Date: Thu, 22 Feb 90 19:16:07 -0500 (EST)
From: Dan Hoey <hoey@aic.nrl.navy.mil >
~~~ Subject: Language in Rubik's Cubic Compendium

Well, my order of Rubik's Cubic Compendium came through. I ordered it
through Reiter's (The DC technical bookstore) and paid \$30 for it.
It's basically six largely independent chapters translated from
Hungarian, with foreword and afterword by Singmaster and a
bibliography. There's definitely some neat stuff there.

My favorite piece of the book is in Tamas Varga's ``The Art of
Cubing'', which develops some interesting new additions to what we
used to call ``Rubiksong'', the language we use to describe processes.
He starts by renaming the Up face to be the Top, the advantage of
which is to make all the face names consonants. He then uses vowels
to indicate the direction of turn, "O" for 90 degrees fOrward (or
clOckwise), "A" for 90 degrees bAckward (or Anticlockwise) and "I" for
a 180 degree half-turn (twIce). This works out neatly to allow a
process to be described with a syllable for each quarter- or
half-turn. So Pons Asinorum can be done with FIBITIDIRILI and
Laughter is 3 FOBOROLOs.

But wait, there's more! Remember how Befuddler never was able to
handle whole-cube moves neatly? In this notation, you append a "C" to
a syllable to indicate that instead of turning the face, you turn the
whole cube. So the way I usually do Laughter is really 6 ROLOTOCs.
This notation is not as parsimonious, since FOC=BAC, TOC=DAC, and
ROC=LAC, but it's better than having to stop in the middle and say
``then move the cube''. For instance, Jim Saxe's 28-qt Plummer's
Cross can be done as "FOLIRIFO BOLIRIFO ROFIBIRO LOFIBIRO TIDI", but
the way he originally described it (3 Dec 1980 00:50) was "FOLIRIFO
BOLIRIFO TOC FOLIRIFO BOLIRIFO TIDI", but instead of TOC he had a
couple of lines of text.

He also has a way of talking about the slice moves, where you move
the middle layer of the cube instead of the faces. For moving the
middle, you append "M" to the syllable. So the way most people do a
Spratt wrench is 4 TOROMs, and we can do the Plummer's Cross as
FOLIMBO FOLIMFO TOC FOLIMBO FOLIMFO TIM. Of course, ROM=LAM, etc.
(This could also work for Rubik's revenge, where ROM and LAM are
different, being moves of the inner layers adjacent to the R and L
faces).

It's unfortunate that he doesn't extend the language past the point of
appending "M" and "C". I would like to have a way of talking about
slice moves where you move the faces rather than the middle. Of
course, we could say ROLA, but I'd rather say something like ROS.
This might interfere with the use of "s" for plurals (as they do in
the book and I do above), but that could be fixed by pronouncing the
pluralizing s as "z".

Another idea is to append "N" to syllables for aNtislice moves. So
Laughter would be six RONTOCs. I'm a little concerned though, that "M"
and "N" might be difficult to distinguish.

Another suggestion is to append "P" to allow "deeP" moves, where we do
RO and ROM simultaneously by grabbing two layers of the cube and
turning them while keeping the remaining face fixed.

It might be nice to use "G" to denote the way we "Wring" the cube,
as with ROPRO. So 6 ROGTOC's does an 8-Flip.

To summarize,

F,B,T,D,R,L -- faces Front, Back, Top, Down, Right, Left.
O,A,I -- directions fOrward, bAckward, twIce.
C,M,S,N,P,G -- extensions whole-Cube, Middle, Slice, aNtislice,
deeP, wrinG

All extensions but C are redundant, since

ROM=ROCRALO
ROS=ROLO
RON=ROLA
ROP=ROCLA
ROG=ROCROLO

I'm going over their list of pretty patterns, and hopefully I can find
out which ones are improvements. I did notice they don't have Saxe's
Plummer's cross process.

Dan