The Six Degrees of Leibniz
I submit that on Wikipedia, you can get from the page of any mathematician to Leibniz’ page in 6 clicks or less (even without clicking through the “Mathematician” or “Mathematics” links that show up in like the first sentence of every mathematician’s Wiki page).
Fun Examples for Fun
Starting mathematician: George Polya
Click 1: Probability Theory
Click 2: Probability
Click 3: Christiaan Huygens
Click 4: Gottfried Leibniz
Starting mathematician: George Boole
Click 1: Differential Equation
Click 2: Derivative
Click 3: Gottfried Leibniz
Starting mathematician: John Venn
Click 1: Set Theory
Click 2: Principia Mathematica
Click 3: Philosophiæ Naturalis Principia Mathematica
Click 4: Gottfried Leibniz
Starting mathematician: Sewall Wright
Click 1: Philosophy
Click 2: Gottfried Leibniz
Starting mathematician: Henri Poincaré
Click 1: Bernhard Riemann
Click 2: Riemann Integral
Click 3: Integral
Click 4: Gottfried Leibniz
The Cowardly Average-Sized Toaster Oven is the Brave Little Toaster’s Forgotten Half-Brother
Woah, Coldplay. Woah.
Crank this up and sit in a dark room.
This reminds me of Muse’s Madness in the “this is by one of my favorite groups but doesn’t sound at all like them but it’s even more magnificent because of that” sense.
Apparently there are a lot of mixed feelings about this song, but I really like it. Give it a listen and decide for yourself.
Also: it’s Anosmia Awareness Day today! Go hug a non-smeller and check out this blog run by someone who has anosmia.
Remmus
I get to teach in the summer!!
And what’s better: it’s not the 7:30 AM section!!! It’s the totally reasonable and much more Claudia-friendly 11:30 AM section, which runs for two hours on M/T/W/Th and starts right after spring semester is done.
WOO!!!
I still don’t have any concrete plans past that point—which SUCKS and I hate it—but I’m glad that I at least get to teach in the summer.
Also, this:
Cheez Mentality
Well that was a hell of a dream.
It’s sometime during summer in the dream and I’m in my office on campus talking to a pair of Iranian dudes (I have no idea how I know they’re Iranian) and we’re talking and laughing and blah-blah-ing about all sorts of stuff. Then I look at my watch and realize that I have to go teach in 5 minutes.
The room I teach in is neither in Renfrew nor in the TLC but in some huge auditorium/stadium thing. Actually, now that I think about it, it looked more like a movie theatre without the big projector screen in front.
Anyway, I go in there and because I’m late the university decided to put a guest lecturer in my place. But he wasn’t really doing anything and was just kind of standing in the front of the room looking bewildered. There weren’t too many of us in there—maybe 20 or 30 people—and we were all just calmly sitting in the chairs.
Then, all of a sudden, everyone started freaking out. I think someone saw a pencil on the floor or something and that just sent everything into chaos for whatever reason. The substitute guy was still just standing in front watching all of this nonsense, so I started to move to the front of the classroom (movie theatre?) to try and help calm everyone down. I moved in super slow motion—you know how it is in dreams sometimes—and by the time I was up front, everyone had cooled off.
Then someone saw a Cheez-It and all hell broke loose again. Why? Apparently the Cheez-It was “immoral” and because it was in the room, everyone there was at risk of going to hell. This second freak-out was even louder and more panicked than the first—people were like “oh my god, I’m never going to touch a Cheez-It again! I don’t want to go to hell! I repent! I repent! I need to get out of this room!”
Then, finally, the substitute guy just went off on everyone. He started yelling “SHUT UP! SHUT UP! You are NOT mindless sheep! You will NOT let ONE CHEEZ-IT dictate your life! You’re COLLEGE STUDENTS, for god’s sake! Don’t let this one Cheez-It ruin all the other Cheez-Its in your life!”
As he was talking, I had gone to the chalkboard that had magically appeared in the front of the room and had written “One Cheez-It = One Mistake” with a big copyright symbol behind it, and was super proud of this apparently brilliant phrase.
Then my alarm went off and I woke up.
What the hell.
Hey baby, let me expand your series
This is a really interesting read.
