Rubik's Cube Theory: Commutators

[TheWolffBeast]

Thanks for the great Video - I've been trying to swap two corner pieces, with no real success - is it possible using commutators to DIRECTLY solve two corners or do you have to create a three corner cycle to accomplish this?

[lazercrocdt]

Badmephisto is by far the best Rubik's cube teacher on Youtube. You are awesome.

[Animationnnnn]

So commutators = Algorithms + Setup Moves?

[jkid1134]

@Animationnnnn Algorithms you don't have to memorize.

[ikzelf100]

dude you just made my fucking day, i was busy on solving mine own cube in my own way. and that second algorithm that you teach is that lat one i need to solve mijn cube because i always end up with 2 edges flipped.

[jaibhakti]

@badmephisto: I was expecting you to say you've been cubing since you were 10 years old--haha. My god: you've mastered the cube in such a short time...well done!

Ok...a computer scientist: perhaps that explains your supreme knowledge and in depth understanding of algorithms?

May I please say once more: your videos are brilliant. Thank you for sharing your knowledge.

Could you make a video that explains what the heck 'n' is with regard to algebra??? I just don't get it! It eludes me! :)

[jaibhakti]

I love the last one you did...with the center square moving. That's SO cool looking!

How long have you been cubing?

Are you a mathmatician by trade?

[badmephisto]

@jaibhakti I've been cubing for more than 2, maybe almost 3 years :) And no, I'm something much better: Computer Scientist.

[KapustaCuber]

M follows L.

[heshaaamtube]

Good lesson. Thank you.

[yomushu]

im lost private lesson plz

[bluedasher23]

Algorithm correction at 2:15.

P' should = M', U2, M, U, M', U', M

not

M', U2, M, U, M', U2, M

BTW this is very interesting. THANK YOU for all of your wonderful tutorials.

[FirefoxFreeze]

I like how at 4:42, you said "That's my Q" which sounds like "That's my cue!"

[CCV334]

Can you make a video explaining conjugates

[ViralOblivion]

Cool vid, i actually thought of doing one too :(

[IPwnAllAndLeaveNone]

2:25 parity error on a 3x3x3...? o_O

[Tortak39]

This can be used on teh square 1 which I cannot solve! lol

[ishakyp]

this is hard :D

i think i'll stick to memorizing the OLLs lol

next is OOT

when learning F2L, my average of 12 dropped from 30ish to 50ish

but i feel that i made fewer moves

did this happened to you too?

[Helix7777]

It is interesting. And yes, but as you practice, you time will go down dramatically.

[ishakyp]

@Helix7777 ok... i'll keep on practicing "looking ahead" ... i'm at 40-ish now... PB 21,04

yaaayyyy!!! ^_^

[mynameisdarthtater]

when changing to F2l from LBL, everyone is slower at first. just practice

[geary9]

do u put ur camara on ur head???

[xxetfownsxx]

@geary9 he does

[axis1260]

are you Christopher Mintz-Plasse? you know that thin tall kid from role models.. cos you sould like him :p

[Tortak39]

Nope hes Andrej

[yomister3281]

Im just wondering how i would apply the commutators to solving the Rubik's cube intuitively. Im having trouble being able to recognize patterns and how the stickers rotate. Does that just come with practice? Great tutorial btw, i love your videos man I watch them daily.

[uNamed2lyfe]

this may sound weird...but im not sure why M' is moving the middle layer away from u.....

if u move the M layer away from u, ur moving it in a clockwise manner if u look at it from the 'R' perspective, and its counter clockwise if u look at it from the 'L' perspective....

wht perspective do u take....?

[badmephisto]

it should be from R's perspective by convention. M is like R in direction

[uNamed2lyfe]

ok, so if M is like R, then how come M' is also like R.

in ur vid, when u were showing this weird algorithm that switches the edge piece on the D layer.. that weird M' U2 M.....

for the M', u moved the middle layer away, as if moving the right side clockwise.

u get it?

i understand that the M layer should be from R's perspective, and M is like R in direction, but in ur vid at 1:39, u moved the middle layer away from u for M'.....

thts wht i dont get....

im really confused....

[badmephisto]

ok maybe i made a mistake somewhere. M is like R, end of story.

