Rubik's Cubes

Rubik's cubes are not really all that difficult to solve. You just need to have an algorithm, and to follow it. It was amazingly difficult to find Rubik's cubes in stores this Christmas season, thanks to Will Smith solving one in The Pursuit of Happyness. It really gets me that people think that solving a Rubik's cube is "impossible," or that only "smart" people can do it. It is much like many older people with "technology" (i.e., computers): they decide it is difficult and they do not know how to do it, and like any self-fulfilling prophecy, the task becomes insurmountable.

While it does take a calculating mind capable of 3-D visualization to invent/discover complicated moves that move around certain pieces in a particular way while not disturbing other certain pieces, it takes a much less creative mind to simply follow directions and to figure out which order to apply these moves in. I am in the second category: I do not have the patience or the foresight to come up with complicated maneuvers, but I can look at a cube and figure out what needs to be done in order to solve it. Different people use different algorithms for solving Rubik's cubes. For the classic 3-by-3-by-3 cube, I choose a face (usually the yellow) to start on. I first get the four yellow corners in place, and correctly oriented. You can tell when the four corners are in the correct place when the yellow side is on the same side as the yellow center and the other-colored side (such as, say, blue) is on the same side as the other-colored (e.g., blue) center. I then get the yellow edge pieces in place, with the correct orientation. My next step is to put the four white corner pieces in the correct locations (these being the four remaining corner pieces). Once these four corner pieces are in place, I rotate them so that they have the correct orientation; I usually do this by "storing" one of the white corner pieces in a yellow corner spot while twisting the others around. I then take care of the white edge pieces; it usually possible to get them all in both the correct location with the correct orientation, but sometimes one will have the wrong orientation. This leaves the four other non-yellow and non-white edge pieces, which are easy to move to the correct positions. Sometimes I am left with a pair of edge pieces in the correct locations but with the wrong orientations; correcting this is the only fancy-schmancy "magical" scripted move I use.

If you know how to solve a 3-by-3-by-3 Rubik's cube (3x3x3? I'll call it a 3³), then the 2-by-2-by-2 (a 2³) is easy because it is just like solving the corners of a 3³ one. I haven't quite yet figured out how to solve the 4³ one, which I got for Christmas, though the algorithm I am currently trying is to basically try to reduce it to the 3³ case, which I know how to solve. First, I want to get all of the 2x2 centers together, since the lack of fixed centers in the 4³ cube is one of the reasons it is so tricky. For example, in a 3³ cube, if the yellow and white faces in the solved cube are opposite one another, then it is impossible to make the center yellow and white pieces be on adjacent faces. This is not the case with the 4³ cube. Having completed the step of consolidating the 2x2 centers—with the correct relative orientations—I now want to gather all of the edge pieces together. That is, there are two edge pieces that have blue and white on them, and I would like for them to be next to one another such that the two blue sides are adjacent and the two white sides are adjacent. I have not yet done this part, but I think I know how to. Once I have this done, the 4³ cube will essentially be reduced to the 3³ case: it will have 2x2 centers instead of fixed single centers and two pieces per edge instead of one, but if I treat these groups of pieces like single units, I can solve it like I would a normal 3³ cube. At the end, though, it will be possible that, for instance, one edge will be flipped relative to its neighboring centers, which is not possible in the 3³ case.... but I'll wait until I get there to deal with that.

The 5-by-5-by-5 cube is not mine to play with (and I'm not allowed to mess it up)*, but I am guessing that it is similarly reducible to some combination of the 3³ and 4³ cubes. Because it has fixed centers (thanks to the odd number of pieces per edge), it does not suffer from the same orientation issues as the 4³ cube.

Apparently the original Rubik's cubes and the newer "retro" cubes have opposite faces differing by yellow: red is across from orange, blue is across from green, and white is across from yellow. The Rubik's cube I learned how to solve first, though, had blue and white across from one another (and yellow and green across from each other), so I still get mildly confused when I see an edge piece with both blue and white on it.

The 2³ cube is notoriously stiff and difficult to move. This one in particular is also difficult to solve because the orange and red faces are nigh indistiguishable; I have colored the red squares red with a red Sharpie, but this now means that anyone who plays with it will be repaid with red fingertips. This 3³ one is brand new, and amazingly smooth and easy to twist and turn. (I in fact bought it to replace no fewer than four 3³ cubes that had been used and taken apart so much that none of them moved well anymore, and most of them had stickers of indiscernible color.) The only disappointing part about the new 3³ cube is that the orange color is a rather icky orange. The 4³ and 5³ ones are monstrous and difficult to handle; note also that the more pieces a cube has, the smaller the individual pieces are. The 4³ one one seems more poorly constructed than the 5³ one; the stickers are not exactly in the middle of the squares, and already one piece has simply popped out and had to be stuck back in.

