# Alternative notation



## Stefan (Dec 22, 2008)

Extracted from another thread to keep that one cleaner...



tim said:


> martijn_cube said:
> 
> 
> > DonQuixote said:
> ...





tim said:


> Thomas says, that it's easier to memorize digits (5 1728 1728 6) than letters (FRUR'U'RUR'U'F').



But who memorizes the written alg anyway? Plus he could've used letters instead which I think would've been better. RULURULU!!! Yeah ok that doesn't cover direction right away, but you could use the normal six letters plus similar (sound or shape) for counterclockwise, for example:

U' = O
D' = T
R' = K
L' = I
F' = V
B' = P

The above alg becomes _"F RUKO RUKO V"_ which looks easier to me than the numbers, particularly because I can say it quickly.

I think I've seen something like this suggested already in the old mailing list from the 1980s or 1990s... more than three billion invisible points if someone can dig that out.


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## tim (Dec 22, 2008)

StefanPochmann said:


> tim said:
> 
> 
> > martijn_cube said:
> ...



I wondered the same thing. In my opinion any notation is equally good to memorize algorithms. (yeah, except for things like R' = 1, R = 1, R2 = 1, ...)


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## pjk (Dec 22, 2008)

StefanPochmann said:


> Extracted from another thread to keep that one cleaner...
> 
> 
> 
> ...


Is it necessary? Is saying it quickly necessary?

I see nothing wrong with the current notation. Perhaps if you want to be able to say it quickly, create names for common groups of moves (sexy move, etc.).


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## AvGalen (Dec 22, 2008)

StefanPochmann said:


> Extracted from another thread to keep that one cleaner...
> 
> 
> 
> ...



I don't think this is exactly what you want, but can I at least have 1 invisible point so I can _see _what it looks like 

And PJK, the things I dislike most about the current notation is that ' is hard to read (should have used -), ulfrbd means something different on bigcubes compared to 3x3x3 and xyz follow RUF, but MES follow LDF


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## brunson (Dec 22, 2008)

AvGalen said:


> ... and xyz follow RUF, but MES follow LDF


That's one of my biggest pet peeves. It's too late to change anything now, but if I had my way xyz would be reversed (to conform to the right hand rule of fields from physics) and MES would follow xyz. At least xyz uniformly correspond to a left hand rule of curl.


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## DavidWoner (Dec 22, 2008)

what about U2? M, S, and E? x, y, and z? there are not enough letters to cover all of these.

And I really don't see any problem with current notation. it is simple and very straightforward. I think if we introduce a letter for each turn then we are going to scare beginners away.

I do however agree that having xyz and MES following different sides is stupid.


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## AvGalen (Dec 22, 2008)

There are enough letters (3*6 + 3 +3 < 26), but it would be silly to use A to X


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## Rabid (Dec 22, 2008)

It is NOT too late. Chess switched to algebraic after hundreds of years. Beginners are already scared. I still say PRIME is wonky.


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## Lucas Garron (Dec 22, 2008)

"Prime" is one syllable, "minus" is two. If people like RUR-, you could probably get away with using it already. For URLs, I'm already making my applet store ' as - (and - to hexadecimal). I still suggest pronouncing it prime, though, or something better that's still one syllable.

I think a bigger issue is consistent notation where we don't have any.


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## brunson (Dec 22, 2008)

Prime makes sense to anyone that's had any advanced mathematics classes. By advanced I mean practically anything beyond arithmetic.


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## Dene (Dec 22, 2008)

Lucas Garron said:


> I still suggest pronouncing it prime, though, or something better that's still one syllable.



"Dash"! That's what I use! And it works for both


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## AvGalen (Dec 22, 2008)

I agree with dash, or just min in Dutch

And I had some pretty advanced math (I studied physics for a while), but never encountered '. It might not be as universal as you think

IF we are going to change this, it should be through the WCA

I will make a proposal soon


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## mrbiggs (Dec 23, 2008)

AvGalen said:


> I agree with dash, or just min in Dutch
> 
> And I had some pretty advanced math (I studied physics for a while), but never encountered '. It might not be as universal as you think
> 
> ...