[badmephisto]

ok actually wait i may be confused. The thing is that people use it both ways and we all get confused on what the RIGHT way is. I think I used more the convention that M is like R' actually if I remember correctly now. So lets go with that :D

I know its a mess

[uNamed2lyfe]

firstly, if u say M is like R, then u made a mistake in ur vid, but it turned out right becuz u didnt take M as R, u took it as R'.

so, u took M as R'....hmm...which means ur taking the left perspective. i mean, ur saying that M is like L, rather than R'.

man.....ok, i think i get it. even on ur oll page, ur 18th alg, starts with M, wen u shud start wid M', but as u sed, u took M as R', that way, ur alg is right....but i had to figure that out! lol =)

anyway, ur vids rock man!

[FirefoxFreeze]

@uNamed2lyfe

I believe M takes the style of L

[uNamed2lyfe]

ok....that explains it..

thanks man!

[FirefoxFreeze]

@uNamed2lyfe

Just to explain further, the Notation S will take the style of F

and E takes the style of D.

[uNamed2lyfe]

oh ok, thanks!

[suzeebeezee]

@uNamed2lyfe When you look at mephisto's website and check out notation you will find that M turns the middle layer. Very helpful in the 2 look PLL

[ben1996123]

@uNamed2lyfe M follows L, E follows D, S follows F

[uNamed2lyfe]

@ben1996123 r u sure bout this?

cuz badmephisto is saying that M follows R.....

[ben1996123]

@uNamed2lyfe

Yes im sure.

[twistnturn44]

Reminds me of how you can solve the entire cube using only a t-perm and permutating all corners.

[MrTelefant]

at this time i must say... i have to do 20% scramble... cause i have the same prob... but i definitly will figure that thing out

[MrTelefant]

the result was a oll algorithm TOO LONG :S

[phreddsfishpudding]

ok i understand it but havent managed to do it on my own yet, because i cant figure out an appropriate algorithm to use as P... ?

[RicardoSilva155]

just solve the cross ? i can do it using f2l , 2 lokk OLL and 2 look PLL , or either the beginners method.

by the way, do you have a video about petro method or something like that ?

[TheTurtleman9]

I'm pretty sure f2l, 2 look pll and oll are faster than petrus.

[kevinaddictus]

it dpends on hw the f2l is exctd, if you cn do it n 10 seconds thn it's good. it jst dpnds on f2l.

[vonix11]

if you think about it petrus is an advanced f2l method. And when you have completed f2l (if done correctly) you will already have EOLL done so in effect when you use petrus you only need to know 2-look OLL to be able to orient everything in one algorithm.(In other words i believe petrus is superior to fridrich f2l)

[TheTurtleman9]

Wait..... Can you explain that better? I don't get it.XD

[RicardoSilva155]

didn't get it :x why do we need commutators ?

[badmephisto]

i thought i made it clear that this is an advanced video. If you can only solve the cross, then you have next to no hope here.

commutators are useful in stuff like blindfold cubing, and also for fun!

[tidusvssora]

wow. i knew all of this from just experimenting.

I feel smart :)

[Danielleclain]

in the 3 corner cycle, how do you know where the stickers used to be?

i don't understand

[MailJee]

my dad has a friend who solved one back in the day with group theory. said it took him 2 weeks.

[rubikscuber927]

lots of permutations are commutators just recorded as letters

[vgbjason]

lol at 6:34 that alg is ubur

[FredChipNacho]

I'm at 1:30 right now, and I'd just like to inform anyone watching this that inverse algorithms can be used in the beginner's methods, e.g. R' D' R D. When it takes 4 or 5 repetitions to get the corner where you want it to be with R' D' R D, you can use D' R' D R.

[waparker4]

This was awesome. I majored in math so i loved seeing group theory applied to the cube. I derived the H algorithm and an alg to flip two corners, going to work out some more

[badmephisto]

excellent! There is a LOT of math you can do with it :) Stefan Pochmann in fact has a publication on the Rubik's Cube, try to find that

[zarker24]

some of this is above my head at the moment, but i learned a LOT. i usually learn one thing a day from wikipedia, but this is my daily knowledge for a week. very interesting information.

[lulzcorrupt]

great video! i managed to make an algorithm that flips two corners because of this video, you should make more ;D

[zilali]

Great video. I've been studying group theory in chemistry and its nice to see the similarities

[caphits]

Great video. Easy to understand.

