#solving absolute value equations

[math-journal2]

<— Unit 2: Part 2 — Unit 3 —>

Absolute Values

Page 4

[heybobbygirl]

one time after working on algebra homework for an OBSCENELY long time i was thinking about scenarios with my ocs to help me fall asleep and as i drifted off i genuinely thought “wait…. i need to mmake a negative versio.n…”

[heliosunny]

you have written for both hsr and genshin. any plans for zzz? (also anything for yan!alhaitham pls...... NO PRESSURE BTW!!!!)

I played zzz during the time they release Harumasa and stopped after that. My poor phone couldn't handle Genshin either so I stopped at the beginning of Natlan. My poor laptop is holding on for its dear life since I abuse it w Hsr :)))) Maybe I'll watch people play for the story and characters. I don't want to ruin any character and write things without basic knowledge.

Also, here's a short fic for Alhaitham.

Yandere!Alhaitham x Reader

The first letter arrives on a Monday.

You nearly miss it, slipping your textbooks into your bag as the final bell rings. A crisp white envelope sits neatly atop your desk, unmarked except for your name written in precise, elegant handwriting. The paper is thick, too formal for a casual note from a classmate.

Curiosity wins over caution. You unfold the letter, eyes skimming the words written in deep black ink.

You always prefer sitting by the window, even though the sunlight strains your eyes after a while. I wonder—do you realize how often you rub them when you think no one is looking?

You walked to class today with precisely seven minutes to spare, just like always. Routine is something you value, isn't it? It makes you predictable.

You are an anomaly among the ordinary, an equation I find myself drawn to solve. It is only natural for me to observe.

No signature. No indication of who wrote it. But the words feel… meticulous. Too structured to be a prank. Too detailed to be random.

You glance around the now-empty classroom, your pulse picking up speed.

Someone has been watching you.

You clutch the letter tighter, fingers pressing into the fine paper as a chill creeps up your spine. Who would write something like this? And more importantly—how long have they been watching you?

Shoving the letter into your bag, you push your way out of the classroom and down the hall, searching for something, or rather-someone grounding.

Your friends are waiting at your usual spot near the lockers, chatting about the latest test results. Their presence should be comforting, but the words in your bag linger like a shadow at the back of your mind.

“Hey, you okay?” One of them nudges your shoulder, pulling you out of your thoughts.

“Yeah,” you lied “Just tired.”

You’re about to forget it—convince yourself it was a one-time thing, a strange prank—when your eyes flicker across the hallway.

There, leaning against the far wall, flipping through a book like he’s indifferent to the world, is Alhaitham.

The school’s resident genius. Top of every class. Speaks as if the rest of you are equations to be solved rather than people.

You and your friends don’t interact with him much. He’s polite, but distant—aloof in a way that keeps most people at bay. It’s not that anyone dislikes him, but there’s something too precise about him, like he only engages when absolutely necessary.

Yet now… you can’t shake the feeling that his presence is off.

Because for someone so absorbed in his book, his gaze lifts at the exact moment you look at him.

And he holds your stare.

It lasts only a second before he turns the page, unreadable as ever.

You shake off the strange feeling and went home right after.

The second letter appears on Wednesday, slipped neatly into your locker between your notebooks.

You hesitated today before stepping into the classroom. As if something was weighing on your mind. I wonder, was it the letter? You can lie to your friends, but not to me.

After all, I know you better than you think.

This isn’t a joke.

The handwriting is the same, as if each word was chosen with purpose. The unsettling detail is there too, the kind that makes your skin prickle.

You glance around, paranoia creeping in. The hallway is full of students, everyone wrapped up in their own conversations, laughter echoing off the walls.

No one looks suspicious. No one is watching.

Still, you don’t mention it to your friends. Not yet. You tell yourself it’ll stop if you ignore it.

The Third Letter - Friday. This time, it’s waiting in your backpack when you reach for your notes.

You’ve stopped looking around as much. You’re trying to pretend this doesn’t bother you. Smart. But pointless. You will notice me soon.

Your hands are clammy as you shove it deep into your bag, heart hammering.

This is escalating.

Someone has been close enough to touch your things. Close enough to slip a letter into your backpack without you noticing.

You force yourself to act normal. Laugh at your friends’ jokes. Keep your routine. But the unease lingers, curling in your stomach.

---

It happens late on a Tuesday afternoon.

You’ve stayed behind to finish some work in the library, your friends already gone for the day. The school is quieter now, the usual buzz of voices replaced with the rustle of pages and the faint hum of the air conditioning.

You reach for a book from the shelf and—

Something slips out.

A letter.

Your breath catches as it flutters to the ground, face-up.

You recognize the handwriting immediately.

Your fingers shake as you pick it up. But before you can even read it, a shadow falls over you.

“I wouldn’t take that if I were you” a calm voice says.

Slowly, you turn.

Alhaitham stands there, hands in his pockets, unreadable as always. But this time, there’s something else in his gaze—something sharper.

It takes a second too long for you to find your voice. “...What?”

His eyes flicker to the letter in your grip. His expression remains impassive, but the air around him feels off.

“I was going to retrieve that later” he says simply, as if discussing the weather. “But I suppose this works too.”

No.

No way.

But the letter in your hands says otherwise. The handwriting. The way it just happened to be inside a book you grabbed.

It’s been him.

This entire time.

Alhaitham watches you carefully, as if calculating your next move.

“Well,” he murmurs, tilting his head. “Now what will you do?”

[glitter-gel-pen-era]

Can this HxH character do math?

Gon

Absolutely not. Do not make me laugh.

Killua

Can but won't (he's 13)

Leorio

Can do math but nobody believes he can do math. As if he's not literally a doctor

Kurapika

yeah but maybe not as well as you would assume from just looking at him. most of his brain power is being dedicated to revenge atm

Ging

I mean realistically he probably can?? but also he left Whale Island at age 12 to become a professional adventurer so it's entirely plausible that he never bothered to learn

Hisoka

I believe that he can do math simply because he doesn't seem like he can do math. He's more "party tricks and shock value" than "genuine human person" and i think that seeing him solving equations for fun would send someone into cardiac arrest instantly

Illumi

He could do math, but it's not super relevant to his everyday life so he usually doesn't bother. literally just get a calculator it's not that serious. there are way more useful skills to have. like invulnerability to every poison.

Chrollo

Can do math in practice but not in theory. Like he could probably do some pretty sophisticated calculations in his head mid-battle to figure out the trajectory of his opponent's attack based on the initial velocity and the angle the projectile was fired at (of course taking weather and other external conditions into account), but wouldn't be able to complete a timed multiplication worksheet for children

[inspired-lesson-plans]

Math, grade 7, Ratios and Proportional Relationships 7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Essential Question: How can basic calculations of percent change influence major world events?

Do Now: Calculate the percent increase or decrease in each of the following equations. x = (28 - 17.9)/28 x = (41.5 - 57.7)/57.7

Class Discussion: Remind students about how to perform basic calculations of increase/decrease factors. Ask them whether this calculation would be more complicated if the quantities were dollars instead of just numbers (answer: no). Ask them whether this calculation would be more complicated if the quantities were billions of dollars instead of just dollars (answer: no). Show students that they just performed the exact same calculations that Donald Trump did in order to decide what tariffs should be put upon Indonesia and Thailand, respectively.

Finally, ask students whether important global trade decisions should be calculated with 7th grade math skills, or if perhaps this is insufficient given the severe consequences that could arise from such a dunning-kruger error.

Direct Instruction: Explain what a Dunning-Kruger error is, if for no other reason than to communicate how absolutely maddening has it is for legitimate experts who have dedicated their lives to nudging fiscal policy in the right direction and then watch as their president makes the worst decision possible on purpose.

Take a moment to explain the difference between an import and an export, so that students understand what these billions of dollars actually mean in the real world. Feel free to call out anyone who has ever questioned whether or not they would ever use this kind of math in the real world. Show them that it's happening right now, and make sure they understand how terrifying that is.

