i want to be a mathematician

A story that may have relevance for others, or then again, maybe not:

When I was in college, about ten or so years ago, I was a history major. I wanted to learn to dance, so I joined a swing dance club on campus. To my surprise, this club had about twice as many men as women (in high school, the last time I’d tried dancing, the ratio had gone the other way–lots of girls, and boys only that you could drag by their ears).

But apparently, there had been some kind of word spread specifically to the STEM guys that dance was a way that they could meet girls.

So anyway. I joined the swing dance club, and met a few guys. And at one point, when socializing with the guys outside of dance class, one of them asked me what my research was on. (I had already established that I was an honors history student doing a thesis, just as he had established that he was an honors… I’m not sure if he was CS or Math, but it was one of those.)

So I gave him the thumbnail sketch of my research. Now, to be clear, an honors senior thesis, while nothing like what a graduate student would do, was still fairly in-depth. I had to translate primary sources from the original late-Classical Latin. (My professor said, basically, that while there were plenty of translations of my source material, that I’d only be able to comfortably trust them if I had at least made a stab at a translation of my own. And he was right.) And there was so much secondary material, often contradictory, that I had been carefully sorting through.

But I was able to sift it into a three-sentence summary of my senior thesis work, you know, as one does.

So I gave him that summary, and then asked–since he was also an undergraduate senior doing an honors thesis–what his research was on.

“Oh,” he said, “you wouldn’t understand it.”

Reader, I went home in a frothing rage. Because I had thought we were playing one game–a game of ‘let’s talk about what we’re passionate about!’– and he had been playing another game, which was, one-upsmanship. I had done my best to give a basically understandable brief of my research–and he had used that against me. As if my research, my painstaking translation, my digging through archives and ILLs of esoteric works, my reading of ten thousand articles in Speculum (yes, the pre-eminent medievalist journal in North America is called Speculum, I’m sorry, it’s hilarious/sad but also true), and then my effort to sum it up for him, was nothing. Because his research into some kind of algorithm or other was just too complex for my tiny brain to conceive of. Because I just couldn’t possibly understand his work.

Now, the important note here is that the person I went home to was my senior year roommate. She was a graduate student–normally undergrads and graduate students couldn’t be roommates, but we’d been friends for years, and the tenured faculty-in-residence used his powers for good and permitted us to be roommates that year. Anyway. My senior year roommate was basically… in retrospect I think possibly an avatar of Athena. She was six feet tall, blonde, attractive in a muscular athletic way, a rock climber and racquetball player, sweet but sharp, extremely socially awkward, exceptionally kind even when it cost her to be kind, and an incredibly brilliant computer science major who spent most of her time working on extremely complicated mathematical algorithms. (Yes, I was a little in love with her, why do you ask? But she was as straight as a length of rope, and is now happily married, and so am I, so it worked out.)

(Still, yes, she is my mental image of Athena, to this day.)

Anyway, I came home in a frothing rage to my roommate, the Athena avatar. And I said, “He made me feel like such an idiot, that I could sum up my research to him but his research was just too smart for stupid little me.”

And she shut her book, and smiled at me, with her dark eyes and her high cheekbones and her bright hair, and said, “If he can’t explain his research to you, then he’s not nearly as smart as he thinks he is.”

Now I hesitated, because I’d be in college long enough to have sort of bought into the ridiculous idea that if you couldn’t dazzle them with your brilliance, you should baffle them with your bullshit. But she said, “Look, I’ve been doing work on computer science algorithms that have significantly complicated mathematical underpinnings. What do I do?”

And I said, “Genetic algorithms–that is, self-optimizing algorithms–for prioritization, specifically for scheduling.”

“Right,” she said. “You couldn’t code them because you’re not a computer scientist or a mathematician. But you can understand what I do. If someone can’t explain it like that, it isn’t a problem with you as a person. It’s a problem with them. They either don’t understand it as well as they think they do–or they want to make you feel inferior. And neither is a positive thing.”

So. There.

If you are looking into something and have a question, and someone treats you like an idiot for not understanding right away… here is what I have to say: maybe it isn’t you who is the idiot.

Survivorship Bias

I have posted about survivorship bias and how it affects your career choices: how a Hollywood actor giving the classic “follow your dreams and never give up” line is bad advice and is pure survivorship bias at work.

