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Memorizing algs by following cubies

MagicVince

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Sep 2, 2019
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Each one of us has different tricks to memorize algs until they go to the muscle memory.
For instance, I break x'RU'RD / RUR'D' / RUR'D / RUR'D'x into 4 lines when I write it on a cheat sheet, or I learn the rhythm of 2-gen algs like M2U' M2U' M'U2 M2U2 M'U2.

Something that works well for me is to follow the movement of some pairs or some cubie while I perform the alg. The typical case is Sune or Anti-Sune, for which you follow the front-right solved F2L pair. I guess everybody learned it like this (or am I wrong?). This video series from Caleb Miler uses this trick for different OLL.

Recently, I found a French video on that was mentioning that the sexy move of this Rb alg R' U2 R U2 R' F (R U R' U') R' F' R2 U' was breaking a pair and rebuilding it right away. I tried to follow this solved F2L pair from the beginning of the alg (it is on the right-back), I find it rather easy to memorize it this way.

So I was wondering if there were more algs for which following a pair or even a single cubie would make them easy to memorize (at least for me).
I wanted to generalize this process for all the algs, by defining a sort of "maximum bandage cube" on which the alg could execute, and finding the block that was moving the greater number of times. But it was rather difficult and at the end of the day, most blocks become single cubies so I decided instead, for a given alg, to count the number of moves for each cubie. Then if by looking which cubies are moving at the same time as the most moving cubie, the blocks could hopefully be found out.

I modified my Formula Analyzer page to show some stats (how many times did a cubie move, and with which other cubies), and here are the results for the Rb alg already mentioned: R' U2 R U2 R' F (R U R' U') R' F' R2 U' (14 rotations, AUF included)
u u u u d d d d
b r f l r f l b u u u u d d d d b f f b
r f l b b r f l r f l b r f l b r r l l
ubr [ 8, 4, 3, 5, 7, 3, 2, 0, 3, 5, 3, 4, 3, 2, 0, 0, 7, 3, 2, 0]
urf [ 4, 9, 4, 6, 6, 4, 3, 0, 6, 6, 4, 5, 4, 1, 0, 0, 3, 4, 3, 0]
ufl [ 3, 4, 7, 5, 4, 4, 1, 0, 3, 4, 7, 3, 4, 0, 0, 0, 2, 4, 1, 0]
ulb [ 5, 6, 5,10, 7, 5, 2, 0, 4, 7, 5, 7, 5, 1, 0, 0, 4, 5, 2, 0]
drb [ 7, 6, 4, 7,11, 5, 4, 0, 4, 8, 4, 5, 5, 2, 0, 0, 7, 5, 4, 0]
dfr [ 3, 4, 4, 5, 5, 7, 0, 0, 2, 2, 4, 3, 7, 0, 0, 0, 3, 7, 0, 0]
dlf [ 2, 3, 1, 2, 4, 0, 4, 0, 2, 4, 1, 1, 0, 2, 0, 0, 2, 0, 4, 0]

dbl [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ur [ 3, 6, 3, 4, 4, 2, 2, 0, 6, 4, 3, 3, 2, 0, 0, 0, 2, 2, 2, 0]
uf [ 5, 6, 4, 7, 8, 2, 4, 0, 4, 9, 4, 5, 2, 2, 0, 0, 4, 2, 4, 0]
ul [ 3, 4, 7, 5, 4, 4, 1, 0, 3, 4, 7, 3, 4, 0, 0, 0, 2, 4, 1, 0]
ub [ 4, 5, 3, 7, 5, 3, 1, 0, 3, 5, 3, 7, 3, 0, 0, 0, 3, 3, 1, 0]
dr [ 3, 4, 4, 5, 5, 7, 0, 0, 2, 2, 4, 3, 7, 0, 0, 0, 3, 7, 0, 0]
df [ 2, 1, 0, 1, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0]
dl [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
db [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
br [ 7, 3, 2, 4, 7, 3, 2, 0, 2, 4, 2, 3, 3, 2, 0, 0, 7, 3, 2, 0]
fr [ 3, 4, 4, 5, 5, 7, 0, 0, 2, 2, 4, 3, 7, 0, 0, 0, 3, 7, 0, 0]
fl [ 2, 3, 1, 2, 4, 0, 4, 0, 2, 4, 1, 1, 0, 2, 0, 0, 2, 0, 4, 0]
bl [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

The diagonal of the matrix show how many times a cubie moved. The DRB corner moved 11 times (out of 14) which is the maximum, as expected. So this is working fine.
Instead, regarding the BR edge, it only moved 7 times (and each time simultaneously with DRB: you can see it by looking at the intersection of BR line with DRB column showing also 7). These are less moves than ULB for instance (10 times), and even worse, if you look at the edges that move the more often simultaneously with DRB then UF does better (8 times) than BR. So I am a bit disappointed regarding blocks.

