Cubies and Simple Groups

Even though I love to solve puzzles, it was only recently that I finally got around to learning how to solve the Rubik's Cube. I could only ever get one face at a time, and I never had the patience to learn how to keep that face from messing up while I tackled another part. I got a tip from a friend that the second phase involves working on the second “layer”, thinking of the completed face as being the top/bottom of the cube. But I still couldn't figure it out.

Then I got an email newsletter from the American Mathematical Society pointing me to an article in Scientific American about some new puzzles that are similar to the Rubik's Cube. (You can read about the puzzles here or play them here.) These puzzles are based on so-called simple groups, and require slightly different techniques to solve than the Rubik's Cube. It was at this point that I realized that I never learned the Cube, so I was probably at an even bigger disadvantage with these new puzzles.

At first I found a few web sites that teach you a series of moves to try depending on what state your cube is in. But this felt sort of hollow, as though I were simply memorizing sequences of moves with no real pattern behind them. Then I checked out a few books from the library that teach the “theory” behind the cube: Handbook of Cubik Math by Alexander H. Frey, Jr. and David Singmaster; and Rubik's Cube Compendium by Ernö Rubik, Tamás Varga, Gerzson Kéri, György Marx, and Tamás Vekerdy. These books explain various solution methods in terms of what you're actually trying to accomplish, which I found much easier to remember.

Now I can solve the Rubik's Cube, though I'm not very fast. It's still pretty satisfying, to mix up the cube, and then methodically solve the bottom layer, then the middle layer, and finally the top layer.

So what are these “groups”, and what do they have to do with puzzles? I don't have time to really explore group theory, the branch of mathematics that studies groups, but I can try to give a brief explanation. A group is a concept which involves some objects and a single operation on those objects. A really good example here is the integers (0, ±1, ±2, ±3, …) along with addition. For the Rubik's Cube, you can think of the objects as the rotations of the faces, and the operation is doing one rotation followed by another one. The goal of the Rubik's Cube is to “undo” all the rotations that put the cube in the scrambled state.

Simple groups are a little harder to define, but it suffices to say that you can build up any finite group out of finite simple groups. So they are like the building blocks of group theory. These groups really aren't “simple” in any usual sense of the word, and the puzzles in the Scientific American article above are quite challenging. I hope to tackle the first one soon, now that I've learned the basic concepts of the Rubik's Cube.

Unashamed about the T&N back catalog

As part of the effort to rip my entire CD collection, last night I tackled some old-school hardcore albums like the Helpless Amongst Friends compilation, Overcome's “Blessed Are The Persecuted”, and Unashamed's “Reflection”. Tonight I put the Unashamed album on for some nostalgia, and I must say it's quite good, if you like that kind of hardcore. Some good grooves, and vocals you can actually understand (unlike, say, Zao's vocals).

When I looked at my Last.Fm client to see what it said about Unashamed, it gave me a link to buy that track at Amazon.com. What? But this album is from 1996! Tooth and Nail was still a pretty small label back then, and I thought they'd pretty much given up on their back catalog. Well, think again: everything from Wish For Eden's “Pet The Fish” to Plank Eye's “Spark” and more are available for download in mp3 format! Of course, unless you just can't wait to hear these gems, you can always save money by buying the used copies available through Amazon.com, but at least you can check out the song samples before deciding whether you still like Focused's first album (I do), or whether it's just nostalgia trying to waste your money.

Oh, and for added fun, try reading the customer reviews. Most are from 8-10 years ago, and you get excellent reviews like The heaviness and syncopation of this albumn is awesome. It sets the standard for all Tooth and Nail releases. (about “Pet The Fish”... really...) and Oh man, this is the greatest CD in the history of Christian hard music. (about “Stone” by Sometime Sunday... I'm not making this up...). I mean, I like some of that old stuff, but those people needed to get out more and listen to some good music.

Pinching every last penny

Somewhere between my free-spending days of college (where I built a great CD collection) and my wedding, I went through a dramatic turnaround. I came to realize how stupid it is to carry balances on a credit card, and I developed what was to become the personal budgeting strategy that carried me and my family through graduate school without any real hardships. In that time I have taken an interest in finance, and I hope to talk about it from time to time in this blog.

