values and units

“ You too must love the stranger, for you were strangers in the land of Egypt.” (Deut. 10:19)

WHAT TO DO AT AN ICE CHECKPOINT, ESPECIALLY IF YOU ARE WHITE and/or FEEL THE NEED TO JAM UP THE WORKS.

Here’s the deal:

🔘 Border Patrol can verify citizenship within 100 miles of a border or “external boundary.” This includes coastlines.

🔘 Border patrol can only ask brief questions about citizenship, and they cannot hold you for an extended time without cause.

🔘 You always have the right to remain silent. You do not need to answer their questions.

🔘 WITH THAT SAID, IF YOU ARE A BORN CITIZEN OF THE UNITED STATES AND ESPECIALLY IF YOU ARE WHITE, YOU NEED TO SPEAK UP.

🔘 The most important acts of resistance are the small ones. Make it difficult and uncomfortable for ICE agents to do their jobs. They are counting on citizens to turn a blind eye and allow them to deport undocumented citizens without challenge. Disabuse of that notion.

🔘 If you are on a train, bus, or anything else and ICE or CBP boards, you need to stand up and loudly let everyone know that they have the right to remain silent or only answer questions in the presence of an attorney, no matter their citizenship or immigration status. There have been numerous reports that confronting the agents in this way has caused them to leave without verifying citizenship. THIS CAN SAVE LIVES. 🙌

🔘 If you see anyone being held up by immigration, loudly ask if they are being detained and if they are free to go.

🔘 Immigration officers cannot detain anyone without reasonable suspicion, an agent must have specific facts about you that make it reasonable to believe you are committing or committed, a violation of immigration law or federal law. If an agent detains you, you can ask for their basis for reasonable suspicion, and they should tell you.

🔘 Always say no to a search and let everyone know that they can and should refuse consent to a search.

🔘 They cannot search or arrest anyone without facts about that make it probable that they are committing, or committed, a violation of immigration law or federal law.

🔘 Silence alone meets neither of these standards. Nor does race or ethnicity alone suffice for either probable cause or reasonable suspicion

🔘 As white citizens, we have a level of privilege which protects us from retaliation from ICE for being “rude” and making a scene, which makes it our DUTY to speak up and make sure people without the same privilege know their rights. GET LOUD. YELL. YELL IN SPANISH IF YOU KNOW IT. LET PEOPLE KNOW THEY DON’T HAVE TO SAY ANYTHING. MAKE ICE UNCOMFORTABLE. THROW SAND IN THE GEARS OF WHITE SUPREMACY.

⭐️ Bonus info- ⭐️
🔘It is perfectly legal to record immigration agents as long as you are not on government property or at a port of entry. If your train/bus gets boarded, pull your phone out and start videotaping immediately.

🔘 If you are detained or see someone getting detained, get the agent’s name, number, and any other identifying information. Get it on video if possible.

🔘 Contact the ACLU or your local Immigrant/Migrant support orgs if you see someone’s rights being violated. The phone number for the ACLU of Minnesota is (651) 645-4097. Put it in your phone now, so you’ll have it if you ever need it.

bzfd.it
Donald Trump Has Been Blocked From Visiting Parliament Because Of His "Racism"
"An address by a foreign leader to both houses of parliament is not an automatic right, it is an earned honour," John Bercow, the Speaker of the House of Commons, announced.
By Jim Waterson

Donald Trump should not be given the honour of addressing both houses of parliament on his state visit to Britain later this year because of his “sexism” and “racism”, the speaker of the House of Commons announced on Monday in an extraordinary intervention that drew applause from MPs.

John Bercow, who was a Conservative MP before he becoming the politically neutral presiding officer, said said he would personally block any attempt to allow Trump to address both houses of parliament in the medieval Westminster Hall, an honour given to Barack Obama in 2011.

In a rare break with convention, Bercow declared in no uncertain terms his opposition to the state visit.

“We value our relationship with the United States,” Bercow said in response to a point of order from Labour MP Stephen Doughty. “If a state visit takes place, that is way beyond beyond and above the pay grade of the speaker.

