# no matter how you do the math

Idempotence.

A term I’d always found intriguing, mostly because it’s such an unusual word. It’s a concept from mathematics and computer science but can be applied more generally—not that it often is. Basically, it’s an operation that, no matter how many times you do it, you’ll still get the same result, at least without doing other operations in between. A classic example would be view_your_bank_balance being idempotent, and withdraw_1000 not being idempotent.

HTs: @aidmcg and Ewan Silver who kept saying it

stoi·chi·om·e·try \stoikēˈämitrē\ noun - the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically a ratio of whole integers

For me, one of the more difficult aspects of chemistry was stoichiometry. In basic high school chemistry, stoichiometry is not too hard but can be a bit confusing when you first learn it. This post isn’t necessarily how to do stoichiometry, it’s just tips on how to make it easier so I’m not going to go over the basics (e.g. what a mole is, how to convert mass to moles).

*things in black ink are pieces of information given, anything in color is something you have to find

It doesn’t matter how great at mental math you are or how many numbers you can remember in your head at once, just take the 5 seconds to write your calculations down. Problems like the one above are relatively simple and you may be able to get away with not writing everything down, but it’s much better to form a habit of writing things down so you’ll be used to it by the time you get to really complicated problems.

2. Set up your problem neatly

Many stoichiometry problems will ask for moles, masses, and atoms of the compounds in your reaction. Depending on how many compounds are in your reaction, there can be 12+ numbers and calculations so you want to keep track of them. As you can see in the photo above, I wrote down the original equation, balanced equation, and under those, 4 horizontal rows each labeled with a different piece of information. Do your calculations off to the side and have a designated area on your paper for the answers since you’ll probably need some of them to do other parts of the problem (e.g. you need the moles to find the number of atoms).

3. Space things out

I cannot stress how important this is, I usually write rather small but if I’m doing a stoichiometry problem, I’ll make my writing about two times bigger than normal and space things out a lot. Cramped writing leads to confusion and the whole thing looks messy and difficult to understand.

4. Pay attention to your significant figures

This may not seem very important, but some teachers are very strict on having the right number of significant figures and if you’re not paying attention to them all throughout the problem, it’s much more difficult trying figure out how to modify the calculations you’ve already done so that all the answers have the right significant figures.

Conversations with my mother
• Mother: I've been watching "The Real O'Neals" to see what life must have been like for you as an out gay teenager.
• Me: Mother, do you even know what "out" means because I didn't come out until I was 27? Which, you know, unless Common Core Math has changed the definition of the word teen means I wasn't an "out" gay teen.
• Mother: I saw an episode that featured Olivia Newton-John's hit single, "Physical." I'd forgotten how homoerotic it is. We let you watch that. Do you think that's what turned you gay? Maybe it is our fault.
• Me: Mother, first, please never use the word homoerotic in conversation with me. Like. Ever. Again. It's just creepy. Second, I don't know what's more disturbing - the fact that you think I turned gay, as if I'm a rainbow light bulb, on - gay, off - straight OR that you think the Olivia Newton-John song, "Physical," could turn me gay. If any Olivia Newton-Song has the Turning Someone Gay superpower it would be "Xanadu." Ok?

Me: *Stims around my parents, has a special interest and info dumps to them, shows obvious discomfort at being touched (especially by other people’s feet), has talked about how I can’t stand the texture of some foods/fabrics, goes non verbal frequently, has times where I’m bordering on a meltdown/shutdown and simply cannot deal, has very specific rituals for how I do things, wears socks and jeans everywhere no matter how hot it gets because anything else is sensory hell, is confused about some jokes/levels of sarcasm, Cannot. Understand. Math.*

Also me: *is hella sarcastic, very mature for my age, hides meltdowns/more expressive stims*

My mom: Well, you don’t act like the two autistic children I know, even though I’ve acknowledged that autism is a spectrum. So *obviously* you’re just shy and quirky and need to get out more.

2

I don’t do this often as it’s more time-consuming than other studying techniques (I think), but going through a chapter no matter what you’re studying and writing colorful and organized notes really glues everything to your brain.

Go onto the exam boards site and usually where there are past papers and mark schemes they’ll be a document called “Examiner’s Report”. This may look boring as hell but trust me, read through them- they often have tips and advice from examiners which will help you answer questions, as well as highlighting what actually gains you marks which can help you determine how much you need to write and how much doesn’t matter.