Acknowledge the variables: x: total exports from US to country i m: total imports to US from country i tau (τ): calculated % tariff on all imports to US from country i epsilon (ε): elasticity phi (φ): passthrough

Ask students what they think elasticity and passthrough mean, then show students this passage from ustr.gov:

Parameter Selection To calculate reciprocal tariffs, import and export data from the U.S. Census Bureau for 2024. Parameter values for ε and φ were selected. The price elasticity of import demand, ε, was set at 4. Recent evidence suggests the elasticity is near 2 in the long run (Boehm et al., 2023), but estimates of the elasticity vary. To be conservative, studies that find higher elasticities near 3-4 (e.g., Broda and Weinstein 2006; Simonovska and Waugh 2014; Soderbery 2018) were drawn on. The elasticity of import prices with respect to tariffs, φ, is 0.25. The recent experience with U.S. tariffs on China has demonstrated that tariff passthrough to retail prices was low (Cavallo et al, 2021).

Ask students if this clarified anything about what elasticity and passthrough mean. Most will say "no", but if anyone points out that multiplying 4 by 0.25 cancels them both out, reward them. That student is correct, because elasticity and passthrough have been arbitrarily assigned so as to make this calculation so simple that even Donald Trump can understand it.

Modeled Learning: Show how to apply these tariffs to popular imports such as raw coffee beans. For example, the USDA report of coffee imports from 2024 (page 6) shows that the vast majority of raw coffee is imported from Brazil.

A simple search with Perplexity.ai tells us that in 2024, imports (m) = $42.3 billion and exports (x) = $49.7 billion, so the reciprocal tariff would be (x-m)/m = (49.7-42.3)/42.3 = 17.5%.

Thus, all coffee imports from Brazil will automatically be 17.5% more expensive.

Be sure to highlight that this is happening to every country in the world, even those with total populations less than 1000.

Higher Order Learning:

Students should consider the following facts:

There is very little territory within the United States that can grow coffee.

Almost all coffee in the world is grown within what is called "The Global South", where the climate is warm and the labor is cheap.

The US exports significantly more (sometimes vastly more) to countries in the Global South than we import from them.

Students should then answer the following questions:

What will this universal tariff calculation do to the price of coffee?

Is there any way that US coffee companies can import the same amount of coffee as before without passing on the cost to consumers? Why or why not?

Do you think this tariff program will equalize imports and exports between the US and other countries? What other impacts could it have, good or bad, across the world?

[la-cosmonauta-extraterrestre]

How to learn physics as an adult

I'm creating this post in response to some posts @un-ionizetheradlab made the other day, but I'm creating this as a guide to anyone this is relevant for. It's going to be a long post, but pick and choose what to do from this list based on what works for you and what your goals are, whether it's just to gain basic scientific literacy or become a physicist (or something in between). Also remember that it's a journey not a sprint, so it's ok if you don't understand physics at first (and if it makes you feel better, physics was one of my worst subjects in school and now I have a master's degree in physics). Without further ado:

First Thing's First

There are some mathematical methods you need to learn to understand physics; there's no way around this:

Vectors: This is the most important thing to learn for physics, how to use vectors. It seemed every mathematics or physics class I took in my first year of my physics degree started with an introduction to vectors, and for good reason. You can learn about how vectors work on Khan Academy for free.

Matrices and Tensors: Once you've mastered vectors, learn about matrices and linear algebra, and perhaps go on to learning about tensors once you're at it. You can at least get the basics about matrices from Khan Academy, but you might want to invest in a linear algebra textbook.

Calculus: I said vectors are the most important thing to learn for physics, but it actually might be calculus. If you have absolutely no previous knowledge of calculus, you can watch the video "Calculus at a Fifth Grade Level" on YouTube; it's a little more advanced than fifth grade level but can give you a good feel for what calculus is about. Once you've done that, there are multiple calculus courses available on Khan Academy. There's also a calculus course available on Brilliant, but it might only be available through the paid version.

Ordinary Differential Equations and Boundary Value Problems: You don't need to learn these right away, but if you want to do physics at the upper undergraduate level, you'll need to learn these at some point.

2. Learning to Think Like a Scientist

Some suggestions of apps and things to watch if you don't know much about science so you can start thinking like a scientist:

SciShow: If you don't know much science at all, SciShow on YouTube is a good place to start, I used to watch it and as I recall it's more focused on life sciences but there's some physics videos there, too.

Ciencias De La Ciencia: This is sort of a Spanish version of SciShow but it's more physics-focused. At least some of the videos have subtitles if you don't know Spanish.

Cosmos: If you haven't seen Cosmos (either the old version with Carl Sagan or the new version with Neil DeGrasse Tyson), it's very good and at least some of the episodes are available for free online. It's more pop-science and history of science than actual science content, but at least they make a point of using anecdotes from the history of science to illustrate how the scientific method works.

Sabine Hossenfelder: Highly recommend her YouTube channel; she's one of the most intellectually honest scientific communicators in the world nowadays. Her videos are a good illustration of how to think like a scientist. She also has a blog and has written a few books.

Brilliant: This is an app with mathematics and science courses that places an emphasis on problem-solving. Most of the courses are only available on the paid version of the app (but you should be able to get a discount on it if you're subscribed to any mainstream science YouTubers), but even the free version gives you access to a few courses, plus a forum where people post problems. I had this app back in the day and liked solving problems on the forum (no idea if it's changed since then).

3. Books to Study

If you're committed to learning physics you should study from some textbooks:

Physics LibreTexts: This is a whole collection of university-level physics textbooks for free online. It's an invaluable resource for learning physics. Use it to learn classical mechanics, electricity and magnetism, modern physics (but don't jump into quantum mechanics straight away if you're just starting out in physics).

Landau and Lifshitz Course of Theoretical Physics: This was the physics school curriculum in the Soviet Union; it's a little dated now but if you're just learning the basics it can't be beat given the excellent pedagogy. It's easy enough to find copies of it online, especially on Russian sites. Most if not all of the textbooks in the series have been translated into English, but if you know any Russian, the original is easy to follow.

Introduction to Electrodynamics by David J. Griffiths: Once you've learned mechanics, modern physics and some electricity and magnetism get yourself a copy of this textbook; you can get used editions on Amazon for a reasonable enough price. American physics majors are obsessed with this textbook, refer to it as the Bible, and for good reason.

Every Life is on Fire by Jeremy England: This isn't a textbook, but reading it took me back to my statistical mechanics class and it's way more readable than any actual statmech textbook so if you are interested in learning statmech, this book is a good start. It's actually a general reading book about England's ideas about the origin of life, interspersed with some parallels to the Hebrew Bible because England is also a rabbi. He actually has some interesting ideas about the philosophy of science, though they can be difficult to get behind, so if you're interested go listen to a podcast where they interview him (obligatory I don't condone the Kahaneist politics he sometimes promotes).

4. Learn About Research and Experiments

Physics is an experimental science, so expose yourself to some experiments:

Look for PDFs of high school physics labs online. You can find some for free and it should be cheap enough to do the experiments at home.

Read scientific papers on topics that interest you to try and understand what's happening today. If you find them difficult to understand, try reading older papers and go from there, for example, in undergrad I did a research internship relating to neutron stars, but I found some of the recent scientific papers difficult to understand, but reading the 1938 paper "On Massive Neutron Cores" by Oppenheimer and Volkoff helped me to understand neutron stars better. (When I returned to some of those same papers during my master's degree, I was proud to have understood them well.)

5. Take University-Level Physics Courses

You can take university-level physics courses without committing to a degree:

Search online for MOOCs (Massive Open Online Courses). You can find MOOCs on multiple sites about many physics topics, and they're often free (sometimes you have to pay for them).

If you live in the United States, you can take physics classes at your local community college.

You can enroll in online physics courses through Open University, based in London but you can take the courses from anywhere. It's expensive, but you pay by the credit so you don't have to pay for a whole year of tuition if you're just taking one course.

If you happen to have free time in the summer and the money for it, many American universities (and elite British universities) offer summer courses that one can enroll in even if they don't attend the university. These are usually in-person classes.

6. Get a Physics Degree

Getting a physics degree is ultimately the only course of action if you've decided to become a physicist, the recommended course of action if you're ultimate goal is a PhD in the history of science or philosophy of science, and a good idea if learning physics has made you want a career in science communication of science education. There's no shame in being a non-traditional age student; in both my bachelor's and master's degree in physics I knew students who were non-traditional age. The downside of this is that it's a bad financial decision to get a degree, especially if it's a second bachelor's degree, but there are ways to lessen the financial burden of a degree:

If you attend an American university with American tuition, you can usually get an on-campus job, though that's pocket change compared to the costs of tuition.

