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Alternative notation

I started cubing with a book that used different notation. R+ for right clockwise, R- for right counterclockwise. I thought it was pretty ridiculous that speedcubing notation used up and down instead of top and bottom. Back was called posterior.
 
I don't exactly like the part about R L being equivalent to R L' in standard notation, because I think it's more consistent to use clockwise/cclockwise instead of up/down because it depends on your perspective. But I think you have a good idea with the part about enclosing moves that can be made together in square brackets. For example for U D'(standard notation) could just be [U D'], just to make the notation a bit easier to translate into real moves and fingertricks.
 
People used to just use parentheses for that. In the old days it was common to see algorithms with (Rr) and (Rr'), and sometimes (rm') or even (rm'l'). Since parentheses already group moves together into chunks, I don't think brackets add anything that parentheses don't. I'd also point out that in some notations brackets mean to read the moves as rotations...
 
I don't exactly like the part about R L being equivalent to R L' in standard notation, because I think it's more consistent to use clockwise/cclockwise instead of up/down because it depends on your perspective.

Think about when you hold the cube, and apply R and then L'. They are both turning in the same direction if you are looking at the front of the cube. They are only spinning in different directions if you rotate the R to the front and L to the front as you make the actual turn.

I treat each turn as if your hand is reaching through the cube, magically. You reach L as if grabbing from the R, and you reach D as if coming from U (of course I use different letters). This also has the added benefit of resolving the ambiguity for middle slices on large odd-cubes. For example, M and M' would follow R, and in my case it is v+ = front to the top and v- = top to the front, grabbing the middle vertical slice.

The most extreme case is when you move F and then B'. Same direction as you look right at the cube, but opposite notation-wise. Did not make sense to me, so that is the primary reason I came up with my alternative.

But I think you have a good idea with the part about enclosing moves that can be made together in square brackets. For example for U D'(standard notation) could just be [U D'], just to make the notation a bit easier to translate into real moves and fingertricks.

I only include moves inside square brackets when 1) You can grab then both with one hand and 2) they are spinning in the same direction. So [Ff]+ [TT]- [Rr]+ are all natural candidates for being bracketed moves.
 
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I find it convenient to memorize an alg. by applying my letter scheme for BLD solving to describe the dance of one selected corner facelet and memorizing the letter sequence. For instance, the "T" OLL oriented so that the "T" part is upside-down, with the chameleon corners can be solved in 8 face turns:
Code:
_E _H _T _U|_T _H _E _U _T _Q
describing
Code:
 F U F' U' F' L F L'
. It is read as follows:
_E to _H is the first turn F
_H to _T is the second turn U
_T to _U is the third turn F'
the notation _U|_T directs the reader to refocus to the _T facelet after arriving at the _U facelet without making any moves
_U|_T to _H is the fourth turn U'
_H to _E is the fifth turn F'
_E to _U is the sixth turn L
_U to _T is the seventh turn F
_T to _Q is the eighth turn L'

The advantages: It describes what usually develops in my minds eye about half-way through acquiring an algorithm. This letter sequence is usually easier to determine the position in an algorithm as twenty-four letters are provide a richer description field to memorize than a sequence with only six repeating letters. Also, it is easier to see conjugate patterns or reversed subsequences. "_E _H _T _U" and "_T _H _E _U" is clearly a conjugate pattern to the F' move (_T _U) because "_E _H _T" is the reverse of "_T _H _E". There is also much more descriptive space. For instance the same sequence could be described by chasing another of the twenty-four corner faces. I developed a program that attempts to find the longest running face-chasing dance by simply trying all eight possibilities.
 
I had stumbled upon this post a few years back, and it took a few years of thinking to come up with less cumbersome system notation which I am calling the 'Yo Notation'.

https://docs.google.com/document/d/1bfDsydw6pxBftd8Xwik95FNjILGkdrJMBO5EORbftII/edit?usp=sharing

Yo Notation Tutorial Doc


David Singmaster notation is good to generate scrambles and stuff, but not good enough for memorization.


Video link: Yo Notation
I have also added ways to memorize wide moves and rotations, which was not covered in the above video.


For wide moves,

u - QA

u' - BP

u2 - RC

f - SV

f' - WT

f2 - XU

l' - NH

l - MG

l2 - OI

r - NJ

r' - MK

r2 - OL


x - LI

x' - MITU

y - GI

y' - KJ

z - QP

z' -DP

(I have chosen these letter pairs as these were rarer in the algorithm string, and had strong imagery in my letter pair scheme)


For normal face turning moves,

U - A

U' - B

U2 - C

D - D

D' - E

D2 - F

L - G

L' - H

L2 - I

M - M

M' - N

M2 - O

R - J

R' - K

R2 - L

S - S

S' - T

S2 - U

E - P

E' - Q

E2 - R

F - V

F' - W

F2 - X

B - Y

B' - Z


There are also an insane amount of cancellations I have come up with, but it will be pretty advanced if you are trying this for the first time

This system may take some time to get accustomed to.


2. Memorizing commutators

Translating the entire move sequence doesn’t work well in the case of a commutator.

Commutator Doc reference


For example,

AB - [R' D' U' : [R' D R, U']]

Extended Yo notation translation- kebk djbk ejcdj

Shortcut - (keb,kdja) : from the first element inside the bracket we get to know the setup moves, and the second element becomes the insertion and interchange move. With a little bit of training, we can find out ‘kdj’ is an insertion and ‘a’ is the interchange move, and the whole sequence reads [R' D R, U'].



3. Memorizing 5-style edge algs


Remembering algorithms via triggers will work in the 5-cycle case (oiag) : [U : [M,F]]

but not in the case (dula): F2 M' F' E2 F' L' F E2 F' l, which have some 3 move insertion in its sequence but no triggers or straightforward [A,B] commutator form inside it.

So, it is best to memorize ‘dula’ as ‘xnwr whvr wmg’, from which we can form 3 images and memorize the sequence without having a mental note to take care of.
 
I would not care much for 6 more letters to confuse me.
I'm still overcoming the french notation: Bas, Haut, Gauche, Droit, Arriere, Frontal (B H G D A F) which is in english D U L R B F
As you see, B and D are a concern.

As for speaking it, saying 'not' would be quick enough, as in are-you-arenot-younot.
But with "i" it is even easier. The inverses of

el, are, you, dee, eff, bee

becomes

lie, rye, ui (why), die, fie, bye.
 
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