Commutators and conjugates?

[CalebW]

Hello, I'm pretty new to the world of cubing (just started about a month ago) and I had started learning the CFLOP method. I learned all of the 4LL but the idea of learning 60+ more algorithms seemed a little daunting. Also I wanted to learn how to really solve the 3x3x3 cube by intuition which lead me to the heise method. The first couple of steps are prety straightfoward, but I get stuck when it comes to using commutators(and by association conjugates). I understand the basic principle but I don't really understand how to actually make my own. Are there any guides or turtorials y'all would sugggest that would help?

 

[cmhardw]

Noah has a good thread with video tutorials.

Brian Yu has a good thread too, also with videos.

Search around in the blindfold forum for more, or ask here if you want more info.

 

[irtjames14]

Question on commutators

Hi everyone,

I've been wondering.. how many commutators should I be left with whenever I solve the last 2 centers on the 6x6 and up cubes?

For 6x6 and 7x7, I get at max 1 commutator, but...

- for 8x8 and 9x9, I get at max 4 commutators (3 on outer layer, 1 on the 2nd outer layer)
- for 10x10, I get at max 7 commutators (4 on outer layer, 2 on 2nd outer layer, 1 on 3rd outer layer). (I would assume this would be the same for the 11x11 as well, since I don't own a 11x11 currently.)

I think I can definitely improve on the max number of commutators that I get stuck with for 8x8 and up...

Thanks!

 

[brian724080]

You only need one - the Niklas is enough

For a 7x7, you want to solve the middle 1x5 line in front of you, then filling out the 1x5 lines from middle on out, starting with the left side. The order would be middle - second to the left - left - second to the right - right (assuming you're right-handed). For anything bigger you just use the same concept. This may leave you with one piece unsolved, so you only need one commutator

 

[irtjames14]

I don't understand how only one commutator can be needed for 8x8 and up..

For the 8x8, I can solve the third to the left 1x6, then second to the left 1x6, then left, followed third to the right 4R as full 1x6 lines, but I don't see how a full 1x6 line for the second to the right can be done unless you get lucky, since you can't move the 2 middle layers.. and then for the last remaining right 1x6 similarly.. since you can't move the middle 4 layers..

 

[Christopher Mowla]

I think he means something like how I explain on pages 6-8 of my PDF. You can use variations of the Niklas to solve different piece types and different quantities of pieces.

 

[brian724080]

I think he means something like how I explain on pages 6-8 of my PDF. You can use variations of the Niklas to solve different piece types and different quantities of pieces.

Yes - that's what I meant by one commutator, since they're essentially the same.

 

[Tgrede]

Unsure about Commutators? (and conjugates)

Hello all, I just started attempting to learn more about the cube theory and as I am looking at commutators (so I can better solve my 5x5) I don't quite understand how it works even on a 3x3. I have watched several tutorial videos and read several posts and not only do I just not understand HOW this works, how to know what pieces are affected and everything else, but a thing that bothers me is being told a commutator is A B A' B'. but for example lets assume A = R' D' R and then B = U. well in this case B' would be U' And i fully agree, but from what everything sounds like an inverse of moves for A' should be R D R' and that doesnt seem to be the case. Why do we say A' is an inverse of A when its actually A' is an inverse of A, excluding the first rotation which is the same as in A, in this case R' stays R' instead of switching to R for the inverse. All in all this commutator stuff doesn't make too much sense to me yet the way tutorials are explaining it.

 

[Christopher Mowla]

The inverse of an algorithm A is defined as doing the reverse of algorithm A + applying a prime symbol to each and every move. Therefore if A = R' D' R, then A' = R' D R.

This is best commutator video I have ever seen on the internet. Please give it a watch and let me know if commutators make more sense afterwards. However, you must heed the definition of inverse. There's no way around that.

I do note that some algorithms are equal to their reverse.

Example:
Rw U' Rw U2 R' U2 Rw' U' Rw U2 Rw R U2 Rw U' Rw' U2 R' U2 Rw U' Rw

 

[Stefan]

A' means doing A backwards as in undoing A. Undoing R' D' R means R' D R, not R D R'.

 

[Tgrede]

A' means doing A backwards as in undoing A. Undoing R' D' R means R' D R, not R D R'.

I think that is exactly what i'm looking for. So A' is literally taking A, doing A moves from the end to beginning but swapping clockwise with counter and vise versa. so applying it to a longer piece of moves (I dont know if this is a thing but) R U' R D' as A would be D R' U R'?

 

[TheSquareOne]

I think that is exactly what i'm looking for. So A' is literally taking A, doing A moves from the end to beginning but swapping clockwise with counter and vise versa. so applying it to a longer piece of moves (I dont know if this is a thing but) R U' R D' as A would be D R' U R'?

That’s correct.

A’ cancels out A. In your example, R U’ R D’ D R’ U R’ would get you back to your original state.

 

[jokeeffe]

This issue seems to come up fairly frequently. Is there a good FAQ or video that we can point to which explains in detail how to invert algs?

 

[Tgrede]

So after scavenging YouTube for any video I could find on the subject I actually found madmephisto had the one video that made some sense to me, and explained clearly how to find the inverse, and what each piece does. Surprisingly only 30 thousand views after 7 years of being posted, probably not as much recognition as it deserves.
https://www.youtube.com/watch?v=7yZoDi_B1lI

 

[stoic]

This is best commutator video I have ever seen on the internet.

That's a really great video, thanks for posting.

 

[cmhardw]

This issue seems to come up fairly frequently. Is there a good FAQ or video that we can point to which explains in detail how to invert algs?

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