Allan C. Wechsler asks for general reminiscences from people who solved
the cube. It's just as well hardly anyone's replied, or the list would be
swamped with boring anecdotes ! So maybe I'll add an anecdote or two of
>While I'm reminiscing, I should confess that my standard corner operator
>is still the same as it was then: (FUR)^5, which exchanges two corners,
>leaves the rest of the corners alone, and fucks the edges completely.
Happens to me also. I still use operators I found myself in favour of
(shorter) processes found later in books. I remember them better!
Very true. This reminds me of what I read in (I think) the math games
column of Scientific American, about mid-to-late 80's. The cubing craze had
largely passed, and someone who had been an addict, but hadn't touched it
for some years, had occasion to try it again. He realized with horror, that he
couldn't remember a single thing! However, as he began to fiddle with the
cube rather disconsolately, he found himself automatically doing the right
things. "I couldn't remember how to do it, but my fingers could !!", he said.
This was my experience too, a few years ago. It's quite uncanny, like
starting to ride a bike again after decades of not doing; only more so.
That's what comes of sticking loyally to your first halfway-decent discoveries
on cube-solving. From madly over-addictive use, they become burned into
your brain tissue. My own pet method has always been to put all the edges
right first, using only common sense (except maybe at the very end some
slight method needed); then put the corners right using the basic
"8-fold way"..... R~ U L U~ R U L~ U~ . We found this eightfold way quite
easy to remember, the face order is very natural, and the sequence of
clockwise vs anti-clockwise turns, i.e. ACCA CCAA, seems somehow like a
sonnet rhyming scheme (now burnt irrevocably into my finger-moving cortex).
This eightfold way is just a commutator of a face move and (a commutator of
two face moves)); so it turns out to be group-theoretically natural, as
commutators do "as little as possible". The eight-fold way can also be
viewed in a natural geometric light, as just a standard 3-permutation of
corners, similaritied away from one another to avoid interference. (Don't
know what the standard technical terms for all this are, sorry; it's probably
old hat to most readers here.) Viewing it this way, one can quickly re-create
several (8-fold) variants, and some 10-fold ones, all of the same type, and
all variously useful. By similarities, one can usually put a corner into a
more useful spot, so as to get two corners done at a time, with one 8-fold.
ENOUGH; of teaching grandmothers to suck eggs. I was going to reminisce. Not
many people seem to do the cube this way, that is, edges first. It was shown
to me by my late colleague Brent Wilson (the other of the "we" refered to
above). At first it seemed a little unnatural, but once you get used to it,
it seems super efficient. I suppose everyone feels that way about their own
methods. The particular 8-fold mentioned above was my own invention, so I've
always had a soft spot for it.
Brent and I both started out on the cube the same way, which is
I suppose standard. We spent some little time learning to do the base. Then we
spent some considerably longer time learning to do the middle layer. We found
later that we had both expected the same thing:- that when the middle and
base layers were all successfully done, the top layer would automatically
have to be right !! So of course, we were both temporarily devastated when
it turned out otherwise; and we both realized that we were in the presence
of a mighty puzzle, and were in for some great fun. So we went ahead and
discovered all the usual group-theoretic things, one by one, over the months.
I have anothger reminiscence to tell about my colleague. I once read of
someone, (J.H.Conway ?), who was alleged to do the cube behind his back !
Well Brent practiced this trick also (unaware of anyone else having
done it, if indeed it was done the same way, even). He invented the method
after having discovered the only all-commuting position, i.e. with all
edges flipped, corners all correct. He perfected a smooth method of doing
this behind his back. The trick is, of course, merely to have a pre-prepared
cube in this position. It doesn't QUITE look random, but if you ADD to it
a couple of random twists, it now looks totally random; at first (and second)
glance. He would show this "random" cube to us, let us hold it (very briefly!),
then take it and do the "all-flips" behind his back. Keeping up a continuous
patter, as he brought it back he would be saying "...so there's only a couple
of twists to go", and then as it appeared he would do the last two twists by
sight, without hesitation. As the two "randomizing" twists commute with
the other position, he didn't have to memorize them; indeed he could even
let the audience do them ! Of course this would mean he would have to have
the pure "flipped" pattern to start with, which was easier to detect, alas.
Well, one time, he was to give a talk to some school kids. He wanted to do
the cube behind his back, as a piece-de-resistance. He decided to train
himself up into being able to undo FOUR random twists by sight. He duly did
this. Then when the talk came around, he had a cube prepared in "all-flip"
position, with two twists added, to make it look quite random. Then, when
the highlight of the talk came around, he would display it to the class,
let one or two handle it briefly, to agree it was just another muddled up
cube. Then, HE WOULD EVEN ASK two members of the audience to add an extra
random twist each (just to prove the cube wasn't in a prepared position!)
Then he would do the all-flips operation behind his back, keeping up his
patter. He expected to be able to handle undoing the four random flips left
over, by sight, as he was completing his patter.
When the great event came along, everything went perfectly, without a hitch.
BUT, amazingly, by a 144-to-1 chance, the two flips that the audience added
exactly undid the two that he had put on himself ! So when he brought it
from behind his back, it was already perfectly done. Without batting an
eyelid, he brought his patter to a halt then and there. Needless to say, the
kids were even more staggered than they would have been otherwise. He
resisted all imploring entreaties to tell them how it was done (like all
good conjurers); and I don't thimk he ever did the trick again!
By great good luck, however, I have a vieotape of him doing this trick, from
the demo itself. So if any of you are ever in New Zealand, you can
look me up, and ask to see this amazing event !
Like Allan Wechsler, I would be delighted to hear anyone else's reminiscences,
or cube anecdotes generally. There must be tons, so, don't be shy!
Cheers, Bill Taylor.