“However, as far as this place [the House of Commons] is concerned, I feel very strongly that our opposition to racism and to sexism and our support for equality before the law and an independent judiciary are hugely important considerations in the House of Commons.

Continue reading.

We are all created in the same Image of God, regardless of the gender we were assigned at birth.

In the wake of disheartening policies aimed at hurting non-cis people in the United States of America, let us hold hands and work together to fight against disheartening and despicable transphobic policies that seek to erase human beings and their genders from our nation.

Hillel said, “im lo achshav,” if not now,” “imatai?” “When?”

When is now.  Right now.   We are all in this fight together.

Make sure that you vote on November 6th, and make your voice HEARD.

#resist

The reality is that when it comes to supporting real family values like paid leave, the United States lags behind every major country on earth, and virtually all poor countries as well. Out of 188 countries, the U.S and Papa New Guinea are the only two that don’t provide some form of paid leave. Or, to put that another way: the citizens of every other major industrialized country get more protection for their families than we do here in the United States.“ 

- Bernie “The Man” Sanders

youtube

Nearly 60 percent of Americans admit knowing nothing at all about Sikhs. That lack of knowledge comes at a deadly cost. In the wake of recent incidents from the 2012 Oak Creek Massacre to a shooting of a Sikh man in Washington this March, the Sikh community is taking a more vocal stand against hate.

This month, the National Sikh Campaign, an advocacy group led by former political strategists, launched a $1.3 million awareness campaign, “We are Sikhs.” Funded entirely by grass-roots donations, the campaign’s ads will air nationally on CNN and Fox News as well as on TV channels in central California — home to nearly 50 percent of the Sikh American population — and online.

The ad, which aims to tackle misperceptions of Sikhism, shows Sikh men and women speaking about how values of their faith — tolerance, religious freedom and gender equality — align with American values. According to Gurwin Singh Ahuja, the executive director of the National Sikh Campaign, “These are core values of the United States, yet we’re often perceived as anti-American or as religious extremists. Our community is hurt by bigotry and ignorance, which is, in many ways, compounded by our own silence. To change these perceptions, I felt we had an obligation to share our stories with our neighbors.”

Why American Sikhs Think They Need A Publicity Campaign

gffa said: “no one asked but i want to talk about the jedi and how they make me…”

A CONNECTING OF THE SOULS in a way that doesn’t have to be romantic, that’s just about two hearts and minds and the very essence of what makes a person who they are, touching on the essence of what makes someone else who they are, that way of reaching out and truly feeling someone in a way that these physical bodies cannot fully convey, that there’s this piece that’s slightly missing with everyone else, that you can touch them, you can see them, you can even feel what they’re feeling, but they can’t feel YOU, they can’t reach BACK. They’re still people, you still feel their emotions, they’re still hugely important, they can be wonderful or horrible, having all that pressing on your mind, but they can never truly reach back. 

And then you find another person who, all of a sudden, they know what that’s like. To be on the other side of a glass wall between you and the rest of the galaxy. But they’re on the side you’re on. And they know how to reach out to you, they know how to feel you and show you how to feel them. And suddenly there’s this entire GALAXY of connection that you can feel, imagine what it’s like to be able to connect to every living thing with your mind, to feel that energy that flows through every part of you. And to find someone else who knows what that’s like. 

And then they also show you how to control it, how to keep it from overwhelming you, how to interpret it and process it so that the galaxy isn’t just a huge blaring signal in your head when you connect to it, but instead you’re part of this great, huge cosmic FORCE, and if you do it right, it’s warmth and connection and BELONGING, that’s what the Force and the Jedi ARE.

ok this deserves its own post

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The Global Peace group is a manufactured movement gaining traction with young peoples living under mega corporations. It is “manufactured” in the sense that it was created as a puppet organization by Otto Volker to push his social agenda. The group advocates a return to traditionalist 20th values of strong family units, self betterment, powerful authority structures and healthy living. It also pushes against the consumerism, nihilism, and lax moral values plaguing society as a whole.