The guiding principal of my budget is that every penny that comes into my possession is labeled and categorized, and every penny that leaves is as well. Each financial transaction has to be accounted for, and this keeps me from spending too much without realizing it.

Today I spent a few hours completing the transition from keeping my money in a normal bank (okay, credit union) and instead putting most of it in a money market account through Vanguard. I have my paycheck direct-deposited there, and I have two automatic monthly withdrawals that will move money back to my bank for things like rent and auto insurance. I hope to get some good return instead of having my monthly expenses just sit in a checking account.

Final Four Time!

Earlier today my NCAA Champion pick, Memphis, beat UCLA to advance to the finals. Right now I'm watching one of the more exciting games I've seen in the tournament this year: North Carolina is clawing their way back against Kansas. I picked UNC to lose to Memphis, so naturally I'm rooting for them in this game, but I really don't like either UNC or Kansas.

I've been a little disappointed with the tournament this year (and not just because IU was eliminated early (again)). The teams at the top have been so dominating that several of the games were decided in the first half. I haven't run the numbers, but I'd love to see different stats on average margin of victory and number of blowouts this year compared to usual. And of course this is the first time in history that all four 1 seeds made it to the Final Four.

UNC closed to 4, then Kansas (finally) scored a few times, and now it's a five-point game. Very exciting.

Update: And then UNC stopped playing. Another blowout.

No more Indiana teams left

I just got done watching Butler fight to the finish against Tennessee. They were so close to pulling off the upset, and I still say that was goaltending when A.J. Graves drove to the basket near the end of overtime. I'm really impressed with how well this team without any superstars almost beat a team that was #1 for a week or so this year.

Not to make excuses, but I think the NCAA Tournament committee that did the seeding really hurt Butler in this one. While they should have been able to beat Tennessee if they were really a championship contender, they shouldn't have been a #7 seed. IU's #8 seed also didn't seem deserved at the time, though with the way they played their last few games, maybe it was accurate.

Purdue and Notre Dame lost yesterday, so we're out of Indiana teams now. So who do I root for? I picked Memphis to win it all, so of course I'd like to see them make it. But other than wanting to win my bracket group, I have no attachment for Memphis. I'd like to see Wisconsin win it all, representing the Big Ten. It would be cool to have another George Mason-like run from a team like Western Kentucky (who I haven't had the chance to watch yet) or Davidson. I think West Virginia has been playing well, but it's hard to say whether they'll be able to sustain it. They're in a good bracket, facing Xavier next and then possibly UCLA, who struggled with Texas A&M yesterday.

Memphis and Mississippi State are tied 8 minutes in. This should be a good game.

A quick note about this blog

I re-used an old blogspot URL that I had for another blog, so if you subscribe to the feed and find several old posts from about a year ago, that's the explanation. That blog was from my former life as a mathematics graduate student. I hope to talk about math in this fancy new blog, but I'm not going to theme this blog into a rut like that one. So there you have it.

New music I actually found on the radio

I had been radio-free for several years before I started commuting to work everyday. Gone are the days of putting headphones in on the bus ride to UIUC. It helps that we have two or three good radio stations out here in Santa Clara: Channel 104.9, Live 105, and the off-and-on fabulous KSCU. The first two do a good job of mostly playing 90's hits like Nirvana, Green Day, and Social Distortion with a mix of new rock, while KSCU has a few DJs that play some awesome indie stuff.

What I particularly like about 104.9 is the selection of more obscure songs from the past – not that no one listened to these songs, but more like very few people would listen to them today. I think I've heard at least four or five songs from Social Distortion's self-titled album (which I need to get someday), as well as great songs from Dramarama and Butthole Surfers. It makes me feel old to realize that the music of my formative years is coming up on its twentieth birthday within the next few years.

My most recent discovery is a band from L.A. that reminds me so much of Rose Blossom Punch that I expected to look them up and find Aaron Sprinkle's name in the list of band members – Silversun Pickups. The radio single “well thought out twinkles” is really good, and the rest of the album didn't disappoint me at all.

Other songs that I have to admit that I like: “Empty Walls” by Serj Tankian and “Never Too Late” by Three Days Grace.