[tylerzackmcnell]

this is like the formal definition to an integral of a limit in calc

[badmephisto]

what is? and isnt integral of a limit just the limit of the integral? for continuous functions at least

[samkeen]

thank you for this video, very lucidly described and easy to understand.

[badmephisto]

thank you, i think so as well! I watch it sometimes and it looks like it makes sense, and yet it is not a very popular video...

[xxxJOHNALEXxxx]

sweet!

[redfoxdude]

Cool! I really liked that. You definitely got me interested! I want to mess around with this concept, and maybe I'll come up with my own set of moves to solve the cube!

Thanks again, RFD

[xxxJOHNALEXxxx]

yes. how about try making a combined OLL and PLL.

For example, you need to do a certain algorithm for a sune or other OLLs right? try coming up with an algorithm that you solve the sune at the same time you solved the whole cube.

[Buggy793]

That would be called "Fridrich Method"

: )

Very cool subject to get into! I'll check it out and test with it a bit.

[RubiksAddict95]

No, that would be called 1 look last layer. Combining OLL and PLL would require a lot of algorithms, but it is possible.

[coasterfreak666]

i use commutators to solve the megaminx, works like magic =)

[EyethnxUgay]

lol, i look at the date and it says jan 21

so i'm like 'wow a video today'

but it was 2008 xP

exactly 1 year :)

[EDismename]

dude im confused

[HaLoFrEaK696969]

old fashion geometry logic

[KireinaCAT]

O hai

can you help me with centers of big cubes? im trying to learn 4x4 bld and i cant do centers :(

[KireinaCAT]

oh sry i didnt see Seerusgod's videos!

but this still helped me :D thanks

[CubeTalk]

r2 is all you need

[mic24oni]

whow, now I know how does Friedrich made her algorithms, thanx, man!

[Danielleclain]

Hie.

can you please expplain more about 3 stickers cycle?

[i656ier]

Is it possible to solve big cubes with no method, just the understanding of commutators

[CUB3FR34K]

Yes you can, like solving big cubes blindfolded.

[CubeTalk]

like micheal gottlieb and mike hugley

[cubejunkies]

and rowe hessler and ville seppanean, world record holders using them

[looklikecool]

hey, you are good.

a have a question.

can the Rubik's cube solve by just do some stupid move hundred's of time like R U RI UI D L DI LI, it was just example, and do over and over.

[badmephisto]

together with setup moves? yes. just by itself, and with only cube rotations allowed? no.

[lunchisoverrated]

so why do commutators even matter...

[dudewhoisnotfunny]

if u understand Commutators then you can sovle with out any algorithms and it helps to understand the rubiks cube

[InfinitiM13]

The algorithm (flip) doesn't work on the reverse.

[InfinitiM13]

The Y' had 2 U2s when the original had one U2!!!

[CrumpetWarrior]

Badmephisto, you are so good at life.

[jnoort]

Hey, nice videos! And thanks for linking to my page :)

[badmephisto]

oh hey Joel! Thank you very much! I link to your pages quite often :) I think I did so also for both my BLD tut and also the Beginner's tut - its a very good page :)

[InfinitiM13]

I understand commutators, I just don't know how other people use them. (like on the K4 method for 4x4)

[dragonslyer1995]

plz tell me how to memorize F2Ls cause they're really hard and so many cases

[LNOL]

DON'T MEMORIZE THEM ALL!!! Use your brain to solve most cases... Only memorize hard ones.

[SmithSolver]

These commutators really remind me of the Pochmann method (blindfold method).

[badmephisto]

you are correct, there are many similarities. In both cases the goal is to modify as few of the pieces on the cube as possible.

[ImaginaryHuman072889]

commutators are definitely completely superior to algorithms. if you know how commutators work, you basically know every algorithm that exists. i will admit algorithms are better for speedcubing, but commutators allow you to solve the cube in fewer moves and its more fun that way =]

[badmephisto]

hahaha no they dont allow you to solve it using fewer moves :) That's why in speedcubing we dont use commutators, its because they suck in move count :p

[1234funsies]

nice teaching! i actually understood something that a small child couldnt have (hopefully)

[Danielleclain]

hi

Can you please explain a 2x2 conmutators?

thanks

5 stars

[Danielleclain]

Hi i have seen your video. 5 stars

Could you please explain about corner 3 cycles, pair 3 cycles and edges 3 cycles.