On the bright side, if you already have a bachelor's degree you can probably get credit for general requirements at American universities, so a second bachelor's degree in physics might not take long.

You can also do a part-time degree while you work at many universities.

Just some general advice, if you go the American university route go to a university with a Society of Physics Students and get a student membership in American Physical Society; you get all kinds of benefits like access to Physics Today magazine, scholarships, internships, conferences, an honour society induction.

All that said, it's difficult to attend an American university without losing money. For that matter it's difficult to attend any university in the world without losing money, but you can lessen that burden by going to a country where university is cheaper. There the limiting factor is going to be language; although English is the international language of physics and the medium of most postgraduate physics degrees around the world, physics bachelor's degrees are usually in the local language. Some possible exceptions I found to this, for those who are not fluent in a language other than English:

Apparently there are world-class English-medium physics degree programmes in France? I figure there must be some kind of catch given the way the French are about their language, but given the high research output France has in physics, this is worth getting into.

There are English-medium physics bachelor's degrees in the Czech Republic, and tuition there is pretty affordable (for the English-language degrees; it's free for Czech-language degrees if you happen to be fluent in Czech). I don't know Czechia to have a lot of physics research output today, but back in the day Prague was a major centre of scientific research (Einstein briefly lived and worked as a physics professor in Prague), so it you're goal is to do a PhD in the history of science...I'm just gonna say that there's an English-medium physics bachelor's degree programme at Charles University and you'd have time when you're not studying to explore the city and it's history (but you should learn some Czech if you're going to live there).

University degrees in South Africa are usually English-medium, and tuition there is pretty affordable. There's also a fair amount of research output from South African universities. (Though I understand not wanting to live in South Africa.)

[thedeafprophet]

🚂train, 🖍crayon, and 🎭 masks for josie?

🚆 TRAIN - what is their answer to the trolley problem?

Oh gosh, starting off light I see... Well, on a fundamental level, Josephine would say to pull the lever. She is fundmaentally an 'ends justify the means' person. The logical choice is clear: sacrifice one to save the many. It's a simple equation, a way of maximizing the amount of lives saved, which is, of course, the most efficient choice.

But realistically, are things ever really that simple? In a real scenario, the person on the tracks isn’t just a faceless figure. If it were someone she knew... Well, Josephine might claim the opposite, but I have no doubt she’d sacrifice the lives of others to save the ones she cares about, whether she'd admit it or not.

and lets be honest, Josephine would be far more the type to give a pedantic run about of needing to break down the system thats tying people to train tracks in the first place

🖍️ CRAYON - what advice would you give to them?

Take a moment to breath, to feel, to just be. You can't solve everything with just logic and facts, sometimes you have to let the emotions win. Its okay that they're a part of you too. It’s okay to not have all the answers right now.

🎭 MASKS - do they act differently around certain people? what's different between the way they act around friends, family, strangers, etc.?

Oh yes, Josephine absolutely acts differently around certain people. Around strangers, she's pretty much all Professionalism and Straight to the point - calm, collected, distanced. Her tone is sharp, posture precise, and she interacts strictly within the bounds of propriety or whatever goal she’s after. She’s polite, but you won’t get much more than that. You never know what to expect from someone at the beginning. With interesting strangers, though? She may even engage with you like a new research subject. (Something I’m sure the Marigold situation demonstrates rather well-)

Around people she knows and friends though, that's a little trickier. Josephine doesn’t let her guard down easily, but she’s a bit more relaxed. A bit more herself. You’ll catch glimpses of humor, the rare pun she’ll deny was on purpose, and the dry wit and sarcasm she’s far too capable of. You may even earn a first-name basis - imagine that! With close friends, she may even be vulnerable now and then, willing to pull back the curtain and talk about the messier questions. Josephine values respect in her friendships. A mutual understanding.

With her family, Josephine is at her softest. Caring, almost doting in her own strange way, and utterly, fiercely protective. There’s a constant anxiety behind it all, of course - how could there not be? And things are… complicated, especially when it comes to her brother. The past carries a weight all of it own, the future an end thats never known....

and don't even get me started on the aspects of the trio. The past is a tangled thing, and the Josephine of then isn’t quite the same as the Josephine of now, you know?

I'd say every person meets a somewhat different side of her, in their own way. After all, every experiment requires its own unique set of parameters.

Ask game from here

[quantumlogician]

Late-Night love confession — @flightofthestarscream

Late nights was a commonality, dare he say, a staple for Shockwave. He's burned through moonlight more often than he does the sun, always chasing the quiet hours to work diligently on his endless stack projects.

And, more aptly, he had always spent these long hours alone. It had been this way since he was abandoned on Cybertron and it didn't change so much when he returned to the Nemesis, save for the occasional guard that would be stationed outside of his lab after normal patrol hours. Vehicons didn't constitute for much company, as they were often mute or too terrified to speak to one of the few High Command.

That did change, much against Shockwave's best interest, in the shape of a sleek grey-metal Seeker. Given the sort of clumsy nonsense and absolute theatrics driven by his pride, the scientist wanted nothing of him anywhere near his work. He'd have half the mind to toss him into the cage with Predaking and have filth sort itself out — but he wouldn't dare inconvenience his predacon such a way.

Yet, someway, somehow, he found himself beginning to rely on the bot. At times, he'd often wonder where the other had been when he didn't report to his main lab. A servo twitching when the Seeker would be too hasty to contest their leader, wanting to anchor him back from trouble. A searching optic in drawing near him.

It was maddening and Shockwave tried to write it off as a sort of sickness clouding his clarity. But, even he was too smart to fool himself, easy and convenient it would be to pack away these pesky... emotions.

He had to call it for what it was because Primus forbid he say so, he felt his spark misstep from its steady thrum over absolute nonsense. It was nothing important, just Starscream solving a long-form equation for quantum jumping; it was less the success of his solving and more the usual crowding into Shockwave's space with optics expectant of praise. Actually, it was the elation. The bot carried this sort of energy about his work Shockwave seems to have missed since the falling of the Golden Age.

" Starscream, " he called to SIC, nudging into his space this time, with a gentle caress of his knuckle over an onyx shoulder pauldron. He couldn't divine whether the other had fallen into rest or was choosing to ignore him in the usual fashion, but he continued, wanting to rid himself of these words that threaten to claw out of his throat daily, " I do not care if you reciprocate me. I do not care to know your thoughts. If your response is unsavory, keep it to yourself. "

" You've smitten me. It has become a plague on my conscious. I want nothing to do with it, nor you, yet I do. I'm contesting my own nature about how I feel about you when such workplace fraternization is decidedly unprofessional. I want you to stay with me for the rest this war, and should we survive into the peaceful era, for the rest of our lives. My day is never dull with you and I've come to appreciate those underappreciated values about you. I think I could learn to love more, if you'd let me. "

He stops the flow of foul prose, waiting for violent rejection or anything, but waited a second too long to discover he actually didn't want to know at all. He'll pull away, escaping the situation before the mistake haunts him — because as he said, he did not care to know.

[msfbgraves]

From the creators of "Daniel was the real bully all along", aka "Cobra Kai"...

We have Ralphie hinting at a "Daniel second guesses Miyagi-Do, aka Miyagi-Do has always been evil".

Look, Ralphie loves hanging out with Billy for these promos and I love seeing them together because they deserve to have a good time really they do. Yuji, Billy and Ralphie deserve to enjoy themselves because they have brought their absolute A games to the show and it shows and I love them for it.