There is nothing even an organized militia could do to hurt any mega corporation. Instead the Global Peace Group focuses its attention on targeting those who work corporate positions that they deem contribute to cultural and societal decay. 

The face of Global Peace group is a synthetic vigilante known as “Red Yr”. The general population is quite enamored with vigilante justice against higher powers. Being completely irrelevant to the means of production and having no effect on how society is run has made the populous crave purpose. The Red Yr in a way is an extremely effective advertisement for subscribing to Otto Volkers ideology.  

anonymous asked:

Support!reader who has a crush on cuties of your choice that are of a different class, but they're nervous about making a move because "oh I'm just a medic. I'm not nearly as impressive as they are"

(Let’s go withhh…Hanzo, D.Va, and Junkrat!)

Hanzo

Genji quietly watched as you watched Hanzo, waiting for the moment when you’d get up and actually say something to him.

“It has been a long time since someone has expressed romantic interest in my brother,” he pointed out.

“Oh, I don’t doubt it,” you sighed wistfully.

“And he often looks lonely after missions,” he continued.

“Yeah, I’ve noticed,” you mumbled, eyes still glued to the archer.

“…So!” Genji finally groaned.

“So what?” you snapped, finally turning to him.

“Go talk to him!”

“T-Talk to him?” you stuttered nervously, “No way, th-there’s no way he’d want to talk to me. Especially since he’s busy with those targets…”

“He’s always busy with targets,” Genji rolled his eyes from behind his visor, “He doesn’t need the extra practice, he just does it when he’s lonely or troubled,”

“It’s nice to watch…” you smirked a little, watching as his muscular arms drew back the bow.

“[Name!]” Genji brought you back to reality, “Why don’t you go talk to him. You’ve had this crush on him since you came to Overwatch, but you never make a move!”

“Well that’s because–I mean–he’s a sharpshooter, a sniper, a strong warrior of Overwatch! And I’m just a support unit…I hop in and out of fights to help people, relying on my teammates to protect my sorry butt…”

Genji sighed, “So you’re intimidated? Is that it?”

“…Yeah…” you admitted.

“[Name], I’m an offense unit,” he said bluntly, “You weren’t afraid to approach me,”

“Th-this is different,” you stammered, “I didn’t have a crush on you,”

“[Name], none of us think you’re a useless addition to the team. We all value our support units, especially you,” Genji explained softly, “Nobody would ever belittle you for your support status, especially Hanzo. I think he admires those who can save lives so easily,”

You shifted uncomfortably as you thought it over. It was just that grim, dead-set face Hanzo always had. He seemed like he never had time for anyone much less little support units.

“We are defined by who we are, not what we are,” Genji concluded, sounding just as zen as his master.

Taking a deep breathe, you nodded, “Ok, you’re right! I need to stop telling myself I’m not good enough! I-I just…need to go over to him…a-and say something,”

“That’s the spirit!” Genji cheered.

“Well go on,” he urged.

“I can’t. My feet feel like they’re stuck!” you whimpered nervously.

“Just get out there already!” Genji laughed, giving you a nudge towards his brother.

Stumbling forward, you watched the archer hit another bull’s-eye, pulling another arrow to his bow. Cautiously, you came up next to him, watching him release the arrow and hit another target in the center.

“Hello, [Name],” he said gruffly, still totally concentrated on his work, “Is there something you need?”

He looked so scary and powerful! Why were you trying to waste his time?! Aaagh! Nervously, you glanced back towards Genji for some kind of help. The cyborg just gave a little “go on” gesture.

“A-Actually…” you mumbled anxiously, “I–uh–came to watch your target practice a-and um take notes! Yeah, my…my aim really i-isn’t very good so um I mean yours is! So I thought I-I could learn a thing or–uh–two from you…I mean as long as that doesn’t bother you, you know…”

Hanzo suddenly stopped midway from grabbing another arrow. Then his eyes slowly turned toward you, looking more surprised than usual.

“You…want me to teach you?” he asked with a hopeful look in his eye.