When I read up on the wikipedia page, I encountered an interesting story:

During WWII the US  Air Force wanted to minimize bomber losses to enemy fire. The Center for Naval Analyses ran a research on where bombers tend to get hit with the explicit aim of enforcing the parts of the airframe that is most likely to receive incoming fire. This is what they came up with:


So, they said: the red dots are where bombers are most likely to be hit, so put some more armor on those parts to make the bombers more resilient. That looked like a logical conclusion, until Abraham Wald - a mathematician - started asking questions: 

- how did you obtain that data?
- well, we looked at every bomber returning from a raid, marked the damages on the airframe on a sheet and collected the sheets from all allied air bases over months. What you see is the result of hundreds of those sheets.
- and your conclusion?
- well, the red dots are where the bombers were hit. So let’s enforce those parts because they are most exposed to enemy fire. 
- no. the red dots are where a bomber can take a hit and return. The bombers that took a hit to the ailerons, the engines or the cockpit never made it home. That’s why they are absent in your data. The blank spots are exactly where you have to enforce the airframe, so those bombers can return.

This is survivorship bias. You only see a subset of the outcomes. The ones that made it far enough to be visible. Look out for absence of data. Sometimes they tell a story of their own.

BTW: You can see the result of this research today. This is the exact reason the A-10 has the pilot sitting in a titanium armor bathtub and has it’s engines placed high and shielded.

Hey everyone! So sorry that I haven’t been very active recently, been doing some really exciting work on my thesis, and been loaded up with assignments (and battling quite a bad patch mental health wise). Started this morning off with some astrophysics, and some caffeine. On another note, it’s my birthday tomorrow, and all I really want is a research grant … 😂

Sometimes I don’t think the people who constantly berate math understand how discouraging it is as a mathematician to constantly hear people mock your passion. Like any passionate person, I want to share my passion with others and tell them about the exciting thing I’m working on, but I can’t even open my mouth about math without someone ranting about how much “math sucks!”.

I’m trying to be passionate when all I hear is “Math is so boring!” “No one uses algebra!” “Screw math and anyone who enjoys it!” “As an artist, I naturally hate math!” (I’m an artist too, actually) 

Do people not realize how much it starts to wear on you? I’ve honestly considered dropping math so I wouldn’t have to deal with the stereotype that I’m uncreative and hate art and am practically the devil in the eyes of some people.

an analytic approach to proving the nikiforov theorem

so a little while back i was briefly contemplating the mathematicians au of yuri on ice (why), and today it came back with a vengeance and hit me in the face. believe me, i deeply regret all the life choices that have led me to this place.

  • victor nikiforov is a rising star in russian mathematics, particularly known for his off-beat approach to familiar problems and a certain elegance that’s unmistakable. at sixteen he gets invited to a young mathematicians conference in sofia, where he gives a talk about certain properties of the elliptic curve.
  • some weeks later, yuuko, who’s been sharing little puzzles and problems with yuuri for as long as he can remember, finds him with a handful of papers printed from arxiv and says, “look.”
  • it’s the first time yuuri looks at a chain of logic, ruthlessly solid from beginning to end, and feels that certainty all the way through.
  • yuuri presses his fingers to the “victor nikiforov” printed primly under the title and thinks, i want to solve a problem with him. one day.

Keep reading

When I first joined the fandom I can never understand why kidlock au always involves John being the same age as Sherlock? Like maybe it’s just me but I really love their age difference and it’s even more obvious when they’re still kids. Like imagine Sherlock at age 5 and he’s in kindergarten and John is maybe 10 and he’s babysitting for Sherlock and Sherlock is silently reading a book so John thought he’ll just do homework while waiting but then later notices lil Sherlock is beside him and looking at his homework and pointing to John’s answers and saying “that’s wrong, I can teach you though. My mom’s a mathematician and she taught me lots of things” and John just stares in awe at this tiny lil human who still has that chubby baby cheeks offering to teach him 5th grade Maths. John knew at that point that Sherlock was no ordinary kid. But later when Sherlock wanted tea, he asked John to make it for him so John asks “you can do difficult math questions but you can’t make tea?” And Sherlock’s answer is “I understand the technical steps to making tea but….. I can’t reach the cups” and he looks away shyly as if embarrassed by his short height compared to John. And John just finds it adorable that Sherlock might be a genius but he’s still a kid in the end

Love Is... (Peter Parker)

Originally posted by septodragon


Pairing: Peter Parker x Reader
Warning: None
Summary: The Reader recieves a balloon and letter from a secret admirer on Valentine’s day at school due to the annual fundraiser only to find out the letter is from her best friend
Author: Dizzy
A/N: A lovely little Valentine’s day fic about the always cute Peter Parker.