I am really having probles with that.

Thanks you very much

[Mindstormscreator]

wow, that is genious!

[gifoimir]

i am new to blind and am using pjk' tutorial for 2 cycle as its is the easiest method for bld(from what i've read)... i am having problem understanding this commutator:

Commutator for corner orientation: A=(R'D'RD)x2

(12): U'AUA'

(13): U'AU2A'U'

(123 ccw): U'AUAUAU'

(123 cw): U'A'UA'UA'U'

(15): FAU'A'UF'

(Thanks to Macky for list)

Flips 1 and 2 each a different way. (12)...

what does just one of them mean??

[badmephisto]

well he says A=(R'D'RD)x2

so everywhere you see A just substitute that instead. so (12) is actually U'(R'D'RD)x2 U (RDR'D')x2

[gifoimir]

i got it(thanks)..just went through the CO solving phase and oriented the corners properly... but what i am confused about is when to use (1 2)(1 3)etc.. he did not elaborate on whether it should be used when both needs to be oriented CW, CCW or both a different way... i mean for future bld solves i have to understand it..

[masterhacker72]

comutators are very important in BLD right?

[badmephisto]

correct.

[Twister051]

What does BLD mean?

[Twister051]

does it mean blind solve?

[shafiqdms1]

yes it does

[PandaMyCo]

This is really interesting. I wish I would have known this stuff before I could solve the Rubik's cube, so I could tell people I figured out how to do it myself :)

[badmephisto]

exactly same thoughts here :) I wish I could go back and learn all of this before I learned LBL

[Twister051]

What does LBL mean? i want to learn more! By the way, awsome video. You did a good job explaing it.

[travwg33]

layer by layer

[shafiqdms1]

layer by layer

[heymaxsup]

JINX!!!

[hudasboy]

lol!!! jinx!

[heymaxsup]

jinxjinxpersonaljinxyouowemeas­odawearsmyfuckingsoda

[FerrilSamal]

hei! i made commutators for all the permutations of edges. i am not a fredrich user so i dont know their names. thnk u

[zyky2000]

very nice video :)

[LanceTheBlueKnight]

Commutators are very important in the 3 cycle method of Blindfold Solving. This would be a good video for anyone trying to learn that method.

[ApLsToApLsOs]

communators r the one of the most confusing ways to solve a cube. Heise's solution uses this at the end and i cant do it right unless i have a corner that solves itself 1 move

good job on figuring out this badmemphisto :)

*gives u thumbs up*

[badmephisto]

aww i love to use commutators :( sorry you dont understand it

[4jeffm7]

what was that sivlerish cube

[3nZoTheKing]

THANKS! now i can understand the 3 cycle method for BLD

[52ofem]

Where did you get P for the (cleaner) three cycle though?

[badmephisto]

i think i know what you mean;

i made it up. if you know F2L then it should be easy for you. take out a corner from the top, put it somewhere else, then take the corner you just took out, and put it where the 1st one was.

[52ofem]

Now I see... but what about the edge flipper one, at the beginning?

[badmephisto]

well just go through it. First part takes the edge out and the second inserts it back in the right way. its not really from F2L because in F2L your cross is solved. but anyway, its a move i derived, and its not really hard either

[52ofem]

Thanks a lot!

[gtavii]

Cool explanation, if I had to read it I would have zzz zzz. Now I am motivated to read some more about it! Thnx!

[badmephisto]

awesome! it's actually really interesting stuff, not nearly enough people care about it as much as they should. i find the math behind rubiks cube fascinating.

[wegaengine1]

who's holding your cam? just curious.

[badmephisto]

nobody... i trap it against my head with my giant headphones

[wegaengine1]

oh, i see. nice vid by the way.

[Rubiksguy]

there is an error in the edge flipper inverse, the second U2 should be a U', not U2

[badmephisto]

you're right.

[gamemeister27]

3 corner cycle is messing with me

[JasonJRY]

ok, so this would be used on freestyle blindfolding? hav u taken that up yet?

