Blindsolvin'
Step by Step
I've been taking the stairs to my 23rd-floor apartment lately to try to get some exercise. One thing I've tried to do a few times is count the steps, but it's actually quite difficult! For one thing, some flights have 7 steps and others have 8, so my stepping parity gets reversed every two flights. Another challenge is that the stairs go quite fast, so I don't fully have time to subvocalize the numbers as I go, and finally if I try to use kinesthetic or auditory rhythm to regulate the counting, I'm thrown off by the roughly 3 steps or so I have to take to traverse each landing, a variable which also depends upon which foot I finished the last flight on.
My point here is that it's interesting to explore the ways in which the mind works. Some tasks are inherently easy, and others quite difficult... which brings me to my topic for today.
Blindsolving the 2x2
So thanks to my good friend Florent, I've found a new way to pass the time on the buses and trains. My 3x3 cube time has kind of plateaued around 1:30 (I know, it's not the kind of time anyone would admit to on a speedcubing forum, but for the time being I don't see myself putting in the training hours to improve beyond this) so I've taken on a new Rubik's challenge: blindsolving the 2x2 cube.
Basically, the idea is to stare at the cube intently for a while and memorize its state, then close your eyes and twist away. It's quite difficult because it requires meticulous planning, careful memorization, and flawless execution. Until you've done it you probably don't appreciate the frustration that comes from forgetting a single rotation during a complex algorithm, and then continuing to work the cube for 10 minutes, only to end up with a cube that looks as scrambled as when it started.
My technique
What I like about this challenge is the way it lets me explore how my mind works. For example, I'm terrible at memorization, particularly when it comes to sequences of numbers and things. So I've been trying out ways to utilize the different parts of my memory to remember things like which blocks need to be exchanged in which order, and which need to be rotated in which direction. I'm sure this is horribly inefficient, but it's kind of interesting -- for exchanging the positions of blocks, I use musical notes.
It works out well because there are only eight blocks, so it exactly fits a major scale. For example, if the #2 block should be in the #6 position, and the #6 block in the #5 position, #5 in #8, and #8 in #2, then I remember it as Re-La-So-Do. I usually use the "#1" block as a reference to define which colors belong on which axes, so the melodies usually start on #2 or #3 and take on an eerie modal quality. If there are multiple cycles of blocks that need to be exchanged, I mark the divisions in the melody with half-notes.
For orientation of the blocks (which I memorize last and do first to minimize the amount of time I need to remember it, following the advice of some guy on youtube) I find left/right pairs or sets of three blocks that need to be rotated in the same direction. Again I use my audio memory to help me cache the information, but this time I use words. I use my own highly-nontechnical terms to describe the formation, then I use numbers to mark the blocks, and I use English words (right, left) to tag it with a direction, and finally Japanese words (migi, hidari, ue, shita, mae, ushiro) to flag which side of the cube my "reference block" is on, so I can rotate the cube back to the original position when I finish the orientation corrections.
As I said, I'm sure this is horribly inefficient, but it's kind of fun. :)
Results
I've been doing this on the train for about 2 weeks now. It usually takes me around 5-7 minutes to do the whole thing, memorization time included, although I'm still below 50% in terms of success rate. The hardest part for me is the orientation phase, because I have to change my grip and rotate the cube a lot to do it, so often I either fail to return the cube to its original position, or I accidentally rotate the wrong triplet of corners, ending up with two corners mis-rotated in an otherwise perfectly solved cube.
Looking online, people tend to dismiss blindsolving the 2x2 as too easy, citing that it's not that difficult to blindsolve the 3x3. Given that there are 20 "cubies" to move around, that would be almost two octaves on the 12-tone scale. If nothing else, it would be fantastic relative pitch training! I guess it would be possible to use an 8-tone major scale (including high and low "do") with vowels (a,i,u,e,o, and mm) to designate a position on a face. It would be a bit redundant since each corner piece would have three designations and each edge piece would have two, but maybe there would be ... some reason you'd want to do that?
If anyone tries something like this, let me know!