But ffs, creators. I know you felt so called out by a film about a sweet boy teaching us that bullying is evil and that fighting can be a form of self-expression and helping others rather than a pissing contest in which people get killed you had to make a whole show about why bullies are cool actually, absent fathers are dope and kindness doesn't exist because there is no kindness without an ulterior, sinister motive. Because you haven't been kind a single day in your life and even though some part of your conscience has survived for long enough to understand that there is something wrong with that, making you feel bad, you have spent over six years of your life propping up your ego instead. It had to be somebody else's fault. It had to be Daniel's fault. It has to be Miyagi's fault No way that can't have been secretly evil, and we're going to expose it! Because repeatedly saving someone's life, as Miyagi has done for Daniel, can't not be sus, right? Trying to beat someone to death, now, that is upfront manly behaviour. Saying like it is. All this stealthy defense stuff? There's gotta be something going on there, right? They should have killed Daniel and been on their way in film 1, then the Cobras could have had some sympathising manpain and gotten laid after beating up more people for existing. That is how you live a good life! But no, so now we have to right the wrongs perpetuated by films that tell you that a kind handyman can help you beat up a rich bully while also understanding that this bully was probably a product of his environment he was too young to understand was harmful. Can't have that! That would make them wrong! And they can't be wrong, see? They wrote a story too! So there! Pussies!

My only hope is that Ralph has directed an episode of this first bunch and has always done his best to keep infusing this garbage fire with kindness. I know Daniel can be a little saintly, but his heart, that's all Ralph. And the love between Billy and Ralph is also incredibly sincere. So I know they'll do their best with it, and Ralph acts in between lines anyway. But the underlying message since season three at the lastest has been so terribly unkind. In a show about manhood, apparently, they keep celebrating

-Not taking responsibility

-Solving every problem with violence

-Equating kindness with either weakness or deceit

And that is how recognise that these are boys who are never going to grow up. Taking responsibility, practicing restraint and choosing to be kind because you understand basic empathy is how you become an adult. That is what the karate kid franchise taught! The value of hard work, taking responsibility, protecting others and choosing kindness wherever possible. To have this so called homage literally trying to undermine that message at every turn, is feeling like some kind of moral injury.

I will always be grateful to the series for introducing me to these characters. But I am so sick of middle aged men taking over a beloved series about what it takes for men to be decent, be it Sherlock Holmes, Doctor Who or The Karate Kid, and basically raping it to death in the guise of appreciation.

[lyrichi]

sorry for bothering you but

"given that f(x) = x^2 - 5 and g(x) = 2x + 3, what is f(g(x)?" from this post

x^2 - 5 2x + 3 = (x^2 - 5) (2x + 3)

[ use the FOIL METHOD; First, Outer, Inner, Last. search that up if you want to idk ]

= (x^2 · 2x) + (x^2 · 3) + (5 · 2x) + (5 · 3) = 2x^3 + 3x^2 + 10x + 5 = 5x^5 + 25x [ = 30x^6 ]

what the fuck am I doing with my life,, solving a random math problem on tumblr for no reason from some obey me post

im absolutely sure that my solution and equation is utterly incorrect cuz I think so and im a terrible explainator (what isbthag that ia not a word) (and yes i did calculate this on a piece of scrap paper I found on my side tabel cuz I'm boredmele)

Dawg I'mma be real w you I don't understand how I like activated everybody's (in the om fandom) math tingle like 😭😭

so many reposts and/or comments have been ppl solving it and it's kinda funny ngl

I love you and everyone who wants to help me w math that ik how to do :D

OK BUT ANYWAYS

I learned how to solve it differently actually; so instead of using foil (LOVE FOIL FUCK THE BOX METHOD IT CAN KILL ITSELF) you quite literally plug in g(x) as x for f(x) cause it's like.... yk f(g(x)

So it's literally (2x + 3)^2

All you gotta do is plug in the value of g(x) as the x for f

Yeah :DD

[lemonplanter]

I think there's a certain type of person who claims to want to protect and preserve nature who equates that to "humans should never interact with nature in dramatic ways, ever" and I find that both very fascinating and very frustrating.

Like, there's obviously eternal discussions to be had on methods and intensity for any action that humans take; new information and models should always update our plans for the future. And obviously thoroughness, consistency, and safeguarding need to be focused on, and they often times are not; accountability is also important. This is not about that.

But there's a certain attitude I see that intentonal, large scale impacts should be avoided at all costs, and I find that baffling.

Cause, like.... we're already doing that in ways that DESTROY the environment. And while some of those issues can resolve themselves with us simply stopping our activities, or with low impact solutions (cleaning plastic from the oceans doesn't need to be disruptive, for instance - WHICH IS NEAT, I NEED TO STRESS THAT) there are others that will not fix themselves!!!

CO2 in the atmosphere is one example! If we completely stop all CO2 production, it's still likely that we would continue to see warming, because the effects are a positive feedback loop (higher temps melt more snow near the poles, less snow lowers the albedo of the planet, lower albedo leads to more warming - AGAIN, WITH NO NEW CO2). Or invasive species!! My province has an issue with moose, because they are not native to the island and have few-to-no natural predators, so they're increasing I population, causing both higher road accidents and doing more damage to the ecosystem. But there's usually a lot of backlash to hunting initiatives to reduce their populations, because hunting always bad.

Or mosquitos!!! Mosquitos are one of the biggest ones!!!

There are a load of people who think that the measures we want to take to curb mosquito populations should be thrown out altogether because human intervention bad, but human intervention is what caused the increased population to begin with!! Human industry leads to exponentially more stagnant water than would exist otherwise, which is the place that mosquitos breed. we Are the reason that there are so many, and there being so many is the reason that there are so many issues with pathological transmission, and ecological displacement.

So my question to those people is: are we not responsible for remedying the issues that we have caused to the planet? Do we not have a responsibility to correct the ways that we have ALREADY fucked things up? Because if you don't think that we should take action on invasive species, then what is your rational for taking action on climate change?

Do you think we SHOULD address climate change? If so, why are you not willing to engage with the reality that we will need to do radical things to resolve it?

I don't know, it just feels like the attitude got boiled down to "human bad for planet" which is both overly simplistic, and also completely ineffectual for actually solving a lot of the issues that they claim to care about.

[P.S. To be absolutely, clear, this is not about everyone who says they care about the planet. This is a very specific mindset that I see in a very specific type of person. I find it overlaps most with the vibe of "meat is bad, but I'm eating unsustainable quinoa from a country that exploits its workers" or "fur is murder, but I am polluting the planet with all my plastic clothes that I have to throw out in a year" types. Very much the vibe of people who care more about feeling good about their values than they do about actually following through. And i find that performative aspect extra infuriating]

[briar-k]

would a wood chucker still chuck if there was no wood around would they be a chucker still, but with no wood what do they chuck? I think the answer is when you add 56 subtract 78 and get mango, mang mango mango mango mango, which results in chocolate, which is strange, cause I dont like chocolate, which is crazy cause BEANS, Ya know?

HAPPY HALLOWEEN

I see! This equation has got two answers that I'll represent by x1 and x2

Where x1=brown

And x2=yellow (some would argue it should be orange however I decided to use two decimals as opposed to four when solving this problem)

Now I know the answers could be switched but I haven't made the graph yet so maybe it should actually be x1=yellow and x2=brown. I do want to note neither result should be negative as the wood chucked by the woodchuck is an absolute value yes you do have to substract it but you do not have negative wood. You simply don't have wood!

There are many possible solutions for this problem that all depend on the value assigned to the wood (which should not be negative) and I overly simplified here but I thought it would be for the best!

[carewyncromwell]

"Started out on a one-way train -- Always knew where I was gonna go next -- Didn't know until I saw your face I was missin' out on every moment..."

x~x~x~x

HPHM Cardverse developed by @ariparri // read more about "the Counselor" Duncan Ashe here! // See Jacob as Duncan's Right-Hand Man // credit for the new and improved physics lecture goes to @ag907!! Thank you, sweetie!! 💚

x~x~x~x

It wasn't a surprise to much of anyone when Duncan Ashe became the Jack of Spades. He had become a well-respected member of the previous Jack's court even while still at university, and even throughout his schooling, he was known for being both incredibly driven and ambitious. Even if yes, he also became a bit of a rulebreaker upon befriending Coby McQuaid, his strong work ethic and cleverness were never to be questioned. Combine this with a good sense of dress, and most would agree the young man embodied the part of someone who would easily climb the social ladder.