Masterlist Request a Prompt

Y/n sighed as she chewed on the end of her pen, surrounded by red and pink, chatter and the silly cards that were held in the hands of her classmates. Y/n hated Valentine’s day.

It wasn’t that Y/n hated the holiday because she never celebrated it with a special someone, it was that she hated everyone’s overwhelming desire to celebrate a holiday designed to increase card sales.

“Earth to Y/n.” Peter said with a laugh, waving a hand in front of Y/n’s face.

“What is it, Peter? You finally gonna talk to Liz for once?” Y/n glanced over at the boy seated next to her. “Ya know, like you say you will every Valentine’s day?”

It wasn’t just that Y/n was annoyed by the concept of Valentine’s day, but the fact that every year, Peter Parker, the boy she had been in love with since the sixth grade, always claimed he would ask out the girl he had been lusting over for just as long as Y/n had loved him.

“Pfft. What? Me, talking to Liz? Nah, not this year.” Peter replied, leaning back in his chair. “No, this year, this year I’m gonna do something great for the person I really like.”

“What person?” Y/n turned to look into Peter’s eyes.

“I’m not telling.” Peter stated firmly. “You’d ruin my surprise.”

Y/n gasped dramatically and threw a hand onto her chest.

“Me? Ruin a surprise? Oh, I would never.”

“Oh, right, like you didn’t ruin Aunt May’s surprise party for me.”

“It’s not my fault you asked if she was throwing a party for you!”

Peter rolled his eyes as a smile stretched across his face and he argued. “You weren’t supposed to answer!”

“Well, sorry of you’re my best friend who I tell everything to!”

As Peter opened his mouth to argue with the girl, the classroom door opened and a student walked in happily, a balloon and card in hand.

“Special delivery for Y/n L/n!” They chirped as they walked towards her. “It’s really cute and from a special someone.”

Y/n took the balloon and card cautiously, muttering a thank you as she glanced at Peter, who waggled his eyebrows at her.

“What does the card say?” Peter asked.

Y/n gave him a look. “Calm your tits, Parker, I haven’t opened it yet.”

Y/n opened the card, her hands shaking as she glanced over at Peter, a nervous expression on her face. Y/n was embarrassed beyond belief because not only did she get something from a “special someone”, but she also didn’t even know she had one.

Dear Y/n,

I love you like kings love queens
Like a gay geneticist loves designer genes [jeans]
I need you like New Orleans needs a drought
Like Hitler’s father needed to learn to pull out
And I want you, yeah
Like a lawyer-slash-mathematician wants some kind of proof
And I want you, yeah
Like JFK wanted
A car with a roof

Because love is taking that dive
Then getting really comfortable and peeing in the pool
And love is a real-life porn
Minus all the stuff that makes porn cool

And love is a homeless guy, searching for treasure in the middle of the rain and
Finding a bag of gold coins and slowly finding out they’re all filled with chocolate and
Even though he’s heart broken, he can’t complain cause he was hungry in the first place.

Love,

You know who.” Y/n laughed as she read the note. “First, I love whoever wrote this cause they quoted my favorite comedian and second, I wish they wouldn’t be such a pussy ass bitch and tell me who they are.”

“Um, Y/n?”

“Yeah, Peter?”

“I’m the pussy ass bitch you’re talking about.”

“Petey, you have to be joking.” Y/n said, but when Peter’s face didn’t change from red to it’s normal hue, Y/n knew it was true. “Oh, shit, you’re not.”

“It’s cool if you don’t like me too, I mean, why would you-”

Y/n cut Peter off by throwing her arms around his neck and pressing a quick kiss to his cheek.

“I like you too, you dumbass.”

“Really?”

“Hell yeah, I love you like Dora loves Maps.”

“Like a Pope’s toilet loves holy craps?” Peter chuckled.

“Of course.”

“Thank god, cause I love you too.”