What did you use for derivative (or velocity for physics)?

It's also used as a secondary variable, like x and x', though that's not as common.


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## DavidWoner (Dec 23, 2008)

AvGalen said:


> There are enough letters (3*6 + 3 +3 < 26), but it would be silly to use A to X



no there are not, since there is also M2, x' etc. you would need 3*12=36 characters.


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## Jgig1991 (Dec 23, 2008)

AvGalen said:


> And I had some pretty advanced math (I studied physics for a while), but never encountered '. It might not be as universal as you think



Really, never heard of prime? I though every one used it


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## DonQuixote (Dec 23, 2008)

According to Dr. Paul Broca Numbers are indeed easier to analyze and memorize for the human brain. 

Here's an english version of the "Swiss" notation: http://sisyphus.teil.cc/~martin/mmo/mmcc/notation/

Kind Regards
Martin


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## Stefan (Dec 23, 2008)

To clarify: My intention when starting this thread wasn't to suggest we should use this, mainly I didn't like the discussion taking place inside a blindcubing thread so I took it out. But it's also somewhat interesting to talk about.



Lucas Garron said:


> "Prime" is one syllable, "minus" is two.



Hmm... that made me think. Zero syllables would be even better, right? Not necessarily for writing algs, but at least *for team blindsolving* I could imagine this being useful:

Don't add "prime" but change the vowel. When you say "R", you probably say it as "ar". Instead of saying "ar prime" you could say "ir". Instead of "ef prime", say "if". And "bo" instead of "be prime".

I see several advantages of this over the added prime. First, it's shorter by a syllable, and shorter is better. Secondly, the direction is clear right away. When you hear "ar prime" you first hear "ar" and you get ready to do an R turn, but then you hear "prime" and have to rethink. Not the case if you hear "ir". Plus it's probably easier to remember several moves this way, making full cross easier in team blindfold. Usually I have trouble remembering more than 4-5 moves during the haste of inspection time, and I think part of the reason is the added "prime" or "two".

Oh right, the "two" could be replaced similarly, saying "or" instead of "ar two".


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## Stefan (Dec 23, 2008)

DonQuixote said:


> According to Dr. Paul Broca Numbers are indeed easier to analyze and memorize for the human brain.



I'd like to read about this, can you show me where I can? I googled a bit but didn't find anything about this.


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## qqwref (Dec 23, 2008)

Perhaps numbers are easier to memorize, but I don't memorize R U R' U' as "R U R apostrophe U apostrophe". I memorize it by looking at the cube and watching how the pieces move around (which also helps me do it from other angles, on other puzzles, etc.). And I think it's easier to memorize things the way I do it than to try to associate that short commutator with 4 digits...

I do like the idea of using different syllables for team BLD. Might I suggest the following system: represent moves with a syllable of consonant+vowel. The consonant would be B/D/F/L/R/V (V instead of U) and the vowel would be perhaps ah/ee/oo (clockwise, counterclockwise [like the Ri notation], two). So instead of RUR' you could say "rah vah ree" (ravari). Or sune would be ravarivaravuri. Huh, I think I like this.

Back when I tried to do team BLD with Tim Reynolds I remember we always tried to use as few syllables as possible, but without doing too much memorization. So I remember using 'pull' and 'push' for RUR' and RU'R', and giving each OCLL a one-syllable name, and so on. This idea would make it even easier


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## MatsBergsten (Dec 23, 2008)

StefanPochmann said:


> Don't add "prime" but change the vowel. When you say "R", you probably say it as "ar". Instead of saying "ar prime" you could say "ir". Instead of "ef prime", say "if". And "bo" instead of "be prime".



It's like they used to describe chess moves via telegraph a 100 years ago. They used vowels for rank
and consonants for rank or the other way around. (According to my old Colljins "Chess primer")


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## jackolanternsoup (Dec 23, 2008)

IMHO, I think that notation would be great to use because being able to say it quickly and remember it would help to memorise the algs.
It's way easier to say, and remember (T-perm):

R U K O K F R *two* O K O R U K V

rather than

R U R *prime* U *prime* R *prime* F R *two* U *prime* R *prime* U *prime* R U R *prime* F *prime*

And it's more 'solid' because it's easier to differentiate between a B and a P than a 'be' and a 'bo'.

