Commutators - Cube Theory 101

In this video I talk about commutators and why they are so useful in coming up with your own algorithms.

Commutators are algorithm that follow the form of a b a' b' where a and b are both sub algorithms, and a' and b' are the inverse of a and b. The only pieces affected by the commutator algorithm will be pieces that intersect between the 2 sub algorithms.

Usually you will want to keep the pieces that intersect to a minimum so that most of the puzzle will remain unaffected by the algorithm.

Main commutators used in this video:
Corner Cycle:
1: (R' D' R)
2: U'
1': (R' D R)
2': U

Corner Twist:
1: (R' D R D' R' D R)
2: U'
1': (R' D' R D R' D' R)
2': U

Edge Cycle:
1: (F R' F')
2: M
1': (F R F')
2': M'

Edge Flip:
1: (U' R' U R F R' F')
2: M
1': (F R F' R' U' R U)
2': M'

Here's the gear I'm using:

[pipipiwalopimeja]

Thank you! I just used this to solve the cube completely intuitively, which I didn't think was possible.

[TwisterCube]

Great video. Looking forward to the rest of this series.
Suggestion: Why does parity happen on even layer cubes?

[robertevans]

Thank you for this video! I’ve been searching for days for a video that explained the theory instead of just listing algorithms. Cheers! 🛰

[sigalig]

Just curious, are you endorsed by Rubik's or something? I just don't see any other reason why an experienced cuber would be using a Rubik's brand cube

[BlinkLed]

Wow, this was incredible.  I've done this with algorithims before (ie: swapping two pieces intuitively and then doing the red bull algorithm) but I never thought of using an intuitive "algorithm" instead.  This video really opened my eyes to the simplicity of it, and just now I came up with an algorithm to flip two adjacent edges.  This just reinvigorated my puzzle enthusiasm after a long time of not being interested.  Thanks for the awesome video!

[DiscoCokkroach]

Holy Toledo, I actually understand commutators now! Thank you for this tutorial.

[TheUltimateVanquish]

This is one of the most helpful and interesting cubing videos i have watched, keep this kind of thing coming!

[spartin]

This is really cool! Keep doing the Cube Theory series. 

[IAssemble]

Oh, and thanks for including the 3x3x3, 7x7x7 and 13x13x13 spiral patterns in the background ;)

[hushi]

Very nice, finally knows how the algorithm comes up

[gracepeng]

Do a video on how to pick a good cube.

[Shuey]

Totally cool series you've started here man!  I wish I had something like this when I was a kid back when the cube first came out in America :D.  I look forward to seeing more videos in this series :).

[Nuptup]

This is awesome! Can't wait for more from this series. Might be able to squeeze a faster time out of my solves because of this. :)

[DestroyerCB]

For 2 look OLL i solve it intuitively for only 3 cases. Those cases are the cases where you need to orient 2 corners, instead of doing a hard algorithm  you can use R' D' R D on the corner. I learned that alg from the beginners method lol 

[NequissimusMusic]

I'm confused... the M at 5:40(ish)... wasn't that a M' ?

[DrHow]

The double edge flip can also be achieved in only 14 moves.  Such a #1 algorithm is U L2 U' F' L' F (same #2).

If the edges you need to flip are adjacent in an external layer, the method RedKB suggests (or the improvement I suggest) requires 2 moves to set it up.  There is a direct 14 move method with R' E' R2 E2 R' as #1 and U as #2.  With U2 as #2, this method achieves the same effect as the preceding.  So the preceding algorithm is not even needed (but it does do fewer center slice moves).

With the latter #1(using appropriate #2), the worst case (including setup) for _any_ pair of edges is 15 moves.

[PraetorianCuber]

woo Kenneth glad to see another video from you man

[nephildevil]

Great vid on the basics of making your own algorithms, I recommend watching after you've had your coffee though :D

[kylegoodsir]

For the Algorithms at 4:30, you could also do this by doing R U2 R' U' R U' R' L' U2 L U L' U L, which does the exact same thing. A better way to think of this is R U2 R' U' R U' R' and then mirroring it.

[TavartDukod]

You could use U' F R' U F' insead of U' R' U R F R' F' in the algorithm that changes orientation of two edges. That makes final algorithm four moves shorter.