Duncan Ashe knew where he was going. He was going to be successful, and he was going to do it by beating out all of his competition both academically and in life overall. And that is why he took on the responsibility of working under the Jack of Spades, Ulrich Scheller, while also being a full-time student at the University of Spades. It did result in a lack of sleep, sure, and it did make it so he often had to finish homework in strange locations, such as in the middle of press conferences and against the wall of his dormroom while he got dressed in the morning...but it would all be worth it, in the end. Even if he had to finish up complex physics assignments while sitting on the way-too-full trolley heading out of the capitol, Duncan shrugged it off and just kept going.

Or, at least, he did, when he didn't have random strangers standing next to him on the trolley distracting him.

"Physics, huh? That's fun."

Duncan looked up.

Standing over him was a modestly-sized, rather messily-dressed young man about his age with curly dark hair, carrying a beat-up old leather bag at his side. Unlike Duncan, who was dressed in a well-tailored vest and slacks, this person was dressed for hard labor, with his pants tucked into a pair of scuffed-up black boots and faded oil and grease stains on his long-sleeved linen shirt. Even the muscles outlined under his long sleeves were a good indicator that this person was more of a "blue collar" sort than Duncan was.

"What's this? Fourier transforms?" the young man pointed a grubby finger to Duncan’s homework assignment.

Completely taken aback and lost for words, Duncan nodded yes.

"Oh, that's fun!" the stranger said brightly. His almond-shaped blue eyes were very bright as he examined the homework Duncan had in his lap. "You've gotten your sines and cosines mixed up, though -- I think that's what's holding you up on the second one. See, the integral of cosine is sine, not the other way around. Oh, and the answer is supposed to be negative -- we don't use absolute value here. Personally I've always preferred Laplace transforms over Fourier, but they aren't as applicable in physics. The only reason Laplace transforms really took off at all was because of that one fascist prat in Hearts who studied them a long while back -- forgot his name, I'll have to ask Mum -- but even if he was a creep in his politics, he did bring Laplace transforms into the modern era. Reckon people would've had to develop an entirely different way to solve higher order differential equations without them..."

For a moment, all Duncan could do was blink blankly. Finally, like a rubber band, Duncan's surprise and utter disbelief snapped back into defensiveness. He slapped his arms roughly over his work to cover it.

"All right!" he said, his face flushed a bit despite himself. "You've -- you've certainly made your point..."

Duncan couldn't help but goggle a bit.

"Are you a math major or something?" he asked. His black eyes lingered on the boy's dirty shirt and toned arms. Surely not -- any self-respecting university student would have to dress better than this --

The young man, though, only grinned. "Nah, no university for me. I didn't even finish high school."

Duncan's mouth fell open. "You didn't even finish -- ?"

You have got to be kidding me. Some high school drop-out is standing here giving me a lecture about how to do my physics homework?

"Well, the schools up north aren't the greatest -- after a while, I just kind of got fed up," said Jacob. "Plus it's not like getting straight A's or gold stars is any actual indication of intelligence -- it's really more indicative of how well you can jump through hoops, and well, even dumb animals in a circus can do that..."

Duncan flushed, offended.

"And yet those 'dumb animals' could do it, while you couldn't," he said sharply.

"Guess I just like applying my brain to more useful activities," the young man said with a shrug.

"Like fixing mechanical horses and streetcars, I suppose?" Duncan said very dryly, shooting another condescending look at the oil stains on the man's collar.

"Sure," the young man said brightly, not sounding the least bit offended. "Though that's only Mondays and Wednesdays -- got Pik's on Tuesday and Thursday and the library on Fridays..."

He abruptly looked up through the window with slight surprise.

"...Hey, don't you get off here? This is the university."

Duncan realized with a start that the trolley was driving on, passing the university.

With a bolt of panic, he shot up out of his seat, his papers spilling out over the floor so he could get up and pull the string.

"Stop! Stop the trolley!"

The trolley came to a screeching halt. Grumbling in anxiety under his breath, Duncan quickly stuffed his papers into his briefcase and then hurriedly stumbled off the car and off to class.

It wasn't until Duncan took a catalogue of all of his paperwork at home that night that he realized he was missing one page of the physics assignment he'd been working on. He grumbled sourly to Coby about it and the stupid guy on the trolley that made it so he'd now have to do the work all over again for close to a hour, before finally giving up and turning in for the night. He'd just have to work on it tomorrow.

You can imagine Duncan's surprise, therefore, when the following morning, the trolley driver actually handed Duncan a piece of paper after he paid her for the ride as usual.

"Jacob wanted me to give this to you, if I saw you," she said with a wry smile. "He worked on it for the rest of his trolley ride home yesterday -- he saw the due date was in three days, so he hoped I could get it to you before then."

Duncan stared. The page was covered with equations, all scrawled in exquisite detail despite the messiness of the writing.

The stranger who had to be named "Jacob" had finished not only the problem Duncan had been struggling with, but all of them.

~*~

Duncan didn't collide with Jacob again the rest of that week. His hours at Pik's (which turned out to be a tavern -- Coby had heard of it, even if Duncan hadn't) seemed to start very early in the morning, way before Duncan was even out of bed, and whatever library Jacob was assigned to, it must not have been on the route the trolley took into the capitol. Even on the weekend, Jacob was nowhere to be found -- likely taking some well-earned time off at home, Duncan presumed. And so the university student didn't have any potential chance to follow up with Jacob about him having done his work for him until the following week, after Duncan got the assignment back. And when Duncan did see Jacob again, it wasn't on his afternoon trolley ride south to the university -- it was through the trolley's window.

That Monday, Duncan's entire day had gotten off to a terrible start when the trolley's doors had gotten stuck in a half-open position, making it unable to run. As fate would have it, though, Jacob had been at the following stop, and upon being tipped off to the trolley's problem, he ran several blocks up to go help. Soon he'd rolled up his long sleeves and taken a toolkit out of his worn brown bag and immediately set about taking the door apart to fix it.

Duncan looked through the window, tilting his head to try to get a better look at what Jacob was doing.

The curly-haired young man had completely removed the door from the trolley and was now cleaning the interior, scraping out the gunk on the inside and lubricating the rusted hinges with oil. His muscles -- exposed by his rolled-up sleeves -- bulged slightly as he hoisted the door into place and held it there with one arm while screwing the hinge back on with his free hand. His bicep flexed while holding the heavy door, making veins pulse to life through his pale skin.

He was strong.

Duncan caught himself staring and mentally slapped himself. Good thing too, because the very next moment Jacob looked up and caught Duncan's eye through the window.

Jacob blinked, his blue eyes widening just a bit. Then they lit up and he gave a happy little nod, unable to wave due to his hands being full.

"Hey, Ashe!" he greeted.

Duncan was taken aback. "...You know my name?"

"The driver told me," said Jacob. "At least she said she thought that was your name...she caught a glimpse of your student ID once, and she thought it said 'Ashe.' And she reckoned you kind of looked like the rest of the Ashe family -- not that I'd know, never much been anywhere downtown..."

Duncan's lips came together just a bit. He'd never been very close to his family -- his father in particular -- so the reminder that people could see any physical resemblance wasn't particularly cheery.

"The name's Duncan Ashe," he said briskly. "And you would be Jacob, right?"

"Right! Jacob Cromwell," the curly-haired man responded offhandedly.

Duncan raised his eyebrows. "Cromwell? As in the Diamond Empire jewelers?"

Jacob's eyes flashed with dislike. "They're my mum's family. But we don't talk to those prats."

Duncan felt a pang of empathy, thinking of his own family. Something a bit more serious then flickered through Jacob's expression.

"...Were you able to turn in that assignment on time?" Jacob asked. "I hoped you hadn't gotten through it all a second time, by the time you got it back."

Duncan felt his cheeks actually darken with a light flush.

"Oh, ah...yes, I was," he said. He averted his eyes. "I did have to write it out again myself so it'd be in my handwriting, but...what you did was...helpful."

If by "helpful," he meant getting the highest marks he'd gotten in physics class so far.

Jacob gave something of a weak smile. "...Well, I'm sorry you had to write it again -- I'd finished it so you wouldn't have to..."

"Well, yeah, but it wasn't in my handwriting, so someone would've known it wasn't mine, if I'd turned it in that way," Duncan blustered. "Anyway, it...doesn't really matter, it did save me a lot of time, not having to do the math myself. Though I am still a little confused about how you knew how to do it, when you said you never even finished high school."

