#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:

[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.

[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

[biancadoes1]

Let’s forget about everything Nic and Luke have said and shown (crumbs and allowed tags on Nic’s ig) and what they haven’t said and shown (we are just friends and here are our so’s). What are we left with now? Pap photos.

Put yourself in their position. You’re having your picture taken and posted without consent. Its a moment in time and it for sure isn’t painting a full picture of what’s going on. If you feel sneaky, invasive snaps of people you’re supposed to be a fan of, posted by people that don’t give a $#!+ about them outside of how many clicks their sites can get, you may need to step away from the fandom/ off the boat/ whatever.

If that makes you realize that you’re stressing out over hateful, invasive sites and people go back and start thinking about everting we have been given intentionally.

Those people that believe AR was ever an option / continues to be an option, I feel bad for you. Dont bother turning around to get back on the boat. I believe JD is an option 10x more. 10x0 is still 0 but I digress.

[almond-tofu-chan]

Okay so I have realized that every video game that has a big LGBTQ+ fan base falls into one of 3 categories and I have spent years of gay science calculating and doing math until I perfected the formula and I can now present to you:

The Gay Game Diagram™️

FINAL VERSION

[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

[chasemakesart1]

Total Watch Time of the Life Series

I recorded the total watch time for all POV's for each Life Series Season, then the Life Series as a whole to find out how long it truly is.

Third Life💚💛❤️ is about 3,616.53 minutes or 2 days, 12 hours, 16 minutes, and 32 seconds with each episode being about 36 min and 9 seconds long and having a total of 100 episodes.

Last Life❤️‍🩹 is about 4,634.98 minutes, or 3 days, 5 hours, 14 minutes, and 59 seconds with each episode being about 36 minutes and 47 seconds long and having a total of 126 episodes.

Double Life💕 is about 2,889.22 minutes, or 2 days, 9 minutes, and 49 seconds with each episode being about 36 minutes and 66 seconds long and having a total of 80 episodes.

Limited Life⏳ is about 3,446.57 minutes, or 2 days, 9 hours, 26 minutes, and 34 seconds with each episode being about 34 minutes and 7 seconds long and having a total of 101 episodes.

Secret Life📜 is about 6,004.83 minutes, or 4 days, 4 hours, 4 minutes, and 50 seconds with each episode being about 41 minutes and 42 seconds long and having 144 episodes. (Etho combined sessions 8 and 9, but Jimmy had an episode after his death so it balances out)

Wild Life🎲 (as the time I am writing this they are on session 7) is about 5,471.55 minutes, or 3 days, 19 hours, 11 minutes, and 33 seconds with each episode being about 43 minutes and 46 seconds long and having a total of 125 episodes.

Real Life🫀(If your including it) is about 399.87 minutes, or 6 hours, 39 minutes, and 52 seconds with each episode being about 30 minutes and 45 seconds long and having a total of 13 episodes.

As of writing this, the total run time of the Life Series (excluding Real Life) is about 26,063.68 minutes, or 18 days, 2 hours, 23 minutes, and 41 seconds over the course of 676 episodes. If you are including Real Life, the total run time is about 26,463.55 minutes, or 18 days, 9 hours, 3 minutes, and 33 seconds over the course of 689 episodes. That is over two and a half weeks of non-stop watching, not including adds, loading, bathroom breaks, etc. For reference, the total watch time of One Piece is around 26,208 minutes, or 18 days, 4 hours, and 48 minutes long. The Life Series is the new One Piece. Thanks for coming to my Ted Talk.

[anghraine]

Nothing like attempting basic division to sharpen my hatred of "everyone is mentally disabled in their own way :) don't let labels define you :) :)" anti psych posts