warriors: 7 inches. While height isn't directly correlated with dick size, it is reasonable to assume that Warriors would be a bit higher on the list because of this, as well as his overall health in comparison to Hyrule and/or Legend. It's hinted that Warriors was raised in a very military-esque lifestyle, so it's not a surprise that he wouldn't have any true developmental setbacks in terns of penile length. Now, that doesn't mean we can't analyze the reasons why he's like this. Being raised in a militant environment means he was fed appropriately, participated in training regularly, and was likely taught stress-regulation habits (does he use them? no, but at least he knew them during his developmental years). Like Twilight, increased muscle mass is typically linked to elevated testosterone levels, and since Warriors has been training his whole life, it's reasonable to assume that these factors had a positive impact on his penile development. He and Twilight are very similar in this regard, except Twilight's size comes a bit more from favorable, wack genetics, though they both make sure to take care of themselves. However, Warriors is shown to be somewhat vain in Linked Universe canon (to the point that the other heroes have a running joke on it), which means it shouldn't be put past him to try more... under-the-table methods to ensue his 'perfection' reaches all aspects of his body, dick absolutely included. I'll leave it up to y'all on whether it's actual herbal/medical enhancements or sheer force of arrogance, but it's still a fun thought!

Dick-canons: Definitely circumcised (if not, definitely obsessed over keeping that shit squeaky clean). He's not as girthy as Twilight or Sky, but it'll definitely feel like he is from the way he wields it* during the deed. Doesn't have the biggest balls, but they'll definitely smack against any ass he can get his hands on.

*(There's a lot of speculation on whether Warriors is a manwhore or not, but I believe he's got experience. Definitely not in relationships, but one-night stands? Tavern hook-ups? He's done more of those than he's [un]willing to admit, but when it's someone he honestly, truly cares about? Slap a blush on him and call him a virgin, because he sure acts like it!)

Time: 7.3 inches. I saved the best for last. I want to preface this by saying that Time is HUGE, so obvious he's got to have a bitchbreaker in those britches, right? Right? Not exactly, because the version of Time we see in Linked Universe is the 'second' version; the one who got sent back in time by Zelda for Majora's Mask. This is HUGELY relevant because, honestly? Time likely took terrible care of himself over the course of Ocarina of Time, or at least somewhat neglected his needs in favor of completing his quest. Then, when he was sent back to being 12 years old in a new timeline by Zelda (Majora's Mask), you cannot convince me that he didn't have a major epiphany on how to actually take care of himself now that he was literally given another chance to get it right. He still trains, hard, but also knows his limits and, for the first time in his new life, he actually makes a point to start eating vegetables and drinking milk*, which give him all the essential nutrients to bridge the gap between surviving and living, especially during these crucial developmental years. Time genuinely makes an attempt to try. For himself, this time. And it pays off in the form of that fat-ass cock ;)

Dick-canons: a true bitchbreaker that will rail you six ways to Sunday. Not circumcised (bro was basically birthed by a tree), and definitely has breeder balls; he basically acts like he's in rut, and Twilight's got to get that trait from somewhere. Probably pretty veiny, like his hands (HNNNN), with just the slightest curve that'll have him hitting all the right spots.

*(Lon Lon milk all the way, my good readers.)

And, of course, I had to consult google:

[baguetteseagull]

Lucky Luke is known to be shooting faster than his shadow. But how fast is that?

First of all, since light travels at a certain speed, actually everyone and everything is faster than his own shadow or more specifically the movement of your shadow starts with a very very short delay to you. But in this picture you can see, lucky luke shot his shadow before the shadow even startet its movement. So how fast does he have to be, for this picture to be correct?

Light travelles at 299,702,547 meters per second in air and he is standing about 3 meters away from the fence (actually more like 2,5m but we give him some more time)

So this means:

3m ÷ 299,702,547m/s = ca. 0.00000001 sec. Or 10 nanoseconds.

LUCKY LUKE NEEDS LESS THAN 10 NANOSECONDS TO SHOOT

The record holder in fast draw right now is Ernie Hill with 0,208 seconds.

Lucky Luke is 20,800,000 times faster than the fastest draw.

Thats the stuff i think about when I'm in the shower...

[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.

[catgrandpa]

I'm listening to ABBA again and that never means anything good for anyone

Imagine the Batfam all doing their own Bat Things in the cave, just existing in the same space. The kids convinced Bruce to play music over the speakers, he agreed only because he's doing work on the bat computer and therefore has ultimate control over the music.

Chiquitita comes on and Bruce swiftly moves his hand to change the song.