I am someone who has very little mathematical intuition. I mean, I think some people just have a knack for thinking about math and “math things” and for piecing bits of different types of math together. I don’t. Like, even at the most basic levels—simplifying factorial expressions, the logic behind summation rules, all that stuff. I mean, I know I’m a total idiot, but still. At least with other topics I have some degree of intuition.
And I’ve always wondered if others who actually have a more intuitive understanding of math—or at least have delved into it far enough—see advanced math (or math in general) in a different way.
Anyway. Interesting read, check it out.
brb, sleeping furiously
HELLO PEOPLE!
So today is the closing ceremony of the 2014 Winter Olympics. SADNESS!
This year’s Olympics prompted me to do a little stats project: specifically, I wanted to see if there was any sort of correlation between latitude and the quantity of medals earned in both the summer and winter games.
Now before I show you the results/plots, yes, I know that there are a lot of other factors aside from latitude that affect countries medaling in the games (wealth, government, national/international politics, geography, etc.). In fact, I’m sure that several such factors correlate somewhat with latitude on their own—for example, industrialized nations send waaaay more athletes than less-industrialized/developing nations, and many nations that are considered industrialized just happen to be at higher latitudes…that’s just one example. So take all of this nonsense with a grain of salt, m’kay?
Anyway.
Procedure:
I denoted a country’s latitude by the latitude of their capital city. For example, the US is at latitude 38º53’ N, ‘cause that’s where Washington, D.C. is. I realize that this method of measuring latitude is not so accurate for some countries whose capitals are either at the extreme south or extreme north of the country, but I didn’t want to go by, say, the “average” latitude of a country ‘cause then I would have never finished this freaking thing. So capital latitude it was.
I then consulted the almighty Wikipedia for a table of the number of medals won by country in both the summer and winter games (and within both, the total number of gold, solver, and bronze). So medal counts + latitude = my dataset!
Analyses:
First things first: correlations!
- Correlation between latitude and the number of medals won overall: 0.374
- Correlation between latitude and the number of medals won in the summer games: 0.353
- Correlation between latitude and the number of medals won in the winter games: 0.393
The above correlations do not take into account the fact that some countries have participated in almost every Olympic games (like the US) and some have participated in like four or five of them. So I made a new set of variables that took that into account. I took the ratio of the number of medals won to the number of games participated in (so they’re kind of a “how many medals per Olympics” set of variables). I did this for the summer and winter games separately as well as “overall.” The “adjusted” correlations were:
- Correlation between latitude and the number of medals won overall: 0.397
- Correlation between latitude and the number of medals won in the summer games: 0.390
- Correlation between latitude and the number of medals won in the winter games: 0.411
So not too much of a change, especially for the winter games.
(One other correlation to note when looking at the above results: the correlation between latitude and the total number of games participated in is 0.609)
Now let’s look at some graphs!
This first one shows medal count by latitude, split by type (gold, silver, bronze) for the summer games:
(Note that countries who haven’t won a medal are not plotted; those values that look like “zero” are actually indicating that one medal of that respective color has been won.)
(Another note: these are “absolute” latitudes, meaning that I’m not distinguishing between degrees north vs. degrees south; I’m really just interested in how far away from the equator countries are.)
This second one shows medal count by latitude, split by type (gold, silver, bronze) for the winter games:
Also, I didn’t catch this until after I made the graphs (and am too lazy to go back and fix it), but notice the difference in the scales of the y-axes for summer vs. winter.
Anyway.
Cool, huh?
Zounds
I haven’t given you any new music in 2014 yet, have I?
I’LL FIX IT!
(Waaaaaaaay better than the original)
Book Review: Brave New World (Huxley)
Have I read this before: Indeed (one of these days I’ll have the courage to go to the library and face my enormous fees). Back in high school, I believe. Maybe junior high?
Review: My memory of this book was actually pretty accurate—which is rare for me. Anyway, I’ve always really liked books that explore an altered society, and you can’t get much more altered than Brave New World (well, actually, that’s debatable on several levels). I think another thing I really like about this book is the mutability of the main characters. Bernard isn’t constantly against society; in fact, once he starts gaining respect for his dealings with John, he starts to really enjoy being an Alpha-Plus. Lenina seems like a “normal” member of society until she starts expressing actual feelings toward John. And even John lapses in and out of his self-imposed set of morals due to the pressure he’s feeling being in the new society.