“Ummm…” you glanced back to Genji who was nodding furiously and giving you a thumbs-up, “Y-Yes! If it’s not too much trouble!”

“Of course not,” Hanzo shook his head, picking up a practice bow and handing it to you, “I’ve noticed your aim in battle. I was hoping you would try to fix it,”

You cringed. Were you really that bad at hitting your targets?

“But I am glad you sought me out to help you,” he gave a slight smile, “I was afraid you had been avoiding me,”

“Avoiding? Heh, nah o-of course not!” you giggled.

“Support units seem to be so nervous around me,” he said in a ponderous tone, “I was beginning to worry that I had been frightening you away…”

“No, no, it’s not th-that!” you tried to tell him, “I’m shy by nature, I promise!”

He tapped his finger to his chin a few moments before saying, “Very well, let us begin with your stance,”

Your whole face grew hot as Hanzo suddenly stepped behind you, wrapping his arms around yours and guiding your hands into the right positions. Then he nudged your foot with his and instructed you to tighten your grip. You glanced back at Genji again, who looked like he was laughing from behind his visor.

D.Va

You always admired D.Va so much. She fearlessly flew into every fight with her meka, disrupting the enemy’s ranks and wreaking havoc. Then just when they thought they had taken down her meka, she’d shout “nerf this!” and blow them all to smithereens! You thought she was simply amazing and almost made you wish that you were a tank unit. But you were just a support unit, sticking back with the offense units and keeping them supplied with shields and heals.

But one day, during a really rough battle, D.Va started calling on her comm link for extra backup: things like more firepower, defense, and a support unit to keep her going. No other supports responded, so you were the one to answer her call and move to the front lines. It was scary as all hell up there, explosions and bullets flying, yet Hana kept her cool like it was another day at the arcade!

“Thanks for coming to help guys! Their snipers are really annoying but their offense won’t let me get close to them! Could you guys keep their offense busy?” she explained, then turned to you, “And [Name], could you pocket heal me? My meka’s gonna fall apart without your heals!”

“U-Uh–yes! Yes ma’am!” you piped almost like a robot.

“Hee hee!!” Hana snorted, “Who’s ma’am? I’m D.Va, silly!”

You felt a little blush form on your face as she laughed her bubbly laugh.

“R-Right, D.Va…” you muttered.

“Let’s mooove out!” she cheered excitedly, taking off with her boosters.

Somehow you were able to keep up, steadily healing her as she disrupted the snipers, disarming them and booping them out of their nests. It was really hard at times; sometimes her meka’s health would go dangerously low even as you healed her all you could. But luckily, her meka never got wrecked…well until she wrecked it herself.

“Snipers eliminated!” she reported happily into her comm link, then looked back to you, “Watch this, [Name]!”

With that, she boosted her meka into the air, ejecting at the last second and sending it into self-destruct mode. It turned into a big ball of light, soaring through the air and eventually landing in the enemy base with a KABOOM! You watched awe-struck as the whole sky lit up and the base flew into a thousand pieces.

“Woohoo! Bonus points!” Hana cheered.

“That was amazing…” you breathed.

“Yeah, I guess it was,” she shrugged, “But I couldn’t have done it without you, [Name]. Your healing was what really kept me going!”

You blushed again, staring down at your shoes bashfully, “I mean, I wasn’t that great. Nothing different from what I usually do…”

“Hey!” she grinned, taking you by the hand and leading you back to your own base, “Do you wanna hang out sometime?”

“H…Hang out?” you couldn’t believe someone as famous and strong as D.Va was asking you to “hang out!”

“Uh-huh, you know that thing that people do when they wanna spend more time with each other?” she chuckled at you.

Your expression slowly dropped, remembering your place.

“But…you’re a tank unit, and I’m a support unit…” you mumbled.

“Yeah? Why is that important?” she shrugged.

“Because I’m just a support unit,” you admitted, “Don’t you want to hang out with someone cooler like another tank or attack unit?”