Yeah... but it is quite un-intuitive though. you have to learn 6 more letters not that that's a problem Lol.


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## DonQuixote (Dec 23, 2008)

StefanPochmann said:


> I'd like to read about this, can you show me where I can? I googled a bit but didn't find anything about this.


The only reference known to me is "Moshé Feldenkrais: Abenteuer im Dschungel des Gehirns, Der Fall Doris" page 15, but I guess the original source must be out there somewhere, too.

Kind Regards
Martin


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## Bryan (Dec 23, 2008)

Instead of prime, I used to just call it "tick". But I really didn't talk to anyone about algorithms, so it was just in my head....


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## qqwref (Dec 23, 2008)

jackolanternsoup said:


> ...it's easier to differentiate between a B and a P than a 'be' and a 'bo'.



Allow me to disagree. On a bad phone connection (or with a bad memory), it is much easier to mishear a consonant as something similar than to get a vowel wrong.


Anyway, I noticed this U/O notation has a certain lack of ^2. Might I suggest W (for the oo sound).

Oh, and a bit of history: The ' prime is probably a corruption of the original ^–1, which was used back when people talked about cubes using group theory. So R would be a move and then R^-1 (R inverse) would be the inverse of R. I guess people got tired of R^-1 and just started writing R', which looks similar, as shorthand. In general mathematics, ' (called prime) just designates a symbol that is similar to the previous one: so if A is a point in a geometry diagram, A' might be A after a triangle containing A has been rotated around another point, or it might be the point corresponding to A in another diagram. So if you're a math person you can still justify writing R' by considering it as "a turn similar to R". In cubing terminology it's customary to use ' as the inverse, but I think that's just shorthand, because nobody wants to write down an inverse sign all the time.


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## fanwuq (Dec 23, 2008)

qqwref said:


> jackolanternsoup said:
> 
> 
> > ...it's easier to differentiate between a B and a P than a 'be' and a 'bo'.
> ...



I agree with QQ here.
Interesting enough I used the same idea as QQ's notation to memo piece's orientation and permutation together for BLD. I was actually about to suggest this before I read his post!


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## d4m4s74 (Dec 23, 2008)

for team blindfold, can you also say "sune", "sexy move" or "F2L alg 1"?


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## Stefan (Dec 23, 2008)

Yes, you can say anything you want.


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## Pedro (Dec 23, 2008)

I also learned to use prime as differentiation symbol, like
y = f(x)
y' = f'(x)
but, whatever...

I never tried team bld, but the different vowels idea seems cool...


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## Dene (Dec 23, 2008)

StefanPochmann said:


> Don't add "prime" but change the vowel. When you say "R", you probably say it as "ar". Instead of saying "ar prime" you could say "ir".



I was wondering how exactly you pronounce "ir"? Would "er" be easier? Maybe we're thinking about the same thing.


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## Stefan (Dec 23, 2008)

I meant like in b*eer*. Do you mean like in m*er*maid? Well, whatever works best, I guess.


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## Dene (Dec 23, 2008)

Ah ok I see. Yeah I meant as in m"er"maid. Perhaps "ir" as in b"eer" is less clear, or maybe it's just me >.<


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## AvGalen (Dec 23, 2008)

Pedro said:


> I also learned to use prime as differentiation symbol, like
> y = f(x)
> y' = f'(x)
> but, whatever...
> ...



Yep, I used it this way as well. Although I just called it "accent" instead of prime. That's one of the reasons I don't understand why it means inverse in cubing.