[badmephisto]

nah, i don't really enjoy doing blindfold solving... but yes i guess this is how you would do it

[robopanther]

I just make this H perm (R2 U2 R2 U2 R2) U' (R2 U2 R2 U2 R2) U

after watching your video. thanks

[badmephisto]

yep, that's correct :)

[BillyBobsEel]

this dosent seem to work very well for a 4x4x4 because teh edges cant be flipped and stay in the same place. Its ok if you turn your 4x4x4 into a 3x3x3 but it doesnt seem to help with parity

[badmephisto]

no you are indeed correct. I tried for a long time to figure something out, but... it didn't work. Which parity are you talking about though? I think the permutation parity (swapping 2 edges) can be done. Actually you CANNOT swap the two edges only, since that's 1 swap (odd # of swaps). What happens is you switch some of the (identical) center pieces too. (but you don't notice this of course because they all look the same). And orientation parity... I don't know myself :)

[BillyBobsEel]

i was trying to flip the 2 edges that are the same because it has a long algorithm and i thought if i could see what was happening it would be easier to learn(even if it is slow)

I will probly never truly learn the 4x4x4...

[gamemeister27]

for the 4x4, you have to understand what is going on, the edges aren't switching, that is impossible in 3x3 mode, rather, the individual edge pieces in the 3x3 edge are just switching places!

[kasperofny]

i actualy knew alot of this, but i inever put it into words. i understool alot of this. you make it easy to absorbe. thanks alot.

[pwn202]

Really helpful, helped me understand what i didn't know

[BillyBobsEel]

WOOO just used this to solve the MEGAMINX

i think i can say i did it on my own

[badmephisto]

awesome. I think you can indeed. If you can re-derive the moves at any time without any memory work, then you basically are doing it on your own.

Anyways, this is how first people solved the cube in the 80's :) Only mathematicians that knew a lot of group theory like this were able to come up with their own commutators and solve the cube using them. Fun stuff :)

[gamemeister27]

I have always admired the people that figured out their own way to solve the cube.

[gamemeister27]

I'm trying to do the same thing, i'm have trouble with permutating the edges though, can't figure out a 3 cycle.

[gamemeister27]

actually figured it out!

[sarranmanuno]

Also you made a mistake when taling about P' instead of doing U2 at the end it is actually U'

[sarranmanuno]

luv the vid, just subscribed keep up the good work :)

[BillyBobsEel]

i wish id know all this before i started learning it from vids then i could say that i have solved it pretty much on my one(as long as i dont copy any algs)

[4GO57O]

well maybe just maybe...we can solve it on our own...without using algs we learned from the net and use commutators instead...I wish this also :(

[terrapin52]

nice video! I always wondered how LL algs were originally derived and this provides some insight. I guess you can come up with new algs based on your preferences, e.g. left hand dominant, etc.

[badmephisto]

yea I am in college (or University in Canada, in here there is a distinction :) ) And actually one of my majors might end up being math, but i specialize in computer science and physics. So, commutators for me are pretty interesting stuff.

[BillyBobsEel]

how would i do one taht swapa corners and edges....

[badmephisto]

well find a move that swaps some two corners and then a move that swaps some two edges on the top layer somewhere. Write all of this down. Then twist that layer by doing U/U'/U2 and do the inverses to get different things. Remember that it doesn't matter if your algs are long or inneficient, if it works, it works :)

[JasonJRY]

5 honors when i viewed =p

[badmephisto]

heh yes but theres only a couple of vids on HowTo in Canada, so it's not that great :)

[cubestack]

Nice video! it's a bit confusing though.

[badmephisto]

thanks peoples.

It took me at least 2 weeks to really understand commutators, and i have a strong math background too, so... it was confusing for me as well. Anyways, the video shows you what you can do with commutators. If you are interested in more, see the links i gave you, and maybe rewatch this video later on. Take your time :) It can get quite fun once you do get it though.

[BillyBobsEel]

The bit i dont get is how to remember teh first stage and then do it backwards in your head

i would probably have to write it down if it was more than 4 or 5 moves

[badmephisto]

YES! of course you do :) didn't you see the huge sheet of paper full of writing i had in front of me? The reason why I did some of them so quickly was that in process of me making the video i actually learned some of them, due to all the takes I had to make :)

[Leviskatyboard]

very well done, thank you :)