Y/n smiled widely, hugging Peter tight as she realized why everyone loved Valentine’s day.

stats 101 | jikook edition

I really didn’t want to do my actual math assignments (as always), but then I stumbled across a little problem while watching Kookmin World’s newest video. So like I believe every aspiring mathematician/statistician should, I decided use the power of numbers to solve some interesting questions in my spare time (well…my profs do great things like figuring out who’s cheating on their midterms simply by calculating probability but…I’m not there yet LOL). Thus, I decided to calculate the probability of Jimin and Jungkook’s fans appearing next to each three times in a row, just by chance. 

DISCLAIMER: I haven’t done counting problems in awhile so there may be a mistake. I tried to recheck with my notes but I could still be wrong with some of my intuition because I did this purely off the top of my head. If there is please let me know and I shall fix it promptly, but this is merely my way of trying to show how cool math is… Also, I’m not reeeaaallly doing this as a shipper, cause really it doesn’t mean anything that their fans are next to each other (except perhaps maybe there was some instinctive sense as to why they should be together), I just wanted to know the numbers, and perhaps you would too :)

also, please take a look at this it cooler than you think and may help you out with your homework in the future ;)

So. Hurr we go. 


SCENARIO 1: Fans are placed in a circle

So here, we want to know what the probability is that Jimin’s fan is next to Jungkook within this circle, completely by chance.  

Since this is a circle, and circles are pains in the asses to calculate permutation for, there are many different approaches. What I personally did was I defined a fixed point in the rearrangement:

where each circle represents a fan and the blue dot is a fan whose position never changes (because if it did I’d have to divide by two or something fancy and that’s too complicated).

Keep reading

william shakespeare’s son confronted his father one day to talk about something that had been on his mind for a while.
“dad,” the son began, “i need to tell you something.”
“go ahead,” william shakespeare replied.
“i - i don’t want to be a playwright. i want to be a mathematician.”
“but son!” his father exclaimed, “you were going to be a great playwright, and follow in my footsteps!”
“i’m sorry dad,” the son said solemnly, “but i write sines, not tragedies.”

I overheard one of the older ladies (in her 50s) at my flamenco lessons today say that “women have forgotten how to dance sensually, All this feminism, look what it’s done!” (she was being very serious)

I fought back the urge to tell her that gurl, being a feminist doesn’t mean that you can’t like pretty dresses, or love your makeup, or like how you look in a tight dress, or know how to shake that arse or jiggle those boobies, or dance sensually to the music.

Feminism doesn’t make women less feminine, or less sensual, or less anything. It’s about equality of the sexes, about paying women what they deserved to get paid, about letting them dress how they want to dress without judging whether their skirt is too long or too short, without slut shaming them or calling them prudes. Feminism is about telling men they’re no less of a man if it’s their wife who brings home the bacon, that they can be dancers and not be afraid of being called a “sissy”, that colours aren’t gender-coded, that a woman doesn’t have to dream of being a princess, that she can be a mathematician, a scientist, a lawyer, a judge… 

It’s not about women wanting or pretending to be men, or becoming more masculine. It’s about letting everyone be who they want to be, freely.

anonymous asked:

I love the Elsewhere University comic. It's so awesomely surreal and cool. And now I want to know every little detail. But mostly, what other opinions so the fae have about other majors? Math majors? Political Science? Education? What about law? I'm so intrigued by this!!

The Fae don’t really care about the majors that don’t directly involve them in some way, although mathematicians have over the years acquired a reputation as excellent tellers of unguessable riddles, and obviously law gives you an edge in striking deals and getting out of (or into) trouble. And I imagine they respect education majors, at least to some extent - bearers and spreaders of wisdom, you know? That could in the right light have some bard-like roots.

Hello. My name is Silena Beauregard And Charles Beckendorf was the star-crossed love of my life. Ours is an epic love story and I probably won’t be able to get more than a sentence out without disappearing into a puddle of tears. Like all real love stories, ours will die with us, as it should. You know, I’d kind of hoped that he’d be the one eulogizing me, because there is really no one else… Yeah, no, um… I’m not gonna talk about our love story, ‘cause I can’t. So instead I’m gonna talk about math. I’m not a mathematician, but I do know this: There are infinite numbers between zero and one. There’s point one, point one two, point one one two, and an infinite collection of others. Of course, there is a bigger set of infinite numbers between zero and two or between zero and a million. Some infinities are simply bigger than other infinities. You know, I want more numbers than I’m likely to get, and Gods, do I want more days for Beckendorf than what he got. But Charlie, my love, I can not tell you how thankful I am, for our little infinity. You gave me a forever, within the numbered days. And for that I am… I am eternally grateful. I love you so much.
—  Silena, The Last Olympian
3

PICKLE: argh, this just doesn’t make sense to me! how am i ever going to be able to do anything in life if i can’t solve an equation!?

