(Collective) Introduction to Commutators

[StachuK1992]

This is more experimental than most threads, and I've been hoping to do a collective tutorial at some point.

Let's talk about Comms.
How would we go about teaching this very very important subject to noobs, with everything they could need to know?

There have been a few tutorials floating about over the years, and quite a few explanations. I think there needs to finally be a "from noob to optimizer" walkthrough of sorts that can finally bridge this gap.

I won't even contribute right now - surprise me. Let's see where this goes.

statue

 

[qqwref]

Just off the top of my head, here's a rough outline of how I might go about introducing someone to commutators.

Basic stuff (for beginners):
- the structure of a commutator
- intuitive explanation on why this produces useful algs
- some examples of algs people might be familiar with and how they work in commutator form
- general technique for creating your own commutators
- structure and usage of setup moves
- some examples of how to use commutators in less obvious ways (bigcube center comms, F2L tricks, etc)
More advanced stuff, taught in more or less any order:
- exotic types: block commutators, 5-cycles, 2-2-cycles, commutators of commutators (for more difficult twisty puzzles)
- combining commutators (e.g. r'FR'F'rlFRF'l')
- commutator insertions for FMC
- move-optimal cycles (BH stuff)
- group theory stuff

 

[Cubenovice]

Nice idea, here’s my 2 cents:

I think the perfect tutorial for beginners would be one that starts with as little information as possible.
If a tutorial would start with a listing of qqref’s bullit points (as some sort of index) I would run away screaming :confused:

I envision a wiki tutorial page with four tabs:
Beginner
I think the beginner part should only cover:
- the basic 8 move corner commutators ABA’B’ and BAB’A’
- short listing of where you can use it for (I would already like to mention FMC insertion here)
- mention that you can use set up moves for cases that cannot be solved via an 8 mover (see intermediate section)
(perhaps the initial page should contain the short listing of usages)

A proper understanding of ABA’B’ and BAB’A’ is key and you probably need some time to let this sink in before moving onto more advanced stuff.

Then you would have three additional tabs to the more advanced stuff (as mentioned by qqref)
Intermediate
- general technique for creating your own commutators
- structure and usage of setup moves
- some examples of how to use commutators in less obvious ways (bigcube center comms, F2L tricks, etc)
- some examples of algs people might be familiar with and how they work in commutator form

Advanced
- move-optimal cycles (BH stuff) this would basically be Byu’s tutorial
- combining commutators (e.g. r'FR'F'rlFRF'l')
- exotic types: block commutators, 5-cycles, 2-2-cycles, commutators of commutators (for more difficult twisty puzzles)
- group theory stuff

Links section
BH tutorial
Ryan Heise
Joel van Noort
Etc
Etc
As people have different preferences for tutorials (text, applets, video) so the ultimate noob tutorial should include links to various tutorials.
If the ultimate commutator tutotial does not “click” then perhaps one of the others will.


EDIT: an example from today's FMC thread showing why you should know your BAB'A':

my solution for the weekly competition in the german forum. it's 24 moves so i thought it would be interesting to share:

scramble: D' L2 D L2 F2 U' L2 R2 U B2 L' U B2 U2 R B' U L U2 L' R'
2x2x1: U2 R2 U' B (preparing the 2x2x2)
2x2x3: F2 (in order to solve the yellow-red-green F2L pair) L2 D' R
some more blockbuilding: U2 F U F' U * L' F U' F' (leaving 3 corners)
1-move cancellation (this was the best one i could find):
* D' R2 D L D' R2 D L'
=> U2 R2 U' B F2 L2 D' R U2 F U F' U D' R2 D L D' R2 D L2 F U' F' (24 moves, found in ~30 minutes)

Well done, but there's a better insertion:
some more blockbuilding: U2 F U F' U L' (L' F R F' L F R' F') F U' F' (leaving 3 corners)
results in 22 moves.

 

[Godmil]

What a great idea. Just a couple of links... These videos are excellent 4x4 center commutator tutorials by Daniel Sheppard:
4BLD Centers
4BLD Face-Interchange Comms

 

[cmhardw]

For beginners I definitely am of the mindset that simpler is better, although I know some (most?) would probably not agree. I found this site, accompanied by a piece of paper and a pencil to examine the A-perm and see how it is of the same format (It's an A9 corner comm), were all I needed to open to the door to the world of commutators for me.

More advanced stuff can be more flashy and in depth, but in my opinion the only way someone is going to truly understand commutators is to read the basic theory (or watch in a video) and then try to apply that to algs you already know are commutators, but don't yet know how to write them in commutator form.

 

[StachuK1992]

Okay. Let me try to explain what I want to do with this.
I want to focus on 3x3.
-explain what comms are and how they're useful.
-explain 8-movers. Combine explanations from every source possible.
-give a bunch of examples. A bunch.
-explain 9-movers.
---etcetc the other up to 12-movers
-show how you can use comms for, say, ELL on a 4x4. Etc.

What I want to do here is explain comms type-by-type, giving more depth than ever before. I quite simply aren't good enough at comms to approach this.