"I read books in the mathematics section of the library sometimes, during the slower hours," Jacob said with an offhand shrug.

Duncan blinked in surprise.

"You learned all that just from reading library books?" he asked. The courtier couldn't help but be impressed.

"Sure," said Jacob leisurely. "Once you get the theory down, all it really takes is putting it into practice. I just finished up the last of the books on number theory," he added almost as an afterthought. "About a third done with the history section too. Though the science section is actually my favorite to explore -- I recently checked out a book on the biochemistry of various viruses, and it's fascinating. It astounds me that the court of Spades hasn't pushed for using the principle of reverse genetics to develop new vaccines..."

Jacob finally finished screwing the door back into place and, with a bounce in his step, straightened up.

"Go ahead and give it a try now!" he told the trolley driver.

The driver did, and with a ding, the door closed and then opened again like a charm.

Everyone on the trolley burst into applause as Jacob and the other people waiting to board outside all climbed aboard. Several even gave Jacob hearty slaps to the back.

"Thank you so much," the driver said, his blanched face curled up in a weak, relieved smile. "I don't know how I'll ever thank you -- "

"Sounds to me like you just did," Jacob said with a rather handsome smile.

"I've got to at least pay you for your work -- how about -- ?"

"Don't worry about it," said Jacob flippantly.

Without even seeming to notice the driver's attempt to protest, he slid a few coins into the slot by the door to pay for his ride and strolled into the trolley. He sidled into the open seat next to Duncan, grinning broadly. Duncan cocked his eyebrows at the shorter man.

"You could've at the very least accepted a free ride," the well-dressed student pointed out dryly. "The driver was clearly trying to offer it to you."

Then maybe you could save up for some halfway decent clothes, he couldn't help but add to himself, eying Jacob's outfit. It was the exact same one he'd seen him in before, though with perhaps one or two more grease stains.

Jacob blinked. "Really? Huh..."

He shrugged this off very easily, though.

"Oh, well -- I can pay for it, so I may as well. Wasn't doing it for pay in the first place, after all."

Did this guy seriously just shrug off the fact that he could've saved some money when his boots looked like they were a few steps removed from second-hand? Duncan raised his eyebrows.

"Just because you benefited from the trolley being fixed doesn't mean you didn't earn some reward for what you did."

"Oh, I know, but..." Jacob shrugged. "I honestly wasn't even thinking of my own commute, right then. I just knew the driver was having trouble, and I was pretty sure I could help, so I wanted to try. I like solving people's problems," he added with another grin.

Duncan considered Jacob for a moment. It was so strange, how someone who could talk so much about absolutely nothing could come across as so...innocent, in a strange way. So sincere and generous, while also being so clueless about other people's feelings and social cues...

Jacob was a strange person. A strange person, but...interesting.

Little by little, Duncan actually found himself smiling too, though much more wryly.

"...Hm."

Jacob turned his focus to the window as the trolley began to move. Duncan and he fell into a contented silence, which was broken when Duncan initiated conversation again.

"...Which library do you work at?"

"The one uptown, near the museum!" Jacob said with a grin. "My mum recently became a curator there...we generally walk home together those days, so we can pick up Wyn from school on the way. Anyhow, Mum's the most smashing curator -- never been great around lots of people, but she's so smart...she outclasses everyone else there, easily. One day she told me about this new exhibit she's been helping with on the history and short-lived reign of the Knave of Hearts -- bloody as all get out, mind you, but brilliant..."

Before long, Jacob had gone on a long tangent about the history behind the Knave of Hearts's reign and the boom in technological advancements that cropped up in the rest of Cinderhaven in response to refugees fleeing the Kingdom of Hearts. Duncan was having trouble following all of it, but Jacob's passion was remarkable enough to sit through -- it was like sitting beside a raging fire just to enjoy its warmth. And in those times when Duncan found himself on the same wavelength as Jacob, he found a strange excitement pulsing through him as well.

"...And well, out of that, we got new tanks, models of mechanical horses, gas stoves -- even our modern streetcars," said Jacob. "All that, just from immigrants coming here, to explore greater opportunities."

Duncan nodded. "I've put in several proposals to the Jack of Spades, for just that reason."

Not that he's willing to do anything the least bit differently than how they've always been done, he thought dully.

"There's so much potential for growth, if we just invest in projects at home. And if Spades invested more in developing those technologies used for transportation, then it could even encourage other technologically sharp minds in other parts of Cinderhaven to settle here."

Jacob beamed. "Oh, for sure! But you know, I reckon that's only one component, the improving of our transportation methods. It's also about the fuel we use."

"Finding a way to increase coal production to meet demand, you mean?" asked Duncan.

"Yeah, sort of -- but to increase production, we'd also have to make improvements on how it's done," Jacob pointed out. "Coal is smashing and all, but it's still a toxic substance. Prolonged exposure runs the risk of kidney damage, lung damage, heart damage...even it just being too close to running water has proved dangerous. Not to mention coal mines are ridiculously unsafe."

Duncan nodded grimly. The Jack of Spades had received several reports about that, though he'd sort of treated it as "par the course," for such "unskilled" labor.

"So you think the first step would be improving conditions for those coal miners," Duncan surmised.

"Right!" said Jacob. "And well, it wouldn't be too hard! We already have windowed submarines that help us breathe and travel safely underwater...all we'd really need is a way to adapt that concept for use in mines! Some sort of a submarine suit, for use underground instead of underwater...oh!"

The curly-haired man abruptly shot to his feet and grabbed the string, tugging down on it sharply to tell the trolley to stop. Duncan looked up, startled, as the trolley came to a stop right outside the university.

"Didn't want you to miss your stop," said Jacob with a slightly cheeky smile.

"I suppose it is the least you can do," Duncan said coolly, "considering you almost made me miss my stop for a second time."

He got to his feet and headed for the trolley door. In the door frame, though, he paused, and he glanced back at Jacob.

"...You work at Pik's Tavern, right?" he asked.

Jacob blinked. "Yeah -- Tuesdays and Thursdays."

Duncan's lips curled up into a very small smirk. "I'll try to pop in sometime. I could use a place to eat with a good discount...that is, if knowing a guy there would put me in good standing?"

Jacob beamed so brightly that his blue eyes actually sparkled a bit.

"10% off your order, if you ask for me by name!" he said brightly.

Duncan's smirk broadened a bit. "10%? That's not bad. All right -- tomorrow morning, then, before I head into work."

"It's a date, then!" Jacob called back, as Duncan finally climbed off the trolley.

Once he'd stepped off, Duncan found his eyes darting up to the trolley as it closed its doors and drove off. He also found his heart beating just that little bit faster and his cheeks flushing as he brought a hand through his hair, looking away again quickly.

A date, then, he recurred Jacob's offhand remark in his own head. Duncan tried to push the memory down, even as it made his lips spread into an amused smile.

Obviously he'd never date an idiot like Jacob Cromwell...but talking with him some more would be fun. It'd be like spending time with Coby, back in grade school -- except with someone who couldn't read social cues and went on ridiculous, rambling tangents about absolutely nothing...

But it could be fun. Listening to Jacob get carried away by his own passions and getting a bit swept up in them himself for a while...that could be fun.

~*~

That day Duncan ended up bringing up the idea of applying reverse genetics to future vaccinations during a meeting with the Jack of Spades and his other courtiers. It was an idea that prompted an muted nod of approval from the Jack, as well as a few side-long glances from the other courtiers that made it clear they wished they'd proposed the idea.

Jacob would've probably been blissfully unaware of those envious looks, Duncan thought to himself in amusement. He probably would've also gone a whirlwind tangent about how to apply the same vaccination principles to the farming of produce or something.

~*~

When Duncan visited Pik's Tavern the following morning, he wasn't served by Jacob, as he'd expected -- instead, after eating one of the best breakfasts he'd had in his life, Duncan found a scrawled note on the receipt his female server had brought him.

10% off, as promised! Hope I cooked the eggs all right -- if you'd like them runnier next time, just let me know. Jacob C

The bloke could cook. The knowledge made Duncan stare at the little note on the receipt a bit longer than he should've.