Shit in High School That Actually Matters

A lot of students (you guys) ask the question: Why do I have to do this? Why does this matter? How does this apply in the real world?

Why do I have to learn-?

Math: Mainly for logic and decision making, but also because as long as you live in a currency based society, math will be important. Your income and how you spend it will impact how you live, where you live, what you can afford to get by in life, etc. You cannot just say “I’m not a math person.” Bullshit, you don’t like word problems. Get over it. Be a math person and not a broke person.

English: For obvious reasons, it’s the fucking language you speak if you live in the western world. Coherency is a huge part of communicating and being understood. I don’t care if you don’t like grammar- how you write and speak impacts how people perceive you. A well spoken conversation or a well written essay (read as: resume and job application) can change your life.

Literature/The Arts: Books, theatre, artists, and more give us insight. To elaborate, they give us insight into situations and circumstances that impact you and people you know. You have to read The Great Gatsby because it’s the most accessible way to teach you that the American Dream is bullshit and you should strive for more than being famous or wealthy. You’ll have to watch plays like Fences so you, as someone who is presumably not African-American or working class, can understand the struggle and see what life is like outside your bubble. The arts open doorways of comprehension you would have never found before. You need the arts to be a well rounded human being.

Biology/Chemistry/Physics/Sciences: It’s appalling that most people, especially those in the power, don’t understand how the world works. They don’t get climate change, female anatomy, reproductive processes, or fundamental facts of the goddamn universe. That person could be you, and you could be responsible for not only dictating how people live, but how our planet survives. Even if you aren’t, you need to be an informed member of the population who can help make decisions for the better.

History: History repeats. Patterns always emerge and replay themselves over time. I think a huge reason the Gay Civil Rights movement has seen so much progress in the past ten years is because we have a generation of adults who witnessed/studied the Black Civil Rights movement. They understand the similarities in the struggle. The same applies to politicians and methods of discourse used in elections. I won’t name names, but history repeats- unless you do something about it.

PE: For the love of your self, you need to exercise. Our culture is sedentary enough as is, all you need is 30 minutes a day to not gain weight, an hour to lose weight. Develop the habits now while your metabolism is malleable and use the class to find something you like.

Computers: You know the answer already. Technology is only getting more essential. Keep up or get left behind.

But I don’t like that/any of those subjects!

1. Tough titties because you don’t always get to do the things you like to do. Learn to suck it up now and be a better adult for it.
2. It’s not just you in that school. Your peers will take wildly different paths from you. They may need to learn calculus because they’re going to be dealing with abstract figures in their careers. Maybe someone wants to be a college-level professor who can dissect Hamlet with ease. Maybe someone wants to study the human body so they can be a physical therapist and heal their loved ones someday. We all require different things in our lives.

But even if you don’t like any of those, bear this in mind:

Having an overwhelming amount of knowledge in one subject and next to no insight for anything else makes you so goddamn insufferable as a human being. This goes back to an earlier point in that everyone is different and not everybody likes what you do. If you gain a well rounded knowledge with some understanding of many things, you will find so many people to connect to and you will grow as a person. You will even enjoy it, trust me. However, should you choose to live a myopic life where your only interaction is with others who act as a sounding board for your thoughts, then you will live a stunted life unaware that you could have understood anything more than what you already perfected.

School isn’t just about grades and college mills. You are literally being trained to be a functioning adult in our society. Now get to work.

Also, an important note:
Turning in Assignments: Jesus Christ, just do it. Most of your grades in High School are based on your homework. Not even doing it well, just doing it. Seriously, this impacts you later in life because nobody gives a crap about who you are unless you have something to show for it. Just. FUCKING. DO IT.

I was tagged by the amazing @darkharries! Sorry it took so long!

