Thursday, May 17, 2007

Rubik's Cube and Languages

I recently purchased a mini-rubik's cube for my key chain. Since Rubik himself was/is Hungarian, and he invented the "Magic Cube," as it was originally named, in Budapest, I felt that, Westernized or not, I couldn't leave Hungary without one. I've never been much good at solving them. I find myself happily spinning them, hoping that a solution will suddenly occur. This is ridiculous since there are over 43,000,000,000,000,000,000 total permutations of the cube. Now, I've had this cube for three days, two of them being class days. In these two days, I've had two different people say, "here, let me see that" and fiddle with it for a minute or so, and then hand it back completed. ..... I found myself wondering where in the world would this ever occur, having my cube solved by two different people in two days. But then I remembered I'm in a math program, so suddenly this all made sense. There are some very very very smart people with whom I'm rubbing shoulders.

I'm about to use the second Lord of the Rings reference in two consecutive posts... Perhaps I need to get a life? But anyway, I was happily reading The Two Towers the other night, and I noticed a reference to the appendices. Like a good Tolkien fan, I followed the asterisk and flipped back to Appendix F and found the section to which the author was alluding. It was in regards to the language of Entish. It was described as, "slow, sonorous, agglomerated, repetitive, indeed long-winded; formed of a multiplicity of vowel-shades and distinctions of tone and quantity which even the loremasters of the Eldar had not attempted to represent in writing." I THOUGHT OF HUNGARIAN! I think from now on, I'll just tell people that I'm learning Entish, rather than Hungarian. Actually I'm speaking in jest. I was writing an e-mail to a friend from Budapest, and I recounted my reaction to hearing English on the street. I wasn't expecting to hear any English in the part of town through which I was walking, and so when two Americans passed by me (talking loudly and gaudily, I might add) I was quite taken aback. What I noticed, however, was that all I could hear was the dramatic "eeeer's" and "orrrrr's." It sounded very ugly! Now, I wouldn't characterize Hungarian as a romantic, beautiful language, such as French or Italian, but it is definitely very fluid with a lot of soft sounds. It's very relaxing to listen to Hungarian, or really any foreign language, but for the first time, I realized perhaps not all nationalities feel the same about English. In any case, I thought the line describing Entish was a funny way to think of Hungarian.
Although, to set one fact straight, there is very little repetition in Hungarian, and in fact one of the techniques we were taught in my class was to reduce unnecessary repetition using all manners of suffixes and prefixes.

Today I had my last class with BSM. Now for finals! I'm concerned about my Combinatorics final, because it's cumulative, and while I really like graph theory, basic enumeration completely eludes me. I'm in for a fantastic weekend of trying to apply the binomial theorem to going to a flower shop and buying 4 roses, 5 tulips, and 6 daisies, all in a specific order.

My Number Theory final is all on Diophantine equations. Those are basically equations without solutions, and it's our job to prove that they indeed don't have solutions. Non-math people, I'm sorry, just bear with me. I think it's cool, but I suppose it sounds like a mildly rhetorical technique.

In Elementary Problem Solving, my final is cumulative, but it'll be fun! Strangely enough, I have found a sudden interest in Game Theory (or the Theory of Gaming... I'm not really sure of the difference). Before, I thought it was pretty pointless, but then I got introduced to a technique using the Grundy Numbers, which I have never studied before. It basically involves assigning a number to each possibility in a game (using a basic algorithm) and then converting these numbers to base 2 (binary) and working with them, yielding a winning strategy. I'd like to take Computer Science 1 again, and use this strategy in our lab on NIM. I expect this would have yielded a better grade than my guess-and-check strategy I hypothesized. However, I am sad to admit that I got a point off on my last test because I asserted that 3^2=6. My brilliance sometimes amazes me.

Anyway, I hope everyone is enjoying the fabulous weather, and good luck on any springtime finals or projects, or whatever grown-ups do in the real world!

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The Narrator said...

When I was a kid in the 80s, Rubik's Cubes hit the scene and became a cultural phenomenon. We had one at our house and it sat around for weeks before anyone could solve it - even Dad. He worked and worked at and couldn't get it.

Then one night Mom took all the colored stickers off all the squares and re-stuck them. She left the (apparently) solved Rubik's Cube where Dad would find it the next morning.

I don't remember exactly what happened, but I do recall that Dad didn't believe for one second that she had actually solved it.

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I had a thought last night about Game THeory, Rubik Cube, and how it applies to education.

I woke up this morning and googled "game theory rubik cube",and came across your post. It is funny we came up with similar ideas.

I work in high poverty urban settings where most of the students are not meeting expectations. As a teacher I have always had success in the classroom because I focused on teaching strategies rather than content. I always believed content would come through discovery if a student had strategies.

Trying to get others to buy into this has been challenging. The typical answer educators have for solving low performance is more work, longer classes. The content of those classes is always the same. As a result, the students are still not improving.

Anyway, I was on a flight home from Los Angeles yesterday. We were working on school reform issues. Quite a bit of the talk was around more courses, more content, and more time on task. The idea of how we change our approach to the problem has not changed. Typical results will follow; of this I'm sure.

For some reason I started thinking about a rubik cube on the plane ride home (They always frustrated the hell out of me. I, too, used to pop the squares off with a screw driver and try to put them back in order. I also did the sticker peel trick).

Basically, what we are doing in education is handing the rubik cube to the kids and giving them more time with it. We are also putting more pressure on them by standing over them telling them their life is on the line if they don't solve it. Of course we know more time and more pressure isn't the answer (you mentioned your recent obsession).

They need a strategy. Your math people who solved your cube had a strategy.

I am looking up strategies to solve the cube today. I will study as much as possible. I won't pick up a cube until I'm satisfied I have a winning strategy learned. I'm going to bet I will finally be able to solve the puzzle.

OK, sorry for the rant. Couldn't sleep last night trying to think of a way I could prove it is all about strategy rather than content.

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