Favorite part: Chapter 3. I love the intermixing snippets of Lenina and Fanny, Mustapha Mond and the students, Bernard, and the explanation of the Alphas/Betas/Gammas/Deltas/Epsilons.
Rating: 6/10
Dutch
As of today, the Netherlands has 22 medals. 21 of them are from speed skating events.
So the obvious question: why are they so freaking good at speed skating?
According to a few articles I’ve read on the subject, not only are they tall (average height is above 6 feet), which allows them to take very long strides, but speed skating is very much a part of their culture. A lot of the country’s top athletes go into speed skating rather than anything else (aside from soccer) and there are 17 training ovals for speed skaters throughout the country (the US has two).
There are 7 commercial speed skating teams in the Netherlands with around 60 professionals total, and when the Dutch Olympic trials are held, the speed skating portion is said to be the most competitive in the world because so many Dutch people are good skaters.
So it sounds like speed skating is just something the Dutch do, and clearly, they do it well.
Stories?
Woah, this actually looks really cool.
From the Wiki page: Ren’Py supports nearly all features that a visual novel might reasonably be expected to have, including branching stories, save file systems, rollback to previous points in the story, a variety of scene transitions and so on. Ren’Py scripts have a screenplay-like syntax, and can additionally include blocks of Python code to allow advanced users to add new features of their own.
Miiiiight have to download this and try it out.
Zz
So this video quality sucks because my camera—the thing I usually take video with—is out of batteries and all I’ve got is my iPod, but this is a shot of one of the fluorescent light tubes in my office.
I thiiiiiink it’s starting to die on me. But if it dies, it’s going out in style!
Hey Foolios
I just wanted to apologize for my blog posts being really sucky as of late (and also for my uploading a slew of them like once a month). I don’t feel like going into the details right now (just because they’re long and involved), but I’m currently lacking any long-term plans past summer due to several factors…and that really stresses me out. Not having at least a two-year plan is really, really difficult for me, so I’ve pretty much been a little ball of anxiety for the past month and a half or so and thus haven’t been feeling particularly humorous/creative/fun/entertaining—hence the crap posts.
I’m trying to just fake it through No Plan Land right now, but it’s hard. Please bear with (or unsubscribe if you want, I won’t be offended or anything, haha).
BYE!
Book Review: Candide (Voltaire)
Have I read this before: Yes! First time was in Literature of Western Civilization, the class that first got me interested in philosophy. I’ve read it many times since, but it’s been awhile since I last read it.
Review: *dramatic sigh* THIS FREAKING LITTLE NOVELLA. I’m so conflicted. On the one hand, it’s probably the best bit of satire I’ve ever read (and is hilarious and tragic and disturbing all at the same time). On the other hand, one of the major things being parodied is Leibniz’ optimism and Leibniz himself—you can’t tell me there aren’t personal jabs in there, ‘CAUSE THERE ARE! [see the last line of chapter 28], and that makes me sad. Especially since his philosophy is definitely oversimplified and entirely not what he meant “the best of all possible worlds” to be.
But Voltaire is Voltaire, so what can we do?
Favorite part: It’s hard to pick one since it’s so short and everything really flows together. There are some great lines, though:
- Candide, trembling like a philosopher, hid himself as best he could during this heroic carnage.
- Candide said to himself, “If this is the best of all possible worlds, what are the others like?”
- “What’s optimism?” asked Cacambo.
“Alas,” said Candide, “it’s a mania for insisting that everything is all right when everything is going wrong.”
Book Review: a Tree Grows in Brooklyn (Smith)
Have I read this before: NO! I found a copy at Goodwill for like 99 cents, so I bought it.
Review: I’m usually not a huge fan of coming-of-age stories, but this one was actually quite enjoyable. The book follows Francie Nolan’s growing up in Brooklyn in the early 1900s, but gives a very comprehensive non-chronological-order history of her family as well. I think one of the reasons I’m not a coming-of-age fan is because in most of those types of stories I’ve read, it’s really quite difficult to see the change in the main character (assuming they’re the one that’s coming of age). In this book, however, it’s very clear when Francie starts seeing a change in the way she views the world and when she becomes mature enough to acknowledge that she’s viewing the world differently than she had. And this is all told in a very engaging tone, too, so it was fun to read.
