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03 April 2008 @ 03:21 am
Solutions: Lost and Found  
You might think that this is out there, très nerdy, or even hopelessly indulgent, but I'd like to talk about something which has boosted my self esteem in the last few weeks: my Rubik's Cubes.

First, a little history. Once upon a time, in the early `80s, when most of you were still in your fathers' pants, I bought an original 3x3x3 Rubik's Cube and proceeded to drive myself crazy trying to solve it. Very quickly, solve books came out, then speed competitions, but I wanted to do it on my own without help. Basically, I wanted to prove to myself that I was as smart as everyone seemed to be telling me. Well, it didn't happen. I actually did solve the cube a few times, but never by thinking it out; never by figuring out how to. After breaking it from taking it apart too many times, I finally threw it away in frustration and forgot about it.

Flash forward about twenty years. In the interim, I'd gotten laid, smoked a haystack's worth of pot, and gotten shot in the back, while Rubik had developed the 4x4x4 Rubik's Revenge and the 5x5x5 Professor's Cube. There was now even the Gabbasoft cube simulator, which can allow you to go insane over cubes of 20x20x20! One day, while surfing randomly, I came upon a Youtube video of one of those simulated cubes being solved and immediately felt the flames of envy. Still, I thought, I wanted the real, solid thing in my hands to practice with. So, I bought one. To my utter amazement, I had the 3x3x3 solved in under an hour! Within a week, I bought the Rubik's Revenge, but its queer decentralized nature had me going for the whole weekend that I spent with my sisters in Oklahoma (I still wonder what they thought about me, a 38 year old, playing with a kid's toy). After that, I simply had to have a Professor's Cube to finally prove my prowess. Well, my truth and beauty fans, I was able to solve that one in ten minutes right out of the box. Now I've done the Gabbasoft up to 13x13x13, but it's redundant at this point. It's no longer a puzzle. There are really only two variants of the cube; odd and even. I can solve one of any size, but my purpose here isn't to brag, exactly. There's a lesson.

When I was trying to do it back in middle school, I had no knowledge of real problem solving, strategy, or algorithms. I knew very little about three dimensional geometry and nothing about transformational groups or cohomology. Still, even that far back, I could guess at the importance of, say, getting the corners right, even if how to do it was beyond me. Finally, when I bought a new 3x3x3, I had all that to work from and used it naturally; almost intuitively. I didn't go about trying to solve it all at once, but instead learned how to manipulate it first; what its inherent idiosyncrasies were. I found out, for instance, how to 'swap' two corner pieces or to turn two of them one-third the way around. I also learned what had vexed me incessantly before; how to switch any two edge pieces. I found out that each was accomplished through a set combination of moves. Once those were learned, the cube was no longer more than a pastime.

When I got the 4x4x4 Rubik's Revenge, which I had only tried perhaps two or three times in my life, I really had a new puzzle. For one thing, there were no center face pieces (which, in 'odd' cubes, stay in their same positions regardless of rotations) to guide me in keeping the faces distinct. I realized quickly, however, that by fixing the corners, I could use them for that purpose. Also, I had to relearn how to swap edge pieces, because now two pieces which belonged on the same edge could still be reversed. Finally, I had the face pieces to worry about. It took me hours of screwing up the whole cube just to find out how to swap face pieces without changing any others. In short, whereas before I had concentrated on filling in faces one after another, now I understood the problem to be centered on the types of pieces themselves. Each, center, edge, or corner, had its own special moves, its own algorithms for transformation. Once I had made that leap, I knew that it wasn't just a question of learning each bigger cube on its own. Once I understood the algorithmic nature of cube solving in general, I had solved them all.

So, when I got the Professor's cube, I already knew that it would cause me no trouble, because it was only a sort of amalgamation of the other three kinds; 2x2x2 (corners only), 3x3x3 (face-centers and edge-centers), and 4x4x4 ('even numbered' face and edge). I already knew all the moves I needed, all that I would ever need for any sized cube. To be sure, I had my mother mix it up for five minutes, then went at it. The only reason that it took me longer than the 3x3x3 and the 4x4x4 (both of which I could finish at will, almost blindfolded), was simply that there were more pieces to move. Since then, I have retired my 3x3x3 and 4x4x4 and only use the 5x5x5 as a distraction. Like I said above, I've done the Gabbasoft, but that only proved what I already knew. I had conquered the dragon of my youth in what was for me unbelievable time, and without taking apart the cubes once (and long since 'ruining my mind' on teh devil's weed).

Where is the lesson, you might ask? That's even easier than learning the cube. Don't feel stupid because you fail at a test or a puzzle. You probably just haven't learned the right mental tools yet. And even if you can't imagine that you'll ever be smart enough to do it, give it time. You learn so much from life that you'll pick up those tools sooner or later, even if you didn't know they were the right ones or where to find them. And this goes for everything from Rubik's Cubes to relationships to career choices. If you look long enough, and keep learning all the while, you'll solve the puzzle.
 
 
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