PUDDING: deep breaths, bro. we will get you through this. it’s not like you want to be a mathematician anyway, is it?

PICKLE: no… i was actually thinking about trying out at the police academy?

PUMPKIN: i think you’d be great at that, actually. now we have our goal!

okay me @film​ makers, and cartoon artists and so on, wouldn’t it be way cooler to use advanced math when making movies about MATHEMATICIANS or cartoons about them, and shit or showing like WOW THIS PERSONS REALLY SMart!!!!!!!!!!!!!!!!!! instead of stuff you learn as a child. 

come on film makers come on cartoonists. THIS IS WHAT THE PEOPLE WANT. TRUST ME I’M A PEOPLE. I KNOW. GIVE US WHAT WE NEED. i swear this is important, LET THE PEOPLE KNOW THE TRUE DEPTH OF MATHEMATICS. as radical praxis. lmaaaoo

5

Reader x Klaus

Requested By Anon


“How’s you studying coming along?” Klaus chuckled when you thundered down the stairs and tore into your dinner as if you haven’t eaten for a week.

 

“Elijah likes to go on a bit.” You sighed and he chuckled, putting a finger to his lips as Elijah headed to see where you’d gone.

 

“I was wondering where you’d gotten to.” Elijah sighed and Klaus glanced between the two of you.

 

“She was attempting to escape your lecture, pity humans get hungry really, it interrupts you monologues.” Klaus teased and you had to hide the giggle that threatened to escape you.

Keep reading

L’Hopital Rule – interesting history

I always thought that the person that came up with was indeed very intelligent. From this you can imagine that I was a little shocked to find out that not L’Hopital found this rule, but Johann Bernoulli. It turns up that these two have met towards the end of 1691, when Bernoulli was just 24 and new in the mathematics world. In that time, L’Hopital was already a member of an important circle at the Congregation of the Oratory which contained many leading mathematicians and scientists of Paris. It turns up that L’Hopital observed the potential of Bernoulli and wanted to learn from him. Therefor, he employed Bernoulli to give him private lessons for a short period of time.

So far so good… Now the story gets to a controversial point. Some time in March 1694, L’Hopital sends a letter to Bernoulli with an incredible proposition:

“ I will be happy to give you a retainer of 300 pounds, beginning with the first of January of this year. … I promise shortly to increase this retainer, which I know is very modest, as soon as my affairs are somewhat straightened out. … I am not so unreasonable as to demand in return all of your time, but I will ask you to give me at intervals some hours of your time to work on what I request and also to communicate to me your discoveries, at the same time asking you not to disclose any of them to others. I ask you even not to send here to Mr Varignon or to others any copies of the writings you have left with me; if they are published, I will not be at all pleased. Answer me regarding all this … “

No copy of Bernoulli’s answer was found, but from other letters it is easy to observe that he accepted L’Hopital’s proposition. In another letter from 1695, Bernoulli writes:

“You have only to let me know your definite wishes, if I am to publish nothing more in my life, for I will follow them precisely and nothing more by me will be seen.”

At first glance I was quite shocked about it and felt that I was mislead and I was annoyed by the story. But if I think more about it, there is nothing wrong in this. Bernoulli accepted to be paid for his work, there is nothing wrong in that. I don’t feel 100% happy for this, but it was his choice and I am convinced that nowadays there are many scientists all over the world that discover incredible things, but we just know the company they work for. From this point of view I agree with Truesdell’s opinion about this story: 


“We should not judge L’Hôpital’s procedure too harshly. While perhaps financial necessity compelled Bernoulli to accept the arrangement initially, it continued after he had settled in his professorship at Groningen in 1695. L’Hôpital, being a noblemen, was accustomed to pay for the services of others, and what he did would not have been considered wrong had Bernoulli been a politician, a lawyer, perhaps even an architect. Certainly it was nothing for L’Hôpital to be proud of. Careful examination of the letters in which L’Hôpital reported his mathematical progress to Leibniz and Huygens shows that with one or two possible exceptions L’Hôpital did not lie, but rather referred to Bernoulli in a condescending tone without acknowledging any debt whatever to him and in matters of provenance wrote in such a way as to suggest without actually asserting. “

What do you think about this story? Do you agree with Truesdell’s opinion or do you think we should blame L’Hopital? 

