Shared Joy is Twice the Joy, Shared Pain is Half the Pain

Posts tagged “math

My Newest Addiction

When I was a kid, I always ate everything on my plate one thing at a time. I wasn’t one of those kids who threw a fit if my peas touched my potatoes, but I always ate all my peas and then all my potatoes. Or all my potatoes and then all my peas, depending on if I was facing the worst first and saving the best for last, or visa versa.

I no longer eat all my food one item at a time, but I still have an obsession not too different. Instead of eating one thing at a time, I absorb things all at once. I might go on a Tess Garritson whim, and read all of her books in a few weeks. Or I might get really obsessed with the variety of games that on the surface require nothing more than a swiping finger and the ability to add 2+2 or 3+3. I’m talking, of course, of Threes and 2048, and all the subsequent versions that have boomed in popularity over the last month or so.

*In the interest of fairness to the creators, I will state that Threes existed first, and 2048 is a version of it. Actually, 2048 is a version of 1024, which I haven’t played; 1024 is a version of Threes. I will also state that the only official version of Threes is available as an app for $1.99. An unofficial version is here.

When you have a facebook wall full of math and science nerds from around the country, it is hard to not notice that a nerdy game is blowing up. And so you wander over to the website to see what the fuss is all about, and two hours later you’ve downloaded the game onto your iPad because you absolutely, positively, must have this game for your 45 minute commute every day. It has absolutely nothing to do with the desire to beat Madeline’s record, which has to this day proved impossible.

At this point, you probably want to know what exactly it is that I’m talking about. Below is the link to play, but I hope you’ll finish reading before you just go off and play. Because once you start playing, you will NEVER COME BACK. Before clicking the link, I warn you to set a timer or some other way to prevent yourself from falling into the dark hole of a time suck that 2048 is. Because it is a time sink. You think, “oh! I was so close! Just one more game and I’ll get there,” and then, once you do, “hm! that wasn’t so hard. I wonder if I can get to 4096 too…?” Apparently, I am not the only person who feels this way. Buzzfeed is very rarely good for anything, but here it gives an accurate impression of the mind of a 2048-player. Since you want to play anyway, here you go.

Threes and 2048 as fall into the only category of online games I truly enjoy – those that are a) incredibly simple to learn, b) easy to play and c) almost impossible to win. The premise is simple: combine like numbers to get to the highest numbers you can.


Threes starts with blue 1 and red 2 tiles. Combine them, and 1+2=3 (The 3 tiles are white, as are all the larger tiles). Each time you move, the tiles collectively move one square in that direction. You can see the next tile coming, but you don’t know exactly where it will show up. You do know, however, that it will come from the direction you’re swiping. So, if you move left to right, the next tile will show up somewhere in the left-most column. Usually, the new tile is a 1, 2, or 3, but sometimes larger tiles show up too. These are signified by a white tile with a “+” on them. Higher tiles become more and more adorable monsters, egging you on to find out what their elder brethren look like.

The furthest I’ve ever gotten was to 768, which apparently has been reached by less than 5% of the players of Threes. My next goal – 1536 – would put me in the 99.82% percentile. (See Threes’ official infographic)

The key to making progress in Threes is to keep an eye on what the next card is, in order consider both the moves you want to make on the board AND the next move you can make with your next card.


2048, while similar, is different. For one, you’re combining powers of two, not three. Like in Threes, you get the low tiles thrown at you – 2’s and 4’s. But unlike Threes, you’re never going to get a bigger tile added in; you’re always going to have to build up yourself. In 2048, the tiles go all the way to the end, so if you swipe left to right, all the tiles go all the way to the right, which means it is easier to combine multiple pairs into bigger numbers at once. On the other hand, you have no idea what number will show up next or where, because any empty spot is fair game.