By the way, if you know where I could obtain a 1-by-1-by-1 Rubik's cube, please let me know. We'd like to complete the collection at the small-n end.


* Playing with Rubik's cubes is really really bad for your wrists, especially if you already have wrist problems induced from RSI (Repetitive Stress/Strain Injury). This means that Rubik's cubes are dangerous to have around if you have RSI and are ... compulsive.

Egg Nog

My father said I could share our super-secret family recipe for egg nog, as long as you all promise not to tell it to anyone. It's real egg nog, none of this wussy nasty syrupy stuff they sell in grocery stores these days. It's also about 40 proof and so fluffy and soft you don't even notice as it slides on down.

6 eggs (you want these to be fresh, so don't buy them a week before making the egg nog!)
3/4 cups sugar
1 pint whipping cream
1 pint half & half
1 1/2 cups Jack Daniel's
1 oz rum (though when my father and I are in charge, we usually assume "1 oz" means "1/4 cup")

About a day before you plan on actually having the egg nog, separate the eggs. Beat the yolks with 1/2 cups sugar until lemon colored and thick. Add the whisky, rum, and half & half. Separately, beat the egg whites with 1/4 cups sugar until stiff. Fold this into the yolk mixture.

Age this mixture in the refrigerator overnight. This is so that the alcohol can "cook" the eggs, making the final product completely safe to drink. The next day, whip the whipping cream (with a dash of vanilla). Fold the whipped cream into the refrigerated mixture; you don't want to mix them too much. The final mixture will be somewhat heterogenous at first, but after sitting for a bit will be light and fluffy and delicious. It is also quite yummy with a touch of nutmeg.

Here's to a happy rest-of 2006 and a delightful 2007!

Seed

For the big gift-exhanging holiday of December, my brother gave* me a subscription to Seed magazine, along with a copy of the current (November 2006) edition. The seed media group is the same group that puts out ScienceBlogs—a brilliant move, by the way, as I had kind-of-sort-of heard of them before ScienceBlogs, but now there is that instant name recognition. The magazine itself is really pretty: large shiny pages with gorgeous high resolution pictures and interesting layouts. I have only flipped through the magazine a few times, but so far it seems to be couched at a level that, while not too technical, doesn't "dumb things down" like many other popular science magazines tend to do. They are also quite clearly unafraid of tackling issues of science and culture; indeed, their slogan is "Science is Culture."

There was one article I really liked as I was flipping through the November edition, looking at pretty pictures. It's on page 31, and the title is: From Shanghai to Stockholm, A new program attempts to fast-track China's quest for science gold. I wasn't even going to bother reading the article (perusing for pretty pictures, remember?) until the three little letters "RSI" jumped up at me. Yes, it's a short article about the RSI-Fudan program I was a staff member at for two weeks this summer. If I have been able to determine on a personal level what the role of RSI should be in improving education in China, I have certainly not yet been able to verbalize it. Regardless, it's always entertaining to open up a magazine and unexpectedly see someone quoted on a topic I discussed with her just last weekend ...


* Standing in front of the magazine rack and mentioning, 'I wouldn't mind having a subscription to this magazine, myself,' helped in this decision.

A Case of "It's Funny 'Cuz It's True"

I'm currently "taking time off." This means that I wasn't paying attention while booking flights this year and am spending an extra week "away" than I had really planned on. But that's okay, because I can work on my paper from anywhere, because I have a laptop and many many papers strewn about this table and room. So far, I'm somewhere around panels 3–5, but without the little kids running around:

Panel #2 was also nice, especially seeing as how I didn't sleep at all on Saturday night.

You can also refer to this particular post if you're wondering why the blogging is ... less often and of lower quality over the next few weeks than usually.

Grand Canonical Ensemble

Will has pointed me to the new webpage for his band of second year Harvard physics grad students. Go. Revel in the unspoken euphenisms, metaphors, and sheer nerdiness of their subtitle of, "bringing you to the critical point." Laugh as they try to not laugh at their own abso-friggin-lutely hilarious lyrics as they ask the timeless question: How many roots of a Henkel function, between one point seven and three? If you've been looking for the proper way to immortalize George Smoot (who was, coincidentally, Will's undergraduate advisor), then the ode "Crack the Cosmos" will be right up your alley. Still confused about that rogue former planet, Pluto? The go check out "Planet Nine." And while I'm completely unqualified to comment on it, the actual music isn't glaringly awful either ...