“Nope!” she smiled, “I wanna hang out with you, [Name]! Units don’t matter! They’re just dumb, stuffy titles,”

With that she slung an arm over your shoulder and pulled you close, making you stiffen up. You were so close to her! She smelled like bubblegum and new car…

“So what do you want to do? We could play video games or go to the arcade or go shopping–ooh! Do you like ice cream? I know this great place that gives me free…”

She’d be talking all the way back to base.

Junkrat

“Oi! I need healin’!” “Where’s my heals?” “Oi! Healer, over here!”

Why did you have to fall for a guy who treated supports like servants? Why did he only ever call you “Healer” or “Doc?” He was so tall and lanky, yet muscle-y at the same time, with a cute laugh and an outgoing attitude. Junkrat was everything you looked for in a guy, despite your friends saying you were crazy for it.

But you never once made a move. It always seemed like an arsonist would never have any time for a support unit, especially when he seemed to think they were so unimportant to the team. A lot of the other support units would get bad at him for his rude tone around him. They’d punish him with a smack on the head or a “no heal” policy for at least one battle. Some supports had given up on healing him altogether–he was the one who’d accidentally drop grenades on himself, after all.

But you just couldn’t keep yourself from healing him. It meant you got to admire him up close…even if you never said anything to him. Sometimes he’d even give you a little “Thanks, mate!” But as far as you were concerned, Jamison would never like a support unit. It wasn’t until the end of one of your missions that you were proven wrong.

“Hooly dooly, that was some fight!” Junkrat marveled at the wreckage as his hair smoked.

“No kidding,” you huffed as you tried to catch your breath, “I thought for sure we were gonna lose the point,”

“Same! We were the only ones on it!” he laughed, “I kept waitin’ for them to punt me off, but you kept me goin’!”

“Oh, yeah whatever,” you shrugged as you flopped down on the ground exhausted, “Well you did all the hard work,”

“Me? You were the one dodgin’ all those bullets and givin’ me all them buffs!” he pointed out as he sat down next to you, “I wouldn’t’ve been able to hold the point if it weren’t for you!”

A small blush crept its way onto your face, but you quickly shook your head and waved your hand dismissively.

“No, I wouldn’t have survived it if it weren’t for you blowing up anyone who came close to me.”

Seriously. Any flanker who’d try to sneak up on you would get a “Not my healer, you bitch!” from Junkrat.

“Well at least we can admit we work well together, eh?” he chuckled.

“Sure…” you mumbled bashfully, “Why not?”

“Eh c’mon, why ya hidin’ yer face now?” he smirked as he took your chin and gently guided it toward him.

“I-I’m not!” you squeaked in shock.

You hadn’t expected him to do that! His fingers felt all sooty and calloused…

“Yeah you are!” he sang.

“Sh-shut up…” you pouted, pulling away.

“Oi, why can’t ya just accept the complement?” he whined.

You crossed your arms, “Because I know you don’t mean it. You don’t care about support units in the slightest, Jamison,”

“The hell I do!” he retorted, “Well, only the good ones, that is,”

You gave him a glare and he put up his hands in defense, “I get it, I get it, you support-y types don’t like me. But you’re one of the only good ones on the team! You actually heal me and stick by me unlike all the other pricks who up and leave me for being ‘rude.’”

“But you, [Name], you’re a healer I can lean on!” he grinned, “ya’ve never let me down! That’s what I like about you!”

That’s what he…liked about you? Your face went red as you processed his words, looking like you had seen a giant spider.

“So…you don’t hate support units?” you asked.

“Hate ‘em? Nah!” he cackled, wrapping an arm around your waist and pulling you close to him, “Just drongos who don’t give me the time of day!”

Slowly, a smile appeared on your lips as you melted into him, letting him hold you closer. Jamison was a prickly guy and hard to get close to, and you always thought you’d never get very far with him, but all that time you had spent around him had been one big step towards knowing the real him.

–Mod Sirana

Beyards say a lot about their Paladins, probably. 

Kieth: The Knight, sword in hand to defend with inborn and hard earned skill, unafraid to press forward. An agent of someone else, but highborn. Someone others think highly of even without meeting. 