Rules: Answer the questions and tag nine people you want to get to know better :)

How old are you: 14 (IK IT’s EMBARRASSING)

Current job: Don’t have one at the moment

What are you good at: nothing lol

What’s a goal you are trying to achieve: become better in math

What’s your aesthetic: a mixture of things

Do you collect anything: Movie tickets

Pet peeves: when people bounce their leg, don’t wear shoes outside, metal scraping,heavy breathing

Three songs i recommend: Wichita Lineman by Glen Campbell, Hot Dreams by Timber Timbre, and Say You Won’t Let Go by James Arthur

## October 10, 2015 《Saturday》

“It does not matter how slowly you go, as long as you do not stop.” -Confucius

Attacking math today. Failed the test (miserably) and I’m determined to understand it before I move towards anything else. Math isn’t my strongest subject, but I won’t let it break me.

Why!!!! Put a spell on you is now addicting! I love your Harry Potter Au stories and combined with Gruvia!!! It's like chocolate 🍫 the first bite is an temptation and you can't stop until you finish eating everything! Ohhhh I love Gray! He is so freaking hot! Is he flirting with Juvia!? How many chapters will it probably have? Please write more! I need an update soon!!!

HAHA A few years ago I made a pact so all my stories end up as addictive as chocolate.

lol I’m kidding, of course. But I’m glad you liked it! Gray was maybe inda perhaps flirting a bit? I mean, I based that scene on this:

COME ON, LOOK AT HIS FREAKING FACE. I made him wink at her in a friendly matter (because he’s almost winking here), but you know: he IS fourteen and Juvia is a pretty girl. Just do the math from there. LOL

No idea how many chapters more. Maybe two. AND THIS WAS SUPPOSED TO BE A ONE SHOT, THEN A TWO SHOT, THEN THREE NOW PERHAPS FIVE? You guys’ reaction to it are just too overwhelming!

Just a hint, though: I still gotta go through the Triwizard Tournament which means: YULE BALL MY PEOPLE. ❤

I The Beginning

Before you even start studying maths you’ve gotta get your things together. The notebook you use to do your homework problems, your revision notebook, extra grid paper, textbooks, pens, pencils, rulers, geometry sets whatever you will need in this study session. Now maths is one of those subjects where no matter how long you redo your homework problems you won’t do as well as you hoped if you don’t learn how to apply the maths. So I’ll be focusing on how you can learn to apply mathematics, along with a few techniques that will prevent the ‘3 stages of downfall’.

II Applying this weird things called mathematics

Theory is a good place to start, however, don’t just parrot the theory so you can trek through those problems. How did people come up with these theories? Were they derived from another concept? Do these rules apply to all areas of this topic? What is the purpose of the concept itself? These are the types of questions you should ask yourself so that you aren’t limiting your brain. Here’s an example: ooh I recognise this problem, I’m going to do it the same way I did it originally to get it right. If you have this mentality in an exam, when a harder question decides to knock on your door, will you know how to do it? Hmm…

III The first stage of downfall

‘I make so many silly errors’. This is actually my life and I’m working towards fixing this. I tried out this method and it seems to be working so far: when you’re redoing problems from your own textbook and other textbooks, mark it and for me, most of the time the questions I get wrong are silly errors. If you have sufficient working, you can look back and see what made you draw the conclusion that was wrong. Write all these reasons on a sticky note and each time you attempt a question, go through the list of causes in your head and after you’ve completed the problem, go through the checklist again to make sure you haven’t done anything on the list. For me, it actually had to do with my handwriting- something that I could easily control. In the actual test, if you have enough time, redo each and every question to make sure that you haven’t made any stupid mistakes. My original working is in pen and my checking is in pencil (I outline this on the front of the test so my teacher isn’t like what the hell is this???).

IV The second stage of downfall

'I didn’t have enough time’. Again, actually my life. So, when you’re doing the practice problems, time yourself and go as quickly as you can but make sure you are 100% accurate. That’s why it’s important to recognise the causes of your silly errors first. Write down the average time it takes you to complete a problem belonging to a specific subtopic, but it doesn’t count if you got the problem wrong. Then you can not only figure out what questions in the test to focus more on based on your time and accuracy, but you can figure out what subtopics are your weaknesses and you can make them your strengths :))

V The final stage of downfall

'I’m not good at maths’. Yes, the final stage of downfall is your mentality. If you constantly believe that you’re horrible at maths, you won’t try as hard because 'what’s the point I’ll fail anyway’. So not true. YOU ARE CAPABLE OF ABSOLUTELY EVERYTHING A LITTLE MATHS PROBLEM IS FREAKIN NOTHING FOR YOU BECAUSE YOU ARE A GOD/GODDESS WHO IS HELLA INTELLIGENT AND CAPABLE OF EVERY SINGLE THING