To beat 2048, you need to set up a line of increasing tiles that you can combine. If you have a 1024 next to a 512 next to a 256 next to a 128 next to a 64 next to a 32 next to a 16 next to an 8 next to a 4, beating the game is just a matter of combining two 2’s and completing the trivial steps to win. But then, it asks you if you want to keep going.

My personal highest card is 4096, although I did have one game with a 4096 and a 2048, so I’m well on my way to the 8192 tile. I’ve got to get there if I want to beat Madeline.

The Offspring

Like any good game, 2048 has spawned dozens of fakes. Most of which are stupid, but hilarious, but some are fun, and some are impossibly difficult. My personal favorites:

1. The Tufts Theater version. Tufts is full of Computer Science people, and even the Theater department isn’t immune. So, when the make-your-own-2048 website became a thing, Artoun was kind enough to take pictures of Tufts Theater people and create our very own version. Fair warning: there are no numbers, so this is not a game you want to play necessarily unless you a) know people in Tufts Theater or b) enjoy randomly hitting the arrow keys. Also, you will not find me in any of the pictures. That is what happens when you live backstage…

2. The Nuclear Fusion version. This one, I’ll be honest, is a version I have yet to master. Because, just like Threes and 2048 are different and thus have different strategies, Fe[26] also plays by its own set of rules. Complete with frustrating 3Helium when you want 4Helium, and inconvenient decays. Can you fuse atoms together to make 56Iron?

Please please please don’t forget that you have a life! And go outside sometimes too…?

Happy Pi Day

That’s it. Also, this post was published at 1:59. Just saying.

Menger Sponges

Since Erin’s second son was born earlier this week, Congratulations are in order, and I can finally put this post, which I first wrote last summer, online. So, congratulations, Erin! Can’t wait to get to meet him. 🙂

Remember my circus quilt for my (then) to-be niece? Well, afterwards, I made her big brother Jacob a Menger sponge, which is basically a three-dimensional version of a Sierpinski carpet, which is one of my favorite fractals ever. Someday I’m going to make a quilt just like this one, from Anabeth Dollins:

Hers is 41.5″ square, but I think I’d make a full or queen sized quilt when I get around to this crazy endeavor. But I digress.

A fractal, for those of you who doesn’t know, is a series of iterations. They are mathematically and visually beautiful, and I’ve been obsessed since seventh grade, when I was first introduced. The Koch Snowflake, here on the left, begins with a simple equilateral triangle. Imagine pulling the center of each side out, to create a new triangle. Now you have a six pointed star, with twelve sides instead of three. If you repeat this process for all twelve sides, now you have 48 sides. If you continue this forever, you get the shape below, with an infinite perimeter but a finite area.

But back to the Menger sponge. I created just the first iteration of the sponge, and I used a tutorial found on Miss Gioia’s blog, here.


For Jacob’s sponge, I used fabrics out of the baby blanket scrap. The animals (monkey, lion, elephant, and turtle) are off the quilt backing, and the blues are from the balloons/balls/hoop on the front. I did alter the pattern Miss Gioia used to utilize all six blues and the four animals. It isn’t so hard though, as long you lay out the entire cube before you start pinning/sewing to make sure the pattern is right. Additionally, I sewed the edges slightly differently, to give the cube a bit more texture. When I first made Jacob his rocket ship quilt, he apparently loved Saturn’s rings because of their texture, so I figured I’d give him texture in this gift too!

Since the first one was so easy, I decided to make another one. Because why not? I had a sneaking suspicion Erin was pregnant, and wanted to make a fun but math-themed present for baby #2 that wasn’t a quilt. (Because her mom makes my quilts look like child’s play, which they basically are.) So I decided to make them a Menger cube as well. But this one was more fun and more crazy because it had seven cubes. A fractal, we already know, is repeated over and over again. So that’s what I did.

Let’s just say it was a long process. I started with the same sized pieces, just in a rainbow color scheme.


I sewed it all together, took some time to stick it on my head, and to have a minor fight against my project. (I won.)

I then repeated the process for six baby cubes. So tiny that my fingers barely fit inside to sew the inside seams together.