Favorite part: I like this recurring idea of loving/being loved/being needed that Francie keeps coming back to over and over as she grows up. Like at the end of chapter 39:
“Maybe,” thought Francie, “she doesn’t love me as much as she loves Neeley. But she needs me more than she needs him and I guess being needed is almost as good as being loved. Maybe better.”
Or at the end of chapter 53:
“No! I don’t want to need anybody. I want someone to need me…I want someone to need me.”
A very relatable feeling.
Rating: 6/10
More Figure Skating
Aw, this was so sad to watch.
I hope he didn’t cause any more permanent damage to his back during the team skates.
Edit (2/22): okay, wow, so it sounds like he needs back surgery again because one of the screws already in his spine snapped. Ouch.
Ouchie
I’m 10 days into the “No Health Insurance Zone” and what do I do? Practically amputate my toe.
Story:
I have an old science beaker that has been in my possession for like 6 years now. When I was up in Vancouver I just put a bunch of fake flowers in it, but since I’ve been back in Moscow my drive to decorate the basement has been practically zero, so the beaker’s been sitting on my bookshelf.
Well, at some point it got broken. And by “broken” I mean that something must have rammed into it because a large chunk of glass is now missing from the side. The general structure is still okay, though, so I just kept it on the shelf.
A couple weeks ago I moved it off the shelf (for some reason, who knows what) and set it on the floor by the bookshelf. Because I’m me, I haven’t moved it back.
So tonight I was screwing around doing twirls and stuff in the living room (don’t ask) and I manage to ram my pinky toe riiiiight into the jagged glass. And you know how you can peel an apple all the way around with a peeler? That’s pretty much what the glass did to my toe.
So now I’ve got like 5 bandages on it and have got it (somewhat) elevated. I think the bleeding’s pretty much stopped, but it’ll be just my luck to jam it into the TV stand or something.
I kinda mashed two surveys together
1. What would you pick as a major, if you could go back to college and do it again?
I did go back to college and do it again (or am doing it again, I guess). I picked math.
2. Who is the one celebrity with whom you would most like to have an in-depth conversation?
Leibniz. He’s a celebrity. YES HE IS, SHUT UP AND LET ME LIVE IN MY FANTASY WORLD.
3. If you could make a living doing ANYthing, what would that be?
Doing statistics, teaching statistics, writing, blogging, raving about Leibniz.
4. What’s your all-time very favorite dessert?
Peanut M&Ms. Yup, I’m classy like that.
5. How many pairs of jeans do you own?
Jeans are for squares.
(I’m a triangle)
6. What is your favorite flower, and why?
I’m not much of a flower person. I can’t smell them so that kind of takes away some of their appeal. Sunflowers are badass, though.
7. What book has most changed your life?
Candide, ‘cause it got me interested in philosophy, which took my education in a very different direction.
It also introduced me to Leibniz. There’s not too much else I can say about that. ;)
8. What is your least favorite vegetable? Is there any way you can be persuaded to eat it?
Celery is the most disgusting thing ever (texture-wise). You can eat a stick of it with a whole jar of peanut butter and it will still be terrible.
9. If you could take a nonstop first class flight to any destination, where would you pick to land?
Either Antarctica (South Pole please?) or Hanover (Leibniz’ archives, please?)
10. If your 15 minutes of fame included a stint on American Idol, what song would be your trademark solo?
Well if we go off of what I sang in Rock Band, it would either be Peace of Mind or Maps.
11. If you could pick one former friend (who has remained elusive in this wild Facebook world) to reunite with, who would you unearth?
Anastasia!
12. What period of history is your favorite to read about?
The European Enlightenment!!!!!
13. What is your favorite genre of fiction?
Historical’s always good.
14. Do you choose a book by its cover?
I choose a book by whether it’s on my list or not.
15. Where do you do most of your reading?
At the rec center on the recumbent bike.