I hope this helped you guys + go smash that maths test Xxxxxx

• Beast Boy: You know, Cinderblock, normally the bad guys break out of jail.
• Robin: And I can think of five good reasons why you don't want to break in.
• Robin: One!
• Starfire: Two!
• Beast Boy: Three!
• Raven: Four!
• Cyborg: Five!
• Robin: No matter how you do the math, it all adds up to you going down. So, are you going to go quietly...
• Cyborg: ...or is this gonna get loud?
• Robin: Titans! Go!
Solution to the Two Envelopes Problem

Wait!  If you haven’t taken even a moment to read my previous post, slow down cowgirl (or boy).  At least take a crack at it.  Reading the answer without at least thinking about the question is kind of like….well, you get the idea.  It’s not as good as thinking about it first.

But first a math joke:

Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?
A: Pumpkin Pi

## Solution to the Two Envelopes Problem

The problem wasn’t a paradox.  It was a trick.  But the trick was a wee bit subtle and easy to miss.

As you realized when you read the problem, Bill Murray was right.  It just doesn’t matter.  If you have two envelopes and you don’t know how much is in either one, you have no logical basis to choose one over the other.  It doesn’t even matter that I told you one has twice the amount of the other. I could tell you one has a million dollars and the other is empty.  Or I could tell you nothing.  In any case, knowing nothing to distinguish one envelope from the other, you have no basis to choose one or the other, and you can pick either one randomly and switch as many times as you want, or not switch at all, for all the difference it will make. Whatever you do or don’t do, the expected value of the envelope you end up with will be the average of the amounts in the two envelopes.

But what about the fancy mathematical proof I showed you, which “proved” that you will increase the expected value of your envelope from A to 5/4 A by switching?  That was nothing more than a cheap parlor trick.

The problem with the “proof” started in it’s very first sentence: “Let A be the amount in the envelope you picked.”  That was a trick.  Remember a cardinal rule of solving math problems: A variable needs to represent only one thing.  The value of the thing it represents is variable, but the thing the variable represents must be specific. If you were solving an algebra problem and you said “Let X equal the number of boys in the class”, would you also say “Let X equal the total number of children in the class”?  Of course not!  If X represents more than one thing in the same problem, your solution will be a mishmash.

But here, I made “A” represent two different things while making it seem – through sleight of hand – like it only represented one thing.  I said A represented the amount of money in the envelope you chose, which seems to be a single thing.   But since your envelope contains either the smaller or larger amount, I’ve created a variable that will represent two different things in the same problem – the smaller amount and the larger amount.  That is not allowed.

Because I set up the proof in a way that makes no sense, of course it leads to a mishmash.  Watch how.  I said the other envelope could either have twice the amount in your envelope, or half that amount –  2A or ½ A. So your envelope has A dollars, and the other envelope has either 2A or 1/2A dollars.  So we’re talking about three amounts – A, 1/2A and 2A.  What? But that’s not our problem!  Our problem has only two amounts, not three.  As they say, “garbage in, garbage out”.  Setting up the problem wrong yields an absurd result.

The correct way to set up the problem is to have the variable - A - represent one of the two amounts – either the smaller or the larger.  If A represents the smaller amount, then 2A represents the larger amount.  (And there is no 1/2A.)  If you set it up correctly, you see that if the envelope you picked has value A, switching increases it to 2A, adding A to your coffers.  If the envelope you picked has value 2A, switching decreases it to A, taking A from your coffers.  The possible increase and decrease is identical - A -  so there is no reason to switch or not switch.

So what about the “proof” I offered in the previous problem?.  It’s actually a great proof, but for a different problem!  Can you figure out what problem that proof solved?  Think about it before you read on.

## The different problem

Suppose I actually had three envelopes, and I handed you one.  I tell you that you can keep the envelope I gave you, or trade it for one of the two envelopes I’m holding.  I tell you further that one of my envelopes has twice as much as yours, and one has ½ as much.  Should you trade envelopes?

You already know the answer.  In this case, let A represent the amount in your envelope. The two envelopes I’m holding contain 2A and 1/2A.  And, as we’ve already proven, with these three amounts, not two, in play, you will have an expected value of 5/4A if you switch, so you should switch.