Random thoughts on common core math.

I’m now at an age where a lot of my friends have kids who are in school.  And a lot of them complain on the Internet about how stupid common core math is, so I just had a few random thoughts I wanted to put out into the Internet.

1) The US has fallen behind in math (and science) because our kids don’t understand math – they just memorize it.  Common core is a push to get kids to understand why they’re doing what they’re doing instead of just how to do it so that those same principles can be applied outside of Barbara has three bananas and Ken has seventeen apples blah blah blah…

2) You probably do “common core math” anyway whenever you deal with money.  If your bill is $9.47 and you give the cashier a $10 bill, you know what the change is, not because you figured out that 10.00 minus 9.47 is .53 by borrowing from the 1 in the tens place and making the ones-place a ten so you could subtract nine and then borrowing from the ones place to the tenths place and so forth.  That’s the way you would do it on paper, but you don’t have to because you automatically see the 9.47 as 9.50, being the closest reference point for easy mental math.  You’re going to get fifty cents back plus three pennies.  This is a popular example that gets passed around as evidence of how stupid common core is.

It’s badly worded, but the concept is there.  Every kid can memorize 8+5=13.  Common core is just testing your understanding of what you’ve done.  You’ve made ten and you have three left over.  It’s not the best example, but one awkward problem doesn’t negate the entire standard.

3) Most of the aversion to common core comes from parents who are embarrassed that they can’t “get it” immediately.  I can’t do my second-grader’s math so it must be stupid and useless as opposed to I can’t do my second-grader’s math because I’ve been doing it the same way for 40 years.  People in general have the tendency to look at something they don’t understand and either hate it or deem it worthless.  Don’t do that to your kid’s education.  Your struggle with common core isn’t a reflection on your intelligence.  Once you take yourself out of the equation (so to speak) and stop making it about you, you’d probably realize that most teachers are more than happy to sit with your child and you to explain concepts so you can help them at home.

4) Common core is kind of an odd term that’s misused.  It really refers to standards across a number of subjects that have been adopted by most of the states in the US.  There was a lot of fluctuation between the standards of one state and the standards of the next, so the goal is to get all American kids on the same page as well as make them more competitive in the global marketplace.  When you’re someone who looks at common core math and you “get it” immediately, but you still think it’s stupid because you can help your kid or sibling get the right answer with an “easier” method, you’re really just hurting them down the line.  You’re not preparing them for higher math concepts and it’ll be harder for them to go into math-based subjects in college.  We outsource that talent to other countries because we don’t give our kids the building blocks to really think through math.  Maybe your answer is “well my kid wants to be an English teacher so all this stress about math is dumb.”  And my response is “well maybe your kid would’ve wanted to be a mathematician instead if you had a more positive outlook on the subject.”

That’s all.  I might add some more later, but I just had a FB discussion with a few people who think common core math is the worst thing to happen to our educational system so I had some thoughts to jot down.  This pretty much says everything about why the system is the way it is:

Update with the times, sir.

March CAS Challenge Day 16- Scientist

I still haven’t seen Hidden Figures (I KNOWWWW! I’m The Literal Worst I want to see it SO bad) but I wanted to do a simmified Taraji P. Henson as Katherine Johnson. 

“Katherine Coleman Goble Johnson was born August 26, 1918. She is an African-American physicist and mathematician who made contributions to the United States’ aeronautics and space programs at NASA. She was known for accuracy in computerized celestial navigation, and she conducted technical work at NASA that spanned decades. During this time, she calculated the trajectories, launch windows, and emergency back-up return paths for many flights from Project Mercury, including the early NASA missions of John Glenn and Alan Shepard, and the 1969 Apollo 11 flight to the Moon, through the Space Shuttle program. Her calculations were critical to the success of these missions. 

In 2015, Katherine received the Presidential Medal of Freedom.”