Pidge: The Spy, small and sharp and dangerous. She slips into places others wouldn’t be able to and she might not look like she could kill you but that’s before you feel the bite of her weapon. People assume little of her, but that’s how she likes it. She doesn’t need a weapon to defeat you. It’s there to grease the cogs. 

Hunk: The Bomber. Smarter than he looks, stronger than you’d think, he carries around a cannon and you think people don’t respect that? But more than that he knows where to shoot to cause the most damage. He’s Mulan’s last cannon and he’s not afraid to crush his enemies under a one-shot avalanche. It might not be subtle, or noble, but it is obviously impressive. He might die in the process but he’ll make sure he takes everyone else out with him. Someone who’s mind is technical and precise and does not shy away from mass carnage. 

Lance: The Soldier. He’s not fancy. His weapon does not particularly suit itself to sharpshooting, like a sniper, but is meant to be out on the front lines. He’s not one-of-a-kind; his is the never ending bombardment of someone who relies on his brothers in arms to defeat a more powerful enemy. Someone who values a unit. Someone who is thought simple, and not particularly intelligent, who is not special or specialized. Common. Dangerous. The second oldest profession in the world. The Soldier is the place of the lowborn, the common, the crude. Soldiers are rarely the heroes of fairytales, and they don’t get happily ever afters. 

anonymous asked:

why are you anti-usa? like i agree the current policies are literal horseshit but a lot of kind people live here, and usa has done some amazing things.

in all honesty, I’m very big on the values the united states claims to stand for, and what we’ve represented to many people. i’m all about equality and liberty and the chance to make a better life for oneself.

but abstract ideals are one thing, and material reality is another. fact is those kind people are regularly fighting an uphill battle against capitalist hegemony, and that the united states as a geopolitical entity was build on genocide and slavery and hasn’t even fully renounced either, let alone begun to make amends for those crimes.

We saved 155 lives on the Hudson. Now let’s vote for leaders who’ll protect us all.

By Chesley B. ‘Sully’ Sullenberger III October 29 at 6:52 PM

Chesley B. “Sully” Sullenberger is a safety expert, author and speaker on leadership and culture. (and lifelong Republican)

Nearly 10 years ago, I led 154 people to safety as the captain of US Airways Flight 1549, which suffered bird strikes, lost thrust in the engines and was forced to make an emergency landing on the Hudson River. Some called it “the Miracle on the Hudson.” But it was not a miracle. It was, in microcosm, an example of what is needed in emergencies — including the current national crisis — and what is possible when we serve a cause greater than ourselves.

On our famous flight, I witnessed the best in people who rose to the occasion. Passengers and crew worked together to help evacuate an elderly passenger and a mother with a 9-month-old child. New York Waterway took the initiative to radio their vessels to head toward us when they saw us approaching. This successful landing, in short, was the result of good judgment, experience, skill — and the efforts of many.

But as captain, I ultimately was responsible for everything that happened. Had even one person not survived, I would have considered it a tragic failure that I would have felt deeply for the rest of my life. To navigate complex challenges, all leaders must take responsibility and have a moral compass grounded in competence, integrity and concern for the greater good.

I am often told how calm I sounded speaking to passengers, crew and air traffic control during the emergency. In every situation, but especially challenging ones, a leader sets the tone and must create an environment in which all can do their best. You get what you project. Whether it is calm and confidence — or fear, anger and hatred — people will respond in kind. Courage can be contagious.

Today, tragically, too many people in power are projecting the worst. Many are cowardly, complicit enablers, acting against the interests of the United States, our allies and democracy; encouraging extremists at home and emboldening our adversaries abroad; and threatening the livability of our planet. Many do not respect the offices they hold; they lack — or disregard — a basic knowledge of history, science and leadership; and they act impulsively, worsening a toxic political environment.

As a result, we are in a struggle for who and what we are as a people. We have lost what in the military we call unit cohesion. The fabric of our nation is under attack, while shame — a timeless beacon of right and wrong — seems dead.

This is not the America I know and love. We’re better than this. Our ideals, shared facts and common humanity are what bind us together as a nation and a people. Not one of these values is a political issue, but the lack of them is.