I still like the n[UFRBLDufrbld]m notation (add 6 more letters for megaminx)
n means the layer, counted from the outside to start on
UFRBLD means all the layers (wide turn), ufrbld means only one layer (slice turn)
m is the amount of turns (2 to indicate ' on a pyraminx, 3 to indicate ' on a cube, 4 to indicate ' on a megaminx)

MES become unnecessary because of ufrbld. l would be equal to M on a 3x3x3
xyz become unnecessary because you can use n=count(layers). 3R would be equal x on a 3x3x3
And when n=1 or m=1 they don't need to be written.
This doesn't make normal scrambles longer, it doesn't require subscript or other math-like constructions and it is easy to read and usable on many puzzles (not square-1, clock or magic)
It does require spaces between moves


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## qqwref (Dec 24, 2008)

The ' symbol *only* means differentiation in calculus. In group theory there is no need to take a derivative.



AvGalen said:


> I still like the n[UFRBLDufrbld]m notation (add 6 more letters for megaminx)
> n means the layer, counted from the outside to start on
> UFRBLD means all the layers (wide turn), ufrbld means only one layer (slice turn)
> m is the amount of turns (2 to indicate ' on a pyraminx, 3 to indicate ' on a cube, 4 to indicate ' on a megaminx)



SiGN notation is better. It is better for uppercase letters to mean slices because we have used ufrbld for double-layer turns for a long time (and uppercase MES for slices, right?) and this would just be confusing. Also it is silly to make m a number and never use ', because then it is just a way to encode the moves, it doesn't describe what you are doing. No serious speedcuber would insist on doing their algorithms with only clockwise turns. (Also, we need a way to write inverse, and "^-1" is way, way too long.) Any generalized notation system should (at the very least) be up to the task of describing any move that can be executed.


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## AvGalen (Jan 1, 2009)

Sorry for the late reply, but:

* I don't care if uppercase or lowercase means slices. Just as long as it is consistent. Right now u means something different on 3x3x3 compared to 4x4x4.
* Why would a notation system describe how a move should be executed? Does D2-D4 (chess) describe how?
* Is there a notation system that describes how to perform a l' + r slice on a 5x5x5 (can be done as 1 move) or how to perform a r slice with layers 4 to 6 on a 7x7x7?


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## jenni (Jan 1, 2009)

There is another notation I have seen on Dan Brown's youtube video's where intead of using ' for denoting the inverse, he uses a lower case i.

So R U R' would become R U Ri.

Since I'm still new to cubing, I've no idea if this has not already been mentioned for a reason (i.e. if it's rubbish lol) but it helped me remember one of the first algorithms I came across:

Fi U Li Ui - to learn this, I would say it almost as if it was one word, so phoenetically it was like saying "fee-oo-lee-oo-ee".

Just my 2p's worth anyway


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## MistArts (Jan 1, 2009)

jenni said:


> There is another notation I have seen on Dan Brown's youtube video's where intead of using ' for denoting the inverse, he uses a lower case i.
> 
> So R U R' would become R U Ri.
> 
> ...



I think "*i*" is inferior to "*'*" because I confuse it with "*l*" and it take longer to write in FM.


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## qqwref (Jan 1, 2009)

AvGalen said:


> * I don't care if uppercase or lowercase means slices. Just as long as it is consistent. Right now u means something different on 3x3x3 compared to 4x4x4.



Personally I started using r to mean a double layer turn on bigcubes when I started cubing (i.e. before I started speedcubing), and it helped for patterns because I was doing a lot more double layer 3x3 patterns than slice commutators. I think it also makes more sense, by analogy with the 3x3 - using r for M' on 3x3 looks and feels weird, and I prefer to be able to describe block turns without using circumlocutions like (Rr). Besides, anyone who's used to multislice scrambling (which everyone uses, right?) should find it somewhat natural to use r for a double layer turn.



AvGalen said:


> * Why would a notation system describe how a move should be executed? Does D2-D4 (chess) describe how?



Why not? It doesn't take much extra notation to be able to describe not only what the move is, but how it was executed. By allowing both U and U3' (and U5 and so on), or both M and r' R, our notation is not just suitable for scrambling and optimal solutions - we can also use it for writing down algorithms with fingertricks included. If we can condense all the applications into one notation, the notation becomes much more useful, because we don't need to deal with two different notations if we're interested in both scrambling and learning algorithms.