Dick: Ah, actually B, could we keep this song on? ABBA always makes me feel closer to my mom, and this in particular was one of her favorite songs.

Jason: Weird Dickie, ABBA was my mom's favorite band too.

Bruce: Hn. They were my mothers favorite too, that's why I was changing it.

Jason: Of course, Old Man, cant expect you to let yourself feel an emotion, after all, can you?

Tim: Not to interrupt your regularly scheduled make-fun-of-Batman enrichment time Jay, but ABBA was my mom's favorite too. She would play Money, Money, Money every time she got ready for any big business deal.

Duke: Okay, that's really weird? My parents danced to I Do, I Do, I Do, I Do, I Do at their wedding. 5 of our moms having the same favorite band is a wild ass coincidence.

Steph: 6 actually.... *narrows her eyes and looks around the room* Well, at least we don't have to worry about The Daughter of the Demon liking ABBA.

Damian: And to no one's surprise, Brown is confidently wrong once again. *dodges a thrown book* Mother never found ABBA as frivolous as other western music, for whatever reason.

Cass: I don't believe Lady Shiva has ever listened to music before so I think I'm out of this one.

Tim: Ahh, sorry Cass but Shiva did actually play music during our training at times, and ABBA was on heavy rotation.

Cass: :(

Bruce: Hnnnn

*music cuts out*

Barbara, over the speakers: Before any of you pull out some ridiculous conspiracy theory revolving around 80's Swedish Pop sensation ABBA, let me remind you that they are literally peak Mom Music. Moms love ABBA, it's not weird. It's hardly even a coincidence. I would be more surprised if your mothers DIDN'T listen to ABBA when you were growing up.

(Bruce is still compiling a file of possible ways ABBA could be used for evil.)

[3-aem]

deeply perplexed by the idea that you can draw a 1x1 square but if you draw a diagonal line between two points you’re telling me that that value is irrational and infinite even though you literally just drew the line But Also theres no specified unit for this square so is the square root of 2cm vs 2 inch vs 2 cosmic measurements hypothetically sometimes rational

[bettsfic]

okay so i saw The Bikeriders today and i knew i wouldn't be normal about this movie and even though my expectations were impossibly high it exceeded them. i was happy for it to just be a cool movie for the sake of being a cool movie, toxic masculinity ultraviolence whatever, and it was but with Jodie Comer's character narrating about what fucking idiots all these macho biker dudes are. it's like if a woman narrated Fight Club while constantly pointing out how stupid Fight Club is

also, most of it was filmed near where i live and it was so exciting seeing places i recognized! it's been all over the news for weeks

things i loved about it:

protective older woman/loose cannon younger man

lowkey romantic stalking

a relationship suspiciously close to a throuple, by which i mean protective older woman goes to war against possessive older man, re: their mutual intense love for loose cannon younger man. and that's not even subtext that's just text

hot sadboy who doesn’t talk much and is so cool he doesn’t know how cool he is

british people doing midwestern accents

NO PLOT, god bless. just stuff happening and a lot of gay tension building

accurate portrayals of the aftermath of the vietnam war

accurate portrayals of mid-century small-town life

accurate portrayals of men being fucking pathetic

things i did not love about it:

for the love of god please wear a helmet

idk man it's just a whole-ass movie about how vietnam changed the very definition of masculinity, and that awkward era between wwii and vietnam when guys were rebellious for the aesthetic, rebel without a cause shit, twinks in leather jackets manhood. the movie even points that out, like they're so against rules but then they make all these rules for their silly little biker gang because they're bored. and then allll these vets come home from a war nobody wanted and they're actually rebelling, full anti-establishment, and there's just no more honor anymore because everybody's broken. which is all to say, somebody please come into my ask and be insane about this movie with me.

anyway i'm seeing it again tomorrow and i have already started an ot3 fic goodbye

[bleue-flora]

[reblogged post]

@sketchehm now that is an interesting thought…

So let’s see, if a Minecraft day is 20 minutes long and the dsmp was 933 days long then converting that to see how many Minecraft days that’d be [(933(days)x24(hours)x60(mins))/20(min)] we get 67,176 days or about 184 years. Meaning if we determined time by the Minecraft day and night cycle, the dsmp happened across a span of 184 years… lol yea that doesn’t quite work huh…

For funzies though let’s look at some other events:

L’manberg (101 days) & Techno’s imprisonment (100 days) -> around 7,200 days or almost 20 years.

Quackity visited for 83 days -> 5,976 days or over 16 years (no wonder he’s tired and bored of it lol :] )

Finally, Dream’s imprisonment (314 days) -> 22,708 days or a little over 62 years……… yikes