You can see that clearly, if you use numbers. There’s \$10 in your envelope.  The two I’m holding contain \$5 and \$20.  If you switch you’ll gain \$10 half the time and lose \$5 half the time.  To figure out the average effect of switching, just add \$10 to negative \$5 and divide by two.  That’s \$5/2 or \$2.50.

So, you start with \$10 and, if you switch, on average you will end up with \$12.50.  How does \$12.50 compare to \$10?  Do the math and you’ll get 5/4.  Set up a math problem correctly, and, lo and behold, you get the right answer.

tfw you have to do a final copy of a project and the teacher gave you constructive criticism on the rough copy and you get immediately offended and defensive

“are you sure these sources are trustworthy”

ITS A MATH PAPER IT DOESNT MATER IF THE SOURCES ARE TRUSTWORTHY ALL THAT MATTERS IS IF I DO MY MATH RIGHT AND YOU DIDNT SEEM TO CARE ABOUT TRUSTWORTHY SOURCES WHEN I FIRST SHOWED THEM TO YOU

I’m planning an herb garden right now and I’m so excited! I plan on making an herb spiral which looks like this:

I don’t have too much money to make it. I’ve been using my retired math skills to calculate circumference etc to estimate how many rocks I’ll need and it’s basically A LOT OF ROCKS. I have awesome home-grown compost, straw and more organic matter for mulch but I need to start looking for rocks on craigslist/outdoors. I already have seeds I want to use and then after that I’ll pretty much just have additional plant expenses. I think I’ll be able to do this for under \$25?

Herb spirals create microclimates where you can have hardy plants at the top of the spiral and gravity will help guide water towards more thirsty plants at the bottom. The slope also creates a shady and sunny side to accommodate the sunlight needs of different plants.

When summer starts to cool down, I want to put an inoculated mushroom log on the cool/moist side! I’m excited for a future of tasty garden treats.

starter for @giingerstallion

He gave a simple, one handed wave to Betty and Veronica through the window as he watched their retreating figures fade from the glow of Pop’s neon sign. It was still early, only a little past seven, but Jughead couldn’t really blame the two for leaving their time-honored hang out spot. The table had been filled with small talk and mindless chatter about things that only mattered on a face value level. Each of them showing up more because of routine and less because they actually wanted to hang out—none of them wanting to bring too much attention to themselves and their issues by not being there.

What do you think you made on that math test? How’s the writing? The weather has been so weird. That shirt looks good on you.

Nothing deeper was spoken and it was clear that each of them had something else on their mind. In a way the teen was thankful for it, he was glad that the drive-in hadn’t been brought up or that an argument over Ms. Grundy hadn’t started, but the feeling of walking on eggshells wasn’t preferred either.

With a tired sigh Jughead brought his gaze away from the window and back to the ginger-haired-golden-boy of Riverdale. There was a sterile kind of silence between the two of them, not quite awkward, but certainly not comfortable. Jughead wasn’t stupid, he’d heard about what had happened with Ms. Grundy from Betty and he knew Archie was still feeling the ripples from it. A part of him was angry, because this was exactly what he’d been worried about—that Archie would be left with the larger wounds in the end, that Grundy didn’t care about Archie the way Archie did, that she would be able to walk away from it and move on with ease. Maybe some of that was unfair, because Jughead didn’t know for certain that she wasn’t hurting too—but damn it, he didn’t care.

That bitch hurt his best friend.

He reached out and slid the basket of fries that Betty had, thankfully, abandoned over to himself. They weren’t warm anymore, but cold fries beat the stale Saltine crackers he’d been eating. Jughead proceeded to grab the ketchup bottle and spray the red substance all over the fries before popping one into his mouth, silently relishing in their flavor. He ate a couple more of the golden sticks before he decided that he was over the quiet. Eggshells were for the birds.

Jughead shifted himself so that he was sitting directly in front of Archie and slid the basket of fries so that it sat between them— an offering if you will.

Listen, I’m not gonna ask if you’re okay, because it wouldn’t be you if you were.” His voice came out stronger than he meant it to and Jughead paused to reel himself back in,

And I’m not gonna say that it’s for the better or whatever—I’m just…sorry that it happened the way it did.”