Can you find them?


They nestle conveniently into the big cube’s holes.


My mom thought I was crazy as I was making them, and I probably am. But all in all, it was good fun, and I can’t wait to see Erin’s two sons throwing Menger sponges at each other during playtime!

Classes! Classes? Classes.

Classes started on Monday, and I’m feeling (along with most people, I think) a little bit torn. For starters, I am ecstatic. I managed to create a schedule that I thoroughly love, and I’m really excited about all of my classes. But I’m also like “Wait, what?”, because I got used to having Czech classes all day every day, and they didn’t have 40-60 page reading assignments. So, classes. The reality of being a student, even if you’re a student on the other side of the world. Here we go!

I’m taking five classes: Czech Language Fast Track, Czech and Central European History, History of the Jews in Bohemia, Economics and Politics of the EU, and Czech Politics. Unsurprisingly, I’m taking a lot of politics-based courses, but I surprised myself by enrolling in two history courses as well. I’m not a huge history buff, but I really want to understand the history of the region I’m living in, as well as my own family history, so there you go. I’ll talk about each class in turn, but I’m excited for all of them. (more…)

String Staircase

My dad told me about this cool thing people once did at MIT. I don’t know if it actually happened or not (I have been unable to find proof on the interwebz), but regardless it is a super cool idea. The premise is to take a spiral staircase and turn it into a work of art with a few pieces of string. I think he first told me about it when I was in seventh grade and really into a school project to make curves out of straight line, like this:

lines - green star

These are still my go-to doodle; I’ve decorated entire math binders with these patterns and Sierpinski triangles. Erin can take the credit for introducing me to both of them; I’ll blame her if I ever get in trouble for doodling in math class. (Also, doodles in math class. Maybe I should make my own youtube channel….)

Anyway, I bought some yarn online and took ten minutes to make this super cool spiral in the staircase with the help of a friend. If anyone doubted it, math is pretty cool.

Trees, Fish, and Einstein

Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.

-Albert Einstein [1]

If you haven’t seen this quote, either you don’t have internet access or you don’t have friends that spend hours and hours aimlessly wandering the internet and posting semi-relevant links and quotes on your facebook wall. If you have seen this quote, you probably looked at it and thought “Huh. Interesting.”

Or you might have thought, “This is the problem with American education. We need to get rid of standardized tests.” That was my response the first time I saw it. I saw this cute cartoon, and I thought it was quite well drawn. Is that a question mark above the fish’s head? A hook to help it climb?


But then I was watching Sir Ken Robinson’s TED talk about schools and the dearth (death?) of creativity they create, and I remembered the quote. But not correctly. I remembered it like this:

If you judge a fish by its ability to climb a tree, it will think it is stupid. [2]

I forgot the “Everybody is a genius” part. Does that mean I don’t think everyone is a genius? No.

Okay, yes.

I think everyone has individual talents. Some people are natural-born artists, others are incredibly skilled at sports. Pelé? Soccer genius. Freddy Adu? Brilliant, amazing, talented. Not a genius. Robbie Rogers? Super brave, certainly skilled. Impressive, but not a genius.

This leads me to something that has bothered me about our education system for a while now. Every parent wants to put their kid into “gifted and talented” programs. Look at the New York City issue with kindergarten testing. Now I’m not oblivious to the harsh realities of our school systems. Rich parents get to send their kids to expensive private schools with smaller class sizes. These schools don’t have to adhere as strictly to state standards, giving these schools and their teachers more time to focus on subjects like art and music, or to emphasize topics within standard educational subjects the students will actually enjoy. I’m not oblivious to this because I lived it. I went to a small private school where we literally voted on what we wanted to study in 7th and 8th grade Humanities. [3]

If we go back to our fish and tree analogy, I am a monkey. Climbing trees comes easily. I got lucky in that my talents fall squarely within what our school system aims to foster. Math, Science, English; they all come easily. I “get it.” Interestingly, when I look back at my small, private school education, my worst grades by far were in Art and Chorus, where I was told I needed to focus more and put my mind to it. I remember getting those comments and being frustrated. These teachers also saw me in Math and Social Studies, they knew I was smart, they knew that I always did my best. Why were they giving me bad grades in classes that I was trying hard in, but good grades in classes I barely had to work at?