After stewing in his thoughts for a moment, Duncan finally decided to bite the bullet and ask his server about when Jacob got off work. The server gave him a knowing smile.

"He's supposed to only work mornings," she explained, "but he always stays later. I reckon Jacob would stay and work for a full twelve hours, if we'd let him...but he always heads out, whenever his sister gets here."

Duncan blinked. "His sister?"

The memory of Jacob mentioning a "Wyn" rippled over his mind.

"Carewyn's her name," said the server fondly. "She's a sweet little thing -- smarter than her brother too, sometimes. She's still in grade school, but she always takes the trolley after school to 'pick Jacob up' when he's working here, so they can head home together." She gave a soft laugh behind her hand. "It's absolutely adorable."

The thought of Coby carrying his sister Veruca on his shoulders when she was little rippled over Duncan's mind, and it made something a little softer flit through his expression.

"...I see..."

Well, there went the idea of talking to Jacob some more after he got off work... Duncan considered his options for a moment before speaking again.

"...I'll be off then," he said at last, his voice incredibly business-like. "Tell Jacob I'll be back Thursday morning -- and if possible, I'd like to give him a review of his cooking in person."

~*~

From then on, Duncan would come into Pik's Tavern every Tuesday and Thursday morning on his way into the capitol, Jacob would cook him a scrumptious breakfast spread, and they would talk while Duncan ate. More than once Duncan would pay for Jacob's meal too so that he could eat with him -- if nothing else, he said gruffly, he should reimburse the Tavern for "stealing" one of their chefs for an hour or so twice a week.

As he and Jacob sat together, they would talk about various things -- economics, dirigibles, medicine, anthropology, music, renewable energy, joke shops, trains, mythology, biodegradable alternatives to household goods...anything and everything. They'd also talk about themselves, sometimes. Jacob would gush about his sister Carewyn, who was as sweet and small as a cherub, but brave and smart as a whip, and his mother Lane, who was soft-spoken and hated crowds, but was the gentlest and smartest person he knew. Duncan would talk about Coby -- about how laid-back and fun he was to be around, about all the trouble they got into at school together...about how much he loved his sister Veruca, and how much Jacob had reminded him of his best friend. Duncan would talk about his father and how they never spoke after the death of his mother -- how Duncan was working at the court of Spades and was determined to really be somebody, his own person, on his own and successful and free to do as he liked. Jacob would talk about how his father abandoned his family, leaving Jacob to drop out of school so as to help keep his family afloat financially through his multiple part-time jobs, and how he taught himself using books from the library, since he lacked the money or qualifications to attend university himself. Sometimes Jacob would even sing! Duncan caught the other man's tenor voice echoing several times out of the kitchen on his way out to greet him, and each time the soaring, carefree tone would make Duncan's heart skip a beat.

The two young men would talk and talk until finally both Jacob and Duncan had cleared their plates and had to get back to their respective jobs. And at Duncan's job in particular, he found the subjects of his meetings with Jacob returning to his mind more and more, whenever he'd meet with the rest of court.

"If we're looking for funds for these projects," Duncan proposed one day, "then perhaps technology could provide some solutions. Sure, we don't have enough money to pay for a new school right now...but investing in energy that's renewable, rather than single-use, could make it cheaper to refuel the machines needed to build these new structures. Water, for instance -- it's still only been used on the large scale right now with dams, but hydroelectric power could be a great alternative, if it could be duplicated on a smaller scale."

Afterward the Jack of Spades actually pulled Duncan aside to speak to him privately.

Ulrich Scheller was a very austere, by-the-book sort of man. Duncan had never once see him smile, and he and Coby both reckoned no one had ever heard him crack a joke in his life. Ulrich was very tall and stiff-shouldered, dressed in a high-necked black and white tweed coat that made him look like a vicar. He was losing some of his blond hair, so he'd combed his gelled hair down a bit to obscure it, but it didn't appear comical: if anything, it only made his forehead appear taller and his face appear longer and pointier, by extension.

"Your idea is really quite inventive," said the older man, his eyes boring into Duncan very carefully. "I hope you don't mind if I discuss it with the King, when next I speak with him?"

Duncan was startled. The Jack actually wanted to tell the King about something he'd suggested?

"Of course not," he said very quickly, once he'd recovered.

"Good," said Ulrich.

He crossed his arms behind him, strolling over to the window and looking out.

"...The King was very positive, when someone passed along your idea about vaccines. He came to me specifically requesting that I invest more in our local laboratories for the coming year. ...I don't think I've ever heard the King speak so passionately about infrastructure before."

The Jack's eyes watched Duncan's reflection in the window carefully. Duncan felt like an invisible hand was squeezing his stomach in a vice grip.

"...Thank you," Duncan said after a moment.

"Your hard work and resourcefulness have garnered quite a lot of attention," the Jack pressed on. "Investing in biodegradable tools, applying submarine technology to mining equipment...even the Ace of Spades has noticed. I think I even caught her expressing some interest in some of your ideas -- or at least, adapting them for her particular department..."

Ulrich gave Duncan an almost curious look.

"I must admit, Mr. Ashe...you are an impressive young man."

Duncan felt ill.

The praise should've been so validating -- after all, Duncan had worked incredibly hard, and he did want to be seen as valuable to the Court of Spades...but he'd only brought up Jacob's ideas because they were objectively good ideas -- they had to be, if the King reacted so well to them! Duncan hadn't really planned to take sole credit for those ideas...and now that he was set to, he found himself feeling trapped. On the one hand, he didn't want to take credit for ideas that Jacob had come up with all by himself, without even a formal education...but on the other hand, he didn't know how the Jack of Spades would respond to the knowledge that Duncan had earned all of this respect through promoting ideas developed by someone else...

"Mr. Ashe?" said Ulrich. "Is something the matter?"

Duncan shot out of his reverie. "No, sir."

He paused. Jacob's grinning face swam over his mind.

"Guess I just like applying my brain to more useful activities."

"Wasn't doing it for pay in the first place, after all."

"I honestly wasn't even thinking of my own commute, right then. I just knew the driver was having trouble, and I was pretty sure I could help, so I wanted to try. I like solving people's problems."

Jacob never looked for any kind of reward, for the work he put in. He didn't ever seem to want anything selfishly for himself. All he ever seemed to care about was solving problems -- knowing that what he'd done had been helpful to others...

Even so...

Duncan swallowed.

"...I can't take credit for those ideas, sir," he admitted lowly at last. "All I did was share them -- "

"Shared them at very critical moments," Ulrich cut him off smoothly. "They were timely and educated suggestions. You clearly put a lot of thought into them..."

"No, I didn't," Duncan said, a bit more loudly than he meant.

He very quickly reigned his emotions back in as best he could.

"...I mean, yes, they were applicable to the task at hand -- and yes, I have worked hard, and I appreciate you noticing..."

The young man swallowed again, trying to steady his courage.

"...But those ideas...I didn't come up with them on my own. They weren't even my ideas in the first place -- they're someone else's."

Duncan averted his eyes, unable to look at his superior.

"...He's the inventive one. I just...recalled his ideas, during those conferences."

The Jack of Spades considered Duncan for a long moment. Then, to Duncan's shock, he actually smirked slightly.

"Mr. Ashe," Ulrich said coolly, "you misunderstood my compliment completely. I never expected all of those ideas to be solely your own invention -- for however smart you fancy yourself to be, you are still only a student," he added rather dryly. "You have so much still to learn -- about politics, about the world. About mankind overall. That's why it's a remarkable talent, to discern which voices to listen to...to pinpoint good ideas when you hear them and promote them to others who might be too afraid to pursue them, despite their novelty. ...It's a talent I've lacked for a very long time..."

The Jack turned around to face Duncan properly, his arms still folded stiffly behind him.

"Yes, perhaps others presumed these ideas were fully germinated from your brain, but I was never so foolish to. Speaking from experience, however -- there's nothing inherently wrong with being influenced by the people around you, especially if they are both valuable and trustworthy. And from the sound of things...the people who've inspired you have been fortunate enough to earn your trust."

Duncan felt that hand squeezing his stomach loosen its grip. He relaxed slightly, relieved that his position hadn't been compromised -- but there was still something restless, in his feet.

"...Thank you, sir," he said.