16. Without looking, guess about how many books are in your TBR pile. Now look. Were you right?
Well, since I just recently re-started my 200 Books list, I’d say there are 195 left. Ah, I was two off. There are 193 left.
17. How many movies on your TBW list?
I have no such list.
18. What’s your favorite genre of movie?
“Horribly Scientifically Inaccurate Disaster Movie”
19. Do you still go to see movies in the theater?
Nope.
20. You have $10,000 and no strings or obligations for one full day. Where do you go and what do you do?
Get up super early and go to Vancouver with my mom!
21. How many songs on your mp3 player?
2,000-something. Quite a few.
22. What comes next? Monster, monkey, helicopter…
Heliosphere.
Internettin’
Haha, oh, Sound Cloud.
Do you remember this? DO YOU REMEMBER THE NIGHTMARES?!
I saw this video quite a few years ago and now this song always reminds me of Vancouver:
Another awesome Rage Quit I don’t think I’ve ever posted on here.
In this blog: Claudia Wordles Stuff
I’M SO FREAKING BORED
I WORDLED “ODOR”
I WORDLED WIKIPEDIA’S “LEIBNIZ” PAGE
I WORDLED MY THESIS
I WORDLED THE LYRICS TO INTERACTIVE’S “DILDO”
I THINK I NEED TO SLEEP
COPERNICUS, NO!
THEY
PLAYED
TROLOLO
IN THE OPENING CEREMONY
RUSSIA I LOVE YOU
But seriously (and my mom can confirm this): a couple weeks ago, I suggested how awesome it would be if one of the figure skaters chose to stake to Trololo.
And then they PUT IT IN THE OPENING CEREMONY (at least for like 5 seconds)
I laughed so hard. Why isn’t the internet freaking out about this?
(I’m freaking out about this)
GAMES
There is no better way to start an Olympic games than with this man:
Evgeni Plushenko!!!
And that was a damn good program he gave us tonight, holy crap.
Have some more pics:
The fact that I was in the same city as him–for a few days, at least–makes me super happy.
(I love him sorry)
In other news (and the reason that this blog is password protected), my STAT 452 class is really starting to suck. I definitely need to rant about this—which will happen later when I have more time and am not absorbed in watching figure skating—but I just needed to mention it somewhere before my head explodes from anger.
TWSB: C is for Complex Number, That’s Good Enough for Me
Well this is one of the coolest things I’ve ever learned about.
So I’m in Complex Variables this semester, right? Today we talked about how to take limits of complex numbers as well as the closely related topic of infinity.
I’m assuming most people who read this regularly (or just happen to stumble upon it) know at least a little about infinity in the context of real numbers. Mainly, if we represent the reals on a number line, we have a direction that goes off towards negative infinity and a direction that goes off to positive infinity. But does this translate to complex numbers?
Well, not really. When we deal with complex numbers, we deal with the complex plane: a 2-D space with one axis representing the real part of a number and the other axis representing the imaginary part of a number. That is, one way we can think of a complex number is as a set of coordinates on the complex plane. For example, if I had the number z = 3 + i2, I could represent it with the coordinates (3,2) and plot it like this:
Since we’re now dealing with a plane, we actually have infinitely many directions that can be thought of as infinity—basically, any direction out from the origin.
So how do we define infinity in the complex plane to allow us to, among other things, take limits involving the point at infinity?
Answer: The Riemann sphere!
The Riemann sphere is a stereographic projection of the complex plane onto the unit sphere at the point (0,0,1). Piccy from Wiki:
So what does this do? Well, for each point A on the complex plane, there exists a line that intersects both the point A and the north pole of the sphere. This line hits the sphere itself at α, point unique to the position of point A in the complex plane—that’s how the plane is “mapped” to the sphere and that unique mapping point is called the “projection” of point A.
The further out you go on the complex plane—that is, the further away from the sphere you go, those projection points get closer and closer to the north pole itself. However, no point is projected directly onto the north pole. So we can think of the north pole as being the image of all the points in the complex plane that are at infinity.
Isn’t that cool? It’s a way to reduce an “infinite number of infinities” to a single point.
We didn’t have time to talk about how we’re going to use it yet, but just that idea is super cool and required a blog post.
Eigenblogger 