Why did they expect me to be a good artist when no-one expects monkeys to swim? [4]

My school was for gifted and talented students, and looking back I realize that definition was independent of species. There was definitely a fish in my class (we’ll call her Talia; she’s an amazing artist and loved Writing but always struggled in Math and Science), and I’d say there were some other types of animals too.

The education I received was wonderfully tailored. There was time for each student to get the help she needed in every subject, and there was time to prepare us all for whatever came next. We each got to pursue our own passions for the full month of January and every Friday afternoon. We learned table manners on school trips to Ashland, Oregon, and made memories everywhere from LA to Japan. Each student was recognized for the animal he or she was, and was given the appropriate challenges. Yes, fish were forced to climb trees and monkeys had to swim, but the teachers really focused on letting each student grow in the direction they wanted to.

But I was lucky, and not everyone has the opportunities I got in terms of individualized education. In normal schools, monkeys are never really forced to swim – the closest they have to get is dipping their toes in. But all the fish have to climb trees. Many of them aren’t very good at it. But some of them are.

Here’s my question, and its two-fold: What do we do about the fish that do climb trees? How should education be changed so that students entering our schools now and in the future aren’t forced to study “normal” subjects they don’t care about, and what do we do about the left-brained students already halfway through their education, torturing themselves to memorize facts for tests they’ll forget in a week?

There is an argument that can be made, and a valid one in my opinion, that every member of society ought to have a broad base of knowledge. Ideally, everyone who graduates from an American school is able to read and write, and has the basic math skills to compute tip when they go out to eat, or calculate the change they are due. But this broad knowledge needs to go beyond what current standardized tests are testing. Graduates should know a bit of world history, and maybe a smattering of a second language. They ought to know how to solve a problem they are facing, and have something to turn to in times of stress.

American high school graduates should not be mathematically inclined English speaking robots. Incoming American students are a diverse group of people, and they should leave our education system the same way. But they should have grown. Each student has a passion; the purpose of the education system ought to be to help each student find and nurture his passion. Kids are incredibly creative, and that creativity shows itself in every imaginable way, and then some. Some kids draw, some tell stories, some have an aptitude for algebra, and some for the violin. We need to stop pretending that there is a job for every college graduate, stop forcing students to major in things they don’t want to study so they’ll get a job.

I’m majoring in Chemical Physics and Political Science. (If you’re in the maths or sciences. If you’re a humanities or social sciences major, I’m majoring in Political Science and Chemical Physics.) Regardless of who I talk to, their first response is always “What are you going to do with that?” I have no idea. Not a flipping clue. I’m interested in Comparative STEM Education Policy. Or Nuclear Energy Policy. Maybe I’ll become the much-needed person sitting at the table with the politicians and scientists translating one language into the other. Maybe I’ll throw away the $200,000 my parents have so kindly spent on my education and travel the world instead. Regardless of what I want to do now or where I think I’ll end up, I’m studying things I love, taking classes in subjects I’m genuinely interested and passionate about. I have hope that my passion and dedication will be enough to get me a job. Because I’m an idealist, and I think it should.


1. Who knows if this quote is actually Einstein? The internet says so, but the internet also says Abraham Lincoln said the thing about quotes on the internet is that you cannot confirm their validity. If you don’t understand the irony here, please leave.

2.In case you’re interested, there actually are fish that climb trees (catfishmangrove killifishgourami).


3. It was South Africa and the Renaissance, if you wanted to know.

4. Most monkeys will cross water bodies when necessary, but prefer not to. Except these guys.