Wednesday, December 22, 2010

Holiday Cubing, and a lot of explanations.

I hear the same things over and over from a variety of people when they see me manipulate a Rubik’s Cube in public.

“There’s like a mathematical formula to it, right?”

“I used to just take the stickers off.”
“But how do you know where it’s supposed to go?”
“I can only get (two/three) sides.”
“I could never do it.”
and the variation
“I tried looking it up ( on the Internet ) and I still couldn't figure it out.”

I will address these here as well, but I was so excited about a new question that it compelled me to talk about this topic at all. I finally got a new question the other day, standing in line at a local big box store in the supposed “Express” lane.

“Is there a rhythm to it?”

I’m sure that this is a reaction to the way that I do some of the multiple-move manipulations (known to cubers as “finger tricks”) in a way that doesn't bind up the mechanism of the cube. If you try to do some moves too fast for a given cube, the pieces just hang up on each other and don’t turn or possibly you will pop a piece out. In a competition, I suppose that you would want to push yourself as much as possible, and the occasional pop would be acceptable if it meant you had other fast times. In line at the store, popping a piece is largely unacceptable to me and it detracts from the showmanship aspect. If people are entertained a little, then it’s rewarding. It’s a nerdy sort or rewarding, but I’ll take it. If I’m digging under the edge of a cash register for a plastic piece, it’s a headache. So, the solution is to keep it at the speed that you know the cube will work well at. For me, even if they’re timing me, it’s better to keep it at a reasonable speed most of the time so I can look ahead to see the next thing to do.

So let’s go back to these other ones.

“There’s like a mathematical formula to it, right?”
The answer is “Yes”, but I always tell people “No”. That mostly has to do with the fact that I’m not able to easily explain why small groups with limited transformations behave in a complex way with rigorous constraints. Maybe I need to re-read all of my set theory and the Christoph Bandelow book “Inside Rubik’s Cube and Beyond” again. The other reason is that when most people say "math", I assume they're talking abut square roots, long division, and ax2+bx+c=0. I never assume they're talking about set theory, bijective functions, or anything with the word 'abelian' in it.

“I used to just take the stickers off.”
I typically tell people that adhesive never works as good once it’s been exposed to air. If you take the stickers off, not only will they likely be misaligned, but they will never stick as good as they originally did. When I re-sticker a cube, it involves cleaning the cube down to the plastic and sometimes even some light abrasion so new stickers have a fighting chance on a new surface.

This is the part where I start showing people - often by removing a piece of the cube - that there are edge pieces and corner pieces, and the center pieces attached to the framework in the middle of the cube. Explaining to them that the center pieces don't move relative to each other is somewhat difficult - I try to relate it to a die. One is always opposite six, five is always opposite two, three is always opposite four. No matter how you turn a die, the relative positions are still the same, and the framework of a Rubik's cube is no different. So, knowing the particular combination of colors on an edge or corner piece dictates where it should go. This is about where I start losing people, because once I pop the piece back in and start turning the faces of the cube, most people see 54 stickers again instead of eight corners, twelve edges and six centers.

"I can only get two sides."
This one I can believe, since it is possible to get two adjacent sides with only three pieces (two corners and the edge between them) completely correct. Those three pieces would be the pieces that comprises the edge between the two correct faces. The remaining ten pieces could be incorrectly placed. If the remaining pieces were correctly placed, there would only be two corners and five edges left, and if they were able to get as much as that done, they would have a real chance at the entire cube. Getting two opposite sides correct might be more difficult since 16 pieces would have to be correctly oriented, but no pieces would have to be correctly placed. This scenario seems unlikely for someone that can't actually solve a cube, I'd have to see it firsthand.

"I can only get three sides."
For as many times as I've heard this one, I never believe it. I'm going to have to start calling people out on this one, or at least pressing them for more details. It involves far too much of the cube being completed. When I solve a cube, the only time I have three sides done is when I am left with only two edges both of which are correctly placed but incorrectly oriented. Again, if you can get this much of the cube done, it seems unlikely that you would be completely unable to do the remainder. Most of the people that I know that have tried to solve the cube on their own fared much better once the corners were resolved, as a lot can be done with a cube without disturbing the corner pieces to move edges around.

This seems like a good time to mention that a cube cannot have only one edge flipped, or only one corner twisted. Edges flip in pairs, corners twist in opposite pairs or three in the same direction. You also cannot have only two pieces out of place. You can have three edges or three corners out of place, or two corners and two edges out of place. Those are the minimums. If you take a cube apart, and reassemble it at random, you only have a one in twelve chance of putting it in a solvable state. I suppose that some of these people that have done two or three sides are fighting against a tampered-with cube, but I don't really know.

"I could never do it."
You could be right about that, but it's true for a lot of things that if you think you can't, you can't. I don't find it to be any more challenging than playing bass or typing, and I would think that playing violin or trombone would be a lot harder than doing a Rubik's cube.

This is the part that I can understand - the standard notation for cube moves is not intuitive to everyone, especially when you're not thinking of the cube as having fixed sides. So if you see

RUR'URU2R' (or R'D'RD'R'D2R if you're old-school top-down) and you don't understand it, but you want to - feel free to ask.

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