Go, be amazed. And then mentally chide them for being Hahvahd students who use myspace.

Questions Raised by ApJ Proofs

My peanut star paper got accepted and is set to be published soon. How soon is unclear, though. On the proofs, after the author list, it says, Received 2006 October 9; accepted 2006 November 8; published 2006 December XX. But at the top of the page, it says, The Astrophysical Journal, 654:L000-L000, 2007 January 1. So what I want to know is: is this paper mollishka et al. (2006), or mollishka et al. (2007)? I know it is probably 2007, but 2006 would make me seem so much more productive and would be much less confusing ... and apparently the page charges are less per page for 2007 than for 2006, but the page charge sheet they sent with the proofs was for 2006 and not 2007.

Also, since when did Kelvins become kelvins?

Epic(?) Bets

Which do you think will be discovered first: the Higg's boson, or an Earth mass planet orbiting a G or K dwarf star* in the habitable zone?

Last night at the astronomy department holiday party, Jason and Jon (two graduate students) put $20 each on a bet that an Earth mass planet orbitting a G or K dwarf star (the Sun is a G dwarf star; K dwarfs are slightly cooler) in the habitable zone will not be discovered by the time the first one of them graduates, which should be roughly summer 2010. Scott, who orchestrated the bet and is set to earn $40 if such planets are discovered by 2010, is an expert on planet finding studies—especially compared to two graduate students! It came out later in the evening that the Kepler mission, a satellite specifically designed to search for planets, hasn't been delayed until 2012 like the grad students thought, but rather, is likely to launch in about two years. The European analog(-ish) to Kepler, COROT, is set to launch in about two weeks. The general expectation is that unless something goes horribly wrong with both of these missions—or Earth is the only Earth-like planet— then an extrasolar Earth analog will be detected by the time I get a Ph.D.

I was unwilling to get in on the planet game, but I did bet Mandeep $1.00 that the Higg's boson will not be discovered by the time I graduate. Coming from a particle physics background, he is certainly more qualified to make such predictions, but that's completely beside the point. The LHC ("Large Hadron Collider") is due to start collecting data in 2007, and there is lots of evidence pointing at if the Higg's boson exists, then it should be detected by the LHC. On the other hand, we know of at least one Earth mass planet orbiting a G dwarf star in the habitable zone, whereas the Higg's boson is still a mere postulation and prediction.


* Aside from Earth itself, of course!
N.B.: This post title is shamelessly stolen from a recent similarly-themed post over on Galactic Interactions.

End of the Quarter

It is officially the end of the quarter. Huzzah.

Now back to our regularly scheduled programming.

Lists

There's this thing I've been (nominally) working on for the past two days which I very muchly so do not want to be working on. In fact, there are many things I would rather be doing. Here is a random list of such alternatives that have come to mind:

1. Calculate π to a 1% uncertainty by throwing frozen hot dogs down the hall. I leave it as an exercise for the reader to calculate how many thows this will require.
   
2. Visit The Federated States of Micronesia. I think the fastest way to get there from here is via Houston and then either Guam or Honolulu on Continental; it should take about two days. Then I could go to Yap! Don't worry; Micronesia still has about an order of magnitude more people than Vatican City, and almost twice as many as Greenland.
   
3. Go candlepin bowling, preferably at the bowling alley near the Alewife T-stop.
4. Fingerpaint in red wine.
5. Make a t-shirt where the front is the image to the right and the back says, "I believe!"
6. Have a free dinner of Indian food with today's speaker, even though I didn't go to this talk because I was supposedly working on this thingie. Note that I do not like Indian food.
   
7. Make a 3-D snowflake.
8. Play with my pet dragon. Or penguin.
9. Fill my office up with a house of cards. And then knock it all down.
   

Of course, what I'm working on isn't all that bad ... if it were, the above list would look more like the following:

1. Be gently flogged to death with scented bootlaces.
2. Marry an axe murderer.
3. Gnaw my fingers off one by one.
4. Watch Gigli again. It's a painfully bad movie—and not in a good way.
5. Read all 3964 3671 messages in my spam folder.
6. Take a swim off of Revere Beach near Boston, MA, right now at night in the cold and rain and mist.
7. Sit at my desk with a stopwatch, staring down the hall, and measure—repeatedly—just how long it takes for the motion sensors to allow the lights to go off.
   

It's interesting to note that #6 on that first list was the only one of these I've actually done, and the item on the first list most likely to make the second as well. I had garlic naan and a mango lassi and some lamb. I don't know what that means, though.