This current absence of civic virtues is not normal, and we must not allow it to become normal. We must rededicate ourselves to the ideals, values and norms that unite us and upon which our democracy depends. We must be engaged and informed voters, and we must get our information from credible, reputable sources.

For the first 85 percent of my adult life, I was a registered Republican. But I have always voted as an American. And this critical Election Day, I will do so by voting for leaders committed to rebuilding our common values and not pandering to our basest impulses.

When I volunteered for military service during wartime, I took an oath that is similar to the one our elected officials take: “I do solemnly swear that I will support and defend the Constitution of the United States against all enemies, foreign and domestic.” I vowed to uphold this oath at the cost of my life, if necessary. We must expect no less from our elected officials. And we must hold accountable those who fail to defend our nation and all our people.

After Flight 1549, I realized that because of the sudden worldwide fame, I had been given a greater voice. I knew I could not walk away but had an obligation to use this bully pulpit for good and as an advocate for the safety of the traveling public. I feel that I now have yet another mission, as a defender of our democracy.

We cannot wait for someone to save us. We must do it ourselves. This Election Day is a crucial opportunity to again demonstrate the best in each of us by doing our duty and voting for leaders who are committed to the values that will unite and protect us. Years from now, when our grandchildren learn about this critical time in our nation’s history, they may ask if we got involved, if we made our voices heard. I know what my answer will be. I hope yours will be “yes.”

Source - The Washington Post

A Musical Tidbit With a Mathematical Explanation

Why we need a special expression for triplets

The question

If you want to write down music you will face the need for a notation to express the length for which a given note is supposed to be played, its note value. For reasons of perceived rhythmicality, note values arise from repeatedly halving (or occasionally doubling) a pre-set standard unit that is usually dictated by the beat. Denoting the standard unit by “1“ this is the notation we get: 

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I left out the signs denoting doubling of the standard unit because they are less common. I also stopped at 1/16th, even though you can keep on halving notes to get 1/32ths, 1/64ths etc. and denote them by adding more tiny flags to the notes. Let’s call these values the standard values. Relative to the standard unit they always have the length 1/(2^n), where n is an integer. 

You can even add standard values together to create new values, like so: 

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So far, the system seems pretty expressive. And I am, in fact, fairly sure that the note values of a great percentage of every musical piece I ever encountered can be expressed in this system. You only need one little addition, the triplet. You produce a triplet by taking a standard value and, instead of halving it which would yield another standard value, you split it into three parts. Here is an example of a triplet derived from the standard unit 1: 

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The little “3” and the brackets above the notes signify that the notes do not represent standard values but the aforementioned third of the next bigger note value. Risking confusion I will refer to both, the group of three notes each valuing a third of a standard value and the individual notes making up the group, as triplets. 

The fact that a new notation had to be invented to express triplets already suggests that they cannot be expressed by standard values. This is in fact so. But why? Many of you mathematicians might already be anticipating the answer at this point, but I certainly did not before taking up mathematics and, to be honest, none of my music teachers could explain to me why you would never be able to create a triplet no matter how small you made the standard values. So the question I intend to answer in a second is: 

How can we be sure that we will never be able to express the note value corresponding to a triplet by using (sums of) standard values?

The answer

Because of the uniqueness of prime factorisation. By the fundamental theorem of arithmetic, every positive integer has a unique prime factorisation. It’s quite obvious that adding together standard values always produces fractions over a power of two. So in order to express a triplet through (sums of) standard values, you would need natural numbers m, n (and, if you like, k =/= 0), so that 

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But 2 and 3 are both primes so the denominators (2^n and 3*k) will never be equal, no matter what numbers you choose for n and k. There is no natural number which can be expressed both as a power of two and as a multiple of three. And that’s why we need the triplet notation. 

Neat, huh?  

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Masquerade, Ekaterina Lukasheva || 2-8, 10, 30 units (7.50 x 7.50, square)
Instructions in Ekaterina Lukasheva’s Modular Origami Kaleidoscope

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