Oh! I forgot to mention, good luck in school, it'll get better trust me ;)

based on the fact that my GPA, which was already low from the start of the year, is getting even lower as time goes on, is not quite a good sign. I don’t show any signs of improving no matter how hard I try to work or focus. My brain is just unable to process any subjects that aren’t grammar or (sometimes) math related. That’s not enough to get a good GPA for the whole year. Last quarter mine was under one goddamn point. Under one point. How do you improve from that when the previous year you barely got over one.

Tip for going into college.

Choose a major doing something you love. Regardless ether it be art, history, math, petroleum engineering, etc. Pick something you’re genuinely interested in. It doesn’t matter about how much money the job offers because you will not want to go to class about something you don’t give a shit about.

Mathification for the Knitting Nation

I actually texted my best friend (who is a straight male with zero interest in yarn) about this last night.  The decision was made that I shouldn’t write about knitting math while drinking.  I stand by the validity of this decision.  It means there will be a lot less cursing through this.  And yes, I send intensely lame and grammatically correct drunk  texts.

So this is part of how you shift your thinking from just the stitch to the whole.  And trust me, if you managed to survive sixth grade math, you can do this.  The math itself really isn’t that hard.

First off, you’ve got to accept that no matter how much we don’t like doing them, gauge swatches or at least knowing how to measure your gauge is vital.  Honestly, I do a lot of my pattern adaptation while I’m actually making whatever it is I’m making.  I do them on the fly as I’m going without a whole lot of pre planning.  So for my style, a knit by the seat of my pants style, gauge swatches aren’t the most important thing.  But knowing how to measure gauge is absolutely vital.

Let’s say that I’m working on that classic basic crew necked, drop shouldered sweater that we’ve all made millions of.  I want to change it up and bring it closer to the body underneath the girls for a more tailored look.

C’mon.  You know how to do that.  For this example, I’m going to say that the theoretical gauge is four stitches by three rows.  So one square inch is four stitches across and three rows high.

Step two- Figure out how much change in measurement you want.

For this example, I’m going to say I’m reducing the width by three inches.

Step three- Convert that measurement into how many stitches you’re going to be either decreasing or increasing.

Remember when I said this is easy math?  Well here it is.

3 (inches) x 4 (stitches per inch) = 12

So total, I’ll be reducing the pattern by twelve stitches.

Step four- Figure out the rise.

This one has the most play and is the one that requires some thought.  But don’t worry and don’t over think it.  The rise is the slope you’re making.  People are built with curves (even the gents have no hard lines that match up to a ruler).  Think about a neck and shoulder line.  It’s not a straight square.  It’s sloped.

So think about where you’re putting in the change.  Is it a sharp slope or a gradual slope?  With the neckline to the shoulders, it’s a very sharp slope.  The sharper the slope, the greater the change from the largest to the smallest.  It’s why there’s so many increases or decreases in that area.  With below the girls, the slope is more gradual.  So I don’t need that much change per row.

Every four inches I decrease means I’ve reduced one inch.  While I could reduce all three inches in one row, It would look a little strange. It would look like my boobs were in a pouch.  So instead, I want a gradual slope.  Let’s go with the next option.  I could do four decreases per row.  This is a reduction of one inch.  But again, that’s a pretty dramatic change.

So, because I am looking for a gradual slope, I’m going to do only two per row (half an inch) and I’m going to space them out so that they’re two rows apart.

And that’s it.  What I’m going to recommend to everyone is do some test runs.  Pull out that yarn that’s from your practicing days and play.  Play with increases and decreases.  See how it changes the shape.  Oh and make some stuffed animals.  Seriously, amigurmi can really, REALLY help you to understand the power of shaping.  Not kidding.

okay but do you ever think about space and how big and vast it is, and think about how small and insignificant you are in the grand scheme of things?

well dont. because you are the reason that girl in your math class smiles everyday because of your hushed comments during lecture. you are the reason laughter bubbles up from your friend sitting across from you at lunch. you are the reason someone feels joy when you compliment their shoes, their hair, their art.

you feel, you crave, you create. you can snuggle up in fuzzy socks and a cozy blanket or you can lounge out on the sand of a beach or you can feel the sting of your legs after a good workout.

you are the gravitational center, the sun, of your own little solar system, and it would come crashing down without you.