And you, what are the algorithms you learned by following a block or a cubie? Are the stats showing the same cubies as good candidates to be followed? You can go the Formula Analyzer page, enter your alg and then press F12: I temporarily modified the code so that the console window will show this kind table at the end of the logs.
 
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Osric

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Jun 7, 2020
Messages
43
I am in the habit of memorizing algs in the way you describe and think this approach works well for any alg that starts with R U (eg. J or Y perm) but I recently convinced myself that this was a bad way to do it because for me at least it encourages too much thinking about what's going on.

I'm currently trying a different approach of memorizing the movements rather than the moves - that is, watch videos of someone demonstrating the exact "fingertricks" they are using for an alg and focusing on training my fingers to move in that specific pattern while not thinking about the notation or the moves at all. I am hoping that this holds more promise for mastering not just the memorization of the alg but building the habits that will make my turning faster overall.
 

MagicVince

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Sep 2, 2019
Messages
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Paris (France)
it encourages too much thinking
Yes, all the mnemonics have to be forgotten at some point so that they can be replaced by muscle memory. But when you stop cubing for a long period, remembering your old good tricks can be convenient.
focusing on training my fingers to move in that specific pattern while not thinking about the notation or the moves at all.
Perhaps it will be even easier if in the video the cuber was not having a cube in hands and was just making the hand movements in the void. And this could lead to a new discipline: air cubing! I am sure I can break records (at least for a limited period) in this new competition style. :p
Most commutators I memorize by tracking 3 pieces and their orientation :p
Good point: sometime you begin to follow some cubies, and then switch to other ones.

By the way, here is what I intended by maximum bandage cube for an algorithm:
1667325372601.png
You can do the Sune alg on this bandage cube (2x2x3 on the bottom-left, 2x2x1 on the bottom-back-right and two 2x1x1 blocks: the top-middle-front and the front-right F2L, the one you usually follow). But if you attach any other cubie, it will block at least one move and will prevent you from executing the alg. This is why I call it maximum bandage cube. Of course, in this case it is a bit overkill, but I am sure such a bandage can help seeing what is happening and thus can help memorizing an alg for some of us.
 
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Osric

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Jun 7, 2020
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Inspired by @MagicVince's bandaged cube and enabled by @Lucas Garron's work on cubing.js, I threw together the closest visualization I could of algs that might help you track what's going on. In this visualization, cubies that never move are grey; those that return to their solved positions are dim; and those that are affected are bright. These days in Chrome you can create sharable URLs by just typing in the alg normally after the alg= parameter. Here are some examples:


or visit https://blueroux-5772a.web.app/magicvince and enter your own into the text field.

Osric
 

Lucas Garron

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Inspired by @MagicVince's bandaged cube and enabled by @Lucas Garron's work on cubing.js, I threw together the closest visualization I could of algs that might help you track what's going on. In this visualization, cubies that never move are grey; those that return to their solved positions are dim; and those that are affected are bright.

Woah, that's a great way to highlight different moves!

Some cases you may want to consider:
  • R U R U R U' R' U' R' U' rotates two centers, you may want to mark those as dim if you only care about center permutation.
  • If I paste (R2 U2)6 it sort of works, but isn't calculated correctly? Let me know if you'd like any help with handling nested algs.
These days in Chrome you can create sharable URLs by just typing in the alg normally after the alg= parameter. Here are some examples:

If you also want the URL to update automatically, this is a useful trick:

Code:
const url = new URL(window.location.href);
const params = url.searchParams;
params.set("alg", "R U R'"); // parameter alg here
window.history.replaceState(null, "", url.toString());
 

MagicVince

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I would really love seeing cubing.js displaying the maximum bandage cube for any given algorithm. So thank you very much for this attempt to reach this goal.
I don't know the current features, but something that would help is displaying how many times a cubie is moved on the stickers (or having different shade of color depending on this number). Adjacent cubies with the same number could be part of a bandage block (not guaranteed though).
With what you did, the Sune example works well because the only block located on the top face actually returns to his home position. But it would failed showing that, for OLL33 alg (RUR'U')(R'FRF')(U), one of the two twisted blocks is never broken whereas the other is. And the fact that (for LL algs) all the F2L are necessarily grey or dim is a bit disappointing.
But, once again, I welcome this initiative! Well done!
 

abunickabhi

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Yes, all the mnemonics have to be forgotten at some point so that they can be replaced by muscle memory. But when you stop cubing for a long period, remembering your old good tricks can be convenient.