Chess is a bad analogy, by the way. There is only one way to perform a Chess move (even for castling, I believe you have to move the king first). And the way you perform the move doesn't matter, since only the result is important. But in cubing it is not just important that you solve the cube: it's also important how fast it is, so how you execute a move makes a difference.



AvGalen said:


> * Is there a notation system that describes how to perform a l' + r slice on a 5x5x5 (can be done as 1 move) or how to perform a r slice with layers 4 to 6 on a 7x7x7?



The r slice with layers 4 through 6 (wait, you mean layers 2 to 4 on the R side, right?) is just a block turn, so the full SiGN would write it as 2-4R. You could also write (l'r) on 5x5 as 2,4R if you want, although I don't really like counting that as one move since it's not a single block turn.


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## unsolved (Nov 5, 2014)

On the 5x5x5 I tried to memorize M and E and it did not make sense to me. Capital letters were for slice moves, and these were right smack in the middle of the cube. Also, I keep thinking of the cube having a Top and a Bottom; Up and Down is for Quarks 

So the notation I am using for my own studying and algs:

T= top face
t = top slice
e = equatorial around front, right, back, left, front
b = bottom slice
B = bottom face

F = front face
f = front slice
h = horizontal around top, right, bottom, left, top
k = back slice (last letter of "back")
K = back face

R = right face
r = right slice
v = vertical around front, top, back, bottom, front
l = left slice
L = left face

I use + for clockwise, - for counterclocwise, and 2 for twice

All turns are right-handed from top to bottom, right to left, and front to back.

So T+ t+ B+ and b+ are all in the same direction. It seemed odd to me that U and D' were opposite in notation, though spinning the same way when observed as you solve the cube.
Likewise R+ and L+ both denote a move like R and L' in the standard notation. Ditto for F+ and K+ being equal to F and B'.

I use e for equatorial, but in my case, it actually rotates around what would be the cube's equator if it had a north pole and south pole. E in the other notation does not.
I use h for horizontal because when you look down at the top, the face would be parallel to a piece of paper, and the way h moves in my notation is the way a horizontal line would be drawn on the paper.
I don't think anyone needs an explanation of v for vertical.

For block turns, where 2 moves can be made at once, I enclose them in square brackets, like [Tt]- being equal to U' u'. I made a list of moves sequences for the computer program I am writing to solve the 5x5x5







Anyway, this is the system of notation I will use for the program. If anyone wants a beta copy, send me a message on here. Should be ready by the weekend. You'll need 64-bit hardware to run it.


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## qqwref (Nov 5, 2014)

unsolved said:


> I use e for equatorial, but in my case, it actually rotates around what would be the cube's equator if it had a north pole and south pole. E in the other notation does not.


Um, yes it does? E (equator) is between U and D, M (middle) is between L and R, S (side?) is between F and B. And for larger cubes, it is AFAIK pretty common to use the lowercase letter to signify the middlemost slice only - on a 5x5x5 a lot of people would interpret M as a move of the three middle slices. So a move of the second and third slice would be (m' r), not (M' r). That's also how it works in SiGN, at least for 5x5x5 - there are a few possible ways of doing it on bigger cubes, because M slices aren't part of the base SiGN definition.

BTW, why'd you post this on a 5-year-old thread that's unrelated to your program?


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## unsolved (Nov 6, 2014)

qqwref said:


> BTW, why'd you post this on a 5-year-old thread that's unrelated to your program?



The topic was alternative notation, which is what I was posting about. The spreadsheet was a way to check to make sure I eliminated all of the moves that a program should eliminate, such as U u D U, F R R', etc. It turns out I eliminated too many so I will need to do a 3-ply and 4-ply version of the compound move generator.


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## MennoniteCuber1 (Nov 6, 2014)

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.


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## ketchuphater999 (Nov 7, 2014)

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.


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## qqwref (Nov 7, 2014)

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...


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## unsolved (Nov 7, 2014)

Gallifrey said:


> 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.



Gallifrey said:


> 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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## leeo (Nov 23, 2014)

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: 

```
_E _H _T _U|_T _H _E _U _T _Q
```
 describing

```
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.


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## abunickabhi (Feb 4, 2019)

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.


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