Duncan paused. Then, after a moment, he spoke with a big more strength in his voice.

"Sir?"

"Yes?"

"There's this man I know. He's my age, but his mind...it's inventive, truly inventive, in a way mine isn't. ...I think he'd be invaluable, in developing new interior projects for the Country of Spades."

Ulrich cocked his eyebrows, interested.

"If you think so, perhaps you should invite him to court."

Duncan's heart gave a leap of surprise as Ulrich strolled over to the door of his office.

"...You give your approval, sir?" Duncan asked, delighted.

"After tonight, Mr. Ashe," the Jack said cryptically, "I don't think you'll need it."

He didn't explain himself at all before he strode away.

It was only when Duncan returned home that he found the official Spades-sealed letter that had been delivered to his door.

Dear Mr. Ashe, We are pleased to inform you that you have been nominated -- with nearly universal approval from the Court of Spades -- to take on Master Ulrich Scheller's position as the Jack of Spades.

~*~

Within a few weeks, Duncan had taken on the mantle of the new Jack of Spades. The same day Duncan was inaugurated, Jacob Cromwell put in his letter of resignation at the mechanic shop, Pik's Tavern, and the uptown library near his home and took a full-time job as an advisor and technology expert at the court of Spades under Duncan.

The rest of the courtiers honestly didn't know what to make of Jacob at first, but fortunately even those who'd looked upon him with the most scorn eventually came to see how truly brilliant the young man was. More than a few times, Patricia Rakepick tried to coax Jacob to make some more militaristic modifications to his blueprints -- but to Duncan's satisfaction, Jacob always ended up finding a way to blow the Ace of Spades off.

"Why would you use mining suits on a battlefield anyway?" Jacob asked with a deep frown. "They'd get trashed up so fast you'd have to fix them over and over...so pointless..."

Duncan smiled wryly. "Guess I shouldn't be surprised you have more interest in building mechanical bees than bombs and tanks."

"Well, of course!" said Jacob as if it were obvious. "Mechanical bees can help with the shrinking bee population. With artificial pollinators in the mix, we can both help the environment and improve food and medicine production! Not to mention the technology could be applied to larger models, once it's perfected -- imagine! Mechanical winged horses that can pull our own modified flying carriages! Mechanical carrier pigeons to deliver messages! Maybe even mechanical dragons! Imagine the uses that could give to a welder, or a baker...anyone in the culinary industry, really..."

Duncan found himself smiling absently as he let Jacob go off on another one of his dreamy tangents. His subordinate's blue eyes had drifted skyward ages ago, as it often did whenever he was thinking hard, but they sparkled like happy aquamarine gems.

Jacob hadn't had a lot of opportunities in his life, prior to meeting Duncan. After meeting him, though, Duncan hoped he'd have more, much more.

Because someone this resilient...this brilliant, this passionate, this idealistic and good...even with all the disadvantages he'd had and all the struggles he'd had to overcome and all the reasons he had to resent the world and his place in it...

He deserved to be celebrated. He deserved to be great, and appreciated, and successful -- to be able to do what he wanted to do and chase all of his sky-high dreams as far as they'd take him...

Jacob deserved to feel important. Because...he was. To Duncan, at the very least...he was important.

[sandgame]

Faking a spherical Age for the sake of KI coordinates

Heyo Tumblr, been a while!

Although I haven't used this blog lately, I have still been screwing around with this thing in the background of my life, because at this point I've basically accepted that semi-theorizing about how to make Better Uru is just my pastime.

Anyway. As a result of something else I was contemplating for this bizarre project of mine, I realized that because of how KI coordinates work, game worlds which allowed players to wander sufficiently far from the Age's Maintainer's Mark would need to implement some form of fakery in order to properly simulate the effect of walking around on a sphere while using a cylindrical coordinate system.

The "obvious" solution of just making the game world a sphere is… not really smart, though, so what's a game dev who is overcommitted to the concept of realism in this game to do?

Well, first let's finish defining the problem.

As you walk away from the Zero point of an Age, your elevation coordinate will decrease (generally; local surface geometry like mountains notwithstanding) until you reach the Zero’s exact antipode, because walking across the surface of the sphere will always send you "down" relative to the placement of the Maintainer's Mark. It should then increase back to 0 as you proceed back toward the Zero point across the other half of the planet.

But because game worlds are flat, this effect would have to be simulated for sufficiently large maps.

To do this, we have to know the following values:

The average radius of the planet

The distance traveled from the Zero point

The Zero point’s elevation relative to the planet’s average radius

The player’s local elevation relative to the planet’s radius

Using the equation for the length of a circular arc, we can reverse engineer the angular distance traveled:

L = θ * r

Or

θ = L / r

Where L is the length of the arc travelled (how far from the zero point the player is in a straight line), and r is the planet’s radius. 

NOTE: The math in the next part assumes you never travel more than 90 degrees around the planet, which I think is generally acceptable for the purposes of this hypothetical, but just be aware that what's presented here is not a completely comprehensive solution.

Solving for θ lets us construct a right triangle whose hypotenuse is the planet’s radius plus the player’s current elevation above that radius, and whose long leg is the planet’s radius minus the vertical distance the player has travelled away from the Zero point. We find the length of the leg with this function:

a = c × sin(θ)

Once we have a, we subtract it from the planet’s radius to get the elevation KI coordinate.

It may be necessary to make adjustments to certain values going into the equation solving for a in cases where the player has moved more than 90 degrees around the planet from the Zero point. 

The distance coordinate is calculated using the following formula to get the horizontal “opposite” leg of the right triangle formed by the radius of the planet and the angle the player is away from the Zero axis—which extends straight through the center of the planet, or:

b = c × cos(θ)

The value of b is our horizontal distance from the axis of the Zero point. (I should point out that we can't just use the XZ vector distance between the player and the Zero point for this measurement, as the player's travel is being treated as an arc for the purposes of simulating a sphere, and the arc's length would be greater than the actual absolute linear distance traveled if the map were actually spherical.)

The angle coordinate is the simplest to calculate, as it’s simply the player position’s angle from the vector of the Zero point (the “line” of the Zero), converted to torantee. 

In addition to faking the KI coordinates, a shader may also be used to post-process the geometry of the scene such that it falls over a false “horizon”, much like Animal Crossing New Horizons’ island terrain does (though the effect would be far less dramatic in this case). 

[weaselle]

i am an artist, and i do stove top cooking. If it gets cooked in a skillet, it's in my domain. I love to taste and add. I love to improvise. I love to wave my hand over what i'm cooking and bless it with flavors in amounts measured in "a pinch" "a dash" "a bunch" "a splash" or "a swallow". You can give me ten random ingredients and i can make you a delicious dish out of it

My brother is a computer programmer with a degree in physics. He is a baker. He follows strict protocols and uses incredibly precise measurements. Everything is timed to the second. You can give him a cookie and ask him why it's not the specific texture you want and he can tell you exactly how you made it and what you should do instead just by taking a bite.

I love to cook so much that i did it in restaurants for a long time (and you have to love it to do it in restaurants, for the same reason you have to really love someone if you're going to visit hell to see them)

One place i worked i had to make batches of dough. In order to do this I had to do a fucking math equation.

I am not joking. I had to look up the humidity that day, check the temperature of the room, and remember what the elevation above fucking sea level was (at least that never changed) and then enter those three values in a godsdamned math equation and solve for ingredient measurements.

a math equation! remember where i said i'm an artist? I fucking hated batching that dough. My brother could have come up with that math equation on his own and done it in his head.

anyway, baking is an absolutely insane proposition to me. Let me wave my magic flavor hands over a stove top instead.

my brother and i have a deep respect for each other's preference, and each secretly think the other is mad for preferring it

the funniest dynamc between my boyfriend and i is the chef/baker divide runs so deep. experimentally my boyfriend is a genius with figuring out what flavor profiles will not just taste good together but also will be enjoyed by the specific audience he is cooking for. a recipe is not a guidebook so much as a suggestion and he will frankenstein ideas together to get exactly what he wants to happen. he also didnt know that sugar will not work properly if you dont mix it with the wet ingredients in banana bread and when i asked 'why didnt you do it in the order of the recipe' he said 'i didnt really think it mattered'. autistically i exploded his head in my mind