Perhaps it will be even easier if in the video the cuber was not having a cube in hands and was just making the hand movements in the void. And this could lead to a new discipline: air cubing! I am sure I can break records (at least for a limited period) in this new competition style. :p

Good point: sometime you begin to follow some cubies, and then switch to other ones.

By the way, here is what I intended by maximum bandage cube for an algorithm:
View attachment 21073
You can do the Sune alg on this bandage cube (2x2x3 on the bottom-left, 2x2x1 on the bottom-back-right and two 2x1x1 blocks: the top-middle-front and the front-right F2L, the one you usually follow). But if you attach any other cubie, it will block at least one move and will prevent you from executing the alg. This is why I call it maximum bandage cube. Of course, in this case it is a bit overkill, but I am sure such a bandage can help seeing what is happening and thus can help memorizing an alg for some of us.
Super cool to see bandaged cubes on cubing.js

Memorizing algs depend a lot on the alg-type.
For CFOP algs we have groups of triggers to understand the alg.

For BLD as Samuel pointed out, we just trace out the commutator which has an insertion and an interchange component.

For algsets like 1LLL and UF5, I use Yo notation to systematically chunk the algorithm and visualized it as a story comprising of images.

Overall muscle memory wins over all this, but this is good techniques to have as a placeholder.
 

guelda

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Inspired by @MagicVince's bandaged cube and enabled by @Lucas Garron's work on cubing.js, I threw together the closest visualization I could of algs that might help you track what's going on. In this visualization, cubies that never move are grey; those that return to their solved positions are dim; and those that are affected are bright. These days in Chrome you can create sharable URLs by just typing in the alg normally after the alg= parameter. Here are some examples: (...)
Great idea and app! It should be noted that " U2' " doesn't work (so use "U2" instead).
 

Osric

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R U R U R U' R' U' R' U' rotates two centers, you may want to mark those as dim if you only care about center permutation.
I was really trying to get "close" to the bandage cube, and it's important to see that the centers are "connected" to their corresponding edge cubies. In the current hack, this kinda-sorta-works depending on the case, but I don't want to obscure it by dimming all centers.

  • If I paste (R2 U2)6 it sort of works, but isn't calculated correctly? Let me know if you'd like any help with handling nested algs.
I didn't consider more complex notation, this was easily fixed by calling `expand` before analyzing the alg's effect.
const url = new URL(window.location.href);
const params = url.searchParams;
params.set("alg", "R U R'"); // parameter alg here
window.history.replaceState(null, "", url.toString());
Thanks. I didn't want to lose the user's history and svelte's way of doing this is totally different, but I did update it so that each time you commit the field (by hitting enter or losing focus) it will update the URL, so you wind up with a history of your "saved" states.

@guelda I couldn't reproduce your issue. Can you post or PM me a broken link?

Osric
 
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Osric

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Jun 7, 2020
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I cobbled together an "almost-working" bandage cube version. Is this worth finishing? I can't judge whether the visualizaiton is useful enough. If you have more examples that would show it off, I'd be interested to see them...

Here are the ones I have done to try to check it out:

cubeB.gifScreen Shot 2022-11-06 at 2.59.14 PM.png
cubeSune10B.gif
Thanks in advance for feedback
Osric
 

MagicVince

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@Osric this is fantastic! This is exactly the kind of representation I was wishing. Yes, please, go ahead with it!
Apart from the visualization glitches, the last example you gave is not the *maximal* bandage cube (the "ld" 2x2x3 block should be one piece as in your first example, the FRd 2x1x1 block, that is FR edge and FRD corner, too).
But the concept and the realization is great. I am sure this can help understanding better how the cubies move relative to each other by removing the useless details and concentrating on blocks instead of cubies.
Thank you for your work!

[EDIT]
To give you another example, here are the two 2x1x1 blocks I am following for a Jb Perm: R U R' F' R U R' U' R' F R2 U' R' (this is not the maximum bandage cube, it is just a cube showing the two blocks I am refering to)
1668267093409.png
 
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